TSTP Solution File: SWW314+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW314+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n015.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 00:13:39 EDT 2023
% Result : Theorem 28.25s 28.10s
% Output : CNFRefutation 28.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW314+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 21:06:24 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.52 start to proof:theBenchmark
% 27.72/27.91 %-------------------------------------------
% 27.72/27.91 % File :CSE---1.6
% 27.72/27.91 % Problem :theBenchmark
% 27.72/27.91 % Transform :cnf
% 27.72/27.91 % Format :tptp:raw
% 27.72/27.91 % Command :java -jar mcs_scs.jar %d %s
% 27.72/27.91
% 27.72/27.91 % Result :Theorem 22.600000s
% 27.72/27.91 % Output :CNFRefutation 22.600000s
% 27.72/27.91 %-------------------------------------------
% 27.72/27.92 %------------------------------------------------------------------------------
% 27.72/27.92 % File : SWW314+1 : TPTP v8.1.2. Released v5.2.0.
% 27.72/27.92 % Domain : Software Verification
% 27.72/27.92 % Problem : Hoare's Logic with Procedures 434973, 5000 axioms selected
% 27.72/27.92 % Version : Especial.
% 27.72/27.92 % English :
% 27.72/27.92
% 27.72/27.92 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 27.72/27.92 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 27.72/27.92 % Source : [Bla11]
% 27.72/27.92 % Names : hoare_434973.5000.p [Bla11]
% 27.72/27.92
% 27.72/27.92 % Status : Theorem
% 27.72/27.92 % Rating : 0.39 v7.5.0, 0.44 v7.4.0, 0.50 v7.3.0, 0.45 v7.2.0, 0.41 v7.1.0, 0.57 v6.4.0, 0.54 v6.2.0, 0.64 v6.1.0, 0.70 v6.0.0, 0.61 v5.5.0, 0.67 v5.4.0, 0.68 v5.3.0, 0.74 v5.2.0
% 27.72/27.92 % Syntax : Number of formulae : 5231 (1642 unt; 0 def)
% 27.72/27.92 % Number of atoms : 12840 (4418 equ)
% 27.72/27.92 % Maximal formula atoms : 13 ( 2 avg)
% 27.72/27.92 % Number of connectives : 8580 ( 971 ~; 148 |; 711 &)
% 27.72/27.92 % ( 892 <=>;5858 =>; 0 <=; 0 <~>)
% 27.72/27.92 % Maximal formula depth : 22 ( 6 avg)
% 27.72/27.92 % Maximal term depth : 19 ( 2 avg)
% 27.72/27.92 % Number of predicates : 152 ( 151 usr; 0 prp; 1-6 aty)
% 27.72/27.92 % Number of functors : 377 ( 377 usr; 48 con; 0-7 aty)
% 27.72/27.92 % Number of variables : 16689 (16533 !; 156 ?)
% 27.72/27.92 % SPC : FOF_THM_RFO_SEQ
% 27.72/27.92
% 27.72/27.92 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 27.72/27.92 % 2011-03-01 11:42:48
% 27.72/27.92 %------------------------------------------------------------------------------
% 27.72/27.92 %----Relevant facts (4985)
% 27.72/27.92 fof(fact_ext,axiom,
% 27.72/27.92 ! [V_g_2,V_f_2] :
% 27.72/27.92 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 27.72/27.92 => V_f_2 = V_g_2 ) ).
% 27.72/27.92
% 27.72/27.92 fof(fact_asm,axiom,
% 27.72/27.92 ! [V_G_2,V_tsa_2,T_b] :
% 27.72/27.92 ( 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))
% 27.72/27.92 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ).
% 27.72/27.92
% 27.72/27.92 fof(fact_weaken,axiom,
% 27.72/27.92 ! [V_tsa_2,V_ts_H_2,V_G_2,T_b] :
% 27.72/27.92 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2)
% 27.72/27.92 => ( 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))
% 27.72/27.92 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ) ).
% 27.72/27.92
% 27.72/27.92 fof(fact_cut,axiom,
% 27.72/27.92 ! [V_G_2,V_tsa_2,V_G_Ha_2,T_b] :
% 27.72/27.92 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
% 27.72/27.92 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2)
% 27.72/27.92 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ) ).
% 27.72/27.92
% 27.72/27.92 fof(fact_equalityI,axiom,
% 27.72/27.92 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 27.72/27.92 => V_A_2 = V_B_2 ) ) ).
% 27.72/27.92
% 27.72/27.92 fof(fact_order__refl,axiom,
% 27.72/27.92 ! [V_x,T_a] :
% 27.72/27.92 ( class_Orderings_Opreorder(T_a)
% 27.72/27.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 27.72/27.92
% 27.72/27.92 fof(fact_le__fun__def,axiom,
% 27.72/27.92 ! [V_g_2,V_f_2,T_b,T_c] :
% 27.72/27.92 ( class_Orderings_Oord(T_c)
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 27.72/27.93 <=> ! [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))) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_le__funD,axiom,
% 27.72/27.93 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 27.72/27.93 ( class_Orderings_Oord(T_c)
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 27.72/27.93 => 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))) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_le__funE,axiom,
% 27.72/27.93 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 27.72/27.93 ( class_Orderings_Oord(T_c)
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 27.72/27.93 => 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))) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_subset__refl,axiom,
% 27.72/27.93 ! [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)) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_set__eq__subset,axiom,
% 27.72/27.93 ! [T_b,V_B_2,V_A_2] :
% 27.72/27.93 ( V_A_2 = V_B_2
% 27.72/27.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_rev__predicate1D,axiom,
% 27.72/27.93 ! [V_Q_2,T_b,V_x_2,V_P_2] :
% 27.72/27.93 ( hBOOL(hAPP(V_P_2,V_x_2))
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
% 27.72/27.93 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_equalityD1,axiom,
% 27.72/27.93 ! [T_b,V_B_2,V_A_2] :
% 27.72/27.93 ( V_A_2 = V_B_2
% 27.72/27.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_equalityD2,axiom,
% 27.72/27.93 ! [T_b,V_B_2,V_A_2] :
% 27.72/27.93 ( V_A_2 = V_B_2
% 27.72/27.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_predicate1D,axiom,
% 27.72/27.93 ! [V_x_2,V_Q_2,V_P_2,T_b] :
% 27.72/27.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
% 27.72/27.93 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 27.72/27.93 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_subset__trans,axiom,
% 27.72/27.93 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 27.72/27.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 27.72/27.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_linorder__le__cases,axiom,
% 27.72/27.93 ! [V_y,V_x,T_a] :
% 27.72/27.93 ( class_Orderings_Olinorder(T_a)
% 27.72/27.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 27.72/27.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_xt1_I6_J,axiom,
% 27.72/27.93 ! [V_z,V_x,V_y,T_a] :
% 27.72/27.93 ( class_Orderings_Oorder(T_a)
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 27.72/27.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_xt1_I5_J,axiom,
% 27.72/27.93 ! [V_x,V_y,T_a] :
% 27.72/27.93 ( class_Orderings_Oorder(T_a)
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 27.72/27.93 => V_x = V_y ) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_order__trans,axiom,
% 27.72/27.93 ! [V_z,V_y,V_x,T_a] :
% 27.72/27.93 ( class_Orderings_Opreorder(T_a)
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 27.72/27.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_order__antisym,axiom,
% 27.72/27.93 ! [V_y,V_x,T_a] :
% 27.72/27.93 ( class_Orderings_Oorder(T_a)
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 27.72/27.93 => V_x = V_y ) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_xt1_I4_J,axiom,
% 27.72/27.93 ! [V_c,V_a,V_b,T_a] :
% 27.72/27.93 ( class_Orderings_Oorder(T_a)
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 27.72/27.93 => ( V_b = V_c
% 27.72/27.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_ord__le__eq__trans,axiom,
% 27.72/27.93 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.93 ( class_Orderings_Oord(T_a)
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 27.72/27.93 => ( V_b = V_c
% 27.72/27.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_xt1_I3_J,axiom,
% 27.72/27.93 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.93 ( class_Orderings_Oorder(T_a)
% 27.72/27.93 => ( V_a = V_b
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 27.72/27.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_ord__eq__le__trans,axiom,
% 27.72/27.93 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.93 ( class_Orderings_Oord(T_a)
% 27.72/27.93 => ( V_a = V_b
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 27.72/27.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_order__antisym__conv,axiom,
% 27.72/27.93 ! [V_x_2,V_y_2,T_b] :
% 27.72/27.93 ( class_Orderings_Oorder(T_b)
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 27.72/27.93 <=> V_x_2 = V_y_2 ) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_order__eq__refl,axiom,
% 27.72/27.93 ! [V_y,V_x,T_a] :
% 27.72/27.93 ( class_Orderings_Opreorder(T_a)
% 27.72/27.93 => ( V_x = V_y
% 27.72/27.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_order__eq__iff,axiom,
% 27.72/27.93 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.93 ( class_Orderings_Oorder(T_b)
% 27.72/27.93 => ( V_x_2 = V_y_2
% 27.72/27.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 27.72/27.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_linorder__linear,axiom,
% 27.72/27.93 ! [V_y,V_x,T_a] :
% 27.72/27.93 ( class_Orderings_Olinorder(T_a)
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 27.72/27.93 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_equalityE,axiom,
% 27.72/27.93 ! [T_b,V_B_2,V_A_2] :
% 27.72/27.93 ( V_A_2 = V_B_2
% 27.72/27.93 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.93 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_Powp__mono,axiom,
% 27.72/27.93 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.93 => 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))) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_order__fun_I1_J,axiom,
% 27.72/27.93 ! [V_g_2,V_f_2,T_b,T_c] :
% 27.72/27.93 ( ( class_Orderings_Oorder(T_c)
% 27.72/27.93 & class_Enum_Oenum(T_b) )
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 27.72/27.93 <=> 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))) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_Least__le,axiom,
% 27.72/27.93 ! [V_k_2,V_P_2,T_b] :
% 27.72/27.93 ( class_Orderings_Owellorder(T_b)
% 27.72/27.93 => ( hBOOL(hAPP(V_P_2,V_k_2))
% 27.72/27.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Orderings_Oord__class_OLeast(T_b,V_P_2)),V_k_2)) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_le__funI,axiom,
% 27.72/27.93 ! [T_b,V_g_2,V_f_2,T_c] :
% 27.72/27.93 ( class_Orderings_Oord(T_c)
% 27.72/27.93 => ( ! [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)))
% 27.72/27.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_inv__imagep__def,axiom,
% 27.72/27.93 ! [V_y_2,V_x_2,V_f_2,V_r_2,T_c,T_b] :
% 27.72/27.93 ( c_Predicate_Oinv__imagep(T_b,T_c,V_r_2,V_f_2,V_x_2,V_y_2)
% 27.72/27.93 <=> hBOOL(hAPP(hAPP(V_r_2,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_strict__mono__less__eq,axiom,
% 27.72/27.93 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 27.72/27.93 ( ( class_Orderings_Oorder(T_c)
% 27.72/27.93 & class_Orderings_Olinorder(T_b) )
% 27.72/27.93 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 27.72/27.93 => ( 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)))
% 27.72/27.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_greaterThan__subset__iff,axiom,
% 27.72/27.93 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.93 ( class_Orderings_Olinorder(T_b)
% 27.72/27.93 => ( 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)))
% 27.72/27.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_lessThan__subset__iff,axiom,
% 27.72/27.93 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.93 ( class_Orderings_Olinorder(T_b)
% 27.72/27.93 => ( 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)))
% 27.72/27.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_atLeast__subset__iff,axiom,
% 27.72/27.93 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.93 ( class_Orderings_Oorder(T_b)
% 27.72/27.93 => ( 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)))
% 27.72/27.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_atMost__subset__iff,axiom,
% 27.72/27.93 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.93 ( class_Orderings_Oorder(T_b)
% 27.72/27.93 => ( 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)))
% 27.72/27.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_SUP__subset,axiom,
% 27.72/27.93 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 27.72/27.93 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.93 => 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))) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_INF__subset,axiom,
% 27.72/27.93 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 27.72/27.93 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 27.72/27.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.93 => 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))) ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_SUPR__apply,axiom,
% 27.72/27.93 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 27.72/27.93 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.93 => 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)) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_INFI__apply,axiom,
% 27.72/27.93 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 27.72/27.93 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.93 => 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)) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_greaterThan__eq__iff,axiom,
% 27.72/27.93 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.93 ( class_Orderings_Olinorder(T_b)
% 27.72/27.93 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 27.72/27.93 <=> V_x_2 = V_y_2 ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_lessThan__eq__iff,axiom,
% 27.72/27.93 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.93 ( class_Orderings_Olinorder(T_b)
% 27.72/27.93 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 27.72/27.93 <=> V_x_2 = V_y_2 ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_atLeast__eq__iff,axiom,
% 27.72/27.93 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.93 ( class_Orderings_Olinorder(T_b)
% 27.72/27.93 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 27.72/27.93 <=> V_x_2 = V_y_2 ) ) ).
% 27.72/27.93
% 27.72/27.93 fof(fact_atMost__eq__iff,axiom,
% 27.72/27.93 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.93 ( class_Orderings_Olinorder(T_b)
% 27.72/27.93 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 27.72/27.94 <=> V_x_2 = V_y_2 ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_SUP__commute,axiom,
% 27.72/27.94 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 27.72/27.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.94 => 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))) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_INF__commute,axiom,
% 27.72/27.94 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 27.72/27.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.94 => 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))) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_all__code,axiom,
% 27.72/27.94 ! [V_P_2,T_b] :
% 27.72/27.94 ( class_Enum_Oenum(T_b)
% 27.72/27.94 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 27.72/27.94 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2)) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_enum__all,axiom,
% 27.72/27.94 ! [V_P_2,T_b] :
% 27.72/27.94 ( class_Enum_Oenum(T_b)
% 27.72/27.94 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2))
% 27.72/27.94 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_LeastI__ex,axiom,
% 27.72/27.94 ! [V_P_2,T_b] :
% 27.72/27.94 ( class_Orderings_Owellorder(T_b)
% 27.72/27.94 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 27.72/27.94 => hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_strict__mono__eq,axiom,
% 27.72/27.94 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 27.72/27.94 ( ( class_Orderings_Oorder(T_c)
% 27.72/27.94 & class_Orderings_Olinorder(T_b) )
% 27.72/27.94 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 27.72/27.94 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 27.72/27.94 <=> V_x_2 = V_y_2 ) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_INT__subset__iff,axiom,
% 27.72/27.94 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 27.72/27.94 ( 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)))
% 27.72/27.94 <=> ! [B_x] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 27.72/27.94 => 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))) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_UN__subset__iff,axiom,
% 27.72/27.94 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 27.72/27.94 ( 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))
% 27.72/27.94 <=> ! [B_x] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 27.72/27.94 => 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)) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_LeastI,axiom,
% 27.72/27.94 ! [V_k_2,V_P_2,T_b] :
% 27.72/27.94 ( class_Orderings_Owellorder(T_b)
% 27.72/27.94 => ( hBOOL(hAPP(V_P_2,V_k_2))
% 27.72/27.94 => hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_le__INF__iff,axiom,
% 27.72/27.94 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 27.72/27.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.94 => ( 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)))
% 27.72/27.94 <=> ! [B_x] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 27.72/27.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_SUP__le__iff,axiom,
% 27.72/27.94 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 27.72/27.94 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.94 => ( 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))
% 27.72/27.94 <=> ! [B_x] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 27.72/27.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_in__inv__imagep,axiom,
% 27.72/27.94 ! [V_y_2,V_x_2,V_f_2,V_r_2,T_c,T_b] :
% 27.72/27.94 ( c_Predicate_Oinv__imagep(T_b,T_c,V_r_2,V_f_2,V_x_2,V_y_2)
% 27.72/27.94 <=> hBOOL(hAPP(hAPP(V_r_2,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_Least__equality,axiom,
% 27.72/27.94 ! [V_x_2,V_P_2,T_b] :
% 27.72/27.94 ( class_Orderings_Oorder(T_b)
% 27.72/27.94 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 27.72/27.94 => ( ! [B_y] :
% 27.72/27.94 ( hBOOL(hAPP(V_P_2,B_y))
% 27.72/27.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 27.72/27.94 => c_Orderings_Oord__class_OLeast(T_b,V_P_2) = V_x_2 ) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_Pow__mono,axiom,
% 27.72/27.94 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.94 => 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))) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_Inter__anti__mono,axiom,
% 27.72/27.94 ! [V_A_2,V_B_2,T_b] :
% 27.72/27.94 ( 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))
% 27.72/27.94 => 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))) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_INF__leI,axiom,
% 27.72/27.94 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 27.72/27.94 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 27.72/27.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 27.72/27.94 => 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))) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_le__SUPI,axiom,
% 27.72/27.94 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 27.72/27.94 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 27.72/27.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 27.72/27.94 => 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))) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_atLeastLessThan__subset__iff,axiom,
% 27.72/27.94 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 27.72/27.94 ( class_Orderings_Olinorder(T_b)
% 27.72/27.94 => ( 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)))
% 27.72/27.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 27.72/27.94 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 27.72/27.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_Compl__greaterThan,axiom,
% 27.72/27.94 ! [V_k_2,T_b] :
% 27.72/27.94 ( class_Orderings_Olinorder(T_b)
% 27.72/27.94 => 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) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_Compl__atMost,axiom,
% 27.72/27.94 ! [V_k_2,T_b] :
% 27.72/27.94 ( class_Orderings_Olinorder(T_b)
% 27.72/27.94 => 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) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_atLeastatMost__subset__iff,axiom,
% 27.72/27.94 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 27.72/27.94 ( class_Orderings_Oorder(T_b)
% 27.72/27.94 => ( 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)))
% 27.72/27.94 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 27.72/27.94 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 27.72/27.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_Compl__lessThan,axiom,
% 27.72/27.94 ! [V_k_2,T_b] :
% 27.72/27.94 ( class_Orderings_Olinorder(T_b)
% 27.72/27.94 => 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) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_Compl__atLeast,axiom,
% 27.72/27.94 ! [V_k_2,T_b] :
% 27.72/27.94 ( class_Orderings_Olinorder(T_b)
% 27.72/27.94 => 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) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_Union__mono,axiom,
% 27.72/27.94 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.94 ( 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))
% 27.72/27.94 => 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))) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_equalityCE,axiom,
% 27.72/27.94 ! [V_c_2,T_b,V_B_2,V_A_2] :
% 27.72/27.94 ( V_A_2 = V_B_2
% 27.72/27.94 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 27.72/27.94 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) )
% 27.72/27.94 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 27.72/27.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_INF2__E,axiom,
% 27.72/27.94 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 27.72/27.94 ( 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))
% 27.72/27.94 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 27.72/27.94 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_INF2__D,axiom,
% 27.72/27.94 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 27.72/27.94 ( 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))
% 27.72/27.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.94 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_SUP2__I,axiom,
% 27.72/27.94 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.94 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 27.72/27.94 => 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)) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_subsetD,axiom,
% 27.72/27.94 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 27.72/27.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_ComplI,axiom,
% 27.72/27.94 ! [V_A_2,V_c_2,T_b] :
% 27.72/27.94 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 27.72/27.94 => 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))) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_UnionI,axiom,
% 27.72/27.94 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 27.72/27.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 27.72/27.94 => 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))) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_InterE,axiom,
% 27.72/27.94 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 27.72/27.94 ( 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)))
% 27.72/27.94 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 27.72/27.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_InterD,axiom,
% 27.72/27.94 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 27.72/27.94 ( 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)))
% 27.72/27.94 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 27.72/27.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_PowI,axiom,
% 27.72/27.94 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.94 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_UN__I,axiom,
% 27.72/27.94 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.94 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 27.72/27.94 => 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))) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_SUP1__I,axiom,
% 27.72/27.94 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.94 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 27.72/27.94 => 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)) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_INT__D,axiom,
% 27.72/27.94 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 27.72/27.94 ( 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)))
% 27.72/27.94 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 27.72/27.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_INT__E,axiom,
% 27.72/27.94 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 27.72/27.94 ( 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)))
% 27.72/27.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 27.72/27.94 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_INF1__E,axiom,
% 27.72/27.94 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 27.72/27.94 ( 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))
% 27.72/27.94 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 27.72/27.94 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_INF1__D,axiom,
% 27.72/27.94 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 27.72/27.94 ( 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))
% 27.72/27.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.94 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_UN__UN__flatten,axiom,
% 27.72/27.94 ! [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)) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_UN__simps_I9_J,axiom,
% 27.72/27.94 ! [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)) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_INT__simps_I9_J,axiom,
% 27.72/27.94 ! [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)) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_ball__UN,axiom,
% 27.72/27.94 ! [V_P_2,V_B_2,V_A_2,T_c,T_b] :
% 27.72/27.94 ( ! [B_x] :
% 27.72/27.94 ( 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)))
% 27.72/27.94 => hBOOL(hAPP(V_P_2,B_x)) )
% 27.72/27.94 <=> ! [B_x] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 27.72/27.94 => ! [B_xa] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 27.72/27.94 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_UN__extend__simps_I9_J,axiom,
% 27.72/27.94 ! [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) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_INT__extend__simps_I9_J,axiom,
% 27.72/27.94 ! [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) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_Union__Pow__eq,axiom,
% 27.72/27.94 ! [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 ).
% 27.72/27.94
% 27.72/27.94 fof(fact_INF1__iff,axiom,
% 27.72/27.94 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 27.72/27.94 ( 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))
% 27.72/27.94 <=> ! [B_x] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.94 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_SUP1__iff,axiom,
% 27.72/27.94 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 27.72/27.94 ( 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))
% 27.72/27.94 <=> ? [B_x] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.94 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_ComplE,axiom,
% 27.72/27.94 ! [V_A_2,V_c_2,T_b] :
% 27.72/27.94 ( 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)))
% 27.72/27.94 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_ComplD,axiom,
% 27.72/27.94 ! [V_A_2,V_c_2,T_b] :
% 27.72/27.94 ( 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)))
% 27.72/27.94 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_eq__mem__trans,axiom,
% 27.72/27.94 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 27.72/27.94 ( V_a_2 = V_b_2
% 27.72/27.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 27.72/27.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_eqelem__imp__iff,axiom,
% 27.72/27.94 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 27.72/27.94 ( V_x_2 = V_y_2
% 27.72/27.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.94 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_eqset__imp__iff,axiom,
% 27.72/27.94 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 27.72/27.94 ( V_A_2 = V_B_2
% 27.72/27.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.94 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_Compl__eq__Compl__iff,axiom,
% 27.72/27.94 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.94 ( 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)
% 27.72/27.94 <=> V_A_2 = V_B_2 ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_eq__mem,axiom,
% 27.72/27.94 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 27.72/27.94 <=> V_x_2 = V_y_2 ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_Compl__iff,axiom,
% 27.72/27.94 ! [V_A_2,V_c_2,T_b] :
% 27.72/27.94 ( 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)))
% 27.72/27.94 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_mem__def,axiom,
% 27.72/27.94 ! [V_A_2,V_x_2,T_b] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.94 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_double__complement,axiom,
% 27.72/27.94 ! [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 ).
% 27.72/27.94
% 27.72/27.94 fof(fact_Pow__top,axiom,
% 27.72/27.94 ! [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))) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_Union__upper,axiom,
% 27.72/27.94 ! [V_A_2,V_B_2,T_b] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 27.72/27.94 => 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))) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_Inter__lower,axiom,
% 27.72/27.94 ! [V_A_2,V_B_2,T_b] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 27.72/27.94 => 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)) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_Compl__INT,axiom,
% 27.72/27.94 ! [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)) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_Compl__UN,axiom,
% 27.72/27.94 ! [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)) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_Union__def,axiom,
% 27.72/27.94 ! [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))) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_INT__extend__simps_I8_J,axiom,
% 27.72/27.94 ! [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) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_UN__extend__simps_I8_J,axiom,
% 27.72/27.94 ! [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) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_INT__simps_I8_J,axiom,
% 27.72/27.94 ! [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)) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_UN__simps_I8_J,axiom,
% 27.72/27.94 ! [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)) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_Pow__iff,axiom,
% 27.72/27.94 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 27.72/27.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 27.72/27.94
% 27.72/27.94 fof(fact_PowD,axiom,
% 27.72/27.94 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.94 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 27.72/27.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_pred__equals__eq,axiom,
% 27.72/27.95 ! [V_S_2,V_R_2,T_b] :
% 27.72/27.95 ( 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)
% 27.72/27.95 <=> V_R_2 = V_S_2 ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_INT__iff,axiom,
% 27.72/27.95 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 27.72/27.95 ( 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)))
% 27.72/27.95 <=> ! [B_x] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 27.72/27.95 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_UN__iff,axiom,
% 27.72/27.95 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 27.72/27.95 ( 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)))
% 27.72/27.95 <=> ? [B_x] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 27.72/27.95 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Sup__upper,axiom,
% 27.72/27.95 ! [V_A_2,V_x_2,T_b] :
% 27.72/27.95 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.95 => 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))) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Inf__lower,axiom,
% 27.72/27.95 ! [V_A_2,V_x_2,T_b] :
% 27.72/27.95 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.95 => 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)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Inter__def,axiom,
% 27.72/27.95 ! [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))) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Powp__Pow__eq,axiom,
% 27.72/27.95 ! [V_x_2,V_A_2,T_b] :
% 27.72/27.95 ( 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))
% 27.72/27.95 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Pow__INT__eq,axiom,
% 27.72/27.95 ! [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)) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_subset__Pow__Union,axiom,
% 27.72/27.95 ! [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)))) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Compl__anti__mono,axiom,
% 27.72/27.95 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.95 => 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))) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Compl__subset__Compl__iff,axiom,
% 27.72/27.95 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.95 ( 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)))
% 27.72/27.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_set__mp,axiom,
% 27.72/27.95 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.95 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_set__rev__mp,axiom,
% 27.72/27.95 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.95 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_in__mono,axiom,
% 27.72/27.95 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.95 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_pred__subset__eq,axiom,
% 27.72/27.95 ! [V_S_2,V_R_2,T_b] :
% 27.72/27.95 ( 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)))
% 27.72/27.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_UN__upper,axiom,
% 27.72/27.95 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.95 => 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))) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_INT__lower,axiom,
% 27.72/27.95 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.95 => 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))) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Sup__le__iff,axiom,
% 27.72/27.95 ! [V_b_2,V_A_2,T_b] :
% 27.72/27.95 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.95 => ( 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))
% 27.72/27.95 <=> ! [B_x] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_le__Inf__iff,axiom,
% 27.72/27.95 ! [V_A_2,V_b_2,T_b] :
% 27.72/27.95 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.95 => ( 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)))
% 27.72/27.95 <=> ! [B_x] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_UN__Pow__subset,axiom,
% 27.72/27.95 ! [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)))) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_atMost__iff,axiom,
% 27.72/27.95 ! [V_k_2,V_i_2,T_b] :
% 27.72/27.95 ( class_Orderings_Oord(T_b)
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 27.72/27.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_atLeast__iff,axiom,
% 27.72/27.95 ! [V_k_2,V_i_2,T_b] :
% 27.72/27.95 ( class_Orderings_Oord(T_b)
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 27.72/27.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_fun__Compl__def,axiom,
% 27.72/27.95 ! [V_x_2,V_A_2,T_c,T_b] :
% 27.72/27.95 ( class_Groups_Ouminus(T_b)
% 27.72/27.95 => 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)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_uminus__apply,axiom,
% 27.72/27.95 ! [V_x_2,V_A_2,T_c,T_b] :
% 27.72/27.95 ( class_Groups_Ouminus(T_b)
% 27.72/27.95 => 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)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 27.72/27.95 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 27.72/27.95 ( 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)))
% 27.72/27.95 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 27.72/27.95 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 27.72/27.95 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 27.72/27.95 ( 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)))
% 27.72/27.95 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 27.72/27.95 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 27.72/27.95 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 27.72/27.95 ( 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)))
% 27.72/27.95 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 27.72/27.95 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 27.72/27.95 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 27.72/27.95 ( 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)))
% 27.72/27.95 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 27.72/27.95 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_ord_OgreaterThan__iff,axiom,
% 27.72/27.95 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 27.72/27.95 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_ord_OlessThan__iff,axiom,
% 27.72/27.95 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 27.72/27.95 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_ord_OatLeast__iff,axiom,
% 27.72/27.95 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 27.72/27.95 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_ord_OatMost__iff,axiom,
% 27.72/27.95 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 27.72/27.95 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_compl__mono,axiom,
% 27.72/27.95 ! [V_y,V_x,T_a] :
% 27.72/27.95 ( class_Lattices_Oboolean__algebra(T_a)
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 27.72/27.95 => 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))) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_le__imp__neg__le,axiom,
% 27.72/27.95 ! [V_b,V_a,T_a] :
% 27.72/27.95 ( class_Groups_Oordered__ab__group__add(T_a)
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 27.72/27.95 => 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))) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_SUP2__iff,axiom,
% 27.72/27.95 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 27.72/27.95 ( 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))
% 27.72/27.95 <=> ? [B_x] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.95 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_INF2__iff,axiom,
% 27.72/27.95 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 27.72/27.95 ( 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))
% 27.72/27.95 <=> ! [B_x] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.95 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_compl__eq__compl__iff,axiom,
% 27.72/27.95 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.95 ( class_Lattices_Oboolean__algebra(T_b)
% 27.72/27.95 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 27.72/27.95 <=> V_x_2 = V_y_2 ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_neg__equal__iff__equal,axiom,
% 27.72/27.95 ! [V_b_2,V_a_2,T_b] :
% 27.72/27.95 ( class_Groups_Ogroup__add(T_b)
% 27.72/27.95 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 27.72/27.95 <=> V_a_2 = V_b_2 ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_minus__equation__iff,axiom,
% 27.72/27.95 ! [V_b_2,V_a_2,T_b] :
% 27.72/27.95 ( class_Groups_Ogroup__add(T_b)
% 27.72/27.95 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
% 27.72/27.95 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_equation__minus__iff,axiom,
% 27.72/27.95 ! [V_b_2,V_a_2,T_b] :
% 27.72/27.95 ( class_Groups_Ogroup__add(T_b)
% 27.72/27.95 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 27.72/27.95 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_double__compl,axiom,
% 27.72/27.95 ! [V_x,T_a] :
% 27.72/27.95 ( class_Lattices_Oboolean__algebra(T_a)
% 27.72/27.95 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_minus__minus,axiom,
% 27.72/27.95 ! [V_a,T_a] :
% 27.72/27.95 ( class_Groups_Ogroup__add(T_a)
% 27.72/27.95 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_le__minus__iff,axiom,
% 27.72/27.95 ! [V_b_2,V_a_2,T_b] :
% 27.72/27.95 ( class_Groups_Oordered__ab__group__add(T_b)
% 27.72/27.95 => ( 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)))
% 27.72/27.95 <=> 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))) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_minus__le__iff,axiom,
% 27.72/27.95 ! [V_b_2,V_a_2,T_b] :
% 27.72/27.95 ( class_Groups_Oordered__ab__group__add(T_b)
% 27.72/27.95 => ( 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))
% 27.72/27.95 <=> 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)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_neg__le__iff__le,axiom,
% 27.72/27.95 ! [V_a_2,V_b_2,T_b] :
% 27.72/27.95 ( class_Groups_Oordered__ab__group__add(T_b)
% 27.72/27.95 => ( 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)))
% 27.72/27.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_compl__le__compl__iff,axiom,
% 27.72/27.95 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.95 ( class_Lattices_Oboolean__algebra(T_b)
% 27.72/27.95 => ( 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)))
% 27.72/27.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_InterI,axiom,
% 27.72/27.95 ! [V_A_2,V_C_2,T_b] :
% 27.72/27.95 ( ! [B_X] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 27.72/27.95 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 27.72/27.95 => 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))) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_UnionE,axiom,
% 27.72/27.95 ! [V_C_2,V_A_2,T_b] :
% 27.72/27.95 ( 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)))
% 27.72/27.95 => ~ ! [B_X] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 27.72/27.95 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_SUP2__E,axiom,
% 27.72/27.95 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 27.72/27.95 ( 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))
% 27.72/27.95 => ~ ! [B_x] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.95 => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_INF2__I,axiom,
% 27.72/27.95 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,T_b] :
% 27.72/27.95 ( ! [B_x] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.95 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) )
% 27.72/27.95 => 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)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_ivl__disj__un_I13_J,axiom,
% 27.72/27.95 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.95 ( class_Orderings_Olinorder(T_b)
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 27.72/27.95 => 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) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_ivl__disj__un_I10_J,axiom,
% 27.72/27.95 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.95 ( class_Orderings_Olinorder(T_b)
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 27.72/27.95 => 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) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_INT__greatest,axiom,
% 27.72/27.95 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] :
% 27.72/27.95 ( ! [B_x] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.95 => 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))) )
% 27.72/27.95 => 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))) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_INT__anti__mono,axiom,
% 27.72/27.95 ! [V_g_2,V_f_2,T_c,V_A_2,V_B_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 27.72/27.95 => ( ! [B_x] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.95 => 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))) )
% 27.72/27.95 => 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))) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_UN__least,axiom,
% 27.72/27.95 ! [V_C_2,V_B_2,T_c,V_A_2,T_b] :
% 27.72/27.95 ( ! [B_x] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.95 => 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)) )
% 27.72/27.95 => 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)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_UN__mono,axiom,
% 27.72/27.95 ! [V_g_2,V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.95 => ( ! [B_x] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.95 => 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))) )
% 27.72/27.95 => 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))) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_le__INFI,axiom,
% 27.72/27.95 ! [V_M_2,V_u_2,V_A_2,T_b,T_c] :
% 27.72/27.95 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 27.72/27.95 => ( ! [B_i] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 27.72/27.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_u_2),hAPP(V_M_2,B_i))) )
% 27.72/27.95 => 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))) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup1CI,axiom,
% 27.72/27.95 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 27.72/27.95 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 27.72/27.95 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 27.72/27.95 => 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)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup1E,axiom,
% 27.72/27.95 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 27.72/27.95 ( 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))
% 27.72/27.95 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 27.72/27.95 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_UnCI,axiom,
% 27.72/27.95 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 27.72/27.95 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 27.72/27.95 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
% 27.72/27.95 => 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))) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_UnE,axiom,
% 27.72/27.95 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 27.72/27.95 ( 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)))
% 27.72/27.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 27.72/27.95 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup__apply,axiom,
% 27.72/27.95 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 27.72/27.95 ( class_Lattices_Olattice(T_b)
% 27.72/27.95 => 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)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup__assoc,axiom,
% 27.72/27.95 ! [V_z,V_y,V_x,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => 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)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_inf__sup__aci_I6_J,axiom,
% 27.72/27.95 ! [V_z,V_y,V_x,T_a] :
% 27.72/27.95 ( class_Lattices_Olattice(T_a)
% 27.72/27.95 => 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)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup_Oassoc,axiom,
% 27.72/27.95 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => 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)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup__left__commute,axiom,
% 27.72/27.95 ! [V_z,V_y,V_x,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => 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)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_inf__sup__aci_I7_J,axiom,
% 27.72/27.95 ! [V_z,V_y,V_x,T_a] :
% 27.72/27.95 ( class_Lattices_Olattice(T_a)
% 27.72/27.95 => 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)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup_Oleft__commute,axiom,
% 27.72/27.95 ! [V_c,V_a,V_b,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => 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)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup__left__idem,axiom,
% 27.72/27.95 ! [V_y,V_x,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => 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) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_inf__sup__aci_I8_J,axiom,
% 27.72/27.95 ! [V_y,V_x,T_a] :
% 27.72/27.95 ( class_Lattices_Olattice(T_a)
% 27.72/27.95 => 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) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup_Oleft__idem,axiom,
% 27.72/27.95 ! [V_b,V_a,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => 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) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup__commute,axiom,
% 27.72/27.95 ! [V_y,V_x,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => 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) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_inf__sup__aci_I5_J,axiom,
% 27.72/27.95 ! [V_y,V_x,T_a] :
% 27.72/27.95 ( class_Lattices_Olattice(T_a)
% 27.72/27.95 => 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) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup_Ocommute,axiom,
% 27.72/27.95 ! [V_b,V_a,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => 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) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup__fun__def,axiom,
% 27.72/27.95 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 27.72/27.95 ( class_Lattices_Olattice(T_b)
% 27.72/27.95 => 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)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup__idem,axiom,
% 27.72/27.95 ! [V_x,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup_Oidem,axiom,
% 27.72/27.95 ! [V_a,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup1I2,axiom,
% 27.72/27.95 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 27.72/27.95 ( hBOOL(hAPP(V_B_2,V_x_2))
% 27.72/27.95 => 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)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup1I1,axiom,
% 27.72/27.95 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 27.72/27.95 ( hBOOL(hAPP(V_A_2,V_x_2))
% 27.72/27.95 => 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)) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_ball__Un,axiom,
% 27.72/27.95 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 27.72/27.95 ( ! [B_x] :
% 27.72/27.95 ( 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)))
% 27.72/27.95 => hBOOL(hAPP(V_P_2,B_x)) )
% 27.72/27.95 <=> ( ! [B_x] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.95 => hBOOL(hAPP(V_P_2,B_x)) )
% 27.72/27.95 & ! [B_x] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 27.72/27.95 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_bex__Un,axiom,
% 27.72/27.95 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 27.72/27.95 ( ? [B_x] :
% 27.72/27.95 ( 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)))
% 27.72/27.95 & hBOOL(hAPP(V_P_2,B_x)) )
% 27.72/27.95 <=> ( ? [B_x] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.95 & hBOOL(hAPP(V_P_2,B_x)) )
% 27.72/27.95 | ? [B_x] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 27.72/27.95 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Un__assoc,axiom,
% 27.72/27.95 ! [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)) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Un__left__commute,axiom,
% 27.72/27.95 ! [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)) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Un__left__absorb,axiom,
% 27.72/27.95 ! [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) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Un__commute,axiom,
% 27.72/27.95 ! [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) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Un__absorb,axiom,
% 27.72/27.95 ! [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 ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Union__Un__distrib,axiom,
% 27.72/27.95 ! [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)) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_le__supE,axiom,
% 27.72/27.95 ! [V_x,V_b,V_a,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => ( 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))
% 27.72/27.95 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 27.72/27.95 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup__mono,axiom,
% 27.72/27.95 ! [V_d,V_b,V_c,V_a,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 27.72/27.95 => 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))) ) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup__least,axiom,
% 27.72/27.95 ! [V_z,V_x,V_y,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 27.72/27.95 => 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)) ) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_le__supI,axiom,
% 27.72/27.95 ! [V_b,V_x,V_a,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 27.72/27.95 => 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)) ) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup__absorb1,axiom,
% 27.72/27.95 ! [V_x,V_y,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 27.72/27.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup__absorb2,axiom,
% 27.72/27.95 ! [V_y,V_x,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 27.72/27.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_le__supI2,axiom,
% 27.72/27.95 ! [V_a,V_b,V_x,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 27.72/27.95 => 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))) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_le__supI1,axiom,
% 27.72/27.95 ! [V_b,V_a,V_x,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 27.72/27.95 => 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))) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_le__sup__iff,axiom,
% 27.72/27.95 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_b)
% 27.72/27.95 => ( 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))
% 27.72/27.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 27.72/27.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_le__iff__sup,axiom,
% 27.72/27.95 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_b)
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 27.72/27.95 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup__ge2,axiom,
% 27.72/27.95 ! [V_x,V_y,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => 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))) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_inf__sup__ord_I4_J,axiom,
% 27.72/27.95 ! [V_x,V_y,T_a] :
% 27.72/27.95 ( class_Lattices_Olattice(T_a)
% 27.72/27.95 => 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))) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup__ge1,axiom,
% 27.72/27.95 ! [V_y,V_x,T_a] :
% 27.72/27.95 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.95 => 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))) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_inf__sup__ord_I3_J,axiom,
% 27.72/27.95 ! [V_y,V_x,T_a] :
% 27.72/27.95 ( class_Lattices_Olattice(T_a)
% 27.72/27.95 => 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))) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_UnI2,axiom,
% 27.72/27.95 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 27.72/27.95 => 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))) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_UnI1,axiom,
% 27.72/27.95 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 27.72/27.95 => 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))) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Un__iff,axiom,
% 27.72/27.95 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 27.72/27.95 ( 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)))
% 27.72/27.95 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 27.72/27.95 | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Un__mono,axiom,
% 27.72/27.95 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 27.72/27.95 => 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))) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Un__least,axiom,
% 27.72/27.95 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 27.72/27.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 27.72/27.95 => 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)) ) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Un__absorb2,axiom,
% 27.72/27.95 ! [V_A_2,V_B_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 27.72/27.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Un__absorb1,axiom,
% 27.72/27.95 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_subset__Un__eq,axiom,
% 27.72/27.95 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.95 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Un__upper2,axiom,
% 27.72/27.95 ! [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))) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Un__upper1,axiom,
% 27.72/27.95 ! [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))) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Un__Pow__subset,axiom,
% 27.72/27.95 ! [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)))) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_sup__Un__eq,axiom,
% 27.72/27.95 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 27.72/27.95 ( 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))
% 27.72/27.95 <=> 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))) ) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_UN__Un__distrib,axiom,
% 27.72/27.95 ! [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)) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_UN__Un,axiom,
% 27.72/27.95 ! [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)) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_INT__simps_I7_J,axiom,
% 27.72/27.95 ! [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)) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_INT__simps_I6_J,axiom,
% 27.72/27.95 ! [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) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_INT__extend__simps_I7_J,axiom,
% 27.72/27.95 ! [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)) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Un__INT__distrib,axiom,
% 27.72/27.95 ! [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)) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_INT__extend__simps_I6_J,axiom,
% 27.72/27.95 ! [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)) ).
% 27.72/27.95
% 27.72/27.95 fof(fact_Un__INT__distrib2,axiom,
% 27.72/27.96 ! [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))) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_ivl__disj__un_I17_J,axiom,
% 27.72/27.96 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 27.72/27.96 ( class_Orderings_Olinorder(T_b)
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 27.72/27.96 => 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) ) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_UN__absorb,axiom,
% 27.72/27.96 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 27.72/27.96 => 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) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_ivl__disj__un_I21_J,axiom,
% 27.72/27.96 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 27.72/27.96 ( class_Orderings_Olinorder(T_b)
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 27.72/27.96 => 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) ) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_ivl__disj__un_I8_J,axiom,
% 27.72/27.96 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.96 ( class_Orderings_Olinorder(T_b)
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 27.72/27.96 => 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) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_ivl__disj__un_I14_J,axiom,
% 27.72/27.96 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.96 ( class_Orderings_Olinorder(T_b)
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 27.72/27.96 => 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) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Un__Inter,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_ivl__disj__un_I11_J,axiom,
% 27.72/27.96 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.96 ( class_Orderings_Olinorder(T_b)
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 27.72/27.96 => 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) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_ivl__disj__un_I9_J,axiom,
% 27.72/27.96 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.96 ( class_Orderings_Olinorder(T_b)
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 27.72/27.96 => 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) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_SUP__leI,axiom,
% 27.72/27.96 ! [V_u_2,V_M_2,V_A_2,T_b,T_c] :
% 27.72/27.96 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 27.72/27.96 => ( ! [B_i] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 27.72/27.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,B_i)),V_u_2)) )
% 27.72/27.96 => 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)) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_ivl__disj__un_I22_J,axiom,
% 27.72/27.96 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 27.72/27.96 ( class_Orderings_Olinorder(T_b)
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 27.72/27.96 => 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) ) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Inter__greatest,axiom,
% 27.72/27.96 ! [V_C_2,V_A_2,T_b] :
% 27.72/27.96 ( ! [B_X] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 27.72/27.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),B_X)) )
% 27.72/27.96 => 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))) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Union__least,axiom,
% 27.72/27.96 ! [V_C_2,V_A_2,T_b] :
% 27.72/27.96 ( ! [B_X] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 27.72/27.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) )
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_INF1__I,axiom,
% 27.72/27.96 ! [T_c,V_b_2,V_B_2,V_A_2,T_b] :
% 27.72/27.96 ( ! [B_x] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.96 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) )
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_INT__I,axiom,
% 27.72/27.96 ! [V_B_2,V_b_2,T_c,V_A_2,T_b] :
% 27.72/27.96 ( ! [B_x] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.96 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,B_x))) )
% 27.72/27.96 => 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))) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_SUP1__E,axiom,
% 27.72/27.96 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 27.72/27.96 ( 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))
% 27.72/27.96 => ~ ! [B_x] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.96 => ~ hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_UN__E,axiom,
% 27.72/27.96 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 27.72/27.96 ( 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)))
% 27.72/27.96 => ~ ! [B_x] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 27.72/27.96 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Inf__greatest,axiom,
% 27.72/27.96 ! [V_z_2,V_A_2,T_b] :
% 27.72/27.96 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.96 => ( ! [B_x] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),B_x)) )
% 27.72/27.96 => 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))) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_ivl__disj__un_I20_J,axiom,
% 27.72/27.96 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 27.72/27.96 ( class_Orderings_Olinorder(T_b)
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 27.72/27.96 => 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) ) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Sup__least,axiom,
% 27.72/27.96 ! [V_z_2,V_A_2,T_b] :
% 27.72/27.96 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.96 => ( ! [B_x] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_z_2)) )
% 27.72/27.96 => 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)) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Sup__fin_Oidem,axiom,
% 27.72/27.96 ! [V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Olattice(T_a)
% 27.72/27.96 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Un__Union__image,axiom,
% 27.72/27.96 ! [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))) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_subsetI,axiom,
% 27.72/27.96 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.96 ( ! [B_x] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.96 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
% 27.72/27.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Inter__Un__subset,axiom,
% 27.72/27.96 ! [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)))) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__uminus__atLeast,axiom,
% 27.72/27.96 ! [V_x_2,T_b] :
% 27.72/27.96 ( class_Groups_Oordered__ab__group__add(T_b)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__uminus__atMost,axiom,
% 27.72/27.96 ! [V_x_2,T_b] :
% 27.72/27.96 ( class_Groups_Oordered__ab__group__add(T_b)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__uminus__greaterThan,axiom,
% 27.72/27.96 ! [V_x_2,T_b] :
% 27.72/27.96 ( class_Groups_Oordered__ab__group__add(T_b)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__uminus__lessThan,axiom,
% 27.72/27.96 ! [V_x_2,T_b] :
% 27.72/27.96 ( class_Groups_Oordered__ab__group__add(T_b)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_INT__cong,axiom,
% 27.72/27.96 ! [T_c,V_D_2,V_C_2,T_b,V_B_2,V_A_2] :
% 27.72/27.96 ( V_A_2 = V_B_2
% 27.72/27.96 => ( ! [B_x] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 27.72/27.96 => hAPP(V_C_2,B_x) = hAPP(V_D_2,B_x) )
% 27.72/27.96 => 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) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_sup__compl__top,axiom,
% 27.72/27.96 ! [V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Oboolean__algebra(T_a)
% 27.72/27.96 => 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) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_UNIV__I,axiom,
% 27.72/27.96 ! [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)))) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf1E,axiom,
% 27.72/27.96 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 27.72/27.96 ( 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))
% 27.72/27.96 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 27.72/27.96 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf1I,axiom,
% 27.72/27.96 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 27.72/27.96 ( hBOOL(hAPP(V_A_2,V_x_2))
% 27.72/27.96 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 27.72/27.96 => 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)) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__eqI,axiom,
% 27.72/27.96 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
% 27.72/27.96 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 27.72/27.96 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_IntE,axiom,
% 27.72/27.96 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 27.72/27.96 ( 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)))
% 27.72/27.96 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 27.72/27.96 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_IntI,axiom,
% 27.72/27.96 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 27.72/27.96 => 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))) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_rangeI,axiom,
% 27.72/27.96 ! [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))))) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_range__eqI,axiom,
% 27.72/27.96 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
% 27.72/27.96 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 27.72/27.96 => 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))))) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__apply,axiom,
% 27.72/27.96 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 27.72/27.96 ( class_Lattices_Olattice(T_b)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__assoc,axiom,
% 27.72/27.96 ! [V_z,V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__sup__aci_I2_J,axiom,
% 27.72/27.96 ! [V_z,V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Olattice(T_a)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf_Oassoc,axiom,
% 27.72/27.96 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__eq__top__iff,axiom,
% 27.72/27.96 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.96 ( class_Lattices_Obounded__lattice__top(T_b)
% 27.72/27.96 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 27.72/27.96 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 27.72/27.96 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__left__commute,axiom,
% 27.72/27.96 ! [V_z,V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__sup__aci_I3_J,axiom,
% 27.72/27.96 ! [V_z,V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Olattice(T_a)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf_Oleft__commute,axiom,
% 27.72/27.96 ! [V_c,V_a,V_b,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__left__idem,axiom,
% 27.72/27.96 ! [V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => 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) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__sup__aci_I4_J,axiom,
% 27.72/27.96 ! [V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Olattice(T_a)
% 27.72/27.96 => 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) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf_Oleft__idem,axiom,
% 27.72/27.96 ! [V_b,V_a,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => 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) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__commute,axiom,
% 27.72/27.96 ! [V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => 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) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__sup__aci_I1_J,axiom,
% 27.72/27.96 ! [V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Olattice(T_a)
% 27.72/27.96 => 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) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf_Ocommute,axiom,
% 27.72/27.96 ! [V_b,V_a,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => 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) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__fun__def,axiom,
% 27.72/27.96 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 27.72/27.96 ( class_Lattices_Olattice(T_b)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__idem,axiom,
% 27.72/27.96 ! [V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf_Oidem,axiom,
% 27.72/27.96 ! [V_a,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__top__right,axiom,
% 27.72/27.96 ! [V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Obounded__lattice__top(T_a)
% 27.72/27.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__top__left,axiom,
% 27.72/27.96 ! [V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Obounded__lattice__top(T_a)
% 27.72/27.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Inf__fin_Oidem,axiom,
% 27.72/27.96 ! [V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Olattice(T_a)
% 27.72/27.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf1D2,axiom,
% 27.72/27.96 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 27.72/27.96 ( 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))
% 27.72/27.96 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf1D1,axiom,
% 27.72/27.96 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 27.72/27.96 ( 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))
% 27.72/27.96 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__assoc,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_range__composition,axiom,
% 27.72/27.96 ! [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)))) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__left__commute,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__left__absorb,axiom,
% 27.72/27.96 ! [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) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__commute,axiom,
% 27.72/27.96 ! [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) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__absorb,axiom,
% 27.72/27.96 ! [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 ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__UNIV__right,axiom,
% 27.72/27.96 ! [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 ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__UNIV__left,axiom,
% 27.72/27.96 ! [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 ).
% 27.72/27.96
% 27.72/27.96 fof(fact_top__apply,axiom,
% 27.72/27.96 ! [V_x_2,T_c,T_b] :
% 27.72/27.96 ( class_Orderings_Otop(T_b)
% 27.72/27.96 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__Int__subset,axiom,
% 27.72/27.96 ! [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)))) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__image,axiom,
% 27.72/27.96 ! [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) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__Pow__surj,axiom,
% 27.72/27.96 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 27.72/27.96 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 27.72/27.96 => 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) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Pow__Int__eq,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Union__UNIV,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Pow__UNIV,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Sup__UNIV,axiom,
% 27.72/27.96 ! [T_b] :
% 27.72/27.96 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.96 => 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) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_rev__image__eqI,axiom,
% 27.72/27.96 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.96 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 27.72/27.96 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_imageI,axiom,
% 27.72/27.96 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.96 => 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))) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__iff,axiom,
% 27.72/27.96 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 27.72/27.96 <=> ? [B_x] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 27.72/27.96 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Union__Int__subset,axiom,
% 27.72/27.96 ! [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)))) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_le__infE,axiom,
% 27.72/27.96 ! [V_b,V_a,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => ( 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)))
% 27.72/27.96 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 27.72/27.96 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__mono,axiom,
% 27.72/27.96 ! [V_d,V_b,V_c,V_a,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 27.72/27.96 => 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))) ) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__greatest,axiom,
% 27.72/27.96 ! [V_z,V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 27.72/27.96 => 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))) ) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_le__infI,axiom,
% 27.72/27.96 ! [V_b,V_a,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 27.72/27.96 => 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))) ) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__absorb2,axiom,
% 27.72/27.96 ! [V_x,V_y,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 27.72/27.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__absorb1,axiom,
% 27.72/27.96 ! [V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 27.72/27.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_le__infI2,axiom,
% 27.72/27.96 ! [V_a,V_x,V_b,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 27.72/27.96 => 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)) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_le__infI1,axiom,
% 27.72/27.96 ! [V_b,V_x,V_a,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 27.72/27.96 => 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)) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_le__inf__iff,axiom,
% 27.72/27.96 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_b)
% 27.72/27.96 => ( 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)))
% 27.72/27.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 27.72/27.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_le__iff__inf,axiom,
% 27.72/27.96 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_b)
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 27.72/27.96 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__le2,axiom,
% 27.72/27.96 ! [V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__sup__ord_I2_J,axiom,
% 27.72/27.96 ! [V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Olattice(T_a)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__le1,axiom,
% 27.72/27.96 ! [V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__sup__ord_I1_J,axiom,
% 27.72/27.96 ! [V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Olattice(T_a)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__mono,axiom,
% 27.72/27.96 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.96 => 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))) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_subset__image__iff,axiom,
% 27.72/27.96 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 27.72/27.96 ( 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)))
% 27.72/27.96 <=> ? [B_AA] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 27.72/27.96 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__Un,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_sup__inf__distrib2,axiom,
% 27.72/27.96 ! [V_x,V_z,V_y,T_a] :
% 27.72/27.96 ( class_Lattices_Odistrib__lattice(T_a)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__sup__distrib2,axiom,
% 27.72/27.96 ! [V_x,V_z,V_y,T_a] :
% 27.72/27.96 ( class_Lattices_Odistrib__lattice(T_a)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_sup__inf__distrib1,axiom,
% 27.72/27.96 ! [V_z,V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Odistrib__lattice(T_a)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__sup__distrib1,axiom,
% 27.72/27.96 ! [V_z,V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Odistrib__lattice(T_a)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_sup__inf__absorb,axiom,
% 27.72/27.96 ! [V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Olattice(T_a)
% 27.72/27.96 => 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 ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__sup__absorb,axiom,
% 27.72/27.96 ! [V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Olattice(T_a)
% 27.72/27.96 => 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 ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_IntD2,axiom,
% 27.72/27.96 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 27.72/27.96 ( 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)))
% 27.72/27.96 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_IntD1,axiom,
% 27.72/27.96 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 27.72/27.96 ( 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)))
% 27.72/27.96 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__iff,axiom,
% 27.72/27.96 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 27.72/27.96 ( 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)))
% 27.72/27.96 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 27.72/27.96 & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__mono,axiom,
% 27.72/27.96 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 27.72/27.96 => 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))) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__greatest,axiom,
% 27.72/27.96 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 27.72/27.96 => 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))) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__absorb1,axiom,
% 27.72/27.96 ! [V_A_2,V_B_2,T_b] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 27.72/27.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__absorb2,axiom,
% 27.72/27.96 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__lower2,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__lower1,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Un__Int__crazy,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Un__Int__distrib2,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__Un__distrib2,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Un__Int__distrib,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__Un__distrib,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_subset__UNIV,axiom,
% 27.72/27.96 ! [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)))) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Un__UNIV__right,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Un__UNIV__left,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__Inter__image,axiom,
% 27.72/27.96 ! [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))) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_UN__extend__simps_I10_J,axiom,
% 27.72/27.96 ! [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) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__UN,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_UN__simps_I10_J,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_INT__extend__simps_I10_J,axiom,
% 27.72/27.96 ! [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) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_INT__simps_I10_J,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_inf__Int__eq,axiom,
% 27.72/27.96 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 27.72/27.96 ( 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))
% 27.72/27.96 <=> 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))) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_UN__simps_I5_J,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_UN__simps_I4_J,axiom,
% 27.72/27.96 ! [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) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_UN__extend__simps_I5_J,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__UN__distrib,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_UN__extend__simps_I4_J,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__UN__distrib2,axiom,
% 27.72/27.96 ! [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))) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__Pow__mono,axiom,
% 27.72/27.96 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.96 ( 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))
% 27.72/27.96 => 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))) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_INT__Int__distrib,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 27.72/27.96 ! [V_B_2,V_A_2,T_c,T_b] :
% 27.72/27.96 ( 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)
% 27.72/27.96 <=> ! [B_x] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 27.72/27.96 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 27.72/27.96 ! [V_B_2,V_A_2,T_b,T_c] :
% 27.72/27.96 ( 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))
% 27.72/27.96 <=> ! [B_x] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 27.72/27.96 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_top__greatest,axiom,
% 27.72/27.96 ! [V_x,T_a] :
% 27.72/27.96 ( class_Orderings_Otop(T_a)
% 27.72/27.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_sup__top__right,axiom,
% 27.72/27.96 ! [V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Obounded__lattice__top(T_a)
% 27.72/27.96 => 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) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_sup__top__left,axiom,
% 27.72/27.96 ! [V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Obounded__lattice__top(T_a)
% 27.72/27.96 => 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) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_distrib__sup__le,axiom,
% 27.72/27.96 ! [V_z,V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Olattice(T_a)
% 27.72/27.96 => 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)))) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_distrib__inf__le,axiom,
% 27.72/27.96 ! [V_z,V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Olattice(T_a)
% 27.72/27.96 => 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)))) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_compl__sup,axiom,
% 27.72/27.96 ! [V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Oboolean__algebra(T_a)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_compl__inf,axiom,
% 27.72/27.96 ! [V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Oboolean__algebra(T_a)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__uminus__atLeastAtMost,axiom,
% 27.72/27.96 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.96 ( class_Groups_Oordered__ab__group__add(T_b)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Un__Int__assoc__eq,axiom,
% 27.72/27.96 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 27.72/27.96 ( 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))
% 27.72/27.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Compl__Un,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Compl__Int,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Compl__partition2,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Compl__partition,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_UNION__eq__Union__image,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Union__image__eq,axiom,
% 27.72/27.96 ! [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) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_INT__absorb,axiom,
% 27.72/27.96 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 27.72/27.96 => 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) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_INTER__eq__Inter__image,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Inter__image__eq,axiom,
% 27.72/27.96 ! [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) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_INT__Un,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_SUP__UN__eq,axiom,
% 27.72/27.96 ! [V_x_2,V_r_2,T_c,T_b] :
% 27.72/27.96 ( 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))
% 27.72/27.96 <=> 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))) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_INF__INT__eq,axiom,
% 27.72/27.96 ! [V_x_2,V_r_2,T_c,T_b] :
% 27.72/27.96 ( 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))
% 27.72/27.96 <=> 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))) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__Union,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Inter__Un__distrib,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__Union2,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__Union,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 27.72/27.96 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.96 ( class_Groups_Oordered__ab__group__add(T_b)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__uminus__atLeastLessThan,axiom,
% 27.72/27.96 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.96 ( class_Groups_Oordered__ab__group__add(T_b)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_compl__sup__top,axiom,
% 27.72/27.96 ! [V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Oboolean__algebra(T_a)
% 27.72/27.96 => 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) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_surj__Compl__image__subset,axiom,
% 27.72/27.96 ! [V_A_2,V_f_2,T_b,T_c] :
% 27.72/27.96 ( 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))
% 27.72/27.96 => 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)))) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Cantors__paradox,axiom,
% 27.72/27.96 ! [V_A_2,T_b] :
% 27.72/27.96 ~ ? [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) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Least__mono,axiom,
% 27.72/27.96 ! [V_S_2,V_f_2,T_b,T_c] :
% 27.72/27.96 ( ( class_Orderings_Oorder(T_c)
% 27.72/27.96 & class_Orderings_Oorder(T_b) )
% 27.72/27.96 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 27.72/27.96 => ( ? [B_x] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 27.72/27.96 & ! [B_xa] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_S_2))
% 27.72/27.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) )
% 27.72/27.96 => 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))) ) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_compl__unique,axiom,
% 27.72/27.96 ! [V_y,V_x,T_a] :
% 27.72/27.96 ( class_Lattices_Oboolean__algebra(T_a)
% 27.72/27.96 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 27.72/27.96 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 27.72/27.96 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__ident,axiom,
% 27.72/27.96 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 27.72/27.96
% 27.72/27.96 fof(fact_imageE,axiom,
% 27.72/27.96 ! [V_A_2,V_f_2,T_c,V_b_2,T_b] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 27.72/27.96 => ~ ! [B_x] :
% 27.72/27.96 ( V_b_2 = hAPP(V_f_2,B_x)
% 27.72/27.96 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__subsetI,axiom,
% 27.72/27.96 ! [V_B_2,V_f_2,T_c,V_A_2,T_b] :
% 27.72/27.96 ( ! [B_x] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.96 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,B_x)),V_B_2)) )
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_ivl__disj__int_I5_J,axiom,
% 27.72/27.96 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.96 ( class_Orderings_Oorder(T_b)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_ivl__disj__int_I3_J,axiom,
% 27.72/27.96 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.96 ( class_Orderings_Oorder(T_b)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_ivl__disj__int_I7_J,axiom,
% 27.72/27.96 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.96 ( class_Orderings_Oorder(T_b)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_ivl__disj__int_I8_J,axiom,
% 27.72/27.96 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.96 ( class_Orderings_Oorder(T_b)
% 27.72/27.96 => 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)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_top1I,axiom,
% 27.72/27.96 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_emptyE,axiom,
% 27.72/27.96 ! [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)))) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_empty__subsetI,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_UNIV__not__empty,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_bot__fun__def,axiom,
% 27.72/27.96 ! [V_x_2,T_c,T_b] :
% 27.72/27.96 ( class_Orderings_Obot(T_b)
% 27.72/27.96 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_bot__apply,axiom,
% 27.72/27.96 ! [V_x_2,T_c,T_b] :
% 27.72/27.96 ( class_Orderings_Obot(T_b)
% 27.72/27.96 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Union__empty,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Sup__empty,axiom,
% 27.72/27.96 ! [T_b] :
% 27.72/27.96 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.96 => 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) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_all__not__in__conv,axiom,
% 27.72/27.96 ! [V_A_2,T_b] :
% 27.72/27.96 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.96 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_ex__in__conv,axiom,
% 27.72/27.96 ! [V_A_2,T_b] :
% 27.72/27.96 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.96 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_empty__iff,axiom,
% 27.72/27.96 ! [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)))) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_equals0D,axiom,
% 27.72/27.96 ! [V_a_2,T_b,V_A_2] :
% 27.72/27.96 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.96 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_subset__empty,axiom,
% 27.72/27.96 ! [V_A_2,T_b] :
% 27.72/27.96 ( 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))))
% 27.72/27.96 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_empty__is__image,axiom,
% 27.72/27.96 ! [V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.96 ( 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)
% 27.72/27.96 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__empty,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_image__is__empty,axiom,
% 27.72/27.96 ! [V_A_2,V_f_2,T_b,T_c] :
% 27.72/27.96 ( 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))
% 27.72/27.96 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Un__empty__left,axiom,
% 27.72/27.96 ! [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 ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Un__empty__right,axiom,
% 27.72/27.96 ! [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 ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Un__empty,axiom,
% 27.72/27.96 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.96 ( 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))
% 27.72/27.96 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.96 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__empty__left,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Int__empty__right,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_disjoint__iff__not__equal,axiom,
% 27.72/27.96 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.96 ( 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))
% 27.72/27.96 <=> ! [B_x] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.96 => ! [B_xa] :
% 27.72/27.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 27.72/27.96 => B_x != B_xa ) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Compl__empty__eq,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Compl__UNIV__eq,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_empty,axiom,
% 27.72/27.96 ! [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))) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 27.72/27.96 ! [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))) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Pow__not__empty,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Inter__UNIV,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_Inter__empty,axiom,
% 27.72/27.96 ! [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)) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_monoD,axiom,
% 27.72/27.96 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 27.72/27.96 ( ( class_Orderings_Oorder(T_c)
% 27.72/27.96 & class_Orderings_Oorder(T_b) )
% 27.72/27.96 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 27.72/27.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 27.72/27.96 => 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))) ) ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_bot__empty__eq,axiom,
% 27.72/27.96 ! [V_x_2,T_b] :
% 27.72/27.96 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 27.72/27.96 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_bot__least,axiom,
% 27.72/27.96 ! [V_x,T_a] :
% 27.72/27.96 ( class_Orderings_Obot(T_a)
% 27.72/27.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_SUP__const,axiom,
% 27.72/27.96 ! [V_M_2,T_b,V_A_2,T_c] :
% 27.72/27.96 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 27.72/27.96 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.96 => 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 ) ) ).
% 27.72/27.96
% 27.72/27.96 fof(fact_UNION__empty__conv_I2_J,axiom,
% 27.72/27.96 ! [V_B_2,V_A_2,T_b,T_c] :
% 27.72/27.97 ( 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))
% 27.72/27.97 <=> ! [B_x] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 27.72/27.97 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_UN__constant,axiom,
% 27.72/27.97 ! [V_c_2,T_c,T_b,V_A_2] :
% 27.72/27.97 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) )
% 27.72/27.97 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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 ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_UN__empty2,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_UNION__empty__conv_I1_J,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,T_c,T_b] :
% 27.72/27.97 ( 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)
% 27.72/27.97 <=> ! [B_x] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 27.72/27.97 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_INF__const,axiom,
% 27.72/27.97 ! [V_M_2,T_b,V_A_2,T_c] :
% 27.72/27.97 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 27.72/27.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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 ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_INT__empty,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_INT__constant,axiom,
% 27.72/27.97 ! [V_c_2,T_c,T_b,V_A_2] :
% 27.72/27.97 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) )
% 27.72/27.97 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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 ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_sup__bot__left,axiom,
% 27.72/27.97 ! [V_x,T_a] :
% 27.72/27.97 ( class_Lattices_Obounded__lattice__bot(T_a)
% 27.72/27.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_sup__bot__right,axiom,
% 27.72/27.97 ! [V_x,T_a] :
% 27.72/27.97 ( class_Lattices_Obounded__lattice__bot(T_a)
% 27.72/27.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_sup__eq__bot__iff,axiom,
% 27.72/27.97 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.97 ( class_Lattices_Obounded__lattice__bot(T_b)
% 27.72/27.97 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 27.72/27.97 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 27.72/27.97 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_inf__bot__left,axiom,
% 27.72/27.97 ! [V_x,T_a] :
% 27.72/27.97 ( class_Lattices_Obounded__lattice__bot(T_a)
% 27.72/27.97 => 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) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_inf__bot__right,axiom,
% 27.72/27.97 ! [V_x,T_a] :
% 27.72/27.97 ( class_Lattices_Obounded__lattice__bot(T_a)
% 27.72/27.97 => 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) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Inf__UNIV,axiom,
% 27.72/27.97 ! [T_b] :
% 27.72/27.97 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.97 => 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) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_strict__mono__mono,axiom,
% 27.72/27.97 ! [V_f_2,T_b,T_c] :
% 27.72/27.97 ( ( class_Orderings_Oorder(T_c)
% 27.72/27.97 & class_Orderings_Oorder(T_b) )
% 27.72/27.97 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 27.72/27.97 => c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_atLeastatMost__empty__iff2,axiom,
% 27.72/27.97 ! [V_b_2,V_a_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => ( 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)
% 27.72/27.97 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_atLeastatMost__empty__iff,axiom,
% 27.72/27.97 ! [V_b_2,V_a_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => ( 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))
% 27.72/27.97 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_atLeastLessThan__empty,axiom,
% 27.72/27.97 ! [V_a_2,V_b_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__int_I11_J,axiom,
% 27.72/27.97 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_subset__Compl__self__eq,axiom,
% 27.72/27.97 ! [V_A_2,T_b] :
% 27.72/27.97 ( 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)))
% 27.72/27.97 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Compl__disjoint,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Compl__disjoint2,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_greaterThanAtMost__empty,axiom,
% 27.72/27.97 ! [V_k_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Inf__empty,axiom,
% 27.72/27.97 ! [T_b] :
% 27.72/27.97 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.97 => 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) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Union__disjoint,axiom,
% 27.72/27.97 ! [V_A_2,V_C_2,T_b] :
% 27.72/27.97 ( 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))
% 27.72/27.97 <=> ! [B_x] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Pow__bottom,axiom,
% 27.72/27.97 ! [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))) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__int_I14_J,axiom,
% 27.72/27.97 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_mono__Un,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.97 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2)
% 27.72/27.97 => 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)))) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_mono__Int,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.97 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2)
% 27.72/27.97 => 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)))) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_UN__simps_I3_J,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 27.72/27.97 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) )
% 27.72/27.97 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_UN__simps_I2_J,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 27.72/27.97 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) )
% 27.72/27.97 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_UN__extend__simps_I3_J,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 27.72/27.97 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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 )
% 27.72/27.97 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_UN__extend__simps_I2_J,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 27.72/27.97 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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 )
% 27.72/27.97 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_INT__extend__simps_I2_J,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 27.72/27.97 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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 )
% 27.72/27.97 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_INT__extend__simps_I1_J,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 27.72/27.97 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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 )
% 27.72/27.97 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_INT__simps_I1_J,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 27.72/27.97 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) )
% 27.72/27.97 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_INT__simps_I2_J,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 27.72/27.97 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) )
% 27.72/27.97 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_mono__sup,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 27.72/27.97 ( ( class_Lattices_Osemilattice__sup(T_c)
% 27.72/27.97 & class_Lattices_Osemilattice__sup(T_b) )
% 27.72/27.97 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 27.72/27.97 => 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)))) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_mono__inf,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 27.72/27.97 ( ( class_Lattices_Osemilattice__inf(T_c)
% 27.72/27.97 & class_Lattices_Osemilattice__inf(T_b) )
% 27.72/27.97 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 27.72/27.97 => 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)))) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_inf__compl__bot,axiom,
% 27.72/27.97 ! [V_x,T_a] :
% 27.72/27.97 ( class_Lattices_Oboolean__algebra(T_a)
% 27.72/27.97 => 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) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_compl__inf__bot,axiom,
% 27.72/27.97 ! [V_x,T_a] :
% 27.72/27.97 ( class_Lattices_Oboolean__algebra(T_a)
% 27.72/27.97 => 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) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_compl__top__eq,axiom,
% 27.72/27.97 ! [T_a] :
% 27.72/27.97 ( class_Lattices_Oboolean__algebra(T_a)
% 27.72/27.97 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_compl__bot__eq,axiom,
% 27.72/27.97 ! [T_a] :
% 27.72/27.97 ( class_Lattices_Oboolean__algebra(T_a)
% 27.72/27.97 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_disjoint__eq__subset__Compl,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.97 ( 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))
% 27.72/27.97 <=> 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))) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__int_I15_J,axiom,
% 27.72/27.97 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__int_I4_J,axiom,
% 27.72/27.97 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__int_I2_J,axiom,
% 27.72/27.97 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__int_I16_J,axiom,
% 27.72/27.97 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_iso__tuple__UNIV__I,axiom,
% 27.72/27.97 ! [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)))) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__un_I5_J,axiom,
% 27.72/27.97 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_b)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 27.72/27.97 => 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) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__un_I6_J,axiom,
% 27.72/27.97 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_b)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 27.72/27.97 => 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) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_coinduct3__mono__lemma,axiom,
% 27.72/27.97 ! [V_B_2,V_X_2,V_f_2,T_c,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => ( c_Orderings_Oorder__class_Omono(T_b,tc_fun(T_c,tc_HOL_Obool),V_f_2)
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__int_I6_J,axiom,
% 27.72/27.97 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__int_I1_J,axiom,
% 27.72/27.97 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__int_I10_J,axiom,
% 27.72/27.97 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__un_I1_J,axiom,
% 27.72/27.97 ! [V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_b)
% 27.72/27.97 => 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) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_INT__simps_I4_J,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 27.72/27.97 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) )
% 27.72/27.97 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_atMost__Int__atLeast,axiom,
% 27.72/27.97 ! [V_n_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => 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))) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insertCI,axiom,
% 27.72/27.97 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 27.72/27.97 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 27.72/27.97 => V_a_2 = V_b_2 )
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insertE,axiom,
% 27.72/27.97 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 27.72/27.97 => ( V_a_2 != V_b_2
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_DiffE,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 27.72/27.97 ( 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)))
% 27.72/27.97 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_DiffI,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 27.72/27.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 27.72/27.97 => 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))) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__insert,axiom,
% 27.72/27.97 ! [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)))) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__insert2,axiom,
% 27.72/27.97 ! [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) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insert__Diff__single,axiom,
% 27.72/27.97 ! [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) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insert__Diff__if,axiom,
% 27.72/27.97 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 27.72/27.97 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 27.72/27.97 => 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) )
% 27.72/27.97 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insert__Diff1,axiom,
% 27.72/27.97 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 27.72/27.97 => 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) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_diff__eq__diff__eq,axiom,
% 27.72/27.97 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 27.72/27.97 ( class_Groups_Oab__group__add(T_b)
% 27.72/27.97 => ( 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)
% 27.72/27.97 => ( V_a_2 = V_b_2
% 27.72/27.97 <=> V_c_2 = V_d_2 ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_minus__apply,axiom,
% 27.72/27.97 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 27.72/27.97 ( class_Groups_Ominus(T_b)
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_fun__diff__def,axiom,
% 27.72/27.97 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 27.72/27.97 ( class_Groups_Ominus(T_b)
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insert__code,axiom,
% 27.72/27.97 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 27.72/27.97 <=> ( V_y_2 = V_x_2
% 27.72/27.97 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__idemp,axiom,
% 27.72/27.97 ! [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) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insert__commute,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insert__absorb2,axiom,
% 27.72/27.97 ! [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) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insert__Diff,axiom,
% 27.72/27.97 ! [V_A_2,V_a_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.97 => 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 ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__insert__absorb,axiom,
% 27.72/27.97 ! [V_A_2,V_x_2,T_b] :
% 27.72/27.97 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.97 => 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 ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_diff__eq__diff__less__eq,axiom,
% 27.72/27.97 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 27.72/27.97 ( class_Groups_Oordered__ab__group__add(T_b)
% 27.72/27.97 => ( 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)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 27.72/27.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_single__Diff__lessThan,axiom,
% 27.72/27.97 ! [V_k_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => 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))) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_minus__diff__eq,axiom,
% 27.72/27.97 ! [V_b,V_a,T_a] :
% 27.72/27.97 ( class_Groups_Oab__group__add(T_a)
% 27.72/27.97 => 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) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_DiffD2,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 27.72/27.97 ( 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)))
% 27.72/27.97 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_DiffD1,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 27.72/27.97 ( 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)))
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__iff,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 27.72/27.97 ( 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)))
% 27.72/27.97 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 27.72/27.97 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insert__absorb,axiom,
% 27.72/27.97 ! [V_A_2,V_a_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.97 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insertI2,axiom,
% 27.72/27.97 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insert__ident,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 27.72/27.97 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 27.72/27.97 => ( 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)
% 27.72/27.97 <=> V_A_2 = V_B_2 ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insert__iff,axiom,
% 27.72/27.97 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 27.72/27.97 <=> ( V_a_2 = V_b_2
% 27.72/27.97 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insertI1,axiom,
% 27.72/27.97 ! [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))) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__cancel,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__empty,axiom,
% 27.72/27.97 ! [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 ).
% 27.72/27.97
% 27.72/27.97 fof(fact_empty__Diff,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_singleton__inject,axiom,
% 27.72/27.97 ! [V_b_2,V_a_2,T_b] :
% 27.72/27.97 ( 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)))
% 27.72/27.97 => V_a_2 = V_b_2 ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_doubleton__eq__iff,axiom,
% 27.72/27.97 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 27.72/27.97 ( 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))))
% 27.72/27.97 <=> ( ( V_a_2 = V_c_2
% 27.72/27.97 & V_b_2 = V_d_2 )
% 27.72/27.97 | ( V_a_2 = V_d_2
% 27.72/27.97 & V_b_2 = V_c_2 ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insert__not__empty,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_empty__not__insert,axiom,
% 27.72/27.97 ! [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) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_double__diff,axiom,
% 27.72/27.97 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 27.72/27.97 => 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 ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__mono,axiom,
% 27.72/27.97 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 27.72/27.97 => 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))) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__subset,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Un__Diff,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Un__Diff__cancel2,axiom,
% 27.72/27.97 ! [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) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Un__Diff__cancel,axiom,
% 27.72/27.97 ! [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) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__Int2,axiom,
% 27.72/27.97 ! [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) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__Int__distrib2,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Int__Diff,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__Int__distrib,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insert__mono,axiom,
% 27.72/27.97 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 27.72/27.97 => 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))) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_subset__insertI2,axiom,
% 27.72/27.97 ! [V_b_2,V_B_2,V_A_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.97 => 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))) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_subset__insertI,axiom,
% 27.72/27.97 ! [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))) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_image__insert,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Un__insert__left,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Un__insert__right,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insert__inter__insert,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_hoare__derivs_Oinsert,axiom,
% 27.72/27.97 ! [V_tsa_2,V_t_2,V_G_2,T_b] :
% 27.72/27.97 ( 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))))
% 27.72/27.97 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_subset__insert__iff,axiom,
% 27.72/27.97 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 27.72/27.97 ( 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)))
% 27.72/27.97 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.97 => 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)) )
% 27.72/27.97 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_diff__single__insert,axiom,
% 27.72/27.97 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 27.72/27.97 ( 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))
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.97 => 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))) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_UN__simps_I6_J,axiom,
% 27.72/27.97 ! [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) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_UN__extend__simps_I6_J,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_INT__simps_I5_J,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_INT__extend__simps_I5_J,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_diff__eq,axiom,
% 27.72/27.97 ! [V_y,V_x,T_a] :
% 27.72/27.97 ( class_Lattices_Oboolean__algebra(T_a)
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_singletonE,axiom,
% 27.72/27.97 ! [V_a_2,V_b_2,T_b] :
% 27.72/27.97 ( 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)))))
% 27.72/27.97 => V_b_2 = V_a_2 ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_singleton__iff,axiom,
% 27.72/27.97 ! [V_a_2,V_b_2,T_b] :
% 27.72/27.97 ( 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)))))
% 27.72/27.97 <=> V_b_2 = V_a_2 ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insert__subset,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 27.72/27.97 ( 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))
% 27.72/27.97 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 27.72/27.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_subset__insert,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 27.72/27.97 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.97 => ( 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)))
% 27.72/27.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insert__image,axiom,
% 27.72/27.97 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.97 => 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) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__UNIV,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Int__insert__left__if1,axiom,
% 27.72/27.97 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Int__insert__right__if1,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Int__insert__left__if0,axiom,
% 27.72/27.97 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 27.72/27.97 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 27.72/27.97 => 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) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Int__insert__right__if0,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 27.72/27.97 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.97 => 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) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Int__insert__left,axiom,
% 27.72/27.97 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 27.72/27.97 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 27.72/27.97 => 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)) )
% 27.72/27.97 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 27.72/27.97 => 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) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Int__insert__right,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 27.72/27.97 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.97 => 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)) )
% 27.72/27.97 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.97 => 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) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__triv,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.97 ( 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))
% 27.72/27.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__disjoint,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_image__diff__subset,axiom,
% 27.72/27.97 ! [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)))) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_subset__singletonD,axiom,
% 27.72/27.97 ! [V_x_2,V_A_2,T_b] :
% 27.72/27.97 ( 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)))))
% 27.72/27.97 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 | 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))) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__subset__conv,axiom,
% 27.72/27.97 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 27.72/27.97 ( 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))
% 27.72/27.97 <=> 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))) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__partition,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.97 => 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 ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_insert__is__Un,axiom,
% 27.72/27.97 ! [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) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Un__Diff__Int,axiom,
% 27.72/27.97 ! [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 ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__Un,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__Int,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__diff,axiom,
% 27.72/27.97 ! [V_m_2,V_n_2,V_i_2,T_b] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_b)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
% 27.72/27.97 => 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) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_atLeastAtMost__singleton_H,axiom,
% 27.72/27.97 ! [V_b_2,V_a_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => ( V_a_2 = V_b_2
% 27.72/27.97 => 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))) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 27.72/27.97 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => ( 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)))
% 27.72/27.97 <=> ( V_a_2 = V_b_2
% 27.72/27.97 & V_b_2 = V_c_2 ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_atLeastAtMost__singleton,axiom,
% 27.72/27.97 ! [V_a_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => 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))) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Sup__singleton,axiom,
% 27.72/27.97 ! [V_a_2,T_b] :
% 27.72/27.97 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.97 => 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 ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Sup__insert,axiom,
% 27.72/27.97 ! [V_A_2,V_a_2,T_b] :
% 27.72/27.97 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 27.72/27.97 ! [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) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Compl__Diff__eq,axiom,
% 27.72/27.97 ! [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) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__Compl,axiom,
% 27.72/27.97 ! [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) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Diff__eq,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Inf__singleton,axiom,
% 27.72/27.97 ! [V_a_2,T_b] :
% 27.72/27.97 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.97 => 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 ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Inf__insert,axiom,
% 27.72/27.97 ! [V_A_2,V_a_2,T_b] :
% 27.72/27.97 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Union__insert,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Un__eq__Union,axiom,
% 27.72/27.97 ! [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))))) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Pow__empty,axiom,
% 27.72/27.97 ! [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))) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Inter__insert,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Int__eq__Inter,axiom,
% 27.72/27.97 ! [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))))) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_UN__insert__distrib,axiom,
% 27.72/27.97 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_image__constant__conv,axiom,
% 27.72/27.97 ! [V_c_2,T_c,T_b,V_A_2] :
% 27.72/27.97 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) )
% 27.72/27.97 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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))) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_UN__extend__simps_I1_J,axiom,
% 27.72/27.97 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 27.72/27.97 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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))) )
% 27.72/27.97 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_UN__singleton,axiom,
% 27.72/27.97 ! [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 ).
% 27.72/27.97
% 27.72/27.97 fof(fact_UN__simps_I1_J,axiom,
% 27.72/27.97 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 27.72/27.97 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) )
% 27.72/27.97 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_INT__insert__distrib,axiom,
% 27.72/27.97 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_UN__insert,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_UN__simps_I7_J,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_UN__extend__simps_I7_J,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_INT__insert,axiom,
% 27.72/27.97 ! [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)) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_greaterThanLessThan__empty,axiom,
% 27.72/27.97 ! [V_k_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 27.72/27.97 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.97 ( class_Groups_Oordered__ab__group__add(T_b)
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Sup__binary,axiom,
% 27.72/27.97 ! [V_b_2,V_a_2,T_b] :
% 27.72/27.97 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.97 => 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) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Inf__binary,axiom,
% 27.72/27.97 ! [V_b_2,V_a_2,T_b] :
% 27.72/27.97 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.97 => 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) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_image__constant,axiom,
% 27.72/27.97 ! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.97 => 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))) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_INT__simps_I3_J,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 27.72/27.97 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) )
% 27.72/27.97 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_INT__extend__simps_I3_J,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 27.72/27.97 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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) )
% 27.72/27.97 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_image__eq__UN,axiom,
% 27.72/27.97 ! [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)))) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_INT__extend__simps_I4_J,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 27.72/27.97 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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 )
% 27.72/27.97 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Pow__insert,axiom,
% 27.72/27.97 ! [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))) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__int_I12_J,axiom,
% 27.72/27.97 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__int_I13_J,axiom,
% 27.72/27.97 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__un_I2_J,axiom,
% 27.72/27.97 ! [V_u_2,T_b] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_b)
% 27.72/27.97 => 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) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__int_I9_J,axiom,
% 27.72/27.97 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => 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)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_the__elem__eq,axiom,
% 27.72/27.97 ! [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 ).
% 27.72/27.97
% 27.72/27.97 fof(fact_fun__upd__image,axiom,
% 27.72/27.97 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 27.72/27.97 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.97 => 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)))))) )
% 27.72/27.97 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.97 => 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) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_Inter__subset,axiom,
% 27.72/27.97 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.97 ( ! [B_X] :
% 27.72/27.97 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 27.72/27.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 27.72/27.97 => 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)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__un_I19_J,axiom,
% 27.72/27.97 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_b)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 27.72/27.97 => 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) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__un_I4_J,axiom,
% 27.72/27.97 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_b)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 27.72/27.97 => 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) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__un_I18_J,axiom,
% 27.72/27.97 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_b)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 27.72/27.97 => 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) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ivl__disj__un_I3_J,axiom,
% 27.72/27.97 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_b)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 27.72/27.97 => 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) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_coinduct__set,axiom,
% 27.72/27.97 ! [V_X_2,V_a_2,V_f_2,T_b] :
% 27.72/27.97 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 27.72/27.97 => ( 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)))))
% 27.72/27.97 => 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))) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_def__coinduct__set,axiom,
% 27.72/27.97 ! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
% 27.72/27.97 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 27.72/27.97 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 27.72/27.97 => ( 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))))
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_fun__upd__triv,axiom,
% 27.72/27.97 ! [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 ).
% 27.72/27.97
% 27.72/27.97 fof(fact_order__less__irrefl,axiom,
% 27.72/27.97 ! [V_x,T_a] :
% 27.72/27.97 ( class_Orderings_Opreorder(T_a)
% 27.72/27.97 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_linorder__neq__iff,axiom,
% 27.72/27.97 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_b)
% 27.72/27.97 => ( V_x_2 != V_y_2
% 27.72/27.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 27.72/27.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_not__less__iff__gr__or__eq,axiom,
% 27.72/27.97 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_b)
% 27.72/27.97 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 27.72/27.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 27.72/27.97 | V_x_2 = V_y_2 ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_linorder__less__linear,axiom,
% 27.72/27.97 ! [V_y,V_x,T_a] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 27.72/27.97 | V_x = V_y
% 27.72/27.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_linorder__antisym__conv3,axiom,
% 27.72/27.97 ! [V_x_2,V_y_2,T_b] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_b)
% 27.72/27.97 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 27.72/27.97 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 27.72/27.97 <=> V_x_2 = V_y_2 ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_linorder__neqE,axiom,
% 27.72/27.97 ! [V_y,V_x,T_a] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_a)
% 27.72/27.97 => ( V_x != V_y
% 27.72/27.97 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_less__imp__neq,axiom,
% 27.72/27.97 ! [V_y,V_x,T_a] :
% 27.72/27.97 ( class_Orderings_Oorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 27.72/27.97 => V_x != V_y ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_order__less__not__sym,axiom,
% 27.72/27.97 ! [V_y,V_x,T_a] :
% 27.72/27.97 ( class_Orderings_Opreorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 27.72/27.97 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_order__less__imp__not__less,axiom,
% 27.72/27.97 ! [V_y,V_x,T_a] :
% 27.72/27.97 ( class_Orderings_Opreorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 27.72/27.97 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_order__less__imp__not__eq,axiom,
% 27.72/27.97 ! [V_y,V_x,T_a] :
% 27.72/27.97 ( class_Orderings_Oorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 27.72/27.97 => V_x != V_y ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_order__less__imp__not__eq2,axiom,
% 27.72/27.97 ! [V_y,V_x,T_a] :
% 27.72/27.97 ( class_Orderings_Oorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 27.72/27.97 => V_y != V_x ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_order__less__asym_H,axiom,
% 27.72/27.97 ! [V_b,V_a,T_a] :
% 27.72/27.97 ( class_Orderings_Opreorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 27.72/27.97 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_xt1_I9_J,axiom,
% 27.72/27.97 ! [V_a,V_b,T_a] :
% 27.72/27.97 ( class_Orderings_Oorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 27.72/27.97 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ord__eq__less__trans,axiom,
% 27.72/27.97 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.97 ( class_Orderings_Oord(T_a)
% 27.72/27.97 => ( V_a = V_b
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_xt1_I1_J,axiom,
% 27.72/27.97 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.97 ( class_Orderings_Oorder(T_a)
% 27.72/27.97 => ( V_a = V_b
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_ord__less__eq__trans,axiom,
% 27.72/27.97 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.97 ( class_Orderings_Oord(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 27.72/27.97 => ( V_b = V_c
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_xt1_I2_J,axiom,
% 27.72/27.97 ! [V_c,V_a,V_b,T_a] :
% 27.72/27.97 ( class_Orderings_Oorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 27.72/27.97 => ( V_b = V_c
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_order__less__trans,axiom,
% 27.72/27.97 ! [V_z,V_y,V_x,T_a] :
% 27.72/27.97 ( class_Orderings_Opreorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_xt1_I10_J,axiom,
% 27.72/27.97 ! [V_z,V_x,V_y,T_a] :
% 27.72/27.97 ( class_Orderings_Oorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_order__less__asym,axiom,
% 27.72/27.97 ! [V_y,V_x,T_a] :
% 27.72/27.97 ( class_Orderings_Opreorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 27.72/27.97 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_linorder__cases,axiom,
% 27.72/27.97 ! [V_y,V_x,T_a] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_a)
% 27.72/27.97 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 27.72/27.97 => ( V_x != V_y
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_fun__upd__idem__iff,axiom,
% 27.72/27.97 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 27.72/27.97 ( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2
% 27.72/27.97 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_fun__upd__upd,axiom,
% 27.72/27.97 ! [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) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_fun__upd__same,axiom,
% 27.72/27.97 ! [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 ).
% 27.72/27.97
% 27.72/27.97 fof(fact_fun__upd__apply,axiom,
% 27.72/27.97 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 27.72/27.97 ( ( V_z_2 = V_x_2
% 27.72/27.97 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 )
% 27.72/27.97 & ( V_z_2 != V_x_2
% 27.72/27.97 => 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) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_fun__upd__twist,axiom,
% 27.72/27.97 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
% 27.72/27.97 ( V_a_2 != V_c_2
% 27.72/27.97 => 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) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_fun__upd__other,axiom,
% 27.72/27.97 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 27.72/27.97 ( V_z_2 != V_x_2
% 27.72/27.97 => 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) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_fun__upd__idem,axiom,
% 27.72/27.97 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 27.72/27.97 ( hAPP(V_f_2,V_x_2) = V_y_2
% 27.72/27.97 => c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2 ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_lessThan__strict__subset__iff,axiom,
% 27.72/27.97 ! [V_n_2,V_m_2,T_b] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_b)
% 27.72/27.97 => ( 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)))
% 27.72/27.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_fun__upd__def,axiom,
% 27.72/27.97 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 27.72/27.97 ( ( V_x_2 = V_a_2
% 27.72/27.97 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2 )
% 27.72/27.97 & ( V_x_2 != V_a_2
% 27.72/27.97 => 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) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_atLeastatMost__psubset__iff,axiom,
% 27.72/27.97 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => ( 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)))
% 27.72/27.97 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 27.72/27.97 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 27.72/27.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
% 27.72/27.97 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2))
% 27.72/27.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) )
% 27.72/27.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_less__fun__def,axiom,
% 27.72/27.97 ! [V_g_2,V_f_2,T_b,T_c] :
% 27.72/27.97 ( class_Orderings_Oord(T_c)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 27.72/27.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 27.72/27.97 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_linorder__not__less,axiom,
% 27.72/27.97 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_b)
% 27.72/27.97 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 27.72/27.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_linorder__not__le,axiom,
% 27.72/27.97 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_b)
% 27.72/27.97 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 27.72/27.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_linorder__le__less__linear,axiom,
% 27.72/27.97 ! [V_y,V_x,T_a] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 27.72/27.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_order__less__le,axiom,
% 27.72/27.97 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 27.72/27.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 27.72/27.97 & V_x_2 != V_y_2 ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_less__le__not__le,axiom,
% 27.72/27.97 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.97 ( class_Orderings_Opreorder(T_b)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 27.72/27.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 27.72/27.97 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_order__le__less,axiom,
% 27.72/27.97 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.97 ( class_Orderings_Oorder(T_b)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 27.72/27.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 27.72/27.97 | V_x_2 = V_y_2 ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_leI,axiom,
% 27.72/27.97 ! [V_y,V_x,T_a] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_a)
% 27.72/27.97 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_not__leE,axiom,
% 27.72/27.97 ! [V_x,V_y,T_a] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_a)
% 27.72/27.97 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_linorder__antisym__conv1,axiom,
% 27.72/27.97 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_b)
% 27.72/27.97 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 27.72/27.97 <=> V_x_2 = V_y_2 ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_order__neq__le__trans,axiom,
% 27.72/27.97 ! [V_b,V_a,T_a] :
% 27.72/27.97 ( class_Orderings_Oorder(T_a)
% 27.72/27.97 => ( V_a != V_b
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_xt1_I12_J,axiom,
% 27.72/27.97 ! [V_b,V_a,T_a] :
% 27.72/27.97 ( class_Orderings_Oorder(T_a)
% 27.72/27.97 => ( V_a != V_b
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_leD,axiom,
% 27.72/27.97 ! [V_x,V_y,T_a] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 27.72/27.97 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_order__less__imp__le,axiom,
% 27.72/27.97 ! [V_y,V_x,T_a] :
% 27.72/27.97 ( class_Orderings_Opreorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_linorder__antisym__conv2,axiom,
% 27.72/27.97 ! [V_y_2,V_x_2,T_b] :
% 27.72/27.97 ( class_Orderings_Olinorder(T_b)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 27.72/27.97 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 27.72/27.97 <=> V_x_2 = V_y_2 ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_order__le__imp__less__or__eq,axiom,
% 27.72/27.97 ! [V_y,V_x,T_a] :
% 27.72/27.97 ( class_Orderings_Oorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 27.72/27.97 | V_x = V_y ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_order__le__neq__trans,axiom,
% 27.72/27.97 ! [V_b,V_a,T_a] :
% 27.72/27.97 ( class_Orderings_Oorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 27.72/27.97 => ( V_a != V_b
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_xt1_I11_J,axiom,
% 27.72/27.97 ! [V_a,V_b,T_a] :
% 27.72/27.97 ( class_Orderings_Oorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 27.72/27.97 => ( V_a != V_b
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_order__less__le__trans,axiom,
% 27.72/27.97 ! [V_z,V_y,V_x,T_a] :
% 27.72/27.97 ( class_Orderings_Opreorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 27.72/27.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 27.72/27.97
% 27.72/27.97 fof(fact_xt1_I7_J,axiom,
% 27.72/27.97 ! [V_z,V_x,V_y,T_a] :
% 27.72/27.97 ( class_Orderings_Oorder(T_a)
% 27.72/27.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_order__le__less__trans,axiom,
% 27.72/27.98 ! [V_z,V_y,V_x,T_a] :
% 27.72/27.98 ( class_Orderings_Opreorder(T_a)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_xt1_I8_J,axiom,
% 27.72/27.98 ! [V_z,V_x,V_y,T_a] :
% 27.72/27.98 ( class_Orderings_Oorder(T_a)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_psubsetD,axiom,
% 27.72/27.98 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_not__psubset__empty,axiom,
% 27.72/27.98 ! [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)))) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_diff__eq__diff__less,axiom,
% 27.72/27.98 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 27.72/27.98 ( class_Groups_Oordered__ab__group__add(T_b)
% 27.72/27.98 => ( 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)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 27.72/27.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_less__supI1,axiom,
% 27.72/27.98 ! [V_b,V_a,V_x,T_a] :
% 27.72/27.98 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 27.72/27.98 => 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))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_less__supI2,axiom,
% 27.72/27.98 ! [V_a,V_b,V_x,T_a] :
% 27.72/27.98 ( class_Lattices_Osemilattice__sup(T_a)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 27.72/27.98 => 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))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_less__infI1,axiom,
% 27.72/27.98 ! [V_b,V_x,V_a,T_a] :
% 27.72/27.98 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 27.72/27.98 => 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)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_less__infI2,axiom,
% 27.72/27.98 ! [V_a,V_x,V_b,T_a] :
% 27.72/27.98 ( class_Lattices_Osemilattice__inf(T_a)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 27.72/27.98 => 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)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_neg__less__iff__less,axiom,
% 27.72/27.98 ! [V_a_2,V_b_2,T_b] :
% 27.72/27.98 ( class_Groups_Oordered__ab__group__add(T_b)
% 27.72/27.98 => ( 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)))
% 27.72/27.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_minus__less__iff,axiom,
% 27.72/27.98 ! [V_b_2,V_a_2,T_b] :
% 27.72/27.98 ( class_Groups_Oordered__ab__group__add(T_b)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 27.72/27.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_less__minus__iff,axiom,
% 27.72/27.98 ! [V_b_2,V_a_2,T_b] :
% 27.72/27.98 ( class_Groups_Oordered__ab__group__add(T_b)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 27.72/27.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_psubset__eq,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.98 & V_A_2 != V_B_2 ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_subset__iff__psubset__eq,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.98 | V_A_2 = V_B_2 ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_psubset__imp__subset,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_psubset__subset__trans,axiom,
% 27.72/27.98 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_subset__psubset__trans,axiom,
% 27.72/27.98 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_atLeastLessThan__eq__iff,axiom,
% 27.72/27.98 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 27.72/27.98 ( class_Orderings_Olinorder(T_b)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 27.72/27.98 => ( 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)
% 27.72/27.98 <=> ( V_a_2 = V_c_2
% 27.72/27.98 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 27.72/27.98 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 27.72/27.98 ( class_Orderings_Olinorder(T_b)
% 27.72/27.98 => ( 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)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 27.72/27.98 => V_a_2 = V_c_2 ) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 27.72/27.98 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 27.72/27.98 ( class_Orderings_Olinorder(T_b)
% 27.72/27.98 => ( 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)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 27.72/27.98 => V_b_2 = V_d_2 ) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_less__Sup__iff,axiom,
% 27.72/27.98 ! [V_S_2,V_a_2,T_b] :
% 27.72/27.98 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 & class_Orderings_Olinorder(T_b) )
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 27.72/27.98 <=> ? [B_x] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 27.72/27.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_Inf__less__iff,axiom,
% 27.72/27.98 ! [V_a_2,V_S_2,T_b] :
% 27.72/27.98 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 & class_Orderings_Olinorder(T_b) )
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 27.72/27.98 <=> ? [B_x] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 27.72/27.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_less__SUP__iff,axiom,
% 27.72/27.98 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 27.72/27.98 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 & class_Orderings_Olinorder(T_b) )
% 27.72/27.98 => ( 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)))
% 27.72/27.98 <=> ? [B_x] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 27.72/27.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_INF__less__iff,axiom,
% 27.72/27.98 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 27.72/27.98 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 & class_Orderings_Olinorder(T_b) )
% 27.72/27.98 => ( 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))
% 27.72/27.98 <=> ? [B_x] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 27.72/27.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_gfp__upperbound,axiom,
% 27.72/27.98 ! [V_f_2,V_X_2,T_b] :
% 27.72/27.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,V_X_2)))
% 27.72/27.98 => 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))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_strict__mono__less,axiom,
% 27.72/27.98 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 27.72/27.98 ( ( class_Orderings_Oorder(T_c)
% 27.72/27.98 & class_Orderings_Olinorder(T_b) )
% 27.72/27.98 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 27.72/27.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_strict__monoD,axiom,
% 27.72/27.98 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 27.72/27.98 ( ( class_Orderings_Oorder(T_c)
% 27.72/27.98 & class_Orderings_Oorder(T_b) )
% 27.72/27.98 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_not__less__Least,axiom,
% 27.72/27.98 ! [V_P_2,V_k_2,T_b] :
% 27.72/27.98 ( class_Orderings_Owellorder(T_b)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),c_Orderings_Oord__class_OLeast(T_b,V_P_2)))
% 27.72/27.98 => ~ hBOOL(hAPP(V_P_2,V_k_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_def__gfp__unfold,axiom,
% 27.72/27.98 ! [V_f_2,V_A_2,T_b] :
% 27.72/27.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
% 27.72/27.98 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 27.72/27.98 => V_A_2 = hAPP(V_f_2,V_A_2) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_gfp__unfold,axiom,
% 27.72/27.98 ! [V_f_2,T_b] :
% 27.72/27.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 27.72/27.98 => 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)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_atLeastatMost__empty,axiom,
% 27.72/27.98 ! [V_a_2,V_b_2,T_b] :
% 27.72/27.98 ( class_Orderings_Oorder(T_b)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
% 27.72/27.98 => 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)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 27.72/27.98 ! [V_b_2,V_a_2,T_b] :
% 27.72/27.98 ( class_Orderings_Oorder(T_b)
% 27.72/27.98 => ( 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)
% 27.72/27.98 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_atLeastLessThan__empty__iff,axiom,
% 27.72/27.98 ! [V_b_2,V_a_2,T_b] :
% 27.72/27.98 ( class_Orderings_Oorder(T_b)
% 27.72/27.98 => ( 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))
% 27.72/27.98 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_lessThan__iff,axiom,
% 27.72/27.98 ! [V_k_2,V_i_2,T_b] :
% 27.72/27.98 ( class_Orderings_Oord(T_b)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 27.72/27.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 27.72/27.98 ! [V_l_2,V_k_2,T_b] :
% 27.72/27.98 ( class_Orderings_Oorder(T_b)
% 27.72/27.98 => ( 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)
% 27.72/27.98 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 27.72/27.98 ! [V_l_2,V_k_2,T_b] :
% 27.72/27.98 ( class_Orderings_Oorder(T_b)
% 27.72/27.98 => ( 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))
% 27.72/27.98 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_greaterThan__iff,axiom,
% 27.72/27.98 ! [V_k_2,V_i_2,T_b] :
% 27.72/27.98 ( class_Orderings_Oord(T_b)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 27.72/27.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_weak__coinduct,axiom,
% 27.72/27.98 ! [V_f_2,V_X_2,V_a_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 27.72/27.98 => ( 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)))
% 27.72/27.98 => 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))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_gfp__lemma3,axiom,
% 27.72/27.98 ! [V_f_2,T_b] :
% 27.72/27.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 27.72/27.98 => 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))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_gfp__lemma2,axiom,
% 27.72/27.98 ! [V_f_2,T_b] :
% 27.72/27.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 27.72/27.98 => 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)))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_weak__coinduct__image,axiom,
% 27.72/27.98 ! [V_f_2,V_g_2,T_c,V_X_2,V_a_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 27.72/27.98 => ( 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))))
% 27.72/27.98 => 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))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_gfp__fun__UnI2,axiom,
% 27.72/27.98 ! [V_X_2,V_a_2,V_f_2,T_b] :
% 27.72/27.98 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 27.72/27.98 => ( 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)))
% 27.72/27.98 => 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))))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_ivl__disj__un_I15_J,axiom,
% 27.72/27.98 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 27.72/27.98 ( class_Orderings_Olinorder(T_b)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 27.72/27.98 => 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) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_ivl__disj__un_I16_J,axiom,
% 27.72/27.98 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 27.72/27.98 ( class_Orderings_Olinorder(T_b)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 27.72/27.98 => 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) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_def__coinduct,axiom,
% 27.72/27.98 ! [V_X_2,V_f_2,V_A_2,T_b] :
% 27.72/27.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
% 27.72/27.98 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 27.72/27.98 => ( 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))))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),V_A_2)) ) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_coinduct__lemma,axiom,
% 27.72/27.98 ! [V_f_2,V_X_2,T_b] :
% 27.72/27.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 => ( 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)))))
% 27.72/27.98 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 27.72/27.98 => 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))))) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_coinduct,axiom,
% 27.72/27.98 ! [V_X_2,V_f_2,T_b] :
% 27.72/27.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 27.72/27.98 => ( 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)))))
% 27.72/27.98 => 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))) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_ivl__disj__un_I7_J,axiom,
% 27.72/27.98 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.98 ( class_Orderings_Olinorder(T_b)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 27.72/27.98 => 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) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_ivl__disj__un_I12_J,axiom,
% 27.72/27.98 ! [V_u_2,V_l_2,T_b] :
% 27.72/27.98 ( class_Orderings_Olinorder(T_b)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 27.72/27.98 => 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) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_psubset__insert__iff,axiom,
% 27.72/27.98 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 27.72/27.98 ( 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)))
% 27.72/27.98 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 27.72/27.98 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 27.72/27.98 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.98 => 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)) )
% 27.72/27.98 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_coinduct3,axiom,
% 27.72/27.98 ! [V_X_2,V_a_2,V_f_2,T_b] :
% 27.72/27.98 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 27.72/27.98 => ( 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))))))
% 27.72/27.98 => 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))) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_def__coinduct3,axiom,
% 27.72/27.98 ! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
% 27.72/27.98 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 27.72/27.98 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 27.72/27.98 => ( 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)))))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_coinduct3__lemma,axiom,
% 27.72/27.98 ! [V_f_2,V_X_2,T_b] :
% 27.72/27.98 ( 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))))))
% 27.72/27.98 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 27.72/27.98 => 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)))))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_the__elem__def,axiom,
% 27.72/27.98 ! [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))))) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 27.72/27.98 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.98 => ( 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)
% 27.72/27.98 => 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)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_insert__partition,axiom,
% 27.72/27.98 ! [V_F_2,V_x_2,T_b] :
% 27.72/27.98 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 27.72/27.98 => ( ! [B_x] :
% 27.72/27.98 ( 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)))
% 27.72/27.98 => ! [B_xa] :
% 27.72/27.98 ( 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)))
% 27.72/27.98 => ( B_x != B_xa
% 27.72/27.98 => 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)) ) ) )
% 27.72/27.98 => 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)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_def__lfp__induct,axiom,
% 27.72/27.98 ! [V_P_2,V_f_2,V_A_2,T_b] :
% 27.72/27.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
% 27.72/27.98 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 27.72/27.98 => ( 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))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_A_2),V_P_2)) ) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_lfp__induct,axiom,
% 27.72/27.98 ! [V_P_2,V_f_2,T_b] :
% 27.72/27.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 27.72/27.98 => ( 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))
% 27.72/27.98 => 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)) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__Un,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( 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))
% 27.72/27.98 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 27.72/27.98 & 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)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__empty,axiom,
% 27.72/27.98 ! [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))) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__uminus,axiom,
% 27.72/27.98 ! [V_A_2,T_b] :
% 27.72/27.98 ( class_Groups_Oordered__ab__group__add(T_b)
% 27.72/27.98 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_psubset__trans,axiom,
% 27.72/27.98 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__fun,axiom,
% 27.72/27.98 ! [T_d,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 27.72/27.98 => 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))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__def,axiom,
% 27.72/27.98 ! [V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 <=> ! [B_x] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.98 => ! [B_xa] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 27.72/27.98 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 27.72/27.98 => B_x = B_xa ) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__id2,axiom,
% 27.72/27.98 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_lfp__const,axiom,
% 27.72/27.98 ! [V_t_2,T_b] :
% 27.72/27.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 => c_Inductive_Ocomplete__lattice__class_Olfp(T_b,hAPP(c_COMBK(T_b,T_b),V_t_2)) = V_t_2 ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__contraD,axiom,
% 27.72/27.98 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 => ( V_x_2 != V_y_2
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 27.72/27.98 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__iff,axiom,
% 27.72/27.98 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 27.72/27.98 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 27.72/27.98 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__onD,axiom,
% 27.72/27.98 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 27.72/27.98 => V_x_2 = V_y_2 ) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_subset__inj__on,axiom,
% 27.72/27.98 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.98 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_injD,axiom,
% 27.72/27.98 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 27.72/27.98 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 27.72/27.98 => V_x_2 = V_y_2 ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__eq,axiom,
% 27.72/27.98 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 27.72/27.98 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 27.72/27.98 <=> V_x_2 = V_y_2 ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__strict__subset,axiom,
% 27.72/27.98 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.98 => 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))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__Int,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 27.72/27.98 => 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)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__diff,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 => 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)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 27.72/27.98 ! [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) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 27.72/27.98 ! [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) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_strict__mono__imp__inj__on,axiom,
% 27.72/27.98 ! [V_A_2,V_f_2,T_b,T_c] :
% 27.72/27.98 ( ( class_Orderings_Oorder(T_c)
% 27.72/27.98 & class_Orderings_Olinorder(T_b) )
% 27.72/27.98 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 27.72/27.98 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_lfp__lowerbound,axiom,
% 27.72/27.98 ! [V_A_2,V_f_2,T_b] :
% 27.72/27.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_A_2)),V_A_2))
% 27.72/27.98 => 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)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__image__eq__iff,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 27.72/27.98 => ( 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)
% 27.72/27.98 <=> V_A_2 = V_B_2 ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( 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))
% 27.72/27.98 => ( 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)
% 27.72/27.98 <=> V_A_2 = V_B_2 ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_lfp__unfold,axiom,
% 27.72/27.98 ! [V_f_2,T_b] :
% 27.72/27.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 27.72/27.98 => 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)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_def__lfp__unfold,axiom,
% 27.72/27.98 ! [V_f_2,V_h_2,T_b] :
% 27.72/27.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 => ( V_h_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
% 27.72/27.98 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 27.72/27.98 => V_h_2 = hAPP(V_f_2,V_h_2) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_range__ex1__eq,axiom,
% 27.72/27.98 ! [V_b_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 27.72/27.98 => ( 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)))))
% 27.72/27.98 <=> ? [B_x] :
% 27.72/27.98 ( V_b_2 = hAPP(V_f_2,B_x)
% 27.72/27.98 & ! [B_y] :
% 27.72/27.98 ( V_b_2 = hAPP(V_f_2,B_y)
% 27.72/27.98 => B_y = B_x ) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__image__mem__iff,axiom,
% 27.72/27.98 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 27.72/27.98 => ( 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)))
% 27.72/27.98 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__image__subset__iff,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 27.72/27.98 => ( 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)))
% 27.72/27.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__image__Int,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 27.72/27.98 => 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)) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_image__Int,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 27.72/27.98 => 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)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__image__set__diff,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 27.72/27.98 => 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)) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_image__set__diff,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 27.72/27.98 => 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)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__fun__updI,axiom,
% 27.72/27.98 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 27.72/27.98 => 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) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__singleton,axiom,
% 27.72/27.98 ! [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))) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_lfp__lemma3,axiom,
% 27.72/27.98 ! [V_f_2,T_b] :
% 27.72/27.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 27.72/27.98 => 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)))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_lfp__lemma2,axiom,
% 27.72/27.98 ! [V_f_2,T_b] :
% 27.72/27.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.98 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 27.72/27.98 => 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))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__image__Compl__subset,axiom,
% 27.72/27.98 ! [V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 27.72/27.98 => 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)))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__insert,axiom,
% 27.72/27.98 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 27.72/27.98 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 & ~ 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))))))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__iff__surj,axiom,
% 27.72/27.98 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 27.72/27.98 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.98 => ( ? [B_f] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 27.72/27.98 & 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)) )
% 27.72/27.98 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_enum__the__def,axiom,
% 27.72/27.98 ! [V_P_2,T_b] : c_Enum_Oenum__the(T_b,V_P_2) = c_HOL_OThe(T_b,V_P_2) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_flat__lub__def,axiom,
% 27.72/27.98 ! [V_b_2,V_A_2,T_b] :
% 27.72/27.98 ( ( 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)))))
% 27.72/27.98 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 )
% 27.72/27.98 & ( ~ 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)))))
% 27.72/27.98 => 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)))))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 27.72/27.98 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 27.72/27.98 ( 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))
% 27.72/27.98 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.98 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 27.72/27.98 | ? [B_x,B_y] :
% 27.72/27.98 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 27.72/27.98 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 27.72/27.98 & 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) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_image__INT,axiom,
% 27.72/27.98 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 27.72/27.98 => ( ! [B_x] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 27.72/27.98 => 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)) )
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 27.72/27.98 => 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)) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_the__inv__into__into,axiom,
% 27.72/27.98 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.98 => 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)) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__vimage__singleton,axiom,
% 27.72/27.98 ! [V_a_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 27.72/27.98 => 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))))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__Inter,axiom,
% 27.72/27.98 ! [V_f_2,T_c,T_b,V_S_2] :
% 27.72/27.98 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 27.72/27.98 => ( ! [B_A] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 27.72/27.98 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 27.72/27.98 => 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)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimageI,axiom,
% 27.72/27.98 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
% 27.72/27.98 ( hAPP(V_f_2,V_a_2) = V_b_2
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__ident,axiom,
% 27.72/27.98 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__code,axiom,
% 27.72/27.98 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 27.72/27.98 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__eq,axiom,
% 27.72/27.98 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 27.72/27.98 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimageD,axiom,
% 27.72/27.98 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimageI2,axiom,
% 27.72/27.98 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__empty,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__mono,axiom,
% 27.72/27.98 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.98 => 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))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__UNIV,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__Un,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__Int,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__Diff,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__Compl,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__UN,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__INT,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_image__vimage__subset,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_surj__image__vimage__eq,axiom,
% 27.72/27.98 ! [V_A_2,V_f_2,T_b,T_c] :
% 27.72/27.98 ( 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))
% 27.72/27.98 => 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 ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__Union,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__singleton__eq,axiom,
% 27.72/27.98 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
% 27.72/27.98 ( 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))))))
% 27.72/27.98 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__insert,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__subsetD,axiom,
% 27.72/27.98 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 27.72/27.98 ( 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))
% 27.72/27.98 => ( 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))
% 27.72/27.98 => 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))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_image__vimage__eq,axiom,
% 27.72/27.98 ! [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)))) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__vimage__image__eq,axiom,
% 27.72/27.98 ! [V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 27.72/27.98 => 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 ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__const,axiom,
% 27.72/27.98 ! [T_c,V_A_2,V_c_2,T_b] :
% 27.72/27.98 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 27.72/27.98 => 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)) )
% 27.72/27.98 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 27.72/27.98 => 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)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__eq__UN,axiom,
% 27.72/27.98 ! [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))))) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_the__inv__into__f__f,axiom,
% 27.72/27.98 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.98 => 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 ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_the__inv__into__f__eq,axiom,
% 27.72/27.98 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.98 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_the__inv__f__f,axiom,
% 27.72/27.98 ! [V_x_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 27.72/27.98 => 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 ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_the__inv__into__onto,axiom,
% 27.72/27.98 ! [V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 => 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 ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__the__inv__into,axiom,
% 27.72/27.98 ! [V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 => 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)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__subsetI,axiom,
% 27.72/27.98 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 27.72/27.98 => ( 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)))
% 27.72/27.98 => 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)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_the__inv__into__def,axiom,
% 27.72/27.98 ! [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))) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__if,axiom,
% 27.72/27.98 ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
% 27.72/27.98 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 27.72/27.98 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 27.72/27.98 => 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)) )
% 27.72/27.98 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 27.72/27.98 => 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 ) ) )
% 27.72/27.98 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 27.72/27.98 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 27.72/27.98 => 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) )
% 27.72/27.98 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 27.72/27.98 => 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)) ) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_f__the__inv__into__f,axiom,
% 27.72/27.98 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 27.72/27.98 => 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 ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_order__fun_I2_J,axiom,
% 27.72/27.98 ! [V_g_2,V_f_2,T_b,T_c] :
% 27.72/27.98 ( ( class_Orderings_Oorder(T_c)
% 27.72/27.98 & class_Enum_Oenum(T_b) )
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 27.72/27.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 27.72/27.98 & 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)))) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__INTER,axiom,
% 27.72/27.98 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 27.72/27.98 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.98 => ( ! [B_i] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 27.72/27.98 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 27.72/27.98 => 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)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fun__left__comm__idem__remove,axiom,
% 27.72/27.98 ! [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))))) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_the__eq__trivial,axiom,
% 27.72/27.98 ! [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 ).
% 27.72/27.98
% 27.72/27.98 fof(fact_the__sym__eq__trivial,axiom,
% 27.72/27.98 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 27.72/27.98
% 27.72/27.98 fof(fact_Diff1__fold__graph,axiom,
% 27.72/27.98 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( 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))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.98 => 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))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_rangeE,axiom,
% 27.72/27.98 ! [V_f_2,T_c,V_b_2,T_b] :
% 27.72/27.98 ( 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)))))
% 27.72/27.98 => ~ ! [B_x] : V_b_2 != hAPP(V_f_2,B_x) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_mk__less__def,axiom,
% 27.72/27.98 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 27.72/27.98 ( c_Partial__Function_Omk__less(T_b,V_R_2,V_x_2,V_y_2)
% 27.72/27.98 <=> ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 27.72/27.98 & ~ hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_exists__code,axiom,
% 27.72/27.98 ! [V_P_2,T_b] :
% 27.72/27.98 ( class_Enum_Oenum(T_b)
% 27.72/27.98 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 27.72/27.98 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_enum__ex,axiom,
% 27.72/27.98 ! [V_P_2,T_b] :
% 27.72/27.98 ( class_Enum_Oenum(T_b)
% 27.72/27.98 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2))
% 27.72/27.98 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 27.72/27.98 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 27.72/27.98 => 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) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 27.72/27.98 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 27.72/27.98 => 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)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fold__graph_OemptyI,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_empty__fold__graphE,axiom,
% 27.72/27.98 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( 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))
% 27.72/27.98 => V_x_2 = V_z_2 ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fun__left__comm__idem__insert,axiom,
% 27.72/27.98 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fun__left__comm__idem__sup,axiom,
% 27.72/27.98 ! [T_b] :
% 27.72/27.98 ( class_Lattices_Osemilattice__sup(T_b)
% 27.72/27.98 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fun__left__comm__idem__inf,axiom,
% 27.72/27.98 ! [T_b] :
% 27.72/27.98 ( class_Lattices_Osemilattice__inf(T_b)
% 27.72/27.98 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fold__graph_OinsertI,axiom,
% 27.72/27.98 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 27.72/27.98 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.98 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 27.72/27.98 => 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))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fold1Set_Ointros,axiom,
% 27.72/27.98 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 27.72/27.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.98 => 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)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fold__graph__permute__diff,axiom,
% 27.72/27.98 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
% 27.72/27.98 ( class_Groups_Oab__semigroup__mult(T_b)
% 27.72/27.98 => ( 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))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 27.72/27.98 => 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)) ) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__subset__eq,axiom,
% 27.72/27.98 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( 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)))
% 27.72/27.98 => ( 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))
% 27.72/27.98 <=> 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))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_psubset__imp__ex__mem,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.98 => ? [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))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_the__inv__into__comp,axiom,
% 27.72/27.98 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 27.72/27.98 ( 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))
% 27.72/27.98 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 27.72/27.98 => ( 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))))
% 27.72/27.98 => 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) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_override__on__def,axiom,
% 27.72/27.98 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 27.72/27.98 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.98 => 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) )
% 27.72/27.98 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.98 => 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) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__inter__cong,axiom,
% 27.72/27.98 ! [V_y_2,T_c,V_g_2,V_f_2,V_S_2,T_b] :
% 27.72/27.98 ( ! [B_w] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_w),V_S_2))
% 27.72/27.98 => hAPP(V_f_2,B_w) = hAPP(V_g_2,B_w) )
% 27.72/27.98 => 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) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_folding__one_Osingleton,axiom,
% 27.72/27.98 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 27.72/27.98 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 27.72/27.98 => 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 ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_K__record__comp,axiom,
% 27.72/27.98 ! [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 ).
% 27.72/27.98
% 27.72/27.98 fof(fact_o__eq__dest__lhs,axiom,
% 27.72/27.98 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 27.72/27.98 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_c_2
% 27.72/27.98 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_times_Oidem,axiom,
% 27.72/27.98 ! [V_a,T_a] :
% 27.72/27.98 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 27.72/27.98 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_mult__idem,axiom,
% 27.72/27.98 ! [V_x,T_a] :
% 27.72/27.98 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 27.72/27.98 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_mult__left__idem,axiom,
% 27.72/27.98 ! [V_b,V_a,T_a] :
% 27.72/27.98 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 27.72/27.98 => 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) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 27.72/27.98 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.98 ( class_Groups_Oab__semigroup__mult(T_a)
% 27.72/27.98 => 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)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_o__def,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_o__assoc,axiom,
% 27.72/27.98 ! [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) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_o__apply,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_o__eq__dest,axiom,
% 27.72/27.98 ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 27.72/27.98 ( 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)
% 27.72/27.98 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_o__eq__elim,axiom,
% 27.72/27.98 ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 27.72/27.98 ( 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)
% 27.72/27.98 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__betw__comp__iff,axiom,
% 27.72/27.98 ! [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] :
% 27.72/27.98 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 27.72/27.98 => ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 27.72/27.98 <=> 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) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__betw__trans,axiom,
% 27.72/27.98 ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 27.72/27.98 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2)
% 27.72/27.98 => 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) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__comp,axiom,
% 27.72/27.98 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 27.72/27.98 ( 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)))
% 27.72/27.98 => ( 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)))
% 27.72/27.98 => 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))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__betw__comp__iff2,axiom,
% 27.72/27.98 ! [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] :
% 27.72/27.98 ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 27.72/27.98 => ( 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))
% 27.72/27.98 => ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2)
% 27.72/27.98 <=> 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) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_image__compose,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__imageI2,axiom,
% 27.72/27.98 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 27.72/27.98 ( 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)
% 27.72/27.98 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__betw__empty2,axiom,
% 27.72/27.98 ! [V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( 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)))
% 27.72/27.98 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__betw__empty1,axiom,
% 27.72/27.98 ! [V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( 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)
% 27.72/27.98 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fun__upd__comp,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_vimage__compose,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__betw__imp__inj__on,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 27.72/27.98 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 27.72/27.98 ! [V_x_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 27.72/27.98 => 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) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__betw__the__inv__into,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 27.72/27.98 => 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) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fun__left__comm__idem,axiom,
% 27.72/27.98 ! [T_b] :
% 27.72/27.98 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 27.72/27.98 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_comp__surj,axiom,
% 27.72/27.98 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 27.72/27.98 ( 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))
% 27.72/27.98 => ( 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))
% 27.72/27.98 => 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)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_UN__o,axiom,
% 27.72/27.98 ! [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) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__comp,axiom,
% 27.72/27.98 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 27.72/27.98 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 27.72/27.98 => 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))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__imageI,axiom,
% 27.72/27.98 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 27.72/27.98 ( 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)
% 27.72/27.98 => 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)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_comp__inj__on,axiom,
% 27.72/27.98 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 => ( 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))
% 27.72/27.98 => 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) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_comp__inj__on__iff,axiom,
% 27.72/27.98 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 => ( 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))
% 27.72/27.98 <=> 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) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__betw__subset,axiom,
% 27.72/27.98 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 27.72/27.98 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2
% 27.72/27.98 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__betw__imp__surj,axiom,
% 27.72/27.98 ! [V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( 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)))
% 27.72/27.98 => 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)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__is__surj,axiom,
% 27.72/27.98 ! [V_f_2,T_c,T_b] :
% 27.72/27.98 ( 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)))
% 27.72/27.98 => 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)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__is__inj,axiom,
% 27.72/27.98 ! [V_f_2,T_c,T_b] :
% 27.72/27.98 ( 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)))
% 27.72/27.98 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_inj__on__imp__bij__betw,axiom,
% 27.72/27.98 ! [V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 => 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)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__betw__def,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 27.72/27.98 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 27.72/27.98 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2 ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fold1Set__nonempty,axiom,
% 27.72/27.98 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 27.72/27.98 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_empty__fold1SetE,axiom,
% 27.72/27.98 ! [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)) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__betw__combine,axiom,
% 27.72/27.98 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 27.72/27.98 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2)
% 27.72/27.98 => ( 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))
% 27.72/27.98 => 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)) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__betw__Disj__Un,axiom,
% 27.72/27.98 ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] :
% 27.72/27.98 ( 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))
% 27.72/27.98 => ( 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))
% 27.72/27.98 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 27.72/27.98 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2)
% 27.72/27.98 => 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)) ) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__def,axiom,
% 27.72/27.98 ! [V_f_2,T_c,T_b] :
% 27.72/27.98 ( 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)))
% 27.72/27.98 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 27.72/27.98 & 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)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bijI,axiom,
% 27.72/27.98 ! [V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 27.72/27.98 => ( 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))
% 27.72/27.98 => 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))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_override__on__apply__in,axiom,
% 27.72/27.98 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.98 => 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) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_override__on__apply__notin,axiom,
% 27.72/27.98 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 27.72/27.98 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.98 => 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) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__image__Compl__eq,axiom,
% 27.72/27.98 ! [V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( 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)))
% 27.72/27.98 => 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)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_override__on__emptyset,axiom,
% 27.72/27.98 ! [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 ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fold__graph__insert__swap,axiom,
% 27.72/27.98 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
% 27.72/27.98 ( class_Groups_Oab__semigroup__mult(T_b)
% 27.72/27.98 => ( 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))
% 27.72/27.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 27.72/27.98 => 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))) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__image__INT,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] :
% 27.72/27.98 ( 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)))
% 27.72/27.98 => 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)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fold1Set__sing,axiom,
% 27.72/27.98 ! [V_b_2,V_a_2,V_f_2,T_b] :
% 27.72/27.98 ( 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))
% 27.72/27.98 <=> V_a_2 = V_b_2 ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_minus__mult__right,axiom,
% 27.72/27.98 ! [V_b,V_a,T_a] :
% 27.72/27.98 ( class_Rings_Oring(T_a)
% 27.72/27.98 => 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)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_minus__mult__left,axiom,
% 27.72/27.98 ! [V_b,V_a,T_a] :
% 27.72/27.98 ( class_Rings_Oring(T_a)
% 27.72/27.98 => 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) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_minus__mult__commute,axiom,
% 27.72/27.98 ! [V_b,V_a,T_a] :
% 27.72/27.98 ( class_Rings_Oring(T_a)
% 27.72/27.98 => 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)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_minus__mult__minus,axiom,
% 27.72/27.98 ! [V_b,V_a,T_a] :
% 27.72/27.98 ( class_Rings_Oring(T_a)
% 27.72/27.98 => 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) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_square__eq__iff,axiom,
% 27.72/27.98 ! [V_b_2,V_a_2,T_b] :
% 27.72/27.98 ( class_Rings_Oidom(T_b)
% 27.72/27.98 => ( 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)
% 27.72/27.98 <=> ( V_a_2 = V_b_2
% 27.72/27.98 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_folding__one_Oremove,axiom,
% 27.72/27.98 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 27.72/27.98 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 27.72/27.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.98 => ( ( hAPP(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))
% 27.72/27.98 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 27.72/27.98 & ( hAPP(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))
% 27.72/27.98 => 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)))))) ) ) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fold1Set_Oequations,axiom,
% 27.72/27.98 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 27.72/27.98 ( 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))
% 27.72/27.98 <=> ? [B_a,B_A] :
% 27.72/27.98 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 27.72/27.98 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 27.72/27.98 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_insert__fold1SetE,axiom,
% 27.72/27.98 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 27.72/27.98 ( 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))
% 27.72/27.98 => ~ ! [B_a,B_A] :
% 27.72/27.98 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 27.72/27.98 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite_OemptyI,axiom,
% 27.72/27.98 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite_OinsertI,axiom,
% 27.72/27.98 ! [V_a_2,V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__imageI,axiom,
% 27.72/27.98 ! [V_h_2,T_c,V_F_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 27.72/27.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__Int,axiom,
% 27.72/27.98 ! [V_G_2,V_F_2,T_b] :
% 27.72/27.98 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 27.72/27.98 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2)) )
% 27.72/27.98 => 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))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__Diff,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.98 => 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))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__Inter,axiom,
% 27.72/27.98 ! [V_M_2,T_b] :
% 27.72/27.98 ( ? [B_x] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 27.72/27.98 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 27.72/27.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__INT,axiom,
% 27.72/27.98 ! [V_A_2,T_c,V_I_2,T_b] :
% 27.72/27.98 ( ? [B_x] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 27.72/27.98 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 27.72/27.98 => 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))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__Pow__iff,axiom,
% 27.72/27.98 ! [V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 27.72/27.98 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__code,axiom,
% 27.72/27.98 ! [V_A_2,T_b] :
% 27.72/27.98 ( class_Finite__Set_Ofinite(T_b)
% 27.72/27.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite,axiom,
% 27.72/27.98 ! [V_A_2,T_b] :
% 27.72/27.98 ( class_Finite__Set_Ofinite(T_b)
% 27.72/27.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__UnionD,axiom,
% 27.72/27.98 ! [V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 27.72/27.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__Prod__UNIV,axiom,
% 27.72/27.98 ! [T_c,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 27.72/27.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 27.72/27.98 => 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)))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__Plus__UNIV__iff,axiom,
% 27.72/27.98 ! [T_c,T_b] :
% 27.72/27.98 ( 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))))
% 27.72/27.98 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 27.72/27.98 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__option__UNIV,axiom,
% 27.72/27.98 ! [T_b] :
% 27.72/27.98 ( 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))))
% 27.72/27.98 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite_Oequations_I1_J,axiom,
% 27.72/27.98 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__insert,axiom,
% 27.72/27.98 ! [V_A_2,V_a_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 27.72/27.98 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__fun__UNIVD2,axiom,
% 27.72/27.98 ! [T_c,T_b] :
% 27.72/27.98 ( 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))))
% 27.72/27.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__subset,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_rev__finite__subset,axiom,
% 27.72/27.98 ! [V_A_2,V_B_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 27.72/27.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__UNIV,axiom,
% 27.72/27.98 ! [T_b] :
% 27.72/27.98 ( class_Finite__Set_Ofinite(T_b)
% 27.72/27.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__Un,axiom,
% 27.72/27.98 ! [V_G_2,V_F_2,T_b] :
% 27.72/27.98 ( 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)))
% 27.72/27.98 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 27.72/27.98 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__UnI,axiom,
% 27.72/27.98 ! [V_G_2,V_F_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 27.72/27.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
% 27.72/27.98 => 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))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__Diff2,axiom,
% 27.72/27.98 ! [V_A_2,V_B_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.98 => ( 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)))
% 27.72/27.98 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__UN,axiom,
% 27.72/27.98 ! [V_B_2,T_c,V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.98 => ( 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)))
% 27.72/27.98 <=> ! [B_x] :
% 27.72/27.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_bij__betw__finite,axiom,
% 27.72/27.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 27.72/27.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.98 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_fold__graph__imp__finite,axiom,
% 27.72/27.98 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 27.72/27.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__surj,axiom,
% 27.72/27.98 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.98 => ( 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)))
% 27.72/27.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__Diff__insert,axiom,
% 27.72/27.98 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 27.72/27.98 ( 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))))
% 27.72/27.98 <=> 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))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__imageD,axiom,
% 27.72/27.98 ! [V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 27.72/27.98 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 27.72/27.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__compl,axiom,
% 27.72/27.98 ! [V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 27.72/27.98 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__range__imageI,axiom,
% 27.72/27.98 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 27.72/27.98 ( 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)))))
% 27.72/27.98 => 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))))) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_linorder__neqE__linordered__idom,axiom,
% 27.72/27.98 ! [V_y,V_x,T_a] :
% 27.72/27.98 ( class_Rings_Olinordered__idom(T_a)
% 27.72/27.98 => ( V_x != V_y
% 27.72/27.98 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 27.72/27.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__surj__inj,axiom,
% 27.72/27.98 ! [V_f_2,V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.98 => ( 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)))
% 27.72/27.98 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_endo__inj__surj,axiom,
% 27.72/27.98 ! [V_f_2,V_A_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.98 => ( 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))
% 27.72/27.98 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 27.72/27.98 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__UNIV__surj__inj,axiom,
% 27.72/27.98 ! [V_f_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 27.72/27.98 => ( 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))
% 27.72/27.98 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 27.72/27.98
% 27.72/27.98 fof(fact_finite__UNIV__inj__surj,axiom,
% 27.72/27.98 ! [V_f_2,T_b] :
% 27.72/27.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 27.72/27.99 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 27.72/27.99 => 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)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_finite__vimageD,axiom,
% 27.72/27.99 ! [V_F_2,V_h_2,T_c,T_b] :
% 27.72/27.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 27.72/27.99 => ( 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))
% 27.72/27.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_finite__vimageI,axiom,
% 27.72/27.99 ! [V_h_2,T_c,V_F_2,T_b] :
% 27.72/27.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 27.72/27.99 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 27.72/27.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_finite__vimage__iff,axiom,
% 27.72/27.99 ! [V_F_2,V_h_2,T_c,T_b] :
% 27.72/27.99 ( 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)))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 27.72/27.99 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__one_Oinsert,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => 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)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__one_Oinsert__remove,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( ( hAPP(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))
% 27.72/27.99 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 27.72/27.99 & ( hAPP(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))
% 27.72/27.99 => 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)))))) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__one_Ounion__inter,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => ( 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))
% 27.72/27.99 => 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)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__one_Ounion__disjoint,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( 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))
% 27.72/27.99 => 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)) ) ) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding_Oremove,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__image__simple_Oremove,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 27.72/27.99 => 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)))))) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__image_Oreindex,axiom,
% 27.72/27.99 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 27.72/27.99 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 27.72/27.99 => 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) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding_Ounion,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => ( 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))
% 27.72/27.99 => 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)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding_Oinsert__remove,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => 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)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 27.72/27.99 => ( 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))
% 27.72/27.99 => 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)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 27.72/27.99 => 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)))))) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Inf__fin_Oremove,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.99 => ( ( hAPP(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))
% 27.72/27.99 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 27.72/27.99 & ( hAPP(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))
% 27.72/27.99 => 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)))))) ) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 27.72/27.99 ! [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] :
% 27.72/27.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding_Ocommute__comp,axiom,
% 27.72/27.99 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding_Ocommute__left__comp,axiom,
% 27.72/27.99 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__image__simple_Oempty,axiom,
% 27.72/27.99 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 27.72/27.99 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Inf__fin_Osingleton,axiom,
% 27.72/27.99 ! [V_x_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => 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 ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__image_Odistrib,axiom,
% 27.72/27.99 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 27.72/27.99 => 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)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 27.72/27.99 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 27.72/27.99 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => 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)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding_Ocommute__comp_H,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => 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)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_sup__Inf__absorb,axiom,
% 27.72/27.99 ! [V_a_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.99 => 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 ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Inf__fin_Oin__idem,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.99 => 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) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Inf__fin__Inf,axiom,
% 27.72/27.99 ! [V_A_2,T_b] :
% 27.72/27.99 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Inf__fin_Osubset__idem,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 27.72/27.99 => 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) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Inf__fin_Ounion__idem,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => 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)) ) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__image__simple_Oinsert,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 27.72/27.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Inf__fin_Oinsert,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => 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)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( ( hAPP(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))
% 27.72/27.99 => 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 )
% 27.72/27.99 & ( hAPP(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))
% 27.72/27.99 => 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)))))) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( 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))
% 27.72/27.99 => 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)) ) ) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Inf__fin_Ounion__inter,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => ( 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))
% 27.72/27.99 => 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)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding_Oinsert,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding_Ounion__inter,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Inf__fin_Oclosed,axiom,
% 27.72/27.99 ! [V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( ! [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))))))
% 27.72/27.99 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_finite__Union,axiom,
% 27.72/27.99 ! [V_A_2,T_b] :
% 27.72/27.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 27.72/27.99 => ( ! [B_M] :
% 27.72/27.99 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 27.72/27.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 27.72/27.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Sup__fin_Oremove,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.99 => ( ( hAPP(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))
% 27.72/27.99 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 27.72/27.99 & ( hAPP(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))
% 27.72/27.99 => 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)))))) ) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__idem_Ounion__idem,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 27.72/27.99 => 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) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__idem_Oinsert__idem,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => 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)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__one_Oclosed,axiom,
% 27.72/27.99 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( ! [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))))))
% 27.72/27.99 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.99 => 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) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Sup__fin_Osingleton,axiom,
% 27.72/27.99 ! [V_x_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => 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 ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 27.72/27.99 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__idem_Oidem__comp,axiom,
% 27.72/27.99 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Sup__fin_Oin__idem,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.99 => 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) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_inf__Sup__absorb,axiom,
% 27.72/27.99 ! [V_a_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.99 => 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 ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Sup__fin__Sup,axiom,
% 27.72/27.99 ! [V_A_2,T_b] :
% 27.72/27.99 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Sup__fin_Osubset__idem,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 27.72/27.99 => 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) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Sup__fin_Ounion__idem,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => 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)) ) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Inf__le__Sup,axiom,
% 27.72/27.99 ! [V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => 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))) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Sup__fin_Oinsert,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => 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)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( ( hAPP(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))
% 27.72/27.99 => 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 )
% 27.72/27.99 & ( hAPP(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))
% 27.72/27.99 => 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)))))) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Sup__fin_Ounion__inter,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => ( 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))
% 27.72/27.99 => 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)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( 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))
% 27.72/27.99 => 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)) ) ) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Sup__fin_Oclosed,axiom,
% 27.72/27.99 ! [V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( ! [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))))))
% 27.72/27.99 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Inf__fin_Ohom__commute,axiom,
% 27.72/27.99 ! [V_N_2,V_h_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( ! [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))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 27.72/27.99 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => 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)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Sup__fin_Ohom__commute,axiom,
% 27.72/27.99 ! [V_N_2,V_h_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( ! [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))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 27.72/27.99 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => 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)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_finite__empty__induct,axiom,
% 27.72/27.99 ! [V_P_2,V_A_2,T_b] :
% 27.72/27.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(V_P_2,V_A_2))
% 27.72/27.99 => ( ! [B_a,B_A] :
% 27.72/27.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 27.72/27.99 => ( hBOOL(hAPP(V_P_2,B_A))
% 27.72/27.99 => 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)))))) ) ) )
% 27.72/27.99 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => 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)) ) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_finite__subset__induct,axiom,
% 27.72/27.99 ! [V_P_2,V_A_2,V_F_2,T_b] :
% 27.72/27.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 27.72/27.99 => ( ! [B_a,B_F] :
% 27.72/27.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 27.72/27.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 27.72/27.99 => ( hBOOL(hAPP(V_P_2,B_F))
% 27.72/27.99 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 27.72/27.99 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 27.72/27.99 => 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) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__one__idem_Oidem,axiom,
% 27.72/27.99 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 27.72/27.99 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__one__idem_Oin__idem,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.99 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_image__eq__fold__image,axiom,
% 27.72/27.99 ! [V_f_2,T_c,V_A_2,T_b] :
% 27.72/27.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_fold1__Un,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Groups_Oab__semigroup__mult(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( 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))
% 27.72/27.99 => 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)) ) ) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 27.72/27.99 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 27.72/27.99 => ( ! [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))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 27.72/27.99 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => 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)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 27.72/27.99 => ( ! [B_x] :
% 27.72/27.99 ( 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)))
% 27.72/27.99 => hAPP(V_g_2,B_x) = V_z_2 )
% 27.72/27.99 => 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)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_fold1__insert,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Groups_Oab__semigroup__mult(T_b)
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.99 => 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)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_fold__image__reindex,axiom,
% 27.72/27.99 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 27.72/27.99 ( class_Groups_Oab__semigroup__mult(T_d)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 27.72/27.99 => 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) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_finite__UN__I,axiom,
% 27.72/27.99 ! [V_B_2,T_c,V_A_2,T_b] :
% 27.72/27.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( ! [B_a] :
% 27.72/27.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 27.72/27.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 27.72/27.99 => 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))) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_fold__image__empty,axiom,
% 27.72/27.99 ! [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 ).
% 27.72/27.99
% 27.72/27.99 fof(fact_fold1__singleton__def,axiom,
% 27.72/27.99 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 27.72/27.99 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 27.72/27.99 => 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 ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_fold1__singleton,axiom,
% 27.72/27.99 ! [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 ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 27.72/27.99 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 27.72/27.99 => 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) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__image_Oeq__fold,axiom,
% 27.72/27.99 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 27.72/27.99 => 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) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_folding__one_Oeq__fold,axiom,
% 27.72/27.99 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 27.72/27.99 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_fold1__def,axiom,
% 27.72/27.99 ! [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)) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Sup__fin_OF__eq,axiom,
% 27.72/27.99 ! [V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => 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) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_Inf__fin_OF__eq,axiom,
% 27.72/27.99 ! [V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Olattice(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => 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) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_fold__image__insert,axiom,
% 27.72/27.99 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 27.72/27.99 ( class_Groups_Oab__semigroup__mult(T_c)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_fold1__belowI,axiom,
% 27.72/27.99 ! [V_a_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Osemilattice__inf(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_below__fold1__iff,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Osemilattice__inf(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( 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)))
% 27.72/27.99 <=> ! [B_x] :
% 27.72/27.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_fold1__insert__idem,axiom,
% 27.72/27.99 ! [V_x_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_fold1__Un2,axiom,
% 27.72/27.99 ! [V_B_2,V_A_2,T_b] :
% 27.72/27.99 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => 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)) ) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_semilattice__big_OF__eq,axiom,
% 27.72/27.99 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 27.72/27.99 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__monoid__big_OF__eq,axiom,
% 27.72/27.99 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 27.72/27.99 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 27.72/27.99 => 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) )
% 27.72/27.99 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 27.72/27.99 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_fold1__in,axiom,
% 27.72/27.99 ! [V_A_2,T_b] :
% 27.72/27.99 ( class_Groups_Oab__semigroup__mult(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( ! [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))))))
% 27.72/27.99 => 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)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_hom__fold1__commute,axiom,
% 27.72/27.99 ! [V_N_2,V_h_2,T_b] :
% 27.72/27.99 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 27.72/27.99 => ( ! [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))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 27.72/27.99 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => 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)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_fold__Un__disjoint,axiom,
% 27.72/27.99 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__mult(T_c)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => ( 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))
% 27.72/27.99 => 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)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__diff1,axiom,
% 27.72/27.99 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 27.72/27.99 ( class_Groups_Oab__group__add(T_c)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.99 => 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)) )
% 27.72/27.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.99 => 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) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__diff1__ring,axiom,
% 27.72/27.99 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 27.72/27.99 ( class_Rings_Oring(T_c)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_one__reorient,axiom,
% 27.72/27.99 ! [V_x_2,T_b] :
% 27.72/27.99 ( class_Groups_Oone(T_b)
% 27.72/27.99 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 27.72/27.99 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__commute,axiom,
% 27.72/27.99 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__add(T_b)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__diff__nat__ivl,axiom,
% 27.72/27.99 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 27.72/27.99 ( class_Groups_Oab__group__add(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_mult__1__left,axiom,
% 27.72/27.99 ! [V_a,T_a] :
% 27.72/27.99 ( class_Groups_Omonoid__mult(T_a)
% 27.72/27.99 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_mult__1,axiom,
% 27.72/27.99 ! [V_a,T_a] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__mult(T_a)
% 27.72/27.99 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_mult__1__right,axiom,
% 27.72/27.99 ! [V_a,T_a] :
% 27.72/27.99 ( class_Groups_Omonoid__mult(T_a)
% 27.72/27.99 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_mult_Ocomm__neutral,axiom,
% 27.72/27.99 ! [V_a,T_a] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__mult(T_a)
% 27.72/27.99 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__right__distrib,axiom,
% 27.72/27.99 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 27.72/27.99 ( class_Rings_Osemiring__0(T_b)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__left__distrib,axiom,
% 27.72/27.99 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( class_Rings_Osemiring__0(T_b)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__product,axiom,
% 27.72/27.99 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( class_Rings_Osemiring__0(T_b)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__subtractf,axiom,
% 27.72/27.99 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( class_Groups_Oab__group__add(T_b)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__negf,axiom,
% 27.72/27.99 ! [V_A_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( class_Groups_Oab__group__add(T_b)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_less__1__mult,axiom,
% 27.72/27.99 ! [V_n,V_m,T_a] :
% 27.72/27.99 ( class_Rings_Olinordered__semidom(T_a)
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 27.72/27.99 => 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))) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_square__eq__1__iff,axiom,
% 27.72/27.99 ! [V_x_2,T_b] :
% 27.72/27.99 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 27.72/27.99 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 27.72/27.99 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 27.72/27.99 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__diff__nat,axiom,
% 27.72/27.99 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 27.72/27.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 27.72/27.99 => 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)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__reindex,axiom,
% 27.72/27.99 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__add(T_d)
% 27.72/27.99 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 27.72/27.99 => 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) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_fold__image__distrib,axiom,
% 27.72/27.99 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__mult(T_c)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => 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)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__diff1__nat,axiom,
% 27.72/27.99 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 27.72/27.99 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.99 => 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)) )
% 27.72/27.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.99 => 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) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__diff,axiom,
% 27.72/27.99 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 27.72/27.99 ( class_Groups_Oab__group__add(T_c)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum_Oreindex,axiom,
% 27.72/27.99 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__add(T_c)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 27.72/27.99 => 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) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 27.72/27.99 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 27.72/27.99 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 27.72/27.99 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_fold__image__Un__Int,axiom,
% 27.72/27.99 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__mult(T_c)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => 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))) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 27.72/27.99 ! [V_x,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__ring__1(T_a)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_fold__image__Un__one,axiom,
% 27.72/27.99 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__mult(T_c)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 27.72/27.99 => ( ! [B_x] :
% 27.72/27.99 ( 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)))
% 27.72/27.99 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 27.72/27.99 => 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)) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 27.72/27.99 ! [V_a,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 27.72/27.99 ! [V_a,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__strict__mono,axiom,
% 27.72/27.99 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 27.72/27.99 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 27.72/27.99 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 27.72/27.99 => ( ! [B_x] :
% 27.72/27.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 27.72/27.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 27.72/27.99 => 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))) ) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum_Oremove,axiom,
% 27.72/27.99 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__add(T_c)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.99 => 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)))))) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__diff1_H,axiom,
% 27.72/27.99 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__add(T_c)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 27.72/27.99 => 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)))))) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_finite__atLeastLessThan,axiom,
% 27.72/27.99 ! [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))) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__add__nat__ivl,axiom,
% 27.72/27.99 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__add(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__ub__add__nat,axiom,
% 27.72/27.99 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__add(T_b)
% 27.72/27.99 => ( 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))))
% 27.72/27.99 => 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)))) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 27.72/27.99 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__add(T_b)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 27.72/27.99 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__add(T_b)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__head,axiom,
% 27.72/27.99 ! [V_P_2,V_n_2,V_m_2,T_b] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__add(T_b)
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 27.72/27.99 => 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))) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 27.72/27.99 ! [V_N_2] :
% 27.72/27.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 27.72/27.99 <=> ? [B_m] :
% 27.72/27.99 ! [B_x] :
% 27.72/27.99 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 27.72/27.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_crossproduct__eq,axiom,
% 27.72/27.99 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 27.72/27.99 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 27.72/27.99 => ( 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))
% 27.72/27.99 <=> ( V_w_2 = V_x_2
% 27.72/27.99 | V_y_2 = V_z_2 ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 27.72/27.99 ! [V_b,V_m,V_a,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 27.72/27.99 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_crossproduct__noteq,axiom,
% 27.72/27.99 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 27.72/27.99 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 27.72/27.99 => ( ( V_a_2 != V_b_2
% 27.72/27.99 & V_c_2 != V_d_2 )
% 27.72/27.99 <=> 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)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 27.72/27.99 ! [V_z,V_y,V_x,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_image__add__atLeastLessThan,axiom,
% 27.72/27.99 ! [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)) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_atLeastLessThan__add__Un,axiom,
% 27.72/27.99 ! [V_k_2,V_j_2,V_i_2] :
% 27.72/27.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 27.72/27.99 => 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))) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__right__imp__eq,axiom,
% 27.72/27.99 ! [V_c,V_a,V_b,T_a] :
% 27.72/27.99 ( class_Groups_Ocancel__semigroup__add(T_a)
% 27.72/27.99 => ( 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)
% 27.72/27.99 => V_b = V_c ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__imp__eq,axiom,
% 27.72/27.99 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 27.72/27.99 => ( 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)
% 27.72/27.99 => V_b = V_c ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__left__imp__eq,axiom,
% 27.72/27.99 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Ocancel__semigroup__add(T_a)
% 27.72/27.99 => ( 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)
% 27.72/27.99 => V_b = V_c ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__right__cancel,axiom,
% 27.72/27.99 ! [V_c_2,V_a_2,V_b_2,T_b] :
% 27.72/27.99 ( class_Groups_Ocancel__semigroup__add(T_b)
% 27.72/27.99 => ( 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)
% 27.72/27.99 <=> V_b_2 = V_c_2 ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__left__cancel,axiom,
% 27.72/27.99 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 27.72/27.99 ( class_Groups_Ocancel__semigroup__add(T_b)
% 27.72/27.99 => ( 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)
% 27.72/27.99 <=> V_b_2 = V_c_2 ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 27.72/27.99 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Oab__semigroup__add(T_a)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 27.72/27.99 ! [V_c,V_a,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 27.72/27.99 ! [V_d,V_c,V_a,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 27.72/27.99 ! [V_d,V_c,V_a,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 27.72/27.99 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 27.72/27.99 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 27.72/27.99 ! [V_d,V_c,V_b,V_a,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__le__imp__le__left,axiom,
% 27.72/27.99 ! [V_b,V_a,V_c,T_a] :
% 27.72/27.99 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 27.72/27.99 => ( 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)))
% 27.72/27.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__le__imp__le__right,axiom,
% 27.72/27.99 ! [V_b,V_c,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 27.72/27.99 => ( 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)))
% 27.72/27.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__mono,axiom,
% 27.72/27.99 ! [V_d,V_c,V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 27.72/27.99 => 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))) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__left__mono,axiom,
% 27.72/27.99 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 27.72/27.99 => 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))) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__right__mono,axiom,
% 27.72/27.99 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 27.72/27.99 => 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))) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__le__cancel__left,axiom,
% 27.72/27.99 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 27.72/27.99 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 27.72/27.99 => ( 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)))
% 27.72/27.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__le__cancel__right,axiom,
% 27.72/27.99 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 27.72/27.99 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 27.72/27.99 => ( 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)))
% 27.72/27.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__less__imp__less__left,axiom,
% 27.72/27.99 ! [V_b,V_a,V_c,T_a] :
% 27.72/27.99 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 27.72/27.99 => ( 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)))
% 27.72/27.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__less__imp__less__right,axiom,
% 27.72/27.99 ! [V_b,V_c,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 27.72/27.99 => ( 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)))
% 27.72/27.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__strict__mono,axiom,
% 27.72/27.99 ! [V_d,V_c,V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 27.72/27.99 => 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))) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__strict__left__mono,axiom,
% 27.72/27.99 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 27.72/27.99 => 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))) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__strict__right__mono,axiom,
% 27.72/27.99 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 27.72/27.99 => 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))) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__less__cancel__left,axiom,
% 27.72/27.99 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 27.72/27.99 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 27.72/27.99 => ( 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)))
% 27.72/27.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__less__cancel__right,axiom,
% 27.72/27.99 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 27.72/27.99 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 27.72/27.99 => ( 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)))
% 27.72/27.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_combine__common__factor,axiom,
% 27.72/27.99 ! [V_c,V_b,V_e,V_a,T_a] :
% 27.72/27.99 ( class_Rings_Osemiring(T_a)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__class_Odistrib,axiom,
% 27.72/27.99 ! [V_c,V_b,V_a,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring(T_a)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__diff__cancel,axiom,
% 27.72/27.99 ! [V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Ogroup__add(T_a)
% 27.72/27.99 => 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 ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_diff__add__cancel,axiom,
% 27.72/27.99 ! [V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Ogroup__add(T_a)
% 27.72/27.99 => 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 ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_minus__add__distrib,axiom,
% 27.72/27.99 ! [V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Oab__group__add(T_a)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_minus__add,axiom,
% 27.72/27.99 ! [V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Ogroup__add(T_a)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__minus__cancel,axiom,
% 27.72/27.99 ! [V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Ogroup__add(T_a)
% 27.72/27.99 => 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 ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_minus__add__cancel,axiom,
% 27.72/27.99 ! [V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Ogroup__add(T_a)
% 27.72/27.99 => 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 ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 27.72/27.99 ! [V_m,V_a,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 27.72/27.99 ! [V_a,V_m,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 27.72/27.99 ! [V_m,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 27.72/27.99 ! [V_y,V_x,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__ring__1(T_a)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__addf,axiom,
% 27.72/27.99 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__add(T_b)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__le__less__mono,axiom,
% 27.72/27.99 ! [V_d,V_c,V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 27.72/27.99 => 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))) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_add__less__le__mono,axiom,
% 27.72/27.99 ! [V_d,V_c,V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 27.72/27.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 27.72/27.99 => 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))) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_less__add__one,axiom,
% 27.72/27.99 ! [V_a,T_a] :
% 27.72/27.99 ( class_Rings_Olinordered__semidom(T_a)
% 27.72/27.99 => 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)))) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_eq__add__iff2,axiom,
% 27.72/27.99 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 27.72/27.99 ( class_Rings_Oring(T_b)
% 27.72/27.99 => ( 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)
% 27.72/27.99 <=> 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) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_eq__add__iff1,axiom,
% 27.72/27.99 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 27.72/27.99 ( class_Rings_Oring(T_b)
% 27.72/27.99 => ( 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)
% 27.72/27.99 <=> 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 ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_diff__def,axiom,
% 27.72/27.99 ! [V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Ogroup__add(T_a)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_ab__diff__minus,axiom,
% 27.72/27.99 ! [V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Oab__group__add(T_a)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_diff__minus__eq__add,axiom,
% 27.72/27.99 ! [V_b,V_a,T_a] :
% 27.72/27.99 ( class_Groups_Ogroup__add(T_a)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum_Odistrib,axiom,
% 27.72/27.99 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__add(T_c)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => 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)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_le__add__iff1,axiom,
% 27.72/27.99 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 27.72/27.99 ( class_Rings_Oordered__ring(T_b)
% 27.72/27.99 => ( 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)))
% 27.72/27.99 <=> 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)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_le__add__iff2,axiom,
% 27.72/27.99 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 27.72/27.99 ( class_Rings_Oordered__ring(T_b)
% 27.72/27.99 => ( 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)))
% 27.72/27.99 <=> 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))) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_less__add__iff2,axiom,
% 27.72/27.99 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 27.72/27.99 ( class_Rings_Oordered__ring(T_b)
% 27.72/27.99 => ( 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)))
% 27.72/27.99 <=> 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))) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_less__add__iff1,axiom,
% 27.72/27.99 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 27.72/27.99 ( class_Rings_Oordered__ring(T_b)
% 27.72/27.99 => ( 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)))
% 27.72/27.99 <=> 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)) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__Un__nat,axiom,
% 27.72/27.99 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 27.72/27.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/27.99 => 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))) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 27.72/27.99 ! [V_b,V_a,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 27.72/27.99 ! [V_ry,V_rx,V_lx,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 27.72/27.99 ! [V_ry,V_rx,V_lx,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 27.72/27.99 ! [V_rx,V_ly,V_lx,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 27.72/27.99 ! [V_rx,V_ly,V_lx,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 27.72/27.99 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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))) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 27.72/27.99 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 27.72/27.99 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 27.72/27.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/27.99 => 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)) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum_Oinsert,axiom,
% 27.72/27.99 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__add(T_c)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/27.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 27.72/27.99 => 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)) ) ) ) ).
% 27.72/27.99
% 27.72/27.99 fof(fact_setsum__insert,axiom,
% 27.72/27.99 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 27.72/27.99 ( class_Groups_Ocomm__monoid__add(T_c)
% 27.72/27.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 27.72/27.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 27.72/28.00 => 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)) ) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_setsum__Un__Int,axiom,
% 27.72/28.00 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 27.72/28.00 ( class_Groups_Ocomm__monoid__add(T_c)
% 27.72/28.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/28.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/28.00 => 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)) ) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_setsum_Oinsert__remove,axiom,
% 27.72/28.00 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 27.72/28.00 ( class_Groups_Ocomm__monoid__add(T_c)
% 27.72/28.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/28.00 => 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)))))) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_setsum__Un__disjoint,axiom,
% 27.72/28.00 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 27.72/28.00 ( class_Groups_Ocomm__monoid__add(T_c)
% 27.72/28.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/28.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/28.00 => ( 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))
% 27.72/28.00 => 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)) ) ) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_setsum__Un,axiom,
% 27.72/28.00 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 27.72/28.00 ( class_Groups_Oab__group__add(T_c)
% 27.72/28.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 27.72/28.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 27.72/28.00 => 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))) ) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__less__add__iff2,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 27.72/28.00 => ( 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)))
% 27.72/28.00 <=> 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))) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__less__add__iff1,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 27.72/28.00 => ( 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)))
% 27.72/28.00 <=> 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)) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__le__add__iff1,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 27.72/28.00 => ( 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)))
% 27.72/28.00 <=> 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)) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__diff__add__eq1,axiom,
% 27.72/28.00 ! [V_n,V_m,V_u,V_i,V_j] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 27.72/28.00 => 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) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__eq__add__iff1,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 27.72/28.00 => ( 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)
% 27.72/28.00 <=> 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 ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__le__add__iff2,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 27.72/28.00 => ( 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)))
% 27.72/28.00 <=> 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))) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__diff__add__eq2,axiom,
% 27.72/28.00 ! [V_n,V_m,V_u,V_j,V_i] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 27.72/28.00 => 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)) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_finite__greaterThanLessThan,axiom,
% 27.72/28.00 ! [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))) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_finite__atMost,axiom,
% 27.72/28.00 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_finite__lessThan,axiom,
% 27.72/28.00 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_finite__atLeastAtMost,axiom,
% 27.72/28.00 ! [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))) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_finite__greaterThanAtMost,axiom,
% 27.72/28.00 ! [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))) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_left__add__mult__distrib,axiom,
% 27.72/28.00 ! [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) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_UN__le__add__shift,axiom,
% 27.72/28.00 ! [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) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_image__add__atLeastAtMost,axiom,
% 27.72/28.00 ! [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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_finite__nat__set__iff__bounded,axiom,
% 27.72/28.00 ! [V_N_2] :
% 27.72/28.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 27.72/28.00 <=> ? [B_m] :
% 27.72/28.00 ! [B_x] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 27.72/28.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_infinite__UNIV__nat,axiom,
% 27.72/28.00 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__eq__add__iff2,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 27.72/28.00 => ( 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)
% 27.72/28.00 <=> 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) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__add__assoc2,axiom,
% 27.72/28.00 ! [V_i,V_j,V_k] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 27.72/28.00 => 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) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__diff__assoc2,axiom,
% 27.72/28.00 ! [V_i,V_j,V_k] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 27.72/28.00 => 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) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__add__assoc,axiom,
% 27.72/28.00 ! [V_i,V_j,V_k] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 27.72/28.00 => 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)) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le__imp__diff__is__add,axiom,
% 27.72/28.00 ! [V_k_2,V_j_2,V_i_2] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 27.72/28.00 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 27.72/28.00 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le__add__diff__inverse2,axiom,
% 27.72/28.00 ! [V_m,V_n] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 27.72/28.00 => 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 ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le__diff__conv2,axiom,
% 27.72/28.00 ! [V_i_2,V_j_2,V_k_2] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 27.72/28.00 => ( 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)))
% 27.72/28.00 <=> 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)) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__diff__assoc,axiom,
% 27.72/28.00 ! [V_i,V_j,V_k] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 27.72/28.00 => 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) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_INT__greaterThan__UNIV,axiom,
% 27.72/28.00 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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_UN__lessThan__UNIV,axiom,
% 27.72/28.00 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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_UN__atLeast__UNIV,axiom,
% 27.72/28.00 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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_UN__atMost__UNIV,axiom,
% 27.72/28.00 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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_less__not__refl,axiom,
% 27.72/28.00 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__neq__iff,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2] :
% 27.72/28.00 ( V_m_2 != V_n_2
% 27.72/28.00 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 27.72/28.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_linorder__neqE__nat,axiom,
% 27.72/28.00 ! [V_y,V_x] :
% 27.72/28.00 ( V_x != V_y
% 27.72/28.00 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 27.72/28.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_less__irrefl__nat,axiom,
% 27.72/28.00 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_less__not__refl2,axiom,
% 27.72/28.00 ! [V_m,V_n] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 27.72/28.00 => V_m != V_n ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_less__not__refl3,axiom,
% 27.72/28.00 ! [V_t,V_s] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 27.72/28.00 => V_s != V_t ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__less__cases,axiom,
% 27.72/28.00 ! [V_P_2,V_n_2,V_m_2] :
% 27.72/28.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 27.72/28.00 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 27.72/28.00 => ( ( V_m_2 = V_n_2
% 27.72/28.00 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 27.72/28.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 27.72/28.00 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 27.72/28.00 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__add__right__cancel,axiom,
% 27.72/28.00 ! [V_n_2,V_k_2,V_m_2] :
% 27.72/28.00 ( 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)
% 27.72/28.00 <=> V_m_2 = V_n_2 ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__add__left__cancel,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2,V_k_2] :
% 27.72/28.00 ( 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)
% 27.72/28.00 <=> V_m_2 = V_n_2 ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__add__assoc,axiom,
% 27.72/28.00 ! [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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__add__left__commute,axiom,
% 27.72/28.00 ! [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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__add__commute,axiom,
% 27.72/28.00 ! [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) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le__refl,axiom,
% 27.72/28.00 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__le__linear,axiom,
% 27.72/28.00 ! [V_n,V_m] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 27.72/28.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_eq__imp__le,axiom,
% 27.72/28.00 ! [V_n,V_m] :
% 27.72/28.00 ( V_m = V_n
% 27.72/28.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le__trans,axiom,
% 27.72/28.00 ! [V_k,V_j,V_i] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 27.72/28.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le__antisym,axiom,
% 27.72/28.00 ! [V_n,V_m] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 27.72/28.00 => V_m = V_n ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__commute,axiom,
% 27.72/28.00 ! [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) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__mult__assoc,axiom,
% 27.72/28.00 ! [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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__mult__commute,axiom,
% 27.72/28.00 ! [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) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_inj__on__add__nat,axiom,
% 27.72/28.00 ! [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) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__lessD1,axiom,
% 27.72/28.00 ! [V_k,V_j,V_i] :
% 27.72/28.00 ( 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))
% 27.72/28.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_less__add__eq__less,axiom,
% 27.72/28.00 ! [V_n,V_m,V_l,V_k] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 27.72/28.00 => ( 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)
% 27.72/28.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__less__mono,axiom,
% 27.72/28.00 ! [V_l,V_k,V_j,V_i] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 27.72/28.00 => 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))) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__less__mono1,axiom,
% 27.72/28.00 ! [V_k,V_j,V_i] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 27.72/28.00 => 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_trans__less__add2,axiom,
% 27.72/28.00 ! [V_m,V_j,V_i] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 27.72/28.00 => 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_trans__less__add1,axiom,
% 27.72/28.00 ! [V_m,V_j,V_i] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 27.72/28.00 => 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__add__left__cancel__less,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2,V_k_2] :
% 27.72/28.00 ( 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)))
% 27.72/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_not__add__less2,axiom,
% 27.72/28.00 ! [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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_not__add__less1,axiom,
% 27.72/28.00 ! [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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__less__le,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 27.72/28.00 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 27.72/28.00 & V_m_2 != V_n_2 ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le__eq__less__or__eq,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 27.72/28.00 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 27.72/28.00 | V_m_2 = V_n_2 ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_less__imp__le__nat,axiom,
% 27.72/28.00 ! [V_n,V_m] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 27.72/28.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le__neq__implies__less,axiom,
% 27.72/28.00 ! [V_n,V_m] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 27.72/28.00 => ( V_m != V_n
% 27.72/28.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_less__or__eq__imp__le,axiom,
% 27.72/28.00 ! [V_n,V_m] :
% 27.72/28.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 27.72/28.00 | V_m = V_n )
% 27.72/28.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le__add2,axiom,
% 27.72/28.00 ! [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))) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le__add1,axiom,
% 27.72/28.00 ! [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))) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le__iff__add,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 27.72/28.00 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__add__left__cancel__le,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2,V_k_2] :
% 27.72/28.00 ( 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)))
% 27.72/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_trans__le__add1,axiom,
% 27.72/28.00 ! [V_m,V_j,V_i] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 27.72/28.00 => 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_trans__le__add2,axiom,
% 27.72/28.00 ! [V_m,V_j,V_i] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 27.72/28.00 => 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__le__mono1,axiom,
% 27.72/28.00 ! [V_k,V_j,V_i] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 27.72/28.00 => 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__le__mono,axiom,
% 27.72/28.00 ! [V_l,V_k,V_j,V_i] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 27.72/28.00 => 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))) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__leD2,axiom,
% 27.72/28.00 ! [V_n,V_k,V_m] :
% 27.72/28.00 ( 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))
% 27.72/28.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__leD1,axiom,
% 27.72/28.00 ! [V_n,V_k,V_m] :
% 27.72/28.00 ( 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))
% 27.72/28.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__leE,axiom,
% 27.72/28.00 ! [V_n,V_k,V_m] :
% 27.72/28.00 ( 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))
% 27.72/28.00 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 27.72/28.00 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__less__mono2,axiom,
% 27.72/28.00 ! [V_l,V_n,V_m] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 27.72/28.00 => 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))) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_less__imp__diff__less,axiom,
% 27.72/28.00 ! [V_n,V_k,V_j] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 27.72/28.00 => 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)) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__add__inverse2,axiom,
% 27.72/28.00 ! [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 ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__add__inverse,axiom,
% 27.72/28.00 ! [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 ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__diff__left,axiom,
% 27.72/28.00 ! [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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__cancel,axiom,
% 27.72/28.00 ! [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) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__cancel2,axiom,
% 27.72/28.00 ! [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) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__mult__distrib2,axiom,
% 27.72/28.00 ! [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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__mult__distrib,axiom,
% 27.72/28.00 ! [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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__le__self,axiom,
% 27.72/28.00 ! [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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__le__mono2,axiom,
% 27.72/28.00 ! [V_l,V_n,V_m] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 27.72/28.00 => 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__le__mono,axiom,
% 27.72/28.00 ! [V_l,V_n,V_m] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 27.72/28.00 => 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__diff__cancel,axiom,
% 27.72/28.00 ! [V_n,V_i] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 27.72/28.00 => 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 ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_eq__diff__iff,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2,V_k_2] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 27.72/28.00 => ( 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)
% 27.72/28.00 <=> V_m_2 = V_n_2 ) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_Nat_Odiff__diff__eq,axiom,
% 27.72/28.00 ! [V_n,V_m,V_k] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 27.72/28.00 => 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) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le__diff__iff,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2,V_k_2] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 27.72/28.00 => ( 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)))
% 27.72/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_mult__le__mono,axiom,
% 27.72/28.00 ! [V_l,V_k,V_j,V_i] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 27.72/28.00 => 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))) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_mult__le__mono2,axiom,
% 27.72/28.00 ! [V_k,V_j,V_i] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 27.72/28.00 => 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_mult__le__mono1,axiom,
% 27.72/28.00 ! [V_k,V_j,V_i] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 27.72/28.00 => 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le__cube,axiom,
% 27.72/28.00 ! [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)))) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le__square,axiom,
% 27.72/28.00 ! [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))) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__mult__distrib,axiom,
% 27.72/28.00 ! [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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__mult__distrib2,axiom,
% 27.72/28.00 ! [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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__mult__1,axiom,
% 27.72/28.00 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__1__eq__mult__iff,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2] :
% 27.72/28.00 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 27.72/28.00 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 27.72/28.00 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__mult__1__right,axiom,
% 27.72/28.00 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__mult__eq__1__iff,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2] :
% 27.72/28.00 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 27.72/28.00 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 27.72/28.00 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__diff__inverse,axiom,
% 27.72/28.00 ! [V_n,V_m] :
% 27.72/28.00 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 27.72/28.00 => 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 ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_less__diff__conv,axiom,
% 27.72/28.00 ! [V_k_2,V_j_2,V_i_2] :
% 27.72/28.00 ( 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)))
% 27.72/28.00 <=> 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)) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_less__diff__iff,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2,V_k_2] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 27.72/28.00 => ( 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)))
% 27.72/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__less__mono,axiom,
% 27.72/28.00 ! [V_c,V_b,V_a] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 27.72/28.00 => 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))) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__diff__right,axiom,
% 27.72/28.00 ! [V_i,V_j,V_k] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 27.72/28.00 => 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) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le__diff__conv,axiom,
% 27.72/28.00 ! [V_i_2,V_k_2,V_j_2] :
% 27.72/28.00 ( 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))
% 27.72/28.00 <=> 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le__add__diff,axiom,
% 27.72/28.00 ! [V_m,V_n,V_k] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 27.72/28.00 => 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le__add__diff__inverse,axiom,
% 27.72/28.00 ! [V_m,V_n] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 27.72/28.00 => 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 ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_arith__series__general,axiom,
% 27.72/28.00 ! [V_n_2,V_d_2,V_a_2,T_b] :
% 27.72/28.00 ( class_Rings_Ocomm__semiring__1(T_b)
% 27.72/28.00 => 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)))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_setsum__natinterval__difff,axiom,
% 27.72/28.00 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 27.72/28.00 ( class_Groups_Oab__group__add(T_b)
% 27.72/28.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 27.72/28.00 => 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)))) )
% 27.72/28.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 27.72/28.00 => 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) ) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_termination__basic__simps_I3_J,axiom,
% 27.72/28.00 ! [V_z,V_y,V_x] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 27.72/28.00 => 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_termination__basic__simps_I4_J,axiom,
% 27.72/28.00 ! [V_y,V_z,V_x] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 27.72/28.00 => 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_termination__basic__simps_I5_J,axiom,
% 27.72/28.00 ! [V_y,V_x] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 27.72/28.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_termination__basic__simps_I2_J,axiom,
% 27.72/28.00 ! [V_y,V_z,V_x] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 27.72/28.00 => 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_termination__basic__simps_I1_J,axiom,
% 27.72/28.00 ! [V_z,V_y,V_x] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 27.72/28.00 => 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_less__zeroE,axiom,
% 27.72/28.00 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le0,axiom,
% 27.72/28.00 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_of__nat__0__less__iff,axiom,
% 27.72/28.00 ! [V_n_2,T_b] :
% 27.72/28.00 ( class_Rings_Olinordered__semidom(T_b)
% 27.72/28.00 => ( 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)))
% 27.72/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_of__nat__less__0__iff,axiom,
% 27.72/28.00 ! [V_m,T_a] :
% 27.72/28.00 ( class_Rings_Olinordered__semidom(T_a)
% 27.72/28.00 => ~ 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_of__nat__0,axiom,
% 27.72/28.00 ! [T_a] :
% 27.72/28.00 ( class_Rings_Osemiring__1(T_a)
% 27.72/28.00 => 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) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_of__nat__eq__iff,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2,T_b] :
% 27.72/28.00 ( class_Nat_Osemiring__char__0(T_b)
% 27.72/28.00 => ( 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)
% 27.72/28.00 <=> V_m_2 = V_n_2 ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_of__nat__0__le__iff,axiom,
% 27.72/28.00 ! [V_n,T_a] :
% 27.72/28.00 ( class_Rings_Olinordered__semidom(T_a)
% 27.72/28.00 => 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_zero__le__imp__of__nat,axiom,
% 27.72/28.00 ! [V_m,T_a] :
% 27.72/28.00 ( class_Rings_Olinordered__semidom(T_a)
% 27.72/28.00 => 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_zero__reorient,axiom,
% 27.72/28.00 ! [V_x_2,T_b] :
% 27.72/28.00 ( class_Groups_Ozero(T_b)
% 27.72/28.00 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 27.72/28.00 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__0__iff,axiom,
% 27.72/28.00 ! [V_a_2,V_b_2,T_b] :
% 27.72/28.00 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 27.72/28.00 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
% 27.72/28.00 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 27.72/28.00 ! [V_a,T_a] :
% 27.72/28.00 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/28.00 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 27.72/28.00 ! [V_a,T_a] :
% 27.72/28.00 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/28.00 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__0__left,axiom,
% 27.72/28.00 ! [V_a,T_a] :
% 27.72/28.00 ( class_Groups_Omonoid__add(T_a)
% 27.72/28.00 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__0,axiom,
% 27.72/28.00 ! [V_a,T_a] :
% 27.72/28.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 27.72/28.00 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_double__zero__sym,axiom,
% 27.72/28.00 ! [V_a_2,T_b] :
% 27.72/28.00 ( class_Groups_Olinordered__ab__group__add(T_b)
% 27.72/28.00 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 27.72/28.00 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__0__right,axiom,
% 27.72/28.00 ! [V_a,T_a] :
% 27.72/28.00 ( class_Groups_Omonoid__add(T_a)
% 27.72/28.00 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add_Ocomm__neutral,axiom,
% 27.72/28.00 ! [V_a,T_a] :
% 27.72/28.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 27.72/28.00 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_mult__zero__left,axiom,
% 27.72/28.00 ! [V_a,T_a] :
% 27.72/28.00 ( class_Rings_Omult__zero(T_a)
% 27.72/28.00 => 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) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_mult__zero__right,axiom,
% 27.72/28.00 ! [V_a,T_a] :
% 27.72/28.00 ( class_Rings_Omult__zero(T_a)
% 27.72/28.00 => 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) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_mult__eq__0__iff,axiom,
% 27.72/28.00 ! [V_b_2,V_a_2,T_b] :
% 27.72/28.00 ( class_Rings_Oring__no__zero__divisors(T_b)
% 27.72/28.00 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 27.72/28.00 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 27.72/28.00 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_no__zero__divisors,axiom,
% 27.72/28.00 ! [V_b,V_a,T_a] :
% 27.72/28.00 ( class_Rings_Ono__zero__divisors(T_a)
% 27.72/28.00 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 27.72/28.00 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 27.72/28.00 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_divisors__zero,axiom,
% 27.72/28.00 ! [V_b,V_a,T_a] :
% 27.72/28.00 ( class_Rings_Ono__zero__divisors(T_a)
% 27.72/28.00 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 27.72/28.00 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 27.72/28.00 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 27.72/28.00 ! [V_a,T_a] :
% 27.72/28.00 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/28.00 => 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) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 27.72/28.00 ! [V_a,T_a] :
% 27.72/28.00 ( class_Rings_Ocomm__semiring__1(T_a)
% 27.72/28.00 => 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) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__0__right,axiom,
% 27.72/28.00 ! [V_a,T_a] :
% 27.72/28.00 ( class_Groups_Ogroup__add(T_a)
% 27.72/28.00 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__self,axiom,
% 27.72/28.00 ! [V_a,T_a] :
% 27.72/28.00 ( class_Groups_Ogroup__add(T_a)
% 27.72/28.00 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_eq__iff__diff__eq__0,axiom,
% 27.72/28.00 ! [V_b_2,V_a_2,T_b] :
% 27.72/28.00 ( class_Groups_Oab__group__add(T_b)
% 27.72/28.00 => ( V_a_2 = V_b_2
% 27.72/28.00 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_right__minus__eq,axiom,
% 27.72/28.00 ! [V_b_2,V_a_2,T_b] :
% 27.72/28.00 ( class_Groups_Ogroup__add(T_b)
% 27.72/28.00 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 27.72/28.00 <=> V_a_2 = V_b_2 ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_one__neq__zero,axiom,
% 27.72/28.00 ! [T_a] :
% 27.72/28.00 ( class_Rings_Ozero__neq__one(T_a)
% 27.72/28.00 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_zero__neq__one,axiom,
% 27.72/28.00 ! [T_a] :
% 27.72/28.00 ( class_Rings_Ozero__neq__one(T_a)
% 27.72/28.00 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_neg__equal__zero,axiom,
% 27.72/28.00 ! [V_a_2,T_b] :
% 27.72/28.00 ( class_Groups_Olinordered__ab__group__add(T_b)
% 27.72/28.00 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 27.72/28.00 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_neg__equal__0__iff__equal,axiom,
% 27.72/28.00 ! [V_a_2,T_b] :
% 27.72/28.00 ( class_Groups_Ogroup__add(T_b)
% 27.72/28.00 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 27.72/28.00 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_equal__neg__zero,axiom,
% 27.72/28.00 ! [V_a_2,T_b] :
% 27.72/28.00 ( class_Groups_Olinordered__ab__group__add(T_b)
% 27.72/28.00 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 27.72/28.00 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_neg__0__equal__iff__equal,axiom,
% 27.72/28.00 ! [V_a_2,T_b] :
% 27.72/28.00 ( class_Groups_Ogroup__add(T_b)
% 27.72/28.00 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 27.72/28.00 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_minus__zero,axiom,
% 27.72/28.00 ! [T_a] :
% 27.72/28.00 ( class_Groups_Ogroup__add(T_a)
% 27.72/28.00 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_not__less0,axiom,
% 27.72/28.00 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_neq0__conv,axiom,
% 27.72/28.00 ! [V_n_2] :
% 27.72/28.00 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 27.72/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_less__nat__zero__code,axiom,
% 27.72/28.00 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_gr__implies__not0,axiom,
% 27.72/28.00 ! [V_n,V_m] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 27.72/28.00 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_gr0I,axiom,
% 27.72/28.00 ! [V_n] :
% 27.72/28.00 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 27.72/28.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__eq__self__zero,axiom,
% 27.72/28.00 ! [V_n,V_m] :
% 27.72/28.00 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 27.72/28.00 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__is__0,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2] :
% 27.72/28.00 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 27.72/28.00 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 27.72/28.00 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_Nat_Oadd__0__right,axiom,
% 27.72/28.00 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 27.72/28.00
% 27.72/28.00 fof(fact_plus__nat_Oadd__0,axiom,
% 27.72/28.00 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 27.72/28.00
% 27.72/28.00 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 27.72/28.00 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_le__0__eq,axiom,
% 27.72/28.00 ! [V_n_2] :
% 27.72/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 27.72/28.00 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__0__eq__0,axiom,
% 27.72/28.00 ! [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) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_minus__nat_Odiff__0,axiom,
% 27.72/28.00 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diff__self__eq__0,axiom,
% 27.72/28.00 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_diffs0__imp__equal,axiom,
% 27.72/28.00 ! [V_n,V_m] :
% 27.72/28.00 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 27.72/28.00 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 27.72/28.00 => V_m = V_n ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2,V_k_2] :
% 27.72/28.00 ( 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)
% 27.72/28.00 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 27.72/28.00 | V_m_2 = V_n_2 ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_mult__cancel2,axiom,
% 27.72/28.00 ! [V_n_2,V_k_2,V_m_2] :
% 27.72/28.00 ( 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)
% 27.72/28.00 <=> ( V_m_2 = V_n_2
% 27.72/28.00 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_mult__cancel1,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2,V_k_2] :
% 27.72/28.00 ( 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)
% 27.72/28.00 <=> ( V_m_2 = V_n_2
% 27.72/28.00 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_mult__is__0,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2] :
% 27.72/28.00 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 27.72/28.00 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 27.72/28.00 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_mult__0__right,axiom,
% 27.72/28.00 ! [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) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_mult__0,axiom,
% 27.72/28.00 ! [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) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_inj__of__nat,axiom,
% 27.72/28.00 ! [T_b] :
% 27.72/28.00 ( class_Nat_Osemiring__char__0(T_b)
% 27.72/28.00 => 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))) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_atLeastLessThan0,axiom,
% 27.72/28.00 ! [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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_atLeast__0,axiom,
% 27.72/28.00 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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_lessThan__0,axiom,
% 27.72/28.00 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)) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_atMost__0,axiom,
% 27.72/28.00 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))) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_setsum__0,axiom,
% 27.72/28.00 ! [V_A_2,T_c,T_b] :
% 27.72/28.00 ( class_Groups_Ocomm__monoid__add(T_b)
% 27.72/28.00 => 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) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_of__nat__less__imp__less,axiom,
% 27.72/28.00 ! [V_n,V_m,T_a] :
% 27.72/28.00 ( class_Rings_Olinordered__semidom(T_a)
% 27.72/28.00 => ( 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)))
% 27.72/28.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_less__imp__of__nat__less,axiom,
% 27.72/28.00 ! [V_n,V_m,T_a] :
% 27.72/28.00 ( class_Rings_Olinordered__semidom(T_a)
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 27.72/28.00 => 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))) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_of__nat__less__iff,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2,T_b] :
% 27.72/28.00 ( class_Rings_Olinordered__semidom(T_b)
% 27.72/28.00 => ( 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)))
% 27.72/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_of__nat__le__iff,axiom,
% 27.72/28.00 ! [V_n_2,V_m_2,T_b] :
% 27.72/28.00 ( class_Rings_Olinordered__semidom(T_b)
% 27.72/28.00 => ( 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)))
% 27.72/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_of__nat__add,axiom,
% 27.72/28.00 ! [V_n,V_m,T_a] :
% 27.72/28.00 ( class_Rings_Osemiring__1(T_a)
% 27.72/28.00 => 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)) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 27.72/28.00 ! [V_a_2,T_b] :
% 27.72/28.00 ( class_Groups_Olinordered__ab__group__add(T_b)
% 27.72/28.00 => ( 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)))
% 27.72/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 27.72/28.00 ! [V_a_2,T_b] :
% 27.72/28.00 ( class_Groups_Olinordered__ab__group__add(T_b)
% 27.72/28.00 => ( 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)))
% 27.72/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__nonneg__nonneg,axiom,
% 27.72/28.00 ! [V_b,V_a,T_a] :
% 27.72/28.00 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 27.72/28.00 => 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))) ) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__nonneg__eq__0__iff,axiom,
% 27.72/28.00 ! [V_y_2,V_x_2,T_b] :
% 27.72/28.00 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 27.72/28.00 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 27.72/28.00 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 27.72/28.00 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__increasing,axiom,
% 27.72/28.00 ! [V_c,V_b,V_a,T_a] :
% 27.72/28.00 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 27.72/28.00 => 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))) ) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__increasing2,axiom,
% 27.72/28.00 ! [V_a,V_b,V_c,T_a] :
% 27.72/28.00 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 27.72/28.00 => 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))) ) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_add__nonpos__nonpos,axiom,
% 27.72/28.00 ! [V_b,V_a,T_a] :
% 27.72/28.00 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 27.72/28.00 => 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))) ) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_split__mult__neg__le,axiom,
% 27.72/28.00 ! [V_b,V_a,T_a] :
% 27.72/28.00 ( class_Rings_Oordered__cancel__semiring(T_a)
% 27.72/28.00 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 27.72/28.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 27.72/28.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 27.72/28.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 27.72/28.00 => 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))) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_split__mult__pos__le,axiom,
% 27.72/28.00 ! [V_b,V_a,T_a] :
% 27.72/28.00 ( class_Rings_Oordered__ring(T_a)
% 27.72/28.00 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 27.72/28.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 27.72/28.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 27.72/28.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 27.72/28.00 => 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))) ) ) ).
% 27.72/28.00
% 27.72/28.00 fof(fact_mult__mono,axiom,
% 27.72/28.00 ! [V_d,V_c,V_b,V_a,T_a] :
% 27.72/28.00 ( class_Rings_Oordered__semiring(T_a)
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 27.72/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.00 => 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))) ) ) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__mono_H,axiom,
% 28.01/28.00 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Oordered__semiring(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.00 => 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))) ) ) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__left__mono__neg,axiom,
% 28.01/28.00 ! [V_c,V_a,V_b,T_a] :
% 28.01/28.00 ( class_Rings_Oordered__ring(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__right__mono__neg,axiom,
% 28.01/28.00 ! [V_c,V_a,V_b,T_a] :
% 28.01/28.00 ( class_Rings_Oordered__ring(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_comm__mult__left__mono,axiom,
% 28.01/28.00 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Oordered__comm__semiring(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__left__mono,axiom,
% 28.01/28.00 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Oordered__semiring(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__right__mono,axiom,
% 28.01/28.00 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Oordered__semiring(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__nonpos__nonpos,axiom,
% 28.01/28.00 ! [V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Oordered__ring(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__nonpos__nonneg,axiom,
% 28.01/28.00 ! [V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Oordered__cancel__semiring(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__nonneg__nonpos2,axiom,
% 28.01/28.00 ! [V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Oordered__cancel__semiring(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__nonneg__nonpos,axiom,
% 28.01/28.00 ! [V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Oordered__cancel__semiring(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__nonneg__nonneg,axiom,
% 28.01/28.00 ! [V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Oordered__cancel__semiring(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__le__0__iff,axiom,
% 28.01/28.00 ! [V_b_2,V_a_2,T_b] :
% 28.01/28.00 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.01/28.00 => ( 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)))
% 28.01/28.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 28.01/28.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 28.01/28.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_zero__le__mult__iff,axiom,
% 28.01/28.00 ! [V_b_2,V_a_2,T_b] :
% 28.01/28.00 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.01/28.00 => ( 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)))
% 28.01/28.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 28.01/28.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 28.01/28.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_zero__le__square,axiom,
% 28.01/28.00 ! [V_a,T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__ring(T_a)
% 28.01/28.00 => 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))) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_pos__add__strict,axiom,
% 28.01/28.00 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 28.01/28.00 ! [V_a_2,T_b] :
% 28.01/28.00 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.01/28.00 => ( 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)))
% 28.01/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 28.01/28.00 ! [V_a_2,T_b] :
% 28.01/28.00 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.01/28.00 => ( 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)))
% 28.01/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_add__pos__pos,axiom,
% 28.01/28.00 ! [V_b,V_a,T_a] :
% 28.01/28.00 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_add__neg__neg,axiom,
% 28.01/28.00 ! [V_b,V_a,T_a] :
% 28.01/28.00 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__strict__left__mono__neg,axiom,
% 28.01/28.00 ! [V_c,V_a,V_b,T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__ring__strict(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__strict__right__mono__neg,axiom,
% 28.01/28.00 ! [V_c,V_a,V_b,T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__ring__strict(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_comm__mult__strict__left__mono,axiom,
% 28.01/28.00 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__strict__left__mono,axiom,
% 28.01/28.00 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__strict__right__mono,axiom,
% 28.01/28.00 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__neg__neg,axiom,
% 28.01/28.00 ! [V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__ring__strict(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__neg__pos,axiom,
% 28.01/28.00 ! [V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__less__cancel__left__neg,axiom,
% 28.01/28.00 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.01/28.00 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.00 => ( 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)))
% 28.01/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_zero__less__mult__pos2,axiom,
% 28.01/28.00 ! [V_a,V_b,T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.01/28.00 => ( 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)))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_zero__less__mult__pos,axiom,
% 28.01/28.00 ! [V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.01/28.00 => ( 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)))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__pos__neg2,axiom,
% 28.01/28.00 ! [V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__pos__neg,axiom,
% 28.01/28.00 ! [V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__pos__pos,axiom,
% 28.01/28.00 ! [V_b,V_a,T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__less__cancel__left__pos,axiom,
% 28.01/28.00 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.01/28.00 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.00 => ( 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)))
% 28.01/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__less__cancel__left__disj,axiom,
% 28.01/28.00 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.01/28.00 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.01/28.00 => ( 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)))
% 28.01/28.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 28.01/28.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__less__cancel__right__disj,axiom,
% 28.01/28.00 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 28.01/28.00 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.01/28.00 => ( 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)))
% 28.01/28.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 28.01/28.00 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_not__square__less__zero,axiom,
% 28.01/28.00 ! [V_a,T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__ring(T_a)
% 28.01/28.00 => ~ 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))) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_of__nat__mult,axiom,
% 28.01/28.00 ! [V_n,V_m,T_a] :
% 28.01/28.00 ( class_Rings_Osemiring__1(T_a)
% 28.01/28.00 => 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)) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_le__iff__diff__le__0,axiom,
% 28.01/28.00 ! [V_b_2,V_a_2,T_b] :
% 28.01/28.00 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 28.01/28.00 <=> 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))) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_less__iff__diff__less__0,axiom,
% 28.01/28.00 ! [V_b_2,V_a_2,T_b] :
% 28.01/28.00 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 28.01/28.00 <=> 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))) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_add__scale__eq__noteq,axiom,
% 28.01/28.00 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 28.01/28.00 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 28.01/28.00 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.00 => ( ( V_a = V_b
% 28.01/28.00 & V_c != V_d )
% 28.01/28.00 => 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)) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_not__one__le__zero,axiom,
% 28.01/28.00 ! [T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.00 => ~ 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))) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_zero__le__one,axiom,
% 28.01/28.00 ! [T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.00 => 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))) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_not__one__less__zero,axiom,
% 28.01/28.00 ! [T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.00 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_zero__less__one,axiom,
% 28.01/28.00 ! [T_a] :
% 28.01/28.00 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_minus__le__self__iff,axiom,
% 28.01/28.00 ! [V_a_2,T_b] :
% 28.01/28.00 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.01/28.00 => ( 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))
% 28.01/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_neg__le__0__iff__le,axiom,
% 28.01/28.00 ! [V_a_2,T_b] :
% 28.01/28.00 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.01/28.00 => ( 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)))
% 28.01/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_le__minus__self__iff,axiom,
% 28.01/28.00 ! [V_a_2,T_b] :
% 28.01/28.00 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.01/28.00 => ( 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)))
% 28.01/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_neg__0__le__iff__le,axiom,
% 28.01/28.00 ! [V_a_2,T_b] :
% 28.01/28.00 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.01/28.00 => ( 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)))
% 28.01/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_neg__less__nonneg,axiom,
% 28.01/28.00 ! [V_a_2,T_b] :
% 28.01/28.00 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 28.01/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_neg__less__0__iff__less,axiom,
% 28.01/28.00 ! [V_a_2,T_b] :
% 28.01/28.00 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.01/28.00 => ( 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)))
% 28.01/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_neg__0__less__iff__less,axiom,
% 28.01/28.00 ! [V_a_2,T_b] :
% 28.01/28.00 ( class_Groups_Oordered__ab__group__add(T_b)
% 28.01/28.00 => ( 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)))
% 28.01/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_less__minus__self__iff,axiom,
% 28.01/28.00 ! [V_a_2,T_b] :
% 28.01/28.00 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 28.01/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_minus__unique,axiom,
% 28.01/28.00 ! [V_b,V_a,T_a] :
% 28.01/28.00 ( class_Groups_Ogroup__add(T_a)
% 28.01/28.00 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.00 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_ab__left__minus,axiom,
% 28.01/28.00 ! [V_a,T_a] :
% 28.01/28.00 ( class_Groups_Oab__group__add(T_a)
% 28.01/28.00 => 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) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_left__minus,axiom,
% 28.01/28.00 ! [V_a,T_a] :
% 28.01/28.00 ( class_Groups_Ogroup__add(T_a)
% 28.01/28.00 => 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) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 28.01/28.00 ! [V_b_2,V_a_2,T_b] :
% 28.01/28.00 ( class_Groups_Ogroup__add(T_b)
% 28.01/28.00 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 28.01/28.00 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_right__minus,axiom,
% 28.01/28.00 ! [V_a,T_a] :
% 28.01/28.00 ( class_Groups_Ogroup__add(T_a)
% 28.01/28.00 => 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) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_of__nat__1,axiom,
% 28.01/28.00 ! [T_a] :
% 28.01/28.00 ( class_Rings_Osemiring__1(T_a)
% 28.01/28.00 => 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) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_diff__0,axiom,
% 28.01/28.00 ! [V_a,T_a] :
% 28.01/28.00 ( class_Groups_Ogroup__add(T_a)
% 28.01/28.00 => 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) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_setsum__empty,axiom,
% 28.01/28.00 ! [V_f_2,T_c,T_b] :
% 28.01/28.00 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.00 => 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) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_setsum_Oempty,axiom,
% 28.01/28.00 ! [V_g_2,T_c,T_b] :
% 28.01/28.00 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.00 => 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) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_setsum__infinite,axiom,
% 28.01/28.00 ! [V_f_2,V_A_2,T_b,T_c] :
% 28.01/28.00 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.00 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.00 => 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) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_setsum_Oinfinite,axiom,
% 28.01/28.00 ! [V_g_2,V_A_2,T_b,T_c] :
% 28.01/28.00 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.00 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.00 => 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) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_add__gr__0,axiom,
% 28.01/28.00 ! [V_n_2,V_m_2] :
% 28.01/28.00 ( 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)))
% 28.01/28.00 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 28.01/28.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_diff__less,axiom,
% 28.01/28.00 ! [V_m,V_n] :
% 28.01/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 28.01/28.00 => 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)) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_zero__less__diff,axiom,
% 28.01/28.00 ! [V_m_2,V_n_2] :
% 28.01/28.00 ( 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)))
% 28.01/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_nat__mult__eq__cancel1,axiom,
% 28.01/28.00 ! [V_n_2,V_m_2,V_k_2] :
% 28.01/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 28.01/28.00 => ( 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)
% 28.01/28.00 <=> V_m_2 = V_n_2 ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_nat__mult__less__cancel1,axiom,
% 28.01/28.00 ! [V_n_2,V_m_2,V_k_2] :
% 28.01/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 28.01/28.00 => ( 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)))
% 28.01/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_nat__0__less__mult__iff,axiom,
% 28.01/28.00 ! [V_n_2,V_m_2] :
% 28.01/28.00 ( 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)))
% 28.01/28.00 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 28.01/28.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__less__cancel1,axiom,
% 28.01/28.00 ! [V_n_2,V_m_2,V_k_2] :
% 28.01/28.00 ( 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)))
% 28.01/28.00 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 28.01/28.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__less__cancel2,axiom,
% 28.01/28.00 ! [V_n_2,V_k_2,V_m_2] :
% 28.01/28.00 ( 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)))
% 28.01/28.00 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 28.01/28.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__less__mono1,axiom,
% 28.01/28.00 ! [V_k,V_j,V_i] :
% 28.01/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 28.01/28.00 => 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))) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__less__mono2,axiom,
% 28.01/28.00 ! [V_k,V_j,V_i] :
% 28.01/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 28.01/28.00 => 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))) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_diff__add__0,axiom,
% 28.01/28.00 ! [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) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_diff__is__0__eq_H,axiom,
% 28.01/28.00 ! [V_n,V_m] :
% 28.01/28.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 28.01/28.00 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_diff__is__0__eq,axiom,
% 28.01/28.00 ! [V_n_2,V_m_2] :
% 28.01/28.00 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_mult__eq__self__implies__10,axiom,
% 28.01/28.00 ! [V_n,V_m] :
% 28.01/28.00 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 28.01/28.00 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 28.01/28.00 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_setsum__eq__0__iff,axiom,
% 28.01/28.00 ! [V_f_2,V_F_2,T_b] :
% 28.01/28.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 28.01/28.00 => ( 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)
% 28.01/28.00 <=> ! [B_x] :
% 28.01/28.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 28.01/28.00 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_atLeast0LessThan,axiom,
% 28.01/28.00 ! [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) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_atLeast0AtMost,axiom,
% 28.01/28.00 ! [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) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_add__pos__nonneg,axiom,
% 28.01/28.00 ! [V_b,V_a,T_a] :
% 28.01/28.00 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_add__nonneg__pos,axiom,
% 28.01/28.00 ! [V_b,V_a,T_a] :
% 28.01/28.00 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_add__strict__increasing,axiom,
% 28.01/28.00 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.00 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 28.01/28.00 => 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))) ) ) ) ).
% 28.01/28.00
% 28.01/28.00 fof(fact_add__strict__increasing2,axiom,
% 28.01/28.00 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.01 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 28.01/28.01 => 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))) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_add__neg__nonpos,axiom,
% 28.01/28.01 ! [V_b,V_a,T_a] :
% 28.01/28.01 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.01 => 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))) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_add__nonpos__neg,axiom,
% 28.01/28.01 ! [V_b,V_a,T_a] :
% 28.01/28.01 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.01 => 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))) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mult__le__cancel__left__pos,axiom,
% 28.01/28.01 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.01/28.01 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.01 => ( 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)))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mult__le__cancel__left__neg,axiom,
% 28.01/28.01 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.01/28.01 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.01 => ( 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)))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mult__strict__mono,axiom,
% 28.01/28.01 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.01/28.01 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.01 => 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))) ) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mult__strict__mono_H,axiom,
% 28.01/28.01 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.01/28.01 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.01 => 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))) ) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mult__less__le__imp__less,axiom,
% 28.01/28.01 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.01/28.01 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.01 => 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))) ) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mult__le__less__imp__less,axiom,
% 28.01/28.01 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.01/28.01 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.01 => 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))) ) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mult__right__less__imp__less,axiom,
% 28.01/28.01 ! [V_b,V_c,V_a,T_a] :
% 28.01/28.01 ( class_Rings_Olinordered__semiring(T_a)
% 28.01/28.01 => ( 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)))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mult__less__imp__less__right,axiom,
% 28.01/28.01 ! [V_b,V_c,V_a,T_a] :
% 28.01/28.01 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.01/28.01 => ( 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)))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mult__left__less__imp__less,axiom,
% 28.01/28.01 ! [V_b,V_a,V_c,T_a] :
% 28.01/28.01 ( class_Rings_Olinordered__semiring(T_a)
% 28.01/28.01 => ( 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)))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mult__less__imp__less__left,axiom,
% 28.01/28.01 ! [V_b,V_a,V_c,T_a] :
% 28.01/28.01 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.01/28.01 => ( 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)))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mult__right__le__imp__le,axiom,
% 28.01/28.01 ! [V_b,V_c,V_a,T_a] :
% 28.01/28.01 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.01/28.01 => ( 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)))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mult__left__le__imp__le,axiom,
% 28.01/28.01 ! [V_b,V_a,V_c,T_a] :
% 28.01/28.01 ( class_Rings_Olinordered__semiring__strict(T_a)
% 28.01/28.01 => ( 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)))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mult__right__le__one__le,axiom,
% 28.01/28.01 ! [V_y,V_x,T_a] :
% 28.01/28.01 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 28.01/28.01 => 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)) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mult__left__le__one__le,axiom,
% 28.01/28.01 ! [V_y,V_x,T_a] :
% 28.01/28.01 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 28.01/28.01 => 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)) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zero__less__two,axiom,
% 28.01/28.01 ! [T_a] :
% 28.01/28.01 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.01 => 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)))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_of__nat__diff,axiom,
% 28.01/28.01 ! [V_m,V_n,T_a] :
% 28.01/28.01 ( class_Rings_Oring__1(T_a)
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 28.01/28.01 => 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)) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_nat__diff__split,axiom,
% 28.01/28.01 ! [V_b_2,V_a_2,V_P_2] :
% 28.01/28.01 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 28.01/28.01 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 28.01/28.01 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 28.01/28.01 & ! [B_d] :
% 28.01/28.01 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 28.01/28.01 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_nat__diff__split__asm,axiom,
% 28.01/28.01 ! [V_b_2,V_a_2,V_P_2] :
% 28.01/28.01 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 28.01/28.01 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 28.01/28.01 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 28.01/28.01 | ? [B_d] :
% 28.01/28.01 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 28.01/28.01 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_nat__mult__le__cancel1,axiom,
% 28.01/28.01 ! [V_n_2,V_m_2,V_k_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 28.01/28.01 => ( 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)))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mult__le__cancel2,axiom,
% 28.01/28.01 ! [V_n_2,V_k_2,V_m_2] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mult__le__cancel1,axiom,
% 28.01/28.01 ! [V_n_2,V_m_2,V_k_2] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_comp__cong,axiom,
% 28.01/28.01 ! [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] :
% 28.01/28.01 ( 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))
% 28.01/28.01 => 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) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_setsum__eq__1__iff,axiom,
% 28.01/28.01 ! [V_f_2,V_A_2,T_b] :
% 28.01/28.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.01 => ( 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)
% 28.01/28.01 <=> ? [B_x] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.01 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 28.01/28.01 & ! [B_xa] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 28.01/28.01 => ( B_x != B_xa
% 28.01/28.01 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_setsum__delta_H,axiom,
% 28.01/28.01 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 28.01/28.01 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.01/28.01 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.01/28.01 => 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) )
% 28.01/28.01 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.01/28.01 => 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) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_setsum__delta,axiom,
% 28.01/28.01 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 28.01/28.01 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.01/28.01 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.01/28.01 => 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) )
% 28.01/28.01 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.01/28.01 => 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) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_convex__bound__le,axiom,
% 28.01/28.01 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 28.01/28.01 ( class_Rings_Olinordered__semiring__1(T_a)
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 28.01/28.01 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 28.01/28.01 => 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)) ) ) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_UN__UN__finite__eq,axiom,
% 28.01/28.01 ! [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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_setsum_Oeq__fold,axiom,
% 28.01/28.01 ! [V_g_2,V_A_2,T_b,T_c] :
% 28.01/28.01 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.01 => 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) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_setsum_OF__eq,axiom,
% 28.01/28.01 ! [V_g_2,V_A_2,T_b,T_c] :
% 28.01/28.01 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.01 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.01 => 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) )
% 28.01/28.01 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.01 => 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) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_setsum__restrict__set,axiom,
% 28.01/28.01 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 28.01/28.01 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.01 => 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) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_convex__bound__lt,axiom,
% 28.01/28.01 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 28.01/28.01 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 28.01/28.01 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 28.01/28.01 => 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)) ) ) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 28.01/28.01 ! [V_x_2,V_y_2,V_c_2] :
% 28.01/28.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 28.01/28.01 => 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)) )
% 28.01/28.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 28.01/28.01 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 28.01/28.01 => 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))) )
% 28.01/28.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 28.01/28.01 => 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)) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_UN__le__eq__Un0,axiom,
% 28.01/28.01 ! [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))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_gauss__sum,axiom,
% 28.01/28.01 ! [V_n_2,T_b] :
% 28.01/28.01 ( class_Rings_Ocomm__semiring__1(T_b)
% 28.01/28.01 => 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))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mult__eq__if,axiom,
% 28.01/28.01 ! [V_n,V_m] :
% 28.01/28.01 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.01 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.01/28.01 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.01 => 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)) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_not__sum__squares__lt__zero,axiom,
% 28.01/28.01 ! [V_y,V_x,T_a] :
% 28.01/28.01 ( class_Rings_Olinordered__ring(T_a)
% 28.01/28.01 => ~ 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))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_sum__squares__gt__zero__iff,axiom,
% 28.01/28.01 ! [V_y_2,V_x_2,T_b] :
% 28.01/28.01 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.01/28.01 => ( 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))))
% 28.01/28.01 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.01 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_sum__squares__ge__zero,axiom,
% 28.01/28.01 ! [V_y,V_x,T_a] :
% 28.01/28.01 ( class_Rings_Olinordered__ring(T_a)
% 28.01/28.01 => 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)))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_sum__squares__le__zero__iff,axiom,
% 28.01/28.01 ! [V_y_2,V_x_2,T_b] :
% 28.01/28.01 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.01/28.01 => ( 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)))
% 28.01/28.01 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.01 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_of__nat__setsum,axiom,
% 28.01/28.01 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.01 ( class_Rings_Osemiring__1(T_b)
% 28.01/28.01 => 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) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 28.01/28.01 ! [V_n_2,T_b] :
% 28.01/28.01 ( class_Rings_Osemiring__1(T_b)
% 28.01/28.01 => 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)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 28.01/28.01 ! [V_i_2,V_inc_2,T_b] :
% 28.01/28.01 ( class_Rings_Osemiring__1(T_b)
% 28.01/28.01 => 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 ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_bot__nat__def,axiom,
% 28.01/28.01 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_int__zle__neg,axiom,
% 28.01/28.01 ! [V_m_2,V_n_2] :
% 28.01/28.01 ( 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))))
% 28.01/28.01 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.01 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_int__le__0__conv,axiom,
% 28.01/28.01 ! [V_n_2] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_int__eq__0__conv,axiom,
% 28.01/28.01 ! [V_n_2] :
% 28.01/28.01 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.01 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_int__0,axiom,
% 28.01/28.01 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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_negative__eq__positive,axiom,
% 28.01/28.01 ! [V_m_2,V_n_2] :
% 28.01/28.01 ( 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)
% 28.01/28.01 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.01 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zless__int,axiom,
% 28.01/28.01 ! [V_n_2,V_m_2] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zero__less__int__conv,axiom,
% 28.01/28.01 ! [V_n_2] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zmult__zless__mono2__lemma,axiom,
% 28.01/28.01 ! [V_k,V_j,V_i] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 28.01/28.01 => 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))) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zadd__int,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zadd__int__left,axiom,
% 28.01/28.01 ! [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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zle__int,axiom,
% 28.01/28.01 ! [V_n_2,V_m_2] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_int__mult,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zmult__int,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_int__1,axiom,
% 28.01/28.01 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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_inj__int,axiom,
% 28.01/28.01 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))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_int__setsum,axiom,
% 28.01/28.01 ! [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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_double__eq__0__iff,axiom,
% 28.01/28.01 ! [V_a_2,T_b] :
% 28.01/28.01 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.01/28.01 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.01 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zdiff__int,axiom,
% 28.01/28.01 ! [V_m,V_n] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 28.01/28.01 => 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)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_even__less__0__iff,axiom,
% 28.01/28.01 ! [V_a_2,T_b] :
% 28.01/28.01 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.01 => ( 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)))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_sum__squares__eq__zero__iff,axiom,
% 28.01/28.01 ! [V_y_2,V_x_2,T_b] :
% 28.01/28.01 ( class_Rings_Olinordered__ring__strict(T_b)
% 28.01/28.01 => ( 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)
% 28.01/28.01 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.01 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_ex__nat__less,axiom,
% 28.01/28.01 ! [V_P_2,V_n_2] :
% 28.01/28.01 ( ? [B_m] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 28.01/28.01 & hBOOL(hAPP(V_P_2,B_m)) )
% 28.01/28.01 <=> ? [B_x] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_all__nat__less,axiom,
% 28.01/28.01 ! [V_P_2,V_n_2] :
% 28.01/28.01 ( ! [B_m] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 28.01/28.01 => hBOOL(hAPP(V_P_2,B_m)) )
% 28.01/28.01 <=> ! [B_x] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_ex__nat__less__eq,axiom,
% 28.01/28.01 ! [V_P_2,V_n_2] :
% 28.01/28.01 ( ? [B_m] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 28.01/28.01 & hBOOL(hAPP(V_P_2,B_m)) )
% 28.01/28.01 <=> ? [B_x] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_all__nat__less__eq,axiom,
% 28.01/28.01 ! [V_P_2,V_n_2] :
% 28.01/28.01 ( ! [B_m] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 28.01/28.01 => hBOOL(hAPP(V_P_2,B_m)) )
% 28.01/28.01 <=> ! [B_x] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zdiff__int__split,axiom,
% 28.01/28.01 ! [V_y_2,V_x_2,V_P_2] :
% 28.01/28.01 ( 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))))
% 28.01/28.01 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 28.01/28.01 => 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)))) )
% 28.01/28.01 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 28.01/28.01 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_UN__finite2__subset,axiom,
% 28.01/28.01 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 28.01/28.01 ( ! [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)))
% 28.01/28.01 => 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))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_negative__zle,axiom,
% 28.01/28.01 ! [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))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_negative__zle__0,axiom,
% 28.01/28.01 ! [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))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zero__zle__int,axiom,
% 28.01/28.01 ! [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))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_int__int__eq,axiom,
% 28.01/28.01 ! [V_n_2,V_m_2] :
% 28.01/28.01 ( 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)
% 28.01/28.01 <=> V_m_2 = V_n_2 ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zminus__0,axiom,
% 28.01/28.01 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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_int__0__less__1,axiom,
% 28.01/28.01 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))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_int__0__neq__1,axiom,
% 28.01/28.01 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_pos__zmult__eq__1__iff,axiom,
% 28.01/28.01 ! [V_n_2,V_m_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 28.01/28.01 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 28.01/28.01 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 28.01/28.01 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zmult__zless__mono2,axiom,
% 28.01/28.01 ! [V_k,V_j,V_i] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 28.01/28.01 => 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))) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_not__int__zless__negative,axiom,
% 28.01/28.01 ! [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)))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_int__less__0__conv,axiom,
% 28.01/28.01 ! [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))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_less__bin__lemma,axiom,
% 28.01/28.01 ! [V_l_2,V_k_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 28.01/28.01 <=> 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))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zadd__0__right,axiom,
% 28.01/28.01 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zadd__0,axiom,
% 28.01/28.01 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zle__iff__zadd,axiom,
% 28.01/28.01 ! [V_z_2,V_w_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 28.01/28.01 <=> ? [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)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zadd__zminus__inverse2,axiom,
% 28.01/28.01 ! [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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_image__add__int__atLeastLessThan,axiom,
% 28.01/28.01 ! [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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 28.01/28.01 ! [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))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_odd__nonzero,axiom,
% 28.01/28.01 ! [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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_int__one__le__iff__zero__less,axiom,
% 28.01/28.01 ! [V_z_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_le__imp__0__less,axiom,
% 28.01/28.01 ! [V_z] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 28.01/28.01 => 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))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_odd__less__0,axiom,
% 28.01/28.01 ! [V_z_2] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_simp__from__to,axiom,
% 28.01/28.01 ! [V_i_2,V_j_2] :
% 28.01/28.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 28.01/28.01 => 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)) )
% 28.01/28.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 28.01/28.01 => 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)) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zle__diff1__eq,axiom,
% 28.01/28.01 ! [V_z_2,V_w_2] :
% 28.01/28.01 ( 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))))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zless__add1__eq,axiom,
% 28.01/28.01 ! [V_z_2,V_w_2] :
% 28.01/28.01 ( 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))))
% 28.01/28.01 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 28.01/28.01 | V_w_2 = V_z_2 ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zless__imp__add1__zle,axiom,
% 28.01/28.01 ! [V_z,V_w] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 28.01/28.01 => 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)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_add1__zle__eq,axiom,
% 28.01/28.01 ! [V_z_2,V_w_2] :
% 28.01/28.01 ( 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))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zle__add1__eq__le,axiom,
% 28.01/28.01 ! [V_z_2,V_w_2] :
% 28.01/28.01 ( 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))))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zadd__zmult__distrib,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zadd__zmult__distrib2,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zdiff__zmult__distrib,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zdiff__zmult__distrib2,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_diff__int__def,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_diff__int__def__symmetric,axiom,
% 28.01/28.01 ! [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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zminus__zadd__distrib,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zadd__left__mono,axiom,
% 28.01/28.01 ! [V_k,V_j,V_i] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 28.01/28.01 => 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))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zadd__commute,axiom,
% 28.01/28.01 ! [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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zadd__left__commute,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zadd__assoc,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zless__le,axiom,
% 28.01/28.01 ! [V_w_2,V_z_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 28.01/28.01 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 28.01/28.01 & V_z_2 != V_w_2 ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zadd__zless__mono,axiom,
% 28.01/28.01 ! [V_z,V_z_H,V_w,V_w_H] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 28.01/28.01 => 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))) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zadd__strict__right__mono,axiom,
% 28.01/28.01 ! [V_k,V_j,V_i] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 28.01/28.01 => 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))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zless__linear,axiom,
% 28.01/28.01 ! [V_y,V_x] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 28.01/28.01 | V_x = V_y
% 28.01/28.01 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zmult__zminus,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zmult__commute,axiom,
% 28.01/28.01 ! [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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zmult__assoc,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zmult__1__right,axiom,
% 28.01/28.01 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zmult__1,axiom,
% 28.01/28.01 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zminus__zminus,axiom,
% 28.01/28.01 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zle__antisym,axiom,
% 28.01/28.01 ! [V_w,V_z] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 28.01/28.01 => V_z = V_w ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zle__trans,axiom,
% 28.01/28.01 ! [V_k,V_j,V_i] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zle__linear,axiom,
% 28.01/28.01 ! [V_w,V_z] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 28.01/28.01 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zle__refl,axiom,
% 28.01/28.01 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 28.01/28.01 ! [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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 28.01/28.01 ! [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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 28.01/28.01 ! [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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_self__quotient__aux1,axiom,
% 28.01/28.01 ! [V_q,V_r,V_a] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.01/28.01 => ( 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))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_self__quotient__aux2,axiom,
% 28.01/28.01 ! [V_q,V_r,V_a] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.01/28.01 => ( 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))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_q__pos__lemma,axiom,
% 28.01/28.01 ! [V_r_H,V_q_H,V_b_H] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_q__neg__lemma,axiom,
% 28.01/28.01 ! [V_r_H,V_q_H,V_b_H] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_unique__quotient__lemma,axiom,
% 28.01/28.01 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zdiv__mono2__lemma,axiom,
% 28.01/28.01 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 28.01/28.01 ( 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)
% 28.01/28.01 => ( 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)))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_finite__atLeastAtMost__int,axiom,
% 28.01/28.01 ! [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))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_finite__atLeastLessThan__int,axiom,
% 28.01/28.01 ! [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))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_finite__greaterThanAtMost__int,axiom,
% 28.01/28.01 ! [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))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_finite__greaterThanLessThan__int,axiom,
% 28.01/28.01 ! [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))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_infinite__UNIV__int,axiom,
% 28.01/28.01 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 28.01/28.01 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 28.01/28.01 ( 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)
% 28.01/28.01 => ( 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)))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_unique__quotient__lemma__neg,axiom,
% 28.01/28.01 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 28.01/28.01 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))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 28.01/28.01 ! [V_A_2] :
% 28.01/28.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 28.01/28.01 <=> 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))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 28.01/28.01 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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 28.01/28.01 ! [V_y_2,V_x_2] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 28.01/28.01 ! [V_B_2,V_A_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.01/28.01 <=> 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))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 28.01/28.01 ! [V_B_2,V_A_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.01/28.01 <=> 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))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 28.01/28.01 ! [V_B_2,V_A_2] :
% 28.01/28.01 ( V_A_2 = V_B_2
% 28.01/28.01 <=> 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) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 28.01/28.01 ! [V_A_2,V_x_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 28.01/28.01 <=> 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))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 28.01/28.01 ! [V_y_2,V_x_2] :
% 28.01/28.01 ( 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)
% 28.01/28.01 <=> V_x_2 = V_y_2 ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 28.01/28.01 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))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 28.01/28.01 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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 28.01/28.01 ! [V_y,V_x] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.01/28.01 => 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))) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 28.01/28.01 ! [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))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 28.01/28.01 ! [V_P_2] :
% 28.01/28.01 ( ? [B_x] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 28.01/28.01 & hBOOL(hAPP(V_P_2,B_x)) )
% 28.01/28.01 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 28.01/28.01 ! [V_P_2] :
% 28.01/28.01 ( ! [B_x] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 28.01/28.01 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.01/28.01 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 28.01/28.01 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))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 28.01/28.01 ! [V_y,V_x] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.01/28.01 => 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))) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 28.01/28.01 ! [V_y_2,V_x_2] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_aset_I8_J,axiom,
% 28.01/28.01 ! [V_t_2,V_A_2,V_D_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.01/28.01 => ! [B_x] :
% 28.01/28.01 ( ! [B_xa] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => ! [B_xb] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 28.01/28.01 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 28.01/28.01 => 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))) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_bset_I6_J,axiom,
% 28.01/28.01 ! [V_t_2,V_B_2,V_D_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.01/28.01 => ! [B_x] :
% 28.01/28.01 ( ! [B_xa] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => ! [B_xb] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 28.01/28.01 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 28.01/28.01 => 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)) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_aset_I6_J,axiom,
% 28.01/28.01 ! [V_A_2,V_t_2,V_D_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.01/28.01 => ( 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))
% 28.01/28.01 => ! [B_x] :
% 28.01/28.01 ( ! [B_xa] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => ! [B_xb] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 28.01/28.01 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 28.01/28.01 => 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)) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_bset_I8_J,axiom,
% 28.01/28.01 ! [V_B_2,V_t_2,V_D_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.01/28.01 => ( 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))
% 28.01/28.01 => ! [B_x] :
% 28.01/28.01 ( ! [B_xa] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => ! [B_xb] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 28.01/28.01 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 28.01/28.01 => 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))) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_setsum__mono2,axiom,
% 28.01/28.01 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 28.01/28.01 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 28.01/28.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.01/28.01 => ( ! [B_b] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 28.01/28.01 => 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))) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_periodic__finite__ex,axiom,
% 28.01/28.01 ! [V_P_2,V_d_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 28.01/28.01 => ( ! [B_x,B_k] :
% 28.01/28.01 ( hBOOL(hAPP(V_P_2,B_x))
% 28.01/28.01 <=> 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)))) )
% 28.01/28.01 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 28.01/28.01 <=> ? [B_x] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_aset_I4_J,axiom,
% 28.01/28.01 ! [V_A_2,V_t_2,V_D_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 28.01/28.01 => ! [B_x] :
% 28.01/28.01 ( ! [B_xa] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => ! [B_xb] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 28.01/28.01 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.01/28.01 => ( B_x != V_t_2
% 28.01/28.01 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_bset_I4_J,axiom,
% 28.01/28.01 ! [V_B_2,V_t_2,V_D_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 28.01/28.01 => ! [B_x] :
% 28.01/28.01 ( ! [B_xa] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => ! [B_xb] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 28.01/28.01 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.01/28.01 => ( B_x != V_t_2
% 28.01/28.01 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_bset_I7_J,axiom,
% 28.01/28.01 ! [V_B_2,V_t_2,V_D_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 28.01/28.01 => ! [B_x] :
% 28.01/28.01 ( ! [B_xa] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => ! [B_xb] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 28.01/28.01 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 28.01/28.01 => 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))) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_aset_I5_J,axiom,
% 28.01/28.01 ! [V_A_2,V_t_2,V_D_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 28.01/28.01 => ! [B_x] :
% 28.01/28.01 ( ! [B_xa] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => ! [B_xb] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 28.01/28.01 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 28.01/28.01 => 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)) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_aset_I3_J,axiom,
% 28.01/28.01 ! [V_A_2,V_t_2,V_D_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.01/28.01 => ( 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))
% 28.01/28.01 => ( ! [B_x] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => ! [B_xa] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 28.01/28.01 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 28.01/28.01 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_bset_I3_J,axiom,
% 28.01/28.01 ! [V_B_2,V_t_2,V_D_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.01/28.01 => ( 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))
% 28.01/28.01 => ( ! [B_x] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => ! [B_xa] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 28.01/28.01 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 28.01/28.01 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_aset_I7_J,axiom,
% 28.01/28.01 ! [V_t_2,V_A_2,V_D_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.01/28.01 => ! [B_x] :
% 28.01/28.01 ( ! [B_xa] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => ! [B_xb] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 28.01/28.01 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 28.01/28.01 => 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))) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_bset_I5_J,axiom,
% 28.01/28.01 ! [V_t_2,V_B_2,V_D_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 28.01/28.01 => ! [B_x] :
% 28.01/28.01 ( ! [B_xa] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => ! [B_xb] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 28.01/28.01 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 28.01/28.01 => 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)) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_setsum__Un__zero,axiom,
% 28.01/28.01 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 28.01/28.01 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.01/28.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 28.01/28.01 => ( ! [B_x] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 28.01/28.01 => 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)) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 28.01/28.01 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 28.01/28.01 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.01 => ( ! [B_x] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 28.01/28.01 => 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)) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_setsum__mono3,axiom,
% 28.01/28.01 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 28.01/28.01 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.01 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 28.01/28.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.01/28.01 => ( ! [B_x] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 28.01/28.01 => 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))) ) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_setsum__reindex__nonzero,axiom,
% 28.01/28.01 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 28.01/28.01 ( class_Groups_Ocomm__monoid__add(T_d)
% 28.01/28.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.01/28.01 => ( ! [B_x] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 28.01/28.01 => ! [B_y] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 28.01/28.01 => ( B_x != B_y
% 28.01/28.01 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 28.01/28.01 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 28.01/28.01 => 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) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_UN__finite2__eq,axiom,
% 28.01/28.01 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 28.01/28.01 ( ! [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)
% 28.01/28.01 => 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) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_UN__finite__subset,axiom,
% 28.01/28.01 ! [V_C_2,V_A_2,T_b] :
% 28.01/28.01 ( ! [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))
% 28.01/28.01 => 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)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_tsub__def,axiom,
% 28.01/28.01 ! [V_x,V_y] :
% 28.01/28.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 28.01/28.01 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 28.01/28.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 28.01/28.01 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Ints__odd__less__0,axiom,
% 28.01/28.01 ! [V_a_2,T_b] :
% 28.01/28.01 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.01/28.01 => ( 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)))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_arith__series__nat,axiom,
% 28.01/28.01 ! [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)))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_card__Diff__singleton,axiom,
% 28.01/28.01 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.01 => 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)) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_lessI,axiom,
% 28.01/28.01 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Suc__mono,axiom,
% 28.01/28.01 ! [V_n,V_m] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_zero__less__Suc,axiom,
% 28.01/28.01 ! [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))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_negative__zless,axiom,
% 28.01/28.01 ! [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))) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_card__atMost,axiom,
% 28.01/28.01 ! [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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_n__not__Suc__n,axiom,
% 28.01/28.01 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Suc__n__not__n,axiom,
% 28.01/28.01 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 28.01/28.01
% 28.01/28.01 fof(fact_nat_Oinject,axiom,
% 28.01/28.01 ! [V_nat_H_2,V_nat_2] :
% 28.01/28.01 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 28.01/28.01 <=> V_nat_2 = V_nat_H_2 ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Suc__inject,axiom,
% 28.01/28.01 ! [V_y,V_x] :
% 28.01/28.01 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 28.01/28.01 => V_x = V_y ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mono__Suc,axiom,
% 28.01/28.01 c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_card__atLeastAtMost,axiom,
% 28.01/28.01 ! [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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_mono__iff__le__Suc,axiom,
% 28.01/28.01 ! [V_f_2,T_b] :
% 28.01/28.01 ( class_Orderings_Oorder(T_b)
% 28.01/28.01 => ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,T_b,V_f_2)
% 28.01/28.01 <=> ! [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)))) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_card__UNIV__unit,axiom,
% 28.01/28.01 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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Suc__neq__Zero,axiom,
% 28.01/28.01 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Zero__neq__Suc,axiom,
% 28.01/28.01 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_nat_Osimps_I3_J,axiom,
% 28.01/28.01 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Suc__not__Zero,axiom,
% 28.01/28.01 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_nat_Osimps_I2_J,axiom,
% 28.01/28.01 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Zero__not__Suc,axiom,
% 28.01/28.01 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_not__less__eq,axiom,
% 28.01/28.01 ! [V_n_2,V_m_2] :
% 28.01/28.01 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_less__Suc__eq,axiom,
% 28.01/28.01 ! [V_n_2,V_m_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 28.01/28.01 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 28.01/28.01 | V_m_2 = V_n_2 ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Suc__less__eq,axiom,
% 28.01/28.01 ! [V_n_2,V_m_2] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_not__less__less__Suc__eq,axiom,
% 28.01/28.01 ! [V_m_2,V_n_2] :
% 28.01/28.01 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 28.01/28.01 <=> V_n_2 = V_m_2 ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_less__antisym,axiom,
% 28.01/28.01 ! [V_m,V_n] :
% 28.01/28.01 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 28.01/28.01 => V_m = V_n ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_less__SucI,axiom,
% 28.01/28.01 ! [V_n,V_m] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Suc__lessI,axiom,
% 28.01/28.01 ! [V_n,V_m] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.01/28.01 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_less__trans__Suc,axiom,
% 28.01/28.01 ! [V_k,V_j,V_i] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.01/28.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_less__SucE,axiom,
% 28.01/28.01 ! [V_n,V_m] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 28.01/28.01 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.01/28.01 => V_m = V_n ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Suc__lessD,axiom,
% 28.01/28.01 ! [V_n,V_m] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Suc__less__SucD,axiom,
% 28.01/28.01 ! [V_n,V_m] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_add__Suc__shift,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_add__Suc,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_add__Suc__right,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Suc__n__not__le__n,axiom,
% 28.01/28.01 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_not__less__eq__eq,axiom,
% 28.01/28.01 ! [V_n_2,V_m_2] :
% 28.01/28.01 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_le__Suc__eq,axiom,
% 28.01/28.01 ! [V_n_2,V_m_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 28.01/28.01 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.01/28.01 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Suc__le__mono,axiom,
% 28.01/28.01 ! [V_m_2,V_n_2] :
% 28.01/28.01 ( 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)))
% 28.01/28.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_le__SucI,axiom,
% 28.01/28.01 ! [V_n,V_m] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_le__SucE,axiom,
% 28.01/28.01 ! [V_n,V_m] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 28.01/28.01 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 28.01/28.01 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Suc__leD,axiom,
% 28.01/28.01 ! [V_n,V_m] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 28.01/28.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_bij__betw__same__card,axiom,
% 28.01/28.01 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.01 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 28.01/28.01 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_diff__Suc__Suc,axiom,
% 28.01/28.01 ! [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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Suc__diff__diff,axiom,
% 28.01/28.01 ! [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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Suc__mult__cancel1,axiom,
% 28.01/28.01 ! [V_n_2,V_m_2,V_k_2] :
% 28.01/28.01 ( 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)
% 28.01/28.01 <=> V_m_2 = V_n_2 ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_card__greaterThanLessThan,axiom,
% 28.01/28.01 ! [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)) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_card__lessThan,axiom,
% 28.01/28.01 ! [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 ).
% 28.01/28.01
% 28.01/28.01 fof(fact_card__insert__if,axiom,
% 28.01/28.01 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.01 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.01 => 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) )
% 28.01/28.01 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.01 => 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)) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_card__insert__disjoint,axiom,
% 28.01/28.01 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.01 => 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)) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_Least__Suc,axiom,
% 28.01/28.01 ! [V_n_2,V_P_2] :
% 28.01/28.01 ( hBOOL(hAPP(V_P_2,V_n_2))
% 28.01/28.01 => ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 28.01/28.01 => 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))) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 28.01/28.01 ! [V_i_2,V_n_2,V_inc_2,T_b] :
% 28.01/28.01 ( class_Rings_Osemiring__1(T_b)
% 28.01/28.01 => 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)) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_card__insert,axiom,
% 28.01/28.01 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.01 => 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)))))) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_card_Oempty,axiom,
% 28.01/28.01 ! [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) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_card__infinite,axiom,
% 28.01/28.01 ! [V_A_2,T_b] :
% 28.01/28.01 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.01 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_inj__Suc,axiom,
% 28.01/28.01 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 28.01/28.01 ! [V_A_2,T_b] :
% 28.01/28.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 28.01/28.01 => ( 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)))
% 28.01/28.01 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_card__image,axiom,
% 28.01/28.01 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.01 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.01/28.01 => 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) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_BIJ,axiom,
% 28.01/28.01 ! [V_B_2,T_c,V_A_2,T_b] :
% 28.01/28.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.01/28.01 => ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2)
% 28.01/28.01 <=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ).
% 28.01/28.01
% 28.01/28.01 fof(fact_less__Suc__eq__0__disj,axiom,
% 28.01/28.01 ! [V_n_2,V_m_2] :
% 28.01/28.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 28.01/28.01 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.01 | ? [B_j] :
% 28.01/28.02 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 28.01/28.02 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_less__Suc0,axiom,
% 28.01/28.02 ! [V_n_2] :
% 28.01/28.02 ( 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))))
% 28.01/28.02 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_gr0__conv__Suc,axiom,
% 28.01/28.02 ! [V_n_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 28.01/28.02 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_one__is__add,axiom,
% 28.01/28.02 ! [V_n_2,V_m_2] :
% 28.01/28.02 ( 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)
% 28.01/28.02 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 28.01/28.02 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.01/28.02 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.02 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_add__is__1,axiom,
% 28.01/28.02 ! [V_n_2,V_m_2] :
% 28.01/28.02 ( 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))
% 28.01/28.02 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 28.01/28.02 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.01/28.02 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.02 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_less__add__Suc1,axiom,
% 28.01/28.02 ! [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)))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_less__add__Suc2,axiom,
% 28.01/28.02 ! [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)))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_less__iff__Suc__add,axiom,
% 28.01/28.02 ! [V_n_2,V_m_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 28.01/28.02 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_less__eq__Suc__le,axiom,
% 28.01/28.02 ! [V_m_2,V_n_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_less__Suc__eq__le,axiom,
% 28.01/28.02 ! [V_n_2,V_m_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Suc__le__eq,axiom,
% 28.01/28.02 ! [V_n_2,V_m_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_le__imp__less__Suc,axiom,
% 28.01/28.02 ! [V_n,V_m] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 28.01/28.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Suc__leI,axiom,
% 28.01/28.02 ! [V_n,V_m] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.01/28.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_le__less__Suc__eq,axiom,
% 28.01/28.02 ! [V_n_2,V_m_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 28.01/28.02 <=> V_n_2 = V_m_2 ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Suc__le__lessD,axiom,
% 28.01/28.02 ! [V_n,V_m] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 28.01/28.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_mult__eq__1__iff,axiom,
% 28.01/28.02 ! [V_n_2,V_m_2] :
% 28.01/28.02 ( 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))
% 28.01/28.02 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 28.01/28.02 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__atLeastLessThan,axiom,
% 28.01/28.02 ! [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) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_diff__less__Suc,axiom,
% 28.01/28.02 ! [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))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Suc__mult__less__cancel1,axiom,
% 28.01/28.02 ! [V_n_2,V_m_2,V_k_2] :
% 28.01/28.02 ( 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)))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_mult__Suc,axiom,
% 28.01/28.02 ! [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)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_mult__Suc__right,axiom,
% 28.01/28.02 ! [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)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Suc__diff__le,axiom,
% 28.01/28.02 ! [V_m,V_n] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Suc__mult__le__cancel1,axiom,
% 28.01/28.02 ! [V_n_2,V_m_2,V_k_2] :
% 28.01/28.02 ( 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)))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_One__nat__def,axiom,
% 28.01/28.02 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Suc__eq__plus1,axiom,
% 28.01/28.02 ! [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)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Suc__eq__plus1__left,axiom,
% 28.01/28.02 ! [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) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_diff__Suc__1,axiom,
% 28.01/28.02 ! [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 ).
% 28.01/28.02
% 28.01/28.02 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 28.01/28.02 ! [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) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 28.01/28.02 ! [V_k_2,V_f_2] :
% 28.01/28.02 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__Suc__Diff1,axiom,
% 28.01/28.02 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.02 => 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) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 28.01/28.02 ! [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) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_less__eq__Suc__le__raw,axiom,
% 28.01/28.02 ! [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)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__eq__setsum,axiom,
% 28.01/28.02 ! [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) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__greaterThanAtMost,axiom,
% 28.01/28.02 ! [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) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_lessThan__Suc__atMost,axiom,
% 28.01/28.02 ! [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) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_lessThan__Suc,axiom,
% 28.01/28.02 ! [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)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_image__Suc__atLeastLessThan,axiom,
% 28.01/28.02 ! [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)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_atMost__Suc,axiom,
% 28.01/28.02 ! [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)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_finite__fun__UNIVD1,axiom,
% 28.01/28.02 ! [T_c,T_b] :
% 28.01/28.02 ( 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))))
% 28.01/28.02 => ( 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))
% 28.01/28.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 28.01/28.02 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 28.01/28.02 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_image__Suc__atLeastAtMost,axiom,
% 28.01/28.02 ! [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)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 28.01/28.02 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 28.01/28.02 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__eq__0__iff,axiom,
% 28.01/28.02 ! [V_A_2,T_b] :
% 28.01/28.02 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.02 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.02 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 28.01/28.02 ! [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) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__ge__0__finite,axiom,
% 28.01/28.02 ! [V_A_2,T_b] :
% 28.01/28.02 ( 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)))
% 28.01/28.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__insert__le,axiom,
% 28.01/28.02 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => 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)))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__mono,axiom,
% 28.01/28.02 ! [V_A_2,V_B_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.01/28.02 => 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))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__seteq,axiom,
% 28.01/28.02 ! [V_A_2,V_B_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.01/28.02 => ( 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)))
% 28.01/28.02 => V_A_2 = V_B_2 ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__image__le,axiom,
% 28.01/28.02 ! [V_f_2,T_c,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => 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))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 28.01/28.02 ! [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) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Ints__0,axiom,
% 28.01/28.02 ! [T_b] :
% 28.01/28.02 ( class_Rings_Oring__1(T_b)
% 28.01/28.02 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_eq__card__imp__inj__on,axiom,
% 28.01/28.02 ! [V_f_2,T_c,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => ( 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)
% 28.01/28.02 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_inj__on__iff__eq__card,axiom,
% 28.01/28.02 ! [V_f_2,T_c,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.01/28.02 <=> 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) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_pigeonhole,axiom,
% 28.01/28.02 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.02 ( 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)))
% 28.01/28.02 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Ints__add,axiom,
% 28.01/28.02 ! [V_b_2,V_a_2,T_b] :
% 28.01/28.02 ( class_Rings_Oring__1(T_b)
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.01/28.02 => 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))) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Ints__mult,axiom,
% 28.01/28.02 ! [V_b_2,V_a_2,T_b] :
% 28.01/28.02 ( class_Rings_Oring__1(T_b)
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.01/28.02 => 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))) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Ints__diff,axiom,
% 28.01/28.02 ! [V_b_2,V_a_2,T_b] :
% 28.01/28.02 ( class_Rings_Oring__1(T_b)
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.01/28.02 => 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))) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Ints__1,axiom,
% 28.01/28.02 ! [T_b] :
% 28.01/28.02 ( class_Rings_Oring__1(T_b)
% 28.01/28.02 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Ints__minus,axiom,
% 28.01/28.02 ! [V_a_2,T_b] :
% 28.01/28.02 ( class_Rings_Oring__1(T_b)
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.01/28.02 => 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))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Ints__of__nat,axiom,
% 28.01/28.02 ! [V_n_2,T_b] :
% 28.01/28.02 ( class_Rings_Oring__1(T_b)
% 28.01/28.02 => 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))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_psubset__card__mono,axiom,
% 28.01/28.02 ! [V_A_2,V_B_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.01/28.02 => 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))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__nat__Suc,axiom,
% 28.01/28.02 ! [V_m,T_a] :
% 28.01/28.02 ( class_Rings_Osemiring__1(T_a)
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Suc__pred,axiom,
% 28.01/28.02 ! [V_n] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.01/28.02 => 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 ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_diff__Suc__less,axiom,
% 28.01/28.02 ! [V_i,V_n] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_one__less__mult,axiom,
% 28.01/28.02 ! [V_m,V_n] :
% 28.01/28.02 ( 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))
% 28.01/28.02 => ( 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))
% 28.01/28.02 => 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))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_n__less__n__mult__m,axiom,
% 28.01/28.02 ! [V_m,V_n] :
% 28.01/28.02 ( 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))
% 28.01/28.02 => ( 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))
% 28.01/28.02 => 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))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_n__less__m__mult__n,axiom,
% 28.01/28.02 ! [V_m,V_n] :
% 28.01/28.02 ( 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))
% 28.01/28.02 => ( 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))
% 28.01/28.02 => 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))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_one__le__mult__iff,axiom,
% 28.01/28.02 ! [V_n_2,V_m_2] :
% 28.01/28.02 ( 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)))
% 28.01/28.02 <=> ( 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))
% 28.01/28.02 & 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)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_diff__Suc__diff__eq2,axiom,
% 28.01/28.02 ! [V_m,V_j,V_k] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_diff__Suc__diff__eq1,axiom,
% 28.01/28.02 ! [V_m,V_j,V_k] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_int__Suc0__eq__1,axiom,
% 28.01/28.02 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) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_zless__iff__Suc__zadd,axiom,
% 28.01/28.02 ! [V_z_2,V_w_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 28.01/28.02 <=> ? [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))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_int__Suc,axiom,
% 28.01/28.02 ! [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)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__eq__Suc0__iff,axiom,
% 28.01/28.02 ! [V_f_2,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => ( 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))
% 28.01/28.02 <=> ? [B_x] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.02 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 28.01/28.02 & ! [B_xa] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 28.01/28.02 => ( B_x != B_xa
% 28.01/28.02 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__constant,axiom,
% 28.01/28.02 ! [V_A_2,V_y_2,T_c,T_b] :
% 28.01/28.02 ( class_Rings_Osemiring__1(T_b)
% 28.01/28.02 => 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) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_atLeast__Suc__greaterThan,axiom,
% 28.01/28.02 ! [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) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_atLeastAtMostSuc__conv,axiom,
% 28.01/28.02 ! [V_n_2,V_m_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_subset__card__intvl__is__intvl,axiom,
% 28.01/28.02 ! [V_k_2,V_A_2] :
% 28.01/28.02 ( 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)))))
% 28.01/28.02 => 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))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_atLeastLessThan__singleton,axiom,
% 28.01/28.02 ! [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))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__gt__0__iff,axiom,
% 28.01/28.02 ! [V_A_2,T_b] :
% 28.01/28.02 ( 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)))
% 28.01/28.02 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.02 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_finite__UNIV__card__ge__0,axiom,
% 28.01/28.02 ! [T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 28.01/28.02 => 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))))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__lessThan__Suc,axiom,
% 28.01/28.02 ! [V_n_2,V_f_2,T_b] :
% 28.01/28.02 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__Un__Int,axiom,
% 28.01/28.02 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.02 => 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))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card_Ounion__inter,axiom,
% 28.01/28.02 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.02 => 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)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__bij__eq,axiom,
% 28.01/28.02 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.02 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.01/28.02 => ( 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))
% 28.01/28.02 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 28.01/28.02 => ( 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))
% 28.01/28.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.01/28.02 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__atMost__Suc,axiom,
% 28.01/28.02 ! [V_n_2,V_f_2,T_b] :
% 28.01/28.02 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.02 => 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))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__Diff__subset,axiom,
% 28.01/28.02 ! [V_A_2,V_B_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.01/28.02 => 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)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__Diff__subset__Int,axiom,
% 28.01/28.02 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.02 ( 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)))
% 28.01/28.02 => 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))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_diff__card__le__card__Diff,axiom,
% 28.01/28.02 ! [V_A_2,V_B_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.02 => 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)))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__psubset,axiom,
% 28.01/28.02 ! [V_A_2,V_B_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.01/28.02 => ( 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)))
% 28.01/28.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Suc__diff__1,axiom,
% 28.01/28.02 ! [V_n] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.01/28.02 => 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 ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Suc__pred_H,axiom,
% 28.01/28.02 ! [V_n] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.01/28.02 => 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))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_add__eq__if,axiom,
% 28.01/28.02 ! [V_n,V_m] :
% 28.01/28.02 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.02 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 28.01/28.02 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.02 => 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)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_atLeast__Suc,axiom,
% 28.01/28.02 ! [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)))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_greaterThan__Suc,axiom,
% 28.01/28.02 ! [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)))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_not__zle__0__negative,axiom,
% 28.01/28.02 ! [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))))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_negative__zless__0,axiom,
% 28.01/28.02 ! [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))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card_Oeq__fold__g,axiom,
% 28.01/28.02 ! [V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => 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) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__def,axiom,
% 28.01/28.02 ! [V_A_2,T_b] :
% 28.01/28.02 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => 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) )
% 28.01/28.02 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Ints__double__eq__0__iff,axiom,
% 28.01/28.02 ! [V_a_2,T_b] :
% 28.01/28.02 ( class_Int_Oring__char__0(T_b)
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.01/28.02 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.02 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 28.01/28.02 ! [V_k_2,V_f_2,T_b] :
% 28.01/28.02 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.02 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.02 => 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)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__head__upt__Suc,axiom,
% 28.01/28.02 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 28.01/28.02 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 28.01/28.02 => 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))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__head__Suc,axiom,
% 28.01/28.02 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 28.01/28.02 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.01/28.02 => 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))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_atLeastLessThanSuc,axiom,
% 28.01/28.02 ! [V_n_2,V_m_2] :
% 28.01/28.02 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.01/28.02 => 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)) )
% 28.01/28.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.01/28.02 => 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)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__Un__disjoint,axiom,
% 28.01/28.02 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.02 => ( 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))
% 28.01/28.02 => 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)) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__Diff1__le,axiom,
% 28.01/28.02 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => 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))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card_Oinsert,axiom,
% 28.01/28.02 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.02 => 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)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__inj__on__le,axiom,
% 28.01/28.02 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.02 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.01/28.02 => ( 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))
% 28.01/28.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.01/28.02 => 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))) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_inj__on__iff__card__le,axiom,
% 28.01/28.02 ! [V_B_2,T_c,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.01/28.02 => ( ? [B_f] :
% 28.01/28.02 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 28.01/28.02 & 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)) )
% 28.01/28.02 <=> 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))) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 28.01/28.02 ! [V_y,V_x] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.01/28.02 => 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))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_tsub__eq,axiom,
% 28.01/28.02 ! [V_x,V_y] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 28.01/28.02 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 28.01/28.02 ! [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)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 28.01/28.02 ! [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))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__op__ivl__Suc,axiom,
% 28.01/28.02 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 28.01/28.02 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.02 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 28.01/28.02 => 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) )
% 28.01/28.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 28.01/28.02 => 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)) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__cl__ivl__Suc,axiom,
% 28.01/28.02 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 28.01/28.02 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.02 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 28.01/28.02 => 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) )
% 28.01/28.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 28.01/28.02 => 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))) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_greaterThan__0,axiom,
% 28.01/28.02 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))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__Diff1__less,axiom,
% 28.01/28.02 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.02 => 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))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__Diff2__less,axiom,
% 28.01/28.02 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 28.01/28.02 => 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))) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Ints__odd__nonzero,axiom,
% 28.01/28.02 ! [V_a_2,T_b] :
% 28.01/28.02 ( class_Int_Oring__char__0(T_b)
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.01/28.02 => 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) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__Diff__insert,axiom,
% 28.01/28.02 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.02 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 28.01/28.02 => 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)) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card_Oinsert__remove,axiom,
% 28.01/28.02 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => 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)))))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card_Oremove,axiom,
% 28.01/28.02 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.02 => 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)))))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__Diff__singleton__if,axiom,
% 28.01/28.02 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.02 => 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)) )
% 28.01/28.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.02 => 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) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card_Ounion__inter__neutral,axiom,
% 28.01/28.02 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.02 => ( ( ? [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)))
% 28.01/28.02 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.01/28.02 => 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)) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__bounded,axiom,
% 28.01/28.02 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 28.01/28.02 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 28.01/28.02 & class_Rings_Osemiring__1(T_c) )
% 28.01/28.02 => ( ! [B_i] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 28.01/28.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 28.01/28.02 => 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))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__Suc__eq,axiom,
% 28.01/28.02 ! [V_k_2,V_A_2,T_b] :
% 28.01/28.02 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 28.01/28.02 <=> ? [B_b,B_B] :
% 28.01/28.02 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 28.01/28.02 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 28.01/28.02 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 28.01/28.02 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.02 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__Plus__conv__if,axiom,
% 28.01/28.02 ! [V_B_2,T_c,V_A_2,T_b] :
% 28.01/28.02 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 28.01/28.02 => 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)) )
% 28.01/28.02 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 28.01/28.02 => 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) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 28.01/28.02 ! [V_u_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 28.01/28.02 => 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))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__nonneg__0,axiom,
% 28.01/28.02 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 28.01/28.02 ( class_Groups_Oordered__ab__group__add(T_c)
% 28.01/28.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 28.01/28.02 => ( ! [B_i] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 28.01/28.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 28.01/28.02 => ( 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)
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 28.01/28.02 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__int,axiom,
% 28.01/28.02 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__0,axiom,
% 28.01/28.02 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 28.01/28.02 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_eq__nat__nat__iff,axiom,
% 28.01/28.02 ! [V_z_H_2,V_z_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 28.01/28.02 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 28.01/28.02 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 28.01/28.02 ! [V_y_2,V_x_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 28.01/28.02 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 28.01/28.02 <=> V_x_2 = V_y_2 ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_all__nat,axiom,
% 28.01/28.02 ! [V_P_2] :
% 28.01/28.02 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 28.01/28.02 <=> ! [B_x] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 28.01/28.02 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_ex__nat,axiom,
% 28.01/28.02 ! [V_P_2] :
% 28.01/28.02 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 28.01/28.02 <=> ? [B_x] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 28.01/28.02 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 28.01/28.02 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 28.01/28.02 ! [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 ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 28.01/28.02 ! [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))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 28.01/28.02 ! [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) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__atLeastLessThan__int,axiom,
% 28.01/28.02 ! [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)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__greaterThanAtMost__int,axiom,
% 28.01/28.02 ! [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)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 28.01/28.02 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))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__0__iff,axiom,
% 28.01/28.02 ! [V_i_2] :
% 28.01/28.02 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__le__0,axiom,
% 28.01/28.02 ! [V_z] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.02 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_zless__nat__conj,axiom,
% 28.01/28.02 ! [V_z_2,V_w_2] :
% 28.01/28.02 ( 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)))
% 28.01/28.02 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 28.01/28.02 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__mono__iff,axiom,
% 28.01/28.02 ! [V_w_2,V_z_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 28.01/28.02 => ( 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)))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 28.01/28.02 ! [V_y_2,V_x_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 28.01/28.02 => ( 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)))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__1,axiom,
% 28.01/28.02 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__0__le,axiom,
% 28.01/28.02 ! [V_z] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 28.01/28.02 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_int__eq__iff,axiom,
% 28.01/28.02 ! [V_z_2,V_m_2] :
% 28.01/28.02 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 28.01/28.02 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 28.01/28.02 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_int__nat__eq,axiom,
% 28.01/28.02 ! [V_z] :
% 28.01/28.02 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 28.01/28.02 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 28.01/28.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 28.01/28.02 => 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) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_zless__nat__eq__int__zless,axiom,
% 28.01/28.02 ! [V_z_2,V_m_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 28.01/28.02 <=> 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__zminus__int,axiom,
% 28.01/28.02 ! [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) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 28.01/28.02 ! [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))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 28.01/28.02 ! [V_A_2,V_f_2,T_b] :
% 28.01/28.02 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.02 & class_Groups_Ocomm__monoid__mult(T_b) )
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_zero__less__nat__eq,axiom,
% 28.01/28.02 ! [V_z_2] :
% 28.01/28.02 ( 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)))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__less__eq__zless,axiom,
% 28.01/28.02 ! [V_z_2,V_w_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 28.01/28.02 => ( 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)))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 28.01/28.02 ! [V_y_2,V_x_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 28.01/28.02 => ( 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)))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__eq__iff2,axiom,
% 28.01/28.02 ! [V_w_2,V_m_2] :
% 28.01/28.02 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 28.01/28.02 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 28.01/28.02 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 28.01/28.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 28.01/28.02 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__eq__iff,axiom,
% 28.01/28.02 ! [V_m_2,V_w_2] :
% 28.01/28.02 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 28.01/28.02 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 28.01/28.02 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 28.01/28.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 28.01/28.02 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__le__eq__zle,axiom,
% 28.01/28.02 ! [V_z_2,V_w_2] :
% 28.01/28.02 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 28.01/28.02 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 28.01/28.02 => ( 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)))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_split__nat,axiom,
% 28.01/28.02 ! [V_i_2,V_P_2] :
% 28.01/28.02 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
% 28.01/28.02 <=> ( ! [B_n] :
% 28.01/28.02 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 28.01/28.02 => hBOOL(hAPP(V_P_2,B_n)) )
% 28.01/28.02 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.02 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__add__distrib,axiom,
% 28.01/28.02 ! [V_z_H,V_z] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 28.01/28.02 => 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)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 28.01/28.02 ! [V_y,V_x] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.01/28.02 => 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)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__mult__distrib,axiom,
% 28.01/28.02 ! [V_z_H,V_z] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 28.01/28.02 ! [V_y,V_x] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.01/28.02 => 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)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 28.01/28.02 ! [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))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__diff__distrib,axiom,
% 28.01/28.02 ! [V_z,V_z_H] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 28.01/28.02 => 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)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 28.01/28.02 ! [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)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__atLeastAtMost__int,axiom,
% 28.01/28.02 ! [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))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 28.01/28.02 ! [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))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 28.01/28.02 ! [V_y,V_x] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.01/28.02 => 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)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_finite__PlusD_I2_J,axiom,
% 28.01/28.02 ! [V_B_2,V_A_2,T_c,T_b] :
% 28.01/28.02 ( 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)))
% 28.01/28.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_finite__PlusD_I1_J,axiom,
% 28.01/28.02 ! [V_B_2,V_A_2,T_c,T_b] :
% 28.01/28.02 ( 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)))
% 28.01/28.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_finite__Plus,axiom,
% 28.01/28.02 ! [V_B_2,T_c,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.01/28.02 => 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))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_finite__Plus__iff,axiom,
% 28.01/28.02 ! [V_B_2,V_A_2,T_c,T_b] :
% 28.01/28.02 ( 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)))
% 28.01/28.02 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__greaterThanLessThan__int,axiom,
% 28.01/28.02 ! [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)))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_one__less__nat__eq,axiom,
% 28.01/28.02 ! [V_z_2] :
% 28.01/28.02 ( 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)))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__less__iff,axiom,
% 28.01/28.02 ! [V_m_2,V_w_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 28.01/28.02 <=> 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))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 28.01/28.02 ! [V_z] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__mult__distrib__neg,axiom,
% 28.01/28.02 ! [V_z_H,V_z] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.02 => 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))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_card__Plus,axiom,
% 28.01/28.02 ! [V_B_2,T_c,V_A_2,T_b] :
% 28.01/28.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.01/28.02 => 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)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_UNIV__Plus__UNIV,axiom,
% 28.01/28.02 ! [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)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__aux__def,axiom,
% 28.01/28.02 ! [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) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_transfer__morphism__nat__int,axiom,
% 28.01/28.02 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))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Plus__eq__empty__conv,axiom,
% 28.01/28.02 ! [V_B_2,V_A_2,T_c,T_b] :
% 28.01/28.02 ( 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))
% 28.01/28.02 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.02 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 28.01/28.02 ! [V_n_2,V_m_2] :
% 28.01/28.02 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 28.01/28.02 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 28.01/28.02 => 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))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 28.01/28.02 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 28.01/28.02 ! [V_y,V_x] :
% 28.01/28.02 ( c_Nat__Transfer_Ois__nat(V_x)
% 28.01/28.02 => ( c_Nat__Transfer_Ois__nat(V_y)
% 28.01/28.02 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 28.01/28.02 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 28.01/28.02 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 28.01/28.02 ! [V_y,V_x] :
% 28.01/28.02 ( c_Nat__Transfer_Ois__nat(V_x)
% 28.01/28.02 => ( c_Nat__Transfer_Ois__nat(V_y)
% 28.01/28.02 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 28.01/28.02 ! [V_y,V_x] :
% 28.01/28.02 ( c_Nat__Transfer_Ois__nat(V_x)
% 28.01/28.02 => ( c_Nat__Transfer_Ois__nat(V_y)
% 28.01/28.02 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_is__nat__def,axiom,
% 28.01/28.02 ! [V_x_2] :
% 28.01/28.02 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 28.01/28.02 ! [V_B_2,V_A_2] :
% 28.01/28.02 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.01/28.02 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 28.01/28.02 => 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))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 28.01/28.02 ! [V_B_2,V_A_2] :
% 28.01/28.02 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.01/28.02 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 28.01/28.02 => 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))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 28.01/28.02 ! [V_f_2,V_A_2,T_b] :
% 28.01/28.02 ( ! [B_x] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.02 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 28.01/28.02 ! [V_f_2,V_A_2,T_b] :
% 28.01/28.02 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.02 & class_Groups_Ocomm__monoid__mult(T_b) )
% 28.01/28.02 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.01/28.02 => 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)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 28.01/28.02 ! [V_B_2,V_A_2] :
% 28.01/28.02 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.01/28.02 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.01/28.02 <=> 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))) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 28.01/28.02 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 28.01/28.02 ! [V_B_2,V_A_2] :
% 28.01/28.02 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.01/28.02 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 28.01/28.02 => 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)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 28.01/28.02 ! [V_B_2,V_A_2] :
% 28.01/28.02 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.01/28.02 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 28.01/28.02 => 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)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_nat__set__def,axiom,
% 28.01/28.02 ! [V_S_2] :
% 28.01/28.02 ( c_Nat__Transfer_Onat__set(V_S_2)
% 28.01/28.02 <=> ! [B_x] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 28.01/28.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 28.01/28.02 ! [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)) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 28.01/28.02 ! [V_B_2,V_A_2] :
% 28.01/28.02 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.01/28.02 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 28.01/28.02 => ( V_A_2 = V_B_2
% 28.01/28.02 <=> 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) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 28.01/28.02 ! [V_y_2,V_x_2] :
% 28.01/28.02 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 28.01/28.02 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 28.01/28.02 ! [V_x_2,V_A_2] :
% 28.01/28.02 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 28.01/28.02 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 28.01/28.02 ! [V_y_2,V_x_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 28.01/28.02 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 28.01/28.02 ! [V_x_2,V_A_2] :
% 28.01/28.02 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 28.01/28.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 28.01/28.02 ! [V_A_2] :
% 28.01/28.02 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.01/28.02 => 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 ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 28.01/28.02 ! [V_A_2] :
% 28.01/28.02 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.01/28.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 28.01/28.02 <=> 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))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 28.01/28.02 ! [V_A_2] :
% 28.01/28.02 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 28.01/28.02 ! [V_A_2,V_x_2] :
% 28.01/28.02 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 28.01/28.02 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 28.01/28.02 <=> 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))) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 28.01/28.02 ! [V_B_2,V_A_2] :
% 28.01/28.02 ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.01/28.02 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.01/28.02 <=> 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))) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__of__nat,axiom,
% 28.01/28.02 ! [V_k,T_a] :
% 28.01/28.02 ( class_Rings_Oring__1(T_a)
% 28.01/28.02 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.02 => 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)))) )
% 28.01/28.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.02 => 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)) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__nonneg__leq__bound,axiom,
% 28.01/28.02 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 28.01/28.02 ( class_Groups_Oordered__ab__group__add(T_c)
% 28.01/28.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 28.01/28.02 => ( ! [B_i] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 28.01/28.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 28.01/28.02 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 28.01/28.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_sum__diff__distrib,axiom,
% 28.01/28.02 ! [V_n_2,V_P_2,V_Q_2] :
% 28.01/28.02 ( ! [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)))
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_decr__mult__lemma,axiom,
% 28.01/28.02 ! [V_k_2,V_P_2,V_d_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 28.01/28.02 => ( ! [B_x] :
% 28.01/28.02 ( hBOOL(hAPP(V_P_2,B_x))
% 28.01/28.02 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 28.01/28.02 => ! [B_x] :
% 28.01/28.02 ( hBOOL(hAPP(V_P_2,B_x))
% 28.01/28.02 => 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)))) ) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_negD,axiom,
% 28.01/28.02 ! [V_x] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.02 => ? [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))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__eq__iff,axiom,
% 28.01/28.02 ! [V_z_2,V_w_2,T_b] :
% 28.01/28.02 ( class_Int_Oring__char__0(T_b)
% 28.01/28.02 => ( 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)
% 28.01/28.02 <=> V_w_2 = V_z_2 ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__int__eq,axiom,
% 28.01/28.02 ! [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) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__0,axiom,
% 28.01/28.02 ! [T_a] :
% 28.01/28.02 ( class_Rings_Oring__1(T_a)
% 28.01/28.02 => 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) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__0__eq__iff,axiom,
% 28.01/28.02 ! [V_z_2,T_b] :
% 28.01/28.02 ( class_Int_Oring__char__0(T_b)
% 28.01/28.02 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 28.01/28.02 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__eq__0__iff,axiom,
% 28.01/28.02 ! [V_z_2,T_b] :
% 28.01/28.02 ( class_Int_Oring__char__0(T_b)
% 28.01/28.02 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.02 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__le__iff,axiom,
% 28.01/28.02 ! [V_z_2,V_w_2,T_b] :
% 28.01/28.02 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.02 => ( 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)))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__less__iff,axiom,
% 28.01/28.02 ! [V_z_2,V_w_2,T_b] :
% 28.01/28.02 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.02 => ( 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)))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__add,axiom,
% 28.01/28.02 ! [V_z,V_w,T_a] :
% 28.01/28.02 ( class_Rings_Oring__1(T_a)
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__mult,axiom,
% 28.01/28.02 ! [V_z,V_w,T_a] :
% 28.01/28.02 ( class_Rings_Oring__1(T_a)
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__1,axiom,
% 28.01/28.02 ! [T_a] :
% 28.01/28.02 ( class_Rings_Oring__1(T_a)
% 28.01/28.02 => 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) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__diff,axiom,
% 28.01/28.02 ! [V_z,V_w,T_a] :
% 28.01/28.02 ( class_Rings_Oring__1(T_a)
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__of__nat__eq,axiom,
% 28.01/28.02 ! [V_n,T_a] :
% 28.01/28.02 ( class_Rings_Oring__1(T_a)
% 28.01/28.02 => 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) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__minus,axiom,
% 28.01/28.02 ! [V_z,T_a] :
% 28.01/28.02 ( class_Rings_Oring__1(T_a)
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_Ints__of__int,axiom,
% 28.01/28.02 ! [V_z_2,T_b] :
% 28.01/28.02 ( class_Rings_Oring__1(T_b)
% 28.01/28.02 => 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))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__setsum,axiom,
% 28.01/28.02 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.02 ( class_Rings_Oring__1(T_b)
% 28.01/28.02 => 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) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__0__le__iff,axiom,
% 28.01/28.02 ! [V_z_2,T_b] :
% 28.01/28.02 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.02 => ( 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)))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__le__0__iff,axiom,
% 28.01/28.02 ! [V_z_2,T_b] :
% 28.01/28.02 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.02 => ( 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)))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__0__less__iff,axiom,
% 28.01/28.02 ! [V_z_2,T_b] :
% 28.01/28.02 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.02 => ( 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)))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__int__less__0__iff,axiom,
% 28.01/28.02 ! [V_z_2,T_b] :
% 28.01/28.02 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.02 => ( 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)))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_of__nat__nat,axiom,
% 28.01/28.02 ! [V_z,T_a] :
% 28.01/28.02 ( class_Rings_Oring__1(T_a)
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 28.01/28.02 => 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) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_incr__mult__lemma,axiom,
% 28.01/28.02 ! [V_k_2,V_P_2,V_d_2] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 28.01/28.02 => ( ! [B_x] :
% 28.01/28.02 ( hBOOL(hAPP(V_P_2,B_x))
% 28.01/28.02 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 28.01/28.02 => ! [B_x] :
% 28.01/28.02 ( hBOOL(hAPP(V_P_2,B_x))
% 28.01/28.02 => 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)))) ) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_ex__least__nat__less,axiom,
% 28.01/28.02 ! [V_n_2,V_P_2] :
% 28.01/28.02 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 28.01/28.02 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 28.01/28.02 => ? [B_k] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 28.01/28.02 & ! [B_i] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 28.01/28.02 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 28.01/28.02 & 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)))) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_zero__less__imp__eq__int,axiom,
% 28.01/28.02 ! [V_k] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 28.01/28.02 => ? [B_n] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 28.01/28.02 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__mono__zero__left,axiom,
% 28.01/28.02 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 28.01/28.02 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 28.01/28.02 => ( ! [B_x] :
% 28.01/28.02 ( 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)))
% 28.01/28.02 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 28.01/28.02 => 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) ) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__mono__zero__right,axiom,
% 28.01/28.02 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 28.01/28.02 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 28.01/28.02 => ( ! [B_x] :
% 28.01/28.02 ( 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)))
% 28.01/28.02 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 28.01/28.02 => 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) ) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_sgn__if,axiom,
% 28.01/28.02 ! [V_x,T_a] :
% 28.01/28.02 ( class_Groups_Osgn__if(T_a)
% 28.01/28.02 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.02 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 28.01/28.02 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.02 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.01/28.02 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 28.01/28.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.01/28.02 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_sgn__neg,axiom,
% 28.01/28.02 ! [V_a,T_a] :
% 28.01/28.02 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.02 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_sgn__1__neg,axiom,
% 28.01/28.02 ! [V_a_2,T_b] :
% 28.01/28.02 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.02 => ( 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))
% 28.01/28.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_decr__lemma,axiom,
% 28.01/28.02 ! [V_z,V_x,V_d] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_incr__lemma,axiom,
% 28.01/28.02 ! [V_x,V_z,V_d] :
% 28.01/28.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 28.01/28.02 => 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)))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__abs,axiom,
% 28.01/28.02 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.02 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 28.01/28.02 => 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))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_setsum__abs__ge__zero,axiom,
% 28.01/28.02 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.02 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 28.01/28.02 => 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))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_abs__add__abs,axiom,
% 28.01/28.02 ! [V_b,V_a,T_a] :
% 28.01/28.02 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_abs__mult__self,axiom,
% 28.01/28.02 ! [V_a,T_a] :
% 28.01/28.02 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.02 => 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) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_abs__mult,axiom,
% 28.01/28.02 ! [V_b,V_a,T_a] :
% 28.01/28.02 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_abs__minus__commute,axiom,
% 28.01/28.02 ! [V_b,V_a,T_a] :
% 28.01/28.02 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.02 => 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)) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_abs__one,axiom,
% 28.01/28.02 ! [T_a] :
% 28.01/28.02 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.02 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_abs__minus__cancel,axiom,
% 28.01/28.02 ! [V_a,T_a] :
% 28.01/28.02 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.02 => 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) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_abs__of__nat,axiom,
% 28.01/28.02 ! [V_n,T_a] :
% 28.01/28.02 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.02 => 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) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_abs__le__D1,axiom,
% 28.01/28.02 ! [V_b,V_a,T_a] :
% 28.01/28.02 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 28.01/28.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_abs__ge__self,axiom,
% 28.01/28.02 ! [V_a,T_a] :
% 28.01/28.02 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_sgn__sgn,axiom,
% 28.01/28.02 ! [V_a,T_a] :
% 28.01/28.02 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.02 => 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) ) ).
% 28.01/28.02
% 28.01/28.02 fof(fact_abs__idempotent,axiom,
% 28.01/28.02 ! [V_a,T_a] :
% 28.01/28.02 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_mult__sgn__abs,axiom,
% 28.01/28.03 ! [V_x,T_a] :
% 28.01/28.03 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.03 => 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 ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__sgn,axiom,
% 28.01/28.03 ! [V_k,T_a] :
% 28.01/28.03 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__eq__0,axiom,
% 28.01/28.03 ! [V_a_2,T_b] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 28.01/28.03 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.03 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__zero,axiom,
% 28.01/28.03 ! [T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.03 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__int__eq,axiom,
% 28.01/28.03 ! [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) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__setsum__abs,axiom,
% 28.01/28.03 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_sgn__0__0,axiom,
% 28.01/28.03 ! [V_a_2,T_b] :
% 28.01/28.03 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.03 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.03 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_sgn0,axiom,
% 28.01/28.03 ! [T_a] :
% 28.01/28.03 ( class_Groups_Osgn__if(T_a)
% 28.01/28.03 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_sgn__times,axiom,
% 28.01/28.03 ! [V_b,V_a,T_a] :
% 28.01/28.03 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__of__nonneg,axiom,
% 28.01/28.03 ! [V_a,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.03 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__le__zero__iff,axiom,
% 28.01/28.03 ! [V_a_2,T_b] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 28.01/28.03 => ( 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)))
% 28.01/28.03 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__ge__zero,axiom,
% 28.01/28.03 ! [V_a,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.03 => 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))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__of__pos,axiom,
% 28.01/28.03 ! [V_a,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.03 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_zero__less__abs__iff,axiom,
% 28.01/28.03 ! [V_a_2,T_b] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 28.01/28.03 => ( 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)))
% 28.01/28.03 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__not__less__zero,axiom,
% 28.01/28.03 ! [V_a,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.03 => ~ 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))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__triangle__ineq,axiom,
% 28.01/28.03 ! [V_b,V_a,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.03 => 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)))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__mult__less,axiom,
% 28.01/28.03 ! [V_d,V_b,V_c,V_a,T_a] :
% 28.01/28.03 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 28.01/28.03 => 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))) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__triangle__ineq3,axiom,
% 28.01/28.03 ! [V_b,V_a,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.03 => 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)))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__triangle__ineq2,axiom,
% 28.01/28.03 ! [V_b,V_a,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.03 => 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)))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__triangle__ineq2__sym,axiom,
% 28.01/28.03 ! [V_b,V_a,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.03 => 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)))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__le__D2,axiom,
% 28.01/28.03 ! [V_b,V_a,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 28.01/28.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__leI,axiom,
% 28.01/28.03 ! [V_b,V_a,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 28.01/28.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__le__iff,axiom,
% 28.01/28.03 ! [V_b_2,V_a_2,T_b] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 28.01/28.03 => ( 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))
% 28.01/28.03 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 28.01/28.03 & 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)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__ge__minus__self,axiom,
% 28.01/28.03 ! [V_a,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.03 => 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))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__less__iff,axiom,
% 28.01/28.03 ! [V_b_2,V_a_2,T_b] :
% 28.01/28.03 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 28.01/28.03 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 28.01/28.03 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__zmult__eq__1,axiom,
% 28.01/28.03 ! [V_n,V_m] :
% 28.01/28.03 ( 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)
% 28.01/28.03 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__mult__pos,axiom,
% 28.01/28.03 ! [V_y,V_x,T_a] :
% 28.01/28.03 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.01/28.03 => 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)) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__eq__mult,axiom,
% 28.01/28.03 ! [V_b,V_a,T_a] :
% 28.01/28.03 ( class_Rings_Oordered__ring__abs(T_a)
% 28.01/28.03 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 28.01/28.03 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.01/28.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 28.01/28.03 => 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)) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__triangle__ineq4,axiom,
% 28.01/28.03 ! [V_b,V_a,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.03 => 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)))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__diff__triangle__ineq,axiom,
% 28.01/28.03 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.03 => 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))))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__of__nonpos,axiom,
% 28.01/28.03 ! [V_a,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.03 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__minus__le__zero,axiom,
% 28.01/28.03 ! [V_a,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.03 => 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))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__of__neg,axiom,
% 28.01/28.03 ! [V_a,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.03 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__if,axiom,
% 28.01/28.03 ! [V_a,T_a] :
% 28.01/28.03 ( class_Groups_Oabs__if(T_a)
% 28.01/28.03 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.03 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 28.01/28.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.03 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_zabs__less__one__iff,axiom,
% 28.01/28.03 ! [V_z_2] :
% 28.01/28.03 ( 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)))
% 28.01/28.03 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_zabs__def,axiom,
% 28.01/28.03 ! [V_i] :
% 28.01/28.03 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.03 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 28.01/28.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.03 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_nat__abs__mult__distrib,axiom,
% 28.01/28.03 ! [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))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_sgn__less,axiom,
% 28.01/28.03 ! [V_a_2,T_b] :
% 28.01/28.03 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.03 => ( 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)))
% 28.01/28.03 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_sgn__greater,axiom,
% 28.01/28.03 ! [V_a_2,T_b] :
% 28.01/28.03 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.03 => ( 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)))
% 28.01/28.03 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_sgn__1__pos,axiom,
% 28.01/28.03 ! [V_a_2,T_b] :
% 28.01/28.03 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.03 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 28.01/28.03 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_sgn__pos,axiom,
% 28.01/28.03 ! [V_a,T_a] :
% 28.01/28.03 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.03 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_zsgn__def,axiom,
% 28.01/28.03 ! [V_i] :
% 28.01/28.03 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.03 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 28.01/28.03 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.03 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 28.01/28.03 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 28.01/28.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 28.01/28.03 => 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)) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 28.01/28.03 ! [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)))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 28.01/28.03 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 28.01/28.03 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.03 & class_Groups_Ocomm__monoid__mult(T_b) )
% 28.01/28.03 => ( V_A_2 = V_B_2
% 28.01/28.03 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 28.01/28.03 => ( ! [B_x] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 28.01/28.03 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 28.01/28.03 => 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) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_diff__Suc,axiom,
% 28.01/28.03 ! [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)) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_int__val__lemma,axiom,
% 28.01/28.03 ! [V_k_2,V_f_2,V_n_2] :
% 28.01/28.03 ( ! [B_i] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 28.01/28.03 => 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))) )
% 28.01/28.03 => ( 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))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 28.01/28.03 => ? [B_i] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 28.01/28.03 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_nat0__intermed__int__val,axiom,
% 28.01/28.03 ! [V_k_2,V_f_2,V_n_2] :
% 28.01/28.03 ( ! [B_i] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 28.01/28.03 => 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))) )
% 28.01/28.03 => ( 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))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 28.01/28.03 => ? [B_i] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 28.01/28.03 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_nat__case__0,axiom,
% 28.01/28.03 ! [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 ).
% 28.01/28.03
% 28.01/28.03 fof(fact_nat__case__Suc,axiom,
% 28.01/28.03 ! [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) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_card__less__Suc,axiom,
% 28.01/28.03 ! [V_i_2,V_M_2] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 28.01/28.03 => 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))))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_card__less,axiom,
% 28.01/28.03 ! [V_i_2,V_M_2] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_card__less__Suc2,axiom,
% 28.01/28.03 ! [V_i_2,V_M_2] :
% 28.01/28.03 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 28.01/28.03 => 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))))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_ex__bij__betw__nat__finite__1,axiom,
% 28.01/28.03 ! [V_M_2,T_b] :
% 28.01/28.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 28.01/28.03 => ? [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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_inj__on__diff__nat,axiom,
% 28.01/28.03 ! [V_k_2,V_N_2] :
% 28.01/28.03 ( ! [B_x] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 28.01/28.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_CollectI,axiom,
% 28.01/28.03 ! [T_b,V_a_2,V_P_2] :
% 28.01/28.03 ( hBOOL(hAPP(V_P_2,V_a_2))
% 28.01/28.03 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_finite__Collect__conjI,axiom,
% 28.01/28.03 ! [V_Q_2,V_P_2,T_b] :
% 28.01/28.03 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 28.01/28.03 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) )
% 28.01/28.03 => 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)))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_finite__Collect__less__nat,axiom,
% 28.01/28.03 ! [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)))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_finite__Collect__le__nat,axiom,
% 28.01/28.03 ! [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)))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Collect__def,axiom,
% 28.01/28.03 ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),V_P_2) = V_P_2 ).
% 28.01/28.03
% 28.01/28.03 fof(fact_empty__Collect__eq,axiom,
% 28.01/28.03 ! [V_P_2,T_b] :
% 28.01/28.03 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_P_2)
% 28.01/28.03 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Collect__empty__eq,axiom,
% 28.01/28.03 ! [V_P_2,T_b] :
% 28.01/28.03 ( hAPP(c_Set_OCollect(T_b),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Collect__mem__eq,axiom,
% 28.01/28.03 ! [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 ).
% 28.01/28.03
% 28.01/28.03 fof(fact_mem__Collect__eq,axiom,
% 28.01/28.03 ! [V_P_2,V_a_2,T_b] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 28.01/28.03 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_CollectD,axiom,
% 28.01/28.03 ! [V_P_2,V_a_2,T_b] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 28.01/28.03 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_CollectE,axiom,
% 28.01/28.03 ! [V_P_2,V_a_2,T_b] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 28.01/28.03 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_empty__def,axiom,
% 28.01/28.03 ! [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)) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_finite__Collect__disjI,axiom,
% 28.01/28.03 ! [V_Q_2,V_P_2,T_b] :
% 28.01/28.03 ( 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))))
% 28.01/28.03 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 28.01/28.03 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_insert__Collect,axiom,
% 28.01/28.03 ! [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)) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_UNIV__def,axiom,
% 28.01/28.03 ! [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)) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Collect__disj__eq,axiom,
% 28.01/28.03 ! [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)) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Collect__conj__eq,axiom,
% 28.01/28.03 ! [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)) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Collect__neg__eq,axiom,
% 28.01/28.03 ! [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)) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_vimage__Collect__eq,axiom,
% 28.01/28.03 ! [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)) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_insert__compr,axiom,
% 28.01/28.03 ! [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))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_insert__compr__raw,axiom,
% 28.01/28.03 ! [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))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Un__def,axiom,
% 28.01/28.03 ! [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))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Int__def,axiom,
% 28.01/28.03 ! [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))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Int__Collect,axiom,
% 28.01/28.03 ! [V_P_2,V_A_2,V_x_2,T_b] :
% 28.01/28.03 ( 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))))
% 28.01/28.03 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.03 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_singleton__conv2,axiom,
% 28.01/28.03 ! [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))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_singleton__conv,axiom,
% 28.01/28.03 ! [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))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Collect__conv__if2,axiom,
% 28.01/28.03 ! [T_b,V_a_2,V_P_2] :
% 28.01/28.03 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 28.01/28.03 => 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))) )
% 28.01/28.03 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 28.01/28.03 => 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)) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Collect__conv__if,axiom,
% 28.01/28.03 ! [T_b,V_a_2,V_P_2] :
% 28.01/28.03 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 28.01/28.03 => 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))) )
% 28.01/28.03 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 28.01/28.03 => 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)) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_set__diff__eq,axiom,
% 28.01/28.03 ! [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)))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_finite__Collect__not,axiom,
% 28.01/28.03 ! [V_P_2,T_b] :
% 28.01/28.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 28.01/28.03 => ( 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))))
% 28.01/28.03 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_insert__def,axiom,
% 28.01/28.03 ! [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) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Compl__eq,axiom,
% 28.01/28.03 ! [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))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_vimage__def,axiom,
% 28.01/28.03 ! [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)) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Collect__imp__eq,axiom,
% 28.01/28.03 ! [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)) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_finite__M__bounded__by__nat,axiom,
% 28.01/28.03 ! [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))))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setsum__setsum__restrict,axiom,
% 28.01/28.03 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__add(T_d)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 28.01/28.03 => 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) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_if__image__distrib,axiom,
% 28.01/28.03 ! [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))))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_nat__seg__image__imp__finite,axiom,
% 28.01/28.03 ! [V_n_2,V_f_2,T_b,V_A_2] :
% 28.01/28.03 ( 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)))
% 28.01/28.03 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setsum__restrict__set_H,axiom,
% 28.01/28.03 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => 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) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setsum__image__gen,axiom,
% 28.01/28.03 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.01/28.03 => 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)) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setsum__cases,axiom,
% 28.01/28.03 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => 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))))) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 28.01/28.03 ! [V_n_2,V_m_2] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 28.01/28.03 <=> 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setsum__multicount,axiom,
% 28.01/28.03 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 28.01/28.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 28.01/28.03 => ( ! [B_x] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 28.01/28.03 => 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 )
% 28.01/28.03 => 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)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_ex__bij__betw__nat__finite,axiom,
% 28.01/28.03 ! [V_M_2,T_b] :
% 28.01/28.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 28.01/28.03 => ? [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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_lfp__induct__set,axiom,
% 28.01/28.03 ! [V_P_2,V_f_2,V_a_2,T_b] :
% 28.01/28.03 ( 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)))
% 28.01/28.03 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 28.01/28.03 => ( ! [B_x] :
% 28.01/28.03 ( 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)))))
% 28.01/28.03 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.01/28.03 => hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_def__lfp__induct__set,axiom,
% 28.01/28.03 ! [V_P_2,V_a_2,V_f_2,T_b,V_A_2] :
% 28.01/28.03 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 28.01/28.03 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.03 => ( ! [B_x] :
% 28.01/28.03 ( 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)))))
% 28.01/28.03 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.01/28.03 => hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_def__Collect__coinduct,axiom,
% 28.01/28.03 ! [V_X_2,V_a_2,V_P_2,T_b,V_A_2] :
% 28.01/28.03 ( 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))
% 28.01/28.03 => ( 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))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 28.01/28.03 => ( ! [B_z] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_z),V_X_2))
% 28.01/28.03 => 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)) )
% 28.01/28.03 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_finite__Collect__subsets,axiom,
% 28.01/28.03 ! [V_A_2,T_b] :
% 28.01/28.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => 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)))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Pow__def,axiom,
% 28.01/28.03 ! [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)) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 28.01/28.03 ! [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))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 28.01/28.03 ! [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)))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 28.01/28.03 ! [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)))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setsum__multicount__gen,axiom,
% 28.01/28.03 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 28.01/28.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 28.01/28.03 => ( ! [B_x] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 28.01/28.03 => 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) )
% 28.01/28.03 => 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) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_inf__Sup2__distrib,axiom,
% 28.01/28.03 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Lattices_Odistrib__lattice(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.03 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => 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))))))) ) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_inf__Sup1__distrib,axiom,
% 28.01/28.03 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Lattices_Odistrib__lattice(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => 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))))) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_sup__Inf2__distrib,axiom,
% 28.01/28.03 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Lattices_Odistrib__lattice(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.03 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => 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))))))) ) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_sup__Inf1__distrib,axiom,
% 28.01/28.03 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Lattices_Odistrib__lattice(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => 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))))) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_finite__image__set,axiom,
% 28.01/28.03 ! [V_f_2,T_c,V_P_2,T_b] :
% 28.01/28.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 28.01/28.03 => 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))))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_finite__Collect__bounded__ex,axiom,
% 28.01/28.03 ! [V_Q_2,T_c,V_P_2,T_b] :
% 28.01/28.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 28.01/28.03 => ( 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)))))
% 28.01/28.03 <=> ! [B_y] :
% 28.01/28.03 ( hBOOL(hAPP(V_P_2,B_y))
% 28.01/28.03 => 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)))) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Pow__Compl,axiom,
% 28.01/28.03 ! [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))))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_add__Min__commute,axiom,
% 28.01/28.03 ! [V_k_2,V_N_2,T_b] :
% 28.01/28.03 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.01/28.03 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => 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))))) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_add__Max__commute,axiom,
% 28.01/28.03 ! [V_k_2,V_N_2,T_b] :
% 28.01/28.03 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.01/28.03 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => 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))))) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_finite__conv__nat__seg__image,axiom,
% 28.01/28.03 ! [V_A_2,T_b] :
% 28.01/28.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 <=> ? [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))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_pigeonhole__infinite,axiom,
% 28.01/28.03 ! [V_f_2,T_c,V_A_2,T_b] :
% 28.01/28.03 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 28.01/28.03 => ? [B_x] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.03 & ~ 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)))))) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_diff__nat__eq__if,axiom,
% 28.01/28.03 ! [V_z_2,V_z_H_2] :
% 28.01/28.03 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 28.01/28.03 => 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) )
% 28.01/28.03 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 28.01/28.03 => 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)) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_not__neg__0,axiom,
% 28.01/28.03 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_not__neg__int,axiom,
% 28.01/28.03 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_not__neg__1,axiom,
% 28.01/28.03 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_minus__Min__eq__Max,axiom,
% 28.01/28.03 ! [V_S_2,T_b] :
% 28.01/28.03 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.01/28.03 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => 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)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_minus__Max__eq__Min,axiom,
% 28.01/28.03 ! [V_S_2,T_b] :
% 28.01/28.03 ( class_Groups_Olinordered__ab__group__add(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.01/28.03 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => 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)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Min_Osingleton,axiom,
% 28.01/28.03 ! [V_x_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => 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 ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Max_Osingleton,axiom,
% 28.01/28.03 ! [V_x_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => 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 ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_not__neg__eq__ge__0,axiom,
% 28.01/28.03 ! [V_x_2] :
% 28.01/28.03 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 28.01/28.03 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_neg__def,axiom,
% 28.01/28.03 ! [V_Z_2] :
% 28.01/28.03 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 28.01/28.03 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_neg__nat,axiom,
% 28.01/28.03 ! [V_z] :
% 28.01/28.03 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 28.01/28.03 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_not__neg__nat,axiom,
% 28.01/28.03 ! [V_z] :
% 28.01/28.03 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 28.01/28.03 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Max__ge,axiom,
% 28.01/28.03 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.03 => 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))) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Min__le,axiom,
% 28.01/28.03 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.03 => 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)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Min__in,axiom,
% 28.01/28.03 ! [V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Max__in,axiom,
% 28.01/28.03 ! [V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_neg__zminus__int,axiom,
% 28.01/28.03 ! [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))))) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Max__mono,axiom,
% 28.01/28.03 ! [V_N_2,V_M_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 28.01/28.03 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.01/28.03 => 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))) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Min__antimono,axiom,
% 28.01/28.03 ! [V_N_2,V_M_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 28.01/28.03 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.01/28.03 => 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))) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Min_Oremove,axiom,
% 28.01/28.03 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.03 => ( ( hAPP(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))
% 28.01/28.03 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 28.01/28.03 & ( hAPP(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))
% 28.01/28.03 => 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)))))) ) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Max_Oremove,axiom,
% 28.01/28.03 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.03 => ( ( hAPP(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))
% 28.01/28.03 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 28.01/28.03 & ( hAPP(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))
% 28.01/28.03 => 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)))))) ) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setsum__SucD,axiom,
% 28.01/28.03 ! [V_n_2,V_A_2,V_f_2,T_b] :
% 28.01/28.03 ( 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)
% 28.01/28.03 => ? [B_x] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.03 & 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))) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Cantor__Bernstein,axiom,
% 28.01/28.03 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.03 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.01/28.03 => ( 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))
% 28.01/28.03 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 28.01/28.03 => ( 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))
% 28.01/28.03 => ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod_Oremove,axiom,
% 28.01/28.03 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.03 => 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)))))) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_max__of__mono,axiom,
% 28.01/28.03 ! [V_n_2,V_m_2,V_f_2,T_b,T_c] :
% 28.01/28.03 ( ( class_Orderings_Olinorder(T_c)
% 28.01/28.03 & class_Orderings_Olinorder(T_b) )
% 28.01/28.03 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 28.01/28.03 => 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)) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__of__mono,axiom,
% 28.01/28.03 ! [V_n_2,V_m_2,V_f_2,T_b,T_c] :
% 28.01/28.03 ( ( class_Orderings_Olinorder(T_c)
% 28.01/28.03 & class_Orderings_Olinorder(T_b) )
% 28.01/28.03 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 28.01/28.03 => 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)) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_of__int__setprod,axiom,
% 28.01/28.03 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.03 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 28.01/28.03 & class_Rings_Oring__1(T_b) )
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 28.01/28.03 ! [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)) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_le__max__iff__disj,axiom,
% 28.01/28.03 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( 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)))
% 28.01/28.03 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 28.01/28.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Ole__supE,axiom,
% 28.01/28.03 ! [V_x,V_b,V_a,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( 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))
% 28.01/28.03 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 28.01/28.03 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Osup__mono,axiom,
% 28.01/28.03 ! [V_d,V_b,V_c,V_a,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 28.01/28.03 => 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))) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Osup__least,axiom,
% 28.01/28.03 ! [V_z,V_x,V_y,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 28.01/28.03 => 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)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Ole__supI,axiom,
% 28.01/28.03 ! [V_b,V_x,V_a,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 28.01/28.03 => 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)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Osup__absorb1,axiom,
% 28.01/28.03 ! [V_x,V_y,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 28.01/28.03 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Osup__absorb2,axiom,
% 28.01/28.03 ! [V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.01/28.03 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Ole__supI2,axiom,
% 28.01/28.03 ! [V_a,V_b,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 28.01/28.03 => 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))) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Ole__supI1,axiom,
% 28.01/28.03 ! [V_b,V_a,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 28.01/28.03 => 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))) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Ole__sup__iff,axiom,
% 28.01/28.03 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( 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))
% 28.01/28.03 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 28.01/28.03 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Ole__iff__sup,axiom,
% 28.01/28.03 ! [V_y_2,V_x_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.01/28.03 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_le__maxI2,axiom,
% 28.01/28.03 ! [V_x,V_y,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_le__maxI1,axiom,
% 28.01/28.03 ! [V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__le__iff__disj,axiom,
% 28.01/28.03 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( 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))
% 28.01/28.03 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 28.01/28.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Ole__infE,axiom,
% 28.01/28.03 ! [V_b,V_a,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( 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)))
% 28.01/28.03 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 28.01/28.03 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oinf__mono,axiom,
% 28.01/28.03 ! [V_d,V_b,V_c,V_a,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 28.01/28.03 => 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))) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oinf__greatest,axiom,
% 28.01/28.03 ! [V_z,V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 28.01/28.03 => 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))) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Ole__infI,axiom,
% 28.01/28.03 ! [V_b,V_a,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 28.01/28.03 => 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))) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oinf__absorb2,axiom,
% 28.01/28.03 ! [V_x,V_y,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 28.01/28.03 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oinf__absorb1,axiom,
% 28.01/28.03 ! [V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.01/28.03 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Ole__infI2,axiom,
% 28.01/28.03 ! [V_a,V_x,V_b,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 28.01/28.03 => 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)) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Ole__infI1,axiom,
% 28.01/28.03 ! [V_b,V_x,V_a,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 28.01/28.03 => 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)) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Ole__inf__iff,axiom,
% 28.01/28.03 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( 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)))
% 28.01/28.03 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.01/28.03 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Ole__iff__inf,axiom,
% 28.01/28.03 ! [V_y_2,V_x_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.01/28.03 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oinf__le2,axiom,
% 28.01/28.03 ! [V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oinf__le1,axiom,
% 28.01/28.03 ! [V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oless__supI2,axiom,
% 28.01/28.03 ! [V_a,V_b,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 28.01/28.03 => 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))) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oless__supI1,axiom,
% 28.01/28.03 ! [V_b,V_a,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 28.01/28.03 => 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))) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_max__less__iff__conj,axiom,
% 28.01/28.03 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( 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))
% 28.01/28.03 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 28.01/28.03 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_less__max__iff__disj,axiom,
% 28.01/28.03 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( 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)))
% 28.01/28.03 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 28.01/28.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oless__infI2,axiom,
% 28.01/28.03 ! [V_a,V_x,V_b,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 28.01/28.03 => 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)) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oless__infI1,axiom,
% 28.01/28.03 ! [V_b,V_x,V_a,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 28.01/28.03 => 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)) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__less__iff__disj,axiom,
% 28.01/28.03 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( 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))
% 28.01/28.03 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 28.01/28.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__less__iff__conj,axiom,
% 28.01/28.03 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( 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)))
% 28.01/28.03 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 28.01/28.03 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_max__add__distrib__left,axiom,
% 28.01/28.03 ! [V_z,V_y,V_x,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__add__distrib__left,axiom,
% 28.01/28.03 ! [V_z,V_y,V_x,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_max__diff__distrib__left,axiom,
% 28.01/28.03 ! [V_z,V_y,V_x,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__diff__distrib__left,axiom,
% 28.01/28.03 ! [V_z,V_y,V_x,T_a] :
% 28.01/28.03 ( class_Groups_Oordered__ab__group__add(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_max__0L,axiom,
% 28.01/28.03 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 28.01/28.03
% 28.01/28.03 fof(fact_max__0R,axiom,
% 28.01/28.03 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__0L,axiom,
% 28.01/28.03 ! [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) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__0R,axiom,
% 28.01/28.03 ! [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) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_max__Suc__Suc,axiom,
% 28.01/28.03 ! [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)) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__Suc__Suc,axiom,
% 28.01/28.03 ! [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)) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Odistrib__inf__le,axiom,
% 28.01/28.03 ! [V_z,V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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)))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Odistrib__sup__le,axiom,
% 28.01/28.03 ! [V_z,V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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)))) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Max_Oidem,axiom,
% 28.01/28.03 ! [V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Min_Oidem,axiom,
% 28.01/28.03 ! [V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Osup_Oidem,axiom,
% 28.01/28.03 ! [V_a,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oinf_Oidem,axiom,
% 28.01/28.03 ! [V_a,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Osup_Ocommute,axiom,
% 28.01/28.03 ! [V_b,V_a,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Osup__commute,axiom,
% 28.01/28.03 ! [V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oinf_Ocommute,axiom,
% 28.01/28.03 ! [V_b,V_a,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oinf__commute,axiom,
% 28.01/28.03 ! [V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Osup__inf__absorb,axiom,
% 28.01/28.03 ! [V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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 ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 28.01/28.03 ! [V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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 ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 28.01/28.03 ! [V_b,V_a,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Osup__left__idem,axiom,
% 28.01/28.03 ! [V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 28.01/28.03 ! [V_b,V_a,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oinf__left__idem,axiom,
% 28.01/28.03 ! [V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 28.01/28.03 ! [V_c,V_a,V_b,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Osup__left__commute,axiom,
% 28.01/28.03 ! [V_z,V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 28.01/28.03 ! [V_c,V_a,V_b,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oinf__left__commute,axiom,
% 28.01/28.03 ! [V_z,V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 28.01/28.03 ! [V_z,V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 28.01/28.03 ! [V_z,V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Osup_Oassoc,axiom,
% 28.01/28.03 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Osup__assoc,axiom,
% 28.01/28.03 ! [V_z,V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oinf_Oassoc,axiom,
% 28.01/28.03 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oinf__assoc,axiom,
% 28.01/28.03 ! [V_z,V_y,V_x,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 28.01/28.03 ! [V_x,V_z,V_y,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 28.01/28.03 ! [V_x,V_z,V_y,T_a] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_minus__max__eq__min,axiom,
% 28.01/28.03 ! [V_y,V_x,T_a] :
% 28.01/28.03 ( class_Groups_Olinordered__ab__group__add(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_minus__min__eq__max,axiom,
% 28.01/28.03 ! [V_y,V_x,T_a] :
% 28.01/28.03 ( class_Groups_Olinordered__ab__group__add(T_a)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_of__nat__setprod,axiom,
% 28.01/28.03 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.03 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 28.01/28.03 & class_Rings_Osemiring__1(T_b) )
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_int__setprod,axiom,
% 28.01/28.03 ! [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) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__diff,axiom,
% 28.01/28.03 ! [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) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Int__atLeastLessThan,axiom,
% 28.01/28.03 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Int__atLeastAtMost,axiom,
% 28.01/28.03 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Int__greaterThanAtMost,axiom,
% 28.01/28.03 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_inf__min,axiom,
% 28.01/28.03 ! [T_b] :
% 28.01/28.03 ( ( class_Lattices_Osemilattice__inf(T_b)
% 28.01/28.03 & class_Orderings_Olinorder(T_b) )
% 28.01/28.03 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_sup__max,axiom,
% 28.01/28.03 ! [T_b] :
% 28.01/28.03 ( ( class_Lattices_Osemilattice__sup(T_b)
% 28.01/28.03 & class_Orderings_Olinorder(T_b) )
% 28.01/28.03 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Int__greaterThanLessThan,axiom,
% 28.01/28.03 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod__timesf,axiom,
% 28.01/28.03 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_b)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod__1,axiom,
% 28.01/28.03 ! [V_A_2,T_c,T_b] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_b)
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_abs__setprod,axiom,
% 28.01/28.03 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.03 ( class_Fields_Olinordered__field(T_b)
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 28.01/28.03 ! [T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 28.01/28.03 ! [T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 28.01/28.03 ! [V_A_2,V_f_2,T_b] :
% 28.01/28.03 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.03 & class_Groups_Ocomm__monoid__mult(T_b) )
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod__zero,axiom,
% 28.01/28.03 ! [V_f_2,V_A_2,T_b,T_c] :
% 28.01/28.03 ( class_Rings_Ocomm__semiring__1(T_c)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( ? [B_x] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.03 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 28.01/28.03 => 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) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod__zero__iff,axiom,
% 28.01/28.03 ! [V_f_2,V_A_2,T_b,T_c] :
% 28.01/28.03 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 28.01/28.03 & class_Rings_Ono__zero__divisors(T_c) )
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( 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)
% 28.01/28.03 <=> ? [B_x] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.03 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod__empty,axiom,
% 28.01/28.03 ! [V_f_2,T_c,T_b] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_b)
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod_Oempty,axiom,
% 28.01/28.03 ! [V_g_2,T_c,T_b] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_b)
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod__infinite,axiom,
% 28.01/28.03 ! [V_f_2,V_A_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.03 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => 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) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod_Oinfinite,axiom,
% 28.01/28.03 ! [V_g_2,V_A_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.03 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => 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) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod__eq__1__iff,axiom,
% 28.01/28.03 ! [V_f_2,V_F_2,T_b] :
% 28.01/28.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 28.01/28.03 => ( 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)
% 28.01/28.03 <=> ! [B_x] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 28.01/28.03 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 28.01/28.03 ! [V_f_2,V_A_2,T_b] :
% 28.01/28.03 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.03 & class_Groups_Ocomm__monoid__mult(T_b) )
% 28.01/28.03 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 28.01/28.03 => 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)) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_nat__minus__add__max,axiom,
% 28.01/28.03 ! [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) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod_Odistrib,axiom,
% 28.01/28.03 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => 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)) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod__pos__nat__iff,axiom,
% 28.01/28.03 ! [V_f_2,V_S_2,T_b] :
% 28.01/28.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.01/28.03 => ( 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)))
% 28.01/28.03 <=> ! [B_x] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 28.01/28.03 => 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))) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod__reindex__cong,axiom,
% 28.01/28.03 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_d)
% 28.01/28.03 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.01/28.03 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 28.01/28.03 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 28.01/28.03 => 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) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod__reindex,axiom,
% 28.01/28.03 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_d)
% 28.01/28.03 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 28.01/28.03 => 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) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_max__Suc1,axiom,
% 28.01/28.03 ! [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) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_max__Suc2,axiom,
% 28.01/28.03 ! [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) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod__delta_H,axiom,
% 28.01/28.03 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.01/28.03 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.01/28.03 => 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) )
% 28.01/28.03 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.01/28.03 => 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) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod__delta,axiom,
% 28.01/28.03 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.01/28.03 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.01/28.03 => 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) )
% 28.01/28.03 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.01/28.03 => 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) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Max_Oin__idem,axiom,
% 28.01/28.03 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.03 => 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) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Min_Oin__idem,axiom,
% 28.01/28.03 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.03 => 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) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Omono__sup,axiom,
% 28.01/28.03 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 28.01/28.03 ( ( class_Lattices_Osemilattice__sup(T_c)
% 28.01/28.03 & class_Orderings_Olinorder(T_b) )
% 28.01/28.03 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 28.01/28.03 => 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)))) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Omono__inf,axiom,
% 28.01/28.03 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 28.01/28.03 ( ( class_Lattices_Osemilattice__inf(T_c)
% 28.01/28.03 & class_Orderings_Olinorder(T_b) )
% 28.01/28.03 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 28.01/28.03 => 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)))) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Int__atLeastAtMostR1,axiom,
% 28.01/28.03 ! [V_d_2,V_c_2,V_b_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Int__atLeastAtMostL1,axiom,
% 28.01/28.03 ! [V_d_2,V_b_2,V_a_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => 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)) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Int__atLeastAtMostR2,axiom,
% 28.01/28.03 ! [V_d_2,V_c_2,V_a_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Int__atLeastAtMostL2,axiom,
% 28.01/28.03 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => 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) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Max_OF__eq,axiom,
% 28.01/28.03 ! [V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => 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) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Min_OF__eq,axiom,
% 28.01/28.03 ! [V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => 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) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod_Oinsert,axiom,
% 28.01/28.03 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.03 => 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)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod__insert,axiom,
% 28.01/28.03 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.03 => 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)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod__Un__Int,axiom,
% 28.01/28.03 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.03 => 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)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod_Ounion__inter,axiom,
% 28.01/28.03 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.03 => 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)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod_Oreindex,axiom,
% 28.01/28.03 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 28.01/28.03 => 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) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod_Oeq__fold,axiom,
% 28.01/28.03 ! [V_g_2,V_A_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => 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) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod_OF__eq,axiom,
% 28.01/28.03 ! [V_g_2,V_A_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.03 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => 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) )
% 28.01/28.03 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => 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) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__Suc1,axiom,
% 28.01/28.03 ! [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) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__Suc2,axiom,
% 28.01/28.03 ! [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) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Ofold1__belowI,axiom,
% 28.01/28.03 ! [V_a_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.03 => 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)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_fold1__below__iff,axiom,
% 28.01/28.03 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => ( 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))
% 28.01/28.03 <=> ? [B_x] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.03 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 28.01/28.03 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => ( 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)))
% 28.01/28.03 <=> ! [B_x] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_fold1__strict__below__iff,axiom,
% 28.01/28.03 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => ( 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))
% 28.01/28.03 <=> ? [B_x] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.03 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_strict__below__fold1__iff,axiom,
% 28.01/28.03 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => ( 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)))
% 28.01/28.03 <=> ! [B_x] :
% 28.01/28.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Max__insert,axiom,
% 28.01/28.03 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => 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)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Min__insert,axiom,
% 28.01/28.03 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => 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)) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Max_Osubset__idem,axiom,
% 28.01/28.03 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.01/28.03 => 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) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Min_Osubset__idem,axiom,
% 28.01/28.03 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.01/28.03 => 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) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Max__Un,axiom,
% 28.01/28.03 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.03 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => 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)) ) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Min__Un,axiom,
% 28.01/28.03 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.03 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => 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)) ) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod_Oinsert__remove,axiom,
% 28.01/28.03 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => 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)))))) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod__Un__disjoint,axiom,
% 28.01/28.03 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.03 => ( 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))
% 28.01/28.03 => 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)) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_setprod_Ounion__disjoint,axiom,
% 28.01/28.03 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 28.01/28.03 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.03 => ( 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))
% 28.01/28.03 => 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)) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Max_Oinsert,axiom,
% 28.01/28.03 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => 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)) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Min_Oinsert,axiom,
% 28.01/28.03 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => 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)) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_fold1__antimono,axiom,
% 28.01/28.03 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.03 => 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))) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Max_Oinsert__remove,axiom,
% 28.01/28.03 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( ( hAPP(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))
% 28.01/28.03 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 28.01/28.03 & ( hAPP(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))
% 28.01/28.03 => 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)))))) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Max_Ounion__inter,axiom,
% 28.01/28.03 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.03 => ( 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))
% 28.01/28.03 => 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)) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Max_Ounion__disjoint,axiom,
% 28.01/28.03 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.03 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.03 => ( 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))
% 28.01/28.03 => 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)) ) ) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Min_Oinsert__remove,axiom,
% 28.01/28.03 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( ( hAPP(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))
% 28.01/28.03 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 28.01/28.03 & ( hAPP(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))
% 28.01/28.03 => 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)))))) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Min_Ounion__inter,axiom,
% 28.01/28.03 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.03 ( class_Orderings_Olinorder(T_b)
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.03 => ( 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))
% 28.01/28.03 => 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)) ) ) ) ) ).
% 28.01/28.03
% 28.01/28.03 fof(fact_Min_Ounion__disjoint,axiom,
% 28.01/28.04 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.04 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => ( 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))
% 28.01/28.04 => 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)) ) ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_dual__min,axiom,
% 28.01/28.04 ! [T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_dual__max,axiom,
% 28.01/28.04 ! [T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_max__ord__max,axiom,
% 28.01/28.04 ! [T_b] :
% 28.01/28.04 ( class_Orderings_Oord(T_b)
% 28.01/28.04 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__ord__min,axiom,
% 28.01/28.04 ! [T_b] :
% 28.01/28.04 ( class_Orderings_Oord(T_b)
% 28.01/28.04 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 28.01/28.04 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => 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))))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_inf__nat__def,axiom,
% 28.01/28.04 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_sup__nat__def,axiom,
% 28.01/28.04 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 28.01/28.04 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.04 => 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) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 28.01/28.04 ! [V_x_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => 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 ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 28.01/28.04 ! [V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => 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) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 28.01/28.04 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => 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)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 28.01/28.04 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.01/28.04 => 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) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 28.01/28.04 ! [V_a_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.04 => 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 ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 28.01/28.04 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.04 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => 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)) ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 28.01/28.04 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => 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)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 28.01/28.04 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( ( hAPP(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))
% 28.01/28.04 => 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 )
% 28.01/28.04 & ( hAPP(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))
% 28.01/28.04 => 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)))))) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 28.01/28.04 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.04 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => ( 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))
% 28.01/28.04 => 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)) ) ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 28.01/28.04 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.04 => ( 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))
% 28.01/28.04 => 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)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 28.01/28.04 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.04 => ( ( hAPP(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))
% 28.01/28.04 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 28.01/28.04 & ( hAPP(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))
% 28.01/28.04 => 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)))))) ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 28.01/28.04 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.04 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => 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))))))) ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 28.01/28.04 ! [V_f_2,V_A_2,T_b] :
% 28.01/28.04 ( ! [B_x] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.04 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 28.01/28.04 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.04 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => 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))))))) ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 28.01/28.04 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => 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))))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 28.01/28.04 ! [V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => ( ! [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))))))
% 28.01/28.04 => 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)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 28.01/28.04 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.04 => 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) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 28.01/28.04 ! [V_x_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => 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 ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 28.01/28.04 ! [V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => 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) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 28.01/28.04 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => 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)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 28.01/28.04 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.01/28.04 => 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) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 28.01/28.04 ! [V_a_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.04 => 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 ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 28.01/28.04 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.04 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => 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)) ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 28.01/28.04 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => 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)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 28.01/28.04 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( ( hAPP(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))
% 28.01/28.04 => 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 )
% 28.01/28.04 & ( hAPP(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))
% 28.01/28.04 => 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)))))) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 28.01/28.04 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.04 => ( 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))
% 28.01/28.04 => 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)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 28.01/28.04 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.04 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => ( 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))
% 28.01/28.04 => 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)) ) ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 28.01/28.04 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.04 => ( ( hAPP(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))
% 28.01/28.04 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 28.01/28.04 & ( hAPP(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))
% 28.01/28.04 => 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)))))) ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OInf__le__Sup,axiom,
% 28.01/28.04 ! [V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 28.01/28.04 ! [V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => ( ! [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))))))
% 28.01/28.04 => 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)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_Max_Oclosed,axiom,
% 28.01/28.04 ! [V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => ( ! [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))))))
% 28.01/28.04 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_Min_Oclosed,axiom,
% 28.01/28.04 ! [V_A_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => ( ! [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))))))
% 28.01/28.04 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 28.01/28.04 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 28.01/28.04 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.04 => ( ! [B_x] :
% 28.01/28.04 ( 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)))
% 28.01/28.04 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 28.01/28.04 => 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)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_setprod__Un__one,axiom,
% 28.01/28.04 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 28.01/28.04 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 28.01/28.04 => ( ! [B_x] :
% 28.01/28.04 ( 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)))
% 28.01/28.04 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 28.01/28.04 => 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)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_setprod__gen__delta,axiom,
% 28.01/28.04 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 28.01/28.04 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.01/28.04 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.01/28.04 => 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)))) )
% 28.01/28.04 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 28.01/28.04 => 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)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_setprod__diff1,axiom,
% 28.01/28.04 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 28.01/28.04 ( class_Fields_Ofield(T_c)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 28.01/28.04 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.04 => 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)) )
% 28.01/28.04 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.04 => 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) ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 28.01/28.04 ! [V_N_2,V_h_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( ! [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))
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.01/28.04 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => 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)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 28.01/28.04 ! [V_n,V_x] :
% 28.01/28.04 ( c_Nat__Transfer_Ois__nat(V_x)
% 28.01/28.04 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_of__int__power,axiom,
% 28.01/28.04 ! [V_n,V_z,T_a] :
% 28.01/28.04 ( class_Rings_Oring__1(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 28.01/28.04 ! [V_x,T_a] :
% 28.01/28.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.01/28.04 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zpower__zpower,axiom,
% 28.01/28.04 ! [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)) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__zero,axiom,
% 28.01/28.04 ! [V_a,T_a] :
% 28.01/28.04 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__zero__left,axiom,
% 28.01/28.04 ! [V_a,T_a] :
% 28.01/28.04 ( class_Rings_Odivision__ring(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_add__divide__distrib,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Odivision__ring(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_times__divide__eq__right,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Odivision__ring(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_diff__divide__distrib,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Odivision__ring(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 28.01/28.04 ! [V_q,V_y,V_x,T_a] :
% 28.01/28.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__1,axiom,
% 28.01/28.04 ! [V_a,T_a] :
% 28.01/28.04 ( class_Rings_Odivision__ring(T_a)
% 28.01/28.04 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_minus__divide__left,axiom,
% 28.01/28.04 ! [V_b,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Odivision__ring(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_int__power,axiom,
% 28.01/28.04 ! [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) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zpower__int,axiom,
% 28.01/28.04 ! [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)) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 28.01/28.04 ! [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)) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 28.01/28.04 ! [V_q,V_p,V_x,T_a] :
% 28.01/28.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 28.01/28.04 ! [V_n,V_x] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_nat__power__eq,axiom,
% 28.01/28.04 ! [V_n,V_z] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_setsum__divide__distrib,axiom,
% 28.01/28.04 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.04 ( class_Fields_Ofield(T_b)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_nonzero__eq__divide__eq,axiom,
% 28.01/28.04 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.01/28.04 ( class_Rings_Odivision__ring(T_b)
% 28.01/28.04 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.04 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 28.01/28.04 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_nonzero__divide__eq__eq,axiom,
% 28.01/28.04 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 28.01/28.04 ( class_Rings_Odivision__ring(T_b)
% 28.01/28.04 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.04 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 28.01/28.04 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__eq__imp,axiom,
% 28.01/28.04 ! [V_a,V_b,V_c,T_a] :
% 28.01/28.04 ( class_Rings_Odivision__ring(T_a)
% 28.01/28.04 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 28.01/28.04 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_eq__divide__imp,axiom,
% 28.01/28.04 ! [V_b,V_a,V_c,T_a] :
% 28.01/28.04 ( class_Rings_Odivision__ring(T_a)
% 28.01/28.04 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 28.01/28.04 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__self__if,axiom,
% 28.01/28.04 ! [V_a,T_a] :
% 28.01/28.04 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 28.01/28.04 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 28.01/28.04 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__self,axiom,
% 28.01/28.04 ! [V_a,T_a] :
% 28.01/28.04 ( class_Rings_Odivision__ring(T_a)
% 28.01/28.04 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_right__inverse__eq,axiom,
% 28.01/28.04 ! [V_a_2,V_b_2,T_b] :
% 28.01/28.04 ( class_Rings_Odivision__ring(T_b)
% 28.01/28.04 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.04 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
% 28.01/28.04 <=> V_a_2 = V_b_2 ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_nonzero__minus__divide__right,axiom,
% 28.01/28.04 ! [V_a,V_b,T_a] :
% 28.01/28.04 ( class_Rings_Odivision__ring(T_a)
% 28.01/28.04 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_nonzero__minus__divide__divide,axiom,
% 28.01/28.04 ! [V_a,V_b,T_a] :
% 28.01/28.04 ( class_Rings_Odivision__ring(T_a)
% 28.01/28.04 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 28.01/28.04 ! [V_q,V_x,T_a] :
% 28.01/28.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 28.01/28.04 ! [V_q,V_x,T_a] :
% 28.01/28.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 28.01/28.04 ! [V_q,V_x,T_a] :
% 28.01/28.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 28.01/28.04 ! [V_x,T_a] :
% 28.01/28.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 28.01/28.04 ! [V_q,V_p,V_x,T_a] :
% 28.01/28.04 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 28.01/28.04 ! [V_n,V_x] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.01/28.04 => 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))) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zpower__zadd__distrib,axiom,
% 28.01/28.04 ! [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)) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_Ints__power,axiom,
% 28.01/28.04 ! [V_n_2,V_a_2,T_b] :
% 28.01/28.04 ( class_Rings_Oring__1(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 28.01/28.04 => 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))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_setprod__dividef,axiom,
% 28.01/28.04 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 28.01/28.04 ( class_Fields_Ofield__inverse__zero(T_c)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => 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)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_geometric__sum,axiom,
% 28.01/28.04 ! [V_n_2,V_x_2,T_b] :
% 28.01/28.04 ( class_Fields_Ofield(T_b)
% 28.01/28.04 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 28.01/28.04 => 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))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zero__le__zpower__abs,axiom,
% 28.01/28.04 ! [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))) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_setprod__constant,axiom,
% 28.01/28.04 ! [V_y_2,V_A_2,T_b,T_c] :
% 28.01/28.04 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => 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)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__eq__if,axiom,
% 28.01/28.04 ! [V_p,V_m] :
% 28.01/28.04 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.04 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 28.01/28.04 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.04 => 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)))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zero__less__zpower__abs__iff,axiom,
% 28.01/28.04 ! [V_n_2,V_x_2] :
% 28.01/28.04 ( 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)))
% 28.01/28.04 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.04 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_card__Pow,axiom,
% 28.01/28.04 ! [V_A_2,T_b] :
% 28.01/28.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__strict__mono,axiom,
% 28.01/28.04 ! [V_n,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.01/28.04 => 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))) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__diff,axiom,
% 28.01/28.04 ! [V_m,V_n,V_a,T_a] :
% 28.01/28.04 ( class_Fields_Ofield(T_a)
% 28.01/28.04 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 28.01/28.04 => 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)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_one__less__power,axiom,
% 28.01/28.04 ! [V_n,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__increasing__iff,axiom,
% 28.01/28.04 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_field__power__not__zero,axiom,
% 28.01/28.04 ! [V_n,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 28.01/28.04 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__Suc__0,axiom,
% 28.01/28.04 ! [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)) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 28.01/28.04 ! [V_m_2,V_x_2] :
% 28.01/28.04 ( 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))
% 28.01/28.04 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.04 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_nat__power__less__imp__less,axiom,
% 28.01/28.04 ! [V_n,V_m,V_i] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_nat__zero__less__power__iff,axiom,
% 28.01/28.04 ! [V_n_2,V_x_2] :
% 28.01/28.04 ( 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)))
% 28.01/28.04 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 28.01/28.04 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__mult__distrib,axiom,
% 28.01/28.04 ! [V_n,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Groups_Ocomm__monoid__mult(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__commutes,axiom,
% 28.01/28.04 ! [V_n,V_a,T_a] :
% 28.01/28.04 ( class_Groups_Omonoid__mult(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__one,axiom,
% 28.01/28.04 ! [V_n,T_a] :
% 28.01/28.04 ( class_Groups_Omonoid__mult(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_of__nat__power,axiom,
% 28.01/28.04 ! [V_n,V_m,T_a] :
% 28.01/28.04 ( class_Rings_Osemiring__1(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__mult,axiom,
% 28.01/28.04 ! [V_n,V_m,V_a,T_a] :
% 28.01/28.04 ( class_Groups_Omonoid__mult(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__divide,axiom,
% 28.01/28.04 ! [V_n,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Fields_Ofield__inverse__zero(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__abs,axiom,
% 28.01/28.04 ! [V_n,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__one__right,axiom,
% 28.01/28.04 ! [V_a,T_a] :
% 28.01/28.04 ( class_Groups_Omonoid__mult(T_a)
% 28.01/28.04 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zero__le__power,axiom,
% 28.01/28.04 ! [V_n,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.04 => 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))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__mono,axiom,
% 28.01/28.04 ! [V_n,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zero__less__power,axiom,
% 28.01/28.04 ! [V_n,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.04 => 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))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__eq__0__iff,axiom,
% 28.01/28.04 ! [V_n_2,V_a_2,T_b] :
% 28.01/28.04 ( ( class_Power_Opower(T_b)
% 28.01/28.04 & class_Rings_Omult__zero(T_b)
% 28.01/28.04 & class_Rings_Ono__zero__divisors(T_b)
% 28.01/28.04 & class_Rings_Ozero__neq__one(T_b) )
% 28.01/28.04 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.04 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.04 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_one__le__power,axiom,
% 28.01/28.04 ! [V_n,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 28.01/28.04 => 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))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__0__Suc,axiom,
% 28.01/28.04 ! [V_n,T_a] :
% 28.01/28.04 ( ( class_Power_Opower(T_a)
% 28.01/28.04 & class_Rings_Osemiring__0(T_a) )
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__inject__exp,axiom,
% 28.01/28.04 ! [V_n_2,V_m_2,V_a_2,T_b] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 28.01/28.04 => ( 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)
% 28.01/28.04 <=> V_m_2 = V_n_2 ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__Suc,axiom,
% 28.01/28.04 ! [V_n,V_a,T_a] :
% 28.01/28.04 ( class_Power_Opower(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__Suc2,axiom,
% 28.01/28.04 ! [V_n,V_a,T_a] :
% 28.01/28.04 ( class_Groups_Omonoid__mult(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_nat__one__le__power,axiom,
% 28.01/28.04 ! [V_n,V_i] :
% 28.01/28.04 ( 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))
% 28.01/28.04 => 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))) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__0,axiom,
% 28.01/28.04 ! [V_a,T_a] :
% 28.01/28.04 ( class_Power_Opower(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__add,axiom,
% 28.01/28.04 ! [V_n,V_m,V_a,T_a] :
% 28.01/28.04 ( class_Groups_Omonoid__mult(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_nonzero__power__divide,axiom,
% 28.01/28.04 ! [V_n,V_a,V_b,T_a] :
% 28.01/28.04 ( class_Fields_Ofield(T_a)
% 28.01/28.04 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__one__over,axiom,
% 28.01/28.04 ! [V_n,V_a,T_a] :
% 28.01/28.04 ( class_Fields_Ofield__inverse__zero(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_abs__power__minus,axiom,
% 28.01/28.04 ! [V_n,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__less__imp__less__base,axiom,
% 28.01/28.04 ! [V_b,V_n,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( 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)))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.01/28.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__inject__base,axiom,
% 28.01/28.04 ! [V_b,V_n,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( 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))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.01/28.04 => V_a = V_b ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__le__imp__le__base,axiom,
% 28.01/28.04 ! [V_b,V_n,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( 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))))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.01/28.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__less__power__Suc,axiom,
% 28.01/28.04 ! [V_n,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 28.01/28.04 => 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)))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__gt1__lemma,axiom,
% 28.01/28.04 ! [V_n,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 28.01/28.04 => 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)))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__0__left,axiom,
% 28.01/28.04 ! [V_n,T_a] :
% 28.01/28.04 ( ( class_Power_Opower(T_a)
% 28.01/28.04 & class_Rings_Osemiring__0(T_a) )
% 28.01/28.04 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.04 => 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) )
% 28.01/28.04 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.04 => 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) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__gt1,axiom,
% 28.01/28.04 ! [V_n,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 28.01/28.04 => 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)))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__strict__increasing__iff,axiom,
% 28.01/28.04 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__less__imp__less__exp,axiom,
% 28.01/28.04 ! [V_n,V_m,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__strict__increasing,axiom,
% 28.01/28.04 ! [V_a,V_N,V_n,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zero__le__power__abs,axiom,
% 28.01/28.04 ! [V_n,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.04 => 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))) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__increasing,axiom,
% 28.01/28.04 ! [V_a,V_N,V_n,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__minus,axiom,
% 28.01/28.04 ! [V_n,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Oring__1(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__Suc__less,axiom,
% 28.01/28.04 ! [V_n,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__eq__imp__eq__base,axiom,
% 28.01/28.04 ! [V_b,V_n,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( 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)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.01/28.04 => V_a = V_b ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__Suc__less__one,axiom,
% 28.01/28.04 ! [V_n,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__strict__decreasing,axiom,
% 28.01/28.04 ! [V_a,V_N,V_n,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 28.01/28.04 => 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))) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__decreasing,axiom,
% 28.01/28.04 ! [V_a,V_N,V_n,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 28.01/28.04 => 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))) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__le__imp__le__exp,axiom,
% 28.01/28.04 ! [V_n,V_m,V_a,T_a] :
% 28.01/28.04 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_le__divide__eq,axiom,
% 28.01/28.04 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 28.01/28.04 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.04 => 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)) )
% 28.01/28.04 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.04 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.04 => 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))) )
% 28.01/28.04 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__le__eq,axiom,
% 28.01/28.04 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 28.01/28.04 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.01/28.04 => ( 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))
% 28.01/28.04 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.04 => 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))) )
% 28.01/28.04 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.04 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.04 => 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)) )
% 28.01/28.04 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_pos__le__divide__eq,axiom,
% 28.01/28.04 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> 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)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_pos__divide__le__eq,axiom,
% 28.01/28.04 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.04 => ( 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))
% 28.01/28.04 <=> 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_times__divide__times__eq,axiom,
% 28.01/28.04 ! [V_w,V_z,V_y,V_x,T_a] :
% 28.01/28.04 ( class_Fields_Ofield__inverse__zero(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_minus__divide__divide,axiom,
% 28.01/28.04 ! [V_b,V_a,T_a] :
% 28.01/28.04 ( class_Fields_Ofield__inverse__zero(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_minus__divide__right,axiom,
% 28.01/28.04 ! [V_b,V_a,T_a] :
% 28.01/28.04 ( class_Fields_Ofield__inverse__zero(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_abs__divide,axiom,
% 28.01/28.04 ! [V_b,V_a,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__right__mono__neg,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__right__mono,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__le__0__iff,axiom,
% 28.01/28.04 ! [V_b_2,V_a_2,T_b] :
% 28.01/28.04 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 28.01/28.04 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 28.01/28.04 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.04 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zero__le__divide__iff,axiom,
% 28.01/28.04 ! [V_b_2,V_a_2,T_b] :
% 28.01/28.04 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 28.01/28.04 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 28.01/28.04 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.04 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__strict__right__mono__neg,axiom,
% 28.01/28.04 ! [V_c,V_a,V_b,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__strict__right__mono,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__neg__neg,axiom,
% 28.01/28.04 ! [V_y,V_x,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__neg__pos,axiom,
% 28.01/28.04 ! [V_y,V_x,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__pos__neg,axiom,
% 28.01/28.04 ! [V_y,V_x,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__pos__pos,axiom,
% 28.01/28.04 ! [V_y,V_x,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__less__0__iff,axiom,
% 28.01/28.04 ! [V_b_2,V_a_2,T_b] :
% 28.01/28.04 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 28.01/28.04 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 28.01/28.04 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.04 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zero__less__divide__iff,axiom,
% 28.01/28.04 ! [V_b_2,V_a_2,T_b] :
% 28.01/28.04 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 28.01/28.04 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 28.01/28.04 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.04 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_eq__divide__eq,axiom,
% 28.01/28.04 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 28.01/28.04 ( class_Fields_Ofield__inverse__zero(T_b)
% 28.01/28.04 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 28.01/28.04 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.04 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 )
% 28.01/28.04 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.04 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__eq__eq,axiom,
% 28.01/28.04 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 28.01/28.04 ( class_Fields_Ofield__inverse__zero(T_b)
% 28.01/28.04 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 28.01/28.04 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.04 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) )
% 28.01/28.04 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.04 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mult__divide__mult__cancel__right,axiom,
% 28.01/28.04 ! [V_b,V_a,V_c,T_a] :
% 28.01/28.04 ( class_Fields_Ofield__inverse__zero(T_a)
% 28.01/28.04 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mult__divide__mult__cancel__left,axiom,
% 28.01/28.04 ! [V_b,V_a,V_c,T_a] :
% 28.01/28.04 ( class_Fields_Ofield__inverse__zero(T_a)
% 28.01/28.04 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_frac__eq__eq,axiom,
% 28.01/28.04 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 28.01/28.04 ( class_Fields_Ofield(T_b)
% 28.01/28.04 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.04 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.04 => ( 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)
% 28.01/28.04 <=> 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) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_nonzero__abs__divide,axiom,
% 28.01/28.04 ! [V_a,V_b,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__nonneg__pos,axiom,
% 28.01/28.04 ! [V_y,V_x,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__nonneg__neg,axiom,
% 28.01/28.04 ! [V_y,V_x,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_frac__less2,axiom,
% 28.01/28.04 ! [V_z,V_w,V_y,V_x,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 28.01/28.04 => 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))) ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_frac__less,axiom,
% 28.01/28.04 ! [V_z,V_w,V_y,V_x,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 28.01/28.04 => 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))) ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_frac__le,axiom,
% 28.01/28.04 ! [V_z,V_w,V_y,V_x,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 28.01/28.04 => 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))) ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__nonpos__pos,axiom,
% 28.01/28.04 ! [V_y,V_x,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__nonpos__neg,axiom,
% 28.01/28.04 ! [V_y,V_x,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__strict__left__mono__neg,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 => 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))) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__strict__left__mono,axiom,
% 28.01/28.04 ! [V_c,V_a,V_b,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 => 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))) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_neg__divide__less__eq,axiom,
% 28.01/28.04 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.04 => ( 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))
% 28.01/28.04 <=> 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)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_neg__less__divide__eq,axiom,
% 28.01/28.04 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mult__imp__less__div__pos,axiom,
% 28.01/28.04 ! [V_x,V_z,V_y,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.01/28.04 => ( 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))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mult__imp__div__pos__less,axiom,
% 28.01/28.04 ! [V_z,V_x,V_y,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 => 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)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_pos__divide__less__eq,axiom,
% 28.01/28.04 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.04 => ( 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))
% 28.01/28.04 <=> 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_pos__less__divide__eq,axiom,
% 28.01/28.04 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> 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)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__less__eq,axiom,
% 28.01/28.04 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 28.01/28.04 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.01/28.04 => ( 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))
% 28.01/28.04 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.04 => 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))) )
% 28.01/28.04 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.04 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.04 => 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)) )
% 28.01/28.04 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_less__divide__eq,axiom,
% 28.01/28.04 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 28.01/28.04 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.04 => 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)) )
% 28.01/28.04 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.04 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.04 => 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))) )
% 28.01/28.04 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_add__num__frac,axiom,
% 28.01/28.04 ! [V_x,V_z,V_y,T_a] :
% 28.01/28.04 ( class_Fields_Ofield__inverse__zero(T_a)
% 28.01/28.04 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_add__divide__eq__iff,axiom,
% 28.01/28.04 ! [V_y,V_x,V_z,T_a] :
% 28.01/28.04 ( class_Fields_Ofield(T_a)
% 28.01/28.04 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_add__frac__num,axiom,
% 28.01/28.04 ! [V_z,V_x,V_y,T_a] :
% 28.01/28.04 ( class_Fields_Ofield__inverse__zero(T_a)
% 28.01/28.04 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__add__eq__iff,axiom,
% 28.01/28.04 ! [V_y,V_x,V_z,T_a] :
% 28.01/28.04 ( class_Fields_Ofield(T_a)
% 28.01/28.04 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_add__frac__eq,axiom,
% 28.01/28.04 ! [V_w,V_x,V_z,V_y,T_a] :
% 28.01/28.04 ( class_Fields_Ofield(T_a)
% 28.01/28.04 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_diff__divide__eq__iff,axiom,
% 28.01/28.04 ! [V_y,V_x,V_z,T_a] :
% 28.01/28.04 ( class_Fields_Ofield(T_a)
% 28.01/28.04 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__diff__eq__iff,axiom,
% 28.01/28.04 ! [V_y,V_x,V_z,T_a] :
% 28.01/28.04 ( class_Fields_Ofield(T_a)
% 28.01/28.04 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_diff__frac__eq,axiom,
% 28.01/28.04 ! [V_w,V_x,V_z,V_y,T_a] :
% 28.01/28.04 ( class_Fields_Ofield(T_a)
% 28.01/28.04 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_less__half__sum,axiom,
% 28.01/28.04 ! [V_b,V_a,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.01/28.04 => 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))))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_gt__half__sum,axiom,
% 28.01/28.04 ! [V_b,V_a,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 28.01/28.04 => 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)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_abs__div__pos,axiom,
% 28.01/28.04 ! [V_x,V_y,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.01/28.04 => 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)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__left__mono__neg,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 => 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))) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divide__left__mono,axiom,
% 28.01/28.04 ! [V_c,V_a,V_b,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 => 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))) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_neg__divide__le__eq,axiom,
% 28.01/28.04 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.04 => ( 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))
% 28.01/28.04 <=> 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)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_neg__le__divide__eq,axiom,
% 28.01/28.04 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_b)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mult__imp__le__div__pos,axiom,
% 28.01/28.04 ! [V_x,V_z,V_y,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.01/28.04 => ( 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))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mult__imp__div__pos__le,axiom,
% 28.01/28.04 ! [V_z,V_x,V_y,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field(T_a)
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 => 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)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_setprod__Un,axiom,
% 28.01/28.04 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 28.01/28.04 ( class_Fields_Ofield(T_c)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 28.01/28.04 => ( ! [B_x] :
% 28.01/28.04 ( 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)))
% 28.01/28.04 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 28.01/28.04 => 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))) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power__power__power,axiom,
% 28.01/28.04 ! [T_b] :
% 28.01/28.04 ( class_Power_Opower(T_b)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_int__power__div__base,axiom,
% 28.01/28.04 ! [V_k,V_m] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 28.01/28.04 => 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)))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 28.01/28.04 ! [V_N_2,V_h_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( ! [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))
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.01/28.04 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => 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)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zdiv__zero,axiom,
% 28.01/28.04 ! [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) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zdiv__zminus2,axiom,
% 28.01/28.04 ! [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) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zdiv__zminus__zminus,axiom,
% 28.01/28.04 ! [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) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__0,axiom,
% 28.01/28.04 ! [V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__by__0,axiom,
% 28.01/28.04 ! [V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 28.01/28.04 ! [V_y,V_x] :
% 28.01/28.04 ( c_Nat__Transfer_Ois__nat(V_x)
% 28.01/28.04 => ( c_Nat__Transfer_Ois__nat(V_y)
% 28.01/28.04 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__by__1,axiom,
% 28.01/28.04 ! [V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 28.01/28.04 ! [V_y,V_x] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.01/28.04 => 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))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__neg__pos__less0,axiom,
% 28.01/28.04 ! [V_b,V_a] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.04 => 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))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 28.01/28.04 ! [V_a_2,V_b_2] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 28.01/28.04 ! [V_a_2,V_b_2] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zdiv__self,axiom,
% 28.01/28.04 ! [V_a] :
% 28.01/28.04 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.04 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__mult__mult1__if,axiom,
% 28.01/28.04 ! [V_b,V_a,V_c,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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) )
% 28.01/28.04 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__mult__self2__is__id,axiom,
% 28.01/28.04 ! [V_a,V_b,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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 ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__mult__self1__is__id,axiom,
% 28.01/28.04 ! [V_a,V_b,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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 ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__mult__mult2,axiom,
% 28.01/28.04 ! [V_b,V_a,V_c,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__mult__mult1,axiom,
% 28.01/28.04 ! [V_b,V_a,V_c,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__self,axiom,
% 28.01/28.04 ! [V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zdiv__eq__0__iff,axiom,
% 28.01/28.04 ! [V_k_2,V_i_2] :
% 28.01/28.04 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.04 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.04 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 28.01/28.04 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 28.01/28.04 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.04 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 28.01/28.04 ! [V_a_2,V_b_2] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 28.01/28.04 ! [V_i_2,V_k_2] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 28.01/28.04 ! [V_b_2,V_a_2] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 28.01/28.04 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zdiv__mono2,axiom,
% 28.01/28.04 ! [V_b,V_b_H,V_a] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__nonneg__neg__le0,axiom,
% 28.01/28.04 ! [V_b,V_a] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.04 => 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))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__pos__pos__trivial,axiom,
% 28.01/28.04 ! [V_b,V_a] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 28.01/28.04 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 28.01/28.04 ! [V_a_2,V_b_2] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__nonpos__pos__le0,axiom,
% 28.01/28.04 ! [V_b,V_a] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.04 => 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))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zdiv__mono2__neg,axiom,
% 28.01/28.04 ! [V_b,V_b_H,V_a] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 28.01/28.04 => 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))) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__neg__neg__trivial,axiom,
% 28.01/28.04 ! [V_b,V_a] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 28.01/28.04 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zdiv__mono1,axiom,
% 28.01/28.04 ! [V_b,V_a_H,V_a] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.04 => 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))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zdiv__mono1__neg,axiom,
% 28.01/28.04 ! [V_b,V_a_H,V_a] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.04 => 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))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_int__div__less__self,axiom,
% 28.01/28.04 ! [V_k,V_x] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 28.01/28.04 => 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)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zdiv__zmult2__eq,axiom,
% 28.01/28.04 ! [V_b,V_a,V_c] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power_Opower_Opower__0,axiom,
% 28.01/28.04 ! [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 ).
% 28.01/28.04
% 28.01/28.04 fof(fact_power_Opower_Opower__Suc,axiom,
% 28.01/28.04 ! [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)) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__mult__self1,axiom,
% 28.01/28.04 ! [V_c,V_a,V_b,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__mult__self2,axiom,
% 28.01/28.04 ! [V_c,V_a,V_b,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__add__self1,axiom,
% 28.01/28.04 ! [V_a,V_b,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__add__self2,axiom,
% 28.01/28.04 ! [V_a,V_b,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 28.01/28.04 => 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)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_divmod__int__rel__div__eq,axiom,
% 28.01/28.04 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 28.01/28.04 ( 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)
% 28.01/28.04 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 28.01/28.04 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 28.01/28.04 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 28.01/28.04 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 28.01/28.04 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.04 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_split__zdiv,axiom,
% 28.01/28.04 ! [V_k_2,V_n_2,V_P_2] :
% 28.01/28.04 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 28.01/28.04 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.04 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.01/28.04 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 28.01/28.04 => ! [B_i] :
% 28.01/28.04 ( ? [B_j] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 28.01/28.04 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 28.01/28.04 & 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) )
% 28.01/28.04 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 28.01/28.04 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.04 => ! [B_i] :
% 28.01/28.04 ( ? [B_j] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 28.01/28.04 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.04 & 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) )
% 28.01/28.04 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_z3div__def,axiom,
% 28.01/28.04 ! [V_k,V_l] :
% 28.01/28.04 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 28.01/28.04 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 28.01/28.04 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 28.01/28.04 => 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))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_Max_Ohom__commute,axiom,
% 28.01/28.04 ! [V_N_2,V_h_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( ! [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))
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.01/28.04 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => 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)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_Min_Ohom__commute,axiom,
% 28.01/28.04 ! [V_N_2,V_h_2,T_b] :
% 28.01/28.04 ( class_Orderings_Olinorder(T_b)
% 28.01/28.04 => ( ! [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))
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 28.01/28.04 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.04 => 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)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_strong__setprod__reindex__cong,axiom,
% 28.01/28.04 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 28.01/28.04 ( class_Groups_Ocomm__monoid__mult(T_d)
% 28.01/28.04 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.01/28.04 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 28.01/28.04 => ( ! [B_x] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.04 => 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) )
% 28.01/28.04 => 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) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__mult2__eq,axiom,
% 28.01/28.04 ! [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) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__le__mono,axiom,
% 28.01/28.04 ! [V_k,V_n,V_m] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 28.01/28.04 => 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))) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__le__dividend,axiom,
% 28.01/28.04 ! [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)) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__1,axiom,
% 28.01/28.04 ! [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 ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__less,axiom,
% 28.01/28.04 ! [V_n,V_m] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.01/28.04 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_nat__mult__div__cancel__disj,axiom,
% 28.01/28.04 ! [V_n,V_m,V_k] :
% 28.01/28.04 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.04 => 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) )
% 28.01/28.04 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.04 => 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) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zdiv__int,axiom,
% 28.01/28.04 ! [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)) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 28.01/28.04 ! [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)) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__le__mono2,axiom,
% 28.01/28.04 ! [V_k,V_n,V_m] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 28.01/28.04 => 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))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_nat__mult__div__cancel1,axiom,
% 28.01/28.04 ! [V_n,V_m,V_k] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__mult__self1__is__m,axiom,
% 28.01/28.04 ! [V_m,V_n] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.01/28.04 => 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 ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__mult__self__is__m,axiom,
% 28.01/28.04 ! [V_m,V_n] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.01/28.04 => 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 ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__less__dividend,axiom,
% 28.01/28.04 ! [V_m,V_n] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 28.01/28.04 => 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)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__geq,axiom,
% 28.01/28.04 ! [V_m,V_n] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.01/28.04 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.01/28.04 => 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)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__if,axiom,
% 28.01/28.04 ! [V_m,V_n] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.01/28.04 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.01/28.04 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.01/28.04 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.01/28.04 => 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)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_split__div,axiom,
% 28.01/28.04 ! [V_k_2,V_n_2,V_P_2] :
% 28.01/28.04 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 28.01/28.04 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.04 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 28.01/28.04 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.04 => ! [B_i,B_j] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 28.01/28.04 => ( 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)
% 28.01/28.04 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_nat__div__distrib,axiom,
% 28.01/28.04 ! [V_y,V_x] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 28.01/28.04 ! [V_y,V_x] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.01/28.04 => 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)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_le__div__geq,axiom,
% 28.01/28.04 ! [V_m,V_n] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 28.01/28.04 => 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)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_split__div_H,axiom,
% 28.01/28.04 ! [V_n_2,V_m_2,V_P_2] :
% 28.01/28.04 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 28.01/28.04 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.04 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 28.01/28.04 | ? [B_q] :
% 28.01/28.04 ( 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))
% 28.01/28.04 & 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))))
% 28.01/28.04 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_split__div__lemma,axiom,
% 28.01/28.04 ! [V_m_2,V_q_2,V_n_2] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 28.01/28.04 => ( ( 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))
% 28.01/28.04 & 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)))) )
% 28.01/28.04 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 28.01/28.04 ! [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)) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_setprod__mono__one__left,axiom,
% 28.01/28.04 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 28.01/28.04 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 28.01/28.04 => ( ! [B_x] :
% 28.01/28.04 ( 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)))
% 28.01/28.04 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 28.01/28.04 => 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) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_setprod__mono__one__right,axiom,
% 28.01/28.04 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 28.01/28.04 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 28.01/28.04 => ( ! [B_x] :
% 28.01/28.04 ( 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)))
% 28.01/28.04 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 28.01/28.04 => 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) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_card__partition,axiom,
% 28.01/28.04 ! [V_k_2,V_C_2,T_b] :
% 28.01/28.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 28.01/28.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 28.01/28.04 => ( ! [B_c] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 28.01/28.04 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 28.01/28.04 => ( ! [B_c1] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 28.01/28.04 => ! [B_c2] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 28.01/28.04 => ( B_c1 != B_c2
% 28.01/28.04 => 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)) ) ) )
% 28.01/28.04 => 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)) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 28.01/28.04 ! [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)))) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_field__le__mult__one__interval,axiom,
% 28.01/28.04 ! [V_y,V_x,T_a] :
% 28.01/28.04 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 28.01/28.04 => ( ! [B_z] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 28.01/28.04 => 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)) ) )
% 28.01/28.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 28.01/28.04 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 28.01/28.04 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.04 & class_Groups_Ocomm__monoid__mult(T_b) )
% 28.01/28.04 => ( V_A_2 = V_B_2
% 28.01/28.04 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 28.01/28.04 => ( ! [B_x] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 28.01/28.04 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 28.01/28.04 => 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) ) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_split__neg__lemma,axiom,
% 28.01/28.04 ! [V_n_2,V_P_2,V_k_2] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 <=> ! [B_i,B_j] :
% 28.01/28.04 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 28.01/28.04 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.04 & 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) )
% 28.01/28.04 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zpower__zmod,axiom,
% 28.01/28.04 ! [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) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 28.01/28.04 ! [V_y,V_x] :
% 28.01/28.04 ( c_Nat__Transfer_Ois__nat(V_x)
% 28.01/28.04 => ( c_Nat__Transfer_Ois__nat(V_y)
% 28.01/28.04 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zdiff__zmod__right,axiom,
% 28.01/28.04 ! [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) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zdiff__zmod__left,axiom,
% 28.01/28.04 ! [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) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zminus__zmod,axiom,
% 28.01/28.04 ! [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) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmod__zminus__zminus,axiom,
% 28.01/28.04 ! [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)) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmod__zminus2,axiom,
% 28.01/28.04 ! [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)) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__add__cong,axiom,
% 28.01/28.04 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 28.01/28.04 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 28.01/28.04 => 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) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmod__simps_I1_J,axiom,
% 28.01/28.04 ! [V_b,V_c,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmod__simps_I2_J,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__add__eq,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__add__left__eq,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__add__right__eq,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__add__self1,axiom,
% 28.01/28.04 ! [V_a,V_b,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__add__self2,axiom,
% 28.01/28.04 ! [V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__mult__cong,axiom,
% 28.01/28.04 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 28.01/28.04 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 28.01/28.04 => 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) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmod__simps_I4_J,axiom,
% 28.01/28.04 ! [V_b,V_c,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__mult__mult2,axiom,
% 28.01/28.04 ! [V_b,V_c,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__mult__mult1,axiom,
% 28.01/28.04 ! [V_b,V_a,V_c,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__mult__eq,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__mult__left__eq,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__mult__right__eq,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__diff__right__eq,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Oring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__diff__left__eq,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Oring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__diff__eq,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Oring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__diff__cong,axiom,
% 28.01/28.04 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Oring__div(T_a)
% 28.01/28.04 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 28.01/28.04 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 28.01/28.04 => 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) ) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__minus__eq,axiom,
% 28.01/28.04 ! [V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Oring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__minus__cong,axiom,
% 28.01/28.04 ! [V_a_H,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Oring__div(T_a)
% 28.01/28.04 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 28.01/28.04 => 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) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmod__self,axiom,
% 28.01/28.04 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmod__zero,axiom,
% 28.01/28.04 ! [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) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__self,axiom,
% 28.01/28.04 ! [V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__by__0,axiom,
% 28.01/28.04 ! [V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__0,axiom,
% 28.01/28.04 ! [V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__mod__trivial,axiom,
% 28.01/28.04 ! [V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmod__simps_I3_J,axiom,
% 28.01/28.04 ! [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) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmod__zmult1__eq,axiom,
% 28.01/28.04 ! [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) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__mult__self1__is__0,axiom,
% 28.01/28.04 ! [V_a,V_b,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__mult__self2__is__0,axiom,
% 28.01/28.04 ! [V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__mult__self2,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__mult__self1,axiom,
% 28.01/28.04 ! [V_b,V_c,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__by__1,axiom,
% 28.01/28.04 ! [V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__div__trivial,axiom,
% 28.01/28.04 ! [V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmod__le__nonneg__dividend,axiom,
% 28.01/28.04 ! [V_k,V_m] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 28.01/28.04 ! [V_y,V_x] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.01/28.04 => 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))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_pos__mod__bound,axiom,
% 28.01/28.04 ! [V_a,V_b] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.04 => 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)) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_neg__mod__bound,axiom,
% 28.01/28.04 ! [V_a,V_b] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.04 => 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))) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmod__eq__0__iff,axiom,
% 28.01/28.04 ! [V_d_2,V_m_2] :
% 28.01/28.04 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.04 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmod__zminus1__not__zero,axiom,
% 28.01/28.04 ! [V_l,V_k] :
% 28.01/28.04 ( 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)
% 28.01/28.04 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmod__zminus2__not__zero,axiom,
% 28.01/28.04 ! [V_l,V_k] :
% 28.01/28.04 ( 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)
% 28.01/28.04 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmod__zdiv__trivial,axiom,
% 28.01/28.04 ! [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) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_DIVISION__BY__ZERO,axiom,
% 28.01/28.04 ! [V_a] :
% 28.01/28.04 ( 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)
% 28.01/28.04 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zdiv__zadd1__eq,axiom,
% 28.01/28.04 ! [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)) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 28.01/28.04 ! [V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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 ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__div__equality2,axiom,
% 28.01/28.04 ! [V_a,V_b,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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 ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__div__equality,axiom,
% 28.01/28.04 ! [V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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 ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__mod__equality2,axiom,
% 28.01/28.04 ! [V_c,V_a,V_b,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_div__mod__equality,axiom,
% 28.01/28.04 ! [V_c,V_b,V_a,T_a] :
% 28.01/28.04 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.04 => 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) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__neg__neg__trivial,axiom,
% 28.01/28.04 ! [V_b,V_a] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 28.01/28.04 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_neg__mod__conj,axiom,
% 28.01/28.04 ! [V_a,V_b] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 & 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))) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_neg__mod__sign,axiom,
% 28.01/28.04 ! [V_a,V_b] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.04 => 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))) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__pos__pos__trivial,axiom,
% 28.01/28.04 ! [V_b,V_a] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.01/28.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 28.01/28.04 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_pos__mod__conj,axiom,
% 28.01/28.04 ! [V_a,V_b] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.04 => ( 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)))
% 28.01/28.04 & 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)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_pos__mod__sign,axiom,
% 28.01/28.04 ! [V_a,V_b] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.04 => 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))) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmod__zminus2__eq__if,axiom,
% 28.01/28.04 ! [V_b,V_a] :
% 28.01/28.04 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.04 => 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) )
% 28.01/28.04 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.04 => 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) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmod__zminus1__eq__if,axiom,
% 28.01/28.04 ! [V_b,V_a] :
% 28.01/28.04 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.04 => 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) )
% 28.01/28.04 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.04 => 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)) ) ) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmod__zdiv__equality,axiom,
% 28.01/28.04 ! [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)) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zdiv__zmult1__eq,axiom,
% 28.01/28.04 ! [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)) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zdiv__zmod__equality,axiom,
% 28.01/28.04 ! [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) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zdiv__zmod__equality2,axiom,
% 28.01/28.04 ! [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) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmult__div__cancel,axiom,
% 28.01/28.04 ! [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)) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_zmod__zdiv__equality_H,axiom,
% 28.01/28.04 ! [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)) ).
% 28.01/28.04
% 28.01/28.04 fof(fact_mod__pos__neg__trivial,axiom,
% 28.01/28.04 ! [V_b,V_a] :
% 28.01/28.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.01/28.04 => ( 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)))
% 28.01/28.05 => 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) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_split__zmod,axiom,
% 28.01/28.05 ! [V_k_2,V_n_2,V_P_2] :
% 28.01/28.05 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 28.01/28.05 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.05 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 28.01/28.05 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 28.01/28.05 => ! [B_i,B_j] :
% 28.01/28.05 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 28.01/28.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 28.01/28.05 & 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) )
% 28.01/28.05 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 28.01/28.05 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.05 => ! [B_i,B_j] :
% 28.01/28.05 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 28.01/28.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.05 & 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) )
% 28.01/28.05 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zmult2__lemma__aux3,axiom,
% 28.01/28.05 ! [V_q,V_b,V_r,V_c] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 28.01/28.05 => 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))) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zmult2__lemma__aux4,axiom,
% 28.01/28.05 ! [V_q,V_b,V_r,V_c] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 28.01/28.05 => 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))) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zmult2__lemma__aux1,axiom,
% 28.01/28.05 ! [V_q,V_r,V_b,V_c] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.05 => 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))) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zmult2__lemma__aux2,axiom,
% 28.01/28.05 ! [V_q,V_r,V_b,V_c] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.05 => 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))) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_divmod__int__rel__mod__eq,axiom,
% 28.01/28.05 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 28.01/28.05 ( 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)
% 28.01/28.05 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.01/28.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 28.01/28.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 28.01/28.05 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.05 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zmod__zmult2__eq,axiom,
% 28.01/28.05 ! [V_b,V_a,V_c] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zdiv__zminus2__eq__if,axiom,
% 28.01/28.05 ! [V_a,V_b] :
% 28.01/28.05 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.05 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.05 => 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)) )
% 28.01/28.05 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.05 => 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)) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zdiv__zminus1__eq__if,axiom,
% 28.01/28.05 ! [V_a,V_b] :
% 28.01/28.05 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.05 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.05 => 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)) )
% 28.01/28.05 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.05 => 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)) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_split__pos__lemma,axiom,
% 28.01/28.05 ! [V_n_2,V_P_2,V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 28.01/28.05 => ( 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)))
% 28.01/28.05 <=> ! [B_i,B_j] :
% 28.01/28.05 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 28.01/28.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 28.01/28.05 & 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) )
% 28.01/28.05 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_z3mod__def,axiom,
% 28.01/28.05 ! [V_k,V_l] :
% 28.01/28.05 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 28.01/28.05 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 28.01/28.05 => 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)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_setprod__pos__nat,axiom,
% 28.01/28.05 ! [V_f_2,V_S_2,T_b] :
% 28.01/28.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.01/28.05 => ( ! [B_x] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 28.01/28.05 => 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))) )
% 28.01/28.05 => 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))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_card__quotient__disjoint,axiom,
% 28.01/28.05 ! [V_r_2,V_A_2,T_b] :
% 28.01/28.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.05 => ( 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)
% 28.01/28.05 => 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) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_ex__bij__betw__finite__nat,axiom,
% 28.01/28.05 ! [V_M_2,T_b] :
% 28.01/28.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 28.01/28.05 => ? [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))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 28.01/28.05 ! [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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__less,axiom,
% 28.01/28.05 ! [V_n,V_m] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.01/28.05 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__mult__distrib,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__mult__distrib2,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__less__eq__dividend,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_quotient__empty,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_quotient__is__empty2,axiom,
% 28.01/28.05 ! [V_r_2,V_A_2,T_b] :
% 28.01/28.05 ( 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)
% 28.01/28.05 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_quotient__is__empty,axiom,
% 28.01/28.05 ! [V_r_2,V_A_2,T_b] :
% 28.01/28.05 ( 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))
% 28.01/28.05 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__1,axiom,
% 28.01/28.05 ! [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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__Suc,axiom,
% 28.01/28.05 ! [V_n,V_m] :
% 28.01/28.05 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 28.01/28.05 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.01/28.05 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 28.01/28.05 => 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)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__less__divisor,axiom,
% 28.01/28.05 ! [V_m,V_n] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__eq__0__iff,axiom,
% 28.01/28.05 ! [V_d_2,V_m_2] :
% 28.01/28.05 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.05 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__if,axiom,
% 28.01/28.05 ! [V_n,V_m] :
% 28.01/28.05 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.01/28.05 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.01/28.05 => 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) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__geq,axiom,
% 28.01/28.05 ! [V_n,V_m] :
% 28.01/28.05 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__mult__self3,axiom,
% 28.01/28.05 ! [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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_le__mod__geq,axiom,
% 28.01/28.05 ! [V_m,V_n] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zmod__int,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_div__add1__eq,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__gcd_Osimps,axiom,
% 28.01/28.05 ! [V_x,V_y] :
% 28.01/28.05 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.05 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 28.01/28.05 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.05 => 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)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__le__divisor,axiom,
% 28.01/28.05 ! [V_m,V_n] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__mult__self4,axiom,
% 28.01/28.05 ! [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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__mult2__eq,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_div__mult1__eq,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_div__mod__equality_H,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mult__div__cancel,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Divides_Omod__div__equality_H,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_quotient__diff1,axiom,
% 28.01/28.05 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 28.01/28.05 ( 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)
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.05 => 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)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_split__mod,axiom,
% 28.01/28.05 ! [V_k_2,V_n_2,V_P_2] :
% 28.01/28.05 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 28.01/28.05 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.05 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 28.01/28.05 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.05 => ! [B_i,B_j] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 28.01/28.05 => ( 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)
% 28.01/28.05 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__lemma,axiom,
% 28.01/28.05 ! [V_q,V_b,V_r,V_c] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 28.01/28.05 => 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))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Suc__times__mod__eq,axiom,
% 28.01/28.05 ! [V_m,V_k] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 28.01/28.05 ! [V_y,V_x] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.01/28.05 => 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)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__mod__distrib,axiom,
% 28.01/28.05 ! [V_y,V_x] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 28.01/28.05 => 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)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_quotient__def,axiom,
% 28.01/28.05 ! [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)))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_singleton__quotient,axiom,
% 28.01/28.05 ! [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))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_quotientI,axiom,
% 28.01/28.05 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.05 => 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))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_fold__image__1,axiom,
% 28.01/28.05 ! [V_f_2,V_S_2,T_b,T_c] :
% 28.01/28.05 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 28.01/28.05 => ( ! [B_x] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 28.01/28.05 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 28.01/28.05 => 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) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Image__eq__UN,axiom,
% 28.01/28.05 ! [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))))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Image__INT__subset,axiom,
% 28.01/28.05 ! [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)))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Image__Int__subset,axiom,
% 28.01/28.05 ! [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)))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Image__UN,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Image__empty,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Image__mono,axiom,
% 28.01/28.05 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 28.01/28.05 ( 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))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 28.01/28.05 => 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))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Image__Un,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Un__Image,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_quotientE,axiom,
% 28.01/28.05 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 28.01/28.05 ( 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)))
% 28.01/28.05 => ~ ! [B_x] :
% 28.01/28.05 ( 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))))
% 28.01/28.05 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__mod__eq__lemma,axiom,
% 28.01/28.05 ! [V_y,V_n,V_x] :
% 28.01/28.05 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 28.01/28.05 => ? [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)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_card_Oneutral,axiom,
% 28.01/28.05 ! [V_A_2,T_b] :
% 28.01/28.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.05 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.05 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.01/28.05 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__induct__0,axiom,
% 28.01/28.05 ! [V_i_2,V_P_2,V_p_2] :
% 28.01/28.05 ( ! [B_i] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 28.01/28.05 => ( hBOOL(hAPP(V_P_2,B_i))
% 28.01/28.05 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 28.01/28.05 => ( hBOOL(hAPP(V_P_2,V_i_2))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 28.01/28.05 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__by__empty,axiom,
% 28.01/28.05 ! [V_B_2,T_b,V_A_2] :
% 28.01/28.05 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_fold__image__cong,axiom,
% 28.01/28.05 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 28.01/28.05 ( class_Groups_Oab__semigroup__mult(T_c)
% 28.01/28.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.05 => ( ! [B_x] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.05 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 28.01/28.05 => 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) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Max__eqI,axiom,
% 28.01/28.05 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.05 ( class_Orderings_Olinorder(T_b)
% 28.01/28.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.05 => ( ! [B_y] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 28.01/28.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.05 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Min__eqI,axiom,
% 28.01/28.05 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.05 ( class_Orderings_Olinorder(T_b)
% 28.01/28.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.05 => ( ! [B_y] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 28.01/28.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.05 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_expand__Suc,axiom,
% 28.01/28.05 ! [V_v] :
% 28.01/28.05 ( 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)))
% 28.01/28.05 => 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))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_of__nat__number__of__lemma,axiom,
% 28.01/28.05 ! [V_v,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => ( ( 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)))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ 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)))
% 28.01/28.05 => 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) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_number__of__eq,axiom,
% 28.01/28.05 ! [V_k,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_eq__number__of,axiom,
% 28.01/28.05 ! [V_y_2,V_x_2,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 & class_Int_Oring__char__0(T_b) )
% 28.01/28.05 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 28.01/28.05 <=> V_x_2 = V_y_2 ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_number__of__reorient,axiom,
% 28.01/28.05 ! [V_x_2,V_w_2,T_b] :
% 28.01/28.05 ( class_Int_Onumber(T_b)
% 28.01/28.05 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 28.01/28.05 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_of__int__number__of__eq,axiom,
% 28.01/28.05 ! [V_v,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_of__nat__number__of__eq,axiom,
% 28.01/28.05 ! [V_v,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => 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) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_le__number__of__eq__not__less,axiom,
% 28.01/28.05 ! [V_w_2,V_v_2,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber(T_b)
% 28.01/28.05 & class_Orderings_Olinorder(T_b) )
% 28.01/28.05 => ( 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)))
% 28.01/28.05 <=> ~ 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))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_left__distrib__number__of,axiom,
% 28.01/28.05 ! [V_v,V_b,V_a,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber(T_b)
% 28.01/28.05 & class_Rings_Osemiring(T_b) )
% 28.01/28.05 => 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))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_right__distrib__number__of,axiom,
% 28.01/28.05 ! [V_c,V_b,V_v,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber(T_b)
% 28.01/28.05 & class_Rings_Osemiring(T_b) )
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_right__diff__distrib__number__of,axiom,
% 28.01/28.05 ! [V_c,V_b,V_v,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber(T_b)
% 28.01/28.05 & class_Rings_Oring(T_b) )
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_left__diff__distrib__number__of,axiom,
% 28.01/28.05 ! [V_v,V_b,V_a,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber(T_b)
% 28.01/28.05 & class_Rings_Oring(T_b) )
% 28.01/28.05 => 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))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_le__number__of,axiom,
% 28.01/28.05 ! [V_y_2,V_x_2,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 & class_Rings_Olinordered__idom(T_b) )
% 28.01/28.05 => ( 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)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__number__of,axiom,
% 28.01/28.05 ! [V_y_2,V_x_2,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 & class_Rings_Olinordered__idom(T_b) )
% 28.01/28.05 => ( 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)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_min__number__of,axiom,
% 28.01/28.05 ! [V_v,V_u,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber(T_b)
% 28.01/28.05 & class_Orderings_Oord(T_b) )
% 28.01/28.05 => ( ( 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)))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ 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)))
% 28.01/28.05 => 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) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_max__number__of,axiom,
% 28.01/28.05 ! [V_v,V_u,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber(T_b)
% 28.01/28.05 & class_Orderings_Oord(T_b) )
% 28.01/28.05 => ( ( 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)))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ 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)))
% 28.01/28.05 => 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) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_number__of__add,axiom,
% 28.01/28.05 ! [V_w,V_v,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__number__of__eq,axiom,
% 28.01/28.05 ! [V_w,V_v,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__number__of__left,axiom,
% 28.01/28.05 ! [V_z,V_w,V_v,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_number__of__mult,axiom,
% 28.01/28.05 ! [V_w,V_v,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_arith__simps_I32_J,axiom,
% 28.01/28.05 ! [V_w,V_v,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mult__number__of__left,axiom,
% 28.01/28.05 ! [V_z,V_w,V_v,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_number__of__diff,axiom,
% 28.01/28.05 ! [V_w,V_v,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_number__of__minus,axiom,
% 28.01/28.05 ! [V_w,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_arith__simps_I30_J,axiom,
% 28.01/28.05 ! [V_w,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Ints__number__of,axiom,
% 28.01/28.05 ! [V_w_2,T_b] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 => 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))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_divide__eq__eq__number__of1,axiom,
% 28.01/28.05 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 28.01/28.05 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 28.01/28.05 & class_Int_Onumber(T_b) )
% 28.01/28.05 => ( 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
% 28.01/28.05 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.05 => 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)) )
% 28.01/28.05 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.05 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_divide__eq__eq__number__of,axiom,
% 28.01/28.05 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 28.01/28.05 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 28.01/28.05 & class_Int_Onumber(T_b) )
% 28.01/28.05 => ( 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)
% 28.01/28.05 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.05 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_eq__divide__eq__number__of,axiom,
% 28.01/28.05 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 28.01/28.05 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 28.01/28.05 & class_Int_Onumber(T_b) )
% 28.01/28.05 => ( 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)
% 28.01/28.05 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.05 => 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 )
% 28.01/28.05 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.05 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_eq__divide__eq__number__of1,axiom,
% 28.01/28.05 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 28.01/28.05 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 28.01/28.05 & class_Int_Onumber(T_b) )
% 28.01/28.05 => ( 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))
% 28.01/28.05 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.05 => 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 )
% 28.01/28.05 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.05 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__number__of__diff1,axiom,
% 28.01/28.05 ! [V_c,V_w,V_v,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_minus__number__of__mult,axiom,
% 28.01/28.05 ! [V_z,V_w,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_diff__number__of__eq,axiom,
% 28.01/28.05 ! [V_w,V_v,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_divide__less__eq__number__of1,axiom,
% 28.01/28.05 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 28.01/28.05 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.01/28.05 & class_Int_Onumber(T_b) )
% 28.01/28.05 => ( 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))
% 28.01/28.05 <=> ( ( 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)))
% 28.01/28.05 => 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)))) )
% 28.01/28.05 & ( ~ 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)))
% 28.01/28.05 => ( ( 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)))
% 28.01/28.05 => 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)) )
% 28.01/28.05 & ( ~ 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)))
% 28.01/28.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_divide__less__eq__number__of,axiom,
% 28.01/28.05 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 28.01/28.05 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.01/28.05 & class_Int_Onumber(T_b) )
% 28.01/28.05 => ( 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)))
% 28.01/28.05 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.05 => 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))) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.05 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.05 => 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)) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.05 => 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))) ) ) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__divide__eq__number__of,axiom,
% 28.01/28.05 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 28.01/28.05 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.01/28.05 & class_Int_Onumber(T_b) )
% 28.01/28.05 => ( 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)))
% 28.01/28.05 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.05 => 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)) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.05 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.05 => 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))) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.05 => 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))) ) ) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__divide__eq__number__of1,axiom,
% 28.01/28.05 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 28.01/28.05 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.01/28.05 & class_Int_Onumber(T_b) )
% 28.01/28.05 => ( 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))))
% 28.01/28.05 <=> ( ( 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)))
% 28.01/28.05 => 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)) )
% 28.01/28.05 & ( ~ 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)))
% 28.01/28.05 => ( ( 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)))
% 28.01/28.05 => 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)))) )
% 28.01/28.05 & ( ~ 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)))
% 28.01/28.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_abs__number__of,axiom,
% 28.01/28.05 ! [V_x,T_a] :
% 28.01/28.05 ( ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 & class_Rings_Olinordered__idom(T_a) )
% 28.01/28.05 => ( ( 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)))
% 28.01/28.05 => 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)) )
% 28.01/28.05 & ( ~ 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)))
% 28.01/28.05 => 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) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__number__of__diff2,axiom,
% 28.01/28.05 ! [V_w,V_c,V_v,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_divide__le__eq__number__of1,axiom,
% 28.01/28.05 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 28.01/28.05 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.01/28.05 & class_Int_Onumber(T_b) )
% 28.01/28.05 => ( 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))
% 28.01/28.05 <=> ( ( 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)))
% 28.01/28.05 => 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)))) )
% 28.01/28.05 & ( ~ 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)))
% 28.01/28.05 => ( ( 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)))
% 28.01/28.05 => 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)) )
% 28.01/28.05 & ( ~ 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)))
% 28.01/28.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_divide__le__eq__number__of,axiom,
% 28.01/28.05 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 28.01/28.05 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.01/28.05 & class_Int_Onumber(T_b) )
% 28.01/28.05 => ( 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)))
% 28.01/28.05 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.05 => 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))) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.05 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.05 => 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)) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.05 => 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))) ) ) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_le__divide__eq__number__of,axiom,
% 28.01/28.05 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 28.01/28.05 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.01/28.05 & class_Int_Onumber(T_b) )
% 28.01/28.05 => ( 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)))
% 28.01/28.05 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.05 => 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)) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 28.01/28.05 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.05 => 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))) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 28.01/28.05 => 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))) ) ) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_le__divide__eq__number__of1,axiom,
% 28.01/28.05 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 28.01/28.05 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.01/28.05 & class_Int_Onumber(T_b) )
% 28.01/28.05 => ( 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))))
% 28.01/28.05 <=> ( ( 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)))
% 28.01/28.05 => 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)) )
% 28.01/28.05 & ( ~ 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)))
% 28.01/28.05 => ( ( 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)))
% 28.01/28.05 => 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)))) )
% 28.01/28.05 & ( ~ 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)))
% 28.01/28.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_one__mod__nat__number__of,axiom,
% 28.01/28.05 ! [V_v_H] :
% 28.01/28.05 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 28.01/28.05 => 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)) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 28.01/28.05 => 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))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_one__div__nat__number__of,axiom,
% 28.01/28.05 ! [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))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power__number__of__odd__number__of,axiom,
% 28.01/28.05 ! [V_v_2,V_w_2,T_b] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 => ( ( 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)))
% 28.01/28.05 => 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))) )
% 28.01/28.05 & ( ~ 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)))
% 28.01/28.05 => 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) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power__nat__number__of__number__of,axiom,
% 28.01/28.05 ! [V_w,V_v] :
% 28.01/28.05 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => 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)) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => 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))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__eq__number__of__int__code,axiom,
% 28.01/28.05 ! [V_l_2,V_k_2] :
% 28.01/28.05 ( 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)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_number__of__is__id,axiom,
% 28.01/28.05 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__number__of__int__code,axiom,
% 28.01/28.05 ! [V_l_2,V_k_2] :
% 28.01/28.05 ( 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)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_times__numeral__code_I5_J,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_plus__numeral__code_I9_J,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_minus__numeral__code_I5_J,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_neg__number__of__Bit1,axiom,
% 28.01/28.05 ! [V_w_2] :
% 28.01/28.05 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 28.01/28.05 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I51_J,axiom,
% 28.01/28.05 ! [V_l_2,V_k_2] :
% 28.01/28.05 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 28.01/28.05 <=> V_k_2 = V_l_2 ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I17_J,axiom,
% 28.01/28.05 ! [V_l_2,V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__int__code_I16_J,axiom,
% 28.01/28.05 ! [V_k2_2,V_k1_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__eq__int__code_I16_J,axiom,
% 28.01/28.05 ! [V_k2_2,V_k1_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I34_J,axiom,
% 28.01/28.05 ! [V_l_2,V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_int__number__of__def,axiom,
% 28.01/28.05 ! [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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_bin__less__0__simps_I4_J,axiom,
% 28.01/28.05 ! [V_w_2] :
% 28.01/28.05 ( 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)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Bit1__def,axiom,
% 28.01/28.05 ! [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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__number__of,axiom,
% 28.01/28.05 ! [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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__number__of__def,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__number__of__Bit1,axiom,
% 28.01/28.05 ! [V_w_2] :
% 28.01/28.05 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 28.01/28.05 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 28.01/28.05 => 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)))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_number__of__Bit1,axiom,
% 28.01/28.05 ! [V_w,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power__number__of__odd,axiom,
% 28.01/28.05 ! [V_z_2,V_w_2,T_b] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 => ( ( 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)))
% 28.01/28.05 => 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))) )
% 28.01/28.05 & ( ~ 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)))
% 28.01/28.05 => 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) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zpower__number__of__odd,axiom,
% 28.01/28.05 ! [V_z_2,V_w_2] :
% 28.01/28.05 ( ( 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)))
% 28.01/28.05 => 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))) )
% 28.01/28.05 & ( ~ 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)))
% 28.01/28.05 => 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) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_minus__numeral__code_I6_J,axiom,
% 28.01/28.05 ! [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))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_neg__imp__number__of__eq__0,axiom,
% 28.01/28.05 ! [V_v] :
% 28.01/28.05 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_int__eq__iff__number__of,axiom,
% 28.01/28.05 ! [V_v_2,V_m_2] :
% 28.01/28.05 ( 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)
% 28.01/28.05 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 28.01/28.05 & 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))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_eq__nat__number__of,axiom,
% 28.01/28.05 ! [V_v_H_2,V_v_2] :
% 28.01/28.05 ( 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)
% 28.01/28.05 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 28.01/28.05 => 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))) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 28.01/28.05 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 28.01/28.05 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 28.01/28.05 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__number__of__add__left,axiom,
% 28.01/28.05 ! [V_k,V_v_H,V_v] :
% 28.01/28.05 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 28.01/28.05 => 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) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_int__nat__number__of,axiom,
% 28.01/28.05 ! [V_v] :
% 28.01/28.05 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => 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) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__nat__number__of,axiom,
% 28.01/28.05 ! [V_v_H,V_v] :
% 28.01/28.05 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 28.01/28.05 => 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))) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_div__nat__number__of,axiom,
% 28.01/28.05 ! [V_v_H,V_v] :
% 28.01/28.05 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => 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))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power__nat__number__of,axiom,
% 28.01/28.05 ! [V_n,V_v] :
% 28.01/28.05 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => 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)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Suc__nat__number__of__add,axiom,
% 28.01/28.05 ! [V_n,V_v] :
% 28.01/28.05 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => 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) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_diff__nat__number__of,axiom,
% 28.01/28.05 ! [V_v_2,V_v_H_2] :
% 28.01/28.05 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 28.01/28.05 => 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)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_min__Suc__number__of,axiom,
% 28.01/28.05 ! [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)))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_min__number__of__Suc,axiom,
% 28.01/28.05 ! [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)))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_succ__Pls,axiom,
% 28.01/28.05 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I39_J,axiom,
% 28.01/28.05 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I46_J,axiom,
% 28.01/28.05 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I19_J,axiom,
% 28.01/28.05 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_diff__bin__simps_I1_J,axiom,
% 28.01/28.05 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 28.01/28.05
% 28.01/28.05 fof(fact_minus__Pls,axiom,
% 28.01/28.05 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 28.01/28.05
% 28.01/28.05 fof(fact_succ__pred,axiom,
% 28.01/28.05 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I2_J,axiom,
% 28.01/28.05 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Pls__def,axiom,
% 28.01/28.05 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mult__Pls,axiom,
% 28.01/28.05 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__Pls,axiom,
% 28.01/28.05 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__Pls__right,axiom,
% 28.01/28.05 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 28.01/28.05
% 28.01/28.05 fof(fact_number__of__Pls,axiom,
% 28.01/28.05 ! [T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_semiring__norm_I112_J,axiom,
% 28.01/28.05 ! [T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__numeral__0__right,axiom,
% 28.01/28.05 ! [V_a,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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 ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__numeral__0,axiom,
% 28.01/28.05 ! [V_a,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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 ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_bin__less__0__simps_I1_J,axiom,
% 28.01/28.05 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__number__of__Pls,axiom,
% 28.01/28.05 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_semiring__norm_I113_J,axiom,
% 28.01/28.05 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zero__is__num__zero,axiom,
% 28.01/28.05 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I22_J,axiom,
% 28.01/28.05 ! [V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I12_J,axiom,
% 28.01/28.05 ! [V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Suc__diff__number__of,axiom,
% 28.01/28.05 ! [V_m,V_v] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 28.01/28.05 => 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))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_not__neg__number__of__Pls,axiom,
% 28.01/28.05 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__number__of__add__1,axiom,
% 28.01/28.05 ! [V_v] :
% 28.01/28.05 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.01/28.05 => 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)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__1__add__number__of,axiom,
% 28.01/28.05 ! [V_v] :
% 28.01/28.05 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.01/28.05 => 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)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_le__iff__pred__less,axiom,
% 28.01/28.05 ! [V_l_2,V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_minus__Bit1,axiom,
% 28.01/28.05 ! [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))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_pred__def,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__number__of__diff__1,axiom,
% 28.01/28.05 ! [V_v] :
% 28.01/28.05 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 28.01/28.05 => 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)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mult__numeral__1,axiom,
% 28.01/28.05 ! [V_a,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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 ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mult__numeral__1__right,axiom,
% 28.01/28.05 ! [V_a,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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 ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_divide__Numeral0,axiom,
% 28.01/28.05 ! [V_x,T_a] :
% 28.01/28.05 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 28.01/28.05 & class_Int_Onumber__ring(T_a) )
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_numeral__1__eq__1,axiom,
% 28.01/28.05 ! [T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_semiring__norm_I110_J,axiom,
% 28.01/28.05 ! [T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_eq__0__number__of,axiom,
% 28.01/28.05 ! [V_v_2] :
% 28.01/28.05 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_eq__number__of__0,axiom,
% 28.01/28.05 ! [V_v_2] :
% 28.01/28.05 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_number__of2,axiom,
% 28.01/28.05 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))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I5_J,axiom,
% 28.01/28.05 ! [V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I29_J,axiom,
% 28.01/28.05 ! [V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__nat__number__of,axiom,
% 28.01/28.05 ! [V_v_H_2,V_v_2] :
% 28.01/28.05 ( 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)))
% 28.01/28.05 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 28.01/28.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 28.01/28.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_divide__Numeral1,axiom,
% 28.01/28.05 ! [V_x,T_a] :
% 28.01/28.05 ( ( class_Fields_Ofield(T_a)
% 28.01/28.05 & class_Int_Onumber__ring(T_a) )
% 28.01/28.05 => 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 ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_divide__numeral__1,axiom,
% 28.01/28.05 ! [V_a,T_a] :
% 28.01/28.05 ( ( class_Fields_Ofield(T_a)
% 28.01/28.05 & class_Int_Onumber__ring(T_a) )
% 28.01/28.05 => 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 ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_le__nat__number__of,axiom,
% 28.01/28.05 ! [V_v_H_2,V_v_2] :
% 28.01/28.05 ( 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)))
% 28.01/28.05 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 28.01/28.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_one__is__num__one,axiom,
% 28.01/28.05 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__numeral__1__eq__1,axiom,
% 28.01/28.05 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Numeral1__eq1__nat,axiom,
% 28.01/28.05 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 28.01/28.05 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_succ__def,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_le__special_I3_J,axiom,
% 28.01/28.05 ! [V_x_2,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 & class_Rings_Olinordered__idom(T_b) )
% 28.01/28.05 => ( 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)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_le__special_I1_J,axiom,
% 28.01/28.05 ! [V_y_2,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 & class_Rings_Olinordered__idom(T_b) )
% 28.01/28.05 => ( 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)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__special_I1_J,axiom,
% 28.01/28.05 ! [V_y_2,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 & class_Rings_Olinordered__idom(T_b) )
% 28.01/28.05 => ( 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)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__special_I3_J,axiom,
% 28.01/28.05 ! [V_x_2,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 & class_Rings_Olinordered__idom(T_b) )
% 28.01/28.05 => ( 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)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__0__number__of,axiom,
% 28.01/28.05 ! [V_v_2] :
% 28.01/28.05 ( 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)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_numeral__3__eq__3,axiom,
% 28.01/28.05 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)))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_numeral__1__eq__Suc__0,axiom,
% 28.01/28.05 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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power3__eq__cube,axiom,
% 28.01/28.05 ! [V_a,T_a] :
% 28.01/28.05 ( class_Groups_Omonoid__mult(T_a)
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 28.01/28.05 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))))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Suc3__eq__add__3,axiom,
% 28.01/28.05 ! [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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__nat__number__of,axiom,
% 28.01/28.05 ! [V_v_H,V_v] :
% 28.01/28.05 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.01/28.05 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 28.01/28.05 => 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)) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 28.01/28.05 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)))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 28.01/28.05 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)))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_number__of__succ,axiom,
% 28.01/28.05 ! [V_k,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_number__of__pred,axiom,
% 28.01/28.05 ! [V_w,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_le__special_I4_J,axiom,
% 28.01/28.05 ! [V_x_2,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 & class_Rings_Olinordered__idom(T_b) )
% 28.01/28.05 => ( 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)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_le__special_I2_J,axiom,
% 28.01/28.05 ! [V_y_2,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 & class_Rings_Olinordered__idom(T_b) )
% 28.01/28.05 => ( 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)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__special_I4_J,axiom,
% 28.01/28.05 ! [V_x_2,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 & class_Rings_Olinordered__idom(T_b) )
% 28.01/28.05 => ( 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)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__special_I2_J,axiom,
% 28.01/28.05 ! [V_y_2,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 & class_Rings_Olinordered__idom(T_b) )
% 28.01/28.05 => ( 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)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__special_I3_J,axiom,
% 28.01/28.05 ! [V_v,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__special_I2_J,axiom,
% 28.01/28.05 ! [V_w,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 28.01/28.05 ! [V_m,V_n] :
% 28.01/28.05 ( 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))
% 28.01/28.05 => 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)))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__number__of__mult__left,axiom,
% 28.01/28.05 ! [V_k,V_v_H,V_v] :
% 28.01/28.05 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.01/28.05 => 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) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mult__nat__number__of,axiom,
% 28.01/28.05 ! [V_v_H,V_v] :
% 28.01/28.05 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.01/28.05 => 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) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 28.01/28.05 => 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)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_neg__number__of__pred__iff__0,axiom,
% 28.01/28.05 ! [V_v_2] :
% 28.01/28.05 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 28.01/28.05 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 28.01/28.05 ! [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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_div__Suc__eq__div__add3,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Suc__div__eq__add3__div,axiom,
% 28.01/28.05 ! [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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_diff__special_I1_J,axiom,
% 28.01/28.05 ! [V_w,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_diff__special_I2_J,axiom,
% 28.01/28.05 ! [V_v,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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)))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Suc__eq__number__of,axiom,
% 28.01/28.05 ! [V_v_2,V_n_2] :
% 28.01/28.05 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 28.01/28.05 <=> 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))))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_eq__number__of__Suc,axiom,
% 28.01/28.05 ! [V_n_2,V_v_2] :
% 28.01/28.05 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 28.01/28.05 <=> 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))))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__case__number__of,axiom,
% 28.01/28.05 ! [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))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__number__of__Suc,axiom,
% 28.01/28.05 ! [V_n_2,V_v_2] :
% 28.01/28.05 ( 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)))
% 28.01/28.05 <=> 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)))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__Suc__number__of,axiom,
% 28.01/28.05 ! [V_v_2,V_n_2] :
% 28.01/28.05 ( 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)))
% 28.01/28.05 <=> 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))))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_le__Suc__number__of,axiom,
% 28.01/28.05 ! [V_v_2,V_n_2] :
% 28.01/28.05 ( 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)))
% 28.01/28.05 <=> 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))))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_le__number__of__Suc,axiom,
% 28.01/28.05 ! [V_n_2,V_v_2] :
% 28.01/28.05 ( 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)))
% 28.01/28.05 <=> 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)))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Suc__nat__number__of,axiom,
% 28.01/28.05 ! [V_v] :
% 28.01/28.05 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 28.01/28.05 => 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)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_max__Suc__number__of,axiom,
% 28.01/28.05 ! [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)))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_max__number__of__Suc,axiom,
% 28.01/28.05 ! [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)))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__case__add__eq__if,axiom,
% 28.01/28.05 ! [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)))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__rec__add__eq__if,axiom,
% 28.01/28.05 ! [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))))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_eq__special_I2_J,axiom,
% 28.01/28.05 ! [V_y_2,T_b] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 28.01/28.05 <=> 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)))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_eq__special_I4_J,axiom,
% 28.01/28.05 ! [V_x_2,T_b] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 28.01/28.05 <=> 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))))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__rec__number__of,axiom,
% 28.01/28.05 ! [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)))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_iszero__def,axiom,
% 28.01/28.05 ! [V_z_2,T_b] :
% 28.01/28.05 ( class_Rings_Osemiring__1(T_b)
% 28.01/28.05 => ( c_Int_Oiszero(T_b,V_z_2)
% 28.01/28.05 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_iszero__0,axiom,
% 28.01/28.05 ! [T_a] :
% 28.01/28.05 ( class_Rings_Osemiring__1(T_a)
% 28.01/28.05 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_not__iszero__1,axiom,
% 28.01/28.05 ! [T_a] :
% 28.01/28.05 ( class_Rings_Osemiring__1(T_a)
% 28.01/28.05 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__rec__0,axiom,
% 28.01/28.05 ! [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 ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__rec__Suc,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_iszero__Numeral0,axiom,
% 28.01/28.05 ! [T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_iszero__number__of__Bit1,axiom,
% 28.01/28.05 ! [V_w,T_a] :
% 28.01/28.05 ( ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 & class_Int_Oring__char__0(T_a) )
% 28.01/28.05 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_not__iszero__Numeral1,axiom,
% 28.01/28.05 ! [T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_eq__number__of__eq,axiom,
% 28.01/28.05 ! [V_y_2,V_x_2,T_b] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 28.01/28.05 <=> 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)))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_eq__special_I1_J,axiom,
% 28.01/28.05 ! [V_y_2,T_b] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 28.01/28.05 <=> 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)))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_eq__special_I3_J,axiom,
% 28.01/28.05 ! [V_x_2,T_b] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.05 <=> 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)))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_neg__zmod__mult__2,axiom,
% 28.01/28.05 ! [V_b,V_a] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zmod__number__of__Bit1,axiom,
% 28.01/28.05 ! [V_v,V_w] :
% 28.01/28.05 ( ( 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)))
% 28.01/28.05 => 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)) )
% 28.01/28.05 & ( ~ 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)))
% 28.01/28.05 => 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)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_arith__series__int,axiom,
% 28.01/28.05 ! [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)))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I49_J,axiom,
% 28.01/28.05 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I50_J,axiom,
% 28.01/28.05 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I31_J,axiom,
% 28.01/28.05 ! [V_l_2,V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__eq__int__code_I13_J,axiom,
% 28.01/28.05 ! [V_k2_2,V_k1_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_diff__bin__simps_I7_J,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mult__Bit0,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__int__code_I13_J,axiom,
% 28.01/28.05 ! [V_k2_2,V_k1_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I14_J,axiom,
% 28.01/28.05 ! [V_l_2,V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Bit0__def,axiom,
% 28.01/28.05 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__Bit0__Bit0,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I48_J,axiom,
% 28.01/28.05 ! [V_l_2,V_k_2] :
% 28.01/28.05 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 28.01/28.05 <=> V_k_2 = V_l_2 ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_minus__Bit0,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Bit0__Pls,axiom,
% 28.01/28.05 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I38_J,axiom,
% 28.01/28.05 ! [V_l_2] :
% 28.01/28.05 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 28.01/28.05 <=> c_Int_OPls = V_l_2 ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I44_J,axiom,
% 28.01/28.05 ! [V_k_2] :
% 28.01/28.05 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 28.01/28.05 <=> V_k_2 = c_Int_OPls ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_bin__less__0__simps_I3_J,axiom,
% 28.01/28.05 ! [V_w_2] :
% 28.01/28.05 ( 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)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I27_J,axiom,
% 28.01/28.05 ! [V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I21_J,axiom,
% 28.01/28.05 ! [V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__eq__int__code_I14_J,axiom,
% 28.01/28.05 ! [V_k2_2,V_k1_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I32_J,axiom,
% 28.01/28.05 ! [V_l_2,V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I4_J,axiom,
% 28.01/28.05 ! [V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I10_J,axiom,
% 28.01/28.05 ! [V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I16_J,axiom,
% 28.01/28.05 ! [V_l_2,V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__int__code_I15_J,axiom,
% 28.01/28.05 ! [V_k2_2,V_k1_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__Bit0__Bit1,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__Bit1__Bit0,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_diff__bin__simps_I3_J,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_diff__bin__simps_I10_J,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_diff__bin__simps_I9_J,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zdiv__number__of__Bit0,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_neg__number__of__Bit0,axiom,
% 28.01/28.05 ! [V_w_2] :
% 28.01/28.05 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 28.01/28.05 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_pred__Bit1,axiom,
% 28.01/28.05 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_pred__Bit0,axiom,
% 28.01/28.05 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_iszero__number__of__Bit0,axiom,
% 28.01/28.05 ! [V_w_2,T_b] :
% 28.01/28.05 ( ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 & class_Int_Oring__char__0(T_b) )
% 28.01/28.05 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 28.01/28.05 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_succ__Bit0,axiom,
% 28.01/28.05 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_succ__Bit1,axiom,
% 28.01/28.05 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__number__of__Bit0,axiom,
% 28.01/28.05 ! [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))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_number__of__Bit0,axiom,
% 28.01/28.05 ! [V_w,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I15_J,axiom,
% 28.01/28.05 ! [V_l_2,V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__int__code_I14_J,axiom,
% 28.01/28.05 ! [V_k2_2,V_k1_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I33_J,axiom,
% 28.01/28.05 ! [V_l_2,V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__eq__int__code_I15_J,axiom,
% 28.01/28.05 ! [V_k2_2,V_k1_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_card__UNIV__bool,axiom,
% 28.01/28.05 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))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mult__Bit1,axiom,
% 28.01/28.05 ! [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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_diff__bin__simps_I8_J,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__Bit1__Bit1,axiom,
% 28.01/28.05 ! [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))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power__number__of__even,axiom,
% 28.01/28.05 ! [V_w_2,V_z_2,T_b] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 => 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))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zpower__number__of__even,axiom,
% 28.01/28.05 ! [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))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_double__number__of__Bit0,axiom,
% 28.01/28.05 ! [V_w,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_number__of1,axiom,
% 28.01/28.05 ! [V_n] :
% 28.01/28.05 ( 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)))
% 28.01/28.05 => ( 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))))
% 28.01/28.05 & 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)))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 28.01/28.05 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power__number__of__even__number__of,axiom,
% 28.01/28.05 ! [V_w_2,V_v_2,T_b] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_b)
% 28.01/28.05 => 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))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mult__2__right,axiom,
% 28.01/28.05 ! [V_z,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mult__2,axiom,
% 28.01/28.05 ! [V_z,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_one__add__one__is__two,axiom,
% 28.01/28.05 ! [T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zero__power2,axiom,
% 28.01/28.05 ! [T_a] :
% 28.01/28.05 ( class_Rings_Osemiring__1(T_a)
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zero__eq__power2,axiom,
% 28.01/28.05 ! [V_a_2,T_b] :
% 28.01/28.05 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 28.01/28.05 => ( 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)
% 28.01/28.05 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_numeral__2__eq__2,axiom,
% 28.01/28.05 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))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_semiring__norm_I115_J,axiom,
% 28.01/28.05 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))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 28.01/28.05 ! [V_x,T_a] :
% 28.01/28.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.01/28.05 => 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)))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power2__eq__square,axiom,
% 28.01/28.05 ! [V_a,T_a] :
% 28.01/28.05 ( class_Groups_Omonoid__mult(T_a)
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 28.01/28.05 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))))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__2__eq__Suc_H,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__2__eq__Suc,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_one__power2,axiom,
% 28.01/28.05 ! [T_a] :
% 28.01/28.05 ( class_Rings_Osemiring__1(T_a)
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power2__minus,axiom,
% 28.01/28.05 ! [V_a,T_a] :
% 28.01/28.05 ( class_Rings_Oring__1(T_a)
% 28.01/28.05 => 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)))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__mult__2__right,axiom,
% 28.01/28.05 ! [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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__mult__2,axiom,
% 28.01/28.05 ! [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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power__even__eq,axiom,
% 28.01/28.05 ! [V_n,V_a,T_a] :
% 28.01/28.05 ( class_Groups_Omonoid__mult(T_a)
% 28.01/28.05 => 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)))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 28.01/28.05 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)))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 28.01/28.05 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)))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_abs__power2,axiom,
% 28.01/28.05 ! [V_a,T_a] :
% 28.01/28.05 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.05 => 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)))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power2__abs,axiom,
% 28.01/28.05 ! [V_a,T_a] :
% 28.01/28.05 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.05 => 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)))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__1__add__1,axiom,
% 28.01/28.05 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))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod2__Suc__Suc,axiom,
% 28.01/28.05 ! [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)))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_div2__Suc__Suc,axiom,
% 28.01/28.05 ! [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))))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zmod__number__of__Bit0,axiom,
% 28.01/28.05 ! [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))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__self__div__2,axiom,
% 28.01/28.05 ! [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 ).
% 28.01/28.05
% 28.01/28.05 fof(fact_half__gt__zero,axiom,
% 28.01/28.05 ! [V_r,T_a] :
% 28.01/28.05 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 28.01/28.05 & class_Int_Onumber__ring(T_a) )
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 28.01/28.05 => 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)))))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_half__gt__zero__iff,axiom,
% 28.01/28.05 ! [V_r_2,T_b] :
% 28.01/28.05 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 28.01/28.05 & class_Int_Onumber__ring(T_b) )
% 28.01/28.05 => ( 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))))))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power2__eq__imp__eq,axiom,
% 28.01/28.05 ! [V_y,V_x,T_a] :
% 28.01/28.05 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.05 => ( 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))))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.01/28.05 => V_x = V_y ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power2__le__imp__le,axiom,
% 28.01/28.05 ! [V_y,V_x,T_a] :
% 28.01/28.05 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.05 => ( 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))))))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.01/28.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zero__le__power2,axiom,
% 28.01/28.05 ! [V_a,T_a] :
% 28.01/28.05 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.05 => 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)))))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power2__less__0,axiom,
% 28.01/28.05 ! [V_a,T_a] :
% 28.01/28.05 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.05 => ~ 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))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zero__less__power2,axiom,
% 28.01/28.05 ! [V_a_2,T_b] :
% 28.01/28.05 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.05 => ( 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))))))
% 28.01/28.05 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_sum__power2__eq__zero__iff,axiom,
% 28.01/28.05 ! [V_y_2,V_x_2,T_b] :
% 28.01/28.05 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.05 => ( 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)
% 28.01/28.05 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.05 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power2__eq__square__number__of,axiom,
% 28.01/28.05 ! [V_w,T_b] :
% 28.01/28.05 ( ( class_Groups_Omonoid__mult(T_b)
% 28.01/28.05 & class_Int_Onumber(T_b) )
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_less__2__cases,axiom,
% 28.01/28.05 ! [V_n] :
% 28.01/28.05 ( 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)))))
% 28.01/28.05 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.05 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nat__2,axiom,
% 28.01/28.05 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))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power2__eq__1__iff,axiom,
% 28.01/28.05 ! [V_a_2,T_b] :
% 28.01/28.05 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 28.01/28.05 => ( 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)
% 28.01/28.05 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 28.01/28.05 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 28.01/28.05 ! [V_n,V_x,T_a] :
% 28.01/28.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power__minus__even,axiom,
% 28.01/28.05 ! [V_n,V_a,T_a] :
% 28.01/28.05 ( class_Rings_Oring__1(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power2__less__imp__less,axiom,
% 28.01/28.05 ! [V_y,V_x,T_a] :
% 28.01/28.05 ( class_Rings_Olinordered__semidom(T_a)
% 28.01/28.05 => ( 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))))))
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 28.01/28.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_sum__power2__ge__zero,axiom,
% 28.01/28.05 ! [V_y,V_x,T_a] :
% 28.01/28.05 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.05 => 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))))))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_sum__power2__le__zero__iff,axiom,
% 28.01/28.05 ! [V_y_2,V_x_2,T_b] :
% 28.01/28.05 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.05 => ( 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)))
% 28.01/28.05 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.05 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_sum__power2__gt__zero__iff,axiom,
% 28.01/28.05 ! [V_y_2,V_x_2,T_b] :
% 28.01/28.05 ( class_Rings_Olinordered__idom(T_b)
% 28.01/28.05 => ( 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)))))))
% 28.01/28.05 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.01/28.05 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_not__sum__power2__lt__zero,axiom,
% 28.01/28.05 ! [V_y,V_x,T_a] :
% 28.01/28.05 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.05 => ~ 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))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power2__sum,axiom,
% 28.01/28.05 ! [V_y,V_x,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zero__le__even__power_H,axiom,
% 28.01/28.05 ! [V_n,V_a,T_a] :
% 28.01/28.05 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.05 => 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)))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power__odd__eq,axiom,
% 28.01/28.05 ! [V_n,V_a,T_a] :
% 28.01/28.05 ( class_Groups_Omonoid__mult(T_a)
% 28.01/28.05 => 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))))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 28.01/28.05 ! [V_n,V_x,T_a] :
% 28.01/28.05 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.01/28.05 => 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))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power__minus1__even,axiom,
% 28.01/28.05 ! [V_n,T_a] :
% 28.01/28.05 ( class_Rings_Oring__1(T_a)
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zdiv__number__of__Bit1,axiom,
% 28.01/28.05 ! [V_v,V_w] :
% 28.01/28.05 ( ( 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)))
% 28.01/28.05 => 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)) )
% 28.01/28.05 & ( ~ 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)))
% 28.01/28.05 => 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)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mod2__gr__0,axiom,
% 28.01/28.05 ! [V_m_2] :
% 28.01/28.05 ( 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))))))
% 28.01/28.05 <=> 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_div__2__gt__zero,axiom,
% 28.01/28.05 ! [V_n] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 28.01/28.05 => 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)))))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power2__diff,axiom,
% 28.01/28.05 ! [V_y,V_x,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 28.01/28.05 ! [V_n,V_a,T_a] :
% 28.01/28.05 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.05 => ( 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)))))
% 28.01/28.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_odd__power__less__zero,axiom,
% 28.01/28.05 ! [V_n,V_a,T_a] :
% 28.01/28.05 ( class_Rings_Olinordered__idom(T_a)
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 28.01/28.05 => 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))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power__minus1__odd,axiom,
% 28.01/28.05 ! [V_n,T_a] :
% 28.01/28.05 ( class_Rings_Oring__1(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 28.01/28.05 ! [V_n] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.01/28.05 => 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)))))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_of__nat__double,axiom,
% 28.01/28.05 ! [V_x,T_a] :
% 28.01/28.05 ( class_Rings_Osemiring__1(T_a)
% 28.01/28.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 28.01/28.05 => 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))) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_pos__zmod__mult__2,axiom,
% 28.01/28.05 ! [V_b,V_a] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.01/28.05 => 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))) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_pos__zdiv__mult__2,axiom,
% 28.01/28.05 ! [V_b,V_a] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_neg__zdiv__mult__2,axiom,
% 28.01/28.05 ! [V_b,V_a] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_int__of__code,axiom,
% 28.01/28.05 ! [V_k] :
% 28.01/28.05 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.01/28.05 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 28.01/28.05 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.01/28.05 => ( ( 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)
% 28.01/28.05 => 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)))))) )
% 28.01/28.05 & ( 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)
% 28.01/28.05 => 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)) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_of__int__num,axiom,
% 28.01/28.05 ! [V_k_2,T_b] :
% 28.01/28.05 ( class_Rings_Oring__1(T_b)
% 28.01/28.05 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.05 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 28.01/28.05 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.05 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.05 => 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))) )
% 28.01/28.05 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.05 => 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))))) ) ) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_power__m1__odd,axiom,
% 28.01/28.05 ! [V_n,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I45_J,axiom,
% 28.01/28.05 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I42_J,axiom,
% 28.01/28.05 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I37_J,axiom,
% 28.01/28.05 c_Int_OPls != c_Int_OMin ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I40_J,axiom,
% 28.01/28.05 c_Int_OMin != c_Int_OPls ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I7_J,axiom,
% 28.01/28.05 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_code__numeral__zero__minus__one,axiom,
% 28.01/28.05 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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I24_J,axiom,
% 28.01/28.05 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I47_J,axiom,
% 28.01/28.05 ! [V_k_2] :
% 28.01/28.05 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 28.01/28.05 <=> V_k_2 = c_Int_OMin ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I43_J,axiom,
% 28.01/28.05 ! [V_l_2] :
% 28.01/28.05 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 28.01/28.05 <=> c_Int_OMin = V_l_2 ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Bit1__Min,axiom,
% 28.01/28.05 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 28.01/28.05
% 28.01/28.05 fof(fact_bin__less__0__simps_I2_J,axiom,
% 28.01/28.05 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I23_J,axiom,
% 28.01/28.05 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I20_J,axiom,
% 28.01/28.05 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I26_J,axiom,
% 28.01/28.05 ! [V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I30_J,axiom,
% 28.01/28.05 ! [V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I3_J,axiom,
% 28.01/28.05 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I6_J,axiom,
% 28.01/28.05 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I13_J,axiom,
% 28.01/28.05 ! [V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I9_J,axiom,
% 28.01/28.05 ! [V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I28_J,axiom,
% 28.01/28.05 ! [V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I8_J,axiom,
% 28.01/28.05 ! [V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_eq__number__of__Pls__Min,axiom,
% 28.01/28.05 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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_Int_OMin__def,axiom,
% 28.01/28.05 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mult__Min,axiom,
% 28.01/28.05 ! [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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_neg__number__of__Min,axiom,
% 28.01/28.05 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_pred__Pls,axiom,
% 28.01/28.05 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__Min__right,axiom,
% 28.01/28.05 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_add__Min,axiom,
% 28.01/28.05 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_pred__Min,axiom,
% 28.01/28.05 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_nonzero__number__of__Min,axiom,
% 28.01/28.05 ! [T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_succ__Min,axiom,
% 28.01/28.05 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 28.01/28.05
% 28.01/28.05 fof(fact_diff__bin__simps_I2_J,axiom,
% 28.01/28.05 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mult__minus1,axiom,
% 28.01/28.05 ! [V_z,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_mult__minus1__right,axiom,
% 28.01/28.05 ! [V_z,T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_number__of__Min,axiom,
% 28.01/28.05 ! [T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_arith__simps_I31_J,axiom,
% 28.01/28.05 ! [T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_abs__minus__one,axiom,
% 28.01/28.05 ! [T_a] :
% 28.01/28.05 ( ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 & class_Rings_Olinordered__idom(T_a) )
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_divide__minus1,axiom,
% 28.01/28.05 ! [V_x,T_a] :
% 28.01/28.05 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 28.01/28.05 & class_Int_Onumber__ring(T_a) )
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I11_J,axiom,
% 28.01/28.05 ! [V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_rel__simps_I25_J,axiom,
% 28.01/28.05 ! [V_k_2] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 28.01/28.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zmod__minus1__right,axiom,
% 28.01/28.05 ! [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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_diff__bin__simps_I4_J,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_minus__Min,axiom,
% 28.01/28.05 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 28.01/28.05 ! [V_n,V_m] :
% 28.01/28.05 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 28.01/28.05 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 28.01/28.05 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zmult__eq__1__iff,axiom,
% 28.01/28.05 ! [V_n_2,V_m_2] :
% 28.01/28.05 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 28.01/28.05 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 28.01/28.05 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 28.01/28.05 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 28.01/28.05 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_diff__bin__simps_I6_J,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_diff__bin__simps_I5_J,axiom,
% 28.01/28.05 ! [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)) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_of__int__m1,axiom,
% 28.01/28.05 ! [T_a] :
% 28.01/28.05 ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zdiv__minus1__right,axiom,
% 28.01/28.05 ! [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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zero__code__numeral__code,axiom,
% 28.01/28.05 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) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_minus1__divide,axiom,
% 28.01/28.05 ! [V_x,T_a] :
% 28.01/28.05 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 28.01/28.05 & class_Int_Onumber__ring(T_a) )
% 28.01/28.05 => 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)) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_abs__power__minus__one,axiom,
% 28.01/28.05 ! [V_n,T_a] :
% 28.01/28.05 ( ( class_Int_Onumber__ring(T_a)
% 28.01/28.05 & class_Rings_Olinordered__idom(T_a) )
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_div__eq__minus1,axiom,
% 28.01/28.05 ! [V_b] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.05 => 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) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_div__pos__neg__trivial,axiom,
% 28.01/28.05 ! [V_b,V_a] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.01/28.05 => ( 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)))
% 28.01/28.05 => 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) ) ) ).
% 28.01/28.05
% 28.01/28.05 fof(fact_zmod__minus1,axiom,
% 28.01/28.05 ! [V_b] :
% 28.01/28.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.06 => 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_one__code__numeral__code,axiom,
% 28.01/28.06 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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_power__m1__even,axiom,
% 28.01/28.06 ! [V_n,T_a] :
% 28.01/28.06 ( class_Int_Onumber__ring(T_a)
% 28.01/28.06 => 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) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Nitpick_OFrac__def,axiom,
% 28.01/28.06 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)))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_int__ge__less__than2__def,axiom,
% 28.01/28.06 ! [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)))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_int__ge__less__than__def,axiom,
% 28.01/28.06 ! [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)))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_inj__graph,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Nitpick_Oprod__def,axiom,
% 28.01/28.06 ! [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)))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_nat__of__aux__code,axiom,
% 28.01/28.06 ! [V_n,V_i] :
% 28.01/28.06 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.01/28.06 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 28.01/28.06 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__int__rel__def,axiom,
% 28.01/28.06 ! [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))))))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__int__correct,axiom,
% 28.01/28.06 ! [V_a,V_b] :
% 28.01/28.06 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_zmult2__lemma,axiom,
% 28.01/28.06 ! [V_c,V_r,V_q,V_b,V_a] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 28.01/28.06 => 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)))) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_code__numeral_Osize_I1_J,axiom,
% 28.01/28.06 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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Nats__number__of,axiom,
% 28.01/28.06 ! [V_w_2,T_b] :
% 28.01/28.06 ( class_Int_Onumber__ring(T_b)
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 28.01/28.06 => 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))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_bot__empty__eq2,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 <=> 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)))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_pred__equals__eq2,axiom,
% 28.01/28.06 ! [V_S_2,V_R_2,T_c,T_b] :
% 28.01/28.06 ( 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)
% 28.01/28.06 <=> V_R_2 = V_S_2 ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_inf__Int__eq2,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 <=> 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_pred__subset__eq2,axiom,
% 28.01/28.06 ! [V_S_2,V_R_2,T_c,T_b] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 <=> 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_sup__Un__eq2,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 <=> 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_enum__ex__prod__def,axiom,
% 28.01/28.06 ! [V_P_2,T_b,T_c] :
% 28.01/28.06 ( ( class_Enum_Oenum(T_c)
% 28.01/28.06 & class_Enum_Oenum(T_b) )
% 28.01/28.06 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_P_2))
% 28.01/28.06 <=> 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))))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_enum__all__prod__def,axiom,
% 28.01/28.06 ! [V_P_2,T_b,T_c] :
% 28.01/28.06 ( ( class_Enum_Oenum(T_c)
% 28.01/28.06 & class_Enum_Oenum(T_b) )
% 28.01/28.06 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_P_2))
% 28.01/28.06 <=> 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))))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Image__iff,axiom,
% 28.01/28.06 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 28.01/28.06 <=> ? [B_x] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 28.01/28.06 & 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_rev__ImageI,axiom,
% 28.01/28.06 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.06 => ( 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))
% 28.01/28.06 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_unique__remainder,axiom,
% 28.01/28.06 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => V_r = V_r_H ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_unique__quotient,axiom,
% 28.01/28.06 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => V_q = V_q_H ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_self__remainder,axiom,
% 28.01/28.06 ! [V_r,V_q,V_a] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__int__rel__0,axiom,
% 28.01/28.06 ! [V_b] :
% 28.01/28.06 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => 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)))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_SUP__UN__eq2,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 <=> 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_INF__INT__eq2,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 <=> 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_self__quotient,axiom,
% 28.01/28.06 ! [V_r,V_q,V_a] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__int__rel__mod,axiom,
% 28.01/28.06 ! [V_r,V_q,V_b,V_a] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__int__rel__div,axiom,
% 28.01/28.06 ! [V_r,V_q,V_b,V_a] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Nats__0,axiom,
% 28.01/28.06 ! [T_b] :
% 28.01/28.06 ( class_Rings_Osemiring__1(T_b)
% 28.01/28.06 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__int__mod__div,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Nats__add,axiom,
% 28.01/28.06 ! [V_b_2,V_a_2,T_b] :
% 28.01/28.06 ( class_Rings_Osemiring__1(T_b)
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 28.01/28.06 => 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))) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Nats__mult,axiom,
% 28.01/28.06 ! [V_b_2,V_a_2,T_b] :
% 28.01/28.06 ( class_Rings_Osemiring__1(T_b)
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 28.01/28.06 => 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))) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Nats__1,axiom,
% 28.01/28.06 ! [T_b] :
% 28.01/28.06 ( class_Rings_Osemiring__1(T_b)
% 28.01/28.06 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_of__nat__in__Nats,axiom,
% 28.01/28.06 ! [V_n_2,T_b] :
% 28.01/28.06 ( class_Rings_Osemiring__1(T_b)
% 28.01/28.06 => 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Image__singleton__iff,axiom,
% 28.01/28.06 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
% 28.01/28.06 ( 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))))))
% 28.01/28.06 <=> 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__int__rel__div__mod,axiom,
% 28.01/28.06 ! [V_a,V_b] :
% 28.01/28.06 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => 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)))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Image__singleton,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_zadd1__lemma,axiom,
% 28.01/28.06 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => 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)))) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_zminus1__lemma,axiom,
% 28.01/28.06 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => 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))))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__int__relI,axiom,
% 28.01/28.06 ! [V_r,V_q,V_b,V_a] :
% 28.01/28.06 ( 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)
% 28.01/28.06 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 28.01/28.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 28.01/28.06 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 28.01/28.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 28.01/28.06 => 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))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_zmult1__lemma,axiom,
% 28.01/28.06 ! [V_a,V_r,V_q,V_c,V_b] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => 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)))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_pair__imageI,axiom,
% 28.01/28.06 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_norm__frac_Osimps,axiom,
% 28.01/28.06 ! [V_a_2,V_b_2] :
% 28.01/28.06 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.06 => 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)) )
% 28.01/28.06 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.06 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 28.01/28.06 => 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)) )
% 28.01/28.06 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 28.01/28.06 => 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))) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_adjust__eq,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_sup2E,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_sup2CI,axiom,
% 28.01/28.06 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 28.01/28.06 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 28.01/28.06 => 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_inf2I,axiom,
% 28.01/28.06 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_inf2E,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 28.01/28.06 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_mem__splitI,axiom,
% 28.01/28.06 ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
% 28.01/28.06 => 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)))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_splitI,axiom,
% 28.01/28.06 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 28.01/28.06 => 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_prod__caseI,axiom,
% 28.01/28.06 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 28.01/28.06 => 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_bot2E,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_swap__inj__on,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_splitD_H,axiom,
% 28.01/28.06 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_inf2D1,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_inf2D2,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_sup2I1,axiom,
% 28.01/28.06 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 28.01/28.06 => 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_sup2I2,axiom,
% 28.01/28.06 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 28.01/28.06 => 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_rev__predicate2D,axiom,
% 28.01/28.06 ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_P_2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 28.01/28.06 => ( 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))
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_predicate2D,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Pair__inject,axiom,
% 28.01/28.06 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 28.01/28.06 ( 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)
% 28.01/28.06 => ~ ( V_a = V_a_H
% 28.01/28.06 => V_b != V_b_H ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Pair__eq,axiom,
% 28.01/28.06 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 28.01/28.06 ( 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)
% 28.01/28.06 <=> ( V_a_2 = V_a_H_2
% 28.01/28.06 & V_b_2 = V_b_H_2 ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_split__paired__All,axiom,
% 28.01/28.06 ! [T_c,T_b,V_P_2] :
% 28.01/28.06 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 28.01/28.06 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_split__weak__cong,axiom,
% 28.01/28.06 ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 28.01/28.06 ( V_p_2 = V_q_2
% 28.01/28.06 => 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) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_split__twice,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_split__conv,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_prod_Osimps_I2_J,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_splitD,axiom,
% 28.01/28.06 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_split__eta,axiom,
% 28.01/28.06 ! [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 ).
% 28.01/28.06
% 28.01/28.06 fof(fact_The__split__eq,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_split__paired__The,axiom,
% 28.01/28.06 ! [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)))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_adjust__def,axiom,
% 28.01/28.06 ! [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))))))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_in__rel__def,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 28.01/28.06 <=> 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_div__mod__code__numeral__def,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 28.01/28.06 ! [V_w] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( ( 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))))
% 28.01/28.06 => 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))) )
% 28.01/28.06 & ( ~ 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))))
% 28.01/28.06 => 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)))) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_negDivAlg__correct,axiom,
% 28.01/28.06 ! [V_b,V_a] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.06 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_negDivAlg__div__mod,axiom,
% 28.01/28.06 ! [V_l,V_k] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_negDivAlg__minus1,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_negDivAlg_Osimps,axiom,
% 28.01/28.06 ! [V_b,V_a] :
% 28.01/28.06 ( ( ( 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)))
% 28.01/28.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.01/28.06 => 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)) )
% 28.01/28.06 & ( ~ ( 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)))
% 28.01/28.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.01/28.06 => 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))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_negDivAlg__eqn__number__of,axiom,
% 28.01/28.06 ! [V_w,V_v] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( ( 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))))
% 28.01/28.06 => 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))) )
% 28.01/28.06 & ( ~ 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))))
% 28.01/28.06 => 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)))) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_negDivAlg__eqn,axiom,
% 28.01/28.06 ! [V_a,V_b] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.06 => ( ( 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)))
% 28.01/28.06 => 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)) )
% 28.01/28.06 & ( ~ 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)))
% 28.01/28.06 => 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))) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Nitpick_Orefl_H__def,axiom,
% 28.01/28.06 ! [V_r_2,T_b] :
% 28.01/28.06 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 28.01/28.06 <=> ! [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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 28.01/28.06 ! [V_w] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( ( 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)))
% 28.01/28.06 => 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)) )
% 28.01/28.06 & ( ~ 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)))
% 28.01/28.06 => 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)))) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_posDivAlg_Osimps,axiom,
% 28.01/28.06 ! [V_b,V_a] :
% 28.01/28.06 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 28.01/28.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.01/28.06 => 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) )
% 28.01/28.06 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 28.01/28.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.01/28.06 => 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))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_posDivAlg__0,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_posDivAlg__correct,axiom,
% 28.01/28.06 ! [V_b,V_a] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.06 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_posDivAlg__div__mod,axiom,
% 28.01/28.06 ! [V_l,V_k] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_posDivAlg__eqn__number__of,axiom,
% 28.01/28.06 ! [V_w,V_v] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( ( 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)))
% 28.01/28.06 => 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)) )
% 28.01/28.06 & ( ~ 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)))
% 28.01/28.06 => 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)))) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_posDivAlg__eqn,axiom,
% 28.01/28.06 ! [V_a,V_b] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.06 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 28.01/28.06 => 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) )
% 28.01/28.06 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 28.01/28.06 => 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))) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__int__def,axiom,
% 28.01/28.06 ! [V_b,V_a] :
% 28.01/28.06 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.01/28.06 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.06 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 28.01/28.06 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.06 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => 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)) )
% 28.01/28.06 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => 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))) ) ) ) ) )
% 28.01/28.06 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.01/28.06 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.06 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 28.01/28.06 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.06 => 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))) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__nat__step,axiom,
% 28.01/28.06 ! [V_m,V_n] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__int__pdivmod,axiom,
% 28.01/28.06 ! [V_l_2,V_k_2] :
% 28.01/28.06 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => 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)) )
% 28.01/28.06 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => 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) )
% 28.01/28.06 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => 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)))) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_apsnd__compose,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_negateSnd__def,axiom,
% 28.01/28.06 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_apsnd__conv,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__nat__zero,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__nat__base,axiom,
% 28.01/28.06 ! [V_n,V_m] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 28.01/28.06 => 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) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_negateSnd__eq,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__nat__div__mod,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__int__rel__neg,axiom,
% 28.01/28.06 ! [V_qr,V_b,V_a] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__nat__if,axiom,
% 28.01/28.06 ! [V_m_2,V_n_2] :
% 28.01/28.06 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 28.01/28.06 => 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) )
% 28.01/28.06 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_pdivmod__def,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_pdivmod__posDivAlg,axiom,
% 28.01/28.06 ! [V_k,V_l] :
% 28.01/28.06 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => 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)) )
% 28.01/28.06 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__int__code,axiom,
% 28.01/28.06 ! [V_l_2,V_k_2] :
% 28.01/28.06 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => 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)) )
% 28.01/28.06 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => 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) )
% 28.01/28.06 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 => 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)))) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 28.01/28.06 ! [V_a,V_r,V_q,V_c,V_b] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 28.01/28.06 => 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)))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 28.01/28.06 ! [V_c,V_r,V_q,V_b,V_a] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 28.01/28.06 => 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)))) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_negDivAlg_Opsimps,axiom,
% 28.01/28.06 ! [V_b_2,V_a_2] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( ( ( 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)))
% 28.01/28.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.01/28.06 => 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)) )
% 28.01/28.06 & ( ~ ( 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)))
% 28.01/28.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.01/28.06 => 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))) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__nat__rel__unique,axiom,
% 28.01/28.06 ! [V_qr_H,V_qr,V_n,V_m] :
% 28.01/28.06 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 28.01/28.06 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 28.01/28.06 => V_qr = V_qr_H ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 28.01/28.06 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__nat__eq,axiom,
% 28.01/28.06 ! [V_qr,V_n,V_m] :
% 28.01/28.06 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 28.01/28.06 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__nat__def,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_mod__eq,axiom,
% 28.01/28.06 ! [V_r,V_q,V_n,V_m] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_div__eq,axiom,
% 28.01/28.06 ! [V_r,V_q,V_n,V_m] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__nat__rel,axiom,
% 28.01/28.06 ! [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)))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 28.01/28.06 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 28.01/28.06 => 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)))) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_posDivAlg_Opsimps,axiom,
% 28.01/28.06 ! [V_b_2,V_a_2] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 28.01/28.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.01/28.06 => 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) )
% 28.01/28.06 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 28.01/28.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.01/28.06 => 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))) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_norm__frac_Opsimps,axiom,
% 28.01/28.06 ! [V_b_2,V_a_2] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.06 => 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)) )
% 28.01/28.06 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.06 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 28.01/28.06 => 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)) )
% 28.01/28.06 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 28.01/28.06 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 28.01/28.06 => 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))) ) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_negDivAlg_Opinduct,axiom,
% 28.01/28.06 ! [V_P_2,V_a1_2,V_a0_2] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( ! [B_a,B_b] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( ( ~ ( 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)))
% 28.01/28.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.01/28.06 => 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))) )
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_posDivAlg_Opinduct,axiom,
% 28.01/28.06 ! [V_P_2,V_a1_2,V_a0_2] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( ! [B_a,B_b] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 28.01/28.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 28.01/28.06 => 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))) )
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_accp__subset,axiom,
% 28.01/28.06 ! [V_R2_2,V_R1_2,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_mod__pos__neg__1__number__of,axiom,
% 28.01/28.06 ! [V_w] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => 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))))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_snd__eqD,axiom,
% 28.01/28.06 ! [V_a,V_y,V_x,T_a,T_b] :
% 28.01/28.06 ( 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
% 28.01/28.06 => V_y = V_a ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_snd__conv,axiom,
% 28.01/28.06 ! [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 ).
% 28.01/28.06
% 28.01/28.06 fof(fact_snd__def,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_snd__apsnd,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_apsnd__eq__conv,axiom,
% 28.01/28.06 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 28.01/28.06 ( 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)
% 28.01/28.06 <=> 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_mod__int__def,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_accp__downward,axiom,
% 28.01/28.06 ! [V_a_2,V_b_2,V_r_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 28.01/28.06 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_accp_Oequations,axiom,
% 28.01/28.06 ! [V_a_2,V_r_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 28.01/28.06 <=> ! [B_x] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 28.01/28.06 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_accp_Osimps,axiom,
% 28.01/28.06 ! [V_a_2,V_r_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 28.01/28.06 <=> ! [B_x] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 28.01/28.06 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_mod__neg__pos,axiom,
% 28.01/28.06 ! [V_b,V_a] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_mod__pos__pos,axiom,
% 28.01/28.06 ! [V_b,V_a] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_mod__pos__pos__1__number__of,axiom,
% 28.01/28.06 ! [V_w] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_mod__pos__neg,axiom,
% 28.01/28.06 ! [V_b,V_a] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.06 => 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)))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_mod__neg__neg,axiom,
% 28.01/28.06 ! [V_b,V_a] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.06 => 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)))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_nat__gcd_Opsimps,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.06 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 28.01/28.06 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.06 => 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)) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_nat_Osize_I2_J,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_in__measure,axiom,
% 28.01/28.06 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 <=> 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_mod__nat__def,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_nat_Osize_I1_J,axiom,
% 28.01/28.06 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_irrefl__def,axiom,
% 28.01/28.06 ! [V_r_2,T_b] :
% 28.01/28.06 ( c_Relation_Oirrefl(T_b,V_r_2)
% 28.01/28.06 <=> ! [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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_norm__frac_Opinduct,axiom,
% 28.01/28.06 ! [V_P_2,V_a1_2,V_a0_2] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( ! [B_a,B_b] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.06 => 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))) )
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_div__pos__neg__1__number__of,axiom,
% 28.01/28.06 ! [V_w] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => 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))))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Pair__fst__snd__eq,axiom,
% 28.01/28.06 ! [T_c,T_b,V_t_2,V_s_2] :
% 28.01/28.06 ( V_s_2 = V_t_2
% 28.01/28.06 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 28.01/28.06 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_prod__eqI,axiom,
% 28.01/28.06 ! [V_q,V_p,T_b,T_a] :
% 28.01/28.06 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 28.01/28.06 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 28.01/28.06 => V_p = V_q ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_fst__eqD,axiom,
% 28.01/28.06 ! [V_a,V_y,V_x,T_b,T_a] :
% 28.01/28.06 ( 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
% 28.01/28.06 => V_x = V_a ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_fst__conv,axiom,
% 28.01/28.06 ! [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 ).
% 28.01/28.06
% 28.01/28.06 fof(fact_fst__def,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_fst__apsnd,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_pair__collapse,axiom,
% 28.01/28.06 ! [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 ).
% 28.01/28.06
% 28.01/28.06 fof(fact_surjective__pairing,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_prod__case__beta,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_div__int__def,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_split__beta,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_split__comp__eq,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_split__def,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_split__comp,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_The__split,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_div__neg__pos,axiom,
% 28.01/28.06 ! [V_b,V_a] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_div__pos__pos,axiom,
% 28.01/28.06 ! [V_b,V_a] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_div__pos__pos__1__number__of,axiom,
% 28.01/28.06 ! [V_w] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_div__pos__neg,axiom,
% 28.01/28.06 ! [V_b,V_a] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.06 => 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)))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_div__neg__neg,axiom,
% 28.01/28.06 ! [V_b,V_a] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 28.01/28.06 => 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)))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_prod__size__simp,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_exI__realizer,axiom,
% 28.01/28.06 ! [T_b,T_c,V_x_2,V_y_2,V_P_2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
% 28.01/28.06 => 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)))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_conjI__realizer,axiom,
% 28.01/28.06 ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_P_2] :
% 28.01/28.06 ( hBOOL(hAPP(V_P_2,V_p_2))
% 28.01/28.06 => ( hBOOL(hAPP(V_Q_2,V_q_2))
% 28.01/28.06 => ( 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))))
% 28.01/28.06 & 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)))) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_div__nat__def,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_divmod__nat__rel__def,axiom,
% 28.01/28.06 ! [V_qr_2,V_n_2,V_m_2] :
% 28.01/28.06 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 28.01/28.06 <=> ( 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))
% 28.01/28.06 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.06 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.01/28.06 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.06 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 28.01/28.06 => ( 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)))
% 28.01/28.06 & 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)) ) )
% 28.01/28.06 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 28.01/28.06 => ( 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)))
% 28.01/28.06 & 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))) ) ) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_nat__def,axiom,
% 28.01/28.06 ! [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)))))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_nat__gcd_Opinduct,axiom,
% 28.01/28.06 ! [V_P_2,V_a1_2,V_a0_2] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( ! [B_x,B_y] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_inv__image__def,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Rep__Integ__inject,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2] :
% 28.01/28.06 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 28.01/28.06 <=> V_x_2 = V_y_2 ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_in__inv__image,axiom,
% 28.01/28.06 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 <=> 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_rp__inv__image__def,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_equiv__class__nondisjoint,axiom,
% 28.01/28.06 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.06 => ( 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)))))))
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_subset__equiv__class,axiom,
% 28.01/28.06 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.06 => ( 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))))))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 28.01/28.06 => 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)) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Union__quotient,axiom,
% 28.01/28.06 ! [V_r_2,V_A_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.06 => 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 ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_equiv__class__self,axiom,
% 28.01/28.06 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.06 => 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)))))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_quotient__disj,axiom,
% 28.01/28.06 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => ( V_X_2 = V_Y_2
% 28.01/28.06 | 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)) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_equiv__class__eq,axiom,
% 28.01/28.06 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.06 => ( 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))
% 28.01/28.06 => 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)))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_quotient__eq__iff,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 28.01/28.06 => ( V_X_2 = V_Y_2
% 28.01/28.06 <=> 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)) ) ) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_quotient__eqI,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 28.01/28.06 => ( 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))
% 28.01/28.06 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_equiv__class__eq__iff,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.06 => ( 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))
% 28.01/28.06 <=> ( 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))))
% 28.01/28.06 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.06 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_eq__equiv__class,axiom,
% 28.01/28.06 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
% 28.01/28.06 ( 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))))
% 28.01/28.06 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 28.01/28.06 => 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)) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_eq__equiv__class__iff,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 28.01/28.06 => ( 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))))
% 28.01/28.06 <=> 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)) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_equiv__class__subset,axiom,
% 28.01/28.06 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.06 => ( 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))
% 28.01/28.06 => 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)))))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_eq__equiv__class__iff2,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 28.01/28.06 => ( 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)
% 28.01/28.06 <=> 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)) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_UN__equiv__class,axiom,
% 28.01/28.06 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.06 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.06 => 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) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_UN__equiv__class2,axiom,
% 28.01/28.06 ! [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] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 28.01/28.06 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 28.01/28.06 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 28.01/28.06 => 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) ) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_in__finite__psubset,axiom,
% 28.01/28.06 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.01/28.06 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_congruent2__implies__congruent,axiom,
% 28.01/28.06 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 28.01/28.06 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.06 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_congruent2D,axiom,
% 28.01/28.06 ! [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] :
% 28.01/28.06 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 28.01/28.06 => ( 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))
% 28.01/28.06 => ( 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))
% 28.01/28.06 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_congruentD,axiom,
% 28.01/28.06 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 28.01/28.06 => ( 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))
% 28.01/28.06 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_congruent2__implies__congruent__UN,axiom,
% 28.01/28.06 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 28.01/28.06 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 28.01/28.06 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 28.01/28.06 => 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)) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_finite__psubset__def,axiom,
% 28.01/28.06 ! [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)))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_UN__equiv__class__inject,axiom,
% 28.01/28.06 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.06 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 28.01/28.06 => ( 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)
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => ( ! [B_x] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.06 => ! [B_y] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 28.01/28.06 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 28.01/28.06 => 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)) ) ) )
% 28.01/28.06 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_UN__equiv__class__type2,axiom,
% 28.01/28.06 ! [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] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 28.01/28.06 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 28.01/28.06 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => ( ! [B_x1] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 28.01/28.06 => ! [B_x2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 28.01/28.06 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 28.01/28.06 => 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)) ) ) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_UN__equiv__class__type,axiom,
% 28.01/28.06 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.06 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => ( ! [B_x] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.06 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 28.01/28.06 => 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)) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_mlex__leq,axiom,
% 28.01/28.06 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( 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))
% 28.01/28.06 => 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))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_code__numeral_Osize_I2_J,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_mlex__less,axiom,
% 28.01/28.06 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_code__numeral_Oinject,axiom,
% 28.01/28.06 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 28.01/28.06 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 28.01/28.06 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 28.01/28.06 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Suc__code__numeral__minus__one,axiom,
% 28.01/28.06 ! [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 ).
% 28.01/28.06
% 28.01/28.06 fof(fact_code__numeral_Osize_I4_J,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_nat_Osize_I4_J,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_prod_Orecs,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_nat__size,axiom,
% 28.01/28.06 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 28.01/28.06
% 28.01/28.06 fof(fact_nat_Osize_I3_J,axiom,
% 28.01/28.06 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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_code__numeral_Osize_I3_J,axiom,
% 28.01/28.06 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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_lfp__induct2,axiom,
% 28.01/28.06 ! [V_P_2,V_f_2,V_b_2,V_a_2,T_c,T_b] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( 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)
% 28.01/28.06 => ( ! [B_a,B_b] :
% 28.01/28.06 ( 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))))))
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) )
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_P_2,V_a_2),V_b_2)) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_in__lex__prod,axiom,
% 28.01/28.06 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 <=> ( 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))
% 28.01/28.06 | ( V_a_2 = V_a_H_2
% 28.01/28.06 & 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)) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_equivp__equiv,axiom,
% 28.01/28.06 ! [V_A_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 28.01/28.06 <=> 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_identity__equivp,axiom,
% 28.01/28.06 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_equivp__def,axiom,
% 28.01/28.06 ! [V_R_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.01/28.06 <=> ! [B_x,B_y] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 28.01/28.06 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_equivp__reflp,axiom,
% 28.01/28.06 ! [V_x_2,V_R_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_equivp__symp,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_equivp__transp,axiom,
% 28.01/28.06 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 28.01/28.06 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_same__fstI,axiom,
% 28.01/28.06 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_P_2] :
% 28.01/28.06 ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => 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))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_apfst__apsnd,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_apsnd__apfst,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_apfst__conv,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_fst__apfst,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_apfst__eq__conv,axiom,
% 28.01/28.06 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 28.01/28.06 ( 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)
% 28.01/28.06 <=> 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_snd__apfst,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_apfst__compose,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_apsnd__apfst__commute,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_pair__lessI2,axiom,
% 28.01/28.06 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_ImageE,axiom,
% 28.01/28.06 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 28.01/28.06 => ~ ! [B_x] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_mlex__prod__def,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_pair__less__def,axiom,
% 28.01/28.06 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_measure__def,axiom,
% 28.01/28.06 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_less__than__iff,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2] :
% 28.01/28.06 ( 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))
% 28.01/28.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_pair__lessI1,axiom,
% 28.01/28.06 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 28.01/28.06 => 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_pair__leqI2,axiom,
% 28.01/28.06 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_smin__insertI,axiom,
% 28.01/28.06 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 28.01/28.06 => ( 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))
% 28.01/28.06 => ( 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))
% 28.01/28.06 => 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)) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_smax__insertI,axiom,
% 28.01/28.06 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 28.01/28.06 => ( 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))
% 28.01/28.06 => ( 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))
% 28.01/28.06 => 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)) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_smax__emptyI,axiom,
% 28.01/28.06 ! [V_Y_2] :
% 28.01/28.06 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 28.01/28.06 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_smin__emptyI,axiom,
% 28.01/28.06 ! [V_X_2] :
% 28.01/28.06 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 28.01/28.06 => 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_pair__leqI1,axiom,
% 28.01/28.06 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 28.01/28.06 => 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wmax__insertI,axiom,
% 28.01/28.06 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 28.01/28.06 => ( 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))
% 28.01/28.06 => ( 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))
% 28.01/28.06 => 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)) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wmin__insertI,axiom,
% 28.01/28.06 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 28.01/28.06 => ( 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))
% 28.01/28.06 => ( 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))
% 28.01/28.06 => 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)) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Field__insert,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Field__Union,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Field__empty,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_mono__Field,axiom,
% 28.01/28.06 ! [V_s_2,V_r_2,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Field__Un,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_finite__Field,axiom,
% 28.01/28.06 ! [V_r_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 28.01/28.06 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wmin__emptyI,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wmax__emptyI,axiom,
% 28.01/28.06 ! [V_X_2] :
% 28.01/28.06 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 28.01/28.06 => 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_min__weak__def,axiom,
% 28.01/28.06 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)))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_max__weak__def,axiom,
% 28.01/28.06 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)))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Id__on__def,axiom,
% 28.01/28.06 ! [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)))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Id__on__def_H,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Id__on__empty,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Image__Id__on,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Id__on__iff,axiom,
% 28.01/28.06 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 <=> ( V_x_2 = V_y_2
% 28.01/28.06 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Id__on__eqI,axiom,
% 28.01/28.06 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 28.01/28.06 ( V_a_2 = V_b_2
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.06 => 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))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_max__strict__def,axiom,
% 28.01/28.06 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_max__ext__additive,axiom,
% 28.01/28.06 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => 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))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_min__strict__def,axiom,
% 28.01/28.06 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_max__extp__max__ext__eq,axiom,
% 28.01/28.06 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 28.01/28.06 ( 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)
% 28.01/28.06 <=> 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_min__rpair__set,axiom,
% 28.01/28.06 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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_max__rpair__set,axiom,
% 28.01/28.06 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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_rp__inv__image__rp,axiom,
% 28.01/28.06 ! [V_f_2,T_c,V_P_2,T_b] :
% 28.01/28.06 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 28.01/28.06 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_P_2),V_f_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_equiv__intrel__iff,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2] :
% 28.01/28.06 ( 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))))
% 28.01/28.06 <=> 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_intrel__iff,axiom,
% 28.01/28.06 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 28.01/28.06 ( 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))
% 28.01/28.06 <=> 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) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Id__onE,axiom,
% 28.01/28.06 ! [V_A_2,V_c_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2)))
% 28.01/28.06 => ~ ! [B_x] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.06 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_equiv__intrel,axiom,
% 28.01/28.06 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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_of__int,axiom,
% 28.01/28.06 ! [V_j_2,V_i_2,T_b] :
% 28.01/28.06 ( class_Rings_Oring__1(T_b)
% 28.01/28.06 => 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_One__int__def,axiom,
% 28.01/28.06 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))))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_mult,axiom,
% 28.01/28.06 ! [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))))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Rep__Integ__inverse,axiom,
% 28.01/28.06 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 28.01/28.06
% 28.01/28.06 fof(fact_minus,axiom,
% 28.01/28.06 ! [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))))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Zero__int__def,axiom,
% 28.01/28.06 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))))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_int__def,axiom,
% 28.01/28.06 ! [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))))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_add,axiom,
% 28.01/28.06 ! [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))))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_nat,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_minus__int__def,axiom,
% 28.01/28.06 ! [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))))))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_less,axiom,
% 28.01/28.06 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 28.01/28.06 ( 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)))))))
% 28.01/28.06 <=> 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_le,axiom,
% 28.01/28.06 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 28.01/28.06 ( 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)))))))
% 28.01/28.06 <=> 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_eq__Abs__Integ,axiom,
% 28.01/28.06 ! [V_z_2] :
% 28.01/28.06 ~ ! [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))))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Integ__def,axiom,
% 28.01/28.06 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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Rep__Integ,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 28.01/28.06 ! [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 ).
% 28.01/28.06
% 28.01/28.06 fof(fact_type__definition__Integ,axiom,
% 28.01/28.06 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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_accp__acc__eq,axiom,
% 28.01/28.06 ! [V_x_2,V_r_2,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_rel__comp__def,axiom,
% 28.01/28.06 ! [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))))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_rel__compI,axiom,
% 28.01/28.06 ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => ( 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))
% 28.01/28.06 => 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))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_rel__comp__UNION__distrib2,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_rel__comp__UNION__distrib,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_rel__comp__empty1,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_rel__comp__empty2,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_rel__comp__distrib,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_rel__comp__distrib2,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_O__assoc,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_rel__comp__mono,axiom,
% 28.01/28.06 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => ( 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))
% 28.01/28.06 => 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))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_union__comp__emptyR,axiom,
% 28.01/28.06 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => ( 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))
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_union__comp__emptyL,axiom,
% 28.01/28.06 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => ( 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))
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_acc__subset,axiom,
% 28.01/28.06 ! [V_R2_2,V_R1_2,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_acc__downward,axiom,
% 28.01/28.06 ! [V_a_2,V_r_2,V_b_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 28.01/28.06 => ( 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))
% 28.01/28.06 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_acc_Osimps,axiom,
% 28.01/28.06 ! [V_r_2,V_a_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 28.01/28.06 <=> ! [B_x] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_max__ext__compat,axiom,
% 28.01/28.06 ! [V_S_2,V_R_2,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_min__ext__compat,axiom,
% 28.01/28.06 ! [V_S_2,V_R_2,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_type__definition_OAbs__image,axiom,
% 28.01/28.06 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 28.01/28.06 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 28.01/28.06 => 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_type__definition_ORep__range,axiom,
% 28.01/28.06 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 28.01/28.06 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 28.01/28.06 => 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 ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_type__definition_ORep,axiom,
% 28.01/28.06 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 28.01/28.06 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 28.01/28.06 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_type__definition_ORep__inverse,axiom,
% 28.01/28.06 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 28.01/28.06 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 28.01/28.06 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_type__definition_ORep__inject,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 28.01/28.06 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 28.01/28.06 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 28.01/28.06 <=> V_x_2 = V_y_2 ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_type__definition_OAbs__inject,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 28.01/28.06 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 28.01/28.06 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 28.01/28.06 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_type__definition_OAbs__inverse,axiom,
% 28.01/28.06 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 28.01/28.06 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 28.01/28.06 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_pred__comp__rel__comp__eq,axiom,
% 28.01/28.06 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 <=> 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_reduction__pairI,axiom,
% 28.01/28.06 ! [V_S_2,V_R_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_R_2)
% 28.01/28.06 => ( 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))
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_max__extp_Oequations,axiom,
% 28.01/28.06 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 28.01/28.06 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 28.01/28.06 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 28.01/28.06 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.06 & ! [B_x] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 28.01/28.06 => ? [B_xa] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 28.01/28.06 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__less__than,axiom,
% 28.01/28.06 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_pred__comp_Ointros,axiom,
% 28.01/28.06 ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
% 28.01/28.06 => 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__empty,axiom,
% 28.01/28.06 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__inv__image,axiom,
% 28.01/28.06 ! [V_f_2,T_c,V_r_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.06 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__lex__prod,axiom,
% 28.01/28.06 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 28.01/28.06 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 28.01/28.06 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__measure,axiom,
% 28.01/28.06 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__comp__self,axiom,
% 28.01/28.06 ! [V_R_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_R_2)
% 28.01/28.06 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__subset,axiom,
% 28.01/28.06 ! [V_p_2,V_r_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.06 => ( 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))
% 28.01/28.06 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_min__ext__wf,axiom,
% 28.01/28.06 ! [V_r_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.06 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__less,axiom,
% 28.01/28.06 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)))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_pred__comp_Oequations,axiom,
% 28.01/28.06 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 <=> ? [B_b] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 28.01/28.06 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__Int2,axiom,
% 28.01/28.06 ! [V_r_H_2,V_r_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.06 => 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__Int1,axiom,
% 28.01/28.06 ! [V_r_H_2,V_r_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.06 => 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__finite__psubset,axiom,
% 28.01/28.06 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__mlex,axiom,
% 28.01/28.06 ! [V_f_2,V_R_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_R_2)
% 28.01/28.06 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__pair__less,axiom,
% 28.01/28.06 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_max__ext__wf,axiom,
% 28.01/28.06 ! [V_r_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.06 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__not__refl,axiom,
% 28.01/28.06 ! [V_a_2,V_r_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.06 => ~ 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__not__sym,axiom,
% 28.01/28.06 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.06 => ( 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))
% 28.01/28.06 => ~ 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__asym,axiom,
% 28.01/28.06 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.06 => ( 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))
% 28.01/28.06 => ~ 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)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__irrefl,axiom,
% 28.01/28.06 ! [V_a_2,V_r_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.06 => ~ 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__int__ge__less__than,axiom,
% 28.01/28.06 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__int__ge__less__than2,axiom,
% 28.01/28.06 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__acc__iff,axiom,
% 28.01/28.06 ! [V_r_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.06 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_acc__wfD,axiom,
% 28.01/28.06 ! [V_x_2,V_r_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.06 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__no__loop,axiom,
% 28.01/28.06 ! [V_R_2,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__union__merge,axiom,
% 28.01/28.06 ! [V_S_2,V_R_2,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 <=> 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 28.01/28.06 ! [V_r_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.06 <=> ~ ? [B_f] :
% 28.01/28.06 ! [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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wfE__pf,axiom,
% 28.01/28.06 ! [V_A_2,V_R_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_R_2)
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__union__compatible,axiom,
% 28.01/28.06 ! [V_S_2,V_R_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_R_2)
% 28.01/28.06 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 28.01/28.06 => ( 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))
% 28.01/28.06 => 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)) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf,axiom,
% 28.01/28.06 ! [T_b] :
% 28.01/28.06 ( class_Orderings_Owellorder(T_b)
% 28.01/28.06 => 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)))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_reduction__pair__def,axiom,
% 28.01/28.06 ! [V_P_2,T_b] :
% 28.01/28.06 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 28.01/28.06 <=> ( 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))
% 28.01/28.06 & 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))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_reduction__pair__lemma,axiom,
% 28.01/28.06 ! [V_S_2,V_R_2,V_P_2,T_b] :
% 28.01/28.06 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 28.01/28.06 => 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)) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__lenlex,axiom,
% 28.01/28.06 ! [V_r_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.06 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__if__measure,axiom,
% 28.01/28.06 ! [T_b,V_g_2,V_f_2,V_P_2] :
% 28.01/28.06 ( ! [B_x] :
% 28.01/28.06 ( hBOOL(hAPP(V_P_2,B_x))
% 28.01/28.06 => 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))) )
% 28.01/28.06 => 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))))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_max__ext_Ointros,axiom,
% 28.01/28.06 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 28.01/28.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 28.01/28.06 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.06 => ( ! [B_x] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 28.01/28.06 => ? [B_xa] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 28.01/28.06 & 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)) ) )
% 28.01/28.06 => 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))) ) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_pred__nat__def,axiom,
% 28.01/28.06 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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__lex,axiom,
% 28.01/28.06 ! [V_r_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.06 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__lexn,axiom,
% 28.01/28.06 ! [V_n_2,V_r_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.06 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_lex__def,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_lexn_Osimps_I1_J,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__pred__nat,axiom,
% 28.01/28.06 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__same__fst,axiom,
% 28.01/28.06 ! [T_b,V_R_2,T_c,V_P_2] :
% 28.01/28.06 ( ! [B_x] :
% 28.01/28.06 ( hBOOL(hAPP(V_P_2,B_x))
% 28.01/28.06 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 28.01/28.06 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Range__Collect__split,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_RangeI,axiom,
% 28.01/28.06 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Range__Id__on,axiom,
% 28.01/28.06 ! [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 ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Range__Diff__subset,axiom,
% 28.01/28.06 ! [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)))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Range__Union,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Range__empty,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Range__empty__iff,axiom,
% 28.01/28.06 ! [V_r_2,T_b,T_c] :
% 28.01/28.06 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.06 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Range__Un__eq,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_finite__Range,axiom,
% 28.01/28.06 ! [V_r_2,T_c,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 28.01/28.06 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_snd__eq__Range,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Range__iff,axiom,
% 28.01/28.06 ! [V_r_2,T_c,V_a_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 28.01/28.06 <=> ? [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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Range__insert,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Range__Int__subset,axiom,
% 28.01/28.06 ! [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)))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Nitpick_Oone__frac__def,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_RangeP__Range__eq,axiom,
% 28.01/28.06 ! [V_x_2,V_r_2,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_RangeP_Ointros,axiom,
% 28.01/28.06 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 28.01/28.06 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_RangeP_Oequations,axiom,
% 28.01/28.06 ! [V_a2_2,V_r_2,T_c,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 28.01/28.06 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Nitpick_Ofrac__def,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_RangeE,axiom,
% 28.01/28.06 ! [V_r_2,T_c,V_b_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 28.01/28.06 => ~ ! [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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_wf__Un,axiom,
% 28.01/28.06 ! [V_s_2,V_r_2,T_b] :
% 28.01/28.06 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.06 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 28.01/28.06 => ( 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))
% 28.01/28.06 => 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)) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_DomainI,axiom,
% 28.01/28.06 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Domain__Id__on,axiom,
% 28.01/28.06 ! [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 ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Domain__empty,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Domain__empty__iff,axiom,
% 28.01/28.06 ! [V_r_2,T_c,T_b] :
% 28.01/28.06 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.06 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Domain__mono,axiom,
% 28.01/28.06 ! [V_s_2,V_r_2,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 => 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Domain__Un__eq,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_finite__Domain,axiom,
% 28.01/28.06 ! [V_r_2,T_c,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 28.01/28.06 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_fst__eq__Domain,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Domain__iff,axiom,
% 28.01/28.06 ! [V_r_2,T_c,V_a_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 28.01/28.06 <=> ? [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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Domain__insert,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Domain__Int__subset,axiom,
% 28.01/28.06 ! [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)))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Domain__Diff__subset,axiom,
% 28.01/28.06 ! [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)))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Field__def,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Domain__Union,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Domain__Collect__split,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_DomainP__Domain__eq,axiom,
% 28.01/28.06 ! [V_x_2,V_r_2,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_DomainE,axiom,
% 28.01/28.06 ! [V_r_2,T_c,V_a_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 28.01/28.06 => ~ ! [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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_image__split__eq__Sigma,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_DomainP_Ointros,axiom,
% 28.01/28.06 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 28.01/28.06 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_SigmaI,axiom,
% 28.01/28.06 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.06 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 28.01/28.06 => 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))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Sigma__empty1,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Times__eq__cancel2,axiom,
% 28.01/28.06 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 28.01/28.06 => ( 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))
% 28.01/28.06 <=> V_A_2 = V_B_2 ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Sigma__Union,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_card__cartesian__product,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_setsum__cartesian__product,axiom,
% 28.01/28.06 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 28.01/28.06 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.06 => 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Sigma__empty2,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Times__empty,axiom,
% 28.01/28.06 ! [V_B_2,V_A_2,T_c,T_b] :
% 28.01/28.06 ( 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))
% 28.01/28.06 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.06 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Compl__Times__UNIV2,axiom,
% 28.01/28.06 ! [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)))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Compl__Times__UNIV1,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_setprod__cartesian__product,axiom,
% 28.01/28.06 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 28.01/28.06 ( class_Groups_Ocomm__monoid__mult(T_b)
% 28.01/28.06 => 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))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Sigma__Un__distrib2,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Times__Un__distrib1,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Sigma__Un__distrib1,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_rel__comp__subset__Sigma,axiom,
% 28.01/28.06 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 28.01/28.06 ( 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))))
% 28.01/28.06 => ( 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))))
% 28.01/28.06 => 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)))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_swap__product,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_finite__cartesian__product,axiom,
% 28.01/28.06 ! [V_B_2,T_c,V_A_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.01/28.06 => 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)))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_equiv__type,axiom,
% 28.01/28.06 ! [V_r_2,V_A_2,T_b] :
% 28.01/28.06 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.06 => 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)))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Sigma__Int__distrib1,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Times__Int__distrib1,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Sigma__Int__distrib2,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Id__on__subset__Times,axiom,
% 28.01/28.06 ! [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)))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Sigma__Diff__distrib2,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Times__Diff__distrib1,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Sigma__Diff__distrib1,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_DomainP_Oequations,axiom,
% 28.01/28.06 ! [V_a1_2,V_r_2,T_c,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 28.01/28.06 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_UNIV__Times__UNIV,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_SigmaE2,axiom,
% 28.01/28.06 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.06 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_SigmaD2,axiom,
% 28.01/28.06 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_SigmaD1,axiom,
% 28.01/28.06 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_mem__Sigma__iff,axiom,
% 28.01/28.06 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 28.01/28.06 ( 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)))
% 28.01/28.06 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.06 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_card__cartesian__product__singleton,axiom,
% 28.01/28.06 ! [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) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Times__subset__cancel2,axiom,
% 28.01/28.06 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 28.01/28.06 => ( 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))))
% 28.01/28.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Image__subset,axiom,
% 28.01/28.06 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 28.01/28.06 ( 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))))
% 28.01/28.06 => 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)) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_finite__cartesian__productD2,axiom,
% 28.01/28.06 ! [V_B_2,V_A_2,T_c,T_b] :
% 28.01/28.06 ( 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))))
% 28.01/28.06 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.06 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_finite__cartesian__productD1,axiom,
% 28.01/28.06 ! [V_B_2,V_A_2,T_c,T_b] :
% 28.01/28.06 ( 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))))
% 28.01/28.06 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 28.01/28.06 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_SetCompr__Sigma__eq,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_Collect__split,axiom,
% 28.01/28.06 ! [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))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_fst__image__times,axiom,
% 28.01/28.06 ! [V_A_2,T_c,T_b,V_B_2] :
% 28.01/28.06 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.06 => 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)) )
% 28.01/28.06 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.06 => 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 ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_snd__image__times,axiom,
% 28.01/28.06 ! [V_B_2,T_c,T_b,V_A_2] :
% 28.01/28.06 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.06 => 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)) )
% 28.01/28.06 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.06 => 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 ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_insert__times__insert,axiom,
% 28.01/28.06 ! [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)))) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_finite__equiv__class,axiom,
% 28.01/28.06 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 28.01/28.06 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.06 => ( 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))))
% 28.01/28.06 => ( 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)))
% 28.01/28.06 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 28.01/28.06
% 28.01/28.06 fof(fact_vimage__Times,axiom,
% 28.01/28.06 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_UN__Times__distrib,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Sigma__def,axiom,
% 28.01/28.07 ! [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))))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_finite__quotient,axiom,
% 28.01/28.07 ! [V_r_2,V_A_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( 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))))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 28.01/28.07 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 28.01/28.07 ( class_Rings_Osemiring__0(T_d)
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => 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))))))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 28.01/28.07 ! [V_A_2,V_I_2,T_c,T_b] :
% 28.01/28.07 ? [B_f] :
% 28.01/28.07 ( 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))
% 28.01/28.07 & 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fold__image__Sigma,axiom,
% 28.01/28.07 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 28.01/28.07 ( class_Groups_Ocomm__monoid__mult(T_d)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.07 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 28.01/28.07 => 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)) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_bij__betw__id,axiom,
% 28.01/28.07 ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_image__id,axiom,
% 28.01/28.07 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 28.01/28.07
% 28.01/28.07 fof(fact_apsnd__id,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_id__def,axiom,
% 28.01/28.07 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 28.01/28.07
% 28.01/28.07 fof(fact_id__apply,axiom,
% 28.01/28.07 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 28.01/28.07
% 28.01/28.07 fof(fact_vimage__id,axiom,
% 28.01/28.07 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 28.01/28.07
% 28.01/28.07 fof(fact_bij__betw__id__iff,axiom,
% 28.01/28.07 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.07 ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2)
% 28.01/28.07 <=> V_A_2 = V_B_2 ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_inj__on__id,axiom,
% 28.01/28.07 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_o__id,axiom,
% 28.01/28.07 ! [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 ).
% 28.01/28.07
% 28.01/28.07 fof(fact_id__o,axiom,
% 28.01/28.07 ! [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 ).
% 28.01/28.07
% 28.01/28.07 fof(fact_o__eq__id__dest,axiom,
% 28.01/28.07 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 28.01/28.07 ( 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)
% 28.01/28.07 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_apfst__id,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_of__int__eq__id,axiom,
% 28.01/28.07 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_surj__id,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_bij__id,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_folding_Oempty,axiom,
% 28.01/28.07 ! [V_F_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 28.01/28.07 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_split__Pair,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_setsum__reindex__id,axiom,
% 28.01/28.07 ! [V_B_2,V_f_2,T_b,T_c] :
% 28.01/28.07 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.07 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_setprod__reindex__id,axiom,
% 28.01/28.07 ! [V_B_2,V_f_2,T_b,T_c] :
% 28.01/28.07 ( class_Groups_Ocomm__monoid__mult(T_c)
% 28.01/28.07 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_setprod__Sigma,axiom,
% 28.01/28.07 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 28.01/28.07 ( class_Groups_Ocomm__monoid__mult(T_d)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.07 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 28.01/28.07 => 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)) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_setsum__Sigma,axiom,
% 28.01/28.07 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 28.01/28.07 ( class_Groups_Ocomm__monoid__add(T_d)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.07 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 28.01/28.07 => 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)) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_card__SigmaI,axiom,
% 28.01/28.07 ! [V_B_2,T_c,V_A_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.07 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_finite__SigmaI,axiom,
% 28.01/28.07 ! [V_B_2,T_c,V_A_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ! [B_a] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 28.01/28.07 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_SigmaE,axiom,
% 28.01/28.07 ! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ~ ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.07 => ! [B_y] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 28.01/28.07 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_map__pair__surj,axiom,
% 28.01/28.07 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => ( 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))
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_map__pair__imageI,axiom,
% 28.01/28.07 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_map__pair__simp,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_map__pair__ident,axiom,
% 28.01/28.07 ! [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 ).
% 28.01/28.07
% 28.01/28.07 fof(fact_snd__prod__fun,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fst__map__pair,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fst__comp__map__pair,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_snd__comp__map__pair,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_map__pair_Ocomp,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_map__pair__compose,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_map__pair_Ocompositionality,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_map__pair_Oidentity,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_apsnd__def,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_apfst__def,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_map__pair_Oid,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_map__pair__def,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_map__pair__surj__on,axiom,
% 28.01/28.07 ! [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] :
% 28.01/28.07 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 28.01/28.07 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_wf__map__pair__image,axiom,
% 28.01/28.07 ! [V_f_2,T_c,V_r_2,T_b] :
% 28.01/28.07 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.07 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_map__pair__inj__on,axiom,
% 28.01/28.07 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.01/28.07 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_prod__fun__imageE,axiom,
% 28.01/28.07 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ~ ! [B_x,B_y] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => ~ 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_refl__on__def,axiom,
% 28.01/28.07 ! [V_r_2,V_A_2,T_b] :
% 28.01/28.07 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.01/28.07 <=> ( 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))))
% 28.01/28.07 & ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.07 => 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)) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_wfP__def,axiom,
% 28.01/28.07 ! [V_r_2,T_b] :
% 28.01/28.07 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 28.01/28.07 <=> 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_wfP__empty,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_refl__on__Id__on,axiom,
% 28.01/28.07 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_accp__wfPD,axiom,
% 28.01/28.07 ! [V_x_2,V_r_2,T_b] :
% 28.01/28.07 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 28.01/28.07 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_wfP__accp__iff,axiom,
% 28.01/28.07 ! [V_r_2,T_b] :
% 28.01/28.07 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 28.01/28.07 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_wfP__subset,axiom,
% 28.01/28.07 ! [V_p_2,V_r_2,T_b] :
% 28.01/28.07 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 28.01/28.07 => ( 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))
% 28.01/28.07 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_refl__on__empty,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_refl__on__Un,axiom,
% 28.01/28.07 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 28.01/28.07 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.01/28.07 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_refl__on__Int,axiom,
% 28.01/28.07 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 28.01/28.07 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.01/28.07 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_refl__onD2,axiom,
% 28.01/28.07 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 28.01/28.07 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.01/28.07 => ( 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))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_refl__onD1,axiom,
% 28.01/28.07 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 28.01/28.07 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.01/28.07 => ( 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))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_refl__onD,axiom,
% 28.01/28.07 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 28.01/28.07 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.01/28.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_wf__in__rel,axiom,
% 28.01/28.07 ! [V_R_2,T_b] :
% 28.01/28.07 ( c_Wellfounded_Owf(T_b,V_R_2)
% 28.01/28.07 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_wfP__wf__eq,axiom,
% 28.01/28.07 ! [V_r_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_reflp__def,axiom,
% 28.01/28.07 ! [V_r_2,T_b] :
% 28.01/28.07 ( c_Predicate_Oreflp(T_b,V_r_2)
% 28.01/28.07 <=> 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_refl__onI,axiom,
% 28.01/28.07 ! [V_A_2,V_r_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => ( ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.07 => 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)) )
% 28.01/28.07 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_wfP__acyclicP,axiom,
% 28.01/28.07 ! [V_r_2,T_b] :
% 28.01/28.07 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_reflpE,axiom,
% 28.01/28.07 ! [V_x_2,V_r_2,T_b] :
% 28.01/28.07 ( c_Predicate_Oreflp(T_b,V_r_2)
% 28.01/28.07 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_acyclic__subset,axiom,
% 28.01/28.07 ! [V_r_2,V_s_2,T_b] :
% 28.01/28.07 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 28.01/28.07 => ( 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))
% 28.01/28.07 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_wf__acyclic,axiom,
% 28.01/28.07 ! [V_r_2,T_b] :
% 28.01/28.07 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.07 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 28.01/28.07 ! [V_r_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 28.01/28.07 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.07 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_finite__acyclic__wf,axiom,
% 28.01/28.07 ! [V_r_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 28.01/28.07 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 28.01/28.07 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Nitpick_Owf_H__def,axiom,
% 28.01/28.07 ! [V_r_2,T_b] :
% 28.01/28.07 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 28.01/28.07 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 28.01/28.07 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 28.01/28.07 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Rep__Integ__induct,axiom,
% 28.01/28.07 ! [V_P_2,V_y_2] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 28.01/28.07 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
% 28.01/28.07 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Rep__Integ__cases,axiom,
% 28.01/28.07 ! [V_y_2] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 28.01/28.07 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_refl__on__def_H,axiom,
% 28.01/28.07 ! [V_r_2,V_A_2,T_b] :
% 28.01/28.07 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.01/28.07 <=> ( ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 28.01/28.07 => 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)) )
% 28.01/28.07 & ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.07 => 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)) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Abs__Integ__induct,axiom,
% 28.01/28.07 ! [V_x_2,V_P_2] :
% 28.01/28.07 ( ! [B_y] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 28.01/28.07 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 28.01/28.07 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Abs__Integ__cases,axiom,
% 28.01/28.07 ! [V_x_2] :
% 28.01/28.07 ~ ! [B_y] :
% 28.01/28.07 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 28.01/28.07 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Powp__def,axiom,
% 28.01/28.07 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 28.01/28.07 <=> ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 28.01/28.07 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_INFI__bool__eq,axiom,
% 28.01/28.07 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_ball__empty,axiom,
% 28.01/28.07 ! [V_P_2,T_b,B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 28.01/28.07 => hBOOL(hAPP(V_P_2,B_x)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Collect__ball__eq,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_congruent__def,axiom,
% 28.01/28.07 ! [V_f_2,V_r_2,T_c,T_b] :
% 28.01/28.07 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 28.01/28.07 <=> ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_INTER__def,axiom,
% 28.01/28.07 ! [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)))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Inf__Sup,axiom,
% 28.01/28.07 ! [V_A_2,T_b] :
% 28.01/28.07 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.01/28.07 => 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))))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Sup__Inf,axiom,
% 28.01/28.07 ! [V_A_2,T_b] :
% 28.01/28.07 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.01/28.07 => 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)))))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_wfP__SUP,axiom,
% 28.01/28.07 ! [T_b,V_r_2,T_c] :
% 28.01/28.07 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 28.01/28.07 => ( ! [B_i,B_j] :
% 28.01/28.07 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 28.01/28.07 => 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)) )
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_mem__splitE,axiom,
% 28.01/28.07 ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ~ ! [B_x,B_y] :
% 28.01/28.07 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 28.01/28.07 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_mem__splitI2,axiom,
% 28.01/28.07 ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 28.01/28.07 ( ! [B_a,B_b] :
% 28.01/28.07 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Inter__eq,axiom,
% 28.01/28.07 ! [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)))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Eps__split,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_wfI__pf,axiom,
% 28.01/28.07 ! [V_R_2,T_b] :
% 28.01/28.07 ( ! [B_A] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 28.01/28.07 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Sigma__mono,axiom,
% 28.01/28.07 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 28.01/28.07 => ( ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.07 => 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))) )
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_some__sym__eq__trivial,axiom,
% 28.01/28.07 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 28.01/28.07
% 28.01/28.07 fof(fact_some__eq__trivial,axiom,
% 28.01/28.07 ! [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 ).
% 28.01/28.07
% 28.01/28.07 fof(fact_some__eq__ex,axiom,
% 28.01/28.07 ! [T_b,V_P_2] :
% 28.01/28.07 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
% 28.01/28.07 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_someI__ex,axiom,
% 28.01/28.07 ! [T_b,V_P_2] :
% 28.01/28.07 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 28.01/28.07 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_someI,axiom,
% 28.01/28.07 ! [T_b,V_x_2,V_P_2] :
% 28.01/28.07 ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.01/28.07 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_tfl__some,axiom,
% 28.01/28.07 ! [T_b,B_P] :
% 28.01/28.07 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 28.01/28.07 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_exE__some,axiom,
% 28.01/28.07 ! [T_b,V_c_2,V_P_2] :
% 28.01/28.07 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 28.01/28.07 => ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_P_2)
% 28.01/28.07 => hBOOL(hAPP(V_P_2,V_c_2)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_split__paired__Eps,axiom,
% 28.01/28.07 ! [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)))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Eps__split__eq,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_acc_OaccI,axiom,
% 28.01/28.07 ! [V_r_2,V_x_2,T_b] :
% 28.01/28.07 ( ! [B_y] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_not__acc__down,axiom,
% 28.01/28.07 ! [V_R_2,V_x_2,T_b] :
% 28.01/28.07 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 28.01/28.07 => ~ ! [B_z] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_max__ext_Osimps,axiom,
% 28.01/28.07 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 28.01/28.07 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 28.01/28.07 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.07 & ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 28.01/28.07 => ? [B_xa] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 28.01/28.07 & 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)) ) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_wf__no__infinite__down__chainE,axiom,
% 28.01/28.07 ! [V_f_2,V_r_2,T_b] :
% 28.01/28.07 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.07 => ~ ! [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)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_setsum__reindex__cong,axiom,
% 28.01/28.07 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 28.01/28.07 ( class_Groups_Ocomm__monoid__add(T_d)
% 28.01/28.07 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.01/28.07 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 28.01/28.07 => ( ! [B_a] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 28.01/28.07 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 28.01/28.07 => 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) ) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_scomp__unfold,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_scomp__Pair,axiom,
% 28.01/28.07 ! [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 ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Pair__scomp,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_scomp__scomp,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_scomp__apply,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_scomp__def,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_iterate_Osimps,axiom,
% 28.01/28.07 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 28.01/28.07 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.01/28.07 => 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) )
% 28.01/28.07 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_setsum__ivl__cong,axiom,
% 28.01/28.07 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
% 28.01/28.07 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.07 & class_Orderings_Oord(T_b) )
% 28.01/28.07 => ( V_a_2 = V_c_2
% 28.01/28.07 => ( V_b_2 = V_d_2
% 28.01/28.07 => ( ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x))
% 28.01/28.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 28.01/28.07 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 28.01/28.07 => 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)) ) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_log_Osimps,axiom,
% 28.01/28.07 ! [V_i,V_b] :
% 28.01/28.07 ( ( ( 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)))
% 28.01/28.07 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 28.01/28.07 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 28.01/28.07 & ( ~ ( 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)))
% 28.01/28.07 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_minus__shift__def,axiom,
% 28.01/28.07 ! [V_r,V_l,V_k] :
% 28.01/28.07 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 28.01/28.07 => 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) )
% 28.01/28.07 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_inc__shift__def,axiom,
% 28.01/28.07 ! [V_k,V_v] :
% 28.01/28.07 ( ( V_v = V_k
% 28.01/28.07 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 28.01/28.07 & ( V_v != V_k
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_range,axiom,
% 28.01/28.07 ! [V_s,V_k] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => 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)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_less__eq,axiom,
% 28.01/28.07 ! [V_n_2,V_m_2] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_nat__intermed__int__val,axiom,
% 28.01/28.07 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 28.01/28.07 ( ! [B_i] :
% 28.01/28.07 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 28.01/28.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 28.01/28.07 => 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))) )
% 28.01/28.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 28.01/28.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 28.01/28.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 28.01/28.07 => ? [B_i] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 28.01/28.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 28.01/28.07 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_wf__trancl,axiom,
% 28.01/28.07 ! [V_r_2,T_b] :
% 28.01/28.07 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.07 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_less__than__def,axiom,
% 28.01/28.07 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_acyclic__def,axiom,
% 28.01/28.07 ! [V_r_2,T_b] :
% 28.01/28.07 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 28.01/28.07 <=> ! [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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl_Or__into__trancl,axiom,
% 28.01/28.07 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__subset__Field2,axiom,
% 28.01/28.07 ! [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))))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_r__into__trancl_H,axiom,
% 28.01/28.07 ! [V_r_2,V_p_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__empty,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__domain,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__range,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_finite__trancl,axiom,
% 28.01/28.07 ! [V_r_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 28.01/28.07 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__trans,axiom,
% 28.01/28.07 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 28.01/28.07 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( 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))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__into__trancl2,axiom,
% 28.01/28.07 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_r__r__into__trancl,axiom,
% 28.01/28.07 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => ( 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))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__mono,axiom,
% 28.01/28.07 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 28.01/28.07 => ( 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))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__unfold,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__subset__Sigma,axiom,
% 28.01/28.07 ! [V_A_2,V_r_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__Int__subset,axiom,
% 28.01/28.07 ! [V_s_2,V_r_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => ( 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))
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__insert,axiom,
% 28.01/28.07 ! [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)))))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_reflcl__set__eq,axiom,
% 28.01/28.07 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 <=> 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_r__into__rtrancl,axiom,
% 28.01/28.07 ! [V_r_2,V_p_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_IdI,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__into__rtrancl,axiom,
% 28.01/28.07 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__trancl__absorb,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__rtrancl__absorb,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_reflcl__trancl,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__reflcl,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__unfold__left,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__unfold__right,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Image__closed__trancl,axiom,
% 28.01/28.07 ! [V_X_2,V_r_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__Un__subset,axiom,
% 28.01/28.07 ! [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)))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__mono,axiom,
% 28.01/28.07 ! [V_s_2,V_r_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__subset,axiom,
% 28.01/28.07 ! [V_S_2,V_R_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__subset__rtrancl,axiom,
% 28.01/28.07 ! [V_s_2,V_r_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__Int__subset,axiom,
% 28.01/28.07 ! [V_r_2,V_s_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => ( 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))
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Domain__rtrancl,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Range__rtrancl,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__empty,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__unfold,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_in__rtrancl__UnI,axiom,
% 28.01/28.07 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 28.01/28.07 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 28.01/28.07 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 28.01/28.07 => 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__idemp__self__comp,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_r__comp__rtrancl__eq,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__reflcl,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__Un__rtrancl,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__reflcl__absorb,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__idemp,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__trans,axiom,
% 28.01/28.07 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 28.01/28.07 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( 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))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 28.01/28.07 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__r__diff__Id,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_refl__rtrancl,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Image__Id,axiom,
% 28.01/28.07 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 28.01/28.07
% 28.01/28.07 fof(fact_R__O__Id,axiom,
% 28.01/28.07 ! [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 ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Id__O__R,axiom,
% 28.01/28.07 ! [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 ).
% 28.01/28.07
% 28.01/28.07 fof(fact_pair__in__Id__conv,axiom,
% 28.01/28.07 ! [V_b_2,V_a_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 <=> V_a_2 = V_b_2 ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__trancl__trancl,axiom,
% 28.01/28.07 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__rtrancl__trancl,axiom,
% 28.01/28.07 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__into__trancl1,axiom,
% 28.01/28.07 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( 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))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtranclD,axiom,
% 28.01/28.07 ! [V_R_2,V_b_2,V_a_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( V_a_2 = V_b_2
% 28.01/28.07 | ( V_a_2 != V_b_2
% 28.01/28.07 & 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))) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__into__trancl2,axiom,
% 28.01/28.07 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__eq__or__trancl,axiom,
% 28.01/28.07 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 <=> ( V_x_2 = V_y_2
% 28.01/28.07 | ( V_x_2 != V_y_2
% 28.01/28.07 & 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))) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Domain__Id,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Range__Id,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_refl__Id,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_pair__leq__def,axiom,
% 28.01/28.07 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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Not__Domain__rtrancl,axiom,
% 28.01/28.07 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 28.01/28.07 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 28.01/28.07 => ( 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)))
% 28.01/28.07 <=> V_x_2 = V_y_2 ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_acc__downwards,axiom,
% 28.01/28.07 ! [V_b_2,V_r_2,V_a_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_acc__downwards__aux,axiom,
% 28.01/28.07 ! [V_r_2,V_a_2,V_b_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_wf__insert,axiom,
% 28.01/28.07 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.07 & ~ 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_acyclic__insert,axiom,
% 28.01/28.07 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 28.01/28.07 & ~ 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_refl__reflcl,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Id__def,axiom,
% 28.01/28.07 ! [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))))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_irrefl__diff__Id,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_pred__nat__trancl__eq__le,axiom,
% 28.01/28.07 ! [V_n_2,V_m_2] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__subset__Sigma__aux,axiom,
% 28.01/28.07 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( 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))))
% 28.01/28.07 => ( V_a_2 = V_b_2
% 28.01/28.07 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_irrefl__tranclI,axiom,
% 28.01/28.07 ! [V_x_2,V_r_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => ~ 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_sequence__trans,axiom,
% 28.01/28.07 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 28.01/28.07 ( ! [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)))
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__converse,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_converse__Id,axiom,
% 28.01/28.07 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_acyclic__converse,axiom,
% 28.01/28.07 ! [V_r_2,T_b] :
% 28.01/28.07 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 28.01/28.07 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_converse__UNION,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_converseD,axiom,
% 28.01/28.07 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => 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)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_converseI,axiom,
% 28.01/28.07 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_converse__iff,axiom,
% 28.01/28.07 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 <=> 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)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_converse__rel__comp,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_converse__Un,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_converse__Id__on,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_converse__inv__image,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_converse__converse,axiom,
% 28.01/28.07 ! [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 ).
% 28.01/28.07
% 28.01/28.07 fof(fact_converse__Int,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_finite__converse,axiom,
% 28.01/28.07 ! [V_r_2,T_c,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 28.01/28.07 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Field__converse,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_refl__on__converse,axiom,
% 28.01/28.07 ! [V_r_2,V_A_2,T_b] :
% 28.01/28.07 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 28.01/28.07 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_converse__INTER,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__converse,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_wf__converse__trancl,axiom,
% 28.01/28.07 ! [V_r_2,T_b] :
% 28.01/28.07 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 28.01/28.07 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_equiv__comp__eq,axiom,
% 28.01/28.07 ! [V_r_2,V_A_2,T_b] :
% 28.01/28.07 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.07 => 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 ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Range__def,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Domain__converse,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Range__converse,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__converseI,axiom,
% 28.01/28.07 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__converseD,axiom,
% 28.01/28.07 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__converseI,axiom,
% 28.01/28.07 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__converseD,axiom,
% 28.01/28.07 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Image__subset__eq,axiom,
% 28.01/28.07 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 <=> 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))))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_refl__on__comp__subset,axiom,
% 28.01/28.07 ! [V_r_2,V_A_2,T_b] :
% 28.01/28.07 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_comp__equivI,axiom,
% 28.01/28.07 ! [V_A_2,V_r_2,T_b] :
% 28.01/28.07 ( 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
% 28.01/28.07 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 28.01/28.07 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_finite__acyclic__wf__converse,axiom,
% 28.01/28.07 ! [V_r_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 28.01/28.07 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 28.01/28.07 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_converse__def,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Image__INT__eq,axiom,
% 28.01/28.07 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 28.01/28.07 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 28.01/28.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_total__on__diff__Id,axiom,
% 28.01/28.07 ! [V_r_2,V_A_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_single__valued__Id,axiom,
% 28.01/28.07 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_single__valued__rel__comp,axiom,
% 28.01/28.07 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 28.01/28.07 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 28.01/28.07 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_single__valued__subset,axiom,
% 28.01/28.07 ! [V_s_2,V_r_2,T_c,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 28.01/28.07 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_single__valued__Id__on,axiom,
% 28.01/28.07 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_total__on__empty,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_total__on__converse,axiom,
% 28.01/28.07 ! [V_r_2,V_A_2,T_b] :
% 28.01/28.07 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 28.01/28.07 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_single__valued__def,axiom,
% 28.01/28.07 ! [V_r_2,T_c,T_b] :
% 28.01/28.07 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 28.01/28.07 <=> ! [B_x,B_y] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => ! [B_z] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => B_y = B_z ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_single__valuedD,axiom,
% 28.01/28.07 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 28.01/28.07 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 28.01/28.07 => ( 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))
% 28.01/28.07 => ( 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))
% 28.01/28.07 => V_y_2 = V_z_2 ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_total__on__def,axiom,
% 28.01/28.07 ! [V_r_2,V_A_2,T_b] :
% 28.01/28.07 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 28.01/28.07 <=> ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.07 => ! [B_xa] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 28.01/28.07 => ( B_x != B_xa
% 28.01/28.07 => ( 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))
% 28.01/28.07 | 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)) ) ) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_single__valued__confluent,axiom,
% 28.01/28.07 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 28.01/28.07 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => ( 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)))
% 28.01/28.07 | 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))) ) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Image__Int__eq,axiom,
% 28.01/28.07 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 28.01/28.07 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 28.01/28.07 => 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)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 28.01/28.07 ! [V_R_2,V_p_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 28.01/28.07 => 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_acyclicI,axiom,
% 28.01/28.07 ! [V_r_2,T_b] :
% 28.01/28.07 ( ! [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)))
% 28.01/28.07 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_single__valued__rel__pow,axiom,
% 28.01/28.07 ! [V_n_2,V_R_2,T_b] :
% 28.01/28.07 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 28.01/28.07 => 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)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_wf__exp,axiom,
% 28.01/28.07 ! [V_R_2,V_n_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_funpow__mult,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_funpow__swap1,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_comp__funpow,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rel__pow__1,axiom,
% 28.01/28.07 ! [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 ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rel__pow__commute,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rel__pow__imp__rtrancl,axiom,
% 28.01/28.07 ! [V_R_2,V_n_2,V_p_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__power,axiom,
% 28.01/28.07 ! [V_R_2,V_p_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 28.01/28.07 <=> ? [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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_relpow_Osimps_I2_J,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rel__pow__add,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_relpow_Osimps_I1_J,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rel__pow__0__I,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rel__pow__0__E,axiom,
% 28.01/28.07 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => V_x_2 = V_y_2 ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rel__pow__Suc__I,axiom,
% 28.01/28.07 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( 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))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rel__pow__Suc__I2,axiom,
% 28.01/28.07 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_funpow_Osimps_I2_J,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_funpow__add,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_funpow_Osimps_I1_J,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_trancl__power,axiom,
% 28.01/28.07 ! [V_R_2,V_p_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 28.01/28.07 <=> ? [B_n] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 28.01/28.07 & 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_funpow__code__def,axiom,
% 28.01/28.07 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rel__pow__E,axiom,
% 28.01/28.07 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.07 => V_x_2 != V_z_2 )
% 28.01/28.07 => ~ ! [B_y,B_m] :
% 28.01/28.07 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => ~ 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)) ) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rel__pow__E2,axiom,
% 28.01/28.07 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.07 => V_x_2 != V_z_2 )
% 28.01/28.07 => ~ ! [B_y,B_m] :
% 28.01/28.07 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 28.01/28.07 => ( 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))
% 28.01/28.07 => ~ 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))) ) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 28.01/28.07 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => ( ! [B_x] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ! [B_y] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => B_y = B_x ) )
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__Un__separatorE,axiom,
% 28.01/28.07 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => ( ! [B_x] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ! [B_y] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => B_x = B_y ) )
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rel__pow__Suc__E,axiom,
% 28.01/28.07 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ~ ! [B_y] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ~ 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rel__pow__Suc__D2,axiom,
% 28.01/28.07 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ? [B_y] :
% 28.01/28.07 ( 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))
% 28.01/28.07 & 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rel__pow__Suc__E2,axiom,
% 28.01/28.07 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ~ ! [B_y] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => ~ 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_tranclD2,axiom,
% 28.01/28.07 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ? [B_z] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 & 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_tranclD,axiom,
% 28.01/28.07 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ? [B_z] :
% 28.01/28.07 ( 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))
% 28.01/28.07 & 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_IdE,axiom,
% 28.01/28.07 ! [V_p_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 28.01/28.07 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 28.01/28.07 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Orderings_Olinorder(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.07 => 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) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_folding_Oeq__fold,axiom,
% 28.01/28.07 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fold__image__def,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fold__empty,axiom,
% 28.01/28.07 ! [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 ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fold__def,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_union__fold__insert,axiom,
% 28.01/28.07 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fold__sup__insert,axiom,
% 28.01/28.07 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Lattices_Osemilattice__sup(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fold__inf__insert,axiom,
% 28.01/28.07 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Lattices_Osemilattice__inf(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_min__max_Ofold__inf__insert,axiom,
% 28.01/28.07 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Orderings_Olinorder(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_min__max_Ofold__sup__insert,axiom,
% 28.01/28.07 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Orderings_Olinorder(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_sup__Sup__fold__sup,axiom,
% 28.01/28.07 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_inf__Inf__fold__inf,axiom,
% 28.01/28.07 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 28.01/28.07 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 28.01/28.07 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_sup__SUPR__fold__sup,axiom,
% 28.01/28.07 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 28.01/28.07 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_inf__INFI__fold__inf,axiom,
% 28.01/28.07 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 28.01/28.07 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 28.01/28.07 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_sup__le__fold__sup,axiom,
% 28.01/28.07 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Lattices_Osemilattice__sup(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.07 => 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))) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fold__inf__le__inf,axiom,
% 28.01/28.07 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Lattices_Osemilattice__inf(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.07 => 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))) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 28.01/28.07 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Orderings_Olinorder(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.07 => 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))) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 28.01/28.07 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Orderings_Olinorder(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.07 => 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))) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Sup__fold__sup,axiom,
% 28.01/28.07 ! [V_A_2,T_b] :
% 28.01/28.07 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Inf__fold__inf,axiom,
% 28.01/28.07 ! [V_A_2,T_b] :
% 28.01/28.07 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fold1__eq__fold__idem,axiom,
% 28.01/28.07 ! [V_a_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 28.01/28.07 ! [V_a_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Lattices_Olattice(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 28.01/28.07 ! [V_a_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Lattices_Olattice(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 28.01/28.07 ! [V_a_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Orderings_Olinorder(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 28.01/28.07 ! [V_a_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Orderings_Olinorder(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 28.01/28.07 ! [V_a_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Orderings_Olinorder(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 28.01/28.07 ! [V_a_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Orderings_Olinorder(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_minus__fold__remove,axiom,
% 28.01/28.07 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_folding__one_Oeq__fold_H,axiom,
% 28.01/28.07 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.07 => 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) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_SUPR__fold__sup,axiom,
% 28.01/28.07 ! [V_f_2,V_A_2,T_b,T_c] :
% 28.01/28.07 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_INFI__fold__inf,axiom,
% 28.01/28.07 ! [V_f_2,V_A_2,T_b,T_c] :
% 28.01/28.07 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fold1__eq__fold,axiom,
% 28.01/28.07 ! [V_a_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Groups_Oab__semigroup__mult(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.07 => 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) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 28.01/28.07 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Lattices_Olattice(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.07 => 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) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 28.01/28.07 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Lattices_Olattice(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.07 => 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) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Min_Oeq__fold_H,axiom,
% 28.01/28.07 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Orderings_Olinorder(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.07 => 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) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Max_Oeq__fold_H,axiom,
% 28.01/28.07 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Orderings_Olinorder(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.07 => 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) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 28.01/28.07 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Orderings_Olinorder(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.07 => 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) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 28.01/28.07 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.07 => 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)))))) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 28.01/28.07 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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)))))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 28.01/28.07 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.01/28.07 => 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)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 28.01/28.07 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.01/28.07 => 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)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fun__left__comm,axiom,
% 28.01/28.07 ! [T_b] :
% 28.01/28.07 ( class_Groups_Oab__semigroup__mult(T_b)
% 28.01/28.07 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 28.01/28.07 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.01/28.07 => 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)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 28.01/28.07 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 28.01/28.07 => V_y_2 = V_x_2 ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 28.01/28.07 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 28.01/28.07 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 28.01/28.07 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 28.01/28.07 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 28.01/28.07 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.07 => 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) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 28.01/28.07 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.07 => 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)) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 28.01/28.07 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 28.01/28.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.01/28.07 => ? [B_y_H] :
% 28.01/28.07 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 28.01/28.07 & 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)) ) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 28.01/28.07 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.01/28.07 => ( 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))
% 28.01/28.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.07 => ~ ! [B_y] :
% 28.01/28.07 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 28.01/28.07 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 28.01/28.07 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Orderings_Olinorder(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 28.01/28.07 => 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))) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 28.01/28.07 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Orderings_Olinorder(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 28.01/28.07 => 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))) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_inf__le__fold__inf,axiom,
% 28.01/28.07 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Lattices_Osemilattice__inf(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 28.01/28.07 => 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))) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_fold__sup__le__sup,axiom,
% 28.01/28.07 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 28.01/28.07 ( class_Lattices_Osemilattice__sup(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => ( ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 28.01/28.07 => 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))) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_mod__div__decomp,axiom,
% 28.01/28.07 ! [V_b,V_a,T_a] :
% 28.01/28.07 ( class_Divides_Osemiring__div(T_a)
% 28.01/28.07 => 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)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_wf__eq__minimal,axiom,
% 28.01/28.07 ! [V_r_2,T_b] :
% 28.01/28.07 ( c_Wellfounded_Owf(T_b,V_r_2)
% 28.01/28.07 <=> ! [B_Q] :
% 28.01/28.07 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 28.01/28.07 => ? [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 28.01/28.07 & ! [B_y] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 28.01/28.07 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 28.01/28.07 => 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)) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_transfer__nat__int__set__cong,axiom,
% 28.01/28.07 ! [V_P_H_2,V_P_2] :
% 28.01/28.07 ( ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 28.01/28.07 => ( hBOOL(hAPP(V_P_2,B_x))
% 28.01/28.07 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 28.01/28.07 => 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)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 28.01/28.07 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 28.01/28.07 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 28.01/28.07 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.01/28.07 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 28.01/28.07 => 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) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 28.01/28.07 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 28.01/28.07 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 28.01/28.07 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 28.01/28.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.01/28.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 28.01/28.07 => 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) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Int__Collect__mono,axiom,
% 28.01/28.07 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.01/28.07 => ( ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.07 => ( hBOOL(hAPP(V_P_2,B_x))
% 28.01/28.07 => hBOOL(hAPP(V_Q_2,B_x)) ) )
% 28.01/28.07 => 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)))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_converseE,axiom,
% 28.01/28.07 ! [V_r_2,V_yx_2,T_c,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ~ ! [B_x,B_y] :
% 28.01/28.07 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 28.01/28.07 => ~ 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rel__compE,axiom,
% 28.01/28.07 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ~ ! [B_x,B_y,B_z] :
% 28.01/28.07 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 28.01/28.07 => ( 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))
% 28.01/28.07 => ~ 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)) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Nitpick_Oof__frac__def,axiom,
% 28.01/28.07 ! [V_q,T_a,T_b] :
% 28.01/28.07 ( ( class_Rings_Oinverse(T_b)
% 28.01/28.07 & class_Rings_Oring__1(T_b) )
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Nitpick_Oless__frac__def,axiom,
% 28.01/28.07 ! [V_r_2,V_q_2,T_b] :
% 28.01/28.07 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 28.01/28.07 <=> 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 28.01/28.07 ! [V_r_2,V_q_2,T_b] :
% 28.01/28.07 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 28.01/28.07 <=> 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Nitpick_Onum__def,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Nitpick_Odenom__def,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_setprod__pos,axiom,
% 28.01/28.07 ! [V_f_2,V_A_2,T_b,T_c] :
% 28.01/28.07 ( class_Rings_Olinordered__semidom(T_c)
% 28.01/28.07 => ( ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_internal__split__def,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_internal__split__conv,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_setprod__nonneg,axiom,
% 28.01/28.07 ! [V_f_2,V_A_2,T_b,T_c] :
% 28.01/28.07 ( class_Rings_Olinordered__semidom(T_c)
% 28.01/28.07 => ( ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_bool_Osize_I2_J,axiom,
% 28.01/28.07 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_bool_Osize_I1_J,axiom,
% 28.01/28.07 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_finite__less__ub,axiom,
% 28.01/28.07 ! [V_u_2,V_f_2] :
% 28.01/28.07 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
% 28.01/28.07 => 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_lenlex__def,axiom,
% 28.01/28.07 ! [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)))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_lexn__length,axiom,
% 28.01/28.07 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2
% 28.01/28.07 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_neq__if__length__neq,axiom,
% 28.01/28.07 ! [V_ys,V_xs,T_a] :
% 28.01/28.07 ( 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)
% 28.01/28.07 => V_xs != V_ys ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_lenlex__conv,axiom,
% 28.01/28.07 ! [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)))))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_length__sublists,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_length__sublist,axiom,
% 28.01/28.07 ! [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)))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_lexn_Osimps_I2_J,axiom,
% 28.01/28.07 ! [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)))))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_lexord__lex,axiom,
% 28.01/28.07 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 <=> ( 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)))
% 28.01/28.07 & 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_lexord__cons__cons,axiom,
% 28.01/28.07 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 <=> ( 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))
% 28.01/28.07 | ( V_a_2 = V_b_2
% 28.01/28.07 & 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))) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_impossible__Cons,axiom,
% 28.01/28.07 ! [V_x,V_ys,V_xs,T_a] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_list_Oinject,axiom,
% 28.01/28.07 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 28.01/28.07 ( 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)
% 28.01/28.07 <=> ( V_a_2 = V_a_H_2
% 28.01/28.07 & V_list_2 = V_list_H_2 ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_not__Cons__self2,axiom,
% 28.01/28.07 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 28.01/28.07
% 28.01/28.07 fof(fact_not__Cons__self,axiom,
% 28.01/28.07 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_list_Osize_I4_J,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Cons__in__lex,axiom,
% 28.01/28.07 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 <=> ( ( 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))
% 28.01/28.07 & 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) )
% 28.01/28.07 | ( V_x_2 = V_y_2
% 28.01/28.07 & 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))) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_set__Cons__def,axiom,
% 28.01/28.07 ! [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)))))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_pick_Osimps,axiom,
% 28.01/28.07 ! [V_xs,V_x,T_a,V_i] :
% 28.01/28.07 ( ( 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)))
% 28.01/28.07 => 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) )
% 28.01/28.07 & ( ~ 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)))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_select__weight__cons__zero,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 28.01/28.07 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( 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))))
% 28.01/28.07 => 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)))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Cons__acc__listrel1I,axiom,
% 28.01/28.07 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 28.01/28.07 => ( 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))))
% 28.01/28.07 => 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)))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 28.01/28.07 ! [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)))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel1__converse,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel1__mono,axiom,
% 28.01/28.07 ! [V_s_2,V_r_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 28.01/28.07 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel1I2,axiom,
% 28.01/28.07 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel1__eq__len,axiom,
% 28.01/28.07 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => 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) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 28.01/28.07 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => 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) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_in__listrel1__converse,axiom,
% 28.01/28.07 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 <=> 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel1I1,axiom,
% 28.01/28.07 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Cons__listrel1__Cons,axiom,
% 28.01/28.07 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 <=> ( ( 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))
% 28.01/28.07 & V_xs_2 = V_ys_2 )
% 28.01/28.07 | ( V_x_2 = V_y_2
% 28.01/28.07 & 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))) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_list_Osize_I2_J,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel__Cons,axiom,
% 28.01/28.07 ! [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))))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel__rtrancl__refl,axiom,
% 28.01/28.07 ! [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)))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel__mono,axiom,
% 28.01/28.07 ! [V_s_2,V_r_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 28.01/28.07 ! [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)))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel__eq__len,axiom,
% 28.01/28.07 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => 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) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel__rtrancl__trans,axiom,
% 28.01/28.07 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => ( 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))))
% 28.01/28.07 => 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)))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 28.01/28.07 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel1__subset__listrel,axiom,
% 28.01/28.07 ! [V_r_H_2,V_r_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 28.01/28.07 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel_OCons,axiom,
% 28.01/28.07 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrelp__listrel__eq,axiom,
% 28.01/28.07 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 28.01/28.07 ( 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)
% 28.01/28.07 <=> 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel__Cons2,axiom,
% 28.01/28.07 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ~ ! [B_x,B_xs] :
% 28.01/28.07 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 28.01/28.07 => ( 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))
% 28.01/28.07 => ~ 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))) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrelp_OCons,axiom,
% 28.01/28.07 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 28.01/28.07 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrelp_Oequations_I2_J,axiom,
% 28.01/28.07 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 28.01/28.07 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel__Cons1,axiom,
% 28.01/28.07 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ~ ! [B_y,B_ys] :
% 28.01/28.07 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 28.01/28.07 => ( 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))
% 28.01/28.07 => ~ 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))) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel__subset,axiom,
% 28.01/28.07 ! [V_A_2,V_r_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => 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))))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_lists__UNIV,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_lists__mono,axiom,
% 28.01/28.07 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_equiv__listrel,axiom,
% 28.01/28.07 ! [V_r_2,V_A_2,T_b] :
% 28.01/28.07 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.01/28.07 => 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)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel__refl__on,axiom,
% 28.01/28.07 ! [V_r_2,V_A_2,T_b] :
% 28.01/28.07 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.01/28.07 => 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)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Cons__in__lists__iff,axiom,
% 28.01/28.07 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.07 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_lists__accI,axiom,
% 28.01/28.07 ! [V_r_2,V_xs_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_lists__accD,axiom,
% 28.01/28.07 ! [V_r_2,V_xs_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel__iff__nth,axiom,
% 28.01/28.07 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 <=> ( 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)
% 28.01/28.07 & ! [B_n] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => 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)) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_lexord__irreflexive,axiom,
% 28.01/28.07 ! [V_y_2,V_r_2,T_b] :
% 28.01/28.07 ( ! [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))
% 28.01/28.07 => ~ 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_nth__Cons__0,axiom,
% 28.01/28.07 ! [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 ).
% 28.01/28.07
% 28.01/28.07 fof(fact_nth__Cons__Suc,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_list__eq__iff__nth__eq,axiom,
% 28.01/28.07 ! [T_b,V_ys_2,V_xs_2] :
% 28.01/28.07 ( V_xs_2 = V_ys_2
% 28.01/28.07 <=> ( 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)
% 28.01/28.07 & ! [B_i] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_infinite__UNIV__listI,axiom,
% 28.01/28.07 ! [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)))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_nth_Osimps,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_nth__Cons_H,axiom,
% 28.01/28.07 ! [V_xs,V_x,T_a,V_n] :
% 28.01/28.07 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.07 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 28.01/28.07 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_nth__Cons__number__of,axiom,
% 28.01/28.07 ! [V_xs,V_x,T_a,V_v] :
% 28.01/28.07 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.07 => 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 )
% 28.01/28.07 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_lexord__take__index__conv,axiom,
% 28.01/28.07 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 <=> ( ( 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)))
% 28.01/28.07 & 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 )
% 28.01/28.07 | ? [B_i] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 28.01/28.07 & 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)) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_lexord__linear,axiom,
% 28.01/28.07 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 28.01/28.07 ( ! [B_a,B_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 | B_a = B_b
% 28.01/28.07 | 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)) )
% 28.01/28.07 => ( 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)))
% 28.01/28.07 | V_x_2 = V_y_2
% 28.01/28.07 | 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_take__all,axiom,
% 28.01/28.07 ! [V_n,V_xs,T_a] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_nth__take,axiom,
% 28.01/28.07 ! [V_xs,T_a,V_n,V_i] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 28.01/28.07 => 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) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_sublist__upt__eq__take,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_take__take,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_length__take,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_take__Suc__Cons,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_finite__lists__length__le,axiom,
% 28.01/28.07 ! [V_n_2,V_A_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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))))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_set__sublist,axiom,
% 28.01/28.07 ! [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))))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_finite__set,axiom,
% 28.01/28.07 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_set__take__subset,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_in__set__takeD,axiom,
% 28.01/28.07 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_set__ConsD,axiom,
% 28.01/28.07 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => ( V_y_2 = V_x_2
% 28.01/28.07 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_notin__set__sublistI,axiom,
% 28.01/28.07 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 28.01/28.07 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.07 => ~ 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_in__set__sublistD,axiom,
% 28.01/28.07 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_sublists__powset,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_set__subset__Cons,axiom,
% 28.01/28.07 ! [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)))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_set__sublist__subset,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_card__length,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_all__set__conv__all__nth,axiom,
% 28.01/28.07 ! [V_P_2,V_xs_2,T_b] :
% 28.01/28.07 ( ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.07 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.01/28.07 <=> ! [B_i] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_set__take__subset__set__take,axiom,
% 28.01/28.07 ! [V_xs_2,T_b,V_n_2,V_m_2] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.01/28.07 => 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_list__size__estimation,axiom,
% 28.01/28.07 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_list__size__estimation_H,axiom,
% 28.01/28.07 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 28.01/28.07 => 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))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_in__lists__conv__set,axiom,
% 28.01/28.07 ! [V_A_2,V_xs_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 28.01/28.07 <=> ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_length__pos__if__in__set,axiom,
% 28.01/28.07 ! [V_xs_2,V_x_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_in__set__conv__nth,axiom,
% 28.01/28.07 ! [V_xs_2,V_x_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.07 <=> ? [B_i] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_nth__mem,axiom,
% 28.01/28.07 ! [V_xs_2,T_b,V_n_2] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_lists__eq__set,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_set__conv__nth,axiom,
% 28.01/28.07 ! [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))))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_finite__lists__length__eq,axiom,
% 28.01/28.07 ! [V_n_2,V_A_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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))))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel__iff__zip,axiom,
% 28.01/28.07 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 <=> ( 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)
% 28.01/28.07 & ! [B_x] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => 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)) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_set__n__lists,axiom,
% 28.01/28.07 ! [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)))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_length__zip,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_take__zip,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_zip__Cons__Cons,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_list__eq__iff__zip__eq,axiom,
% 28.01/28.07 ! [T_b,V_ys_2,V_xs_2] :
% 28.01/28.07 ( V_xs_2 = V_ys_2
% 28.01/28.07 <=> ( 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)
% 28.01/28.07 & ! [B_x] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_zip__same,axiom,
% 28.01/28.07 ! [V_xs_2,V_b_2,V_a_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.07 & V_a_2 = V_b_2 ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_set__zip__leftD,axiom,
% 28.01/28.07 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_set__zip__rightD,axiom,
% 28.01/28.07 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_in__set__zipE,axiom,
% 28.01/28.07 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.07 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_nth__zip,axiom,
% 28.01/28.07 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_length__n__lists__elem,axiom,
% 28.01/28.07 ! [V_xs_2,V_n_2,V_ys_2,T_b] :
% 28.01/28.07 ( 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))))
% 28.01/28.07 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_length__n__lists,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_set__zip,axiom,
% 28.01/28.07 ! [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)))))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_product__list__set,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_greaterThanLessThan__upto,axiom,
% 28.01/28.07 ! [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)))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_set__upto,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_atLeastAtMost__upto,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_atLeastLessThan__upto,axiom,
% 28.01/28.07 ! [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)))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_greaterThanAtMost__upto,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_nat__list__def,axiom,
% 28.01/28.07 ! [V_l_2] :
% 28.01/28.07 ( c_List_Onat__list(V_l_2)
% 28.01/28.07 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listsum__setsum__nth,axiom,
% 28.01/28.07 ! [V_xs_2,T_b] :
% 28.01/28.07 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 28.01/28.07 ! [V_ns_2] :
% 28.01/28.07 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.07 <=> ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 28.01/28.07 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listsum__simps_I2_J,axiom,
% 28.01/28.07 ! [V_xs,V_x,T_a] :
% 28.01/28.07 ( class_Groups_Omonoid__add(T_a)
% 28.01/28.07 => 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)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_elem__le__listsum__nat,axiom,
% 28.01/28.07 ! [V_ns,V_k] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_list__size__pointwise,axiom,
% 28.01/28.07 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 28.01/28.07 ( ! [B_x] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 28.01/28.07 => 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))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_butlast__take,axiom,
% 28.01/28.07 ! [V_xs,T_a,V_n] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => 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) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_in__set__butlastD,axiom,
% 28.01/28.07 ! [V_xs_2,V_x_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 28.01/28.07 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_take__butlast,axiom,
% 28.01/28.07 ! [V_xs,T_a,V_n] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => 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) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_length__butlast,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_butlast__conv__take,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listsum__update__nat,axiom,
% 28.01/28.07 ! [V_n,V_ns,V_k] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => 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)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_nth__take__lemma,axiom,
% 28.01/28.07 ! [V_ys,V_xs,T_a,V_k] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => ( ! [B_i] :
% 28.01/28.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 28.01/28.07 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 28.01/28.07 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_list__update__beyond,axiom,
% 28.01/28.07 ! [V_x,V_i,V_xs,T_a] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_nth__list__update__neq,axiom,
% 28.01/28.07 ! [V_x,V_xs,T_a,V_j,V_i] :
% 28.01/28.07 ( V_i != V_j
% 28.01/28.07 => 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) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_list__update__id,axiom,
% 28.01/28.07 ! [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 ).
% 28.01/28.07
% 28.01/28.07 fof(fact_length__list__update,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_list__update_Osimps_I2_J,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_list__update__code_I2_J,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_list__update__code_I3_J,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_list__update__overwrite,axiom,
% 28.01/28.07 ! [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) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_list__update__swap,axiom,
% 28.01/28.07 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 28.01/28.07 ( V_i != V_i_H
% 28.01/28.07 => 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) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_update__zip,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_zip__update,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_set__update__subsetI,axiom,
% 28.01/28.07 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 28.01/28.07 ( 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))
% 28.01/28.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_set__update__subset__insert,axiom,
% 28.01/28.07 ! [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)))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_nth__list__update__eq,axiom,
% 28.01/28.07 ! [V_x,V_xs,T_a,V_i] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => 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 ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_list__update__same__conv,axiom,
% 28.01/28.07 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 28.01/28.07 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_nth__list__update,axiom,
% 28.01/28.07 ! [V_x,V_j,V_xs,T_a,V_i] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( ( V_i = V_j
% 28.01/28.07 => 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 )
% 28.01/28.07 & ( V_i != V_j
% 28.01/28.07 => 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) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_set__update__memI,axiom,
% 28.01/28.07 ! [V_x_2,V_xs_2,T_b,V_n_2] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_butlast__list__update,axiom,
% 28.01/28.07 ! [V_x,V_xs,T_a,V_k] :
% 28.01/28.07 ( ( 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))
% 28.01/28.07 => 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) )
% 28.01/28.07 & ( 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))
% 28.01/28.07 => 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) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_listrel1__iff__update,axiom,
% 28.01/28.07 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 <=> ? [B_y,B_n] :
% 28.01/28.07 ( 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))
% 28.01/28.07 & 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)))
% 28.01/28.07 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_distinct__list__update,axiom,
% 28.01/28.07 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.01/28.07 => ( ~ 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))))))
% 28.01/28.07 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_distinct__n__lists,axiom,
% 28.01/28.07 ! [V_n,V_xs,T_a] :
% 28.01/28.07 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.01/28.07 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_distinct__zipI1,axiom,
% 28.01/28.07 ! [V_ys,T_b,V_xs,T_a] :
% 28.01/28.07 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.01/28.07 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_distinct__zipI2,axiom,
% 28.01/28.07 ! [V_xs,T_b,V_ys,T_a] :
% 28.01/28.07 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 28.01/28.07 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_distinct__sublistI,axiom,
% 28.01/28.07 ! [V_I_2,V_xs_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.01/28.07 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_distinct__product,axiom,
% 28.01/28.07 ! [V_ys,T_b,V_xs,T_a] :
% 28.01/28.07 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.01/28.07 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 28.01/28.07 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_distinct__upto,axiom,
% 28.01/28.07 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_distinct__take,axiom,
% 28.01/28.07 ! [V_i,V_xs,T_a] :
% 28.01/28.07 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.01/28.07 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_distinct_Osimps_I2_J,axiom,
% 28.01/28.07 ! [V_xs_2,V_x_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 28.01/28.07 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.07 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_card__distinct,axiom,
% 28.01/28.07 ! [V_xs_2,T_b] :
% 28.01/28.07 ( 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)
% 28.01/28.07 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_distinct__card,axiom,
% 28.01/28.07 ! [V_xs_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.01/28.07 => 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) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_nth__eq__iff__index__eq,axiom,
% 28.01/28.07 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => ( 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)))
% 28.01/28.07 => ( 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)
% 28.01/28.07 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_distinct__conv__nth,axiom,
% 28.01/28.07 ! [V_xs_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.01/28.07 <=> ! [B_i] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ! [B_j] :
% 28.01/28.07 ( 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)))
% 28.01/28.07 => ( B_i != B_j
% 28.01/28.07 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 28.01/28.07 ! [V_xs_2,T_b] :
% 28.01/28.07 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.07 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_Nitpick_Ocard_H__def,axiom,
% 28.01/28.07 ! [V_A_2,T_b] :
% 28.01/28.07 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => 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)))) )
% 28.01/28.07 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.07 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_set__remove1__eq,axiom,
% 28.01/28.07 ! [V_x_2,V_xs_2,T_b] :
% 28.01/28.07 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.01/28.07 => 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_distinct__remove1,axiom,
% 28.01/28.07 ! [V_x,V_xs,T_a] :
% 28.01/28.07 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.01/28.07 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_remove1_Osimps_I2_J,axiom,
% 28.01/28.07 ! [V_xs,T_a,V_y,V_x] :
% 28.01/28.07 ( ( V_x = V_y
% 28.01/28.07 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 28.01/28.07 & ( V_x != V_y
% 28.01/28.07 => 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)) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_remove1__commute,axiom,
% 28.01/28.07 ! [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)) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_remove1__idem,axiom,
% 28.01/28.07 ! [V_xs_2,V_x_2,T_b] :
% 28.01/28.07 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.07 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_notin__set__remove1,axiom,
% 28.01/28.07 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 28.01/28.07 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.07 => ~ 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)))) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_in__set__remove1,axiom,
% 28.01/28.07 ! [V_xs_2,T_b,V_b_2,V_a_2] :
% 28.01/28.07 ( V_a_2 != V_b_2
% 28.01/28.07 => ( 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))))
% 28.01/28.07 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_set__remove1__subset,axiom,
% 28.01/28.07 ! [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))) ).
% 28.01/28.07
% 28.01/28.07 fof(fact_length__remove1,axiom,
% 28.01/28.07 ! [V_xs_2,V_x_2,T_b] :
% 28.01/28.07 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.08 => 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)) )
% 28.01/28.08 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.08 => 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) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sorted__list__of__set__remove,axiom,
% 28.01/28.08 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.08 => 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)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_take__Cons__number__of,axiom,
% 28.01/28.08 ! [V_xs,V_x,T_a,V_v] :
% 28.01/28.08 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.08 => 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) )
% 28.01/28.08 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.08 => 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)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_lists_ONil,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listrel__Nil2,axiom,
% 28.01/28.08 ! [V_r_2,V_xs_2,T_b] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listrel__Nil1,axiom,
% 28.01/28.08 ! [V_r_2,V_xs_2,T_b] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_distinct_Osimps_I1_J,axiom,
% 28.01/28.08 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_distinct__butlast,axiom,
% 28.01/28.08 ! [T_a,V_xs] :
% 28.01/28.08 ( V_xs != c_List_Olist_ONil(T_a)
% 28.01/28.08 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.01/28.08 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_remove1_Osimps_I1_J,axiom,
% 28.01/28.08 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_zip__Nil,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_zip_Osimps_I1_J,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sorted__list__of__set__empty,axiom,
% 28.01/28.08 ! [T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sublist__nil,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listrelp_Oequations_I1_J,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listrelp_ONil,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list_Osize_I1_J,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_upto__empty,axiom,
% 28.01/28.08 ! [V_i,V_j] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 28.01/28.08 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_product_Osimps_I1_J,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list_Osimps_I2_J,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list_Osimps_I3_J,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sublists_Osimps_I1_J,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_take__0,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_take__eq__Nil,axiom,
% 28.01/28.08 ! [V_xs_2,V_n_2,T_b] :
% 28.01/28.08 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 28.01/28.08 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.08 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_take__Nil,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_n__lists__Nil,axiom,
% 28.01/28.08 ! [T_a,V_n] :
% 28.01/28.08 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.08 => 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))) )
% 28.01/28.08 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.08 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_n__lists_Osimps_I1_J,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_set__empty,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] :
% 28.01/28.08 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.01/28.08 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_set__empty2,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] :
% 28.01/28.08 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 28.01/28.08 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_butlast_Osimps_I2_J,axiom,
% 28.01/28.08 ! [V_x,T_a,V_xs] :
% 28.01/28.08 ( ( V_xs = c_List_Olist_ONil(T_a)
% 28.01/28.08 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 28.01/28.08 & ( V_xs != c_List_Olist_ONil(T_a)
% 28.01/28.08 => 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)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__0__conv,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] :
% 28.01/28.08 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.08 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list_Osize_I3_J,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_butlast_Osimps_I1_J,axiom,
% 28.01/28.08 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsum__simps_I1_J,axiom,
% 28.01/28.08 ! [T_a] :
% 28.01/28.08 ( class_Groups_Omonoid__add(T_a)
% 28.01/28.08 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__update__code_I1_J,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__update_Osimps_I1_J,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__update__nonempty,axiom,
% 28.01/28.08 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 28.01/28.08 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 28.01/28.08 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sublist__empty,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__greater__0__conv,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_take__1__Cons,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_not__Nil__listrel1,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_not__listrel1__Nil,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listrel_ONil,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_lexord__Nil__right,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_Nil2__notin__lex,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_Nil__notin__lex,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_take__Cons,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_upto_Osimps,axiom,
% 28.01/28.08 ! [V_j,V_i] :
% 28.01/28.08 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 28.01/28.08 => 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)) )
% 28.01/28.08 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 28.01/28.08 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sublist__singleton,axiom,
% 28.01/28.08 ! [V_x_2,T_b,V_A_2] :
% 28.01/28.08 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 28.01/28.08 => 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)) )
% 28.01/28.08 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 28.01/28.08 => 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) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_lists__empty,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_take__Cons_H,axiom,
% 28.01/28.08 ! [V_xs,V_x,T_a,V_n] :
% 28.01/28.08 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.08 => 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) )
% 28.01/28.08 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.08 => 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)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_upto__rec__number__of,axiom,
% 28.01/28.08 ! [V_n,V_m] :
% 28.01/28.08 ( ( 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)))
% 28.01/28.08 => 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))) )
% 28.01/28.08 & ( ~ 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)))
% 28.01/28.08 => 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) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listrel__Nil,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_set__Cons__sing__Nil,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_upto_Opsimps,axiom,
% 28.01/28.08 ! [V_j_2,V_i_2] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 28.01/28.08 => 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)) )
% 28.01/28.08 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 28.01/28.08 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_select,axiom,
% 28.01/28.08 ! [V_s_2,T_b,V_xs_2] :
% 28.01/28.08 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listset_Osimps_I1_J,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_zip__Cons,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list_Osimps_I5_J,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list_Osimps_I4_J,axiom,
% 28.01/28.08 ! [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 ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listset_Osimps_I2_J,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_zip__Cons1,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_upto_Opinduct,axiom,
% 28.01/28.08 ! [V_P_2,V_a1_2,V_a0_2] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => ( ! [B_i,B_j] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 28.01/28.08 => 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)) )
% 28.01/28.08 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
% 28.01/28.08 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_anamorph_Osimps,axiom,
% 28.01/28.08 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 28.01/28.08 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.01/28.08 => 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) )
% 28.01/28.08 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.01/28.08 => 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)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sublist__Cons,axiom,
% 28.01/28.08 ! [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)))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 28.01/28.08 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 <=> ( ( 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)))
% 28.01/28.08 & V_x_2 = V_y_2 )
% 28.01/28.08 | ( V_xs_2 = V_ys_2
% 28.01/28.08 & 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)) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append__eq__Cons__conv,axiom,
% 28.01/28.08 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 28.01/28.08 ( 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)
% 28.01/28.08 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 28.01/28.08 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 28.01/28.08 | ? [B_ys_H] :
% 28.01/28.08 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 28.01/28.08 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_Cons__eq__append__conv,axiom,
% 28.01/28.08 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 28.01/28.08 ( 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)
% 28.01/28.08 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 28.01/28.08 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 28.01/28.08 | ? [B_ys_H] :
% 28.01/28.08 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 28.01/28.08 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append1__eq__conv,axiom,
% 28.01/28.08 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 <=> ( V_xs_2 = V_ys_2
% 28.01/28.08 & V_x_2 = V_y_2 ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append__Cons,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_Cons__eq__appendI,axiom,
% 28.01/28.08 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 28.01/28.08 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 28.01/28.08 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 28.01/28.08 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append__in__lists__conv,axiom,
% 28.01/28.08 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 28.01/28.08 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append__eq__appendI,axiom,
% 28.01/28.08 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 28.01/28.08 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 28.01/28.08 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 28.01/28.08 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append__same__eq,axiom,
% 28.01/28.08 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 28.01/28.08 ( 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)
% 28.01/28.08 <=> V_ys_2 = V_zs_2 ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_same__append__eq,axiom,
% 28.01/28.08 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 28.01/28.08 ( 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)
% 28.01/28.08 <=> V_ys_2 = V_zs_2 ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append__eq__append__conv2,axiom,
% 28.01/28.08 ! [V_tsa_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 28.01/28.08 ( 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)
% 28.01/28.08 <=> ? [B_us] :
% 28.01/28.08 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 28.01/28.08 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_tsa_2 )
% 28.01/28.08 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 28.01/28.08 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append__assoc,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_set__append,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_zip__append,axiom,
% 28.01/28.08 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 28.01/28.08 ( 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)
% 28.01/28.08 => ( 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)
% 28.01/28.08 => 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)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__append,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsum__append,axiom,
% 28.01/28.08 ! [V_ys,V_xs,T_a] :
% 28.01/28.08 ( class_Groups_Omonoid__add(T_a)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_butlast__append,axiom,
% 28.01/28.08 ! [V_xs,T_a,V_ys] :
% 28.01/28.08 ( ( V_ys = c_List_Olist_ONil(T_a)
% 28.01/28.08 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 28.01/28.08 & ( V_ys != c_List_Olist_ONil(T_a)
% 28.01/28.08 => 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)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append__Nil,axiom,
% 28.01/28.08 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 28.01/28.08
% 28.01/28.08 fof(fact_Nil__is__append__conv,axiom,
% 28.01/28.08 ! [V_ys_2,V_xs_2,T_b] :
% 28.01/28.08 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 28.01/28.08 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 28.01/28.08 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append__Nil2,axiom,
% 28.01/28.08 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 28.01/28.08
% 28.01/28.08 fof(fact_self__append__conv,axiom,
% 28.01/28.08 ! [V_ys_2,T_b,V_xs_2] :
% 28.01/28.08 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 28.01/28.08 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_self__append__conv2,axiom,
% 28.01/28.08 ! [V_xs_2,T_b,V_ys_2] :
% 28.01/28.08 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 28.01/28.08 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append__is__Nil__conv,axiom,
% 28.01/28.08 ! [V_ys_2,V_xs_2,T_b] :
% 28.01/28.08 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 28.01/28.08 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 28.01/28.08 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append__self__conv,axiom,
% 28.01/28.08 ! [V_ys_2,V_xs_2,T_b] :
% 28.01/28.08 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 28.01/28.08 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append__self__conv2,axiom,
% 28.01/28.08 ! [V_ys_2,V_xs_2,T_b] :
% 28.01/28.08 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 28.01/28.08 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_eq__Nil__appendI,axiom,
% 28.01/28.08 ! [T_a,V_ys,V_xs] :
% 28.01/28.08 ( V_xs = V_ys
% 28.01/28.08 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_nth__append__length,axiom,
% 28.01/28.08 ! [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 ).
% 28.01/28.08
% 28.01/28.08 fof(fact_nth__append__length__plus,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_take__append,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__update__append1,axiom,
% 28.01/28.08 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__update__length,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_remove1__append,axiom,
% 28.01/28.08 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 28.01/28.08 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.08 => 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) )
% 28.01/28.08 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.08 => 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)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_in__set__butlast__appendI,axiom,
% 28.01/28.08 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 28.01/28.08 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 28.01/28.08 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 28.01/28.08 => 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))))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_butlast__snoc,axiom,
% 28.01/28.08 ! [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 ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append__listrel1I,axiom,
% 28.01/28.08 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.01/28.08 ( ( ( 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)))
% 28.01/28.08 & V_us_2 = V_vs_2 )
% 28.01/28.08 | ( V_xs_2 = V_ys_2
% 28.01/28.08 & 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))) ) )
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_lexord__append__leftI,axiom,
% 28.01/28.08 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_distinct__append,axiom,
% 28.01/28.08 ! [V_ys_2,V_xs_2,T_b] :
% 28.01/28.08 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 28.01/28.08 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.01/28.08 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 28.01/28.08 & 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)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_nth__append,axiom,
% 28.01/28.08 ! [V_ys,V_xs,T_a,V_n] :
% 28.01/28.08 ( ( 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)))
% 28.01/28.08 => 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) )
% 28.01/28.08 & ( ~ 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)))
% 28.01/28.08 => 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))) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__update__append,axiom,
% 28.01/28.08 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 28.01/28.08 ( ( 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)))
% 28.01/28.08 => 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) )
% 28.01/28.08 & ( ~ 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)))
% 28.01/28.08 => 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)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sublist__append,axiom,
% 28.01/28.08 ! [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)))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listrel1I,axiom,
% 28.01/28.08 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 28.01/28.08 ( 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))
% 28.01/28.08 => ( 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))
% 28.01/28.08 => ( 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))
% 28.01/28.08 => 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))) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_lexord__append__left__rightI,axiom,
% 28.01/28.08 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
% 28.01/28.08 ( 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))
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_take__Suc__conv__app__nth,axiom,
% 28.01/28.08 ! [V_xs,T_a,V_i] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listrel1E,axiom,
% 28.01/28.08 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => ~ ! [B_x,B_y] :
% 28.01/28.08 ( 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))
% 28.01/28.08 => ! [B_us,B_vs] :
% 28.01/28.08 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 28.01/28.08 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_lexord__append__leftD,axiom,
% 28.01/28.08 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => ( ! [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))
% 28.01/28.08 => 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))) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_rotate1__def,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_upd__conv__take__nth__drop,axiom,
% 28.01/28.08 ! [V_a,V_xs,T_a,V_i] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append__take__drop__id,axiom,
% 28.01/28.08 ! [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 ).
% 28.01/28.08
% 28.01/28.08 fof(fact_drop__1__Cons,axiom,
% 28.01/28.08 ! [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 ).
% 28.01/28.08
% 28.01/28.08 fof(fact_drop__Suc__Cons,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_nth__via__drop,axiom,
% 28.01/28.08 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 28.01/28.08 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 28.01/28.08 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_distinct__drop,axiom,
% 28.01/28.08 ! [V_i,V_xs,T_a] :
% 28.01/28.08 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.01/28.08 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_distinct1__rotate,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] :
% 28.01/28.08 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 28.01/28.08 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_drop__zip,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_drop__0,axiom,
% 28.01/28.08 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 28.01/28.08
% 28.01/28.08 fof(fact_drop__drop,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_drop__take,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_take__drop,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_in__set__dropD,axiom,
% 28.01/28.08 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 28.01/28.08 ( 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))))
% 28.01/28.08 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_set__rotate1,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_set__drop__subset,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__drop,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__rotate1,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_butlast__drop,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_drop__butlast,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_drop__Nil,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_rotate1__is__Nil__conv,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] :
% 28.01/28.08 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 28.01/28.08 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_set__drop__subset__set__drop,axiom,
% 28.01/28.08 ! [V_xs_2,T_b,V_m_2,V_n_2] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 28.01/28.08 => 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)))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_drop__eq__Nil,axiom,
% 28.01/28.08 ! [V_xs_2,V_n_2,T_b] :
% 28.01/28.08 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 28.01/28.08 <=> 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_drop__all,axiom,
% 28.01/28.08 ! [V_n,V_xs,T_a] :
% 28.01/28.08 ( 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))
% 28.01/28.08 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_drop__append,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append__eq__conv__conj,axiom,
% 28.01/28.08 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 28.01/28.08 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 28.01/28.08 <=> ( 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)
% 28.01/28.08 & 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) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_drop__Cons,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_drop__Cons_H,axiom,
% 28.01/28.08 ! [V_xs,V_x,T_a,V_n] :
% 28.01/28.08 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.08 => 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) )
% 28.01/28.08 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.08 => 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) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_nth__drop,axiom,
% 28.01/28.08 ! [V_xs,T_a,V_i,V_n] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append__eq__append__conv__if,axiom,
% 28.01/28.08 ! [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] :
% 28.01/28.08 ( 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)
% 28.01/28.08 <=> ( ( 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)))
% 28.01/28.08 => ( 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)
% 28.01/28.08 & 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) ) )
% 28.01/28.08 & ( ~ 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)))
% 28.01/28.08 => ( 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
% 28.01/28.08 & 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 ) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_nth__drop_H,axiom,
% 28.01/28.08 ! [V_xs,T_a,V_i] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_rotate__simps,axiom,
% 28.01/28.08 ! [V_xs,V_x,T_b,T_a] :
% 28.01/28.08 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 28.01/28.08 & 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_drop__Cons__number__of,axiom,
% 28.01/28.08 ! [V_xs,V_x,T_a,V_v] :
% 28.01/28.08 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.08 => 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) )
% 28.01/28.08 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.08 => 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) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_take__add,axiom,
% 28.01/28.08 ! [V_xs,T_a,V_j,V_i] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_rotate1__length01,axiom,
% 28.01/28.08 ! [V_xs,T_a] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_zip__append2,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_zip__append1,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_id__take__nth__drop,axiom,
% 28.01/28.08 ! [V_xs,T_a,V_i] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_take__hd__drop,axiom,
% 28.01/28.08 ! [V_xs,T_a,V_n] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_hd__drop__conv__nth,axiom,
% 28.01/28.08 ! [V_n,T_a,V_xs] :
% 28.01/28.08 ( V_xs != c_List_Olist_ONil(T_a)
% 28.01/28.08 => ( 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)))
% 28.01/28.08 => 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) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_hd_Osimps,axiom,
% 28.01/28.08 ! [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 ).
% 28.01/28.08
% 28.01/28.08 fof(fact_hd__append2,axiom,
% 28.01/28.08 ! [V_ys,T_a,V_xs] :
% 28.01/28.08 ( V_xs != c_List_Olist_ONil(T_a)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_hd__append,axiom,
% 28.01/28.08 ! [V_ys,T_a,V_xs] :
% 28.01/28.08 ( ( V_xs = c_List_Olist_ONil(T_a)
% 28.01/28.08 => 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) )
% 28.01/28.08 & ( V_xs != c_List_Olist_ONil(T_a)
% 28.01/28.08 => 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) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_hd__in__set,axiom,
% 28.01/28.08 ! [T_b,V_xs_2] :
% 28.01/28.08 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_hd__conv__nth,axiom,
% 28.01/28.08 ! [T_a,V_xs] :
% 28.01/28.08 ( V_xs != c_List_Olist_ONil(T_a)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_rotate1__hd__tl,axiom,
% 28.01/28.08 ! [T_a,V_xs] :
% 28.01/28.08 ( V_xs != c_List_Olist_ONil(T_a)
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_hd__rotate__conv__nth,axiom,
% 28.01/28.08 ! [V_n,T_a,V_xs] :
% 28.01/28.08 ( V_xs != c_List_Olist_ONil(T_a)
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_drop__tl,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_tl__drop,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_tl_Osimps_I2_J,axiom,
% 28.01/28.08 ! [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 ).
% 28.01/28.08
% 28.01/28.08 fof(fact_distinct__tl,axiom,
% 28.01/28.08 ! [V_xs,T_a] :
% 28.01/28.08 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.01/28.08 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_distinct__rotate,axiom,
% 28.01/28.08 ! [V_xs_2,V_n_2,T_b] :
% 28.01/28.08 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
% 28.01/28.08 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_rotate__add,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_rotate0,axiom,
% 28.01/28.08 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_rotate__rotate,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_set__rotate,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__rotate,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_tl_Osimps_I1_J,axiom,
% 28.01/28.08 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_rotate__is__Nil__conv,axiom,
% 28.01/28.08 ! [V_xs_2,V_n_2,T_b] :
% 28.01/28.08 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 28.01/28.08 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_rotate__def,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_rotate1__rotate__swap,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_tl__append2,axiom,
% 28.01/28.08 ! [V_ys,T_a,V_xs] :
% 28.01/28.08 ( V_xs != c_List_Olist_ONil(T_a)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_take__tl,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_rotate__conv__mod,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_drop__Suc,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_rotate__Suc,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_tl__append,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_rotate__id,axiom,
% 28.01/28.08 ! [V_xs,T_a,V_n] :
% 28.01/28.08 ( 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)
% 28.01/28.08 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_rotate__length01,axiom,
% 28.01/28.08 ! [V_n,V_xs,T_a] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__tl,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_tl__take,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_take__Suc,axiom,
% 28.01/28.08 ! [V_n,T_a,V_xs] :
% 28.01/28.08 ( V_xs != c_List_Olist_ONil(T_a)
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_rotate__drop__take,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_fold1__set,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] :
% 28.01/28.08 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 28.01/28.08 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 28.01/28.08 => 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)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_lexord__append__rightI,axiom,
% 28.01/28.08 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 28.01/28.08 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_foldl__Nil,axiom,
% 28.01/28.08 ! [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 ).
% 28.01/28.08
% 28.01/28.08 fof(fact_start__le__sum,axiom,
% 28.01/28.08 ! [V_ns_2,V_n_2,V_m_2] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_foldl__assoc,axiom,
% 28.01/28.08 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 28.01/28.08 ( class_Groups_Osemigroup__add(T_b)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_foldl__absorb0,axiom,
% 28.01/28.08 ! [V_zs_2,V_x_2,T_b] :
% 28.01/28.08 ( class_Groups_Omonoid__add(T_b)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_foldl__Cons,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_foldl__append,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsum__foldl,axiom,
% 28.01/28.08 ! [T_b] :
% 28.01/28.08 ( class_Groups_Omonoid__add(T_b)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sum__eq__0__conv,axiom,
% 28.01/28.08 ! [V_ns_2,V_m_2] :
% 28.01/28.08 ( 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)
% 28.01/28.08 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.08 & ! [B_x] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 28.01/28.08 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 28.01/28.08 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 28.01/28.08 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_Sup__set__fold,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] :
% 28.01/28.08 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_Inf__set__fold,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] :
% 28.01/28.08 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_Sup__fin__set__fold,axiom,
% 28.01/28.08 ! [V_xs_2,V_x_2,T_b] :
% 28.01/28.08 ( class_Lattices_Olattice(T_b)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_Inf__fin__set__fold,axiom,
% 28.01/28.08 ! [V_xs_2,V_x_2,T_b] :
% 28.01/28.08 ( class_Lattices_Olattice(T_b)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_Min__fin__set__fold,axiom,
% 28.01/28.08 ! [V_xs_2,V_x_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_Max__fin__set__fold,axiom,
% 28.01/28.08 ! [V_xs_2,V_x_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 28.01/28.08 ! [V_xs_2,V_x_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 28.01/28.08 ! [V_xs_2,V_x_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_SUPR__set__fold,axiom,
% 28.01/28.08 ! [V_f_2,V_xs_2,T_c,T_b] :
% 28.01/28.08 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_INFI__set__fold,axiom,
% 28.01/28.08 ! [V_f_2,V_xs_2,T_c,T_b] :
% 28.01/28.08 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_elem__le__sum,axiom,
% 28.01/28.08 ! [V_ns_2,V_n_2] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sorted__list__of__set__insert,axiom,
% 28.01/28.08 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.08 => 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)))))) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_lexord__Nil__left,axiom,
% 28.01/28.08 ! [V_r_2,V_y_2,T_b] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_insort__key_Osimps_I1_J,axiom,
% 28.01/28.08 ! [V_x_2,V_f_2,T_b,T_c] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_c)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_insort__key_Osimps_I2_J,axiom,
% 28.01/28.08 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => ( ( 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)))
% 28.01/28.08 => 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)) )
% 28.01/28.08 & ( ~ 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)))
% 28.01/28.08 => 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)) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_remove1__insort,axiom,
% 28.01/28.08 ! [V_xs_2,V_x_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => 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 ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_insort__left__comm,axiom,
% 28.01/28.08 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_insort__key__left__comm,axiom,
% 28.01/28.08 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 28.01/28.08 => 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)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_fun__left__comm__insort,axiom,
% 28.01/28.08 ! [T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_set__insort,axiom,
% 28.01/28.08 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_c)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__insort,axiom,
% 28.01/28.08 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_c)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_insort__not__Nil,axiom,
% 28.01/28.08 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_c)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_distinct__insort,axiom,
% 28.01/28.08 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_c)
% 28.01/28.08 => ( 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)))
% 28.01/28.08 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.08 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_insort__insert__insort__key,axiom,
% 28.01/28.08 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => ( ~ 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))))
% 28.01/28.08 => 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) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_insort__insert__insort,axiom,
% 28.01/28.08 ! [V_xs_2,V_x_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.08 => 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) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_distinct__insort__insert,axiom,
% 28.01/28.08 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_c)
% 28.01/28.08 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.01/28.08 => 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))) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_insort__insert__triv,axiom,
% 28.01/28.08 ! [V_xs_2,V_x_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.08 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_set__insort__insert,axiom,
% 28.01/28.08 ! [V_xs_2,V_x_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_insort__insert__key__triv,axiom,
% 28.01/28.08 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => ( 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))))
% 28.01/28.08 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_last__list__update,axiom,
% 28.01/28.08 ! [V_x,V_k,T_a,V_xs] :
% 28.01/28.08 ( V_xs != c_List_Olist_ONil(T_a)
% 28.01/28.08 => ( ( 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))
% 28.01/28.08 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 28.01/28.08 & ( 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))
% 28.01/28.08 => 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) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_last__conv__nth,axiom,
% 28.01/28.08 ! [T_a,V_xs] :
% 28.01/28.08 ( V_xs != c_List_Olist_ONil(T_a)
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_last__appendL,axiom,
% 28.01/28.08 ! [V_xs,T_a,V_ys] :
% 28.01/28.08 ( V_ys = c_List_Olist_ONil(T_a)
% 28.01/28.08 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_last__appendR,axiom,
% 28.01/28.08 ! [V_xs,T_a,V_ys] :
% 28.01/28.08 ( V_ys != c_List_Olist_ONil(T_a)
% 28.01/28.08 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_last__append,axiom,
% 28.01/28.08 ! [V_xs,T_a,V_ys] :
% 28.01/28.08 ( ( V_ys = c_List_Olist_ONil(T_a)
% 28.01/28.08 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 28.01/28.08 & ( V_ys != c_List_Olist_ONil(T_a)
% 28.01/28.08 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_last__ConsL,axiom,
% 28.01/28.08 ! [V_x,T_a,V_xs] :
% 28.01/28.08 ( V_xs = c_List_Olist_ONil(T_a)
% 28.01/28.08 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_last__ConsR,axiom,
% 28.01/28.08 ! [V_x,T_a,V_xs] :
% 28.01/28.08 ( V_xs != c_List_Olist_ONil(T_a)
% 28.01/28.08 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_last_Osimps,axiom,
% 28.01/28.08 ! [V_x,T_a,V_xs] :
% 28.01/28.08 ( ( V_xs = c_List_Olist_ONil(T_a)
% 28.01/28.08 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 28.01/28.08 & ( V_xs != c_List_Olist_ONil(T_a)
% 28.01/28.08 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_last__in__set,axiom,
% 28.01/28.08 ! [T_b,V_as_2] :
% 28.01/28.08 ( V_as_2 != c_List_Olist_ONil(T_b)
% 28.01/28.08 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_last__snoc,axiom,
% 28.01/28.08 ! [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 ).
% 28.01/28.08
% 28.01/28.08 fof(fact_last__drop,axiom,
% 28.01/28.08 ! [V_xs,T_a,V_n] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append__butlast__last__id,axiom,
% 28.01/28.08 ! [T_a,V_xs] :
% 28.01/28.08 ( V_xs != c_List_Olist_ONil(T_a)
% 28.01/28.08 => 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 ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_snoc__eq__iff__butlast,axiom,
% 28.01/28.08 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 28.01/28.08 ( 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
% 28.01/28.08 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 28.01/28.08 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 28.01/28.08 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_lists_Osimps,axiom,
% 28.01/28.08 ! [V_A_2,V_a_2,T_b] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 28.01/28.08 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 28.01/28.08 | ? [B_a,B_l] :
% 28.01/28.08 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 28.01/28.08 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 28.01/28.08 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_select__weigth__select,axiom,
% 28.01/28.08 ! [T_b,V_xs_2] :
% 28.01/28.08 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_inj__mapI,axiom,
% 28.01/28.08 ! [V_f_2,T_c,T_b] :
% 28.01/28.08 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_last__map,axiom,
% 28.01/28.08 ! [V_f_2,T_c,T_b,V_xs_2] :
% 28.01/28.08 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_inj__on__map__eq__map,axiom,
% 28.01/28.08 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => ( 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)
% 28.01/28.08 <=> V_xs_2 = V_ys_2 ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__inj__on,axiom,
% 28.01/28.08 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 28.01/28.08 ( 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)
% 28.01/28.08 => ( 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)))
% 28.01/28.08 => V_xs_2 = V_ys_2 ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_foldl__map,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_rotate__map,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__tl,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__is__Nil__conv,axiom,
% 28.01/28.08 ! [V_xs_2,V_f_2,T_b,T_c] :
% 28.01/28.08 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 28.01/28.08 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map_Osimps_I1_J,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_Nil__is__map__conv,axiom,
% 28.01/28.08 ! [V_xs_2,V_f_2,T_c,T_b] :
% 28.01/28.08 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 28.01/28.08 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__update,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsum__addf,axiom,
% 28.01/28.08 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 28.01/28.08 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsum__0,axiom,
% 28.01/28.08 ! [V_xs_2,T_c,T_b] :
% 28.01/28.08 ( class_Groups_Omonoid__add(T_b)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsum__mult__const,axiom,
% 28.01/28.08 ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
% 28.01/28.08 ( class_Rings_Osemiring__0(T_b)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsum__const__mult,axiom,
% 28.01/28.08 ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
% 28.01/28.08 ( class_Rings_Osemiring__0(T_b)
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsum__subtractf,axiom,
% 28.01/28.08 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 28.01/28.08 ( class_Groups_Oab__group__add(T_b)
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__butlast,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__eq__imp__length__eq,axiom,
% 28.01/28.08 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 28.01/28.08 ( 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)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__map,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__eq__conv,axiom,
% 28.01/28.08 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 28.01/28.08 ( 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)
% 28.01/28.08 <=> ! [B_x] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 28.01/28.08 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_take__map,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__injective,axiom,
% 28.01/28.08 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 28.01/28.08 ( 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)
% 28.01/28.08 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 28.01/28.08 => V_xs_2 = V_ys_2 ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_inj__map__eq__map,axiom,
% 28.01/28.08 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 28.01/28.08 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.01/28.08 => ( 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)
% 28.01/28.08 <=> V_xs_2 = V_ys_2 ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__ident,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 28.01/28.08
% 28.01/28.08 fof(fact_set__map,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map_Osimps_I2_J,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_zip__same__conv__map,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_zip__map__map,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_zip__map1,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__zip__map,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__zip__map2,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_zip__map2,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__append,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_hd__map,axiom,
% 28.01/28.08 ! [V_f_2,T_c,T_b,V_xs_2] :
% 28.01/28.08 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_drop__map,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__size__map,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_List_Omap_Ocomp,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__comp__map,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_List_Omap_Ocompositionality,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__map,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_List_Omap_Oidentity,axiom,
% 28.01/28.08 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_List_Omap_Oid,axiom,
% 28.01/28.08 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_nth__map,axiom,
% 28.01/28.08 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__fun__upd,axiom,
% 28.01/28.08 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 28.01/28.08 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_distinct__map,axiom,
% 28.01/28.08 ! [V_xs_2,V_f_2,T_c,T_b] :
% 28.01/28.08 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 28.01/28.08 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 28.01/28.08 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsum__abs,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] :
% 28.01/28.08 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 28.01/28.08 => 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)))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_uminus__listsum__map,axiom,
% 28.01/28.08 ! [V_xs_2,V_f_2,T_c,T_b] :
% 28.01/28.08 ( class_Groups_Oab__group__add(T_b)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_inj__map,axiom,
% 28.01/28.08 ! [V_f_2,T_c,T_b] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_inj__mapD,axiom,
% 28.01/28.08 ! [V_f_2,T_c,T_b] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 28.01/28.08 ! [V_f_2,V_xs_2,T_b,T_c] :
% 28.01/28.08 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.08 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.01/28.08 => 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)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsum__triv,axiom,
% 28.01/28.08 ! [V_xs_2,V_r_2,T_c,T_b] :
% 28.01/28.08 ( class_Rings_Osemiring__1(T_b)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_product_Osimps_I2_J,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsum__map__remove1,axiom,
% 28.01/28.08 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 28.01/28.08 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.08 => 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)))) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_inj__on__mapI,axiom,
% 28.01/28.08 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 28.01/28.08 ! [V_f_2,V_A_2,T_b,T_c] :
% 28.01/28.08 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.01/28.08 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.08 => 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))))) )
% 28.01/28.08 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.01/28.08 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_pick__same,axiom,
% 28.01/28.08 ! [V_xs_2,T_b,V_l_2] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sublists_Osimps_I2_J,axiom,
% 28.01/28.08 ! [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))))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_less__code__numeral__code,axiom,
% 28.01/28.08 ! [V_m_2,V_n_2] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_zero__code__numeral__def,axiom,
% 28.01/28.08 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 28.01/28.08 ! [V_m_2,V_n_2] :
% 28.01/28.08 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 28.01/28.08 <=> V_n_2 = V_m_2 ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 28.01/28.08 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_times__code__numeral__code,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_one__code__numeral__def,axiom,
% 28.01/28.08 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 28.01/28.08 ! [V_y_2,V_x_2] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 28.01/28.08 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 28.01/28.08 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 28.01/28.08 <=> V_x_2 = V_y_2 ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__fst__zip,axiom,
% 28.01/28.08 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 28.01/28.08 ( 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)
% 28.01/28.08 => 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 ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__snd__zip,axiom,
% 28.01/28.08 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 28.01/28.08 ( 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)
% 28.01/28.08 => 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 ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_number__of__code__numeral__def,axiom,
% 28.01/28.08 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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_zip__map__fst__snd,axiom,
% 28.01/28.08 ! [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 ).
% 28.01/28.08
% 28.01/28.08 fof(fact_plus__code__numeral__code,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_less__eq__code__numeral__code,axiom,
% 28.01/28.08 ! [V_m_2,V_n_2] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_distinct__set__sublists,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] :
% 28.01/28.08 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.01/28.08 => 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)))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_pick__member,axiom,
% 28.01/28.08 ! [V_xs_2,T_b,V_i_2] :
% 28.01/28.08 ( 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))))
% 28.01/28.08 => 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)))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_zip__eq__conv,axiom,
% 28.01/28.08 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 28.01/28.08 ( 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)
% 28.01/28.08 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 28.01/28.08 <=> ( 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
% 28.01/28.08 & 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 ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__size__conv__listsum,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_code__numeral__not__eq__zero,axiom,
% 28.01/28.08 ! [V_i_2] :
% 28.01/28.08 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 28.01/28.08 <=> 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 28.01/28.08 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 28.01/28.08 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 28.01/28.08 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 28.01/28.08 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_select__weight__member,axiom,
% 28.01/28.08 ! [V_s_2,V_xs_2,T_b] :
% 28.01/28.08 ( 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))))
% 28.01/28.08 => 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)))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_select__weight__def,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_select__def,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_subtract__code__numeral__code,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_nat__of__inverse,axiom,
% 28.01/28.08 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 28.01/28.08
% 28.01/28.08 fof(fact_of__nat__nat__of,axiom,
% 28.01/28.08 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 28.01/28.08
% 28.01/28.08 fof(fact_nat__of__of__nat,axiom,
% 28.01/28.08 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 28.01/28.08
% 28.01/28.08 fof(fact_times__code__numeral__def,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 28.01/28.08 ! [V_l_2,V_k_2] :
% 28.01/28.08 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 28.01/28.08 <=> V_k_2 = V_l_2 ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_code__numeral_Onat__of__inject,axiom,
% 28.01/28.08 ! [V_y_2,V_x_2] :
% 28.01/28.08 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 28.01/28.08 <=> V_x_2 = V_y_2 ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_type__definition__code__numeral,axiom,
% 28.01/28.08 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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_less__code__numeral__def,axiom,
% 28.01/28.08 ! [V_m_2,V_n_2] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 28.01/28.08 <=> 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_nat__of,axiom,
% 28.01/28.08 ! [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)))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_nat__of__number,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_int__of__def,axiom,
% 28.01/28.08 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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_less__eq__code__numeral__def,axiom,
% 28.01/28.08 ! [V_m_2,V_n_2] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 28.01/28.08 <=> 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_nat__of__code,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_nat__of__aux__def,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_Suc__code__numeral__def,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_minus__code__numeral__def,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_of__nat__inverse,axiom,
% 28.01/28.08 ! [V_y_2] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 28.01/28.08 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_plus__code__numeral__def,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_div__code__numeral__def,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_subtract__code__numeral__def,axiom,
% 28.01/28.08 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_minus__code__numeral__code,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_mod__code__numeral__def,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_code__numeral__decr,axiom,
% 28.01/28.08 ! [V_k] :
% 28.01/28.08 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsum__mono,axiom,
% 28.01/28.08 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 28.01/28.08 ( ( class_Groups_Omonoid__add(T_c)
% 28.01/28.08 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 28.01/28.08 => ( ! [B_x] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 28.01/28.08 => 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)))) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_partition__set,axiom,
% 28.01/28.08 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 28.01/28.08 ( 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)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_lists__IntI,axiom,
% 28.01/28.08 ! [V_B_2,V_A_2,V_l_2,T_b] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2)))
% 28.01/28.08 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2)))
% 28.01/28.08 => 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)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsp_ONil,axiom,
% 28.01/28.08 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsp_Oequations_I1_J,axiom,
% 28.01/28.08 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_in__listsp__conv__set,axiom,
% 28.01/28.08 ! [V_xs_2,V_A_2,T_b] :
% 28.01/28.08 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 28.01/28.08 <=> ! [B_x] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.08 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsp__infI,axiom,
% 28.01/28.08 ! [V_B_2,V_l_2,V_A_2,T_b] :
% 28.01/28.08 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2))
% 28.01/28.08 => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2))
% 28.01/28.08 => 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)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsp__inf__eq,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsp__conj__eq,axiom,
% 28.01/28.08 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 28.01/28.08 ( 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))
% 28.01/28.08 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2))
% 28.01/28.08 & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsp_Oequations_I2_J,axiom,
% 28.01/28.08 ! [V_a2_2,V_a1_2,V_A_2,T_b] :
% 28.01/28.08 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2)))
% 28.01/28.08 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 28.01/28.08 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_append__in__listsp__conv,axiom,
% 28.01/28.08 ! [V_ys_2,V_xs_2,V_A_2,T_b] :
% 28.01/28.08 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 28.01/28.08 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 28.01/28.08 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsp__mono,axiom,
% 28.01/28.08 ! [V_B_2,V_A_2,T_b] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_partition__P,axiom,
% 28.01/28.08 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 28.01/28.08 ( 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)
% 28.01/28.08 => ( ! [B_x] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 28.01/28.08 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.01/28.08 & ! [B_x] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 28.01/28.08 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_partition_Osimps_I1_J,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_listsp__lists__eq,axiom,
% 28.01/28.08 ! [V_x_2,V_A_2,T_b] :
% 28.01/28.08 ( 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))
% 28.01/28.08 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_partition_Osimps_I2_J,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_lists__Int__eq,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__all2__def,axiom,
% 28.01/28.08 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 28.01/28.08 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 28.01/28.08 <=> ( 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)
% 28.01/28.08 & ! [B_x] :
% 28.01/28.08 ( 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))))
% 28.01/28.08 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_all__nth__imp__all__set,axiom,
% 28.01/28.08 ! [V_x_2,V_P_2,V_xs_2,T_b] :
% 28.01/28.08 ( ! [B_i] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 28.01/28.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.08 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__all2__map1,axiom,
% 28.01/28.08 ! [V_bs_2,V_as_2,V_f_2,T_d,V_P_2,T_c,T_b] :
% 28.01/28.08 ( 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)
% 28.01/28.08 <=> 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__all2__map2,axiom,
% 28.01/28.08 ! [V_bs_2,V_f_2,T_d,V_as_2,V_P_2,T_c,T_b] :
% 28.01/28.08 ( 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))
% 28.01/28.08 <=> 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__all2__append,axiom,
% 28.01/28.08 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
% 28.01/28.08 ( 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)
% 28.01/28.08 => ( 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))
% 28.01/28.08 <=> ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 28.01/28.08 & c_List_Olist__all2(T_b,T_c,V_P_2,V_us_2,V_vs_2) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__all2__appendI,axiom,
% 28.01/28.08 ! [V_d_2,V_c_2,V_b_2,V_a_2,V_P_2,T_c,T_b] :
% 28.01/28.08 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2)
% 28.01/28.08 => ( c_List_Olist__all2(T_b,T_c,V_P_2,V_c_2,V_d_2)
% 28.01/28.08 => 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)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__all2__dropI,axiom,
% 28.01/28.08 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_c,T_b] :
% 28.01/28.08 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,V_bs_2)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__all2__Cons,axiom,
% 28.01/28.08 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_c,T_b] :
% 28.01/28.08 ( 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))
% 28.01/28.08 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 28.01/28.08 & c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__all2__eq,axiom,
% 28.01/28.08 ! [T_b,V_ys_2,V_xs_2] :
% 28.01/28.08 ( V_xs_2 = V_ys_2
% 28.01/28.08 <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__all2__takeI,axiom,
% 28.01/28.08 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 28.01/28.08 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__all2__lengthD,axiom,
% 28.01/28.08 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 28.01/28.08 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__all2__Nil,axiom,
% 28.01/28.08 ! [V_ys_2,V_P_2,T_c,T_b] :
% 28.01/28.08 ( c_List_Olist__all2(T_b,T_c,V_P_2,c_List_Olist_ONil(T_b),V_ys_2)
% 28.01/28.08 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__all2__Nil2,axiom,
% 28.01/28.08 ! [V_xs_2,V_P_2,T_c,T_b] :
% 28.01/28.08 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,c_List_Olist_ONil(T_c))
% 28.01/28.08 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__all2__nthD2,axiom,
% 28.01/28.08 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 28.01/28.08 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 28.01/28.08 => ( 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)))
% 28.01/28.08 => 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))) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__all2__nthD,axiom,
% 28.01/28.08 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 28.01/28.08 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 28.01/28.08 => ( 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)))
% 28.01/28.08 => 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))) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__all2__conv__all__nth,axiom,
% 28.01/28.08 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 28.01/28.08 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 28.01/28.08 <=> ( 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)
% 28.01/28.08 & ! [B_i] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => 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))) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__all2__update__cong2,axiom,
% 28.01/28.08 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 28.01/28.08 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 28.01/28.08 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 28.01/28.08 => ( 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)))
% 28.01/28.08 => 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)) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__all2__update__cong,axiom,
% 28.01/28.08 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_c,V_xs_2,T_b,V_i_2] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 28.01/28.08 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 28.01/28.08 => 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)) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_list__all2I,axiom,
% 28.01/28.08 ! [V_P_2,V_b_2,V_a_2,T_c,T_b] :
% 28.01/28.08 ( ! [B_x] :
% 28.01/28.08 ( 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))))
% 28.01/28.08 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) )
% 28.01/28.08 => ( 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)
% 28.01/28.08 => c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 28.01/28.08 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 28.01/28.08 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_distinct__remdups,axiom,
% 28.01/28.08 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__remdups__leq,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_remdups__eq__nil__iff,axiom,
% 28.01/28.08 ! [V_x_2,T_b] :
% 28.01/28.08 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
% 28.01/28.08 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_remdups__eq__nil__right__iff,axiom,
% 28.01/28.08 ! [V_x_2,T_b] :
% 28.01/28.08 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
% 28.01/28.08 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_remdups_Osimps_I1_J,axiom,
% 28.01/28.08 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__remdups__eq,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] :
% 28.01/28.08 ( 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)
% 28.01/28.08 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_set__remdups,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_remdups__remdups,axiom,
% 28.01/28.08 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_distinct__remdups__id,axiom,
% 28.01/28.08 ! [V_xs,T_a] :
% 28.01/28.08 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.01/28.08 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_remdups__id__iff__distinct,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] :
% 28.01/28.08 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
% 28.01/28.08 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_remdups__map__remdups,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_remove1__remdups,axiom,
% 28.01/28.08 ! [V_x,V_xs,T_a] :
% 28.01/28.08 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_remdups_Osimps_I2_J,axiom,
% 28.01/28.08 ! [V_xs_2,V_x_2,T_b] :
% 28.01/28.08 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.08 => 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) )
% 28.01/28.08 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.08 => 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)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__remdups__card__conv,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__remdups__concat,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_concat_Osimps_I1_J,axiom,
% 28.01/28.08 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_concat__conv__foldl,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_foldl__conv__concat,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_distinct__sort,axiom,
% 28.01/28.08 ! [V_xs_2,V_f_2,T_b,T_c] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_c)
% 28.01/28.08 => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))
% 28.01/28.08 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_set__sort,axiom,
% 28.01/28.08 ! [V_xs_2,V_f_2,T_b,T_c] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_c)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__sort,axiom,
% 28.01/28.08 ! [V_xs_2,V_f_2,T_b,T_c] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_c)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sort__key__simps_I1_J,axiom,
% 28.01/28.08 ! [V_f_2,T_b,T_c] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_c)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_concat_Osimps_I2_J,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_concat__eq__Nil__conv,axiom,
% 28.01/28.08 ! [V_xss_2,T_b] :
% 28.01/28.08 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 28.01/28.08 <=> ! [B_x] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 28.01/28.08 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_Nil__eq__concat__conv,axiom,
% 28.01/28.08 ! [V_xss_2,T_b] :
% 28.01/28.08 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 28.01/28.08 <=> ! [B_x] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 28.01/28.08 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__concat,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__concat,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_set__concat,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sort__key__simps_I2_J,axiom,
% 28.01/28.08 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_c)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_concat__append,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sort__foldl__insort,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_concat__eq__concat__iff,axiom,
% 28.01/28.08 ! [V_ys_2,V_xs_2,T_b] :
% 28.01/28.08 ( ! [B_x] :
% 28.01/28.08 ( 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))))
% 28.01/28.08 => 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)) )
% 28.01/28.08 => ( 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)
% 28.01/28.08 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 28.01/28.08 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_concat__injective,axiom,
% 28.01/28.08 ! [V_ys_2,V_xs_2,T_b] :
% 28.01/28.08 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 28.01/28.08 => ( 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)
% 28.01/28.08 => ( ! [B_x] :
% 28.01/28.08 ( 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))))
% 28.01/28.08 => 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)) )
% 28.01/28.08 => V_xs_2 = V_ys_2 ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_concat__map__singleton,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_n__lists_Osimps_I2_J,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_transpose_Osimps_I3_J,axiom,
% 28.01/28.08 ! [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))))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_transpose__aux__filter__head,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_filter__concat,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_filter__sort,axiom,
% 28.01/28.08 ! [V_xs_2,V_f_2,V_P_2,T_b,T_c] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_c)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_filter__map,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__filter__map,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_filter__insort__triv,axiom,
% 28.01/28.08 ! [V_xs_2,V_f_2,T_b,V_x_2,V_P_2,T_c] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_c)
% 28.01/28.08 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.01/28.08 => 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) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_filter_Osimps_I1_J,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_transpose_Osimps_I1_J,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_filter__empty__conv,axiom,
% 28.01/28.08 ! [V_xs_2,V_P_2,T_b] :
% 28.01/28.08 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 28.01/28.08 <=> ! [B_x] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.08 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__filter__le,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sum__length__filter__compl,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_filter__is__subset,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_filter__id__conv,axiom,
% 28.01/28.08 ! [V_xs_2,V_P_2,T_b] :
% 28.01/28.08 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = V_xs_2
% 28.01/28.08 <=> ! [B_x] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.08 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_filter__filter,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_remove1__filter__not,axiom,
% 28.01/28.08 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 28.01/28.08 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_filter__remove1,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_filter_Osimps_I2_J,axiom,
% 28.01/28.08 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 28.01/28.08 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.01/28.08 => 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)) )
% 28.01/28.08 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.01/28.08 => 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) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_filter__append,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_distinct__filter,axiom,
% 28.01/28.08 ! [V_P_2,V_xs_2,T_b] :
% 28.01/28.08 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.01/28.08 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_partition__filter1,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_partition__filter__conv,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_partition__filter2,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_remdups__filter,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_transpose_Osimps_I2_J,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_nth__transpose,axiom,
% 28.01/28.08 ! [V_xs_2,T_b,V_i_2] :
% 28.01/28.08 ( 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))))
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_transpose__map__map,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_set__filter,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__filter__less,axiom,
% 28.01/28.08 ! [V_P_2,V_xs_2,V_x_2,T_b] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.08 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.01/28.08 => 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))) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_set__minus__filter__out,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_filter__in__sublist,axiom,
% 28.01/28.08 ! [V_s_2,V_xs_2,T_b] :
% 28.01/28.08 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_transpose__empty,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] :
% 28.01/28.08 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 28.01/28.08 <=> ! [B_x] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 28.01/28.08 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__filter__conv__card,axiom,
% 28.01/28.08 ! [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))))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_transpose__aux__filter__tail,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_transpose_Opsimps_I3_J,axiom,
% 28.01/28.08 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => 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))))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_transpose_Opsimps_I2_J,axiom,
% 28.01/28.08 ! [V_xss_2,T_b] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sublist__shift__lemma__Suc,axiom,
% 28.01/28.08 ! [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)))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_select__weigth__drop__zero,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_pick__drop__zero,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_transpose_Opsimps_I1_J,axiom,
% 28.01/28.08 ! [T_b] :
% 28.01/28.08 ( 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))))
% 28.01/28.08 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_transpose__max__length,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_transpose__aux__max,axiom,
% 28.01/28.08 ! [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)))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_foldr_Osimps_I1_J,axiom,
% 28.01/28.08 ! [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 ).
% 28.01/28.08
% 28.01/28.08 fof(fact_foldr_Osimps_I2_J,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_foldr__append,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_foldr__conv__foldl,axiom,
% 28.01/28.08 ! [V_a_2,V_xs_2,T_b] :
% 28.01/28.08 ( class_Groups_Oab__semigroup__add(T_b)
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_foldr__map,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_foldl__foldr1,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] :
% 28.01/28.08 ( class_Groups_Omonoid__add(T_b)
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_foldl__foldr1__lemma,axiom,
% 28.01/28.08 ! [V_xs_2,V_a_2,T_b] :
% 28.01/28.08 ( class_Groups_Omonoid__add(T_b)
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__transpose,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sublist__def,axiom,
% 28.01/28.08 ! [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))))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sublist__shift__lemma,axiom,
% 28.01/28.08 ! [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))))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_atLeastLessThan__upt,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_set__upt,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_distinct__upt,axiom,
% 28.01/28.08 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_upt__add__eq__append,axiom,
% 28.01/28.08 ! [V_k,V_j,V_i] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_upt__Suc,axiom,
% 28.01/28.08 ! [V_j,V_i] :
% 28.01/28.08 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.01/28.08 => 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))) )
% 28.01/28.08 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.01/28.08 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_upt__Suc__append,axiom,
% 28.01/28.08 ! [V_j,V_i] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_drop__upt,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_hd__upt,axiom,
% 28.01/28.08 ! [V_j,V_i] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.01/28.08 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_upt__rec,axiom,
% 28.01/28.08 ! [V_j,V_i] :
% 28.01/28.08 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.01/28.08 => 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)) )
% 28.01/28.08 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.01/28.08 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_upt__conv__Cons,axiom,
% 28.01/28.08 ! [V_j,V_i] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_take__upt,axiom,
% 28.01/28.08 ! [V_n,V_m,V_i] :
% 28.01/28.08 ( 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))
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sorted__list__of__set__range,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_upt__eq__Nil__conv,axiom,
% 28.01/28.08 ! [V_j_2,V_i_2] :
% 28.01/28.08 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 28.01/28.08 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.01/28.08 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_upt__conv__Nil,axiom,
% 28.01/28.08 ! [V_i,V_j] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 28.01/28.08 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_upt__0,axiom,
% 28.01/28.08 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_length__upt,axiom,
% 28.01/28.08 ! [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) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_upt__rec__number__of,axiom,
% 28.01/28.08 ! [V_n,V_m] :
% 28.01/28.08 ( ( 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)))
% 28.01/28.08 => 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))) )
% 28.01/28.08 & ( ~ 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)))
% 28.01/28.08 => 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) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_upt__eq__Cons__conv,axiom,
% 28.01/28.08 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 28.01/28.08 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 28.01/28.08 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 28.01/28.08 & V_i_2 = V_x_2
% 28.01/28.08 & 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 ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_last__upt,axiom,
% 28.01/28.08 ! [V_j,V_i] :
% 28.01/28.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__Suc__upt,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_atLeastAtMost__upt,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_atLeast__upt,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_nth__upt,axiom,
% 28.01/28.08 ! [V_j,V_k,V_i] :
% 28.01/28.08 ( 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))
% 28.01/28.08 => 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) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_greaterThanAtMost__upt,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_greaterThanLessThan__upt,axiom,
% 28.01/28.08 ! [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)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_atMost__upto,axiom,
% 28.01/28.08 ! [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))) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_map__nth,axiom,
% 28.01/28.08 ! [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 ).
% 28.01/28.08
% 28.01/28.08 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 28.01/28.08 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 28.01/28.08 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 28.01/28.08 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 28.01/28.08 ( class_Groups_Ocomm__monoid__add(T_b)
% 28.01/28.08 => 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))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_nth__map__upt,axiom,
% 28.01/28.08 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => 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)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_transpose__rectangle,axiom,
% 28.01/28.08 ! [V_n_2,T_b,V_xs_2] :
% 28.01/28.08 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 28.01/28.08 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 28.01/28.08 => ( ! [B_i] :
% 28.01/28.08 ( 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)))
% 28.01/28.08 => 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 )
% 28.01/28.08 => 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)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_insort__key__remove1,axiom,
% 28.01/28.08 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_c)
% 28.01/28.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.01/28.08 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 28.01/28.08 => ( 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
% 28.01/28.08 => 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 ) ) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sorted_ONil,axiom,
% 28.01/28.08 ! [T_a] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_a)
% 28.01/28.08 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sorted__single,axiom,
% 28.01/28.08 ! [V_x,T_a] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_a)
% 28.01/28.08 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sorted__upt,axiom,
% 28.01/28.08 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sorted__sort,axiom,
% 28.01/28.08 ! [V_xs_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sorted__insort,axiom,
% 28.01/28.08 ! [V_xs_2,V_x_2,T_b] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_b)
% 28.01/28.08 => ( 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))
% 28.01/28.08 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sorted__tl,axiom,
% 28.01/28.08 ! [V_xs,T_a] :
% 28.01/28.08 ( class_Orderings_Olinorder(T_a)
% 28.01/28.08 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 28.01/28.08 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 28.01/28.08
% 28.01/28.08 fof(fact_sorted_Oequations_I1_J,axiom,
% 28.01/28.08 ! [T_a] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_a)
% 28.25/28.08 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__butlast,axiom,
% 28.25/28.08 ! [V_xs,T_a] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_a)
% 28.25/28.08 => ( V_xs != c_List_Olist_ONil(T_a)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 28.25/28.08 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__take,axiom,
% 28.25/28.08 ! [V_n,V_xs,T_a] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_a)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 28.25/28.08 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__upto,axiom,
% 28.25/28.08 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__remove1,axiom,
% 28.25/28.08 ! [V_a,V_xs,T_a] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_a)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 28.25/28.08 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__many,axiom,
% 28.25/28.08 ! [V_zs,V_y,V_x,T_a] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_a)
% 28.25/28.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 28.25/28.08 => 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))) ) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__many__eq,axiom,
% 28.25/28.08 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => ( 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)))
% 28.25/28.08 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 28.25/28.08 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__drop,axiom,
% 28.25/28.08 ! [V_n,V_xs,T_a] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_a)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 28.25/28.08 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__insort__insert,axiom,
% 28.25/28.08 ! [V_x_2,V_xs_2,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 28.25/28.08 => 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)) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__remdups,axiom,
% 28.25/28.08 ! [V_l,T_a] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_a)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 28.25/28.08 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__distinct__set__unique,axiom,
% 28.25/28.08 ! [V_ys_2,V_xs_2,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 28.25/28.08 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 28.25/28.08 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 28.25/28.08 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 28.25/28.08 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__sort__key,axiom,
% 28.25/28.08 ! [V_xs_2,V_f_2,T_c,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => 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))) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__insort__insert__key,axiom,
% 28.25/28.08 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 28.25/28.08 => 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))) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__map__remove1,axiom,
% 28.25/28.08 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 28.25/28.08 => 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))) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__insort__key,axiom,
% 28.25/28.08 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => ( 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)))
% 28.25/28.08 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__filter,axiom,
% 28.25/28.08 ! [V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 28.25/28.08 => 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))) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__map__same,axiom,
% 28.25/28.08 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => 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))) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__same,axiom,
% 28.25/28.08 ! [V_xs_2,V_g_2,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => 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)) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__Cons,axiom,
% 28.25/28.08 ! [V_xs_2,V_x_2,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 28.25/28.08 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 28.25/28.08 & ! [B_x] :
% 28.25/28.08 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__append,axiom,
% 28.25/28.08 ! [V_ys_2,V_xs_2,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 28.25/28.08 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 28.25/28.08 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 28.25/28.08 & ! [B_x] :
% 28.25/28.08 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.08 => ! [B_xa] :
% 28.25/28.08 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 28.25/28.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_filter__insort,axiom,
% 28.25/28.08 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 28.25/28.08 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.25/28.08 => 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)) ) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted_Oequations_I2_J,axiom,
% 28.25/28.08 ! [V_a1_2,V_a2_2,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 28.25/28.08 <=> ( ! [B_x] :
% 28.25/28.08 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 28.25/28.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 28.25/28.08 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__list__of__set,axiom,
% 28.25/28.08 ! [V_A_2,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.25/28.08 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 28.25/28.08 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 28.25/28.08 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_insort__remove1,axiom,
% 28.25/28.08 ! [V_xs_2,V_a_2,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 28.25/28.08 => 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 ) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__nth__mono,axiom,
% 28.25/28.08 ! [V_j,V_i,V_xs,T_a] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_a)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 28.25/28.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.25/28.08 => ( 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)))
% 28.25/28.08 => 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))) ) ) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__equals__nth__mono,axiom,
% 28.25/28.08 ! [V_xs_2,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 28.25/28.08 <=> ! [B_j] :
% 28.25/28.08 ( 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)))
% 28.25/28.08 => ! [B_i] :
% 28.25/28.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 28.25/28.08 => 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))) ) ) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_map__sorted__distinct__set__unique,axiom,
% 28.25/28.08 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_c)
% 28.25/28.08 => ( 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)))
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 28.25/28.08 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 28.25/28.08 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 28.25/28.08 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 28.25/28.08 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_transpose__column,axiom,
% 28.25/28.08 ! [V_i_2,V_xs_2,T_b] :
% 28.25/28.08 ( 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)))
% 28.25/28.08 => ( 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)))
% 28.25/28.08 => 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) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_nth__nth__transpose__sorted,axiom,
% 28.25/28.08 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 28.25/28.08 ( 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)))
% 28.25/28.08 => ( 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))))
% 28.25/28.08 => ( 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))))
% 28.25/28.08 => 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) ) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_inj__on__rev,axiom,
% 28.25/28.08 ! [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) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_rev__is__Nil__conv,axiom,
% 28.25/28.08 ! [V_xs_2,T_b] :
% 28.25/28.08 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 28.25/28.08 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_Nil__is__rev__conv,axiom,
% 28.25/28.08 ! [V_xs_2,T_b] :
% 28.25/28.08 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 28.25/28.08 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_rev_Osimps_I1_J,axiom,
% 28.25/28.08 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_singleton__rev__conv,axiom,
% 28.25/28.08 ! [V_xs_2,V_x_2,T_b] :
% 28.25/28.08 ( 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)
% 28.25/28.08 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_rev__singleton__conv,axiom,
% 28.25/28.08 ! [V_x_2,V_xs_2,T_b] :
% 28.25/28.08 ( 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))
% 28.25/28.08 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_rev__append,axiom,
% 28.25/28.08 ! [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)) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_distinct__rev,axiom,
% 28.25/28.08 ! [V_xs_2,T_b] :
% 28.25/28.08 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 28.25/28.08 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_rev__concat,axiom,
% 28.25/28.08 ! [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))) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_rev__map,axiom,
% 28.25/28.08 ! [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)) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_rev__filter,axiom,
% 28.25/28.08 ! [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)) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_zip__rev,axiom,
% 28.25/28.08 ! [V_ys,T_b,V_xs,T_a] :
% 28.25/28.08 ( 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)
% 28.25/28.08 => 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)) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_set__rev,axiom,
% 28.25/28.08 ! [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) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_listsum__rev,axiom,
% 28.25/28.08 ! [V_xs,T_a] :
% 28.25/28.08 ( class_Groups_Ocomm__monoid__add(T_a)
% 28.25/28.08 => 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) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_rev__is__rev__conv,axiom,
% 28.25/28.08 ! [V_ys_2,V_xs_2,T_b] :
% 28.25/28.08 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 28.25/28.08 <=> V_xs_2 = V_ys_2 ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_rev__swap,axiom,
% 28.25/28.08 ! [V_ys_2,V_xs_2,T_b] :
% 28.25/28.08 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 28.25/28.08 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_rev__rev__ident,axiom,
% 28.25/28.08 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 28.25/28.08
% 28.25/28.08 fof(fact_length__rev,axiom,
% 28.25/28.08 ! [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) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_list__all2__rev1,axiom,
% 28.25/28.08 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 28.25/28.08 ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
% 28.25/28.08 <=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_list__all2__rev,axiom,
% 28.25/28.08 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 28.25/28.08 ( 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))
% 28.25/28.08 <=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_foldl__foldr,axiom,
% 28.25/28.08 ! [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) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_foldr__foldl,axiom,
% 28.25/28.08 ! [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)) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_rev_Osimps_I2_J,axiom,
% 28.25/28.08 ! [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))) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_rev__eq__Cons__iff,axiom,
% 28.25/28.08 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 28.25/28.08 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 28.25/28.08 <=> 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))) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_last__rev,axiom,
% 28.25/28.08 ! [T_a,V_xs] :
% 28.25/28.08 ( V_xs != c_List_Olist_ONil(T_a)
% 28.25/28.08 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_hd__rev,axiom,
% 28.25/28.08 ! [T_a,V_xs] :
% 28.25/28.08 ( V_xs != c_List_Olist_ONil(T_a)
% 28.25/28.08 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__transpose,axiom,
% 28.25/28.08 ! [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)))) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_rev__foldl__cons,axiom,
% 28.25/28.08 ! [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) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_rev__drop,axiom,
% 28.25/28.08 ! [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)) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_rev__take,axiom,
% 28.25/28.08 ! [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)) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_rotate__rev,axiom,
% 28.25/28.08 ! [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)) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_rev__nth,axiom,
% 28.25/28.08 ! [V_xs,T_a,V_n] :
% 28.25/28.08 ( 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)))
% 28.25/28.08 => 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))) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_rev__update,axiom,
% 28.25/28.08 ! [V_y,V_xs,T_a,V_k] :
% 28.25/28.08 ( 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)))
% 28.25/28.08 => 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) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__rev__nth__mono,axiom,
% 28.25/28.08 ! [V_j,V_i,V_xs,T_a] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_a)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 28.25/28.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 28.25/28.08 => ( 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)))
% 28.25/28.08 => 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))) ) ) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_foldr__max__sorted,axiom,
% 28.25/28.08 ! [V_y_2,V_xs_2,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 28.25/28.08 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 28.25/28.08 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 28.25/28.08 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 28.25/28.08 => 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) ) ) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_length__transpose__sorted,axiom,
% 28.25/28.08 ! [V_xs_2,T_b] :
% 28.25/28.08 ( 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)))
% 28.25/28.08 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 28.25/28.08 => 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) )
% 28.25/28.08 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 28.25/28.08 => 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))) ) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_transpose__column__length,axiom,
% 28.25/28.08 ! [V_i_2,V_xs_2,T_b] :
% 28.25/28.08 ( 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)))
% 28.25/28.08 => ( 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)))
% 28.25/28.08 => 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)) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_transpose__transpose,axiom,
% 28.25/28.08 ! [V_xs_2,T_b] :
% 28.25/28.08 ( 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)))
% 28.25/28.08 => 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) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 28.25/28.08 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_sorted__takeWhile,axiom,
% 28.25/28.08 ! [V_P_2,V_xs_2,T_b] :
% 28.25/28.08 ( class_Orderings_Olinorder(T_b)
% 28.25/28.08 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 28.25/28.08 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_length__takeWhile__le,axiom,
% 28.25/28.08 ! [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))) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_set__takeWhileD,axiom,
% 28.25/28.08 ! [V_xs_2,V_P_2,V_x_2,T_b] :
% 28.25/28.08 ( 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))))
% 28.25/28.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.08 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_takeWhile__eq__all__conv,axiom,
% 28.25/28.08 ! [V_xs_2,V_P_2,T_b] :
% 28.25/28.08 ( c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = V_xs_2
% 28.25/28.08 <=> ! [B_x] :
% 28.25/28.08 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.08 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_zip__takeWhile__fst,axiom,
% 28.25/28.08 ! [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)) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_zip__takeWhile__snd,axiom,
% 28.25/28.08 ! [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)) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_takeWhile__map,axiom,
% 28.25/28.08 ! [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)) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_distinct__takeWhile,axiom,
% 28.25/28.08 ! [V_P_2,V_xs_2,T_b] :
% 28.25/28.08 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.25/28.08 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_takeWhile__tail,axiom,
% 28.25/28.08 ! [V_l_2,V_xs_2,T_b,V_x_2,V_P_2] :
% 28.25/28.08 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.25/28.08 => 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) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 28.25/28.08 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 28.25/28.08 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.25/28.08 => 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)) )
% 28.25/28.08 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.25/28.08 => 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) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_takeWhile__eq__take,axiom,
% 28.25/28.08 ! [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) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 28.25/28.08 ! [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) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_return__list__def,axiom,
% 28.25/28.08 ! [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) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_takeWhile__append1,axiom,
% 28.25/28.08 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 28.25/28.08 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.08 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.25/28.08 => 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) ) ) ).
% 28.25/28.08
% 28.25/28.08 fof(fact_takeWhile__nth,axiom,
% 28.25/28.08 ! [V_xs_2,V_P_2,T_b,V_j_2] :
% 28.25/28.09 ( 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))))
% 28.25/28.09 => 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) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_nth__length__takeWhile,axiom,
% 28.25/28.09 ! [V_xs_2,V_P_2,T_b] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => ~ 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))))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_takeWhile__not__last,axiom,
% 28.25/28.09 ! [T_b,V_xs_2] :
% 28.25/28.09 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 28.25/28.09 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.25/28.09 => 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) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 28.25/28.09 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
% 28.25/28.09 ( class_Orderings_Olinorder(T_b)
% 28.25/28.09 => ( 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)))
% 28.25/28.09 => 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) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 28.25/28.09 ! [V_l] :
% 28.25/28.09 ( c_List_Onat__list(V_l)
% 28.25/28.09 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 28.25/28.09 ! [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))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_embed__list__def,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_takeWhile__neq__rev,axiom,
% 28.25/28.09 ! [V_x_2,V_xs_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => 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))) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dropWhile__neq__rev,axiom,
% 28.25/28.09 ! [V_x_2,V_xs_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => 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))) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_takeWhile__dropWhile__id,axiom,
% 28.25/28.09 ! [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 ).
% 28.25/28.09
% 28.25/28.09 fof(fact_sorted__dropWhile,axiom,
% 28.25/28.09 ! [V_P_2,V_xs_2,T_b] :
% 28.25/28.09 ( class_Orderings_Olinorder(T_b)
% 28.25/28.09 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 28.25/28.09 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_P_2,V_xs_2)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_hd__dropWhile,axiom,
% 28.25/28.09 ! [V_xs_2,V_P_2,T_b] :
% 28.25/28.09 ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) != c_List_Olist_ONil(T_b)
% 28.25/28.09 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_length__dropWhile__le,axiom,
% 28.25/28.09 ! [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))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 28.25/28.09 ! [V_xs_2,V_P_2,T_b] :
% 28.25/28.09 ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) = c_List_Olist_ONil(T_b)
% 28.25/28.09 <=> ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_distinct__dropWhile,axiom,
% 28.25/28.09 ! [V_P_2,V_xs_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 28.25/28.09 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 28.25/28.09 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 28.25/28.09 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.25/28.09 => 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) )
% 28.25/28.09 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.25/28.09 => 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) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dropWhile__map,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dropWhile__append1,axiom,
% 28.25/28.09 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.25/28.09 => 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) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 28.25/28.09 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_b] :
% 28.25/28.09 ( 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)
% 28.25/28.09 <=> ( 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))
% 28.25/28.09 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dropWhile__eq__drop,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dropWhile__nth,axiom,
% 28.25/28.09 ! [V_xs_2,V_P_2,T_b,V_j_2] :
% 28.25/28.09 ( 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))))
% 28.25/28.09 => 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)))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_listsum__map__filter,axiom,
% 28.25/28.09 ! [V_f_2,V_P_2,V_xs_2,T_b,T_c] :
% 28.25/28.09 ( class_Groups_Omonoid__add(T_c)
% 28.25/28.09 => ( ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => ( ~ hBOOL(hAPP(V_P_2,B_x))
% 28.25/28.09 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
% 28.25/28.09 => 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)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_sorted__nth__monoI,axiom,
% 28.25/28.09 ! [V_xs,T_a] :
% 28.25/28.09 ( class_Orderings_Olinorder(T_a)
% 28.25/28.09 => ( ! [B_i,B_j] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 28.25/28.09 => ( 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)))
% 28.25/28.09 => 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))) ) )
% 28.25/28.09 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_takeWhile__eq__filter,axiom,
% 28.25/28.09 ! [V_xs_2,V_P_2,T_b] :
% 28.25/28.09 ( ! [B_x] :
% 28.25/28.09 ( 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))))
% 28.25/28.09 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 28.25/28.09 => c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 28.25/28.09 ! [V_P_2,V_xs_2,T_b,V_n_2] :
% 28.25/28.09 ( ! [B_i] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 28.25/28.09 => ( 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)))
% 28.25/28.09 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) )
% 28.25/28.09 => ( ( 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)))
% 28.25/28.09 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) )
% 28.25/28.09 => c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_length__takeWhile__less__P__nth,axiom,
% 28.25/28.09 ! [V_xs_2,T_b,V_P_2,V_j_2] :
% 28.25/28.09 ( ! [B_i] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 28.25/28.09 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 28.25/28.09 => ( 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)))
% 28.25/28.09 => 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)))) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_sorted_Osimps,axiom,
% 28.25/28.09 ! [V_a_2,T_b] :
% 28.25/28.09 ( class_Orderings_Olinorder(T_b)
% 28.25/28.09 => ( c_List_Olinorder__class_Osorted(T_b,V_a_2)
% 28.25/28.09 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 28.25/28.09 | ? [B_xs,B_x] :
% 28.25/28.09 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 28.25/28.09 & ! [B_xa] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs)))
% 28.25/28.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
% 28.25/28.09 & c_List_Olinorder__class_Osorted(T_b,B_xs) ) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_map__removeAll__inj__on,axiom,
% 28.25/28.09 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => 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)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_not__in__set__insert,axiom,
% 28.25/28.09 ! [V_xs_2,V_x_2,T_b] :
% 28.25/28.09 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => 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) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_removeAll__append,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_insert__remdups,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_removeAll__filter__not__eq,axiom,
% 28.25/28.09 ! [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))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_removeAll__filter__not,axiom,
% 28.25/28.09 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 28.25/28.09 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.25/28.09 => 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) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_distinct__insert,axiom,
% 28.25/28.09 ! [V_x,V_xs,T_a] :
% 28.25/28.09 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.25/28.09 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_distinct__removeAll,axiom,
% 28.25/28.09 ! [V_x,V_xs,T_a] :
% 28.25/28.09 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.25/28.09 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_removeAll_Osimps_I2_J,axiom,
% 28.25/28.09 ! [V_xs,T_a,V_y,V_x] :
% 28.25/28.09 ( ( V_x = V_y
% 28.25/28.09 => 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) )
% 28.25/28.09 & ( V_x != V_y
% 28.25/28.09 => 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)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_removeAll_Osimps_I1_J,axiom,
% 28.25/28.09 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_removeAll__id,axiom,
% 28.25/28.09 ! [V_xs_2,V_x_2,T_b] :
% 28.25/28.09 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_distinct__remove1__removeAll,axiom,
% 28.25/28.09 ! [V_x,V_xs,T_a] :
% 28.25/28.09 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 28.25/28.09 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_in__set__insert,axiom,
% 28.25/28.09 ! [V_xs_2,V_x_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_List_Oset__insert,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_insert__Nil,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_map__removeAll__inj,axiom,
% 28.25/28.09 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 28.25/28.09 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.25/28.09 => 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)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_set__removeAll,axiom,
% 28.25/28.09 ! [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)))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_List_Oinsert__def,axiom,
% 28.25/28.09 ! [V_xs_2,V_x_2,T_b] :
% 28.25/28.09 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 )
% 28.25/28.09 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => 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) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_maps__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_concat__map__maps,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_maps__simps_I2_J,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_maps__simps_I1_J,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_distinct__concat,axiom,
% 28.25/28.09 ! [V_xs_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2))
% 28.25/28.09 => ( ! [B_ys] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 28.25/28.09 => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) )
% 28.25/28.09 => ( ! [B_ys] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 28.25/28.09 => ! [B_zs] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 28.25/28.09 => ( B_ys != B_zs
% 28.25/28.09 => 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)) ) ) )
% 28.25/28.09 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_measures__lesseq,axiom,
% 28.25/28.09 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => ( 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)))
% 28.25/28.09 => 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)))) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_wf__measures,axiom,
% 28.25/28.09 ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_in__measures_I1_J,axiom,
% 28.25/28.09 ! [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))))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_measures__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_in__measures_I2_J,axiom,
% 28.25/28.09 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] :
% 28.25/28.09 ( 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))))
% 28.25/28.09 <=> ( 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)))
% 28.25/28.09 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 28.25/28.09 & 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))) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_measures__less,axiom,
% 28.25/28.09 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => 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)))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_foldl__apply,axiom,
% 28.25/28.09 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] :
% 28.25/28.09 ( ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => 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)) )
% 28.25/28.09 => 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)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_zip__obtain__same__length,axiom,
% 28.25/28.09 ! [V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
% 28.25/28.09 ( ( 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))
% 28.25/28.09 => 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)))) )
% 28.25/28.09 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_pos__not__random__dseq__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dropWhile__append2,axiom,
% 28.25/28.09 ! [V_ys_2,V_P_2,V_xs_2,T_b] :
% 28.25/28.09 ( ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.25/28.09 => 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) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__all2__all__nthI,axiom,
% 28.25/28.09 ! [V_P_2,V_b_2,T_c,V_a_2,T_b] :
% 28.25/28.09 ( 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)
% 28.25/28.09 => ( ! [B_n] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => 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))) )
% 28.25/28.09 => c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_finite__sorted__distinct__unique,axiom,
% 28.25/28.09 ! [V_A_2,T_b] :
% 28.25/28.09 ( class_Orderings_Olinorder(T_b)
% 28.25/28.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.25/28.09 => ? [B_x] :
% 28.25/28.09 ( hAPP(c_List_Oset(T_b),B_x) = V_A_2
% 28.25/28.09 & c_List_Olinorder__class_Osorted(T_b,B_x)
% 28.25/28.09 & hBOOL(hAPP(c_List_Odistinct(T_b),B_x))
% 28.25/28.09 & ! [B_y] :
% 28.25/28.09 ( ( hAPP(c_List_Oset(T_b),B_y) = V_A_2
% 28.25/28.09 & c_List_Olinorder__class_Osorted(T_b,B_y)
% 28.25/28.09 & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) )
% 28.25/28.09 => B_y = B_x ) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_takeWhile__append2,axiom,
% 28.25/28.09 ! [V_ys_2,V_P_2,V_xs_2,T_b] :
% 28.25/28.09 ( ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.25/28.09 => 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)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_insort__is__Cons,axiom,
% 28.25/28.09 ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] :
% 28.25/28.09 ( class_Orderings_Olinorder(T_c)
% 28.25/28.09 => ( ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 28.25/28.09 => 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) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_Cons__eq__filter__iff,axiom,
% 28.25/28.09 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 28.25/28.09 ( 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)
% 28.25/28.09 <=> ? [B_us,B_vs] :
% 28.25/28.09 ( 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))
% 28.25/28.09 & ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 28.25/28.09 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 28.25/28.09 & hBOOL(hAPP(V_P_2,V_x_2))
% 28.25/28.09 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_filter__eq__Cons__iff,axiom,
% 28.25/28.09 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_b] :
% 28.25/28.09 ( 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)
% 28.25/28.09 <=> ? [B_us,B_vs] :
% 28.25/28.09 ( 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))
% 28.25/28.09 & ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 28.25/28.09 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 28.25/28.09 & hBOOL(hAPP(V_P_2,V_x_2))
% 28.25/28.09 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__ball__nth,axiom,
% 28.25/28.09 ! [V_P_2,V_xs_2,T_b,V_n_2] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => ( ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.25/28.09 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_sorted_OCons,axiom,
% 28.25/28.09 ! [V_x_2,V_xs_2,T_b] :
% 28.25/28.09 ( class_Orderings_Olinorder(T_b)
% 28.25/28.09 => ( ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
% 28.25/28.09 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 28.25/28.09 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__ex__length,axiom,
% 28.25/28.09 ! [V_xs_2,V_P_2,T_b] :
% 28.25/28.09 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 28.25/28.09 <=> ? [B_n] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_in__set__conv__decomp,axiom,
% 28.25/28.09 ! [V_xs_2,V_x_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 <=> ? [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)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__ex__simps_I1_J,axiom,
% 28.25/28.09 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 28.25/28.09 ( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 28.25/28.09 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.25/28.09 | c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__ex__rev,axiom,
% 28.25/28.09 ! [V_xs_2,V_P_2,T_b] :
% 28.25/28.09 ( c_List_Olist__ex(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 28.25/28.09 <=> c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__ex__iff,axiom,
% 28.25/28.09 ! [V_xs_2,V_P_2,T_b] :
% 28.25/28.09 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 28.25/28.09 <=> ? [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__ex__append,axiom,
% 28.25/28.09 ! [V_ys_2,V_xs_2,V_P_2,T_b] :
% 28.25/28.09 ( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 28.25/28.09 <=> ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 28.25/28.09 | c_List_Olist__ex(T_b,V_P_2,V_ys_2) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__ex__simps_I2_J,axiom,
% 28.25/28.09 ! [V_P_2,T_b] : ~ c_List_Olist__ex(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_in__set__conv__decomp__first,axiom,
% 28.25/28.09 ! [V_xs_2,V_x_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 <=> ? [B_ys] :
% 28.25/28.09 ( ? [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))
% 28.25/28.09 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_in__set__conv__decomp__last,axiom,
% 28.25/28.09 ! [V_xs_2,V_x_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 <=> ? [B_ys,B_zs] :
% 28.25/28.09 ( 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))
% 28.25/28.09 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__all__length,axiom,
% 28.25/28.09 ! [V_xs_2,V_P_2,T_b] :
% 28.25/28.09 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 28.25/28.09 <=> ! [B_n] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_finite__induct,axiom,
% 28.25/28.09 ! [V_P_2,V_F_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 28.25/28.09 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 28.25/28.09 => ( ! [B_x,B_F] :
% 28.25/28.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 28.25/28.09 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
% 28.25/28.09 => ( hBOOL(hAPP(V_P_2,B_F))
% 28.25/28.09 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) )
% 28.25/28.09 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__all__simps_I1_J,axiom,
% 28.25/28.09 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 28.25/28.09 ( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 28.25/28.09 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.25/28.09 & c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__all__rev,axiom,
% 28.25/28.09 ! [V_xs_2,V_P_2,T_b] :
% 28.25/28.09 ( c_List_Olist__all(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 28.25/28.09 <=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__all__iff,axiom,
% 28.25/28.09 ! [V_xs_2,V_P_2,T_b] :
% 28.25/28.09 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 28.25/28.09 <=> ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__all__append,axiom,
% 28.25/28.09 ! [V_ys_2,V_xs_2,V_P_2,T_b] :
% 28.25/28.09 ( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 28.25/28.09 <=> ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 28.25/28.09 & c_List_Olist__all(T_b,V_P_2,V_ys_2) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__all__simps_I2_J,axiom,
% 28.25/28.09 ! [V_P_2,T_b] : c_List_Olist__all(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_Ball__set__list__all,axiom,
% 28.25/28.09 ! [V_P_2,V_xs_2,T_b] :
% 28.25/28.09 ( ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.25/28.09 <=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__all__iff__raw,axiom,
% 28.25/28.09 ! [V_xs_2,V_P_2,T_b] :
% 28.25/28.09 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 28.25/28.09 <=> ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__ex1__simps_I2_J,axiom,
% 28.25/28.09 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 28.25/28.09 ( c_List_Olist__ex1(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 28.25/28.09 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.25/28.09 => 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) )
% 28.25/28.09 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.25/28.09 => c_List_Olist__ex1(T_b,V_P_2,V_xs_2) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_measure__function__int,axiom,
% 28.25/28.09 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))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__ex1__simps_I1_J,axiom,
% 28.25/28.09 ! [V_P_2,T_b] : ~ c_List_Olist__ex1(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_is__measure_Ointros,axiom,
% 28.25/28.09 ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_is__measure_Oequations,axiom,
% 28.25/28.09 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_is__measure_Osimps,axiom,
% 28.25/28.09 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_measure__size,axiom,
% 28.25/28.09 ! [T_b] :
% 28.25/28.09 ( class_Nat_Osize(T_b)
% 28.25/28.09 => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_measure__snd,axiom,
% 28.25/28.09 ! [T_c,V_f_2,T_b] :
% 28.25/28.09 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 28.25/28.09 => 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))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_measure__fst,axiom,
% 28.25/28.09 ! [T_c,V_f_2,T_b] :
% 28.25/28.09 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 28.25/28.09 => 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))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__ex1__iff,axiom,
% 28.25/28.09 ! [V_xs_2,V_P_2,T_b] :
% 28.25/28.09 ( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
% 28.25/28.09 <=> ? [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 & hBOOL(hAPP(V_P_2,B_x))
% 28.25/28.09 & ! [B_y] :
% 28.25/28.09 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 & hBOOL(hAPP(V_P_2,B_y)) )
% 28.25/28.09 => B_y = B_x ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_transfer__morphism__int__nat,axiom,
% 28.25/28.09 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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 28.25/28.09 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 28.25/28.09 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.25/28.09 => 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) )
% 28.25/28.09 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.25/28.09 => 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)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_bool_Osize_I4_J,axiom,
% 28.25/28.09 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_bool_Osize_I3_J,axiom,
% 28.25/28.09 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_neg__bind__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 28.25/28.09 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 28.25/28.09 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.25/28.09 => 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) )
% 28.25/28.09 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 28.25/28.09 => 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)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 28.25/28.09 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_pos__empty__def,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_pos__bind__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_neg__map__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_neg__single__def,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_pos__map__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_pos__single__def,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_New__DSequence_Opos__single__def,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_length__splice,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_splice_Osimps_I3_J,axiom,
% 28.25/28.09 ! [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))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_splice_Osimps_I1_J,axiom,
% 28.25/28.09 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ).
% 28.25/28.09
% 28.25/28.09 fof(fact_splice__Nil2,axiom,
% 28.25/28.09 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ).
% 28.25/28.09
% 28.25/28.09 fof(fact_splice_Osimps_I2_J,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_,axiom,
% 28.25/28.09 ! [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)))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_bij__image__Collect__eq,axiom,
% 28.25/28.09 ! [V_P_2,V_f_2,T_c,T_b] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => 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))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inv__into__f__eq,axiom,
% 28.25/28.09 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.25/28.09 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.25/28.09 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 28.25/28.09 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inv__into__f__f,axiom,
% 28.25/28.09 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 28.25/28.09 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 28.25/28.09 => 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 ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inv__f__f,axiom,
% 28.25/28.09 ! [V_x_2,V_f_2,T_c,T_b] :
% 28.25/28.09 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.25/28.09 => 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 ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inv__f__eq,axiom,
% 28.25/28.09 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 28.25/28.09 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.25/28.09 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 28.25/28.09 => 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 ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inv__into__def,axiom,
% 28.25/28.09 ! [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))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inv__inv__eq,axiom,
% 28.25/28.09 ! [V_f_2,T_c,T_b] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => 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 ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_bij__imp__bij__inv,axiom,
% 28.25/28.09 ! [V_f_2,T_c,T_b] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => 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))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_bij__betw__inv__into,axiom,
% 28.25/28.09 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 28.25/28.09 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 28.25/28.09 => 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) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inv__into__inv__into__eq,axiom,
% 28.25/28.09 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 28.25/28.09 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 28.25/28.09 => 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) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_image__inv__into__cancel,axiom,
% 28.25/28.09 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
% 28.25/28.09 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2))
% 28.25/28.09 => 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 ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_surj__iff__all,axiom,
% 28.25/28.09 ! [V_f_2,T_b,T_c] :
% 28.25/28.09 ( 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))
% 28.25/28.09 <=> ! [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 ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_surj__f__inv__f,axiom,
% 28.25/28.09 ! [V_y_2,V_f_2,T_b,T_c] :
% 28.25/28.09 ( 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))
% 28.25/28.09 => 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 ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_image__surj__f__inv__f,axiom,
% 28.25/28.09 ! [V_A_2,V_f_2,T_b,T_c] :
% 28.25/28.09 ( 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))
% 28.25/28.09 => 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 ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inv__into__injective,axiom,
% 28.25/28.09 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] :
% 28.25/28.09 ( 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)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 28.25/28.09 => V_x_2 = V_y_2 ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inv__into__into,axiom,
% 28.25/28.09 ! [V_A_2,V_f_2,T_c,V_x_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 28.25/28.09 => 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)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_f__inv__into__f,axiom,
% 28.25/28.09 ! [V_A_2,V_f_2,T_c,V_y_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 28.25/28.09 => 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 ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inv__id,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inv__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inj__on__inv__into,axiom,
% 28.25/28.09 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => 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) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inv__into__image__cancel,axiom,
% 28.25/28.09 ! [V_S_2,V_A_2,V_f_2,T_c,T_b] :
% 28.25/28.09 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2))
% 28.25/28.09 => 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 ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inj__imp__surj__inv,axiom,
% 28.25/28.09 ! [V_f_2,T_c,T_b] :
% 28.25/28.09 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.25/28.09 => 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)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_image__inv__f__f,axiom,
% 28.25/28.09 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.25/28.09 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.25/28.09 => 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 ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inv__image__comp,axiom,
% 28.25/28.09 ! [V_X_2,V_f_2,T_c,T_b] :
% 28.25/28.09 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.25/28.09 => 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 ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_surj__imp__inj__inv,axiom,
% 28.25/28.09 ! [V_f_2,T_b,T_c] :
% 28.25/28.09 ( 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))
% 28.25/28.09 => 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))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_o__inv__o__cancel,axiom,
% 28.25/28.09 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 28.25/28.09 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.25/28.09 => 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 ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_o__inv__distrib,axiom,
% 28.25/28.09 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => ( 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)))
% 28.25/28.09 => 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)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inv__into__comp,axiom,
% 28.25/28.09 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 28.25/28.09 ( 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))
% 28.25/28.09 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 28.25/28.09 => ( 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))))
% 28.25/28.09 => 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) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_surj__iff,axiom,
% 28.25/28.09 ! [V_f_2,T_b,T_c] :
% 28.25/28.09 ( 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))
% 28.25/28.09 <=> 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) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inv__o__cancel,axiom,
% 28.25/28.09 ! [V_f_2,T_c,T_b] :
% 28.25/28.09 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.25/28.09 => 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) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inj__iff,axiom,
% 28.25/28.09 ! [V_f_2,T_c,T_b] :
% 28.25/28.09 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.25/28.09 <=> 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) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_bij__vimage__eq__inv__image,axiom,
% 28.25/28.09 ! [V_A_2,V_f_2,T_c,T_b] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => 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) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inj__transfer,axiom,
% 28.25/28.09 ! [V_x_2,V_P_2,V_f_2,T_c,T_b] :
% 28.25/28.09 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 28.25/28.09 => ( ! [B_y] :
% 28.25/28.09 ( 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)))))
% 28.25/28.09 => 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))) )
% 28.25/28.09 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_small__lazy__list_Osimps,axiom,
% 28.25/28.09 ! [V_d_2,T_b] :
% 28.25/28.09 ( class_Lazy__Sequence_Osmall__lazy(T_b)
% 28.25/28.09 => 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)))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_small__lazy__prod__def,axiom,
% 28.25/28.09 ! [V_d,T_b,T_a] :
% 28.25/28.09 ( ( class_Lazy__Sequence_Osmall__lazy(T_a)
% 28.25/28.09 & class_Lazy__Sequence_Osmall__lazy(T_b) )
% 28.25/28.09 => 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)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_New__DSequence_Opos__union__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_acyclicP__converse,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( 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))))
% 28.25/28.09 <=> 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))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_converse__meet,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_conversep__eq,axiom,
% 28.25/28.09 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ).
% 28.25/28.09
% 28.25/28.09 fof(fact_conversep__conversep,axiom,
% 28.25/28.09 ! [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 ).
% 28.25/28.09
% 28.25/28.09 fof(fact_conversep__iff,axiom,
% 28.25/28.09 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 28.25/28.09 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_conversep_Oequations,axiom,
% 28.25/28.09 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
% 28.25/28.09 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_conversep_Ointros,axiom,
% 28.25/28.09 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 28.25/28.09 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_conversepD,axiom,
% 28.25/28.09 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 28.25/28.09 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_conversep__noteq,axiom,
% 28.25/28.09 ! [V_y_2,V_x_2,T_b] :
% 28.25/28.09 ( 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))
% 28.25/28.09 <=> V_x_2 != V_y_2 ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_converse__pred__comp,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_converse__join,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_conversep__converse__eq,axiom,
% 28.25/28.09 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 28.25/28.09 ( 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))
% 28.25/28.09 <=> 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))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_pos__union__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_small__lazy_H_Osimps,axiom,
% 28.25/28.09 ! [V_i,V_d] :
% 28.25/28.09 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 28.25/28.09 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 28.25/28.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 28.25/28.09 => 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)))) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_small__lazy__int__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_small__lazy_H_Opsimps,axiom,
% 28.25/28.09 ! [V_i_2,V_d_2] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 28.25/28.09 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 28.25/28.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 28.25/28.09 => 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)))) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_tl__replicate,axiom,
% 28.25/28.09 ! [V_x,T_a,V_n] :
% 28.25/28.09 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.25/28.09 => 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) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_map__replicate,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_replicate__0,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_empty__replicate,axiom,
% 28.25/28.09 ! [V_x_2,V_n_2,T_b] :
% 28.25/28.09 ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2)
% 28.25/28.09 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_replicate__empty,axiom,
% 28.25/28.09 ! [V_x_2,V_n_2,T_b] :
% 28.25/28.09 ( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b)
% 28.25/28.09 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_concat__replicate__trivial,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_filter__replicate,axiom,
% 28.25/28.09 ! [V_n_2,T_b,V_x_2,V_P_2] :
% 28.25/28.09 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 28.25/28.09 => 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) )
% 28.25/28.09 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 28.25/28.09 => 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) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_append__replicate__commute,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_replicate__add,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_nth__replicate,axiom,
% 28.25/28.09 ! [V_x,T_a,V_n,V_i] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 28.25/28.09 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_replicate__eq__replicate,axiom,
% 28.25/28.09 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] :
% 28.25/28.09 ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2)
% 28.25/28.09 <=> ( V_m_2 = V_n_2
% 28.25/28.09 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.25/28.09 => V_x_2 = V_y_2 ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_Bex__set__replicate,axiom,
% 28.25/28.09 ! [V_P_2,V_a_2,V_n_2,T_b] :
% 28.25/28.09 ( ? [B_x] :
% 28.25/28.09 ( 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))))
% 28.25/28.09 & hBOOL(hAPP(V_P_2,B_x)) )
% 28.25/28.09 <=> ( hBOOL(hAPP(V_P_2,V_a_2))
% 28.25/28.09 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_Ball__set__replicate,axiom,
% 28.25/28.09 ! [V_P_2,V_a_2,V_n_2,T_b] :
% 28.25/28.09 ( ! [B_x] :
% 28.25/28.09 ( 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))))
% 28.25/28.09 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.25/28.09 <=> ( hBOOL(hAPP(V_P_2,V_a_2))
% 28.25/28.09 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_zip__replicate,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_drop__replicate,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_hd__replicate,axiom,
% 28.25/28.09 ! [V_x,T_a,V_n] :
% 28.25/28.09 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.25/28.09 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_take__replicate,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_last__replicate,axiom,
% 28.25/28.09 ! [V_x,T_a,V_n] :
% 28.25/28.09 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.25/28.09 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_rev__replicate,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_replicate__Suc,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_replicate__app__Cons__same,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_map__replicate__const,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_length__replicate,axiom,
% 28.25/28.09 ! [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 ).
% 28.25/28.09
% 28.25/28.09 fof(fact_replicate__length__filter,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_in__set__replicate,axiom,
% 28.25/28.09 ! [V_y_2,V_n_2,V_x_2,T_b] :
% 28.25/28.09 ( 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))))
% 28.25/28.09 <=> ( V_x_2 = V_y_2
% 28.25/28.09 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_replicate__append__same,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_map__replicate__trivial,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_set__replicate,axiom,
% 28.25/28.09 ! [V_x_2,T_b,V_n_2] :
% 28.25/28.09 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.25/28.09 => 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))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_set__replicate__conv__if,axiom,
% 28.25/28.09 ! [V_x_2,T_b,V_n_2] :
% 28.25/28.09 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.25/28.09 => 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)) )
% 28.25/28.09 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.25/28.09 => 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))) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_set__replicate__Suc,axiom,
% 28.25/28.09 ! [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))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_small__lazy_H_Opinduct,axiom,
% 28.25/28.09 ! [V_P_2,V_a1_2,V_a0_2] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => ( ! [B_d,B_i] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 28.25/28.09 => 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)))) )
% 28.25/28.09 => hBOOL(hAPP(hAPP(V_P_2,B_d),B_i)) ) )
% 28.25/28.09 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_eq__comp__r,axiom,
% 28.25/28.09 ! [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 ).
% 28.25/28.09
% 28.25/28.09 fof(fact_field__le__epsilon,axiom,
% 28.25/28.09 ! [V_y,V_x,T_a] :
% 28.25/28.09 ( class_Fields_Olinordered__field(T_a)
% 28.25/28.09 => ( ! [B_e] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
% 28.25/28.09 => 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))) )
% 28.25/28.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_lazy__sequence_Osize_I4_J,axiom,
% 28.25/28.09 ! [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))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact__01,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_lazy__sequence_Oinject,axiom,
% 28.25/28.09 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] :
% 28.25/28.09 ( 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)
% 28.25/28.09 <=> ( V_a_2 = V_a_H_2
% 28.25/28.09 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_lazy__sequence_Osize_I2_J,axiom,
% 28.25/28.09 ! [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))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_size__code,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_lazy__sequence__size__code,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_seq__case,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_yieldn__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_lazy__sequence_Osimps_I5_J,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_refl__on__INTER,axiom,
% 28.25/28.09 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 28.25/28.09 ( ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 28.25/28.09 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 28.25/28.09 => 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)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_in__set__member,axiom,
% 28.25/28.09 ! [V_xs_2,V_x_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 <=> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_member__rec_I1_J,axiom,
% 28.25/28.09 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 28.25/28.09 ( 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))
% 28.25/28.09 <=> ( V_x_2 = V_y_2
% 28.25/28.09 | hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_member__set,axiom,
% 28.25/28.09 ! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_member__rec_I2_J,axiom,
% 28.25/28.09 ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_List_Omember__def,axiom,
% 28.25/28.09 ! [V_x_2,V_xs_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2))
% 28.25/28.09 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_pair__box_Osize_I1_J,axiom,
% 28.25/28.09 ! [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))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__ex1__iff__raw,axiom,
% 28.25/28.09 ! [V_xs_2,V_P_2,T_b] :
% 28.25/28.09 ( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
% 28.25/28.09 <=> ? [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 & hBOOL(hAPP(V_P_2,B_x))
% 28.25/28.09 & ! [B_y] :
% 28.25/28.09 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 & hBOOL(hAPP(V_P_2,B_y)) )
% 28.25/28.09 => B_y = B_x ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_pair__box_Oinject,axiom,
% 28.25/28.09 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 28.25/28.09 ( 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)
% 28.25/28.09 <=> ( V_a_2 = V_a_H_2
% 28.25/28.09 & V_b_2 = V_b_H_2 ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_pair__box_Osize_I2_J,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_pair__box_Orecs,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_pair__box_Osimps_I2_J,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_THE__default__def,axiom,
% 28.25/28.09 ! [V_d_2,T_b,V_P_2] :
% 28.25/28.09 ( ( ? [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(V_P_2,B_x))
% 28.25/28.09 & ! [B_y] :
% 28.25/28.09 ( hBOOL(hAPP(V_P_2,B_y))
% 28.25/28.09 => B_y = B_x ) )
% 28.25/28.09 => c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = c_HOL_OThe(T_b,V_P_2) )
% 28.25/28.09 & ( ~ ? [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(V_P_2,B_x))
% 28.25/28.09 & ! [B_y] :
% 28.25/28.09 ( hBOOL(hAPP(V_P_2,B_y))
% 28.25/28.09 => B_y = B_x ) )
% 28.25/28.09 => c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = V_d_2 ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_setsum__UNION__zero,axiom,
% 28.25/28.09 ! [V_f_2,V_S_2,T_b,T_c] :
% 28.25/28.09 ( class_Groups_Ocomm__monoid__add(T_c)
% 28.25/28.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2))
% 28.25/28.09 => ( ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2))
% 28.25/28.09 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 28.25/28.09 => ( ! [B_T1] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2))
% 28.25/28.09 => ! [B_T2] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2))
% 28.25/28.09 => ( B_T1 != B_T2
% 28.25/28.09 => ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1))
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2))
% 28.25/28.09 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) )
% 28.25/28.09 => 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) ) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_finite__maxlen,axiom,
% 28.25/28.09 ! [V_M_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2))
% 28.25/28.09 => ? [B_n] :
% 28.25/28.09 ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2))
% 28.25/28.09 => 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)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_lazy__sequence_Osize_I3_J,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_lazy__sequence_Osimps_I2_J,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_lazy__sequence_Osimps_I3_J,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact__02,axiom,
% 28.25/28.09 ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq ).
% 28.25/28.09
% 28.25/28.09 fof(fact_lazy__sequence_Osimps_I4_J,axiom,
% 28.25/28.09 ! [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 ).
% 28.25/28.09
% 28.25/28.09 fof(fact_lazy__sequence_Osize_I1_J,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__all__iff__all__interval__int,axiom,
% 28.25/28.09 ! [V_j_2,V_i_2,V_P_2] :
% 28.25/28.09 ( c_List_Olist__all(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
% 28.25/28.09 <=> c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__ex__iff__not__all__inverval__int,axiom,
% 28.25/28.09 ! [V_j_2,V_i_2,V_P_2] :
% 28.25/28.09 ( c_List_Olist__ex(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
% 28.25/28.09 <=> ~ 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) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_all__interval__int__def,axiom,
% 28.25/28.09 ! [V_j_2,V_i_2,V_P_2] :
% 28.25/28.09 ( c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2)
% 28.25/28.09 <=> ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2)))
% 28.25/28.09 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_code__numeral_Orecs_I2_J,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_Random_Osimps,axiom,
% 28.25/28.09 ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
% 28.25/28.09 ( ( 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)))
% 28.25/28.09 => 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)) )
% 28.25/28.09 & ( ~ 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)))
% 28.25/28.09 => 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))))))) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_code__numeral_Orecs_I1_J,axiom,
% 28.25/28.09 ! [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 ).
% 28.25/28.09
% 28.25/28.09 fof(fact_Random__Sequence_Oempty__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_Random__Sequence_Osingle__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_Random__Sequence_Omap__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_exE__realizer,axiom,
% 28.25/28.09 ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_P_2] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => ( ! [B_x,B_y] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(V_P_2,B_y),B_x))
% 28.25/28.09 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
% 28.25/28.09 => 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))) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_Image__Collect__split,axiom,
% 28.25/28.09 ! [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)))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_lexord__trans,axiom,
% 28.25/28.09 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => ( 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)))
% 28.25/28.09 => ( c_Relation_Otrans(T_b,V_r_2)
% 28.25/28.09 => 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))) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_trans__less__than,axiom,
% 28.25/28.09 c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_trans__lex__prod,axiom,
% 28.25/28.09 ! [V_R2_2,T_c,V_R1_2,T_b] :
% 28.25/28.09 ( c_Relation_Otrans(T_b,V_R1_2)
% 28.25/28.09 => ( c_Relation_Otrans(T_c,V_R2_2)
% 28.25/28.09 => c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_transD,axiom,
% 28.25/28.09 ! [V_c_2,V_b_2,V_a_2,V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Otrans(T_b,V_r_2)
% 28.25/28.09 => ( 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))
% 28.25/28.09 => ( 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))
% 28.25/28.09 => 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)) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_trans__def,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Otrans(T_b,V_r_2)
% 28.25/28.09 <=> ! [B_x,B_y] :
% 28.25/28.09 ( 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))
% 28.25/28.09 => ! [B_z] :
% 28.25/28.09 ( 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))
% 28.25/28.09 => 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)) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_UN__eq,axiom,
% 28.25/28.09 ! [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))))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_Union__eq,axiom,
% 28.25/28.09 ! [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)))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_trans__inv__image,axiom,
% 28.25/28.09 ! [V_f_2,T_c,V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Otrans(T_b,V_r_2)
% 28.25/28.09 => c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_trans__O__subset,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Otrans(T_b,V_r_2)
% 28.25/28.09 => 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)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_SUPR__bool__eq,axiom,
% 28.25/28.09 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_trans__Int,axiom,
% 28.25/28.09 ! [V_s_2,V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Otrans(T_b,V_r_2)
% 28.25/28.09 => ( c_Relation_Otrans(T_b,V_s_2)
% 28.25/28.09 => 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)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_bex__UNIV,axiom,
% 28.25/28.09 ! [V_P_2,T_b] :
% 28.25/28.09 ( ? [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 28.25/28.09 & hBOOL(hAPP(V_P_2,B_x)) )
% 28.25/28.09 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_trans__rtrancl,axiom,
% 28.25/28.09 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_lexord__transI,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Otrans(T_b,V_r_2)
% 28.25/28.09 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_trans__finite__psubset,axiom,
% 28.25/28.09 ! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_trans__Id__on,axiom,
% 28.25/28.09 ! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_trancl__id,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Otrans(T_b,V_r_2)
% 28.25/28.09 => c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2 ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_trans__trancl,axiom,
% 28.25/28.09 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_trans__Id,axiom,
% 28.25/28.09 ! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_trans__converse,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 28.25/28.09 <=> c_Relation_Otrans(T_b,V_r_2) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_listrel__trans,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Otrans(T_b,V_r_2)
% 28.25/28.09 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_bex__empty,axiom,
% 28.25/28.09 ! [V_P_2,T_b] :
% 28.25/28.09 ~ ? [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 28.25/28.09 & hBOOL(hAPP(V_P_2,B_x)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_finite__Collect__bex,axiom,
% 28.25/28.09 ! [V_Q_2,T_c,V_A_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.25/28.09 => ( 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)))))
% 28.25/28.09 <=> ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 28.25/28.09 => 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)))) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_trans__reflclI,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Otrans(T_b,V_r_2)
% 28.25/28.09 => 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))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__ex__iff__raw,axiom,
% 28.25/28.09 ! [V_xs_2,V_P_2,T_b] :
% 28.25/28.09 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 28.25/28.09 <=> ? [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_Bex__set__list__ex,axiom,
% 28.25/28.09 ! [V_P_2,V_xs_2,T_b] :
% 28.25/28.09 ( ? [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 28.25/28.09 & hBOOL(hAPP(V_P_2,B_x)) )
% 28.25/28.09 <=> c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_INT__eq,axiom,
% 28.25/28.09 ! [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))))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_Sup__fun__def,axiom,
% 28.25/28.09 ! [V_x_2,V_A_2,T_c,T_b] :
% 28.25/28.09 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.25/28.09 => 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)))))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_Sup__apply,axiom,
% 28.25/28.09 ! [V_x_2,V_A_2,T_c,T_b] :
% 28.25/28.09 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.25/28.09 => 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)))))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_Inf__fun__def,axiom,
% 28.25/28.09 ! [V_x_2,V_A_2,T_c,T_b] :
% 28.25/28.09 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.25/28.09 => 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)))))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_Inf__apply,axiom,
% 28.25/28.09 ! [V_x_2,V_A_2,T_c,T_b] :
% 28.25/28.09 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 28.25/28.09 => 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)))))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_max__extp_Ointros,axiom,
% 28.25/28.09 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 28.25/28.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 28.25/28.09 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.25/28.09 => ( ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 28.25/28.09 => ? [B_xa] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 28.25/28.09 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) )
% 28.25/28.09 => c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2) ) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_transp__def,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Predicate_Otransp(T_b,V_r_2)
% 28.25/28.09 <=> 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))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_transpE,axiom,
% 28.25/28.09 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 28.25/28.09 ( c_Predicate_Otransp(T_b,V_r_2)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2))
% 28.25/28.09 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_equivpE,axiom,
% 28.25/28.09 ! [V_R_2,T_b] :
% 28.25/28.09 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.25/28.09 => ~ ( c_Predicate_Oreflp(T_b,V_R_2)
% 28.25/28.09 => ( c_Predicate_Osymp(T_b,V_R_2)
% 28.25/28.09 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_equivpI,axiom,
% 28.25/28.09 ! [V_R_2,T_b] :
% 28.25/28.09 ( c_Predicate_Oreflp(T_b,V_R_2)
% 28.25/28.09 => ( c_Predicate_Osymp(T_b,V_R_2)
% 28.25/28.09 => ( c_Predicate_Otransp(T_b,V_R_2)
% 28.25/28.09 => c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_sympE,axiom,
% 28.25/28.09 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 28.25/28.09 ( c_Predicate_Osymp(T_b,V_r_2)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 28.25/28.09 => hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_equivp__reflp__symp__transp,axiom,
% 28.25/28.09 ! [V_R_2,T_b] :
% 28.25/28.09 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.25/28.09 <=> ( c_Predicate_Oreflp(T_b,V_R_2)
% 28.25/28.09 & c_Predicate_Osymp(T_b,V_R_2)
% 28.25/28.09 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_max__extp_Osimps,axiom,
% 28.25/28.09 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 28.25/28.09 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 28.25/28.09 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 28.25/28.09 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 28.25/28.09 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.25/28.09 & ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 28.25/28.09 => ? [B_xa] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 28.25/28.09 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_trans__diff__Id,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Otrans(T_b,V_r_2)
% 28.25/28.09 => ( c_Relation_Oantisym(T_b,V_r_2)
% 28.25/28.09 => 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))) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_antisym__empty,axiom,
% 28.25/28.09 ! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_antisym__converse,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 28.25/28.09 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_antisym__Id,axiom,
% 28.25/28.09 ! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_antisym__Id__on,axiom,
% 28.25/28.09 ! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_antisym__subset,axiom,
% 28.25/28.09 ! [V_s_2,V_r_2,T_b] :
% 28.25/28.09 ( 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))
% 28.25/28.09 => ( c_Relation_Oantisym(T_b,V_s_2)
% 28.25/28.09 => c_Relation_Oantisym(T_b,V_r_2) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_antisym__def,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Oantisym(T_b,V_r_2)
% 28.25/28.09 <=> ! [B_x,B_y] :
% 28.25/28.09 ( 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))
% 28.25/28.09 => ( 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))
% 28.25/28.09 => B_x = B_y ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_antisymD,axiom,
% 28.25/28.09 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Oantisym(T_b,V_r_2)
% 28.25/28.09 => ( 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))
% 28.25/28.09 => ( 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))
% 28.25/28.09 => V_a_2 = V_b_2 ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_antisym__reflcl,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_acyclic__impl__antisym__rtrancl,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 28.25/28.09 => c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_fun__lub__def,axiom,
% 28.25/28.09 ! [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)))))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_sym__trans__comp__subset,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Osym(T_b,V_r_2)
% 28.25/28.09 => ( c_Relation_Otrans(T_b,V_r_2)
% 28.25/28.09 => 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)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_symD,axiom,
% 28.25/28.09 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Osym(T_b,V_r_2)
% 28.25/28.09 => ( 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))
% 28.25/28.09 => 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)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_sym__def,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Osym(T_b,V_r_2)
% 28.25/28.09 <=> ! [B_x,B_y] :
% 28.25/28.09 ( 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))
% 28.25/28.09 => 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)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_sym__inv__image,axiom,
% 28.25/28.09 ! [V_f_2,T_c,V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Osym(T_b,V_r_2)
% 28.25/28.09 => c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_sym__Int__converse,axiom,
% 28.25/28.09 ! [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))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_sym__Int,axiom,
% 28.25/28.09 ! [V_s_2,V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Osym(T_b,V_r_2)
% 28.25/28.09 => ( c_Relation_Osym(T_b,V_s_2)
% 28.25/28.09 => 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)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_sym__rtrancl,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Osym(T_b,V_r_2)
% 28.25/28.09 => c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_sym__Id__on,axiom,
% 28.25/28.09 ! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_sym__trancl,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Osym(T_b,V_r_2)
% 28.25/28.09 => c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_sym__Un,axiom,
% 28.25/28.09 ! [V_s_2,V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Osym(T_b,V_r_2)
% 28.25/28.09 => ( c_Relation_Osym(T_b,V_s_2)
% 28.25/28.09 => 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)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_sym__Id,axiom,
% 28.25/28.09 ! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_sym__conv__converse__eq,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Osym(T_b,V_r_2)
% 28.25/28.09 <=> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2 ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_sym__converse,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 28.25/28.09 <=> c_Relation_Osym(T_b,V_r_2) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_listrel__sym,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Relation_Osym(T_b,V_r_2)
% 28.25/28.09 => c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_sym__Un__converse,axiom,
% 28.25/28.09 ! [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))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_equiv__def,axiom,
% 28.25/28.09 ! [V_r_2,V_A_2,T_b] :
% 28.25/28.09 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.25/28.09 <=> ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.25/28.09 & c_Relation_Osym(T_b,V_r_2)
% 28.25/28.09 & c_Relation_Otrans(T_b,V_r_2) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_equivI,axiom,
% 28.25/28.09 ! [V_r_2,V_A_2,T_b] :
% 28.25/28.09 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.25/28.09 => ( c_Relation_Osym(T_b,V_r_2)
% 28.25/28.09 => ( c_Relation_Otrans(T_b,V_r_2)
% 28.25/28.09 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_equivE,axiom,
% 28.25/28.09 ! [V_r_2,V_A_2,T_b] :
% 28.25/28.09 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 28.25/28.09 => ~ ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 28.25/28.09 => ( c_Relation_Osym(T_b,V_r_2)
% 28.25/28.09 => ~ c_Relation_Otrans(T_b,V_r_2) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_symp__def,axiom,
% 28.25/28.09 ! [V_r_2,T_b] :
% 28.25/28.09 ( c_Predicate_Osymp(T_b,V_r_2)
% 28.25/28.09 <=> 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))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_part__equivpI,axiom,
% 28.25/28.09 ! [T_b,V_R_2] :
% 28.25/28.09 ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 28.25/28.09 => ( c_Predicate_Osymp(T_b,V_R_2)
% 28.25/28.09 => ( c_Predicate_Otransp(T_b,V_R_2)
% 28.25/28.09 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_part__equivp__refl__symp__transp,axiom,
% 28.25/28.09 ! [V_R_2,T_b] :
% 28.25/28.09 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 28.25/28.09 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 28.25/28.09 & c_Predicate_Osymp(T_b,V_R_2)
% 28.25/28.09 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_part__equivp__transp,axiom,
% 28.25/28.09 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 28.25/28.09 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 28.25/28.09 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_part__equivp__symp,axiom,
% 28.25/28.09 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 28.25/28.09 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 28.25/28.09 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_part__equivp__def,axiom,
% 28.25/28.09 ! [V_R_2,T_b] :
% 28.25/28.09 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 28.25/28.09 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 28.25/28.09 & ! [B_x,B_y] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 28.25/28.09 <=> ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 28.25/28.09 & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y))
% 28.25/28.09 & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_equivp__implies__part__equivp,axiom,
% 28.25/28.09 ! [V_R_2,T_b] :
% 28.25/28.09 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.25/28.09 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_part__equivpE,axiom,
% 28.25/28.09 ! [V_R_2,T_b] :
% 28.25/28.09 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 28.25/28.09 => ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 28.25/28.09 => ( c_Predicate_Osymp(T_b,V_R_2)
% 28.25/28.09 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_part__equivp__typedef,axiom,
% 28.25/28.09 ! [V_R_2,T_b] :
% 28.25/28.09 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 28.25/28.09 => ? [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))))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_fold__image__UN__disjoint,axiom,
% 28.25/28.09 ! [V_g_2,V_A_2,T_c,V_I_2,T_b,T_d] :
% 28.25/28.09 ( class_Groups_Ocomm__monoid__mult(T_d)
% 28.25/28.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2))
% 28.25/28.09 => ( ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 28.25/28.09 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 28.25/28.09 => ( ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 28.25/28.09 => ! [B_xa] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2))
% 28.25/28.09 => ( B_x != B_xa
% 28.25/28.09 => 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)) ) ) )
% 28.25/28.09 => 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) ) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_nat__of__cases,axiom,
% 28.25/28.09 ! [V_y_2] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 28.25/28.09 => ~ ! [B_x] : V_y_2 != hAPP(c_Code__Numeral_Onat__of,B_x) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_nat__of__induct,axiom,
% 28.25/28.09 ! [V_P_2,V_y_2] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 28.25/28.09 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Code__Numeral_Onat__of,B_x)))
% 28.25/28.09 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_of__nat__cases,axiom,
% 28.25/28.09 ! [V_x_2] :
% 28.25/28.09 ~ ! [B_y] :
% 28.25/28.09 ( V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y)
% 28.25/28.09 => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_of__nat__induct,axiom,
% 28.25/28.09 ! [V_x_2,V_P_2] :
% 28.25/28.09 ( ! [B_y] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 28.25/28.09 => hBOOL(hAPP(V_P_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) )
% 28.25/28.09 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_lazy__sequence_Orecs_I1_J,axiom,
% 28.25/28.09 ! [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 ).
% 28.25/28.09
% 28.25/28.09 fof(fact_lazy__sequence_Orecs_I2_J,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_Least__Suc2,axiom,
% 28.25/28.09 ! [V_m_2,V_Q_2,V_n_2,V_P_2] :
% 28.25/28.09 ( hBOOL(hAPP(V_P_2,V_n_2))
% 28.25/28.09 => ( hBOOL(hAPP(V_Q_2,V_m_2))
% 28.25/28.09 => ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 28.25/28.09 => ( ! [B_k] :
% 28.25/28.09 ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_k)))
% 28.25/28.09 <=> hBOOL(hAPP(V_Q_2,B_k)) )
% 28.25/28.09 => 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)) ) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_beyond__def,axiom,
% 28.25/28.09 ! [V_l,V_k] :
% 28.25/28.09 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 28.25/28.09 => c_Quickcheck_Obeyond(V_k,V_l) = V_l )
% 28.25/28.09 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 28.25/28.09 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_beyond__zero,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_curry__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_refl__on__UNION,axiom,
% 28.25/28.09 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 28.25/28.09 ( ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 28.25/28.09 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 28.25/28.09 => 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)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_curryI,axiom,
% 28.25/28.09 ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
% 28.25/28.09 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 28.25/28.09 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_curry__split,axiom,
% 28.25/28.09 ! [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 ).
% 28.25/28.09
% 28.25/28.09 fof(fact_split__curry,axiom,
% 28.25/28.09 ! [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 ).
% 28.25/28.09
% 28.25/28.09 fof(fact_curry__conv,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_curryD,axiom,
% 28.25/28.09 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 28.25/28.09 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_curryE,axiom,
% 28.25/28.09 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 28.25/28.09 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_bex__reg__eqv,axiom,
% 28.25/28.09 ! [V_P_2,V_R_2,T_b] :
% 28.25/28.09 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.25/28.09 => ( ? [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 28.25/28.09 & hBOOL(hAPP(V_P_2,B_x)) )
% 28.25/28.09 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_wf__weak__decr__stable,axiom,
% 28.25/28.09 ! [V_r_2,V_f_2,T_b] :
% 28.25/28.09 ( ! [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)))
% 28.25/28.09 => ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))
% 28.25/28.09 => ? [B_i] :
% 28.25/28.09 ! [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) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_in__respects,axiom,
% 28.25/28.09 ! [V_R_2,V_x_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2)))
% 28.25/28.09 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_Respects__def,axiom,
% 28.25/28.09 ! [V_x_2,V_R_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2))
% 28.25/28.09 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_bex__reg__right,axiom,
% 28.25/28.09 ! [V_P_2,V_Q_2,V_R_2,T_b] :
% 28.25/28.09 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.25/28.09 => ( ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(V_Q_2,B_x))
% 28.25/28.09 => hBOOL(hAPP(V_P_2,B_x)) )
% 28.25/28.09 => ( ? [B_x1] : hBOOL(hAPP(V_Q_2,B_x1))
% 28.25/28.09 => ? [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 28.25/28.09 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_babs__reg__eqv,axiom,
% 28.25/28.09 ! [V_P_2,T_c,V_R_2,T_b] :
% 28.25/28.09 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 28.25/28.09 => c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_P_2) = V_P_2 ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_Babs__def,axiom,
% 28.25/28.09 ! [V_m_2,T_c,V_p_2,V_x_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2))
% 28.25/28.09 => hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_converse__rtranclE2,axiom,
% 28.25/28.09 ! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_c,T_b] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => ( 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)
% 28.25/28.09 => ~ ! [B_a,B_b] :
% 28.25/28.09 ( 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))
% 28.25/28.09 => ~ 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))) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_converse__rtrancl__induct2,axiom,
% 28.25/28.09 ! [V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2))
% 28.25/28.09 => ( ! [B_a,B_b,B_aa,B_ba] :
% 28.25/28.09 ( 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))
% 28.25/28.09 => ( 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)))
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba))
% 28.25/28.09 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) )
% 28.25/28.09 => hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2)) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_rtrancl__induct2,axiom,
% 28.25/28.09 ! [V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2))
% 28.25/28.09 => ( ! [B_a,B_b] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => ! [B_aa,B_ba] :
% 28.25/28.09 ( 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))
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
% 28.25/28.09 => hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba)) ) ) )
% 28.25/28.09 => hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2)) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_congruent2I_H,axiom,
% 28.25/28.09 ! [T_d,V_f_2,V_r2_2,T_c,V_r1_2,T_b] :
% 28.25/28.09 ( ! [B_y1,B_z1] :
% 28.25/28.09 ( 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))
% 28.25/28.09 => ! [B_y2,B_z2] :
% 28.25/28.09 ( 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))
% 28.25/28.09 => hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2) ) )
% 28.25/28.09 => c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_congruentI,axiom,
% 28.25/28.09 ! [T_c,V_f_2,V_r_2,T_b] :
% 28.25/28.09 ( ! [B_y,B_z] :
% 28.25/28.09 ( 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))
% 28.25/28.09 => hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) )
% 28.25/28.09 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact__03,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact__04,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact__05,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_all__interval__nat__def,axiom,
% 28.25/28.09 ! [V_j_2,V_i_2,V_P_2] :
% 28.25/28.09 ( c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2)
% 28.25/28.09 <=> ! [B_x] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact__06,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact__07,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__all__iff__all__interval__nat,axiom,
% 28.25/28.09 ! [V_j_2,V_i_2,V_P_2] :
% 28.25/28.09 ( c_List_Olist__all(tc_Nat_Onat,V_P_2,c_List_Oupt(V_i_2,V_j_2))
% 28.25/28.09 <=> c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_list__ex__iff__not__all__inverval__nat,axiom,
% 28.25/28.09 ! [V_j_2,V_i_2,V_P_2] :
% 28.25/28.09 ( c_List_Olist__ex(tc_Nat_Onat,V_P_2,c_List_Oupt(V_i_2,V_j_2))
% 28.25/28.09 <=> ~ 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) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_New__DSequence_Opos__map__def,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_folding__image_Ocong,axiom,
% 28.25/28.09 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 28.25/28.09 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 28.25/28.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 28.25/28.09 => ( ! [B_x] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 28.25/28.09 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 28.25/28.09 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_power__dvd__imp__le,axiom,
% 28.25/28.09 ! [V_n,V_m,V_i] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
% 28.25/28.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_finite__nonempty__imp__fold1Set,axiom,
% 28.25/28.09 ! [V_f_2,V_A_2,T_b] :
% 28.25/28.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 28.25/28.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 28.25/28.09 => ? [B_x1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),B_x1)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd_Oorder__refl,axiom,
% 28.25/28.09 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd__0__right,axiom,
% 28.25/28.09 ! [V_a,T_a] :
% 28.25/28.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.25/28.09 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd__1__left,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_unity__coeff__ex,axiom,
% 28.25/28.09 ! [V_l_2,V_P_2,T_b] :
% 28.25/28.09 ( ( class_Rings_Odvd(T_b)
% 28.25/28.09 & class_Rings_Osemiring__0(T_b) )
% 28.25/28.09 => ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
% 28.25/28.09 <=> ? [B_x] :
% 28.25/28.09 ( 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))))
% 28.25/28.09 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd__mult__div__cancel,axiom,
% 28.25/28.09 ! [V_b,V_a,T_a] :
% 28.25/28.09 ( class_Divides_Osemiring__div(T_a)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 28.25/28.09 => 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 ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_div__mult__swap,axiom,
% 28.25/28.09 ! [V_a,V_b,V_c,T_a] :
% 28.25/28.09 ( class_Divides_Osemiring__div(T_a)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 28.25/28.09 => 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) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd__div__mult__self,axiom,
% 28.25/28.09 ! [V_b,V_a,T_a] :
% 28.25/28.09 ( class_Divides_Osemiring__div(T_a)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 28.25/28.09 => 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 ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd__div__mult,axiom,
% 28.25/28.09 ! [V_c,V_b,V_a,T_a] :
% 28.25/28.09 ( class_Divides_Osemiring__div(T_a)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 28.25/28.09 => 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) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_div__mult__div__if__dvd,axiom,
% 28.25/28.09 ! [V_w,V_z,V_x,V_y,T_a] :
% 28.25/28.09 ( class_Divides_Osemiring__div(T_a)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
% 28.25/28.09 => 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)) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd__mult__cancel__left,axiom,
% 28.25/28.09 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 28.25/28.09 ( class_Rings_Oidom(T_b)
% 28.25/28.09 => ( 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)))
% 28.25/28.09 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.25/28.09 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd__mult__cancel__right,axiom,
% 28.25/28.09 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 28.25/28.09 ( class_Rings_Oidom(T_b)
% 28.25/28.09 => ( 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)))
% 28.25/28.09 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 28.25/28.09 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd__mult__right,axiom,
% 28.25/28.09 ! [V_c,V_b,V_a,T_a] :
% 28.25/28.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.25/28.09 => ( 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))
% 28.25/28.09 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd__mult__left,axiom,
% 28.25/28.09 ! [V_c,V_b,V_a,T_a] :
% 28.25/28.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.25/28.09 => ( 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))
% 28.25/28.09 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvdI,axiom,
% 28.25/28.09 ! [V_k,V_b,V_a,T_a] :
% 28.25/28.09 ( class_Rings_Odvd(T_a)
% 28.25/28.09 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
% 28.25/28.09 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_mult__dvd__mono,axiom,
% 28.25/28.09 ! [V_d,V_c,V_b,V_a,T_a] :
% 28.25/28.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
% 28.25/28.09 => 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))) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd__mult,axiom,
% 28.25/28.09 ! [V_b,V_c,V_a,T_a] :
% 28.25/28.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 28.25/28.09 => 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))) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd__mult2,axiom,
% 28.25/28.09 ! [V_c,V_b,V_a,T_a] :
% 28.25/28.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 28.25/28.09 => 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))) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd__triv__right,axiom,
% 28.25/28.09 ! [V_b,V_a,T_a] :
% 28.25/28.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.25/28.09 => 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))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd__triv__left,axiom,
% 28.25/28.09 ! [V_b,V_a,T_a] :
% 28.25/28.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 28.25/28.09 => 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))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_nat__mult__dvd__cancel__disj,axiom,
% 28.25/28.09 ! [V_n_2,V_m_2,V_k_2] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 28.25/28.09 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inf__period_I3_J,axiom,
% 28.25/28.09 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 28.25/28.09 ( ( class_Rings_Ocomm__ring(T_b)
% 28.25/28.09 & class_Rings_Odvd(T_b) )
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 28.25/28.09 => ! [B_x,B_k] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 <=> 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))) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_inf__period_I4_J,axiom,
% 28.25/28.09 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 28.25/28.09 ( ( class_Rings_Ocomm__ring(T_b)
% 28.25/28.09 & class_Rings_Odvd(T_b) )
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 28.25/28.09 => ! [B_x,B_k] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 <=> 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))) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd__div__div__eq__mult,axiom,
% 28.25/28.09 ! [V_d_2,V_b_2,V_c_2,V_a_2,T_b] :
% 28.25/28.09 ( class_Divides_Osemiring__div(T_b)
% 28.25/28.09 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.25/28.09 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_c_2),V_d_2))
% 28.25/28.09 => ( 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)
% 28.25/28.09 <=> 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) ) ) ) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd__div__eq__mult,axiom,
% 28.25/28.09 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 28.25/28.09 ( class_Divides_Osemiring__div(T_b)
% 28.25/28.09 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 28.25/28.09 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 28.25/28.09 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_c_2
% 28.25/28.09 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2) ) ) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
% 28.25/28.09 ! [V_c_2,V_b_2,V_a_2] :
% 28.25/28.09 ( 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)))
% 28.25/28.09 <=> ( V_a_2 = V_b_2
% 28.25/28.09 & V_b_2 = V_c_2 ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd_OatLeastAtMost__singleton,axiom,
% 28.25/28.09 ! [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))) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
% 28.25/28.09 ! [V_b_2,V_a_2] :
% 28.25/28.09 ( V_a_2 = V_b_2
% 28.25/28.09 => 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))) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
% 28.25/28.09 ! [V_k_2,V_l_2] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 28.25/28.09 => 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)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd_OatLeastLessThan__empty,axiom,
% 28.25/28.09 ! [V_a_2,V_b_2] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 28.25/28.09 => 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)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
% 28.25/28.09 ! [V_k_2,V_l_2] :
% 28.25/28.09 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 28.25/28.09 => 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)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
% 28.25/28.09 ! [V_l_2,V_k_2] :
% 28.25/28.09 ( 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))
% 28.25/28.09 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 28.25/28.09 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
% 28.25/28.09 ! [V_b_2,V_a_2] :
% 28.25/28.09 ( 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))
% 28.25/28.09 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 28.25/28.09 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 28.25/28.09
% 28.25/28.09 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
% 28.25/28.09 ! [V_l_2,V_k_2] :
% 28.25/28.09 ( 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)
% 28.25/28.09 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 28.25/28.09 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 28.25/28.09
% 28.25/28.09 %----Arity declarations (220)
% 28.25/28.09 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 28.25/28.09 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 28.25/28.09 ! [T_2,T_1] :
% 28.25/28.09 ( class_Lattices_Obounded__lattice(T_1)
% 28.25/28.09 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 28.25/28.09 ! [T_2,T_1] :
% 28.25/28.09 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 28.25/28.09 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 28.25/28.09 ! [T_2,T_1] :
% 28.25/28.09 ( class_Lattices_Obounded__lattice(T_1)
% 28.25/28.09 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 28.25/28.09 ! [T_2,T_1] :
% 28.25/28.09 ( class_Lattices_Obounded__lattice(T_1)
% 28.25/28.09 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 28.25/28.09 ! [T_2,T_1] :
% 28.25/28.09 ( class_Lattices_Olattice(T_1)
% 28.25/28.09 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 28.25/28.09 ! [T_2,T_1] :
% 28.25/28.09 ( class_Lattices_Olattice(T_1)
% 28.25/28.09 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 28.25/28.09 ! [T_2,T_1] :
% 28.25/28.09 ( class_Lattices_Odistrib__lattice(T_1)
% 28.25/28.09 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 28.25/28.09 ! [T_2,T_1] :
% 28.25/28.09 ( class_Lattices_Oboolean__algebra(T_1)
% 28.25/28.09 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_fun__Orderings_Opreorder,axiom,
% 28.25/28.09 ! [T_2,T_1] :
% 28.25/28.09 ( class_Orderings_Opreorder(T_1)
% 28.25/28.09 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 28.25/28.09 ! [T_1,T_2] :
% 28.25/28.09 ( ( class_Finite__Set_Ofinite(T_2)
% 28.25/28.09 & class_Finite__Set_Ofinite(T_1) )
% 28.25/28.09 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_fun__Lattices_Olattice,axiom,
% 28.25/28.09 ! [T_2,T_1] :
% 28.25/28.09 ( class_Lattices_Olattice(T_1)
% 28.25/28.09 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_fun__Orderings_Oorder,axiom,
% 28.25/28.09 ! [T_2,T_1] :
% 28.25/28.09 ( class_Orderings_Oorder(T_1)
% 28.25/28.09 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_fun__Orderings_Otop,axiom,
% 28.25/28.09 ! [T_2,T_1] :
% 28.25/28.09 ( class_Orderings_Otop(T_1)
% 28.25/28.09 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_fun__Orderings_Oord,axiom,
% 28.25/28.09 ! [T_2,T_1] :
% 28.25/28.09 ( class_Orderings_Oord(T_1)
% 28.25/28.09 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_fun__Orderings_Obot,axiom,
% 28.25/28.09 ! [T_2,T_1] :
% 28.25/28.09 ( class_Orderings_Obot(T_1)
% 28.25/28.09 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_fun__Groups_Ouminus,axiom,
% 28.25/28.09 ! [T_2,T_1] :
% 28.25/28.09 ( class_Groups_Ouminus(T_1)
% 28.25/28.09 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_fun__Groups_Ominus,axiom,
% 28.25/28.09 ! [T_2,T_1] :
% 28.25/28.09 ( class_Groups_Ominus(T_1)
% 28.25/28.09 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_fun__Enum_Oenum,axiom,
% 28.25/28.09 ! [T_1,T_2] :
% 28.25/28.09 ( ( class_Enum_Oenum(T_2)
% 28.25/28.09 & class_Enum_Oenum(T_1) )
% 28.25/28.09 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 28.25/28.09 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 28.25/28.09 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 28.25/28.09 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 28.25/28.09 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 28.25/28.09 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 28.25/28.09 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 28.25/28.09 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 28.25/28.09 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 28.25/28.09 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 28.25/28.09 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 28.25/28.09 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 28.25/28.09 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 28.25/28.09 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 28.25/28.09 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 28.25/28.09 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 28.25/28.09 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 28.25/28.09 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 28.25/28.09 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 28.25/28.09 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 28.25/28.09 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 28.25/28.09 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 28.25/28.09 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom,
% 28.25/28.09 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 28.25/28.09 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 28.25/28.09 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 28.25/28.09 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 28.25/28.09 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 28.25/28.09 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 28.25/28.09 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 28.25/28.09 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 28.25/28.09 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 28.25/28.09 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 28.25/28.09 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 28.25/28.09 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 28.25/28.09 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 28.25/28.09 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 28.25/28.09 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 28.25/28.09 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 28.25/28.09 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 28.25/28.09 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 28.25/28.09 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 28.25/28.09 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 28.25/28.09 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 28.25/28.09 class_Orderings_Opreorder(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 28.25/28.09 class_Orderings_Olinorder(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 28.25/28.09 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 28.25/28.09 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 28.25/28.09 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 28.25/28.09 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 28.25/28.09 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 28.25/28.09 class_Lattices_Olattice(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 28.25/28.09 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 28.25/28.09 class_Divides_Oring__div(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 28.25/28.09 class_Rings_Omult__zero(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 28.25/28.09 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 28.25/28.09 class_Orderings_Oorder(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 28.25/28.09 class_Int_Oring__char__0(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 28.25/28.09 class_Int_Onumber__ring(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 28.25/28.09 class_Rings_Osemiring(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 28.25/28.09 class_Orderings_Oord(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 28.25/28.09 class_Groups_Ouminus(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 28.25/28.09 class_Groups_Osgn__if(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 28.25/28.09 class_Groups_Oabs__if(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 28.25/28.09 class_Rings_Oring__1(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 28.25/28.09 class_Groups_Ominus(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Power_Opower,axiom,
% 28.25/28.09 class_Power_Opower(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 28.25/28.09 class_Groups_Ozero(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Oring,axiom,
% 28.25/28.09 class_Rings_Oring(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 28.25/28.09 class_Rings_Oidom(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Int_Onumber,axiom,
% 28.25/28.09 class_Int_Onumber(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Groups_Oone,axiom,
% 28.25/28.09 class_Groups_Oone(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 28.25/28.09 class_Rings_Odvd(tc_Int_Oint) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 28.25/28.09 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 28.25/28.09 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 28.25/28.09 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 28.25/28.09 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 28.25/28.09 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 28.25/28.09 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 28.25/28.09 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 28.25/28.09 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 28.25/28.09 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 28.25/28.09 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 28.25/28.09 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 28.25/28.09 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 28.25/28.09 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 28.25/28.09 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 28.25/28.09 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 28.25/28.09 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 28.25/28.09 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 28.25/28.09 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 28.25/28.09 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 28.25/28.09 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 28.25/28.09 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 28.25/28.09 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 28.25/28.09 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 28.25/28.09 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 28.25/28.09 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 28.25/28.09 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 28.25/28.09 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 28.25/28.09 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 28.25/28.09 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 28.25/28.09 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 28.25/28.09 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 28.25/28.09 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 28.25/28.09 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 28.25/28.09 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 28.25/28.09 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 28.25/28.09 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 28.25/28.09 class_Lattices_Olattice(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 28.25/28.09 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 28.25/28.09 class_Orderings_Oorder(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 28.25/28.09 class_Rings_Osemiring(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 28.25/28.09 class_Orderings_Oord(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 28.25/28.09 class_Orderings_Obot(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 28.25/28.09 class_Groups_Ominus(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Power_Opower,axiom,
% 28.25/28.09 class_Power_Opower(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 28.25/28.09 class_Groups_Ozero(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 28.25/28.09 class_Int_Onumber(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 28.25/28.09 class_Groups_Oone(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 28.25/28.09 class_Rings_Odvd(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nat__Onat__Nat_Osize,axiom,
% 28.25/28.09 class_Nat_Osize(tc_Nat_Onat) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 28.25/28.09 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 28.25/28.09 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 28.25/28.09 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 28.25/28.09 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 28.25/28.09 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 28.25/28.09 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 28.25/28.09 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 28.25/28.09 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 28.25/28.09 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 28.25/28.09 class_Lattices_Olattice(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 28.25/28.09 class_Orderings_Oorder(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 28.25/28.09 class_Orderings_Otop(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 28.25/28.09 class_Orderings_Oord(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 28.25/28.09 class_Orderings_Obot(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 28.25/28.09 class_Groups_Ouminus(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 28.25/28.09 class_Groups_Ominus(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 28.25/28.09 class_Enum_Oenum(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_HOL__Obool__Nat_Osize,axiom,
% 28.25/28.09 class_Nat_Osize(tc_HOL_Obool) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
% 28.25/28.09 ! [T_1] :
% 28.25/28.09 ( class_Lazy__Sequence_Osmall__lazy(T_1)
% 28.25/28.09 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_List__Olist__Nat_Osize,axiom,
% 28.25/28.09 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 28.25/28.09 ! [T_1,T_2] :
% 28.25/28.09 ( ( class_Finite__Set_Ofinite(T_2)
% 28.25/28.09 & class_Finite__Set_Ofinite(T_1) )
% 28.25/28.09 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_sum__Enum_Oenum,axiom,
% 28.25/28.09 ! [T_1,T_2] :
% 28.25/28.09 ( ( class_Enum_Oenum(T_2)
% 28.25/28.09 & class_Enum_Oenum(T_1) )
% 28.25/28.09 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_sum__Nat_Osize,axiom,
% 28.25/28.09 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 28.25/28.09 ! [T_1] :
% 28.25/28.09 ( class_Finite__Set_Ofinite(T_1)
% 28.25/28.09 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 28.25/28.09 ! [T_1] :
% 28.25/28.09 ( class_Enum_Oenum(T_1)
% 28.25/28.09 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Option__Ooption__Nat_Osize,axiom,
% 28.25/28.09 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom,
% 28.25/28.09 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
% 28.25/28.09 ! [T_1,T_2] :
% 28.25/28.09 ( ( class_Lazy__Sequence_Osmall__lazy(T_2)
% 28.25/28.09 & class_Lazy__Sequence_Osmall__lazy(T_1) )
% 28.25/28.09 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 28.25/28.09 ! [T_1,T_2] :
% 28.25/28.09 ( ( class_Finite__Set_Ofinite(T_2)
% 28.25/28.09 & class_Finite__Set_Ofinite(T_1) )
% 28.25/28.09 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_prod__Enum_Oenum,axiom,
% 28.25/28.09 ! [T_1,T_2] :
% 28.25/28.09 ( ( class_Enum_Oenum(T_2)
% 28.25/28.09 & class_Enum_Oenum(T_1) )
% 28.25/28.09 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_prod__Nat_Osize,axiom,
% 28.25/28.09 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
% 28.25/28.09 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 28.25/28.09 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 28.25/28.09 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
% 28.25/28.09 class_Nat_Osize(tc_Product__Type_Ounit) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
% 28.25/28.09 class_Nat_Osize(tc_Code__Evaluation_Oterm) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
% 28.25/28.09 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 28.25/28.09 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 28.25/28.09 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 28.25/28.09 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 28.25/28.09 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 28.25/28.09 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 28.25/28.09 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 28.25/28.09 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 28.25/28.09 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 28.25/28.09 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 28.25/28.09 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 28.25/28.09 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 28.25/28.09 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 28.25/28.09 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 28.25/28.09 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 28.25/28.09 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 28.25/28.09 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 28.25/28.09 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 28.25/28.09 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 28.25/28.09 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 28.25/28.09 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 28.25/28.09 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 28.25/28.09 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 28.25/28.09 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 28.25/28.09 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 28.25/28.09 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 28.25/28.09 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 28.25/28.09 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 28.25/28.09 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 28.25/28.09 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 28.25/28.09 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 28.25/28.09 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 28.25/28.09 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 28.25/28.09 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 28.25/28.09 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 28.25/28.09 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 28.25/28.09 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 28.25/28.09 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 28.25/28.09 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 28.25/28.09 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 28.25/28.09 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
% 28.25/28.09 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
% 28.25/28.09 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ).
% 28.25/28.09
% 28.25/28.09 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
% 28.25/28.09 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 28.25/28.09
% 28.25/28.09 %----Helper facts (20)
% 28.25/28.09 fof(help_c__COMBI__1,axiom,
% 28.25/28.09 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 28.25/28.09
% 28.25/28.09 fof(help_c__COMBK__1,axiom,
% 28.25/28.09 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 28.25/28.09
% 28.25/28.09 fof(help_c__COMBB__1,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(help_c__COMBC__1,axiom,
% 28.25/28.09 ! [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) ).
% 28.25/28.09
% 28.25/28.09 fof(help_c__COMBS__1,axiom,
% 28.25/28.09 ! [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)) ).
% 28.25/28.09
% 28.25/28.09 fof(help_c__fequal__1,axiom,
% 28.25/28.10 ! [V_y_2,V_x_2] :
% 28.25/28.10 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 28.25/28.10 | V_x_2 = V_y_2 ) ).
% 28.25/28.10
% 28.25/28.10 fof(help_c__fequal__2,axiom,
% 28.25/28.10 ! [V_y_2,V_x_2] :
% 28.25/28.10 ( V_x_2 != V_y_2
% 28.25/28.10 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 28.25/28.10
% 28.25/28.10 fof(help_c__fFalse__1,axiom,
% 28.25/28.10 ~ hBOOL(c_fFalse) ).
% 28.25/28.10
% 28.25/28.10 fof(help_c__fTrue__1,axiom,
% 28.25/28.10 hBOOL(c_fTrue) ).
% 28.25/28.10
% 28.25/28.10 fof(help_c__fNot__1,axiom,
% 28.25/28.10 ! [V_P_2] :
% 28.25/28.10 ( ~ hBOOL(hAPP(c_fNot,V_P_2))
% 28.25/28.10 | ~ hBOOL(V_P_2) ) ).
% 28.25/28.10
% 28.25/28.10 fof(help_c__fNot__2,axiom,
% 28.25/28.10 ! [V_P_2] :
% 28.25/28.10 ( ~ ~ hBOOL(V_P_2)
% 28.25/28.10 | hBOOL(hAPP(c_fNot,V_P_2)) ) ).
% 28.25/28.10
% 28.25/28.10 fof(help_c__fconj__1,axiom,
% 28.25/28.10 ! [V_Q_2,V_P_2] :
% 28.25/28.10 ( ~ hBOOL(V_P_2)
% 28.25/28.10 | ~ hBOOL(V_Q_2)
% 28.25/28.10 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ).
% 28.25/28.10
% 28.25/28.10 fof(help_c__fconj__2,axiom,
% 28.25/28.10 ! [V_Q_2,V_P_2] :
% 28.25/28.10 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 28.25/28.10 | hBOOL(V_P_2) ) ).
% 28.25/28.10
% 28.25/28.10 fof(help_c__fconj__3,axiom,
% 28.25/28.10 ! [V_Q_2,V_P_2] :
% 28.25/28.10 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 28.25/28.10 | hBOOL(V_Q_2) ) ).
% 28.25/28.10
% 28.25/28.10 fof(help_c__fdisj__1,axiom,
% 28.25/28.10 ! [V_Q_2,V_P_2] :
% 28.25/28.10 ( ~ hBOOL(V_P_2)
% 28.25/28.10 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 28.25/28.10
% 28.25/28.10 fof(help_c__fdisj__2,axiom,
% 28.25/28.10 ! [V_P_2,V_Q_2] :
% 28.25/28.10 ( ~ hBOOL(V_Q_2)
% 28.25/28.10 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 28.25/28.10
% 28.25/28.10 fof(help_c__fdisj__3,axiom,
% 28.25/28.10 ! [V_Q_2,V_P_2] :
% 28.25/28.10 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
% 28.25/28.10 | hBOOL(V_P_2)
% 28.25/28.10 | hBOOL(V_Q_2) ) ).
% 28.25/28.10
% 28.25/28.10 fof(help_c__fimplies__1,axiom,
% 28.25/28.10 ! [V_Q_2,V_P_2] :
% 28.25/28.10 ( hBOOL(V_P_2)
% 28.25/28.10 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 28.25/28.10
% 28.25/28.10 fof(help_c__fimplies__2,axiom,
% 28.25/28.10 ! [V_P_2,V_Q_2] :
% 28.25/28.10 ( ~ hBOOL(V_Q_2)
% 28.25/28.10 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 28.25/28.10
% 28.25/28.10 fof(help_c__fimplies__3,axiom,
% 28.25/28.10 ! [V_Q_2,V_P_2] :
% 28.25/28.10 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
% 28.25/28.10 | ~ hBOOL(V_P_2)
% 28.25/28.10 | hBOOL(V_Q_2) ) ).
% 28.25/28.10
% 28.25/28.10 %----Conjectures (6)
% 28.25/28.10 fof(conj_0,hypothesis,
% 28.25/28.10 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G_H,v_ts) ).
% 28.25/28.10
% 28.25/28.10 fof(conj_1,hypothesis,
% 28.25/28.10 ! [B_G] :
% 28.25/28.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G_H),B_G))
% 28.25/28.10 => c_Hoare__Mirabelle_Ohoare__derivs(t_a,B_G,v_ts) ) ).
% 28.25/28.10
% 28.25/28.10 fof(conj_2,hypothesis,
% 28.25/28.10 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_G_H) ).
% 28.25/28.10
% 28.25/28.10 fof(conj_3,hypothesis,
% 28.25/28.10 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga)) ).
% 28.25/28.10
% 28.25/28.10 fof(conj_4,hypothesis,
% 28.25/28.10 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_G_H) ).
% 28.25/28.10
% 28.25/28.10 fof(conj_5,conjecture,
% 28.25/28.10 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts) ).
% 28.25/28.10
% 28.25/28.10 %------------------------------------------------------------------------------
% 28.25/28.10 %-------------------------------------------
% 28.25/28.10 % Proof found
% 28.25/28.10 % SZS status Theorem for theBenchmark
% 28.25/28.10 % SZS output start Proof
% 28.25/28.10 %ClaNum:10536(EqnAxiom:3176)
% 28.25/28.10 %VarNum:81156(SingletonVarNum:23755)
% 28.25/28.10 %MaxLitNum:8
% 28.25/28.10 %MaxfuncDepth:13
% 28.25/28.10 %SharedTerms:997
% 28.25/28.10 %goalClause: 4730
% 28.25/28.10 %singleGoalClaCount:1
% 28.25/28.10 [3180]P1(a179)
% 28.25/28.10 [3181]P2(a923)
% 28.25/28.10 [3182]P2(a925)
% 28.25/28.10 [3183]P2(a1)
% 28.25/28.10 [3184]P2(a91)
% 28.25/28.10 [3185]P3(a923)
% 28.25/28.10 [3186]P3(a925)
% 28.25/28.10 [3187]P3(a1)
% 28.25/28.10 [3188]P3(a91)
% 28.25/28.10 [3189]P4(a925)
% 28.25/28.10 [3190]P4(a1)
% 28.25/28.10 [3191]P4(a91)
% 28.25/28.10 [3192]P113(a923)
% 28.25/28.10 [3193]P113(a925)
% 28.25/28.10 [3194]P113(a1)
% 28.25/28.10 [3195]P113(a91)
% 28.25/28.10 [3196]P5(a923)
% 28.25/28.10 [3197]P5(a928)
% 28.25/28.10 [3198]P114(a925)
% 28.25/28.10 [3199]P6(a923)
% 28.25/28.10 [3200]P67(a923)
% 28.25/28.10 [3201]P67(a1)
% 28.25/28.10 [3202]P96(a923)
% 28.25/28.10 [3203]P68(a1)
% 28.25/28.10 [3204]P69(a1)
% 28.25/28.10 [3205]P102(a923)
% 28.25/28.10 [3206]P102(a925)
% 28.25/28.10 [3207]P102(a1)
% 28.25/28.10 [3208]P107(a923)
% 28.25/28.10 [3209]P107(a925)
% 28.25/28.10 [3210]P107(a1)
% 28.25/28.10 [3211]P108(a923)
% 28.25/28.10 [3212]P108(a925)
% 28.25/28.10 [3213]P108(a1)
% 28.25/28.10 [3214]P103(a923)
% 28.25/28.10 [3215]P115(a923)
% 28.25/28.10 [3216]P106(a923)
% 28.25/28.10 [3217]P106(a925)
% 28.25/28.10 [3218]P106(a1)
% 28.25/28.10 [3219]P109(a923)
% 28.25/28.10 [3220]P109(a925)
% 28.25/28.10 [3221]P104(a923)
% 28.25/28.10 [3222]P70(a1)
% 28.25/28.10 [3223]P83(a923)
% 28.25/28.10 [3224]P83(a925)
% 28.25/28.10 [3225]P83(a1)
% 28.25/28.10 [3226]P83(a91)
% 28.25/28.10 [3227]P76(a925)
% 28.25/28.10 [3228]P76(a1)
% 28.25/28.10 [3229]P76(a91)
% 28.25/28.10 [3230]P116(a1)
% 28.25/28.10 [3231]P117(a1)
% 28.25/28.10 [3232]P71(a923)
% 28.25/28.10 [3233]P71(a928)
% 28.25/28.10 [3234]P126(a1)
% 28.25/28.10 [3235]P78(a925)
% 28.25/28.10 [3236]P78(a1)
% 28.25/28.10 [3237]P78(a91)
% 28.25/28.10 [3238]P86(a925)
% 28.25/28.10 [3239]P86(a1)
% 28.25/28.10 [3240]P86(a91)
% 28.25/28.10 [3241]P79(a925)
% 28.25/28.10 [3242]P79(a1)
% 28.25/28.10 [3243]P79(a91)
% 28.25/28.10 [3244]P87(a925)
% 28.25/28.10 [3245]P87(a1)
% 28.25/28.10 [3246]P87(a91)
% 28.25/28.10 [3247]P143(a925)
% 28.25/28.10 [3248]P143(a1)
% 28.25/28.10 [3249]P143(a91)
% 28.25/28.10 [3250]P129(a925)
% 28.25/28.10 [3251]P129(a1)
% 28.25/28.10 [3252]P129(a91)
% 28.25/28.10 [3253]P144(a1)
% 28.25/28.10 [3254]P118(a1)
% 28.25/28.10 [3255]P121(a925)
% 28.25/28.10 [3256]P121(a1)
% 28.25/28.10 [3257]P121(a91)
% 28.25/28.10 [3258]P89(a925)
% 28.25/28.10 [3259]P89(a1)
% 28.25/28.10 [3260]P89(a91)
% 28.25/28.10 [3261]P148(a925)
% 28.25/28.10 [3262]P148(a1)
% 28.25/28.10 [3263]P80(a925)
% 28.25/28.10 [3264]P80(a1)
% 28.25/28.10 [3265]P80(a91)
% 28.25/28.10 [3266]P81(a925)
% 28.25/28.10 [3267]P81(a1)
% 28.25/28.10 [3268]P81(a91)
% 28.25/28.10 [3269]P77(a925)
% 28.25/28.10 [3270]P77(a1)
% 28.25/28.10 [3271]P77(a91)
% 28.25/28.10 [3272]P90(a925)
% 28.25/28.10 [3273]P90(a1)
% 28.25/28.10 [3274]P90(a91)
% 28.25/28.10 [3275]P91(a925)
% 28.25/28.10 [3276]P91(a1)
% 28.25/28.10 [3277]P91(a91)
% 28.25/28.10 [3278]P146(a925)
% 28.25/28.10 [3279]P146(a1)
% 28.25/28.10 [3280]P146(a91)
% 28.25/28.10 [3281]P122(a925)
% 28.25/28.10 [3282]P122(a1)
% 28.25/28.10 [3283]P122(a91)
% 28.25/28.10 [3284]P132(a1)
% 28.25/28.10 [3285]P149(a925)
% 28.25/28.10 [3286]P149(a1)
% 28.25/28.10 [3287]P149(a91)
% 28.25/28.10 [3288]P110(a925)
% 28.25/28.10 [3289]P110(a1)
% 28.25/28.10 [3290]P110(a91)
% 28.25/28.10 [3291]P97(a925)
% 28.25/28.10 [3292]P97(a1)
% 28.25/28.10 [3293]P97(a91)
% 28.25/28.10 [3294]P88(a925)
% 28.25/28.10 [3295]P88(a1)
% 28.25/28.10 [3296]P88(a91)
% 28.25/28.10 [3297]P84(a1)
% 28.25/28.10 [3298]P133(a925)
% 28.25/28.10 [3299]P133(a1)
% 28.25/28.10 [3300]P133(a91)
% 28.25/28.10 [3301]P147(a1)
% 28.25/28.10 [3302]P138(a925)
% 28.25/28.10 [3303]P138(a1)
% 28.25/28.10 [3304]P138(a91)
% 28.25/28.10 [3305]P150(a925)
% 28.25/28.10 [3306]P150(a1)
% 28.25/28.10 [3307]P150(a91)
% 28.25/28.10 [3308]P93(a925)
% 28.25/28.10 [3309]P93(a1)
% 28.25/28.10 [3310]P93(a91)
% 28.25/28.10 [3311]P139(a925)
% 28.25/28.10 [3312]P139(a1)
% 28.25/28.10 [3313]P139(a91)
% 28.25/28.10 [3314]P141(a925)
% 28.25/28.10 [3315]P141(a1)
% 28.25/28.10 [3316]P141(a91)
% 28.25/28.10 [3317]P140(a925)
% 28.25/28.10 [3318]P140(a1)
% 28.25/28.10 [3319]P140(a91)
% 28.25/28.10 [3320]P130(a1)
% 28.25/28.10 [3321]P131(a1)
% 28.25/28.10 [3322]P127(a925)
% 28.25/28.10 [3323]P127(a1)
% 28.25/28.10 [3324]P127(a91)
% 28.25/28.10 [3325]P134(a925)
% 28.25/28.10 [3326]P134(a1)
% 28.25/28.10 [3327]P134(a91)
% 28.25/28.10 [3328]P135(a925)
% 28.25/28.10 [3329]P135(a1)
% 28.25/28.10 [3330]P135(a91)
% 28.25/28.10 [3331]P145(a1)
% 28.25/28.10 [3332]P136(a1)
% 28.25/28.10 [3333]P137(a1)
% 28.25/28.10 [3334]P98(a1)
% 28.25/28.10 [3335]P94(a1)
% 28.25/28.10 [3336]P92(a1)
% 28.25/28.10 [3337]P142(a1)
% 28.25/28.10 [3338]P82(a1)
% 28.25/28.10 [3339]P85(a925)
% 28.25/28.10 [3340]P85(a1)
% 28.25/28.10 [3341]P85(a91)
% 28.25/28.10 [3342]P119(a925)
% 28.25/28.10 [3343]P119(a1)
% 28.25/28.10 [3344]P119(a91)
% 28.25/28.10 [3345]P65(a925)
% 28.25/28.10 [3346]P65(a1)
% 28.25/28.10 [3347]P65(a91)
% 28.25/28.10 [3348]P66(a1)
% 28.25/28.10 [3349]P99(a1)
% 28.25/28.10 [3350]P100(a925)
% 28.25/28.10 [3351]P100(a1)
% 28.25/28.10 [3352]P100(a91)
% 28.25/28.10 [3353]P95(a925)
% 28.25/28.10 [3354]P95(a1)
% 28.25/28.10 [3355]P95(a91)
% 28.25/28.10 [3356]P112(a923)
% 28.25/28.10 [3357]P112(a925)
% 28.25/28.10 [3358]P112(a928)
% 28.25/28.10 [3359]P112(a91)
% 28.25/28.10 [3360]P112(a315)
% 28.25/28.10 [3361]P111(a1)
% 28.25/28.10 [3362]P111(a928)
% 28.25/28.10 [3363]P123(a925)
% 28.25/28.10 [3364]P123(a1)
% 28.25/28.10 [3365]P123(a91)
% 28.25/28.10 [3366]P120(a1)
% 28.25/28.10 [3367]P105(a923)
% 28.25/28.10 [3382]P38(a925,a232)
% 28.25/28.10 [3383]P38(a925,a309)
% 28.25/28.10 [3384]P39(a925,a232)
% 28.25/28.10 [3464]P15(a922,a934,a936)
% 28.25/28.10 [3465]P15(a922,a935,a934)
% 28.25/28.10 [3466]P15(a922,a937,a934)
% 28.25/28.10 [3467]P41(a925,a925,a104)
% 28.25/28.10 [4713]~E(a89,a77)
% 28.25/28.10 [4714]~E(a89,a77)
% 28.25/28.10 [4715]~P1(a231)
% 28.25/28.10 [4730]~P15(a922,a937,a936)
% 28.25/28.10 [3177]E(f2(a1),a77)
% 28.25/28.10 [3178]E(f92(a91),a3)
% 28.25/28.10 [3179]E(f23(a91),a24)
% 28.25/28.10 [3368]E(f180(a925),f2(a925))
% 28.25/28.10 [3369]E(f93(a925),f224(a925))
% 28.25/28.10 [3370]E(f102(a925),f225(a925))
% 28.25/28.10 [3371]E(f94(a1),f25(a1))
% 28.25/28.10 [3372]E(f78(a231),f2(a925))
% 28.25/28.10 [3373]E(f78(a179),f2(a925))
% 28.25/28.10 [3374]P7(f72(a1))
% 28.25/28.10 [3375]P7(f2(a1))
% 28.25/28.10 [3430]P38(f931(a925,a925),a26)
% 28.25/28.10 [3776]E(f312(a925,a925,a232,a232),a26)
% 28.25/28.10 [4716]~E(f72(a1),f2(a1))
% 28.25/28.10 [3376]E(f4(f2(a91)),f2(a925))
% 28.25/28.10 [3377]E(f103(f2(a925)),f2(a925))
% 28.25/28.10 [3386]E(f319(f73(a1),a77),a77)
% 28.25/28.10 [3389]E(f319(a104,f2(a925)),f72(a925))
% 28.25/28.10 [3390]E(f319(a96,f72(a1)),f72(a925))
% 28.25/28.10 [3391]E(f319(a3,f72(a925)),f72(a91))
% 28.25/28.10 [3392]E(f319(a96,f2(a1)),f2(a925))
% 28.25/28.10 [3393]E(f319(a3,f2(a925)),f2(a91))
% 28.25/28.10 [3394]E(f319(f95(a925),a77),f2(a925))
% 28.25/28.10 [3395]E(f319(f95(a1),a77),f2(a1))
% 28.25/28.10 [3396]E(f319(f95(a91),a77),f2(a91))
% 28.25/28.10 [3397]E(f319(a96,f2(a1)),f2(a925))
% 28.25/28.10 [3398]E(f319(f95(a925),a77),f2(a925))
% 28.25/28.10 [3399]E(f319(f181(a923),a231),f2(a925))
% 28.25/28.10 [3400]E(f319(f181(a923),a179),f2(a925))
% 28.25/28.10 [3406]E(f319(f73(a1),f72(a1)),a89)
% 28.25/28.10 [3411]E(f319(f92(a1),f72(a925)),f72(a1))
% 28.25/28.10 [3412]E(f319(f92(a1),f2(a925)),f2(a1))
% 28.25/28.10 [3413]E(f319(f73(a1),f2(a1)),f2(a1))
% 28.25/28.10 [3414]E(f319(f92(a1),f72(a925)),f72(a1))
% 28.25/28.10 [3415]E(f319(f92(a1),f2(a925)),f2(a1))
% 28.25/28.10 [3416]E(f319(f181(a925),f2(a925)),f2(a925))
% 28.25/28.10 [3417]E(f319(f181(a91),f2(a91)),f2(a925))
% 28.25/28.10 [3427]E(f319(a96,f72(a1)),f319(a104,f2(a925)))
% 28.25/28.10 [3428]E(f310(f931(a925,a925),a26),a27)
% 28.25/28.10 [3429]E(f311(f931(a925,a925),a26),a28)
% 28.25/28.10 [3456]E(f319(f274(a925),f2(a925)),f180(f932(a925,a923)))
% 28.25/28.10 [3457]E(f319(f275(a925),f2(a925)),f234(f932(a925,a923)))
% 28.25/28.10 [3469]P42(f180(f932(a1,a923)))
% 28.25/28.10 [3503]E(f319(f319(f23(a91),f2(a91)),f72(a91)),f2(a91))
% 28.25/28.10 [3547]E(f319(f319(f146(a1,a925),a96),f105(a1)),f105(a925))
% 28.25/28.10 [3578]P1(f319(f319(f227(a1),a89),f2(a1)))
% 28.25/28.10 [3602]P1(f319(f319(f226(a1),f2(a1)),f72(a1)))
% 28.25/28.10 [3603]P1(f319(f319(f226(a1),f2(a1)),f2(a1)))
% 28.25/28.10 [3604]P1(f319(f319(f227(a1),f2(a1)),f72(a1)))
% 28.25/28.10 [3807]E(f319(f319(f281(a925,a925,a925),a309),f299(a925,a309)),a232)
% 28.25/28.10 [3844]P43(a1,a925,a96,f319(f226(a1),f2(a1)))
% 28.25/28.10 [3848]E(f319(f319(f33(a925,f932(a925,a923)),f234(f932(a925,a923))),f274(a925)),f234(f932(a925,a923)))
% 28.25/28.10 [3849]E(f319(f319(f33(a925,f932(a925,a923)),f234(f932(a925,a923))),f275(a925)),f234(f932(a925,a923)))
% 28.25/28.10 [3850]E(f319(f319(f33(a925,f932(a925,a923)),f234(f932(a925,a923))),f293(a925)),f234(f932(a925,a923)))
% 28.25/28.10 [3851]E(f319(f319(f34(a925,f932(a925,a923)),f234(f932(a925,a923))),f296(a925)),f180(f932(a925,a923)))
% 28.25/28.10 [3866]P26(a925,a1,f92(a1),f234(f932(a925,a923)))
% 28.25/28.10 [3880]P43(a925,a1,f92(a1),f319(f16(a923,a925),a179))
% 28.25/28.10 [4016]E(f319(f66(a925,a91,a1,a3),a96),f95(a91))
% 28.25/28.10 [4235]P61(a91,a925,a20,a3,f234(f932(a925,a923)))
% 28.25/28.10 [4240]P61(a1,f932(f931(a925,a925),a923),a99,a83,a90)
% 28.25/28.10 [4494]E(f250(a1,a1,a1,a1,f25(a1),f73(a1)),a45)
% 28.25/28.10 [4725]~E(f319(f95(a1),a89),f319(f95(a1),a77))
% 28.25/28.10 [4726]~P1(f319(a185,f72(a1)))
% 28.25/28.10 [4727]~P1(f319(a185,f2(a1)))
% 28.25/28.10 [4753]~P1(f319(f319(f227(a1),a77),f2(a1)))
% 28.25/28.10 [3448]E(f319(f319(f23(a1),a89),a89),a77)
% 28.25/28.10 [3449]E(f319(f319(f74(a1),a77),a77),a77)
% 28.25/28.10 [3450]E(f319(f319(f74(a1),a77),a89),a89)
% 28.25/28.10 [3463]E(f319(f92(a1),f319(a104,f2(a925))),f72(a1))
% 28.25/28.10 [3532]E(f319(f29(a928),f234(f932(a928,a923))),f72(a925))
% 28.25/28.10 [3552]P1(f319(a185,f319(f95(a1),a89)))
% 28.25/28.10 [3553]P1(f319(f319(f226(a1),a77),a77))
% 28.25/28.10 [3554]P1(f319(f319(f226(a1),a89),a77))
% 28.25/28.10 [3555]P1(f319(f319(f226(a1),a89),a89))
% 28.25/28.10 [3556]P1(f319(f319(f227(a1),a89),a77))
% 28.25/28.10 [3612]E(f319(f319(f301(a925),f2(a925)),f180(f932(a925,a923))),f319(f293(a925),f2(a925)))
% 28.25/28.10 [3667]P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),a77)))
% 28.25/28.10 [3679]E(f319(f302(a925,a925,a104),f234(f932(a925,a923))),f319(f296(a925),f2(a925)))
% 28.25/28.10 [3685]E(f319(f302(a1,a925,a96),f180(f932(a1,a923))),f180(f932(a925,a923)))
% 28.25/28.10 [3693]E(f319(f302(a925,a1,f92(a1)),f180(f932(a925,a923))),f180(f932(a1,a923)))
% 28.25/28.10 [3714]P9(f931(a925,a925),f234(f932(f931(a925,a925),a923)),a100)
% 28.25/28.10 [4023]E(f319(f66(a925,a1,a91,f92(a1)),a20),a22)
% 28.25/28.10 [4082]P38(a925,f319(f254(f931(a925,a925)),f319(f249(a925,a925,a923),f227(a925))))
% 28.25/28.10 [4744]~P1(f319(a185,f319(f95(a1),a77)))
% 28.25/28.10 [4745]~P1(f319(f319(f226(a1),a77),a89))
% 28.25/28.10 [4746]~P1(f319(f319(f227(a1),a77),a77))
% 28.25/28.10 [4747]~P1(f319(f319(f227(a1),a77),a89))
% 28.25/28.10 [4748]~P1(f319(f319(f227(a1),a89),a89))
% 28.25/28.10 [4757]~P1(f319(f55(a925),f234(f932(a925,a923))))
% 28.25/28.10 [4758]~P1(f319(f55(a1),f234(f932(a1,a923))))
% 28.25/28.10 [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)
% 28.25/28.10 [3717]E(f319(f319(f23(a1),f319(f319(f74(a1),a89),a89)),a89),a89)
% 28.25/28.10 [3751]E(f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89),f319(f73(a1),a89))
% 28.25/28.10 [3789]E(f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89),f319(f319(f23(a1),a77),a89))
% 28.25/28.10 [3898]P1(f319(f319(f226(f932(f924(a922),a923)),a935),a937))
% 28.25/28.10 [3950]E(f319(f319(f54(f931(a925,a925)),f234(f932(f931(a925,a925),a923))),a100),a90)
% 28.25/28.10 [3978]E(f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f72(a925))
% 28.25/28.10 [3979]E(f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f72(a1))
% 28.25/28.10 [3980]E(f319(f95(a91),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f72(a91))
% 28.25/28.10 [3981]E(f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f72(a925))
% 28.25/28.10 [3984]E(f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(a104,f2(a925)))
% 28.25/28.10 [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)
% 28.25/28.10 [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))
% 28.25/28.10 [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))
% 28.25/28.10 [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)
% 28.25/28.10 [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))))
% 28.25/28.10 [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))))
% 28.25/28.10 [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)))
% 28.25/28.10 [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))))
% 28.25/28.10 [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))))
% 28.25/28.10 [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))
% 28.25/28.10 [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))
% 28.25/28.10 [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)
% 28.25/28.10 [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)
% 28.25/28.10 [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))))
% 28.25/28.10 [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))))
% 28.25/28.10 [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))))
% 28.25/28.10 [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)))))
% 28.25/28.10 [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)))))
% 28.25/28.10 [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)))
% 28.25/28.10 [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)))
% 28.25/28.10 [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)))
% 28.25/28.10 [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))))
% 28.25/28.10 [3385]P8(x33851,a316)
% 28.25/28.10 [3777]P26(a925,a925,a104,x37771)
% 28.25/28.10 [3378]P112(f924(x33781))
% 28.25/28.10 [3379]P112(f929(x33791))
% 28.25/28.10 [3380]P112(f926(x33801))
% 28.25/28.10 [3381]P112(f927(x33811))
% 28.25/28.10 [3401]P38(a1,f97(x34011))
% 28.25/28.10 [3402]P38(a1,f98(x34021))
% 28.25/28.10 [3452]P38(f932(x34521,a923),f306(x34521))
% 28.25/28.10 [3453]P39(f932(x34531,a923),f306(x34531))
% 28.25/28.10 [3481]E(f235(x34811,x34811,a316),a316)
% 28.25/28.10 [3496]E(f39(a1,x34961,x34961),f2(a1))
% 28.25/28.10 [3549]P16(x35491,f932(x35491,a923),f301(x35491))
% 28.25/28.10 [4717]~E(f319(a104,x47171),x47171)
% 28.25/28.10 [4718]~E(f319(a104,x47181),x47181)
% 28.25/28.10 [4719]~E(f319(a104,x47191),f2(a925))
% 28.25/28.10 [4720]~E(f319(a104,x47201),f2(a925))
% 28.25/28.10 [4721]~E(f319(a104,x47211),f2(a925))
% 28.25/28.10 [4722]~E(f319(a104,x47221),f2(a925))
% 28.25/28.10 [4723]~E(f319(a104,x47231),f2(a925))
% 28.25/28.10 [4724]~E(f319(a104,x47241),f2(a925))
% 28.25/28.10 [3387]E(f319(f95(a1),x33871),x33871)
% 28.25/28.10 [3388]E(f319(f181(a925),x33881),x33881)
% 28.25/28.10 [3403]E(f319(a83,f320(x34031)),x34031)
% 28.25/28.10 [3404]E(f319(a3,f595(x34041)),x34041)
% 28.25/28.10 [3405]E(f233(x34051,f2(a91)),f2(a91))
% 28.25/28.10 [3418]E(f106(x34181,f105(x34181)),f105(x34181))
% 28.25/28.10 [3419]E(f144(x34191,f105(x34191)),f105(x34191))
% 28.25/28.10 [3424]E(f319(f159(x34241),f105(x34241)),f105(x34241))
% 28.25/28.10 [3425]E(f319(f163(x34251),f105(x34251)),f105(x34251))
% 28.25/28.10 [3426]E(f319(f160(x34261),f105(x34261)),f105(x34261))
% 28.25/28.10 [3431]E(f319(f95(a1),x34311),f319(f94(a1),x34311))
% 28.25/28.10 [3432]E(f319(a83,f319(a99,x34321)),x34321)
% 28.25/28.10 [3433]E(f319(a3,f319(a20,x34331)),x34331)
% 28.25/28.10 [3434]E(f319(a3,f319(a20,x34341)),x34341)
% 28.25/28.10 [3435]E(f319(a20,f319(a3,x34351)),x34351)
% 28.25/28.10 [3437]P7(f319(f92(a1),x34371))
% 28.25/28.10 [3446]E(f319(f181(f926(x34461)),f105(x34461)),f2(a925))
% 28.25/28.10 [3447]E(f319(f181(f927(x34471)),f111(x34471)),f2(a925))
% 28.25/28.10 [3472]E(f319(f319(f23(a925),x34721),f2(a925)),x34721)
% 28.25/28.10 [3473]E(f319(f319(f75(a925),x34731),f72(a925)),x34731)
% 28.25/28.10 [3474]E(f319(f319(f75(a1),x34741),f72(a1)),x34741)
% 28.25/28.10 [3475]E(f319(f319(f74(a925),x34751),f2(a925)),x34751)
% 28.25/28.10 [3476]E(f319(f319(f74(a1),x34761),f2(a1)),x34761)
% 28.25/28.10 [3477]E(f319(f319(f225(a925),x34771),f2(a925)),x34771)
% 28.25/28.10 [3478]E(f319(f319(f75(a925),x34781),f2(a925)),f2(a925))
% 28.25/28.10 [3479]E(f319(f319(f224(a925),x34791),f2(a925)),f2(a925))
% 28.25/28.10 [3480]E(f319(f319(f30(a1),x34801),f2(a1)),f2(a1))
% 28.25/28.10 [3487]E(f319(f164(x34871),f105(x34871)),f180(f932(x34871,a923)))
% 28.25/28.10 [3491]P1(f319(f129(x34911),f105(x34911)))
% 28.25/28.10 [3497]E(f319(f146(x34971,x34971),f5(x34971)),f25(f926(x34971)))
% 28.25/28.10 [3498]E(f319(f146(x34981,x34981),f25(x34981)),f25(f926(x34981)))
% 28.25/28.10 [3499]E(f39(a1,x34991,f2(a1)),x34991)
% 28.25/28.10 [3500]E(f319(f226(a925),f319(a104,x35001)),f319(f227(a925),x35001))
% 28.25/28.10 [3501]E(f319(f274(a925),f319(a104,x35011)),f319(f293(a925),x35011))
% 28.25/28.10 [3502]E(f319(f275(a925),f319(a104,x35021)),f319(f296(a925),x35021))
% 28.25/28.10 [3504]E(f39(a1,f2(a1),x35041),f2(a1))
% 28.25/28.10 [3517]E(f319(f319(f74(a925),x35171),f72(a925)),f319(a104,x35171))
% 28.25/28.10 [3526]E(f319(f294(a925,x35261),f2(a925)),f180(f932(a925,a923)))
% 28.25/28.10 [3538]E(f295(a925,f2(a925),x35381),f319(f293(a925),x35381))
% 28.25/28.10 [3581]E(f319(f319(f23(a925),f319(a104,x35811)),f72(a925)),x35811)
% 28.25/28.10 [3593]E(f41(f2(a1),x35931),f319(f319(f244(a1,a1),f2(a1)),f2(a1)))
% 28.25/28.10 [3597]E(f319(f319(f74(a925),f319(a20,x35971)),f2(a925)),f319(a20,x35971))
% 28.25/28.10 [3642]P1(f319(f319(f227(a925),x36421),f319(a104,x36421)))
% 28.25/28.10 [3654]P1(f319(f319(f227(a925),f2(a925)),f319(a104,x36541)))
% 28.25/28.10 [3665]E(f319(f319(f175(f926(x36651),f926(x36651)),f2(a925)),f159(x36651)),f25(f926(x36651)))
% 28.25/28.10 [3879]E(f85(x38791,x38791,f234(f932(x38791,a923)),f25(x38791)),f25(x38791))
% 28.25/28.10 [3937]E(f319(f319(f23(a91),f319(a3,f319(a104,f319(a20,x39371)))),f72(a91)),x39371)
% 28.25/28.10 [4007]P1(f319(f319(f226(a1),f319(f73(a1),f319(f92(a1),x40071))),f2(a1)))
% 28.25/28.10 [4150]P1(f319(f319(f227(a1),f319(f73(a1),f319(f92(a1),f319(a104,x41501)))),f2(a1)))
% 28.25/28.10 [4248]P27(x42481,x42481,f25(x42481),f234(f932(x42481,a923)),f234(f932(x42481,a923)))
% 28.25/28.10 [4733]~E(f234(f932(x47331,a923)),f180(f932(x47331,a923)))
% 28.25/28.10 [4754]~P1(f319(f319(f227(a925),x47541),f2(a925)))
% 28.25/28.10 [4755]~P1(f319(f319(f227(a925),x47551),f2(a925)))
% 28.25/28.10 [4756]~P1(f319(f319(f227(a925),x47561),f2(a925)))
% 28.25/28.10 [4767]~P1(f319(f319(f227(a1),f319(f92(a1),x47671)),f2(a1)))
% 28.25/28.10 [3436]E(f112(x34361,f111(f927(x34361))),f111(x34361))
% 28.25/28.10 [3451]E(f171(x34511,f105(f926(x34511))),f105(f926(x34511)))
% 28.25/28.10 [3454]E(f319(f319(f75(a1),a77),x34541),a77)
% 28.25/28.10 [3455]E(f319(f319(f74(a1),a77),x34551),x34551)
% 28.25/28.10 [3458]E(f319(a96,f319(f92(a1),x34581)),x34581)
% 28.25/28.10 [3459]E(f319(f319(f23(a1),x34591),a77),x34591)
% 28.25/28.10 [3460]E(f319(f319(f74(a1),x34601),a77),x34601)
% 28.25/28.10 [3462]E(f319(f319(f23(a925),x34621),x34621),f2(a925))
% 28.25/28.10 [3470]E(f319(f73(a1),f319(f73(a1),x34701)),x34701)
% 28.25/28.10 [3471]E(f319(f29(a925),f319(f274(a925),x34711)),x34711)
% 28.25/28.10 [3482]E(f319(f319(f75(a925),f72(a925)),x34821),x34821)
% 28.25/28.10 [3483]E(f319(f319(f75(a1),f72(a1)),x34831),x34831)
% 28.25/28.10 [3484]E(f319(f319(f74(a925),f2(a925)),x34841),x34841)
% 28.25/28.10 [3485]E(f319(f319(f74(a1),f2(a1)),x34851),x34851)
% 28.25/28.10 [3486]E(f319(f319(f225(a925),f2(a925)),x34861),x34861)
% 28.25/28.10 [3492]E(f319(f319(f23(a925),f2(a925)),x34921),f2(a925))
% 28.25/28.10 [3493]E(f319(f319(f75(a925),f2(a925)),x34931),f2(a925))
% 28.25/28.10 [3494]E(f319(f319(f224(a925),f2(a925)),x34941),f2(a925))
% 28.25/28.10 [3495]E(f319(f319(f30(a1),f2(a1)),x34951),f2(a1))
% 28.25/28.10 [3505]E(f120(x35051,f319(f73(a1),x35051)),f124(a1,x35051))
% 28.25/28.10 [3510]E(f319(f294(a925,f2(a925)),x35101),f319(f274(a925),x35101))
% 28.25/28.10 [3511]E(f319(f319(f75(a1),a89),x35111),f319(f73(a1),x35111))
% 28.25/28.10 [3518]E(f319(a96,f319(f95(a1),x35181)),f319(f95(a925),x35181))
% 28.25/28.10 [3519]E(f319(a96,f319(f95(a1),x35191)),f319(f95(a925),x35191))
% 28.25/28.10 [3520]E(f319(a20,f319(f95(a91),x35201)),f319(f95(a925),x35201))
% 28.25/28.10 [3521]E(f319(f29(a925),f319(f293(a925),x35211)),f319(a104,x35211))
% 28.25/28.10 [3530]E(f319(f319(f74(a925),f72(a925)),x35301),f319(a104,x35301))
% 28.25/28.10 [3534]E(f319(f94(a1),f319(f92(a1),x35341)),f319(f92(a1),x35341))
% 28.25/28.10 [3535]E(f319(f69(a1),f319(f92(a1),x35351)),f319(f92(a1),x35351))
% 28.25/28.10 [3539]E(f319(f29(x35391),f180(f932(x35391,a923))),f2(a925))
% 28.25/28.10 [3541]E(f319(f319(f30(a925),x35411),f319(a104,f2(a925))),x35411)
% 28.25/28.10 [3550]E(f39(a925,x35501,f319(a104,f2(a925))),f2(a925))
% 28.25/28.10 [3551]E(f39(a1,x35511,f319(f95(a1),a89)),f2(a1))
% 28.25/28.10 [3558]E(f319(f319(f74(a1),a89),x35581),f319(f319(f74(a1),x35581),a89))
% 28.25/28.10 [3565]E(f319(f319(f30(a1),x35651),f319(f95(a1),a89)),f319(f73(a1),x35651))
% 28.25/28.10 [3569]E(f131(a925,f319(f294(a925,x35691),f2(a925))),f105(a925))
% 28.25/28.10 [3570]E(f319(f319(f74(a1),x35701),f72(a1)),f319(f319(f23(a1),x35701),a89))
% 28.25/28.10 [3571]E(f319(f319(f23(a1),x35711),f72(a1)),f319(f319(f74(a1),x35711),a89))
% 28.25/28.10 [3575]P1(f319(f319(f226(a925),x35751),x35751))
% 28.25/28.10 [3576]P1(f319(f319(f226(a1),x35761),x35761))
% 28.25/28.10 [3577]P1(f319(f319(f279(a925),x35771),x35771))
% 28.25/28.10 [3582]E(f319(f73(a1),f319(f95(a1),x35821)),f319(f95(a1),f319(f73(a1),x35821)))
% 28.25/28.10 [3583]P1(f319(f55(a925),f319(f274(a925),x35831)))
% 28.25/28.10 [3584]P1(f319(f55(a925),f319(f293(a925),x35841)))
% 28.25/28.10 [3591]E(f153(x35911,f234(f932(x35911,a923))),f234(f932(f926(x35911),a923)))
% 28.25/28.10 [3595]P1(f319(f319(f226(a925),f2(a925)),x35951))
% 28.25/28.10 [3596]P1(f319(f319(f226(a925),f2(a925)),x35961))
% 28.25/28.10 [3606]E(f319(f319(f74(a925),f103(x36061)),f319(a104,f2(a925))),f103(f319(a104,x36061)))
% 28.25/28.10 [3607]E(f319(f254(x36071),f319(f16(a923,x36071),a179)),f234(f932(x36071,a923)))
% 28.25/28.10 [3608]E(f319(f254(x36081),f319(f16(a923,x36081),a231)),f180(f932(x36081,a923)))
% 28.25/28.10 [3611]E(f319(f319(f301(a925),x36111),f319(f274(a925),x36111)),f319(f274(a925),f319(a104,x36111)))
% 28.25/28.10 [3623]E(f319(f319(f74(a1),f72(a1)),f319(f92(a1),x36231)),f319(f92(a1),f319(a104,x36231)))
% 28.25/28.10 [3625]E(f319(f319(f143(f926(x36251)),f105(x36251)),f105(f926(x36251))),f48(x36251,f105(x36251)))
% 28.25/28.10 [3645]E(f180(f932(f931(x36451,x36451),a923)),f255(x36451,f180(f932(x36451,a923))))
% 28.25/28.10 [3646]E(f319(f300(x36461),f234(f932(x36461,a923))),f234(f932(f932(x36461,a923),a923)))
% 28.25/28.10 [3647]E(f319(f73(f932(x36471,a923)),f234(f932(x36471,a923))),f180(f932(x36471,a923)))
% 28.25/28.10 [3648]E(f319(f73(f932(x36481,a923)),f180(f932(x36481,a923))),f234(f932(x36481,a923)))
% 28.25/28.11 [3649]P1(f319(f55(x36491),f180(f932(x36491,a923))))
% 28.25/28.11 [3650]P1(f319(f55(x36501),f180(f932(x36501,a923))))
% 28.25/28.11 [3652]E(f319(f294(a925,x36521),f319(a104,x36521)),f319(f319(f301(a925),x36521),f180(f932(a925,a923))))
% 28.25/28.11 [3653]E(f79(f931(a925,a925),f42(x36531,f2(a925))),f319(f319(f244(a925,a925),f2(a925)),x36531))
% 28.25/28.11 [3666]E(f319(f319(f301(a925),f319(a104,x36661)),f319(f293(a925),x36661)),f319(f293(a925),f319(a104,x36661)))
% 28.25/28.11 [3670]P38(x36701,f180(f932(f931(x36701,x36701),a923)))
% 28.25/28.11 [3671]P40(x36711,f180(f932(f931(x36711,x36711),a923)))
% 28.25/28.11 [3673]P1(f319(f319(f226(a1),f2(a1)),f319(f92(a1),x36731)))
% 28.25/28.11 [3674]P1(f319(f319(f226(a1),f2(a1)),f319(f92(a1),x36741)))
% 28.25/28.11 [3681]E(f319(f319(f74(a925),f319(f181(a925),x36811)),f319(a104,f2(a925))),f319(f181(a925),f319(a104,x36811)))
% 28.25/28.11 [3727]P1(f319(f319(f321(a925),f595(x37271)),f234(f932(a925,a923))))
% 28.25/28.11 [3729]E(f319(f302(x37291,x37291,f25(x37291)),f234(f932(x37291,a923))),f234(f932(x37291,a923)))
% 28.25/28.11 [3784]P42(f319(f302(a925,a1,f92(a1)),x37841))
% 28.25/28.11 [3822]P57(x38221,f180(f932(x38221,a923)),f180(f932(f931(x38221,x38221),a923)))
% 28.25/28.11 [3840]E(f319(f319(f244(a1,a1),f319(f95(a1),a89)),f319(f319(f23(a1),x38401),f72(a1))),f44(f319(f95(a1),a89),x38401))
% 28.25/28.11 [3841]P1(f319(f319(f321(a925),f319(a20,x38411)),f234(f932(a925,a923))))
% 28.25/28.11 [3892]P64(x38921,f319(f16(f932(x38921,a923),x38921),f319(f16(a923,x38921),a231)))
% 28.25/28.11 [3905]E(f282(a925,f279(a925),x39051,x39051),f319(f319(f301(a925),x39051),f180(f932(a925,a923))))
% 28.25/28.11 [4076]E(f319(f134(f926(x40761),f926(x40761),f126(x40761),f105(x40761)),f105(f926(x40761))),f105(x40761))
% 28.25/28.11 [4094]P1(f319(f319(f321(f932(f931(a925,a925),a923)),f320(x40941)),a90))
% 28.25/28.11 [4119]P1(f319(f319(f321(f932(f931(a925,a925),a923)),f319(a99,x41191)),a90))
% 28.25/28.11 [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)))
% 28.25/28.11 [4728]~E(f319(f319(f74(a1),x47281),x47281),a89)
% 28.25/28.11 [4729]~E(f319(f319(f74(a1),x47291),x47291),a89)
% 28.25/28.11 [4742]~E(f319(a3,f319(a104,f319(a20,x47421))),f2(a91))
% 28.25/28.11 [4743]~E(f319(a3,f319(a104,f319(a20,x47431))),f2(a91))
% 28.25/28.11 [4749]~P1(f319(a185,f319(f92(a1),x47491)))
% 28.25/28.11 [4751]~P1(f319(f319(f227(a925),x47511),x47511))
% 28.25/28.11 [4752]~P1(f319(f319(f227(a925),x47521),x47521))
% 28.25/28.11 [4760]~P1(f319(f319(f226(a925),f319(a104,x47601)),x47601))
% 28.25/28.11 [3598]E(f319(a96,f319(f73(a1),f319(f92(a1),x35981))),f2(a925))
% 28.25/28.11 [3601]E(f319(f319(f74(a1),f319(f73(a1),x36011)),x36011),f2(a1))
% 28.25/28.11 [3605]E(f319(f29(a1),f319(f294(a1,f2(a1)),x36051)),f319(a96,x36051))
% 28.25/28.11 [3616]E(f319(f319(f236(a925),f319(a104,f2(a925))),x36161),f319(a104,f2(a925)))
% 28.25/28.11 [3711]E(f319(f273(x37111),f180(f932(f931(x37111,x37111),a923))),f180(f932(x37111,a923)))
% 28.25/28.11 [3713]P1(f319(f55(a1),f319(f294(a1,f2(a1)),x37131)))
% 28.25/28.11 [3719]E(f32(f932(x37191,a923),f234(f932(f932(x37191,a923),a923))),f180(f932(x37191,a923)))
% 28.25/28.11 [3720]E(f32(f932(x37201,a923),f180(f932(f932(x37201,a923),a923))),f234(f932(x37201,a923)))
% 28.25/28.11 [3721]E(f31(f932(x37211,a923),f234(f932(f932(x37211,a923),a923))),f234(f932(x37211,a923)))
% 28.25/28.11 [3722]E(f31(f932(x37221,a923),f180(f932(f932(x37221,a923),a923))),f180(f932(x37221,a923)))
% 28.25/28.11 [3726]P1(f319(f319(f279(a925),f319(a104,f2(a925))),x37261))
% 28.25/28.11 [3767]E(f319(f319(f301(f926(x37671)),f105(x37671)),f180(f932(f926(x37671),a923))),f153(x37671,f180(f932(x37671,a923))))
% 28.25/28.11 [3768]E(f319(f319(f301(f926(x37681)),f105(x37681)),f180(f932(f926(x37681),a923))),f154(x37681,f105(f932(x37681,a923))))
% 28.25/28.11 [3793]E(f319(f319(f74(a1),f319(f73(a1),x37931)),f319(f73(a1),x37931)),f319(f73(a1),f319(f319(f74(a1),x37931),x37931)))
% 28.25/28.11 [3806]E(f319(f319(f74(a925),f4(x38061)),f319(a104,f2(a925))),f4(f319(a3,f319(a104,f319(a20,x38061)))))
% 28.25/28.11 [3831]E(f319(f29(a1),f319(f302(a925,a1,f92(a1)),x38311)),f319(f29(a925),x38311))
% 28.25/28.11 [3832]P1(f319(f319(f226(a925),x38321),f319(f319(f75(a925),x38321),x38321)))
% 28.25/28.11 [3870]E(f319(f302(a1,a925,a96),f295(a1,f2(a1),f319(f92(a1),x38701))),f319(f293(a925),x38701))
% 28.25/28.11 [3887]E(f319(f319(f30(a925),f319(a104,f2(a925))),f319(f95(a925),x38871)),f319(a96,f319(f319(f30(a1),f72(a1)),f319(f95(a1),x38871))))
% 28.25/28.11 [3889]E(f319(f164(a925),f131(a925,f319(f294(a925,f2(a925)),f319(a104,x38891)))),f319(f293(a925),x38891))
% 28.25/28.11 [3890]E(f319(f319(f74(a925),f319(f181(a91),x38901)),f319(a104,f2(a925))),f319(f181(a91),f319(a3,f319(a104,f319(a20,x38901)))))
% 28.25/28.11 [3910]P39(x39101,f299(x39101,f180(f932(f931(x39101,x39101),a923))))
% 28.25/28.11 [3911]P40(x39111,f299(x39111,f180(f932(f931(x39111,x39111),a923))))
% 28.25/28.11 [3912]P56(x39121,f299(x39121,f180(f932(f931(x39121,x39121),a923))))
% 28.25/28.11 [3913]E(f319(f302(a1,a925,a96),f319(f302(a925,a1,f92(a1)),x39131)),x39131)
% 28.25/28.11 [3943]E(f319(f319(f301(a925),f2(a925)),f319(f302(a925,a925,a104),f319(f274(a925),x39431))),f319(f274(a925),f319(a104,x39431)))
% 28.25/28.11 [3949]P59(x39491,x39491,f299(x39491,f180(f932(f931(x39491,x39491),a923))))
% 28.25/28.11 [3955]P1(f319(a185,f319(f73(a1),f319(f92(a1),f319(a104,x39551)))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [3985]P57(x39851,f234(f932(x39851,a923)),f299(x39851,f180(f932(f931(x39851,x39851),a923))))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [4764]~P1(f319(f55(f926(x47641)),f234(f932(f926(x47641),a923))))
% 28.25/28.11 [4776]~P1(f319(f319(f226(a1),f2(a1)),f319(f73(a1),f319(f92(a1),f319(a104,x47761)))))
% 28.25/28.11 [3746]E(f319(f319(f23(a1),f319(f319(f74(a1),x37461),a89)),a89),x37461)
% 28.25/28.11 [3760]E(f319(f164(a925),f131(a925,f319(f294(a925,f2(a925)),x37601))),f319(f274(a925),x37601))
% 28.25/28.11 [3956]E(f319(f276(x39561,x39561),f299(x39561,f180(f932(f931(x39561,x39561),a923)))),f234(f932(x39561,a923)))
% 28.25/28.11 [3957]E(f319(f256(x39571,x39571),f299(x39571,f180(f932(f931(x39571,x39571),a923)))),f234(f932(x39571,a923)))
% 28.25/28.11 [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))
% 28.25/28.11 [4051]E(f319(f278(x40511,x40511),f299(x40511,f180(f932(f931(x40511,x40511),a923)))),f299(x40511,f180(f932(f931(x40511,x40511),a923))))
% 28.25/28.11 [4097]P1(f319(f319(f226(a925),x40971),f319(f319(f75(a925),x40971),f319(f319(f75(a925),x40971),x40971))))
% 28.25/28.11 [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)))
% 28.25/28.11 [4366]P1(f319(f55(a925),f319(f254(a925),f319(f319(f7(a925,a925,a923),f226(a925)),x43661))))
% 28.25/28.11 [4367]P1(f319(f55(a925),f319(f254(a925),f319(f319(f7(a925,a925,a923),f227(a925)),x43671))))
% 28.25/28.11 [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))))
% 28.25/28.11 [4765]~E(f319(f319(f23(a1),f319(f319(f74(a1),x47651),x47651)),a89),a77)
% 28.25/28.11 [4766]~E(f319(f319(f23(a1),f319(f319(f74(a1),x47661),x47661)),a89),a77)
% 28.25/28.11 [4768]~E(f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x47681)),x47681),f2(a1))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)
% 28.25/28.11 [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)))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [4186]E(f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),x41861),x41861)),a89)),a89),f319(f319(f74(a1),x41861),x41861))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)
% 28.25/28.11 [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)))))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))))))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))
% 28.25/28.11 [3421]P112(f931(x34211,x34212))
% 28.25/28.11 [3422]P112(f933(x34221,x34222))
% 28.25/28.11 [3423]P112(f930(x34231,x34232))
% 28.25/28.11 [3440]P14(a1,f170(x34401,x34402))
% 28.25/28.11 [3441]P38(x34411,f145(x34411,x34412))
% 28.25/28.11 [3442]P39(x34421,f255(x34421,x34422))
% 28.25/28.11 [3443]P39(x34431,f299(x34431,x34432))
% 28.25/28.11 [3444]P40(x34441,f255(x34441,x34442))
% 28.25/28.11 [3445]P56(x34451,f255(x34451,x34452))
% 28.25/28.11 [3512]P32(x35121,x35122,f105(x35121))
% 28.25/28.11 [3545]P57(x35451,x35452,f255(x35451,x35452))
% 28.25/28.11 [3546]P59(x35461,x35461,f255(x35461,x35462))
% 28.25/28.11 [3809]P26(x38091,x38091,f5(x38091),x38092)
% 28.25/28.11 [3810]P26(x38101,x38101,f25(x38101),x38102)
% 28.25/28.11 [3817]P33(x38171,x38172,f105(x38171),f105(x38171))
% 28.25/28.11 [3818]P33(x38181,x38182,f105(x38181),f105(x38181))
% 28.25/28.11 [3825]P26(f926(x38251),f926(x38251),f160(x38251),x38252)
% 28.25/28.11 [4226]P27(x42261,x42261,f25(x42261),x42262,x42262)
% 28.25/28.11 [4738]~P34(x47381,x47382,f105(x47381))
% 28.25/28.11 [4739]~P36(x47391,x47392,f105(x47391))
% 28.25/28.11 [3407]E(f319(f5(x34071),x34072),x34072)
% 28.25/28.11 [3408]E(f319(f254(x34081),x34082),x34082)
% 28.25/28.11 [3409]E(f319(f25(x34091),x34092),x34092)
% 28.25/28.11 [3410]E(f319(f25(x34101),x34102),x34102)
% 28.25/28.11 [3420]E(f319(f183(x34201),x34202),f107(x34201))
% 28.25/28.11 [3438]E(f79(x34381,f319(a316,x34382)),x34382)
% 28.25/28.11 [3439]E(f84(x34391,f319(a316,x34392)),x34392)
% 28.25/28.11 [3461]E(f319(f117(x34611,x34612),f111(x34611)),f2(a925))
% 28.25/28.11 [3468]E(f319(f128(x34681,x34682),f105(x34681)),f105(x34681))
% 28.25/28.11 [3488]E(f299(x34881,f299(x34881,x34882)),f299(x34881,x34882))
% 28.25/28.11 [3489]E(f144(x34891,f144(x34891,x34892)),f144(x34891,x34892))
% 28.25/28.11 [3507]E(f319(f319(f126(x35071),x35072),f105(x35071)),x35072)
% 28.25/28.11 [3513]E(f165(x35131,x35132,f105(x35131)),x35132)
% 28.25/28.11 [3514]E(f165(x35141,f105(x35141),x35142),x35142)
% 28.25/28.11 [3515]E(f108(x35151,f111(x35151),x35152),x35152)
% 28.25/28.11 [3516]E(f161(x35161,f2(a925),x35162),f105(x35161))
% 28.25/28.11 [3522]E(f319(f319(f167(x35221),x35222),f105(x35221)),f105(x35221))
% 28.25/28.11 [3523]E(f319(f319(f130(x35231),x35232),f105(x35231)),f105(x35231))
% 28.25/28.11 [3525]E(f147(x35251,x35252,f105(x35251)),f2(a925))
% 28.25/28.11 [3527]E(f162(x35271,x35272,f105(x35271)),f105(x35271))
% 28.25/28.11 [3528]E(f169(x35281,x35282,f105(x35281)),f105(x35281))
% 28.25/28.11 [3529]E(f168(x35291,f105(x35291),x35292),f105(x35291))
% 28.25/28.11 [3533]E(f319(f164(x35331),f144(x35331,x35332)),f319(f164(x35331),x35332))
% 28.25/28.11 [3536]E(f319(f276(x35361,x35361),f255(x35361,x35362)),x35362)
% 28.25/28.11 [3537]E(f319(f256(x35371,x35371),f255(x35371,x35372)),x35372)
% 28.25/28.11 [3544]E(f319(f278(x35441,x35441),f255(x35441,x35442)),f255(x35441,x35442))
% 28.25/28.11 [3557]E(f299(f926(x35571),f149(x35571,x35572)),f150(x35571,f299(x35571,x35572)))
% 28.25/28.11 [3559]P1(f319(f129(a1),f170(x35591,x35592)))
% 28.25/28.11 [3567]E(f319(f276(x35671,x35671),f299(x35671,x35672)),f234(f932(x35671,a923)))
% 28.25/28.11 [3568]E(f319(f256(x35681,x35681),f299(x35681,x35682)),f234(f932(x35681,a923)))
% 28.25/28.11 [3572]P1(f319(f129(x35721),f144(x35721,x35722)))
% 28.25/28.11 [3573]P1(f319(f152(x35731,x35732),f105(x35731)))
% 28.25/28.11 [3574]P1(f319(f152(x35741,x35742),f105(x35741)))
% 28.25/28.11 [3579]E(f319(f164(a1),f170(x35791,x35792)),f295(a1,x35791,x35792))
% 28.25/28.11 [3580]E(f319(f164(a1),f170(x35801,x35802)),f295(a1,x35801,x35802))
% 28.25/28.11 [3594]P60(x35941,f180(f932(x35941,a923)),x35942)
% 28.25/28.11 [3599]E(f319(f248(a1,a1),f40(x35991,x35992)),f39(a1,x35991,x35992))
% 28.25/28.11 [3600]E(f319(f294(a925,x36001),f319(a104,x36002)),f295(a925,x36001,x36002))
% 28.25/28.11 [3615]E(f319(f319(f143(x36151),x36152),f105(x36151)),f132(x36151,x36152,f105(x36151)))
% 28.25/28.11 [3627]E(f295(a925,f319(a104,x36271),x36272),f297(a925,x36271,x36272))
% 28.25/28.11 [3630]P57(x36301,f234(f932(x36301,a923)),f299(x36301,x36302))
% 28.25/28.11 [3692]E(f319(f319(f23(a925),x36921),f319(a104,x36922)),f319(f29(a925),f298(a925,x36922,x36921)))
% 28.25/28.11 [3747]E(f158(x37471,x37472,f105(x37471)),f319(f319(f244(f926(x37471),f926(x37471)),f105(x37471)),f105(x37471)))
% 28.25/28.11 [3765]E(f319(f249(x37651,x37652,f931(x37651,x37652)),f244(x37651,x37652)),f25(f931(x37651,x37652)))
% 28.25/28.11 [3769]P1(f319(f319(f321(f926(x37691)),f105(x37691)),f153(x37691,x37692)))
% 28.25/28.11 [3770]E(f319(f181(f926(x37701)),f106(x37701,x37702)),f319(f319(f23(a925),f319(f181(f926(x37701)),x37702)),f72(a925)))
% 28.25/28.11 [3778]P1(f319(f55(a925),f295(a925,x37781,x37782)))
% 28.25/28.11 [3779]P1(f319(f55(a925),f297(a925,x37791,x37792)))
% 28.25/28.11 [3780]P1(f319(f55(a925),f298(a925,x37801,x37802)))
% 28.25/28.11 [3781]P1(f319(f55(a1),f295(a1,x37811,x37812)))
% 28.25/28.11 [3782]P1(f319(f55(a1),f297(a1,x37821,x37822)))
% 28.25/28.11 [3783]P1(f319(f55(a1),f298(a1,x37831,x37832)))
% 28.25/28.11 [3886]E(f319(f302(a925,a925,a104),f295(a925,x38861,x38862)),f295(a925,f319(a104,x38861),f319(a104,x38862)))
% 28.25/28.11 [3907]E(f319(f319(f281(x39071,x39071,x39071),f299(x39071,x39072)),f299(x39071,x39072)),f299(x39071,x39072))
% 28.25/28.11 [3941]E(f319(f319(f244(a1,a1),f319(f319(f30(a1),x39411),x39412)),f39(a1,x39411,x39412)),f40(x39411,x39412))
% 28.25/28.11 [3942]E(f319(f319(f244(a91,a91),f319(f319(f30(a91),x39421),x39422)),f39(a91,x39421,x39422)),f21(x39421,x39422))
% 28.25/28.11 [3969]E(f319(f319(f244(a925,a925),f319(f319(f30(a925),x39691),x39692)),f39(a925,x39691,x39692)),f79(f931(a925,a925),f42(x39691,x39692)))
% 28.25/28.11 [4020]P1(f319(f319(f227(a925),f319(f319(f23(a925),x40201),x40202)),f319(a104,x40201)))
% 28.25/28.11 [4068]P39(x40681,f319(f319(f281(x40681,x40681,x40681),x40682),f299(x40681,x40682)))
% 28.25/28.11 [4108]E(f319(f319(f130(x41081),f319(f181(f926(x41081)),f169(x41081,x41082,f105(x41081)))),f105(x41081)),f105(x41081))
% 28.25/28.11 [4118]E(f319(f319(f74(a1),f319(f319(f75(a1),x41181),f319(f319(f30(a1),x41182),x41181))),f39(a1,x41182,x41181)),x41182)
% 28.25/28.11 [4122]E(f319(f319(f33(a925,f932(f931(f926(x41221),f926(x41221)),a923)),f234(f932(a925,a923))),f135(x41221,x41222)),f137(x41221,x41222))
% 28.25/28.11 [4201]E(f319(f128(x42011,f319(f319(f8(a923,a923,x42011),a314),f319(a316,x42012))),f105(x42011)),f105(x42011))
% 28.25/28.11 [4343]P1(f319(f319(f321(f931(f926(x43431),f926(x43431))),f319(f319(f244(f926(x43431),f926(x43431)),f105(x43431)),f105(x43431))),f150(x43431,x43432)))
% 28.25/28.11 [4452]E(f245(x44521,x44521,x44521,a316,f245(x44521,x44521,x44521,x44522,a316)),x44522)
% 28.25/28.11 [4495]E(f250(x44951,x44951,x44952,x44952,f25(x44951),f25(x44952)),f25(f931(x44951,x44952)))
% 28.25/28.11 [4496]E(f250(x44961,x44961,x44962,x44962,f5(x44961),f5(x44962)),f25(f931(x44961,x44962)))
% 28.25/28.11 [4497]E(f250(x44971,x44971,x44972,x44972,f25(x44971),f25(x44972)),f25(f931(x44971,x44972)))
% 28.25/28.11 [4498]E(f250(x44981,x44981,x44982,x44982,f25(x44981),f25(x44982)),f25(f931(x44981,x44982)))
% 28.25/28.11 [3506]E(f319(f160(x35061),f319(f160(x35061),x35062)),x35062)
% 28.25/28.11 [3508]E(f319(f319(f130(x35081),f2(a925)),x35082),x35082)
% 28.25/28.11 [3524]E(f319(f319(f167(x35241),f2(a925)),x35242),f105(x35241))
% 28.25/28.11 [3531]E(f319(f319(f126(x35311),f105(x35311)),x35312),x35312)
% 28.25/28.11 [3540]E(f31(f932(x35401,a923),f319(f300(x35401),x35402)),x35402)
% 28.25/28.11 [3542]E(f319(f164(x35421),f319(f159(x35421),x35422)),f319(f164(x35421),x35422))
% 28.25/28.11 [3543]E(f319(f164(x35431),f319(f160(x35431),x35432)),f319(f164(x35431),x35432))
% 28.25/28.11 [3548]E(f319(f319(f23(a91),x35481),x35482),f319(f319(a24,x35481),x35482))
% 28.25/28.11 [3561]E(f319(f319(f75(a925),x35611),x35612),f319(f319(f75(a925),x35612),x35611))
% 28.25/28.11 [3562]E(f319(f319(f75(a1),x35621),x35622),f319(f319(f75(a1),x35622),x35621))
% 28.25/28.11 [3563]E(f319(f319(f74(a925),x35631),x35632),f319(f319(f74(a925),x35632),x35631))
% 28.25/28.11 [3564]E(f319(f319(f74(a1),x35641),x35642),f319(f319(f74(a1),x35642),x35641))
% 28.25/28.11 [3586]E(f319(f319(f175(x35861,x35861),f2(a925)),x35862),f25(x35861))
% 28.25/28.11 [3587]E(f319(f181(f926(x35871)),f319(f159(x35871),x35872)),f319(f181(f926(x35871)),x35872))
% 28.25/28.11 [3588]E(f319(f181(f926(x35881)),f319(f160(x35881),x35882)),f319(f181(f926(x35881)),x35882))
% 28.25/28.11 [3589]E(f168(x35891,x35892,f180(f932(a925,a923))),f105(x35891))
% 28.25/28.11 [3590]E(f319(f319(f146(x35901,x35901),f5(x35901)),x35902),x35902)
% 28.25/28.11 [3592]E(f319(f243(a1,a1),f40(x35921,x35922)),f319(f319(f30(a1),x35921),x35922))
% 28.25/28.11 [3609]E(f319(f181(f926(x36091)),f144(x36091,x36092)),f319(f29(x36091),f319(f164(x36091),x36092)))
% 28.25/28.11 [3610]E(f319(f273(x36101),f319(f278(x36101,x36101),x36102)),f319(f273(x36101),x36102))
% 28.25/28.11 [3614]P1(f319(f55(x36141),f319(f164(x36141),x36142)))
% 28.25/28.11 [3621]E(f319(f319(f74(a1),x36211),f319(f73(a1),x36212)),f319(f319(f23(a1),x36211),x36212))
% 28.25/28.11 [3622]E(f319(f319(f74(a1),x36221),f319(f73(a1),x36222)),f319(f319(f23(a1),x36221),x36222))
% 28.25/28.11 [3628]P15(x36281,x36282,f180(f932(f924(x36281),a923)))
% 28.25/28.11 [3629]P15(x36291,x36292,f180(f932(f924(x36291),a923)))
% 28.25/28.11 [3631]E(f319(f302(x36311,x36311,f5(x36311)),x36312),x36312)
% 28.25/28.11 [3632]E(f319(f302(x36321,x36321,f25(x36321)),x36322),x36322)
% 28.25/28.11 [3633]E(f319(f303(x36331,x36331,f5(x36331)),x36332),x36332)
% 28.25/28.11 [3634]E(f319(f303(x36341,x36341,f25(x36341)),x36342),x36342)
% 28.25/28.11 [3635]P1(f319(f234(f932(x36351,a923)),x36352))
% 28.25/28.11 [3637]E(f319(f29(a925),f319(f294(a925,x36371),x36372)),f319(f319(f23(a925),x36372),x36371))
% 28.25/28.11 [3638]E(f319(f294(a925,f319(a104,x36381)),x36382),f298(a925,x36381,x36382))
% 28.25/28.11 [3651]E(f319(f319(f301(x36511),x36512),f180(f932(x36511,a923))),f319(f254(x36511),f319(a316,x36512)))
% 28.25/28.11 [3656]E(f299(x36561,f319(f278(x36561,x36561),x36562)),f319(f278(x36561,x36561),f299(x36561,x36562)))
% 28.25/28.11 [3661]E(f319(f319(f74(a925),f319(a104,x36611)),x36612),f319(f319(f74(a925),x36611),f319(a104,x36612)))
% 28.25/28.11 [3662]E(f319(f319(f23(a925),f319(a104,x36621)),f319(a104,x36622)),f319(f319(f23(a925),x36621),x36622))
% 28.25/28.11 [3668]E(f49(x36681,f2(a925),x36682),f319(f319(f143(f926(x36681)),f105(x36681)),f105(f926(x36681))))
% 28.25/28.11 [3669]E(f319(f29(a925),f297(a925,x36691,x36692)),f319(f319(f23(a925),x36692),x36691))
% 28.25/28.11 [3678]P38(x36781,f319(f319(f280(a925,x36781),a232),x36782))
% 28.25/28.11 [3680]P14(a925,f131(a925,f319(f294(a925,x36801),x36802)))
% 28.25/28.11 [3682]P1(f319(f55(a925),f319(f294(a925,x36821),x36822)))
% 28.25/28.11 [3683]P1(f319(f55(a1),f319(f294(a1,x36831),x36832)))
% 28.25/28.11 [3686]E(f319(f278(f926(x36861),f926(x36861)),f149(x36861,x36862)),f149(x36861,f319(f278(x36861,x36861),x36862)))
% 28.25/28.11 [3688]E(f319(f294(a1,x36881),f319(f319(f74(a1),x36882),f72(a1))),f295(a1,x36881,x36882))
% 28.25/28.11 [3691]E(f319(f319(f30(a1),f319(f73(a1),x36911)),f319(f73(a1),x36912)),f319(f319(f30(a1),x36911),x36912))
% 28.25/28.11 [3699]E(f319(f319(f175(f931(x36991,x36991),a923),f72(a925)),x36992),x36992)
% 28.25/28.11 [3701]E(f319(f319(f102(f932(x37011,a923)),x37012),f180(f932(x37011,a923))),x37012)
% 28.25/28.11 [3702]E(f319(f319(f93(f932(x37021,a923)),x37022),f234(f932(x37021,a923))),x37022)
% 28.25/28.11 [3703]E(f319(f319(f23(f932(x37031,a923)),x37032),f180(f932(x37031,a923))),x37032)
% 28.25/28.11 [3704]E(f319(f243(a925,a925),f79(f931(a925,a925),f42(x37041,x37042))),f319(f319(f30(a925),x37041),x37042))
% 28.25/28.11 [3710]E(f295(a1,f319(f319(f74(a1),x37101),f72(a1)),x37102),f297(a1,x37101,x37102))
% 28.25/28.11 [3715]E(f319(f248(a925,a925),f79(f931(a925,a925),f42(x37151,x37152))),f39(a925,x37151,x37152))
% 28.25/28.11 [3724]P1(f319(f319(f321(x37241),x37242),f234(f932(x37241,a923))))
% 28.25/28.11 [3725]P1(f319(f319(f321(x37251),x37252),f234(f932(x37251,a923))))
% 28.25/28.11 [3730]E(f319(f319(f23(a925),f319(a104,x37301)),x37302),f319(f29(a925),f295(a925,x37302,x37301)))
% 28.25/28.11 [3756]E(f319(f319(f102(f932(x37561,a923)),x37562),f234(f932(x37561,a923))),f234(f932(x37561,a923)))
% 28.25/28.11 [3757]E(f319(f319(f93(f932(x37571,a923)),x37572),f180(f932(x37571,a923))),f180(f932(x37571,a923)))
% 28.25/28.11 [3758]E(f319(f319(f23(f932(x37581,a923)),x37582),f234(f932(x37581,a923))),f180(f932(x37581,a923)))
% 28.25/28.11 [3772]E(f39(a1,f319(f92(a1),x37721),f319(f92(a1),x37722)),f319(f92(a1),f39(a925,x37721,x37722)))
% 28.25/28.11 [3773]E(f39(a1,f319(f73(a1),x37731),f319(f73(a1),x37732)),f319(f73(a1),f39(a1,x37731,x37732)))
% 28.25/28.11 [3774]E(f39(a1,f319(f92(a1),x37741),f319(f92(a1),x37742)),f319(f92(a1),f39(a925,x37741,x37742)))
% 28.25/28.11 [3785]E(f319(f181(f926(x37851)),f319(f163(x37851),x37852)),f319(f319(f23(a925),f319(f181(f926(x37851)),x37852)),f72(a925)))
% 28.25/28.11 [3811]E(f319(f319(f30(a1),f39(a1,x38111,x38112)),x38112),f2(a1))
% 28.25/28.11 [3820]E(f319(a3,f39(a925,f319(a20,x38201),f319(a20,x38202))),f39(a91,x38201,x38202))
% 28.25/28.11 [3853]E(f319(a3,f319(f319(f23(a925),f319(a20,x38531)),f319(a20,x38532))),f319(f319(f23(a91),x38531),x38532))
% 28.25/28.11 [3854]E(f319(a3,f319(f319(f75(a925),f319(a20,x38541)),f319(a20,x38542))),f319(f319(f75(a91),x38541),x38542))
% 28.25/28.11 [3855]E(f319(a3,f319(f319(f74(a925),f319(a20,x38551)),f319(a20,x38552))),f319(f319(f74(a91),x38551),x38552))
% 28.25/28.11 [3856]E(f319(a3,f319(f319(f30(a925),f319(a20,x38561)),f319(a20,x38562))),f319(f319(f30(a91),x38561),x38562))
% 28.25/28.11 [3864]E(f319(f302(a925,a925,a104),f319(f294(a925,x38641),x38642)),f319(f294(a925,f319(a104,x38641)),f319(a104,x38642)))
% 28.25/28.11 [3891]P1(f319(f42(x38911,x38912),f79(f931(a925,a925),f42(x38911,x38912))))
% 28.25/28.11 [3916]E(f39(a925,f319(a104,f39(a925,x39161,x39162)),x39162),f39(a925,f319(a104,x39161),x39162))
% 28.25/28.11 [3928]E(f319(f319(f34(f932(x39281,a923),f932(x39281,a923)),x39282),f5(f932(x39281,a923))),f32(f932(x39281,a923),x39282))
% 28.25/28.11 [3929]E(f319(f319(f33(f932(x39291,a923),f932(x39291,a923)),x39292),f5(f932(x39291,a923))),f31(f932(x39291,a923),x39292))
% 28.25/28.11 [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)))
% 28.25/28.11 [3934]P1(f319(f319(f321(f932(x39341,a923)),x39342),f319(f300(x39341),x39342)))
% 28.25/28.11 [3940]E(f39(a1,f319(f73(a1),f39(a1,x39401,x39402)),x39402),f39(a1,f319(f73(a1),x39401),x39402))
% 28.25/28.11 [3951]P1(f319(f319(f226(f932(x39511,a923)),x39512),f234(f932(x39511,a923))))
% 28.25/28.11 [3953]E(f319(f319(f281(x39531,x39531,x39531),f299(x39531,x39532)),f299(x39531,f299(x39531,x39532))),f299(x39531,x39532))
% 28.25/28.11 [3954]E(f319(f319(f102(f932(x39541,a923)),f319(f256(x39541,x39541),x39542)),f319(f276(x39541,x39541),x39542)),f319(f273(x39541),x39542))
% 28.25/28.11 [3975]E(f305(x39751,x39752,f234(f932(x39751,a923)),f234(f932(x39752,a923))),f234(f932(f933(x39751,x39752),a923)))
% 28.25/28.11 [4025]P1(f319(f319(f226(a925),f39(a925,x40251,x40252)),x40251))
% 28.25/28.11 [4049]P1(f319(f319(f226(a1),f319(f73(a1),f319(f92(a1),x40491))),f319(f92(a1),x40492)))
% 28.25/28.11 [4073]P1(f319(f319(f321(f932(x40731,a923)),f180(f932(x40731,a923))),f319(f300(x40731),x40732)))
% 28.25/28.11 [4078]E(f299(x40781,f319(f319(f281(x40781,x40781,x40781),x40782),f299(x40781,x40782))),f299(x40781,x40782))
% 28.25/28.11 [4080]E(f319(f319(f281(x40801,x40801,x40801),f299(x40801,x40802)),x40802),f319(f319(f281(x40801,x40801,x40801),x40802),f299(x40801,x40802)))
% 28.25/28.11 [4081]E(f319(f319(f281(x40811,x40811,x40811),f299(x40811,x40812)),x40812),f319(f319(f281(x40811,x40811,x40811),x40812),f299(x40811,x40812)))
% 28.25/28.11 [4083]E(f319(a96,f319(f319(f74(a1),f319(f319(f23(a1),x40831),x40832)),f72(a1))),f319(f29(a1),f295(a1,x40832,x40831)))
% 28.25/28.11 [4098]E(f319(f276(x40981,x40981),f319(f319(f281(x40981,x40981,x40981),x40982),f299(x40981,x40982))),f319(f276(x40981,x40981),x40982))
% 28.25/28.11 [4099]E(f319(f256(x40991,x40991),f319(f319(f281(x40991,x40991,x40991),x40992),f299(x40991,x40992))),f319(f256(x40991,x40991),x40992))
% 28.25/28.11 [4117]E(f319(f134(f926(x41171),f926(x41171),f126(x41171),f105(x41171)),f161(f926(x41171),x41172,f105(x41171))),f105(x41171))
% 28.25/28.11 [4126]P26(a925,a925,f319(f319(f7(a925,a925,a925),f74(a925)),x41261),x41262)
% 28.25/28.11 [4128]P14(a925,f319(f160(a925),f319(f319(f146(f926(x41281),a925),f181(f926(x41281))),f171(x41281,x41282))))
% 28.25/28.11 [4158]P56(x41581,f319(f319(f102(f932(f931(x41581,x41581),a923)),x41582),f319(f278(x41581,x41581),x41582)))
% 28.25/28.11 [4159]P56(x41591,f319(f319(f93(f932(f931(x41591,x41591),a923)),x41592),f319(f278(x41591,x41591),x41592)))
% 28.25/28.11 [4170]P1(f319(f319(f227(a1),f319(f73(a1),f319(f92(a1),f319(a104,x41701)))),f319(f92(a1),x41702)))
% 28.25/28.11 [4215]E(f319(f134(f926(x42151),x42151,f319(f7(x42151,f926(x42151),f926(x42151)),f143(x42151)),f105(x42151)),x42152),f319(f160(x42151),x42152))
% 28.25/28.11 [4264]P1(f319(f319(f226(f932(f931(f926(x42641),f926(x42641)),a923)),f150(x42641,x42642)),f299(f926(x42641),f149(x42641,x42642))))
% 28.25/28.11 [4293]P1(f319(f42(x42931,x42932),f319(f319(f244(a925,a925),f319(f319(f30(a925),x42931),x42932)),f39(a925,x42931,x42932))))
% 28.25/28.11 [4305]P1(f319(f319(f226(f932(f931(f926(x43051),f926(x43051)),a923)),f149(x43051,f299(x43051,x43052))),f299(f926(x43051),f149(x43051,x43052))))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [4750]~E(f319(f300(x47501),x47502),f180(f932(f932(x47501,a923),a923)))
% 28.25/28.11 [4759]~P1(f319(f319(f164(x47591),f105(x47591)),x47592))
% 28.25/28.11 [4762]~P1(f319(f319(f321(x47621),x47622),f180(f932(x47621,a923))))
% 28.25/28.11 [4763]~P1(f319(f319(f321(x47631),x47632),f180(f932(x47631,a923))))
% 28.25/28.11 [4771]~P1(f319(f319(f227(f932(x47711,a923)),x47712),f180(f932(x47711,a923))))
% 28.25/28.11 [3640]E(f319(f319(f23(a925),x36401),f319(f319(f74(a925),x36401),x36402)),f2(a925))
% 28.25/28.11 [3643]E(f319(f319(f102(f932(x36431,a923)),x36432),x36432),x36432)
% 28.25/28.11 [3644]E(f319(f319(f93(f932(x36441,a923)),x36442),x36442),x36442)
% 28.25/28.11 [3672]E(f319(f319(f23(f932(x36721,a923)),x36722),x36722),f180(f932(x36721,a923)))
% 28.25/28.11 [3675]E(f319(f135(x36751,x36752),f2(a925)),f180(f932(f931(f926(x36751),f926(x36751)),a923)))
% 28.25/28.11 [3676]E(f319(f319(f74(a925),x36761),f319(a104,x36762)),f319(a104,f319(f319(f74(a925),x36761),x36762)))
% 28.25/28.11 [3687]E(f186(f319(f92(a1),x36871),f319(f92(a1),x36872)),f319(f92(a1),f319(f319(f23(a925),x36871),x36872)))
% 28.25/28.11 [3690]E(f319(f319(f30(a1),f319(f73(a1),x36901)),x36902),f319(f319(f30(a1),x36901),f319(f73(a1),x36902)))
% 28.25/28.11 [3694]E(f319(f29(a1),f319(f294(a1,x36941),x36942)),f319(a96,f319(f319(f23(a1),x36942),x36941)))
% 28.25/28.11 [3697]E(f319(f319(f74(a925),f319(a104,x36971)),x36972),f319(a104,f319(f319(f74(a925),x36971),x36972)))
% 28.25/28.11 [3700]E(f319(f73(f932(x37001,a923)),f319(f73(f932(x37001,a923)),x37002)),x37002)
% 28.25/28.11 [3712]E(f171(x37121,f319(f319(f143(f926(x37121)),f105(x37121)),x37122)),f171(x37121,x37122))
% 28.25/28.11 [3716]E(f319(f319(f74(a925),x37161),f319(f319(f75(a925),x37161),x37162)),f319(f319(f75(a925),x37161),f319(a104,x37162)))
% 28.25/28.11 [3723]E(f319(f319(a24,f319(a3,x37231)),f319(a3,x37232)),f319(a3,f319(f319(f23(a925),x37231),x37232)))
% 28.25/28.11 [3737]E(f319(f319(f236(a1),f319(f92(a1),x37371)),x37372),f319(f92(a1),f319(f319(f236(a925),x37371),x37372)))
% 28.25/28.11 [3738]E(f319(f319(f75(a1),f319(f73(a1),x37381)),x37382),f319(f73(a1),f319(f319(f75(a1),x37381),x37382)))
% 28.25/28.11 [3739]E(f319(f319(f236(a1),f319(f92(a1),x37391)),x37392),f319(f92(a1),f319(f319(f236(a925),x37391),x37392)))
% 28.25/28.11 [3740]E(f319(f319(f236(a1),f319(f92(a1),x37401)),x37402),f319(f92(a1),f319(f319(f236(a925),x37401),x37402)))
% 28.25/28.11 [3741]E(f319(f319(f75(a91),f319(a3,x37411)),f319(a3,x37412)),f319(a3,f319(f319(f75(a925),x37411),x37412)))
% 28.25/28.11 [3742]E(f319(f319(f74(a91),f319(a3,x37421)),f319(a3,x37422)),f319(a3,f319(f319(f74(a925),x37421),x37422)))
% 28.25/28.11 [3743]E(f319(f319(f224(a925),f319(a104,x37431)),f319(a104,x37432)),f319(a104,f319(f319(f224(a925),x37431),x37432)))
% 28.25/28.11 [3744]E(f319(f319(f225(a925),f319(a104,x37441)),f319(a104,x37442)),f319(a104,f319(f319(f225(a925),x37441),x37442)))
% 28.25/28.11 [3748]E(f319(f164(a925),f131(a925,f319(f294(a925,x37481),x37482))),f319(f294(a925,x37481),x37482))
% 28.25/28.11 [3749]E(f319(f164(a925),f131(a925,f319(f294(a925,x37491),x37492))),f319(f294(a925,x37491),x37492))
% 28.25/28.11 [3750]E(f304(x37501,f319(f319(f301(x37501),x37502),f180(f932(x37501,a923)))),x37502)
% 28.25/28.11 [3754]E(f319(f276(x37541,x37542),f180(f932(f931(x37541,x37542),a923))),f180(f932(x37542,a923)))
% 28.25/28.11 [3755]E(f319(f256(x37551,x37552),f180(f932(f931(x37551,x37552),a923))),f180(f932(x37551,a923)))
% 28.25/28.11 [3759]E(f319(a96,f319(f319(f23(a1),x37591),x37592)),f319(f29(a1),f297(a1,x37592,x37591)))
% 28.25/28.11 [3764]E(f319(f319(f74(a925),x37641),f319(f319(f75(a925),x37642),x37641)),f319(f319(f75(a925),f319(a104,x37642)),x37641))
% 28.25/28.11 [3766]E(f319(f319(f54(x37661),f180(f932(x37661,a923))),x37662),f180(f932(f932(x37661,a923),a923)))
% 28.25/28.11 [3775]E(f319(f181(f926(a925)),f131(a925,f319(f294(a925,x37751),x37752))),f319(f319(f23(a925),x37752),x37751))
% 28.25/28.11 [3790]E(f319(f319(f102(f932(x37901,a923)),f180(f932(x37901,a923))),x37902),x37902)
% 28.25/28.11 [3791]E(f319(f319(f93(f932(x37911,a923)),f234(f932(x37911,a923))),x37912),x37912)
% 28.25/28.11 [3792]E(f319(f319(f74(a1),f319(f73(a1),x37921)),f319(f73(a1),x37922)),f319(f73(a1),f319(f319(f74(a1),x37921),x37922)))
% 28.25/28.11 [3794]E(f319(f319(f75(a1),f319(f92(a1),x37941)),f319(f92(a1),x37942)),f319(f92(a1),f319(f319(f75(a925),x37941),x37942)))
% 28.25/28.11 [3795]E(f319(f319(f30(a1),f319(f92(a1),x37951)),f319(f92(a1),x37952)),f319(f92(a1),f319(f319(f30(a925),x37951),x37952)))
% 28.25/28.11 [3796]E(f319(f319(f75(a1),f319(f92(a1),x37961)),f319(f92(a1),x37962)),f319(f92(a1),f319(f319(f75(a925),x37961),x37962)))
% 28.25/28.11 [3797]E(f319(f319(f75(a1),f319(f92(a1),x37971)),f319(f92(a1),x37972)),f319(f92(a1),f319(f319(f75(a925),x37971),x37972)))
% 28.25/28.11 [3798]E(f319(f319(f75(a1),f319(f95(a1),x37981)),f319(f95(a1),x37982)),f319(f95(a1),f319(f319(f75(a1),x37981),x37982)))
% 28.25/28.11 [3799]E(f319(f319(f74(a1),f319(f92(a1),x37991)),f319(f92(a1),x37992)),f319(f92(a1),f319(f319(f74(a925),x37991),x37992)))
% 28.25/28.11 [3800]E(f319(f319(f74(a1),f319(f92(a1),x38001)),f319(f92(a1),x38002)),f319(f92(a1),f319(f319(f74(a925),x38001),x38002)))
% 28.25/28.11 [3801]E(f319(f319(f74(a1),f319(f95(a1),x38011)),f319(f95(a1),x38012)),f319(f95(a1),f319(f319(f74(a1),x38011),x38012)))
% 28.25/28.11 [3802]E(f319(f319(f30(a1),f319(f92(a1),x38021)),f319(f92(a1),x38022)),f319(f92(a1),f319(f319(f30(a925),x38021),x38022)))
% 28.25/28.11 [3821]E(f319(f319(f6(x38211,a925),f319(f16(a925,x38211),f72(a925))),x38212),f319(f29(x38211),x38212))
% 28.25/28.11 [3826]E(f319(f73(a1),f39(a1,f319(f73(a1),x38261),x38262)),f39(a1,x38261,f319(f73(a1),x38262)))
% 28.25/28.11 [3828]E(f319(f164(a1),f170(x38281,f319(f319(f23(a1),x38282),f72(a1)))),f319(f294(a1,x38281),x38282))
% 28.25/28.11 [3833]P1(f319(f319(f226(a925),x38331),f319(f319(f74(a925),x38332),x38331)))
% 28.25/28.11 [3834]P1(f319(f319(f226(a925),x38341),f319(f319(f74(a925),x38341),x38342)))
% 28.25/28.11 [3836]E(f319(f319(f102(f932(x38361,a923)),f234(f932(x38361,a923))),x38362),f234(f932(x38361,a923)))
% 28.25/28.11 [3837]E(f319(f319(f93(f932(x38371,a923)),f180(f932(x38371,a923))),x38372),f180(f932(x38371,a923)))
% 28.25/28.11 [3838]E(f319(f319(f23(f932(x38381,a923)),f180(f932(x38381,a923))),x38382),f180(f932(x38381,a923)))
% 28.25/28.11 [3845]E(f319(f319(f244(a1,a1),x38451),f319(f73(a1),x38452)),f319(a45,f319(f319(f244(a1,a1),x38451),x38452)))
% 28.25/28.11 [3846]E(f319(f294(a1,f319(f319(f74(a1),x38461),f72(a1))),x38462),f298(a1,x38461,x38462))
% 28.25/28.11 [3857]E(f319(f319(f75(a925),x38571),f319(f319(f30(a925),x38572),x38571)),f319(f319(f23(a925),x38572),f39(a925,x38572,x38571)))
% 28.25/28.11 [3858]E(f319(f319(f75(a1),x38581),f319(f319(f30(a1),x38582),x38581)),f319(f319(f23(a1),x38582),f39(a1,x38582,x38581)))
% 28.25/28.11 [3861]E(f319(f164(a1),f170(f319(f319(f74(a1),x38611),f72(a1)),x38612)),f297(a1,x38611,x38612))
% 28.25/28.11 [3865]P1(f319(f319(f226(f932(x38651,a923)),x38652),x38652))
% 28.25/28.11 [3868]E(f319(f319(f102(f932(x38681,a923)),x38682),f319(f73(f932(x38681,a923)),x38682)),f234(f932(x38681,a923)))
% 28.25/28.11 [3869]E(f319(f319(f93(f932(x38691,a923)),x38692),f319(f73(f932(x38691,a923)),x38692)),f180(f932(x38691,a923)))
% 28.25/28.11 [3877]E(f319(f319(f23(a925),f319(f319(f23(a925),x38771),f72(a925))),x38772),f319(f319(f23(a925),x38771),f319(a104,x38772)))
% 28.25/28.11 [3883]E(f319(f319(f23(f932(x38831,a923)),f234(f932(x38831,a923))),x38832),f319(f73(f932(x38831,a923)),x38832))
% 28.25/28.11 [3884]E(f319(f319(f23(a1),f319(f95(a1),x38841)),f319(f95(a1),x38842)),f319(f95(a1),f319(f319(f74(a1),x38841),f319(f73(a1),x38842))))
% 28.25/28.11 [3897]E(f319(f164(a925),f131(a925,f319(f294(a925,x38971),f319(a104,x38972)))),f295(a925,x38971,x38972))
% 28.25/28.11 [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)))
% 28.25/28.11 [3932]E(f319(f319(f175(f931(x39321,x39321),a923),f2(a925)),x39322),f299(x39321,f180(f932(f931(x39321,x39321),a923))))
% 28.25/28.11 [3936]P1(f319(f129(a925),f131(a925,f319(f294(a925,x39361),x39362))))
% 28.25/28.11 [3952]E(f319(f302(a1,a925,a96),f295(a1,f319(f92(a1),x39521),f319(f92(a1),x39522))),f295(a925,x39521,x39522))
% 28.25/28.11 [3961]E(f177(a925,f2(a925),f5(a925),f319(f319(f23(a925),x39611),x39612)),f319(f319(f23(a925),x39611),f319(a104,x39612)))
% 28.25/28.11 [3962]E(f319(a96,f319(f319(f23(a1),x39621),f319(f319(f74(a1),x39622),f72(a1)))),f319(f29(a1),f298(a1,x39622,x39621)))
% 28.25/28.11 [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))))
% 28.25/28.11 [4005]E(f319(f164(a1),f170(f319(f319(f74(a1),x40051),f72(a1)),f319(f319(f23(a1),x40052),f72(a1)))),f298(a1,x40051,x40052))
% 28.25/28.11 [4017]P1(f319(f319(f226(f932(x40171,a923)),f180(f932(x40171,a923))),x40172))
% 28.25/28.11 [4021]E(f79(x40211,f319(f319(f7(x40211,x40211,a923),a316),x40212)),x40212)
% 28.25/28.11 [4022]E(f84(x40221,f319(f319(f7(x40221,x40221,a923),a316),x40222)),x40222)
% 28.25/28.11 [4026]E(f319(f164(a925),f131(a925,f319(f294(a925,f319(a104,x40261)),f319(a104,x40262)))),f297(a925,x40261,x40262))
% 28.25/28.11 [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)))
% 28.25/28.11 [4085]E(f319(f254(x40851),f319(f319(f8(a923,a923,x40851),a314),x40852)),f319(f73(f932(x40851,a923)),f319(f254(x40851),x40852)))
% 28.25/28.11 [4088]E(f319(f254(x40881),f319(f319(f7(x40881,x40881,a923),a316),x40882)),f319(f319(f301(x40881),x40882),f180(f932(x40881,a923))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4112]P1(f319(f319(f226(a925),f319(f29(x41121),f319(f164(x41121),x41122))),f319(f181(f926(x41121)),x41122)))
% 28.25/28.11 [4113]P1(f319(f319(f226(a925),f319(f181(f926(x41131)),f144(x41131,x41132))),f319(f181(f926(x41131)),x41132)))
% 28.25/28.11 [4123]E(f319(f254(x41231),f319(f319(f7(x41231,f932(x41231,a923),a923),f321(x41231)),x41232)),x41232)
% 28.25/28.11 [4137]E(f319(f319(f167(x41371),f319(f319(f23(a925),f319(f181(f926(x41371)),x41372)),f72(a925))),x41372),f106(x41371,x41372))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [4188]P1(f319(f319(f226(f932(f932(x41881,a923),a923)),x41882),f319(f300(x41881),f31(f932(x41881,a923),x41882))))
% 28.25/28.11 [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)
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [4772]~P1(f319(f319(f227(a1),f319(f92(a1),x47721)),f319(f73(a1),f319(f92(a1),x47722))))
% 28.25/28.11 [3762]E(f319(f319(f23(a925),f319(f319(f74(a925),x37621),x37622)),x37622),x37621)
% 28.25/28.11 [3763]E(f319(f319(f23(a925),f319(f319(f74(a925),x37631),x37632)),x37631),x37632)
% 28.25/28.11 [3827]E(f319(f319(f74(a925),f319(f319(f23(a925),x38271),x38272)),x38272),f319(f319(f225(a925),x38271),x38272))
% 28.25/28.11 [3939]E(f319(f319(f75(a925),f319(f319(f30(a925),x39391),x39392)),x39392),f319(f319(f23(a925),x39391),f39(a925,x39391,x39392)))
% 28.25/28.11 [3966]E(f319(f164(a925),f131(a925,f319(f294(a925,f319(a104,x39661)),x39662))),f298(a925,x39661,x39662))
% 28.25/28.11 [3974]E(f319(f92(a1),f208(f319(a96,f319(f69(a1),x39741)),f319(a96,f319(f69(a1),x39742)))),f319(f319(a209,x39741),x39742))
% 28.25/28.11 [3976]E(f319(f319(f102(f932(x39761,a923)),f319(f73(f932(x39761,a923)),x39762)),x39762),f234(f932(x39761,a923)))
% 28.25/28.11 [3977]E(f319(f319(f93(f932(x39771,a923)),f319(f73(f932(x39771,a923)),x39772)),x39772),f180(f932(x39771,a923)))
% 28.25/28.11 [3993]P1(f319(f319(f226(a925),f319(f319(f23(a925),x39931),x39932)),x39931))
% 28.25/28.11 [3994]P1(f319(f319(f226(a925),f319(f319(f30(a925),x39941),x39942)),x39941))
% 28.25/28.11 [4018]P1(f319(f319(f227(a925),x40181),f319(a104,f319(f319(f74(a925),x40182),x40181))))
% 28.25/28.11 [4019]P1(f319(f319(f227(a925),x40191),f319(a104,f319(f319(f74(a925),x40191),x40192))))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))
% 28.25/28.11 [4048]P1(f319(f319(f226(a1),f2(a1)),f319(f319(f236(a1),f319(f69(a1),x40481)),x40482)))
% 28.25/28.11 [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))))
% 28.25/28.11 [4135]E(f319(f319(f102(f932(f931(x41351,x41351),a923)),f299(x41351,x41352)),f299(x41351,f180(f932(f931(x41351,x41351),a923)))),f299(x41351,x41352))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [4265]P58(x42651,f319(f319(f23(f932(f931(x42651,x42651),a923)),x42652),f299(x42651,f180(f932(f931(x42651,x42651),a923)))))
% 28.25/28.11 [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)))
% 28.25/28.11 [4287]P57(x42871,f234(f932(x42871,a923)),f319(f319(f102(f932(f931(x42871,x42871),a923)),x42872),f299(x42871,f180(f932(f931(x42871,x42871),a923)))))
% 28.25/28.11 [4326]P1(f319(f319(f321(f931(x43261,x43261)),f319(f319(f244(x43261,x43261),x43262),x43262)),f299(x43261,f180(f932(f931(x43261,x43261),a923)))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))))
% 28.25/28.11 [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))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [4769]~E(f319(f319(f74(a1),x47691),x47691),f319(f319(f23(a1),f319(f319(f74(a1),x47692),x47692)),a89))
% 28.25/28.11 [4770]~E(f319(f319(f74(a1),x47701),x47701),f319(f319(f23(a1),f319(f319(f74(a1),x47702),x47702)),a89))
% 28.25/28.11 [4774]~P1(f319(f319(f227(a925),f319(f319(f74(a925),x47741),x47742)),x47742))
% 28.25/28.11 [4775]~P1(f319(f319(f227(a925),f319(f319(f74(a925),x47751),x47752)),x47751))
% 28.25/28.11 [4053]E(f319(f319(f23(a925),x40531),f319(f319(f75(a925),f319(f319(f30(a925),x40531),x40532)),x40532)),f39(a925,x40531,x40532))
% 28.25/28.11 [4054]E(f319(f319(f23(a1),x40541),f319(f319(f75(a1),f319(f319(f30(a1),x40541),x40542)),x40542)),f39(a1,x40541,x40542))
% 28.25/28.11 [4086]E(f319(f319(f146(a925,x40861),f319(f156(x40861),x40862)),f131(a925,f319(f294(a925,f2(a925)),f319(f181(f926(x40861)),x40862)))),x40862)
% 28.25/28.11 [4143]E(f319(f277(x41431,x41431,f299(x41431,f180(f932(f931(x41431,x41431),a923)))),x41432),x41432)
% 28.25/28.11 [4268]E(f299(x42681,f319(f319(f102(f932(f931(x42681,x42681),a923)),x42682),f299(x42681,f180(f932(f931(x42681,x42681),a923))))),f299(x42681,x42682))
% 28.25/28.11 [4269]E(f299(x42691,f319(f319(f23(f932(f931(x42691,x42691),a923)),x42692),f299(x42691,f180(f932(f931(x42691,x42691),a923))))),f299(x42691,x42692))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))))))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))))
% 28.25/28.11 [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)))))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [4736]~E(f118(x47361,x47362,x47363),f111(x47361))
% 28.25/28.11 [4737]~E(f118(x47371,x47372,x47373),f111(x47371))
% 28.25/28.11 [3490]E(f319(f184(x34901,x34902),x34903),f113(x34901,x34902))
% 28.25/28.11 [3509]E(f319(f191(x35091,x35092),x35093),f319(f121(x35091),x35092))
% 28.25/28.11 [3585]E(f319(f319(f146(x35851,x35852),x35853),f105(x35851)),f105(x35852))
% 28.25/28.11 [3624]E(f319(f176(x36241,x36242,x36243),f2(a925)),x36242)
% 28.25/28.11 [3626]E(f319(f319(f173(x36261,x36262),x36263),f105(x36262)),f105(f931(x36261,x36262)))
% 28.25/28.11 [3641]E(f319(f181(f926(x36411)),f161(x36411,x36412,x36413)),x36412)
% 28.25/28.11 [3660]E(f79(x36601,f56(x36601,x36602,x36603)),f319(f57(x36601,x36602),x36603))
% 28.25/28.11 [3664]E(f235(x36641,x36642,f235(x36642,x36641,x36643)),x36643)
% 28.25/28.11 [3684]E(f319(f160(x36841),f161(x36841,x36842,x36843)),f161(x36841,x36842,x36843))
% 28.25/28.11 [3709]E(f132(x37091,x37092,f144(x37091,x37093)),f144(x37091,f132(x37091,x37092,x37093)))
% 28.25/28.11 [3728]E(f319(f243(f926(x37281),f926(x37281)),f158(x37281,x37282,x37283)),f319(f128(x37281,x37282),x37283))
% 28.25/28.11 [3771]E(f319(f319(f143(x37711),x37712),f161(x37711,x37713,x37712)),f161(x37711,f319(a104,x37713),x37712))
% 28.25/28.11 [3803]E(f177(x38031,x38032,x38033,f2(a925)),x38032)
% 28.25/28.11 [3804]E(f17(x38041,x38042,x38043,f2(a91)),x38042)
% 28.25/28.11 [3805]E(f19(x38051,x38052,x38053,f2(a91)),x38052)
% 28.25/28.11 [3812]E(f155(x38121,x38122,x38123,f105(x38121)),f105(x38122))
% 28.25/28.11 [3813]E(f122(x38131,x38132,x38133,f111(x38131)),f111(x38132))
% 28.25/28.11 [3819]E(f319(f319(f156(x38191),f319(f319(f143(x38191),x38192),x38193)),f2(a925)),x38192)
% 28.25/28.11 [3847]E(f53(x38471,x38472,f105(x38471),x38473),f105(f931(x38471,x38472)))
% 28.25/28.11 [3867]P26(x38671,x38672,x38673,f180(f932(x38671,a923)))
% 28.25/28.11 [3970]E(f257(x39701,x39702,x39703),f319(f244(f932(a91,f932(a923,f929(f927(x39701)))),f931(a91,a91)),f35(x39701)))
% 28.25/28.11 [4027]E(f319(f66(x40271,x40272,x40271,x40273),f25(x40271)),x40273)
% 28.25/28.11 [4202]P1(f319(f319(f321(f931(x42021,x42021)),f319(f319(f244(x42021,x42021),x42022),x42022)),f299(x42021,x42023)))
% 28.25/28.11 [4779]~P1(f319(f319(f321(f931(f926(x47791),f926(x47791))),f319(f319(f244(f926(x47791),f926(x47791)),x47792),f105(x47791))),f137(x47791,x47793)))
% 28.25/28.11 [4780]~P1(f319(f319(f321(f931(f926(x47801),f926(x47801))),f319(f319(f244(f926(x47801),f926(x47801)),x47802),f105(x47801))),f139(x47801,x47803)))
% 28.25/28.11 [4781]~P1(f319(f319(f321(f931(f926(x47811),f926(x47811))),f319(f319(f244(f926(x47811),f926(x47811)),x47812),f105(x47811))),f149(x47811,x47813)))
% 28.25/28.11 [4782]~P1(f319(f319(f321(f931(f926(x47821),f926(x47821))),f319(f319(f244(f926(x47821),f926(x47821)),f105(x47821)),x47822)),f137(x47821,x47823)))
% 28.25/28.11 [4783]~P1(f319(f319(f321(f931(f926(x47831),f926(x47831))),f319(f319(f244(f926(x47831),f926(x47831)),f105(x47831)),x47832)),f149(x47831,x47833)))
% 28.25/28.11 [3560]E(f319(f319(f193(x35601),x35602),x35603),f194(x35601,f207(x35602,x35603)))
% 28.25/28.11 [3613]E(f319(f278(x36131,x36132),f319(f278(x36132,x36131),x36133)),x36133)
% 28.25/28.11 [3636]E(f319(f319(f173(x36361,x36362),f105(x36361)),x36363),f105(f931(x36361,x36362)))
% 28.25/28.11 [3639]E(f168(x36391,x36392,f319(f274(a925),x36393)),f319(f319(f167(x36391),x36393),x36392))
% 28.25/28.11 [3655]E(f319(f256(x36551,x36552),f319(f278(x36552,x36551),x36553)),f319(f276(x36552,x36551),x36553))
% 28.25/28.11 [3657]E(f144(x36571,f319(f128(x36571,x36572),x36573)),f319(f128(x36571,x36572),f144(x36571,x36573)))
% 28.25/28.11 [3658]E(f319(f276(x36581,x36582),f319(f278(x36582,x36581),x36583)),f319(f256(x36582,x36581),x36583))
% 28.25/28.11 [3659]E(f319(f256(x36591,x36592),f319(f278(x36592,x36591),x36593)),f319(f276(x36592,x36591),x36593))
% 28.25/28.11 [3677]E(f319(f128(x36771,x36772),f319(f160(x36771),x36773)),f319(f160(x36771),f319(f128(x36771,x36772),x36773)))
% 28.25/28.11 [3689]E(f319(f319(f130(x36891),x36892),f319(f163(x36891),x36893)),f319(f319(f130(x36891),f319(a104,x36892)),x36893))
% 28.25/28.11 [3705]E(f319(f302(x37051,x37052,x37053),f180(f932(x37051,a923))),f180(f932(x37052,a923)))
% 28.25/28.11 [3706]E(f319(f303(x37061,x37062,x37063),f234(f932(x37062,a923))),f234(f932(x37061,a923)))
% 28.25/28.11 [3707]E(f319(f303(x37071,x37072,x37073),f180(f932(x37072,a923))),f180(f932(x37071,a923)))
% 28.25/28.11 [3708]E(f319(f277(x37081,x37082,x37083),f180(f932(x37081,a923))),f180(f932(x37082,a923)))
% 28.25/28.11 [3734]E(f112(x37341,f118(f927(x37341),x37342,x37343)),f108(x37341,x37342,f112(x37341,x37343)))
% 28.25/28.11 [3735]E(f165(x37351,f319(f319(f143(x37351),x37352),x37353),f105(x37351)),f319(f319(f143(x37351),x37352),x37353))
% 28.25/28.11 [3736]E(f319(f319(f301(x37361),x37362),f319(f164(x37361),x37363)),f319(f164(x37361),f132(x37361,x37362,x37363)))
% 28.25/28.11 [3823]E(f319(f302(f931(x38231,x38232),x38232,f248(x38231,x38232)),x38233),f319(f276(x38231,x38232),x38233))
% 28.25/28.11 [3824]E(f319(f302(f931(x38241,x38242),x38241,f243(x38241,x38242)),x38243),f319(f256(x38241,x38242),x38243))
% 28.25/28.11 [3839]E(f319(f164(x38391),f161(x38391,f319(a104,x38392),x38393)),f319(f319(f301(x38391),x38393),f180(f932(x38391,a923))))
% 28.25/28.11 [3895]E(f319(f319(f244(x38951,x38952),f319(f243(x38951,x38952),x38953)),f319(f248(x38951,x38952),x38953)),x38953)
% 28.25/28.11 [3896]E(f319(f319(f244(x38961,x38962),f319(f243(x38961,x38962),x38963)),f319(f248(x38961,x38962),x38963)),x38963)
% 28.25/28.11 [3904]E(f319(f181(f927(x39041)),f118(x39041,x39042,x39043)),f319(f319(f74(a925),f319(f181(f927(x39041)),x39043)),f319(a104,f2(a925))))
% 28.25/28.11 [3906]E(f319(f319(f249(x39061,x39062,x39061),f16(x39061,x39062)),x39063),f319(f243(x39061,x39062),x39063))
% 28.25/28.11 [4032]E(f319(f66(x40321,x40321,x40322,f25(x40321)),x40323),x40323)
% 28.25/28.11 [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)))
% 28.25/28.11 [4211]P1(f319(f319(f226(f932(x42111,a923)),f319(f164(x42111),f319(f128(x42111,x42112),x42113))),f319(f164(x42111),x42113)))
% 28.25/28.11 [4254]P1(f319(f319(f226(f932(x42541,a923)),f319(f164(x42541),f319(f319(f167(x42541),x42542),x42543))),f319(f164(x42541),x42543)))
% 28.25/28.11 [4255]P1(f319(f319(f226(f932(x42551,a923)),f319(f164(x42551),f319(f319(f130(x42551),x42552),x42553))),f319(f164(x42551),x42553)))
% 28.25/28.11 [4259]P1(f319(f319(f226(f932(x42591,a923)),f319(f164(x42591),f168(x42591,x42592,x42593))),f319(f164(x42591),x42592)))
% 28.25/28.11 [4260]P1(f319(f319(f226(f932(x42601,a923)),f319(f164(x42601),f162(x42601,x42602,x42603))),f319(f164(x42601),x42603)))
% 28.25/28.11 [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)
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [4336]P1(f319(f319(f321(f931(f926(x43361),f926(x43361))),f319(f319(f244(f926(x43361),f926(x43361)),x43362),x43362)),f150(x43361,f299(x43361,x43363))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [4571]E(f319(f250(x45711,x45711,x45712,x45712,f5(x45711),f5(x45712)),x45713),x45713)
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [4731]~E(f319(f319(f143(x47311),x47312),x47313),x47313)
% 28.25/28.11 [4732]~E(f319(f319(f143(x47321),x47322),x47323),x47323)
% 28.25/28.11 [4734]~E(f319(f319(f143(x47341),x47342),x47343),f105(x47341))
% 28.25/28.11 [4735]~E(f319(f319(f143(x47351),x47352),x47353),f105(x47351))
% 28.25/28.11 [4740]~E(f319(f319(f301(x47401),x47402),x47403),f180(f932(x47401,a923)))
% 28.25/28.11 [4741]~E(f319(f319(f301(x47411),x47412),x47413),f180(f932(x47411,a923)))
% 28.25/28.11 [4761]~E(f319(f302(x47611,f932(x47611,a923),x47612),x47613),f319(f300(x47611),x47613))
% 28.25/28.11 [3617]E(f319(f319(f151(x36171,f105(x36171)),x36172),x36173),f105(x36171))
% 28.25/28.11 [3618]E(f319(f319(f151(x36181,f105(x36181)),x36182),x36183),f105(x36181))
% 28.25/28.11 [3619]E(f319(f133(x36191),f319(f319(f143(x36191),x36192),x36193)),x36192)
% 28.25/28.11 [3620]E(f319(f163(x36201),f319(f319(f143(x36201),x36202),x36203)),x36203)
% 28.25/28.11 [3663]E(f319(f319(f130(x36631),f72(a925)),f319(f319(f143(x36631),x36632),x36633)),x36633)
% 28.25/28.11 [3695]E(f106(x36951,f319(f319(f130(x36951),x36952),x36953)),f319(f319(f130(x36951),x36952),f106(x36951,x36953)))
% 28.25/28.11 [3696]E(f106(x36961,f319(f319(f130(x36961),x36962),x36963)),f319(f319(f130(x36961),x36962),f106(x36961,x36963)))
% 28.25/28.11 [3698]E(f319(f319(f151(x36981,x36982),x36983),f319(f319(f156(x36981),x36982),x36983)),x36982)
% 28.25/28.11 [3718]E(f319(f319(f301(x37181),x37182),f319(f319(f301(x37181),x37182),x37183)),f319(f319(f301(x37181),x37182),x37183))
% 28.25/28.11 [3731]E(f319(f319(f301(x37311),x37312),f319(f164(x37311),x37313)),f319(f164(x37311),f319(f319(f143(x37311),x37312),x37313)))
% 28.25/28.11 [3732]E(f319(f319(f130(x37321),x37322),f319(f163(x37321),x37323)),f319(f163(x37321),f319(f319(f130(x37321),x37322),x37323)))
% 28.25/28.11 [3733]E(f319(f319(f130(x37331),x37332),f319(f163(x37331),x37333)),f319(f163(x37331),f319(f319(f130(x37331),x37332),x37333)))
% 28.25/28.11 [3745]E(f319(f319(f167(x37451),f72(a925)),f319(f319(f143(x37451),x37452),x37453)),f319(f319(f143(x37451),x37452),f105(x37451)))
% 28.25/28.11 [3788]E(f319(f57(x37881,x37882),f319(f319(f301(x37881),x37883),f180(f932(x37881,a923)))),x37883)
% 28.25/28.11 [3829]E(f319(f319(f74(a925),x38291),f319(f319(f74(a925),x38292),x38293)),f319(f319(f74(a925),x38292),f319(f319(f74(a925),x38291),x38293)))
% 28.25/28.11 [3830]E(f319(f319(f74(a1),x38301),f319(f319(f74(a1),x38302),x38303)),f319(f319(f74(a1),x38302),f319(f319(f74(a1),x38301),x38303)))
% 28.25/28.11 [3835]E(f319(f319(f246(x38351,x38352),f180(f932(x38351,a923))),x38353),f180(f932(f931(x38351,x38352),a923)))
% 28.25/28.11 [3859]E(f319(f319(f102(f932(x38591,a923)),x38592),x38593),f319(f319(f102(f932(x38591,a923)),x38593),x38592))
% 28.25/28.11 [3860]E(f319(f319(f93(f932(x38601,a923)),x38602),x38603),f319(f319(f93(f932(x38601,a923)),x38603),x38602))
% 28.25/28.11 [3862]E(f319(f319(f126(x38621),x38622),f319(f319(f143(x38621),x38623),f105(x38621))),f319(f159(x38621),f319(f319(f143(x38621),x38623),x38622)))
% 28.25/28.11 [3863]E(f319(f319(f126(x38631),f319(f160(x38631),x38632)),f319(f160(x38631),x38633)),f319(f160(x38631),f319(f319(f126(x38631),x38633),x38632)))
% 28.25/28.11 [3873]E(f319(f163(x38731),f319(f319(f167(x38731),f319(a104,x38732)),x38733)),f319(f319(f167(x38731),x38732),f319(f163(x38731),x38733)))
% 28.25/28.11 [3881]P1(f319(f319(f321(x38811),x38812),f319(f319(f301(x38811),x38812),x38813)))
% 28.25/28.11 [3885]E(f319(f319(f34(x38851,f932(x38852,a923)),f180(f932(x38851,a923))),x38853),f234(f932(x38852,a923)))
% 28.25/28.11 [3888]E(f319(f277(x38881,x38881,f255(x38881,x38882)),x38883),f319(f319(f93(f932(x38881,a923)),x38882),x38883))
% 28.25/28.11 [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))))
% 28.25/28.11 [3908]E(f106(x39081,f319(f319(f126(x39081),x39082),f319(f319(f143(x39081),x39083),f105(x39081)))),x39082)
% 28.25/28.11 [3909]E(f136(x39091,f319(f319(f126(x39091),x39092),f319(f319(f143(x39091),x39093),f105(x39091)))),x39093)
% 28.25/28.11 [3917]E(f319(f319(f126(x39171),f319(f319(f167(x39171),x39172),x39173)),f319(f319(f130(x39171),x39172),x39173)),x39173)
% 28.25/28.11 [3926]E(f319(f319(f23(a925),f319(f319(f74(a925),x39261),x39262)),f319(f319(f74(a925),x39263),x39262)),f319(f319(f23(a925),x39261),x39263))
% 28.25/28.11 [3927]E(f319(f319(f23(a925),f319(f319(f74(a925),x39271),x39272)),f319(f319(f74(a925),x39271),x39273)),f319(f319(f23(a925),x39272),x39273))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [3938]E(f319(f319(f74(a925),f319(f181(f926(x39381)),x39382)),f319(f181(f926(x39381)),x39383)),f319(f181(f926(x39381)),f165(x39381,x39382,x39383)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [3963]E(f319(f319(f93(f932(x39631,a923)),x39632),f319(f73(f932(x39631,a923)),x39633)),f319(f319(f23(f932(x39631,a923)),x39632),x39633))
% 28.25/28.11 [3964]E(f319(f319(f23(f932(x39641,a923)),x39642),f319(f73(f932(x39641,a923)),x39643)),f319(f319(f93(f932(x39641,a923)),x39642),x39643))
% 28.25/28.11 [3986]E(f319(f319(f246(x39861,x39862),x39863),f319(f16(f932(x39862,a923),x39861),f180(f932(x39862,a923)))),f180(f932(f931(x39861,x39862),a923)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4006]E(f319(f319(f33(x40061,f932(x40062,a923)),x40063),f319(f16(f932(x40062,a923),x40061),f180(f932(x40062,a923)))),f180(f932(x40062,a923)))
% 28.25/28.11 [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))
% 28.25/28.11 [4012]E(f39(a1,f319(f319(f75(a1),x40121),f39(a1,x40122,x40123)),x40123),f39(a1,f319(f319(f75(a1),x40121),x40122),x40123))
% 28.25/28.11 [4013]E(f39(a1,f319(f319(f23(a1),x40131),f39(a1,x40132,x40133)),x40133),f39(a1,f319(f319(f23(a1),x40131),x40132),x40133))
% 28.25/28.11 [4014]E(f39(a1,f319(f319(f75(a1),x40141),f39(a1,x40142,x40143)),x40143),f39(a1,f319(f319(f75(a1),x40141),x40142),x40143))
% 28.25/28.11 [4015]P1(f319(f319(f226(f932(x40151,a923)),x40152),f319(f319(f301(x40151),x40153),x40152)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4103]E(f319(f164(x41031),f319(f319(f319(f175(f926(x41031),f926(x41031)),x41032),f159(x41031)),x41033)),f319(f164(x41031),x41033))
% 28.25/28.11 [4107]E(f319(f319(f167(x41071),f319(f181(f926(x41071)),f169(x41071,x41072,x41073))),x41073),f169(x41071,x41072,x41073))
% 28.25/28.11 [4111]E(f319(f181(f926(x41111)),f319(f319(f319(f175(f926(x41111),f926(x41111)),x41112),f159(x41111)),x41113)),f319(f181(f926(x41111)),x41113))
% 28.25/28.11 [4114]E(f319(f319(f249(x41141,x41142,x41142),f319(f16(f932(x41142,x41142),x41141),f5(x41142))),x41143),f319(f248(x41141,x41142),x41143))
% 28.25/28.11 [4120]E(f39(a1,f319(f319(f23(a1),f39(a1,x41201,x41202)),x41203),x41202),f39(a1,f319(f319(f23(a1),x41201),x41203),x41202))
% 28.25/28.11 [4121]E(f39(a1,f319(f319(f236(a1),f39(a1,x41211,x41212)),x41213),x41212),f39(a1,f319(f319(f236(a1),x41211),x41213),x41212))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4148]E(f319(f66(x41481,x41481,x41481,x41482),f319(f319(f175(x41481,x41481),x41483),x41482)),f319(f319(f175(x41481,x41481),f319(a104,x41483)),x41482))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [4203]P1(f319(f319(f226(a925),f319(f181(f926(x42031)),f319(f128(x42031,x42032),x42033))),f319(f181(f926(x42031)),x42033)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4251]P1(f319(f319(f226(a925),f319(f181(f926(x42511)),f169(x42511,x42512,x42513))),f319(f181(f926(x42511)),x42513)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [4382]E(f319(f248(f926(x43821),f926(x43821)),f158(x43821,x43822,x43823)),f319(f128(x43821,f319(f66(a923,a923,x43821,a314),x43822)),x43823))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4773]~P1(f319(f56(x47731,x47732,f180(f932(x47731,a923))),x47733))
% 28.25/28.11 [4778]~P1(f319(f319(f321(f931(x47781,x47781)),f319(f319(f244(x47781,x47781),x47782),x47783)),f145(x47781,f105(f932(x47781,a925)))))
% 28.25/28.11 [3874]E(f319(f181(f926(x38741)),f319(f319(f167(x38741),x38742),x38743)),f319(f319(f224(a925),f319(f181(f926(x38741)),x38743)),x38742))
% 28.25/28.11 [3875]E(f319(f181(f926(x38751)),f319(f319(f130(x38751),x38752),x38753)),f319(f319(f23(a925),f319(f181(f926(x38751)),x38753)),x38752))
% 28.25/28.11 [3902]E(f319(f181(f926(f926(x39021))),f49(x39021,x39022,x39023)),f319(f319(f236(a925),f319(f181(f926(x39021)),x39023)),x39022))
% 28.25/28.11 [3919]E(f319(f319(f30(a925),f319(f319(f30(a925),x39191),x39192)),x39193),f319(f319(f30(a925),x39191),f319(f319(f75(a925),x39192),x39193)))
% 28.25/28.11 [3920]E(f319(f319(f23(a925),f319(f319(f23(a925),x39201),x39202)),x39203),f319(f319(f23(a925),x39201),f319(f319(f74(a925),x39202),x39203)))
% 28.25/28.11 [3921]E(f319(f319(f75(a925),f319(f319(f75(a925),x39211),x39212)),x39213),f319(f319(f75(a925),x39211),f319(f319(f75(a925),x39212),x39213)))
% 28.25/28.11 [3922]E(f319(f319(f75(a1),f319(f319(f75(a1),x39221),x39222)),x39223),f319(f319(f75(a1),x39221),f319(f319(f75(a1),x39222),x39223)))
% 28.25/28.11 [3923]E(f319(f319(f74(a925),f319(f319(f74(a925),x39231),x39232)),x39233),f319(f319(f74(a925),x39231),f319(f319(f74(a925),x39232),x39233)))
% 28.25/28.11 [3924]E(f319(f319(f74(a1),f319(f319(f74(a1),x39241),x39242)),x39243),f319(f319(f74(a1),x39241),f319(f319(f74(a1),x39242),x39243)))
% 28.25/28.11 [3925]E(f319(f319(f236(a1),f319(f319(f236(a1),x39251),x39252)),x39253),f319(f319(f236(a1),x39251),f319(f319(f75(a925),x39252),x39253)))
% 28.25/28.11 [3944]E(f154(x39441,f319(f319(f143(f932(x39441,a923)),x39442),x39443)),f166(x39441,x39442,f154(x39441,x39443)))
% 28.25/28.11 [3987]E(f319(f319(f23(a925),f319(f319(f23(a925),x39871),x39872)),x39873),f319(f319(f23(a925),f319(f319(f23(a925),x39871),x39873)),x39872))
% 28.25/28.11 [3995]E(f319(f319(f93(f932(x39951,a923)),x39952),f319(f319(f23(f932(x39951,a923)),x39953),x39952)),f180(f932(x39951,a923)))
% 28.25/28.11 [3999]E(f319(f319(f146(a925,x39991),f319(f16(x39991,a925),x39992)),f131(a925,f319(f294(a925,f2(a925)),x39993))),f161(x39991,x39993,x39992))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4040]E(f161(x40401,f319(f181(f926(x40401)),f319(f128(x40401,f319(a316,x40402)),x40403)),x40402),f319(f128(x40401,f319(a316,x40402)),x40403))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [4084]E(f319(f319(f281(x40841,x40842,x40842),x40843),f299(x40842,f180(f932(f931(x40842,x40842),a923)))),x40843)
% 28.25/28.11 [4087]E(f319(f319(f102(f932(x40871,a923)),f319(f319(f301(x40871),x40872),f180(f932(x40871,a923)))),x40873),f319(f319(f301(x40871),x40872),x40873))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [4155]P1(f319(f319(f226(f932(x41551,a923)),x41552),f319(f319(f102(f932(x41551,a923)),x41553),x41552)))
% 28.25/28.11 [4156]P1(f319(f319(f226(f932(x41561,a923)),x41562),f319(f319(f102(f932(x41561,a923)),x41562),x41563)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4175]P1(f319(f319(f226(f932(x41751,a923)),f319(f164(x41751),x41752)),f319(f164(x41751),f319(f319(f143(x41751),x41753),x41752))))
% 28.25/28.11 [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)
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4286]E(f319(f319(f126(x42861),f169(x42861,x42862,x42863)),f319(f319(f130(x42861),f319(f181(f926(x42861)),f169(x42861,x42862,x42863))),x42863)),x42863)
% 28.25/28.11 [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)))))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [4060]E(f39(a925,f319(f319(f74(a925),f319(f319(f75(a925),x40601),x40602)),x40603),x40602),f39(a925,x40603,x40602))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [4176]E(f319(f319(f281(x41761,x41761,x41762),f299(x41761,f180(f932(f931(x41761,x41761),a923)))),x41763),x41763)
% 28.25/28.11 [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)))
% 28.25/28.11 [4194]E(f258(x41941,f319(f319(f143(f931(a91,x41941)),f319(f319(f244(a91,x41941),f2(a91)),x41942)),x41943)),f258(x41941,x41943))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [4278]P1(f319(f319(f226(f932(x42781,a923)),f319(f319(f93(f932(x42781,a923)),x42782),x42783)),x42783))
% 28.25/28.11 [4279]P1(f319(f319(f226(f932(x42791,a923)),f319(f319(f93(f932(x42791,a923)),x42792),x42793)),x42792))
% 28.25/28.11 [4280]P1(f319(f319(f226(f932(x42801,a923)),f319(f319(f23(f932(x42801,a923)),x42802),x42803)),x42802))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))))
% 28.25/28.11 [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)))
% 28.25/28.11 [4198]E(f39(a925,f319(a104,f319(f319(f74(a925),f319(f319(f75(a925),x41981),x41982)),x41983)),x41982),f39(a925,f319(a104,x41983),x41982))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [3761]E(f108(x37611,f319(x37612,x37613),f319(x37614,x37613)),f319(f195(x37611,x37612,x37614),x37613))
% 28.25/28.11 [3814]E(f319(f319(f237(x38141,x38142,x38143),x38144),f2(a925)),x38142)
% 28.25/28.11 [3852]E(f177(x38521,x38522,x38523,f319(a104,x38524)),f319(x38523,x38524))
% 28.25/28.11 [3893]E(f162(x38931,x38932,f162(x38931,x38933,x38934)),f162(x38931,x38933,f162(x38931,x38932,x38934)))
% 28.25/28.11 [3894]E(f118(x38941,x38942,f108(x38941,x38943,x38944)),f108(x38941,f118(x38941,x38942,x38943),x38944))
% 28.25/28.11 [4028]E(f319(f148(x40281,x40282,x40283,x40284),f105(x40282)),x40283)
% 28.25/28.11 [4029]E(f319(f134(x40291,x40292,x40293,x40294),f105(x40292)),x40294)
% 28.25/28.11 [4066]E(f319(f181(f930(x40661,x40662)),f212(x40661,x40662,x40663,x40664)),f2(a925))
% 28.25/28.11 [4089]E(f319(f249(x40891,x40892,x40893),f247(x40891,x40892,x40893,x40894)),x40894)
% 28.25/28.11 [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)))
% 28.25/28.11 [4217]E(f319(f319(f251(x42171,x42172,x42173,f931(x42172,x42173)),x42174),f244(x42172,x42173)),x42174)
% 28.25/28.11 [4227]E(f119(x42271,x42272,x42273,x42274,f111(x42272)),x42273)
% 28.25/28.11 [4233]E(f68(x42331,x42332,x42333,x42334,f319(x42333,x42334)),x42333)
% 28.25/28.11 [4499]P44(x44991,x44992,x44993,x44994,f180(f932(x44991,a923)),x44994)
% 28.25/28.11 [4500]P44(x45001,x45002,x45003,x45004,f180(f932(x45001,a923)),x45004)
% 28.25/28.11 [3566]E(f319(f319(f16(x35661,x35662),x35663),x35664),x35663)
% 28.25/28.11 [3842]E(f162(x38421,x38422,f319(f128(x38421,x38423),x38424)),f319(f128(x38421,x38423),f162(x38421,x38422,x38424)))
% 28.25/28.11 [3876]E(f319(f319(f58(x38761,x38762,x38763),x38764),f180(f932(x38761,a923))),x38764)
% 28.25/28.11 [3901]E(f319(f319(f156(x39011),f319(f319(f143(x39011),x39012),x39013)),f319(a104,x39014)),f319(f319(f156(x39011),x39013),x39014))
% 28.25/28.11 [3968]E(f319(f319(x39681,x39682),f319(f176(x39683,x39684,x39681),x39682)),f319(f176(x39683,x39684,x39681),f319(a104,x39682)))
% 28.25/28.11 [4009]E(f247(x40091,x40092,x40093,f319(f249(x40091,x40092,x40093),x40094)),x40094)
% 28.25/28.11 [4064]E(f319(f319(f151(x40641,f319(f319(f143(x40641),x40642),x40643)),f2(a925)),x40644),f319(f319(f143(x40641),x40644),x40643))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4100]E(f112(x41001,f122(x41002,f927(x41001),x41003,x41004)),f319(f110(x41002,x41001,x41004),x41003))
% 28.25/28.11 [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))))
% 28.25/28.11 [4193]E(f319(f134(x41931,x41932,f319(f7(x41932,x41931,x41931),x41933),x41934),f319(f160(x41932),f105(x41932))),x41934)
% 28.25/28.11 [4237]E(f70(x42371,x42372,x42373,x42374,f180(f932(x42371,a923))),x42373)
% 28.25/28.11 [4298]E(f215(x42981,f931(x42982,f927(x42982)),x42983,f319(f249(x42982,f927(x42982),x42981),x42984),f319(f127(x42982),f111(x42982))),x42983)
% 28.25/28.11 [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)
% 28.25/28.11 [3752]E(f319(f248(x37521,x37522),f319(f319(f244(x37521,x37522),x37523),x37524)),x37524)
% 28.25/28.11 [3753]E(f319(f243(x37531,x37532),f319(f319(f244(x37531,x37532),x37533),x37534)),x37533)
% 28.25/28.11 [3786]E(f319(f181(f926(x37861)),f319(f319(f151(x37861,x37862),x37863),x37864)),f319(f181(f926(x37861)),x37862))
% 28.25/28.11 [3787]E(f319(f181(f926(x37871)),f319(f319(f146(x37872,x37871),x37873),x37874)),f319(f181(f926(x37872)),x37874))
% 28.25/28.11 [3808]E(f319(f319(f130(x38081),f319(a104,x38082)),f319(f319(f143(x38081),x38083),x38084)),f319(f319(f130(x38081),x38082),x38084))
% 28.25/28.11 [3871]E(f319(f319(f167(x38711),x38712),f161(x38711,x38713,x38714)),f161(x38711,f319(f319(f224(a925),x38712),x38713),x38714))
% 28.25/28.11 [3872]E(f319(f319(f130(x38721),x38722),f161(x38721,x38723,x38724)),f161(x38721,f319(f319(f23(a925),x38723),x38722),x38724))
% 28.25/28.11 [3878]E(f319(f319(f301(x38781),x38782),f319(f319(f301(x38781),x38783),x38784)),f319(f319(f301(x38781),x38783),f319(f319(f301(x38781),x38782),x38784)))
% 28.25/28.11 [3882]E(f319(f319(f146(x38821,x38822),x38823),f106(x38821,x38824)),f106(x38822,f319(f319(f146(x38821,x38822),x38823),x38824)))
% 28.25/28.11 [3899]E(f319(f160(x38991),f319(f319(f146(x38992,x38991),x38993),x38994)),f319(f319(f146(x38992,x38991),x38993),f319(f160(x38992),x38994)))
% 28.25/28.11 [3900]E(f319(f319(f146(x39001,x39002),x39003),f319(f163(x39001),x39004)),f319(f163(x39002),f319(f319(f146(x39001,x39002),x39003),x39004)))
% 28.25/28.11 [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)))
% 28.25/28.11 [3918]E(f319(f164(x39181),f319(f319(f146(x39182,x39181),x39183),x39184)),f319(f302(x39182,x39181,x39183),f319(f164(x39182),x39184)))
% 28.25/28.11 [3931]E(f319(f319(f146(x39311,x39312),f319(f16(x39312,x39311),x39313)),x39314),f161(x39312,f319(f181(f926(x39311)),x39314),x39313))
% 28.25/28.11 [3967]E(f17(x39671,x39672,x39673,f319(a3,f319(a104,f319(a20,x39674)))),f319(x39673,x39674))
% 28.25/28.11 [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)))
% 28.25/28.11 [3983]E(f144(x39831,f319(f319(f146(x39832,x39831),x39833),f144(x39832,x39834))),f144(x39831,f319(f319(f146(x39832,x39831),x39833),x39834)))
% 28.25/28.11 [3998]E(f319(f278(x39981,x39981),f319(f319(f280(x39982,x39981),x39983),x39984)),f319(f319(f280(x39982,x39981),f319(f278(x39982,x39982),x39983)),x39984))
% 28.25/28.11 [4010]E(f319(f319(f281(x40101,x40102,x40103),x40104),f180(f932(f931(x40102,x40103),a923))),f180(f932(f931(x40101,x40103),a923)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4030]E(f319(f319(f126(x40301),f161(x40301,x40302,x40303)),f161(x40301,x40304,x40303)),f161(x40301,f319(f319(f74(a925),x40302),x40304),x40303))
% 28.25/28.11 [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)))
% 28.25/28.11 [4055]E(f31(f932(x40551,a923),f319(f302(x40552,f932(x40551,a923),x40553),x40554)),f319(f319(f33(x40552,f932(x40551,a923)),x40554),x40553))
% 28.25/28.11 [4056]E(f32(f932(x40561,a923),f319(f302(x40562,f932(x40561,a923),x40563),x40564)),f319(f319(f34(x40562,f932(x40561,a923)),x40564),x40563))
% 28.25/28.11 [4057]E(f32(f932(x40571,a923),f319(f302(x40572,f932(x40571,a923),x40573),x40574)),f319(f319(f34(x40572,f932(x40571,a923)),x40574),x40573))
% 28.25/28.11 [4058]E(f31(f932(x40581,a923),f319(f302(x40582,f932(x40581,a923),x40583),x40584)),f319(f319(f33(x40582,f932(x40581,a923)),x40584),x40583))
% 28.25/28.11 [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)))
% 28.25/28.11 [4061]E(f319(f303(x40611,x40612,x40613),f319(f73(f932(x40612,a923)),x40614)),f319(f73(f932(x40611,a923)),f319(f303(x40611,x40612,x40613),x40614)))
% 28.25/28.11 [4110]E(f319(f303(x41101,x41102,x41103),f319(f254(x41102),x41104)),f319(f254(x41101),f319(f319(f8(x41102,a923,x41101),x41104),x41103)))
% 28.25/28.11 [4127]E(f319(f319(f156(x41271),f319(f319(f126(x41271),x41272),f319(f319(f143(x41271),x41273),x41274))),f319(f181(f926(x41271)),x41272)),x41273)
% 28.25/28.11 [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)))))
% 28.25/28.11 [4168]P1(f319(f319(f321(x41681),f319(x41682,x41683)),f319(f302(x41684,x41681,x41682),f234(f932(x41684,a923)))))
% 28.25/28.11 [4177]E(f19(x41771,x41772,x41773,f319(a3,f319(a104,f319(a20,x41774)))),f319(f319(x41773,x41774),f19(x41771,x41772,x41773,x41774)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))
% 28.25/28.11 [4209]P26(x42091,f931(x42092,x42091),f323(x42093,x42094,x42092,x42091),f319(f319(f33(x42092,f932(x42091,a923)),x42094),x42093))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [4477]P1(f319(f60(x44771,x44772,x44773,x44774,f180(f932(x44771,a923))),x44774))
% 28.25/28.11 [4478]P1(f319(f60(x44781,x44782,x44783,x44784,f180(f932(x44781,a923))),x44784))
% 28.25/28.11 [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))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [3947]E(f319(f319(f167(x39471),x39472),f319(f319(f167(x39471),x39473),x39474)),f319(f319(f167(x39471),f319(f319(f224(a925),x39472),x39473)),x39474))
% 28.25/28.11 [3948]E(f319(f319(f130(x39481),x39482),f319(f319(f130(x39481),x39483),x39484)),f319(f319(f130(x39481),f319(f319(f74(a925),x39482),x39483)),x39484))
% 28.25/28.11 [3959]E(f319(f319(f126(x39591),f319(f319(f143(x39591),x39592),x39593)),x39594),f319(f319(f143(x39591),x39592),f319(f319(f126(x39591),x39593),x39594)))
% 28.25/28.11 [3960]E(f319(f319(f126(x39601),f319(f319(f126(x39601),x39602),x39603)),x39604),f319(f319(f126(x39601),x39602),f319(f319(f126(x39601),x39603),x39604)))
% 28.25/28.11 [4041]E(f319(f319(f156(x40411),f319(f319(f143(x40411),x40412),x40413)),x40414),f177(x40411,x40412,f319(f156(x40411),x40413),x40414))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [4092]E(f319(f319(f319(f175(x40921,x40921),x40922),x40923),f319(x40923,x40924)),f319(x40923,f319(f319(f319(f175(x40921,x40921),x40922),x40923),x40924)))
% 28.25/28.11 [4101]E(f319(f319(f281(x41011,x41012,x41013),f180(f932(f931(x41011,x41012),a923))),x41014),f180(f932(f931(x41011,x41013),a923)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4164]E(f58(x41641,x41642,f319(f319(f8(x41642,f932(x41642,x41642),x41641),x41643),x41644)),f319(f59(x41642,x41641,x41643),x41644))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4439]P1(f319(f319(f226(f932(x44391,a923)),f319(f302(x44392,x44391,x44393),f319(f303(x44392,x44391,x44393),x44394))),x44394))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [4777]~P1(f319(f319(f180(f932(x47771,f932(x47772,a923))),x47773),x47774))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))))
% 28.25/28.11 [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)))))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))))))
% 28.25/28.11 [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))))))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))))))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [3843]E(f319(f319(f146(x38431,x38432),x38433),f161(x38431,x38434,x38435)),f161(x38432,x38434,f319(x38433,x38435)))
% 28.25/28.11 [4174]E(f122(x41741,x41742,x41743,f118(x41741,x41744,x41745)),f118(x41742,f319(x41743,x41744),f122(x41741,x41742,x41743,x41745)))
% 28.25/28.11 [4405]E(f319(f68(x44051,x44052,x44053,x44054,x44055),x44054),x44055)
% 28.25/28.11 [4457]E(f245(x44571,x44572,x44573,f235(x44572,x44571,x44574),f235(x44573,x44572,x44575)),f235(x44573,x44571,f245(x44573,x44572,x44571,x44575,x44574)))
% 28.25/28.11 [4033]E(f319(f319(f249(x40331,x40332,x40333),x40334),x40335),f319(f319(x40334,f319(f243(x40331,x40332),x40335)),f319(f248(x40331,x40332),x40335)))
% 28.25/28.11 [4034]E(f319(f319(f249(x40341,x40342,x40343),x40344),x40345),f319(f319(x40344,f319(f243(x40341,x40342),x40345)),f319(f248(x40341,x40342),x40345)))
% 28.25/28.11 [4035]E(f319(f319(f249(x40351,x40352,x40353),x40354),x40355),f319(f319(x40354,f319(f243(x40351,x40352),x40355)),f319(f248(x40351,x40352),x40355)))
% 28.25/28.11 [4069]E(f319(f319(f319(f59(x40691,x40692,x40693),x40694),x40695),f180(f932(x40692,a923))),x40695)
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4419]E(f79(x44191,f60(x44192,x44191,x44193,x44194,x44195)),f319(f319(f58(x44192,x44191,x44193),x44194),x44195))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4146]E(f319(f319(x41461,x41462),f319(f319(f237(x41463,x41464,x41461),x41462),x41465)),f319(f319(f237(x41463,x41464,x41461),x41462),f319(a104,x41465)))
% 28.25/28.11 [4178]E(f155(x41781,x41782,x41783,f319(f319(f143(x41781),x41784),x41785)),f319(f319(f126(x41782),f319(x41783,x41784)),f155(x41781,x41782,x41783,x41785)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4223]E(f319(f319(f251(x42231,x42232,x42231,x42233),f319(f244(x42232,x42231),x42234)),x42235),f319(x42235,x42234))
% 28.25/28.11 [4247]E(f147(x42471,x42472,f319(f319(f146(x42473,x42471),x42474),x42475)),f147(x42473,f319(f66(x42471,a925,x42473,x42472),x42474),x42475))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))))
% 28.25/28.11 [4614]E(f319(f248(x46141,x46142),f319(f250(x46143,x46141,x46142,x46142,x46144,f25(x46142)),x46145)),f319(f248(x46143,x46142),x46145))
% 28.25/28.11 [4615]E(f319(f243(x46151,x46152),f319(f250(x46151,x46151,x46153,x46152,f25(x46151),x46154),x46155)),f319(f243(x46151,x46153),x46155))
% 28.25/28.11 [4618]E(f319(f243(x46181,x46182),f319(f250(x46183,x46181,x46182,x46182,x46184,f25(x46182)),x46185)),f319(x46184,f319(f243(x46183,x46182),x46185)))
% 28.25/28.11 [4619]E(f319(f248(x46191,x46192),f319(f250(x46191,x46191,x46193,x46192,f25(x46191),x46194),x46195)),f319(x46194,f319(f248(x46191,x46193),x46195)))
% 28.25/28.11 [3815]E(f319(f319(f319(f319(f196(x38151),x38152),x38153),x38154),x38155),f184(x38151,x38152))
% 28.25/28.11 [3816]E(f319(f319(f319(f319(f200(x38161),x38162),x38163),x38164),x38165),f191(x38161,x38162))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [4171]E(f319(f319(f151(x41711,f319(f319(f151(x41711,x41712),x41713),x41714)),x41713),x41715),f319(f319(f151(x41711,x41712),x41713),x41715))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [4329]E(f216(x43291,x43292,x43293,x43294,f212(x43291,x43292,x43295,x43296)),f319(f319(x43294,x43295),x43296))
% 28.25/28.11 [4330]E(f217(x43301,x43302,x43303,x43304,f212(x43301,x43302,x43305,x43306)),f319(f319(x43304,x43305),x43306))
% 28.25/28.11 [4455]E(f119(x44551,x44552,x44553,x44554,f118(x44552,x44555,x44556)),f319(f319(f319(x44554,x44555),x44556),f119(x44551,x44552,x44553,x44554,x44556)))
% 28.25/28.11 [4474]E(f68(x44741,x44742,f68(x44741,x44742,x44743,x44744,x44745),x44744,x44746),f68(x44741,x44742,x44743,x44744,x44746))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4199]E(f319(f319(f66(x41991,x41992,x41993,x41994),x41995),x41996),f319(x41994,f319(x41995,x41996)))
% 28.25/28.11 [4200]E(f319(f319(f66(x42001,x42002,x42003,x42004),x42005),x42006),f319(x42004,f319(x42005,x42006)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))))
% 28.25/28.11 [4000]E(f319(f319(f249(x40001,x40002,x40003),x40004),f319(f319(f244(x40001,x40002),x40005),x40006)),f319(f319(x40004,x40005),x40006))
% 28.25/28.11 [4001]E(f319(f319(f249(x40011,x40012,x40013),x40014),f319(f319(f244(x40011,x40012),x40015),x40016)),f319(f319(x40014,x40015),x40016))
% 28.25/28.11 [4002]E(f319(f319(f249(x40021,x40022,x40023),x40024),f319(f319(f244(x40021,x40022),x40025),x40026)),f319(f319(x40024,x40025),x40026))
% 28.25/28.11 [4062]E(f319(f319(f319(f8(x40621,x40622,x40623),x40624),x40625),x40626),f319(x40624,f319(x40625,x40626)))
% 28.25/28.11 [4063]E(f319(f319(f319(f7(x40631,x40632,x40633),x40634),x40635),x40636),f319(f319(x40634,x40636),x40635))
% 28.25/28.11 [4079]E(f319(f319(f319(f18(x40791,x40792,x40793),x40794),x40795),x40796),f319(f319(x40794,x40796),f319(x40795,x40796)))
% 28.25/28.11 [4102]E(f319(f148(x41021,x41022,x41023,x41024),f319(f319(f143(x41022),x41025),x41026)),f319(f319(x41024,x41025),x41026))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4228]E(f319(f319(f247(x42281,x42282,x42283,x42284),x42285),x42286),f319(x42284,f319(f319(f244(x42281,x42282),x42285),x42286)))
% 28.25/28.11 [4229]E(f319(f319(f247(x42291,x42292,x42293,x42294),x42295),x42296),f319(x42294,f319(f319(f244(x42291,x42292),x42295),x42296)))
% 28.25/28.11 [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))
% 28.25/28.11 [4272]E(f252(x42721,x42722,x42723,x42724,f319(f319(f244(x42721,x42722),x42725),x42726)),f319(f319(x42724,x42725),x42726))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [4256]E(f319(f319(f66(x42561,x42562,x42563,f319(f16(x42562,x42561),x42564)),x42565),x42566),x42564)
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))))))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))))))
% 28.25/28.11 [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)))
% 28.25/28.11 [4616]E(f319(f248(x46161,x46162),f319(f250(x46163,x46161,x46164,x46162,x46165,x46166),x46167)),f319(x46166,f319(f248(x46163,x46164),x46167)))
% 28.25/28.11 [4617]E(f319(f243(x46171,x46172),f319(f250(x46173,x46171,x46174,x46172,x46175,x46176),x46177)),f319(x46175,f319(f243(x46173,x46174),x46177)))
% 28.25/28.11 [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)))
% 28.25/28.11 [4397]E(f319(f319(f319(f251(x43971,x43972,x43973,x43974),x43975),x43976),x43977),f319(f319(f249(x43972,x43973,x43974),x43976),f319(x43975,x43977)))
% 28.25/28.11 [4398]E(f319(f319(f319(f251(x43981,x43982,x43983,x43984),x43985),x43986),x43987),f319(f319(f249(x43982,x43983,x43984),x43986),f319(x43985,x43987)))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [4784]~P5(x47841)+P5(f929(x47841))
% 28.25/28.11 [4785]~P71(x47851)+P71(f929(x47851))
% 28.25/28.11 [4786]~P111(x47861)+P111(f926(x47861))
% 28.25/28.11 [4788]~P150(x47881)+~E(f72(x47881),f2(x47881))
% 28.25/28.11 [4789]~P150(x47891)+~E(f72(x47891),f2(x47891))
% 28.25/28.11 [4791]~E(x47911,f2(a91))+E(f319(a22,x47911),f2(a1))
% 28.25/28.11 [4792]~E(x47921,f2(a1))+E(f76(a1,x47921),f2(a1))
% 28.25/28.11 [4798]~P149(x47981)+P29(x47981,f2(x47981))
% 28.25/28.11 [4799]~P4(x47991)+P14(x47991,f105(x47991))
% 28.25/28.11 [4800]~P4(x48001)+P14(x48001,f105(x48001))
% 28.25/28.11 [4809]P1(x48091)+P1(f319(a314,x48091))
% 28.25/28.11 [4863]~P149(x48631)+~P29(x48631,f72(x48631))
% 28.25/28.11 [4900]~P1(x49001)+~P1(f319(a314,x49001))
% 28.25/28.11 [4921]E(f319(a96,x49211),f2(a925))+~P1(f319(a185,x49211))
% 28.25/28.11 [4987]~P107(x49871)+P16(x49871,x49871,f102(x49871))
% 28.25/28.11 [4988]~P108(x49881)+P16(x49881,x49881,f93(x49881))
% 28.25/28.11 [4989]~P101(x49891)+P16(x49891,x49891,f75(x49891))
% 28.25/28.11 [4990]~P4(x49901)+P16(x49901,x49901,f224(x49901))
% 28.25/28.11 [4991]~P4(x49911)+P16(x49911,x49911,f225(x49911))
% 28.25/28.11 [4992]~P76(x49921)+P18(x49921,x49921,f75(x49921))
% 28.25/28.11 [4795]~E(x47951,f2(a925))+E(f319(f92(a1),x47951),f2(a1))
% 28.25/28.11 [4801]~P99(x48011)+E(f319(f95(x48011),a77),f2(x48011))
% 28.25/28.11 [4802]~P99(x48021)+E(f319(f95(x48021),a77),f2(x48021))
% 28.25/28.11 [4805]~E(f596(x48051),f2(a925))+E(f319(f157(a925),x48051),f2(a925))
% 28.25/28.11 [4806]~P3(x48061)+E(f228(x48061,f226(x48061)),f224(x48061))
% 28.25/28.11 [4807]~P3(x48071)+E(f229(x48071,f226(x48071)),f225(x48071))
% 28.25/28.11 [4808]~P94(x48081)+E(f76(x48081,f2(x48081)),f2(x48081))
% 28.25/28.11 [4817]~P149(x48171)+E(f319(f92(x48171),f72(a925)),f72(x48171))
% 28.25/28.11 [4818]~P149(x48181)+E(f319(f92(x48181),f2(a925)),f2(x48181))
% 28.25/28.11 [4819]~P145(x48191)+E(f319(f94(x48191),f72(a1)),f72(x48191))
% 28.25/28.11 [4820]~P145(x48201)+E(f319(f94(x48201),f2(a1)),f2(x48201))
% 28.25/28.11 [4821]E(x48211,f2(a925))+~E(f319(f92(a1),x48211),f2(a1))
% 28.25/28.11 [4857]~P96(x48571)+E(f319(f73(x48571),f234(x48571)),f180(x48571))
% 28.25/28.11 [4858]~P96(x48581)+E(f319(f73(x48581),f180(x48581)),f234(x48581))
% 28.25/28.11 [4859]~P69(x48591)+E(f319(f73(x48591),f2(x48591)),f2(x48591))
% 28.25/28.11 [4860]~P126(x48601)+E(f319(f69(x48601),f72(x48601)),f72(x48601))
% 28.25/28.11 [4861]~P92(x48611)+E(f319(f69(x48611),f2(x48611)),f2(x48611))
% 28.25/28.11 [4862]~P88(x48621)+E(f319(f157(x48621),f105(x48621)),f2(x48621))
% 28.25/28.11 [4880]~P37(x48801)+P42(f319(f164(a1),x48801))
% 28.25/28.11 [4904]~P99(x49041)+E(f319(f73(x49041),f72(x49041)),f319(f95(x49041),a89))
% 28.25/28.11 [4905]~P99(x49051)+E(f319(f73(x49051),f72(x49051)),f319(f95(x49051),a89))
% 28.25/28.11 [4920]~P99(x49201)+P29(x49201,f319(f95(x49201),a77))
% 28.25/28.11 [4946]P37(x49461)+~P42(f319(f164(a1),x49461))
% 28.25/28.11 [4993]E(f319(f92(a1),f319(a96,x49931)),x49931)+P1(f319(a185,x49931))
% 28.25/28.11 [5063]~P119(x50631)+E(f237(x50631,f72(x50631),f75(x50631)),f236(x50631))
% 28.25/28.11 [5096]~P99(x50961)+~P29(x50961,f319(f95(x50961),a89))
% 28.25/28.11 [5188]~E(x51881,f2(a925))+P1(f319(f319(f226(a925),x51881),f2(a925)))
% 28.25/28.11 [5244]E(f319(f69(a1),x52441),x52441)+P1(f319(f319(f227(a1),x52441),f2(a1)))
% 28.25/28.11 [5262]~E(f319(a96,x52621),f2(a925))+P1(f319(f319(f226(a1),x52621),f2(a1)))
% 28.25/28.11 [5331]~P1(f319(a185,x53311))+P1(f319(f319(f227(a1),x53311),f2(a1)))
% 28.25/28.11 [5374]~P129(x53741)+P1(f319(f319(f226(x53741),f2(x53741)),f72(x53741)))
% 28.25/28.11 [5375]~P145(x53751)+P1(f319(f319(f321(x53751),f72(x53751)),f101(x53751)))
% 28.25/28.11 [5376]~P149(x53761)+P1(f319(f319(f321(x53761),f72(x53761)),f178(x53761)))
% 28.25/28.11 [5377]~P145(x53771)+P1(f319(f319(f321(x53771),f2(x53771)),f101(x53771)))
% 28.25/28.11 [5378]~P149(x53781)+P1(f319(f319(f321(x53781),f2(x53781)),f178(x53781)))
% 28.25/28.11 [5379]~P129(x53791)+P1(f319(f319(f227(x53791),f2(x53791)),f72(x53791)))
% 28.25/28.11 [5432]E(x54321,f2(a925))+~P1(f319(f319(f226(a925),x54321),f2(a925)))
% 28.25/28.11 [5473]E(f319(a96,x54731),f2(a925))+~P1(f319(f319(f226(a1),x54731),f2(a1)))
% 28.25/28.11 [5474]E(f319(a96,x54741),f2(a925))+~P1(f319(f319(f226(a1),x54741),f2(a1)))
% 28.25/28.11 [5529]P1(f319(a185,x55291))+~P1(f319(f319(f227(a1),x55291),f2(a1)))
% 28.25/28.11 [5536]~P4(x55361)+P18(x55361,f926(x55361),f140(x55361,x55361,f5(x55361)))
% 28.25/28.11 [5554]P42(x55541)+~P1(f319(f319(f226(a1),f2(a1)),f327(x55541)))
% 28.25/28.11 [5559]E(f319(f69(a1),x55591),f319(f73(a1),x55591))+~P1(f319(f319(f227(a1),x55591),f2(a1)))
% 28.25/28.11 [5730]~P129(x57301)+~P1(f319(f319(f226(x57301),f72(x57301)),f2(x57301)))
% 28.25/28.11 [5731]~P129(x57311)+~P1(f319(f319(f227(x57311),f72(x57311)),f2(x57311)))
% 28.25/28.11 [5745]~E(x57451,f2(a925))+P1(f319(f319(f226(a1),f319(f92(a1),x57451)),f2(a1)))
% 28.25/28.11 [5746]~E(x57461,f2(a1))+P1(f319(f319(f227(a1),f319(f69(a1),x57461)),f72(a1)))
% 28.25/28.11 [5868]~P88(x58681)+E(f134(x58681,x58681,f74(x58681),f2(x58681)),f157(x58681))
% 28.25/28.11 [6043]~P110(x60431)+P26(a925,x60431,f92(x60431),f234(f932(a925,a923)))
% 28.25/28.11 [6251]E(x62511,f2(a925))+~P1(f319(f319(f226(a1),f319(f92(a1),x62511)),f2(a1)))
% 28.25/28.11 [6252]E(x62521,f2(a1))+~P1(f319(f319(f227(a1),f319(f69(a1),x62521)),f72(a1)))
% 28.25/28.11 [7057]~P1(f319(f319(f227(a1),x70571),f2(a1)))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x70571),x70571)),f2(a1)))
% 28.25/28.11 [7613]P1(f319(f319(f227(a1),x76131),f2(a1)))+~P1(f319(f319(f227(a1),f319(f319(f74(a1),x76131),x76131)),f2(a1)))
% 28.25/28.11 [8160]E(x81601,f319(a3,f2(a925)))+P1(f319(f319(f227(a925),f319(f319(f23(a925),f319(a20,x81601)),f319(a104,f2(a925)))),f319(a20,x81601)))
% 28.25/28.11 [8935]~P1(f319(f319(f227(a1),x89351),f2(a1)))+P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x89351),x89351)),a89)),f2(a1)))
% 28.25/28.11 [9033]~P1(f319(f319(f227(a1),x90331),f2(a1)))+P1(f319(f319(f227(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x90331)),x90331)),f2(a1)))
% 28.25/28.11 [9359]P1(f319(f319(f227(a1),x93591),f2(a1)))+~P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x93591),x93591)),a89)),f2(a1)))
% 28.25/28.11 [9422]P1(f319(f319(f227(a1),x94221),f2(a1)))+~P1(f319(f319(f227(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x94221)),x94221)),f2(a1)))
% 28.25/28.11 [4894]~E(a77,x48941)+E(f319(f319(f74(a1),x48941),x48941),a77)
% 28.25/28.11 [4895]~E(x48951,a77)+E(f319(f319(f74(a1),x48951),x48951),a77)
% 28.25/28.11 [4906]E(x49061,f2(a1))+E(f319(f319(f30(a1),x49061),x49061),f72(a1))
% 28.25/28.11 [5040]E(x50401,a77)+~E(f319(f319(f74(a1),x50401),x50401),a77)
% 28.25/28.11 [5041]E(a77,x50411)+~E(f319(f319(f74(a1),x50411),x50411),a77)
% 28.25/28.11 [5043]~P99(x50431)+E(f319(f94(x50431),f319(f95(a1),a89)),f319(f95(x50431),a89))
% 28.25/28.11 [5053]~P6(x50531)+E(f32(x50531,f234(f932(x50531,a923))),f180(x50531))
% 28.25/28.11 [5054]~P6(x50541)+E(f32(x50541,f180(f932(x50541,a923))),f234(x50541))
% 28.25/28.11 [5055]~P6(x50551)+E(f31(x50551,f234(f932(x50551,a923))),f234(x50551))
% 28.25/28.11 [5056]~P6(x50561)+E(f31(x50561,f180(f932(x50561,a923))),f180(x50561))
% 28.25/28.11 [5057]~P4(x50571)+E(f131(x50571,f180(f932(x50571,a923))),f105(x50571))
% 28.25/28.11 [5199]E(x51991,f2(a925))+P1(f319(f319(f227(a925),f2(a925)),x51991))
% 28.25/28.11 [5200]E(x52001,f2(a925))+P1(f319(f319(f227(a925),f2(a925)),x52001))
% 28.25/28.11 [5219]~P7(x52191)+P1(f319(f319(f226(a1),f2(a1)),x52191))
% 28.25/28.11 [5252]~E(f319(f95(a925),x52521),f2(a925))+P1(f319(f319(f226(a1),x52521),a77))
% 28.25/28.11 [5253]~E(f319(f95(a925),x52531),f2(a925))+P1(f319(f319(f226(a1),x52531),a77))
% 28.25/28.11 [5258]P42(x52581)+P1(f319(f319(f321(a1),f327(x52581)),x52581))
% 28.25/28.11 [5259]E(x52591,f319(a3,f2(a925)))+P1(f319(f319(f226(a91),f72(a91)),x52591))
% 28.25/28.11 [5302]P1(f319(a185,x53021))+P1(f319(f319(f226(a1),f2(a1)),x53021))
% 28.25/28.11 [5356]E(f319(f92(a1),f319(a96,x53561)),f2(a1))+P1(f319(f319(f226(a1),f2(a1)),x53561))
% 28.25/28.11 [5399]~P71(x53991)+P1(f319(f55(x53991),f234(f932(x53991,a923))))
% 28.25/28.11 [5414]E(f319(f92(a1),f319(f95(a925),x54141)),f319(f95(a1),x54141))+P1(f319(a185,f319(f95(a1),x54141)))
% 28.25/28.11 [5417]~E(x54171,f2(a925))+P1(f319(f319(f227(a925),x54171),f319(a104,f2(a925))))
% 28.25/28.11 [5437]E(f319(f95(a925),x54371),f2(a925))+~P1(f319(f319(f226(a1),x54371),a77))
% 28.25/28.11 [5438]E(f319(f95(a925),x54381),f2(a925))+~P1(f319(a185,f319(f95(a1),x54381)))
% 28.25/28.11 [5439]E(f319(f95(a925),x54391),f2(a925))+~P1(f319(f319(f226(a1),x54391),a77))
% 28.25/28.11 [5471]P7(x54711)+~P1(f319(f319(f226(a1),f2(a1)),x54711))
% 28.25/28.11 [5484]~E(x54841,f2(a925))+~P1(f319(f319(f227(a925),f2(a925)),x54841))
% 28.25/28.11 [5539]E(f319(a104,f371(x55391)),x55391)+~P1(f319(f319(f227(a925),f2(a925)),x55391))
% 28.25/28.11 [5548]E(f319(a104,f319(f95(a925),x55481)),f72(a925))+~P1(f319(a185,f319(f95(a1),x55481)))
% 28.25/28.11 [5555]E(f319(f92(a1),f438(x55551)),x55551)+~P1(f319(f319(f227(a1),f2(a1)),x55551))
% 28.25/28.11 [5562]~E(x55621,f319(a3,f2(a925)))+~P1(f319(f319(f226(a91),f72(a91)),x55621))
% 28.25/28.11 [5569]E(f319(f92(a1),f319(f95(a925),x55691)),f2(a1))+~P1(f319(a185,f319(f95(a1),x55691)))
% 28.25/28.11 [5595]E(f319(f157(a925),x55951),f2(a925))+P1(f319(f319(f321(a925),f596(x55951)),f319(f164(a925),x55951)))
% 28.25/28.11 [5614]E(f319(f92(a1),f319(a96,x56141)),x56141)+~P1(f319(f319(f226(a1),f2(a1)),x56141))
% 28.25/28.11 [5615]E(f319(f92(a1),f319(a96,x56151)),x56151)+~P1(f319(f319(f226(a1),f2(a1)),x56151))
% 28.25/28.11 [5623]~P1(f319(a185,x56231))+~P1(f319(f319(f226(a1),f2(a1)),x56231))
% 28.25/28.11 [5723]E(f319(f319(f74(a925),f72(a925)),f319(f95(a925),x57231)),f72(a925))+~P1(f319(f319(f227(a1),x57231),a77))
% 28.25/28.11 [5787]E(x57871,f2(a925))+~P1(f319(f319(f227(a925),x57871),f319(a104,f2(a925))))
% 28.25/28.11 [5826]E(f319(f319(f23(a925),f319(f95(a925),x58261)),f72(a925)),f2(a925))+~P1(f319(f319(f226(a1),x58261),a77))
% 28.25/28.11 [5827]E(f319(f319(f74(a925),f319(f95(a925),x58271)),f72(a925)),f72(a925))+~P1(f319(f319(f227(a1),x58271),a77))
% 28.25/28.11 [5839]~P42(x58391)+E(f319(f29(a925),f319(f302(a1,a925,a96),x58391)),f319(f29(a1),x58391))
% 28.25/28.11 [5869]~P4(x58691)+E(f228(x58691,f319(f7(x58691,x58691,a923),f226(x58691))),f225(x58691))
% 28.25/28.11 [5870]~P4(x58701)+E(f229(x58701,f319(f7(x58701,x58701,a923),f226(x58701))),f224(x58701))
% 28.25/28.11 [5880]E(f39(a925,f319(a104,f2(a925)),f319(f95(a925),x58801)),f319(a104,f2(a925)))+~P1(f319(a185,f319(f95(a1),x58801)))
% 28.25/28.11 [5889]~P1(f319(f319(f227(a1),f2(a1)),x58891))+P1(f319(f319(f226(a1),f72(a1)),x58891))
% 28.25/28.11 [5890]P1(f319(f319(f227(a1),f2(a1)),x58901))+~P1(f319(f319(f226(a1),f72(a1)),x58901))
% 28.25/28.11 [5900]E(f319(a104,f319(f319(f23(a925),x59001),f72(a925))),x59001)+~P1(f319(f319(f227(a925),f2(a925)),x59001))
% 28.25/28.11 [5901]E(f319(a104,f319(f319(f23(a925),x59011),f72(a925))),x59011)+~P1(f319(f319(f227(a925),f2(a925)),x59011))
% 28.25/28.11 [5957]P1(f319(f319(f227(a925),f2(a925)),f438(x59571)))+~P1(f319(f319(f227(a1),f2(a1)),x59571))
% 28.25/28.11 [6018]E(f39(a1,f319(f95(a1),a89),x60181),f319(f319(f23(a1),x60181),f72(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x60181))
% 28.25/28.11 [6056]~P1(f319(f319(f227(a1),a77),x60561))+P1(f319(f319(f227(a925),f2(a925)),f319(f95(a925),x60561)))
% 28.25/28.11 [6061]E(f319(a20,f833(x60611)),x60611)+~P1(f319(f319(f321(a925),x60611),f234(f932(a925,a923))))
% 28.25/28.11 [6115]P1(f319(f319(f227(a925),f2(a925)),f319(a96,x61151)))+~P1(f319(f319(f227(a1),f2(a1)),x61151))
% 28.25/28.11 [6134]E(f319(a20,f319(a3,x61341)),x61341)+~P1(f319(f319(f321(a925),x61341),f234(f932(a925,a923))))
% 28.25/28.11 [6165]~P1(f319(f319(f227(a925),f2(a925)),x61651))+P1(f319(f319(f227(a1),f2(a1)),f319(f92(a1),x61651)))
% 28.25/28.11 [6201]~P1(f319(f319(f227(a925),f2(a925)),f319(a96,x62011)))+P1(f319(f319(f227(a1),f2(a1)),x62011))
% 28.25/28.11 [6219]~P42(x62191)+E(f319(f302(a925,a1,f92(a1)),f319(f302(a1,a925,a96),x62191)),x62191)
% 28.25/28.11 [6232]P1(f319(f319(f227(a1),a77),x62321))+~P1(f319(f319(f227(a925),f2(a925)),f319(f95(a925),x62321)))
% 28.25/28.11 [6287]P1(f319(f319(f227(a925),f2(a925)),x62871))+~P1(f319(f319(f227(a1),f2(a1)),f319(f92(a1),x62871)))
% 28.25/28.11 [6322]E(f171(x63221,f105(f926(x63221))),f105(f926(x63221)))+~P1(f319(f307(f926(f926(x63221)),f172(x63221)),f105(f926(x63221))))
% 28.25/28.11 [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))
% 28.25/28.11 [6417]~P129(x64171)+P1(f319(f319(f227(x64171),f2(x64171)),f319(f319(f74(x64171),f72(x64171)),f72(x64171))))
% 28.25/28.11 [6466]P1(f319(f319(f227(a925),f319(a104,f2(a925))),f319(a96,x64661)))+~P1(f319(f319(f227(a1),f72(a1)),x64661))
% 28.25/28.11 [6565]E(x65651,f2(a1))+P1(f319(f43(f2(a1),x65651),f319(f319(f244(a1,a1),f2(a1)),f2(a1))))
% 28.25/28.11 [6736]~P1(f319(f319(f227(a925),f319(a104,f2(a925))),f319(a96,x67361)))+P1(f319(f319(f227(a1),f72(a1)),x67361))
% 28.25/28.11 [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)))
% 28.25/28.11 [7171]~P114(x71711)+P38(x71711,f319(f254(f931(x71711,x71711)),f319(f249(x71711,x71711,a923),f227(x71711))))
% 28.25/28.11 [5774]E(f319(f95(a925),f319(f319(f23(a1),x57741),a89)),f319(a104,f319(f95(a925),x57741)))+P1(f319(a185,f319(f95(a1),x57741)))
% 28.25/28.11 [5790]~P37(x57901)+E(f319(f319(f146(a925,a1),f92(a1)),f319(f319(f146(a1,a925),a96),x57901)),x57901)
% 28.25/28.11 [5907]E(f319(f73(a1),f319(f92(a1),f319(a104,f439(x59071)))),x59071)+~P1(f319(f319(f227(a1),x59071),f2(a1)))
% 28.25/28.11 [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))
% 28.25/28.11 [5959]E(f319(f319(f30(a1),f319(f95(a1),a89)),x59591),f319(f95(a1),a89))+~P1(f319(f319(f227(a1),f2(a1)),x59591))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [6100]E(f319(a96,f319(f319(f74(a1),f72(a1)),x61001)),f319(a104,f319(a96,x61001)))+~P1(f319(f319(f226(a1),f2(a1)),x61001))
% 28.25/28.11 [6136]E(f319(a104,f319(f319(f23(a925),x61361),f319(a104,f2(a925)))),x61361)+~P1(f319(f319(f227(a925),f2(a925)),x61361))
% 28.25/28.11 [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)))
% 28.25/28.11 [6393]~P1(f319(f319(f226(a1),a77),x63931))+P1(f319(f319(f226(a1),a77),f319(f319(f74(a1),x63931),x63931)))
% 28.25/28.11 [6394]~P1(f319(f319(f227(a1),a89),x63941))+P1(f319(f319(f226(a1),a89),f319(f319(f74(a1),x63941),x63941)))
% 28.25/28.11 [6395]~P1(f319(f319(f227(a1),a77),x63951))+P1(f319(f319(f227(a1),a77),f319(f319(f74(a1),x63951),x63951)))
% 28.25/28.11 [6396]~P1(f319(f319(f227(a1),a89),x63961))+P1(f319(f319(f227(a1),a89),f319(f319(f74(a1),x63961),x63961)))
% 28.25/28.11 [6578]~P1(f319(f55(x65781),f234(f932(x65781,a923))))+P1(f319(f55(f929(x65781)),f234(f932(f929(x65781),a923))))
% 28.25/28.11 [6666]~P1(f319(f319(f226(a1),f2(a1)),x66661))+P1(f319(f319(f227(a1),f2(a1)),f319(f319(f74(a1),f72(a1)),x66661)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [6707]P1(f319(f55(x67071),f234(f932(x67071,a923))))+~P1(f319(f55(f929(x67071)),f234(f932(f929(x67071),a923))))
% 28.25/28.11 [6737]P1(f319(f319(f226(a1),a77),x67371))+~P1(f319(f319(f226(a1),a77),f319(f319(f74(a1),x67371),x67371)))
% 28.25/28.11 [6738]P1(f319(f319(f227(a1),a77),x67381))+~P1(f319(f319(f227(a1),a77),f319(f319(f74(a1),x67381),x67381)))
% 28.25/28.11 [6739]P1(f319(f319(f227(a1),a89),x67391))+~P1(f319(f319(f226(a1),a89),f319(f319(f74(a1),x67391),x67391)))
% 28.25/28.11 [6740]P1(f319(f319(f227(a1),a89),x67401))+~P1(f319(f319(f227(a1),a89),f319(f319(f74(a1),x67401),x67401)))
% 28.25/28.11 [6936]~P1(f319(f55(a925),x69361))+P1(f319(f55(a1),f319(f302(a925,a1,f92(a1)),x69361)))
% 28.25/28.11 [7063]~P1(f319(f55(x70631),f234(f932(x70631,a923))))+P1(f319(f319(f227(a925),f2(a925)),f319(f29(x70631),f234(f932(x70631,a923)))))
% 28.25/28.11 [7651]P1(f319(f55(a925),x76511))+~P1(f319(f55(a1),f319(f302(a925,a1,f92(a1)),x76511)))
% 28.25/28.11 [5698]~E(a89,x56981)+E(f319(f319(f23(a1),f319(f319(f74(a1),x56981),x56981)),a89),a89)
% 28.25/28.11 [5699]~E(x56991,a89)+E(f319(f319(f23(a1),f319(f319(f74(a1),x56991),x56991)),a89),a89)
% 28.25/28.11 [6227]E(x62271,a89)+~E(f319(f319(f23(a1),f319(f319(f74(a1),x62271),x62271)),a89),a89)
% 28.25/28.11 [6228]E(a89,x62281)+~E(f319(f319(f23(a1),f319(f319(f74(a1),x62281),x62281)),a89),a89)
% 28.25/28.11 [6634]~E(f319(f95(a925),x66341),f2(a925))+P1(f319(a185,f319(f95(a1),f319(f319(f74(a1),x66341),a89))))
% 28.25/28.11 [6938]P15(a922,x69381,a936)+~P1(f319(f319(f226(f932(f924(a922),a923)),a934),x69381))
% 28.25/28.11 [6991]~P1(f319(a185,f319(f95(a1),x69911)))+P1(f319(a185,f319(f95(a1),f319(f319(f74(a1),x69911),x69911))))
% 28.25/28.11 [6992]~P1(f319(f319(f226(a1),x69921),a77))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x69921),x69921)),a77))
% 28.25/28.11 [6993]~P1(f319(f319(f226(a1),x69931),a89))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x69931),x69931)),a89))
% 28.25/28.11 [6994]~P1(f319(f319(f227(a1),x69941),a77))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x69941),x69941)),a77))
% 28.25/28.11 [6995]~P1(f319(f319(f226(a1),x69951),a89))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x69951),x69951)),a89))
% 28.25/28.11 [7317]E(f319(f95(a925),x73171),f2(a925))+~P1(f319(a185,f319(f95(a1),f319(f319(f74(a1),x73171),a89))))
% 28.25/28.11 [7568]~P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x75681)))+P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),f319(f319(f74(a1),x75681),x75681))))
% 28.25/28.11 [7569]P1(f319(a185,f319(f95(a1),x75691)))+~P1(f319(a185,f319(f95(a1),f319(f319(f74(a1),x75691),x75691))))
% 28.25/28.11 [7570]P1(f319(f319(f226(a1),x75701),a77))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),x75701),x75701)),a77))
% 28.25/28.11 [7571]P1(f319(f319(f226(a1),x75711),a89))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),x75711),x75711)),a89))
% 28.25/28.11 [7572]P1(f319(f319(f226(a1),x75721),a89))+~P1(f319(f319(f227(a1),f319(f319(f74(a1),x75721),x75721)),a89))
% 28.25/28.11 [7573]P1(f319(f319(f227(a1),x75731),a77))+~P1(f319(f319(f227(a1),f319(f319(f74(a1),x75731),x75731)),a77))
% 28.25/28.11 [7929]E(f319(a99,f589(x79291)),x79291)+~P1(f319(f319(f321(f932(f931(a925,a925),a923)),x79291),a90))
% 28.25/28.11 [6550]~P99(x65501)+E(f319(f95(x65501),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f72(x65501))
% 28.25/28.11 [6551]~P99(x65511)+E(f319(f95(x65511),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f72(x65511))
% 28.25/28.11 [7041]~P1(f319(a185,f319(f95(a1),x70411)))+E(f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),x70411),x70411)),a89)),f2(a925))
% 28.25/28.11 [8105]~P1(f319(f319(f227(a1),f319(f95(a1),x81051)),f2(a1)))+E(f319(f243(a1,a1),f319(a45,f44(f319(f73(a1),f72(a1)),f319(f73(a1),f319(f95(a1),x81051))))),f319(f319(f30(a1),f72(a1)),f319(f95(a1),x81051)))
% 28.25/28.11 [8118]~P1(f319(f319(f227(a1),f319(f95(a1),x81181)),f2(a1)))+E(f319(f248(a1,a1),f319(a45,f44(f319(f73(a1),f72(a1)),f319(f73(a1),f319(f95(a1),x81181))))),f39(a1,f72(a1),f319(f95(a1),x81181)))
% 28.25/28.11 [8168]~P1(f319(f319(f226(a1),a77),x81681))+P1(f319(f319(f226(a1),a77),f319(f319(f23(a1),f319(f319(f74(a1),x81681),x81681)),a89)))
% 28.25/28.11 [8169]~P1(f319(f319(f226(a1),a89),x81691))+P1(f319(f319(f226(a1),a89),f319(f319(f23(a1),f319(f319(f74(a1),x81691),x81691)),a89)))
% 28.25/28.11 [8170]~P1(f319(f319(f226(a1),a77),x81701))+P1(f319(f319(f227(a1),a77),f319(f319(f23(a1),f319(f319(f74(a1),x81701),x81701)),a89)))
% 28.25/28.11 [8171]~P1(f319(f319(f227(a1),a89),x81711))+P1(f319(f319(f227(a1),a89),f319(f319(f23(a1),f319(f319(f74(a1),x81711),x81711)),a89)))
% 28.25/28.11 [8471]~P99(x84711)+~P29(x84711,f319(f95(x84711),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))
% 28.25/28.11 [8655]P1(f319(f319(f226(a1),a77),x86551))+~P1(f319(f319(f226(a1),a77),f319(f319(f23(a1),f319(f319(f74(a1),x86551),x86551)),a89)))
% 28.25/28.11 [8656]P1(f319(f319(f226(a1),a77),x86561))+~P1(f319(f319(f227(a1),a77),f319(f319(f23(a1),f319(f319(f74(a1),x86561),x86561)),a89)))
% 28.25/28.11 [8657]P1(f319(f319(f226(a1),a89),x86571))+~P1(f319(f319(f226(a1),a89),f319(f319(f23(a1),f319(f319(f74(a1),x86571),x86571)),a89)))
% 28.25/28.11 [8658]P1(f319(f319(f227(a1),a89),x86581))+~P1(f319(f319(f227(a1),a89),f319(f319(f23(a1),f319(f319(f74(a1),x86581),x86581)),a89)))
% 28.25/28.11 [8982]E(f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),x89821),x89821)),a89)),f319(f319(f80(a925,a925),f319(f95(a925),x89821)),f319(f319(f8(a925,a925,a925),a104),f319(f319(f18(a925,a925,a925),f74(a925)),f5(a925)))))+P1(f319(a185,f319(f95(a1),x89821)))
% 28.25/28.11 [9854]E(x98541,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)),x98541),f180(f932(f931(a925,a925),a923)))),a27))
% 28.25/28.11 [8909]~P1(f319(a185,f319(f95(a1),x89091)))+P1(f319(a185,f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),x89091),x89091)),a89))))
% 28.25/28.11 [8910]~P1(f319(f319(f227(a1),x89101),a77))+P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x89101),x89101)),a89)),a77))
% 28.25/28.11 [8911]~P1(f319(f319(f226(a1),x89111),a89))+P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x89111),x89111)),a89)),a89))
% 28.25/28.11 [8912]~P1(f319(f319(f227(a1),x89121),a77))+P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x89121),x89121)),a89)),a77))
% 28.25/28.11 [8913]~P1(f319(f319(f227(a1),x89131),a89))+P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x89131),x89131)),a89)),a89))
% 28.25/28.11 [9024]~P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x90241)))+P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),x90241),x90241)),a89))))
% 28.25/28.11 [9187]~P99(x91871)+E(f319(f319(f74(x91871),f72(x91871)),f72(x91871)),f319(f95(x91871),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))))
% 28.25/28.11 [9343]P1(f319(a185,f319(f95(a1),x93431)))+~P1(f319(a185,f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),x93431),x93431)),a89))))
% 28.25/28.11 [9344]P1(f319(f319(f226(a1),x93441),a89))+~P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x93441),x93441)),a89)),a89))
% 28.25/28.11 [9345]P1(f319(f319(f227(a1),x93451),a77))+~P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x93451),x93451)),a89)),a77))
% 28.25/28.11 [9346]P1(f319(f319(f227(a1),x93461),a77))+~P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x93461),x93461)),a89)),a77))
% 28.25/28.11 [9347]P1(f319(f319(f227(a1),x93471),a89))+~P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x93471),x93471)),a89)),a89))
% 28.25/28.11 [9899]~P1(f319(f55(f931(a925,a925)),x98991))+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))),x98991)),a63))
% 28.25/28.11 [9680]~P149(x96801)+E(f319(f319(f236(x96801),f72(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)))),f72(x96801))
% 28.25/28.11 [9681]~P149(x96811)+E(f319(f319(f236(x96811),f2(x96811)),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(x96811))
% 28.25/28.11 [10143]~P1(f319(f319(f227(a925),f72(a925)),x101431))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f30(a925),x101431),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))))))
% 28.25/28.11 [10149]~P1(f319(f319(f227(a925),f2(a925)),x101491))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f30(a925),f319(f319(f74(a925),x101491),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))))))
% 28.25/28.11 [10187]~E(f39(a925,x101871,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,x101871,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))))))
% 28.25/28.11 [10219]E(f39(a925,x102191,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,x102191,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))))))
% 28.25/28.11 [4825]~P8(x48251,x48252)+P50(x48251,x48252)
% 28.25/28.11 [4826]~P8(x48261,x48262)+P50(x48261,x48262)
% 28.25/28.11 [4827]~P38(x48271,x48272)+P62(x48271,x48272)
% 28.25/28.11 [4828]~P45(x48281,x48282)+P62(x48281,x48282)
% 28.25/28.11 [4829]~P8(x48291,x48292)+P54(x48291,x48292)
% 28.25/28.11 [4830]~P8(x48301,x48302)+P54(x48301,x48302)
% 28.25/28.11 [4831]~P17(x48311,x48312)+P54(x48311,x48312)
% 28.25/28.11 [4832]~P17(x48321,x48322)+P54(x48321,x48322)
% 28.25/28.11 [4833]~P8(x48331,x48332)+P55(x48331,x48332)
% 28.25/28.11 [4834]~P8(x48341,x48342)+P55(x48341,x48342)
% 28.25/28.11 [4835]~P17(x48351,x48352)+P55(x48351,x48352)
% 28.25/28.11 [4836]~P17(x48361,x48362)+P55(x48361,x48362)
% 28.25/28.11 [4837]~P8(x48371,x48372)+P17(x48371,x48372)
% 28.25/28.11 [4787]~E(x47871,x47872)+E(f261(x47871,x47872),f72(a91))
% 28.25/28.11 [4790]E(f208(x47901,x47902),x47901)+~E(x47902,f2(a925))
% 28.25/28.11 [4796]~E(x47962,f105(x47961))+E(f144(x47961,x47962),f105(x47961))
% 28.25/28.11 [4797]~E(x47972,f105(x47971))+E(f144(x47971,x47972),f105(x47971))
% 28.25/28.11 [4815]~E(f144(x48152,x48151),f105(x48152))+E(x48151,f105(x48152))
% 28.25/28.11 [4816]~E(f144(x48162,x48161),f105(x48162))+E(x48161,f105(x48162))
% 28.25/28.11 [4841]~P2(x48412)+P2(f932(x48411,x48412))
% 28.25/28.11 [4842]~P3(x48422)+P3(f932(x48421,x48422))
% 28.25/28.11 [4843]~P113(x48432)+P113(f932(x48431,x48432))
% 28.25/28.11 [4844]~P6(x48442)+P6(f932(x48441,x48442))
% 28.25/28.11 [4845]~P67(x48452)+P67(f932(x48451,x48452))
% 28.25/28.11 [4846]~P96(x48462)+P96(f932(x48461,x48462))
% 28.25/28.11 [4847]~P102(x48472)+P102(f932(x48471,x48472))
% 28.25/28.11 [4848]~P102(x48482)+P107(f932(x48481,x48482))
% 28.25/28.11 [4849]~P102(x48492)+P108(f932(x48491,x48492))
% 28.25/28.11 [4850]~P105(x48502)+P103(f932(x48501,x48502))
% 28.25/28.11 [4851]~P115(x48512)+P115(f932(x48511,x48512))
% 28.25/28.11 [4852]~P106(x48522)+P106(f932(x48521,x48522))
% 28.25/28.11 [4853]~P109(x48532)+P109(f932(x48531,x48532))
% 28.25/28.11 [4854]~P105(x48542)+P104(f932(x48541,x48542))
% 28.25/28.11 [4855]~P83(x48552)+P83(f932(x48551,x48552))
% 28.25/28.11 [4856]~P105(x48562)+P105(f932(x48561,x48562))
% 28.25/28.11 [4868]E(x48681,x48682)+~E(f319(a104,x48681),f319(a104,x48682))
% 28.25/28.11 [4869]E(x48691,x48692)+~E(f319(a104,x48691),f319(a104,x48692))
% 28.25/28.11 [4870]E(x48701,x48702)+~E(f319(a99,x48701),f319(a99,x48702))
% 28.25/28.11 [4871]E(x48711,x48712)+~E(f319(a3,x48711),f319(a3,x48712))
% 28.25/28.11 [4872]E(x48721,x48722)+~E(f319(a20,x48721),f319(a20,x48722))
% 28.25/28.11 [4873]E(x48731,x48732)+~E(f319(a20,x48731),f319(a20,x48732))
% 28.25/28.11 [4922]P40(x49221,x49222)+~E(f727(x49222,x49221),f728(x49222,x49221))
% 28.25/28.11 [4952]~P62(x49521,x49522)+P40(x49521,f299(x49521,x49522))
% 28.25/28.11 [4953]~P56(x49531,x49532)+P56(x49531,f299(x49531,x49532))
% 28.25/28.11 [4966]~P65(x49661)+E(f39(x49661,x49662,x49662),f2(x49661))
% 28.25/28.11 [5000]~P38(x50001,x50002)+P38(f926(x50001),f138(x50001,x50002))
% 28.25/28.11 [5001]~P38(x50011,x50012)+P38(f926(x50011),f137(x50011,x50012))
% 28.25/28.11 [5002]~P39(x50021,x50022)+P39(f926(x50021),f139(x50021,x50022))
% 28.25/28.11 [5003]~P39(x50031,x50032)+P39(f926(x50031),f150(x50031,x50032))
% 28.25/28.11 [5004]~P56(x50041,x50042)+P56(f926(x50041),f150(x50041,x50042))
% 28.25/28.11 [5101]~P38(x51011,x51012)+P38(f932(x51011,a923),f310(x51011,x51012))
% 28.25/28.11 [5102]~P38(x51021,x51022)+P38(f932(x51021,a923),f311(x51021,x51022))
% 28.25/28.11 [5228]~P7(x52281)+P42(f295(a1,x52281,x52282))
% 28.25/28.11 [5334]~P38(x53341,x53342)+P64(x53341,f61(x53341,x53341,x53342))
% 28.25/28.11 [5833]~P68(x58331)+P26(x58331,x58331,f73(x58331),x58332)
% 28.25/28.11 [4810]~E(x48102,f105(x48101))+E(f319(f160(x48101),x48102),f105(x48101))
% 28.25/28.11 [4811]~E(x48112,f105(x48111))+E(f319(f159(x48111),x48112),f105(x48111))
% 28.25/28.11 [4812]~E(x48122,f105(x48121))+E(f319(f160(x48121),x48122),f105(x48121))
% 28.25/28.11 [4875]E(x48751,f319(a96,x48752))+~E(f319(f92(a1),x48751),x48752)
% 28.25/28.11 [4877]E(x48771,f105(x48772))+~E(f319(f160(x48772),x48771),f105(x48772))
% 28.25/28.11 [4878]E(x48781,f105(x48782))+~E(f319(f159(x48782),x48781),f105(x48782))
% 28.25/28.11 [4879]E(x48791,f105(x48792))+~E(f319(f160(x48792),x48791),f105(x48792))
% 28.25/28.11 [4891]~P99(x48911)+E(f319(f95(x48911),x48912),f319(f94(x48911),x48912))
% 28.25/28.11 [4898]~P71(x48981)+P1(f319(f55(x48981),x48982))
% 28.25/28.11 [4899]~P71(x48991)+P1(f319(f55(x48991),x48992))
% 28.25/28.11 [4907]~E(f687(x49072,x49071),f105(x49071))+E(f171(x49071,x49072),f105(f926(x49071)))
% 28.25/28.11 [4916]~E(x49162,f105(x49161))+E(f319(f164(x49161),x49162),f180(f932(x49161,a923)))
% 28.25/28.11 [4917]~E(x49172,f105(x49171))+E(f180(f932(x49171,a923)),f319(f164(x49171),x49172))
% 28.25/28.11 [4918]E(x49181,x49182)+~E(f319(f92(a1),x49181),f319(f92(a1),x49182))
% 28.25/28.11 [4919]E(x49191,x49192)+~E(f319(f92(a1),x49191),f319(f92(a1),x49192))
% 28.25/28.11 [4923]E(f206(x49231,x49232),f2(a925))+P1(f319(f55(x49231),x49232))
% 28.25/28.11 [4941]~P126(x49411)+E(f76(x49411,f76(x49411,x49412)),f76(x49411,x49412))
% 28.25/28.11 [4955]~P87(x49551)+E(f319(f319(f236(x49551),x49552),f72(a925)),x49552)
% 28.25/28.11 [4956]~P121(x49561)+E(f319(f319(f236(x49561),x49562),f72(a925)),x49562)
% 28.25/28.11 [4957]~P56(x49571,x49572)+E(f319(f278(x49571,x49571),x49572),x49572)
% 28.25/28.11 [4961]E(x49611,x49612)+E(f261(x49611,x49612),f319(f319(f74(a91),x49612),f72(a91)))
% 28.25/28.11 [4962]E(f319(f29(x49621),x49622),f2(a925))+P1(f319(f55(x49621),x49622))
% 28.25/28.11 [4963]E(f319(f29(x49631),x49632),f2(a925))+P1(f319(f55(x49631),x49632))
% 28.25/28.11 [4964]E(f319(f29(x49641),x49642),f2(a925))+P1(f319(f55(x49641),x49642))
% 28.25/28.11 [4967]~E(f144(x49671,x49672),x49672)+P1(f319(f129(x49671),x49672))
% 28.25/28.11 [4970]~P104(x49701)+E(f319(f319(f102(x49701),x49702),f180(x49701)),x49702)
% 28.25/28.11 [4971]~P103(x49711)+E(f319(f319(f93(x49711),x49712),f234(x49711)),x49712)
% 28.25/28.11 [4972]~P69(x49721)+E(f319(f319(f23(x49721),x49722),f2(x49721)),x49722)
% 28.25/28.11 [4973]~P78(x49731)+E(f319(f319(f75(x49731),x49732),f72(x49731)),x49732)
% 28.25/28.11 [4974]~P87(x49741)+E(f319(f319(f75(x49741),x49742),f72(x49741)),x49742)
% 28.25/28.11 [4975]~P121(x49751)+E(f319(f319(f75(x49751),x49752),f72(x49751)),x49752)
% 28.25/28.11 [4976]~P79(x49761)+E(f319(f319(f74(x49761),x49762),f2(x49761)),x49762)
% 28.25/28.11 [4977]~P121(x49771)+E(f319(f319(f74(x49771),x49772),f2(x49771)),x49772)
% 28.25/28.11 [4978]~P88(x49781)+E(f319(f319(f74(x49781),x49782),f2(x49781)),x49782)
% 28.25/28.11 [4979]~P124(x49791)+E(f319(f319(f283(x49791),x49792),f72(x49791)),x49792)
% 28.25/28.11 [4980]~P65(x49801)+E(f319(f319(f30(x49801),x49802),f72(x49801)),x49802)
% 28.25/28.11 [4981]~P121(x49811)+E(f319(f319(f236(x49811),x49812),f2(a925)),f72(x49811))
% 28.25/28.11 [4982]~P119(x49821)+E(f319(f319(f236(x49821),x49822),f2(a925)),f72(x49821))
% 28.25/28.11 [4983]~E(x49832,f180(f932(x49831,a923)))+E(f319(f29(x49831),x49832),f2(a925))
% 28.25/28.11 [4994]~P65(x49941)+E(f39(x49941,x49942,f2(x49941)),x49942)
% 28.25/28.11 [5005]~P103(x50051)+E(f319(f319(f102(x50051),x50052),f234(x50051)),f234(x50051))
% 28.25/28.11 [5006]~P104(x50061)+E(f319(f319(f93(x50061),x50062),f180(x50061)),f180(x50061))
% 28.25/28.11 [5007]~P121(x50071)+E(f319(f319(f75(x50071),x50072),f2(x50071)),f2(x50071))
% 28.25/28.11 [5008]~P133(x50081)+E(f319(f319(f75(x50081),x50082),f2(x50081)),f2(x50081))
% 28.25/28.11 [5009]~P125(x50091)+E(f319(f319(f283(x50091),x50092),f2(x50091)),f2(x50091))
% 28.25/28.11 [5010]~P65(x50101)+E(f319(f319(f30(x50101),x50102),f2(x50101)),f2(x50101))
% 28.25/28.11 [5012]~P65(x50121)+E(f39(x50121,x50122,f72(x50121)),f2(x50121))
% 28.25/28.11 [5013]~P65(x50131)+E(f39(x50131,f2(x50131),x50132),f2(x50131))
% 28.25/28.11 [5042]E(x50421,f2(a925))+E(f49(x50422,x50421,f105(x50422)),f105(f926(x50422)))
% 28.25/28.11 [5065]P56(x50651,x50652)+~E(f319(f278(x50651,x50651),x50652),x50652)
% 28.25/28.11 [5066]P38(x50661,x50662)+~E(f597(x50662,x50661),f180(f932(x50661,a923)))
% 28.25/28.11 [5067]E(x50671,f105(x50672))+~E(f319(f164(x50672),x50671),f180(f932(x50672,a923)))
% 28.25/28.11 [5068]E(x50681,f105(x50682))+~E(f180(f932(x50682,a923)),f319(f164(x50682),x50681))
% 28.25/28.11 [5071]~E(x50711,x50712)+P1(f319(f319(a316,x50711),x50712))
% 28.25/28.11 [5081]P1(x50811)+P1(f319(f319(a322,x50811),x50812))
% 28.25/28.11 [5082]E(x50821,f105(x50822))+E(f319(f319(f156(x50822),x50821),f2(a925)),f319(f133(x50822),x50821))
% 28.25/28.11 [5084]E(f144(x50841,x50842),x50842)+~P1(f319(f129(x50841),x50842))
% 28.25/28.11 [5085]E(f144(x50851,x50852),x50852)+~P1(f319(f129(x50851),x50852))
% 28.25/28.11 [5092]~P1(x50922)+P1(f319(f319(a318,x50921),x50922))
% 28.25/28.11 [5093]~P1(x50931)+P1(f319(f319(a318,x50931),x50932))
% 28.25/28.11 [5094]~P1(x50942)+P1(f319(f319(a322,x50941),x50942))
% 28.25/28.11 [5104]~E(f688(x51042,x51041),f694(x51042,x51041))+P1(f319(f129(x51041),x51042))
% 28.25/28.11 [5111]E(f319(f254(x51111),x51112),f180(f932(x51111,a923)))+P1(f319(x51112,f325(x51112)))
% 28.25/28.11 [5112]E(f180(f932(x51121,a923)),f319(f254(x51121),x51122))+P1(f319(x51122,f326(x51122)))
% 28.25/28.11 [5182]~P126(x51821)+E(f319(f319(f75(x51821),x51822),f76(x51821,x51822)),f319(f69(x51821),x51822))
% 28.25/28.11 [5192]~E(x51921,f2(a1))+E(f40(x51921,x51922),f319(f319(f244(a1,a1),f2(a1)),f2(a1)))
% 28.25/28.11 [5193]~E(x51931,f2(a1))+E(f40(x51931,x51932),f319(f319(f244(a1,a1),f2(a1)),f2(a1)))
% 28.25/28.11 [5224]~P62(x52241,x52242)+P62(x52241,f319(f278(x52241,x52241),x52242))
% 28.25/28.11 [5225]~P39(x52251,x52252)+P39(x52251,f319(f278(x52251,x52251),x52252))
% 28.25/28.11 [5226]~P40(x52261,x52262)+P40(x52261,f319(f278(x52261,x52261),x52262))
% 28.25/28.11 [5227]~P56(x52271,x52272)+P56(x52271,f319(f278(x52271,x52271),x52272))
% 28.25/28.11 [5249]E(x52491,x52492)+~P1(f319(f319(a316,x52491),x52492))
% 28.25/28.11 [5260]P1(x52601)+~P1(f319(f319(a317,x52602),x52601))
% 28.25/28.11 [5261]P1(x52611)+~P1(f319(f319(a317,x52611),x52612))
% 28.25/28.11 [5266]~P115(x52661)+P1(f319(f319(f226(x52661),x52662),f234(x52661)))
% 28.25/28.11 [5267]~P121(x52671)+P1(f319(f319(f279(x52671),x52672),f2(x52671)))
% 28.25/28.11 [5271]E(x52711,x52712)+~E(f319(x52711,f433(x52712,x52711)),f319(x52712,f433(x52712,x52711)))
% 28.25/28.11 [5304]E(x53041,f2(a925))+E(f208(x53041,f39(a925,x53042,x53041)),f208(x53042,x53041))
% 28.25/28.11 [5309]~P4(x53091)+P14(x53091,f319(f319(f143(x53091),x53092),f105(x53091)))
% 28.25/28.11 [5313]E(x53131,f2(a1))+P1(f319(f43(x53132,x53131),f40(x53132,x53131)))
% 28.25/28.11 [5329]~P17(x53292,x53291)+P1(f319(f319(x53291,f820(x53291)),f820(x53291)))
% 28.25/28.11 [5332]~E(x53321,x53322)+P1(f319(f319(f227(a925),x53321),f319(a104,x53322)))
% 28.25/28.11 [5342]~E(x53421,f2(a925))+P1(f319(f319(f227(a925),x53421),f319(a104,x53422)))
% 28.25/28.11 [5355]P1(f319(x53551,x53552))+P1(f319(f319(f226(a1),f2(a1)),f426(x53551)))
% 28.25/28.11 [5419]P62(x54191,x54192)+~P62(x54191,f319(f278(x54191,x54191),x54192))
% 28.25/28.11 [5420]P39(x54201,x54202)+~P39(x54201,f319(f278(x54201,x54201),x54202))
% 28.25/28.11 [5421]P40(x54211,x54212)+~P40(x54211,f319(f278(x54211,x54211),x54212))
% 28.25/28.11 [5422]P56(x54221,x54222)+~P56(x54221,f319(f278(x54221,x54221),x54222))
% 28.25/28.11 [5425]~E(f39(a925,x54252,x54251),f2(a925))+E(f319(f319(f75(a925),x54251),f452(x54251,x54252)),x54252)
% 28.25/28.11 [5426]~E(f39(a1,x54262,x54261),f2(a1))+E(f319(f319(f75(a1),x54261),f453(x54261,x54262)),x54262)
% 28.25/28.11 [5431]~E(x54311,f319(a104,x54312))+P1(f319(f319(f226(a925),x54311),f319(a104,x54312)))
% 28.25/28.11 [5452]~P1(f319(x54521,x54522))+P1(f319(f319(f226(a1),f2(a1)),f425(x54521)))
% 28.25/28.11 [5463]E(f319(f319(f23(a925),f319(a96,x54631)),f319(a96,x54632)),f319(a96,x54631))+~P1(f319(a185,x54632))
% 28.25/28.11 [5486]E(f264(x54861,x54862),f72(a91))+~P1(f319(f319(f226(a91),x54861),f72(a91)))
% 28.25/28.11 [5581]E(f319(f319(f156(x55811),x55812),f688(x55812,x55811)),f319(f319(f156(x55811),x55812),f694(x55812,x55811)))+P1(f319(f129(x55811),x55812))
% 28.25/28.11 [5624]~P1(f319(x56241,f84(x56242,x56241)))+P1(f319(x56241,f608(x56242,x56241)))
% 28.25/28.11 [5688]P64(x56881,x56882)+~P1(f319(f307(x56881,x56882),f576(x56882,x56881)))
% 28.25/28.11 [5830]~P17(x58302,x58301)+P1(f319(f319(x58301,f821(x58301,x58302)),f821(x58301,x58302)))
% 28.25/28.11 [5831]~P17(x58312,x58311)+P1(f319(f319(x58311,f826(x58311,x58312)),f826(x58311,x58312)))
% 28.25/28.11 [5840]~E(f319(a104,f39(a925,x58401,x58402)),x58402)+E(f39(a925,f319(a104,x58401),x58402),f2(a925))
% 28.25/28.11 [5896]P38(x58961,x58962)+P1(f319(f319(f321(x58961),f628(x58962,x58961)),f629(x58962,x58961)))
% 28.25/28.11 [5903]~P145(x59031)+P1(f319(f319(f321(x59031),f319(f92(x59031),x59032)),f101(x59031)))
% 28.25/28.11 [5904]~P149(x59041)+P1(f319(f319(f321(x59041),f319(f92(x59041),x59042)),f178(x59041)))
% 28.25/28.11 [5905]~P145(x59051)+P1(f319(f319(f321(x59051),f319(f94(x59051),x59052)),f101(x59051)))
% 28.25/28.11 [5906]~P99(x59061)+P1(f319(f319(f321(x59061),f319(f95(x59061),x59062)),f101(x59061)))
% 28.25/28.11 [6040]~P39(x60401,x60402)+E(f319(f319(f281(x60401,x60401,x60401),x60402),f299(x60401,x60402)),x60402)
% 28.25/28.11 [6055]E(f319(a104,f39(a925,x60551,x60552)),x60552)+E(f39(a925,f319(a104,x60551),x60552),f319(a104,f39(a925,x60551,x60552)))
% 28.25/28.11 [6478]P38(x64781,x64782)+~P1(f319(f319(f321(x64781),f559(x64782,x64781)),f308(x64781,x64782)))
% 28.25/28.11 [6516]~P129(x65161)+~P1(f319(f319(f227(x65161),f319(f92(x65161),x65162)),f2(x65161)))
% 28.25/28.11 [6517]~P92(x65171)+~P1(f319(f319(f227(x65171),f319(f69(x65171),x65172)),f2(x65171)))
% 28.25/28.11 [6607]P1(f319(f319(f227(a1),x66071),f39(a1,x66072,x66071)))+~P1(f319(f319(f227(a1),x66071),f2(a1)))
% 28.25/28.11 [6608]P1(f319(f319(f227(a1),x66081),f39(a1,x66082,x66081)))+~P1(f319(f319(f227(a1),x66081),f2(a1)))
% 28.25/28.11 [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)))
% 28.25/28.11 [6798]~P4(x67981)+P14(x67981,f142(x67981,x67981,f5(x67981),x67982))
% 28.25/28.11 [6934]E(f319(f159(x69341),x69342),x69342)+~P1(f319(f319(f226(a925),f319(f181(f926(x69341)),x69342)),f72(a925)))
% 28.25/28.11 [6955]~P92(x69551)+P1(f319(f319(f226(x69551),f319(f73(x69551),f319(f69(x69551),x69552))),f2(x69551)))
% 28.25/28.11 [6987]~P38(x69871,x69872)+P38(x69871,f319(f319(f281(x69871,x69871,x69871),x69872),f299(x69871,x69872)))
% 28.25/28.11 [6988]~P56(x69881,x69882)+P56(x69881,f319(f319(f281(x69881,x69881,x69881),x69882),f299(x69881,x69882)))
% 28.25/28.11 [7210]~P1(f319(f319(f227(a1),x72102),f2(a1)))+P1(f319(f319(f226(a1),f39(a1,x72101,x72102)),f2(a1)))
% 28.25/28.11 [7211]~P1(f319(f319(f227(a1),x72112),f2(a1)))+P1(f319(f319(f226(a1),f39(a1,x72111,x72112)),f2(a1)))
% 28.25/28.11 [7609]~P149(x76091)+E(f182(x76091,f319(f319(f7(x76091,x76091,x76091),f74(x76091)),f72(x76091)),x76092,f2(x76091)),f319(f92(x76091),x76092))
% 28.25/28.11 [7637]~P131(x76371)+~P1(f319(f319(f227(x76371),f319(f319(f75(x76371),x76372),x76372)),f2(x76371)))
% 28.25/28.11 [10313]~P126(x103131)+~P1(f319(f319(f227(x103131),f319(f319(f236(x103131),x103132),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(x103131)))
% 28.25/28.11 [4876]~E(x48762,f105(x48761))+E(f319(f181(f926(x48761)),x48762),f2(a925))
% 28.25/28.11 [4908]~E(x49081,f2(a925))+E(f319(f319(f74(a925),x49081),x49082),x49082)
% 28.25/28.11 [4909]~E(x49092,f2(a925))+E(f319(f319(f75(a925),x49091),x49092),f2(a925))
% 28.25/28.11 [4910]~E(x49101,f2(a925))+E(f319(f319(f75(a925),x49101),x49102),f2(a925))
% 28.25/28.11 [4911]~E(x49111,f2(a925))+E(f319(f319(f75(a925),x49111),x49112),f2(a925))
% 28.25/28.11 [4912]~E(x49122,f2(a925))+E(f319(f319(f236(a925),x49121),x49122),f72(a925))
% 28.25/28.11 [4913]~E(x49132,f2(a1))+E(f319(f319(f30(a1),x49131),x49132),f2(a1))
% 28.25/28.11 [4924]E(x49241,f105(x49242))+~E(f319(f181(f926(x49242)),x49241),f2(a925))
% 28.25/28.11 [4925]~P102(x49251)+E(f319(f319(f102(x49251),x49252),x49252),x49252)
% 28.25/28.11 [4926]~P107(x49261)+E(f319(f319(f102(x49261),x49262),x49262),x49262)
% 28.25/28.11 [4927]~P107(x49271)+E(f319(f319(f102(x49271),x49272),x49272),x49272)
% 28.25/28.11 [4928]~P102(x49281)+E(f319(f319(f93(x49281),x49282),x49282),x49282)
% 28.25/28.11 [4929]~P108(x49291)+E(f319(f319(f93(x49291),x49292),x49292),x49292)
% 28.25/28.11 [4930]~P108(x49301)+E(f319(f319(f93(x49301),x49302),x49302),x49302)
% 28.25/28.11 [4931]~P101(x49311)+E(f319(f319(f75(x49311),x49312),x49312),x49312)
% 28.25/28.11 [4932]~P101(x49321)+E(f319(f319(f75(x49321),x49322),x49322),x49322)
% 28.25/28.11 [4933]~P4(x49331)+E(f319(f319(f224(x49331),x49332),x49332),x49332)
% 28.25/28.11 [4934]~P4(x49341)+E(f319(f319(f224(x49341),x49342),x49342),x49342)
% 28.25/28.11 [4935]~P4(x49351)+E(f319(f319(f225(x49351),x49352),x49352),x49352)
% 28.25/28.11 [4936]~P4(x49361)+E(f319(f319(f225(x49361),x49362),x49362),x49362)
% 28.25/28.11 [4954]~P69(x49541)+E(f319(f319(f23(x49541),x49542),x49542),f2(x49541))
% 28.25/28.11 [4968]~P96(x49681)+E(f319(f73(x49681),f319(f73(x49681),x49682)),x49682)
% 28.25/28.11 [4969]~P69(x49691)+E(f319(f73(x49691),f319(f73(x49691),x49692)),x49692)
% 28.25/28.11 [4986]~E(x49862,f2(a925))+E(f319(f319(f236(a925),x49861),x49862),f319(a104,f2(a925)))
% 28.25/28.11 [5021]~P104(x50211)+E(f319(f319(f102(x50211),f180(x50211)),x50212),x50212)
% 28.25/28.11 [5022]~P103(x50221)+E(f319(f319(f93(x50221),f234(x50221)),x50222),x50222)
% 28.25/28.11 [5023]~P78(x50231)+E(f319(f319(f75(x50231),f72(x50231)),x50232),x50232)
% 28.25/28.11 [5024]~P87(x50241)+E(f319(f319(f75(x50241),f72(x50241)),x50242),x50242)
% 28.25/28.11 [5025]~P121(x50251)+E(f319(f319(f75(x50251),f72(x50251)),x50252),x50252)
% 28.25/28.11 [5026]~P79(x50261)+E(f319(f319(f74(x50261),f2(x50261)),x50262),x50262)
% 28.25/28.11 [5027]~P121(x50271)+E(f319(f319(f74(x50271),f2(x50271)),x50272),x50272)
% 28.25/28.11 [5028]~P88(x50281)+E(f319(f319(f74(x50281),f2(x50281)),x50282),x50282)
% 28.25/28.11 [5046]~P103(x50461)+E(f319(f319(f102(x50461),f234(x50461)),x50462),f234(x50461))
% 28.25/28.11 [5047]~P104(x50471)+E(f319(f319(f93(x50471),f180(x50471)),x50472),f180(x50471))
% 28.25/28.11 [5048]~P121(x50481)+E(f319(f319(f75(x50481),f2(x50481)),x50482),f2(x50481))
% 28.25/28.11 [5049]~P133(x50491)+E(f319(f319(f75(x50491),f2(x50491)),x50492),f2(x50491))
% 28.25/28.11 [5050]~P87(x50501)+E(f319(f319(f236(x50501),f72(x50501)),x50502),f72(x50501))
% 28.25/28.11 [5051]~P124(x50511)+E(f319(f319(f283(x50511),f2(x50511)),x50512),f2(x50511))
% 28.25/28.11 [5052]~P65(x50521)+E(f319(f319(f30(x50521),f2(x50521)),x50522),f2(x50521))
% 28.25/28.11 [5060]E(x50601,f105(x50602))+E(f136(x50602,f319(f160(x50602),x50601)),f319(f133(x50602),x50601))
% 28.25/28.11 [5061]E(x50611,f105(x50612))+E(f319(f133(x50612),f319(f160(x50612),x50611)),f136(x50612,x50611))
% 28.25/28.11 [5062]E(x50621,f2(a925))+~E(f319(f319(f74(a925),x50622),x50621),x50622)
% 28.25/28.11 [5069]~P145(x50691)+E(f319(f94(x50691),f319(f92(a1),x50692)),f319(f92(x50691),x50692))
% 28.25/28.11 [5070]~P99(x50701)+E(f319(f94(x50701),f319(f95(a1),x50702)),f319(f95(x50701),x50702))
% 28.25/28.11 [5075]E(x50751,f72(a925))+~E(f319(f319(f75(a925),x50752),x50751),f72(a925))
% 28.25/28.11 [5076]E(x50761,f72(a925))+~E(f319(f319(f75(a925),x50761),x50762),f72(a925))
% 28.25/28.11 [5077]E(x50771,f72(a925))+~E(f319(f319(f75(a925),x50772),x50771),f72(a925))
% 28.25/28.11 [5078]E(x50781,f72(a925))+~E(f319(f319(f75(a925),x50781),x50782),f72(a925))
% 28.25/28.11 [5079]E(x50791,f2(a925))+~E(f319(f319(f74(a925),x50792),x50791),f2(a925))
% 28.25/28.11 [5080]E(x50801,f2(a925))+~E(f319(f319(f74(a925),x50801),x50802),f2(a925))
% 28.25/28.11 [5097]~P92(x50971)+E(f319(f69(x50971),f319(f73(x50971),x50972)),f319(f69(x50971),x50972))
% 28.25/28.11 [5098]~P126(x50981)+E(f319(f69(x50981),f319(f92(x50981),x50982)),f319(f92(x50981),x50982))
% 28.25/28.11 [5099]~P92(x50991)+E(f319(f69(x50991),f319(f69(x50991),x50992)),f319(f69(x50991),x50992))
% 28.25/28.11 [5100]~P79(x51001)+E(f319(f157(x51001),f319(f160(x51001),x51002)),f319(f157(x51001),x51002))
% 28.25/28.11 [5105]~E(x51051,f319(a104,f2(a925)))+E(f319(f319(f236(a925),x51051),x51052),f319(a104,f2(a925)))
% 28.25/28.11 [5114]~P69(x51141)+E(f319(f319(f23(x51141),f2(x51141)),x51142),f319(f73(x51141),x51142))
% 28.25/28.11 [5115]~E(x51152,f2(a925))+E(f131(a925,f319(f294(a925,x51151),x51152)),f105(a925))
% 28.25/28.11 [5124]~P99(x51241)+E(f319(f319(f74(x51241),x51242),f319(f95(x51241),a77)),x51242)
% 28.25/28.11 [5125]E(x51251,f2(a1))+E(f41(f319(f69(a1),x51252),f319(f69(a1),x51251)),f47(x51252,x51251))
% 28.25/28.11 [5139]~E(x51391,x51392)+P1(f319(f319(f226(a925),x51391),x51392))
% 28.25/28.11 [5140]~E(x51401,x51402)+P1(f319(f319(f226(a925),x51401),x51402))
% 28.25/28.11 [5141]~E(x51411,x51412)+P1(f319(f319(f226(a925),x51411),x51412))
% 28.25/28.11 [5148]~E(x51481,f2(a91))+E(f319(f319(f74(a925),f319(a20,x51481)),x51482),x51482)
% 28.25/28.11 [5149]~E(f319(f95(a1),x51492),f319(f92(a1),x51491))+E(x51491,f319(a96,f319(f95(a1),x51492)))
% 28.25/28.11 [5150]~P6(x51501)+E(f87(x51501,f319(f16(x51501,x51501),x51502)),x51502)
% 28.25/28.11 [5163]~P7(x51631)+P7(f319(f319(f236(a1),x51631),x51632))
% 28.25/28.11 [5164]~P96(x51641)+E(f319(f319(f102(x51641),x51642),f319(f73(x51641),x51642)),f234(x51641))
% 28.25/28.11 [5165]~P96(x51651)+E(f319(f319(f93(x51651),x51652),f319(f73(x51651),x51652)),f180(x51651))
% 28.25/28.11 [5166]~P69(x51661)+E(f319(f319(f74(x51661),x51662),f319(f73(x51661),x51662)),f2(x51661))
% 28.25/28.11 [5190]E(x51901,f2(a925))+~E(f319(f73(a1),f319(f92(a1),x51902)),f319(f92(a1),x51901))
% 28.25/28.11 [5191]E(x51911,f2(a925))+~E(f319(f73(a1),f319(f92(a1),x51911)),f319(f92(a1),x51912))
% 28.25/28.11 [5201]E(f186(x52011,x52012),f2(a1))+P1(f319(f319(f226(a1),x52012),x52011))
% 28.25/28.11 [5202]E(f170(x52021,x52022),f105(a1))+P1(f319(f319(f226(a1),x52021),x52022))
% 28.25/28.11 [5203]E(f233(x52031,x52032),f2(a91))+P1(f319(f319(f227(a91),x52031),x52032))
% 28.25/28.11 [5216]E(x52161,f319(a104,f2(a925)))+~E(f319(f319(f75(a925),x52162),x52161),f319(a104,f2(a925)))
% 28.25/28.11 [5217]E(x52171,f319(a104,f2(a925)))+~E(f319(f319(f75(a925),x52171),x52172),f319(a104,f2(a925)))
% 28.25/28.11 [5218]~P2(x52181)+P1(f319(f319(f226(x52181),x52182),x52182))
% 28.25/28.11 [5221]~P99(x52211)+E(f319(f319(f75(x52211),x52212),f319(f95(x52211),a89)),f319(f73(x52211),x52212))
% 28.25/28.11 [5240]~P99(x52401)+E(f319(f73(x52401),f319(f95(x52401),x52402)),f319(f95(x52401),f319(f73(a1),x52402)))
% 28.25/28.11 [5241]~P145(x52411)+E(f319(f73(x52411),f319(f94(x52411),x52412)),f319(f94(x52411),f319(f73(a1),x52412)))
% 28.25/28.11 [5242]~P99(x52421)+E(f319(f73(x52421),f319(f95(x52421),x52422)),f319(f95(x52421),f319(f73(a1),x52422)))
% 28.25/28.11 [5272]~E(x52721,f319(a104,x52722))+P1(f319(f319(f227(a925),f2(a925)),x52721))
% 28.25/28.11 [5290]~P4(x52901)+E(f319(f73(f932(x52901,a923)),f319(f296(x52901),x52902)),f319(f293(x52901),x52902))
% 28.25/28.11 [5291]~P4(x52911)+E(f319(f73(f932(x52911,a923)),f319(f274(x52911),x52912)),f319(f275(x52911),x52912))
% 28.25/28.11 [5292]~P4(x52921)+E(f319(f73(f932(x52921,a923)),f319(f275(x52921),x52922)),f319(f274(x52921),x52922))
% 28.25/28.11 [5293]~P4(x52931)+E(f319(f73(f932(x52931,a923)),f319(f293(x52931),x52932)),f319(f296(x52931),x52932))
% 28.25/28.11 [5303]~E(f319(f92(a1),x53032),x53031)+P1(f319(f319(f226(a1),f2(a1)),x53031))
% 28.25/28.11 [5312]~E(x53122,f2(a1))+E(f47(x53121,x53122),f319(f319(f244(a1,a1),f2(a1)),f319(f69(a1),x53121)))
% 28.25/28.11 [5314]~P109(x53141)+P1(f319(f319(f226(x53141),f180(x53141)),x53142))
% 28.25/28.11 [5347]E(x53471,x53472)+~E(f319(f319(f74(a1),x53471),x53471),f319(f319(f74(a1),x53472),x53472))
% 28.25/28.11 [5354]~P1(f319(x53541,x53542))+P1(f319(x53541,f319(a96,f425(x53541))))
% 28.25/28.11 [5380]~P126(x53801)+E(f319(f319(f75(x53801),f76(x53801,x53802)),f319(f69(x53801),x53802)),x53802)
% 28.25/28.11 [5387]~E(x53872,f2(a925))+E(f79(f931(a925,a925),f42(x53871,x53872)),f319(f319(f244(a925,a925),f2(a925)),x53871))
% 28.25/28.11 [5388]~E(x53881,x53882)+~P1(f319(f319(f227(a925),x53881),x53882))
% 28.25/28.11 [5389]~E(x53891,x53892)+~P1(f319(f319(f227(a925),x53891),x53892))
% 28.25/28.11 [5390]~E(x53901,x53902)+~P1(f319(f319(f227(a925),x53901),x53902))
% 28.25/28.11 [5391]~E(x53911,x53912)+~P1(f319(f319(f227(a925),x53911),x53912))
% 28.25/28.11 [5392]~E(x53921,x53922)+~P1(f319(f319(f227(a925),x53921),x53922))
% 28.25/28.11 [5393]~E(x53931,x53932)+~P1(f319(f319(f227(a1),x53931),x53932))
% 28.25/28.11 [5396]~P149(x53961)+E(f319(f319(f74(x53961),f72(x53961)),f319(f92(x53961),x53962)),f319(f92(x53961),f319(a104,x53962)))
% 28.25/28.11 [5400]~E(x54001,f2(a925))+~P1(f319(f319(f227(a925),x54002),x54001))
% 28.25/28.11 [5415]E(f144(x54151,x54152),x54152)+~E(f319(f181(f926(x54151)),f144(x54151,x54152)),f319(f181(f926(x54151)),x54152))
% 28.25/28.11 [5416]E(f319(f29(x54161),f319(f164(x54161),x54162)),f319(f181(f926(x54161)),x54162))+~P1(f319(f129(x54161),x54162))
% 28.25/28.11 [5430]~P1(f319(x54301,f329(x54301)))+P1(f319(x54301,f319(f92(a1),x54302)))
% 28.25/28.11 [5440]E(f233(x54401,x54402),x54402)+~P1(f319(f319(f227(a91),x54401),x54402))
% 28.25/28.11 [5442]E(f264(x54421,x54422),f72(a91))+~P1(f319(f319(f227(a91),x54422),x54421))
% 28.25/28.11 [5443]E(f170(x54431,x54432),f105(a1))+~P1(f319(f319(f227(a1),x54432),x54431))
% 28.25/28.11 [5444]E(f120(x54441,x54442),f107(a1))+~P1(f319(f319(f227(a1),x54441),x54442))
% 28.25/28.11 [5446]~P113(x54461)+E(f295(x54461,x54462,x54462),f319(f319(f301(x54461),x54462),f180(f932(x54461,a923))))
% 28.25/28.11 [5466]~E(f319(f319(f23(a925),x54661),x54662),f2(a925))+P1(f319(f319(f226(a925),x54661),x54662))
% 28.25/28.11 [5483]~E(x54832,f2(a925))+E(f49(x54831,x54832,f105(x54831)),f319(f319(f143(f926(x54831)),f105(x54831)),f105(f926(x54831))))
% 28.25/28.11 [5487]~P2(x54871)+~P1(f319(f319(f227(x54871),x54872),x54872))
% 28.25/28.11 [5488]~E(f39(a1,x54881,x54882),f2(a1))+E(f39(a1,x54881,f319(f73(a1),x54882)),f2(a1))
% 28.25/28.11 [5489]~E(f39(a1,x54891,x54892),f2(a1))+E(f39(a1,x54891,f319(f73(a1),x54892)),f2(a1))
% 28.25/28.11 [5490]~E(f39(a1,x54901,x54902),f2(a1))+E(f39(a1,f319(f73(a1),x54901),x54902),f2(a1))
% 28.25/28.11 [5491]~E(f39(a1,x54911,x54912),f2(a1))+E(f39(a1,f319(f73(a1),x54911),x54912),f2(a1))
% 28.25/28.11 [5498]E(f319(f294(a925,x54981),f319(a104,x54982)),f180(f932(a925,a923)))+P1(f319(f319(f226(a925),x54981),x54982))
% 28.25/28.11 [5521]E(f131(a925,f319(f294(a925,x55211),x55212)),f105(a925))+P1(f319(f319(f227(a925),x55211),x55212))
% 28.25/28.11 [5526]~E(f319(f29(x55261),f319(f164(x55261),x55262)),f319(f181(f926(x55261)),x55262))+P1(f319(f129(x55261),x55262))
% 28.25/28.11 [5530]~P1(f319(f129(x55301),x55302))+P1(f319(f129(x55301),f319(f159(x55301),x55302)))
% 28.25/28.11 [5531]~P1(f319(f129(x55311),x55312))+P1(f319(f129(x55311),f319(f163(x55311),x55312)))
% 28.25/28.11 [5532]~P1(f319(f129(x55321),x55322))+P1(f319(f129(x55321),f319(f160(x55321),x55322)))
% 28.25/28.11 [5540]P1(f319(x55401,x55402))+~P1(f319(x55401,f319(a96,f426(x55401))))
% 28.25/28.11 [5541]P1(f319(f319(f226(a925),x55412),x55411))+P1(f319(f319(f226(a925),x55411),x55412))
% 28.25/28.11 [5542]P1(f319(f319(f226(a1),x55422),x55421))+P1(f319(f319(f226(a1),x55421),x55422))
% 28.25/28.11 [5546]~P92(x55461)+P1(f319(f319(f226(x55461),x55462),f319(f69(x55461),x55462)))
% 28.25/28.11 [5549]P1(f319(x55491,f330(x55491)))+~P1(f319(x55491,f319(f92(a1),x55492)))
% 28.25/28.11 [5572]E(f319(f319(f23(a925),x55721),x55722),f2(a925))+~P1(f319(f319(f226(a925),x55721),x55722))
% 28.25/28.11 [5573]E(f319(f319(f23(a925),x55731),x55732),f2(a925))+~P1(f319(f319(f226(a925),x55731),x55732))
% 28.25/28.11 [5574]E(f319(f319(f30(a925),x55741),x55742),f2(a925))+~P1(f319(f319(f227(a925),x55741),x55742))
% 28.25/28.11 [5592]E(f39(a925,x55921,x55922),x55921)+~P1(f319(f319(f227(a925),x55921),x55922))
% 28.25/28.11 [5593]E(f39(a925,x55931,x55932),x55931)+~P1(f319(f319(f227(a925),x55931),x55932))
% 28.25/28.11 [5601]E(f39(a1,x56011,f319(f73(a1),x56012)),f284(x56011,x56012))+P1(f319(f319(f226(a1),f2(a1)),x56012))
% 28.25/28.11 [5612]E(f319(f319(f23(a1),x56121),x56122),f186(x56121,x56122))+~P1(f319(f319(f226(a1),x56122),x56121))
% 28.25/28.11 [5613]E(f319(f319(f23(a1),x56131),x56132),f186(x56131,x56132))+~P1(f319(f319(f226(a1),x56132),x56131))
% 28.25/28.11 [5633]P1(f319(f319(f226(a1),f2(a1)),f329(x56331)))+P1(f319(x56331,f319(f92(a1),x56332)))
% 28.25/28.11 [5645]~P129(x56451)+P1(f319(f319(f226(x56451),f2(x56451)),f319(f92(x56451),x56452)))
% 28.25/28.11 [5646]~P129(x56461)+P1(f319(f319(f226(x56461),f2(x56461)),f319(f92(x56461),x56462)))
% 28.25/28.11 [5647]~P92(x56471)+P1(f319(f319(f226(x56471),f2(x56471)),f319(f69(x56471),x56472)))
% 28.25/28.11 [5674]E(f319(f319(f74(a925),x56741),f331(x56742,x56741)),x56742)+~P1(f319(f319(f226(a925),x56741),x56742))
% 28.25/28.11 [5686]~E(f319(f95(a1),x56861),f319(f92(a1),x56862))+P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x56861)))
% 28.25/28.11 [5689]E(f295(a1,x56891,x56892),f180(f932(a1,a923)))+~P1(f319(f319(f227(a1),x56892),x56891))
% 28.25/28.11 [5692]~P126(x56921)+E(f319(f319(f75(x56921),f319(f69(x56921),x56922)),f319(f69(x56921),x56922)),f319(f319(f75(x56921),x56922),x56922))
% 28.25/28.11 [5697]E(f131(a925,f319(f294(a925,x56971),f319(a104,x56972))),f105(a925))+P1(f319(f319(f226(a925),x56971),x56972))
% 28.25/28.11 [5701]E(f319(f319(f30(a1),x57011),x57012),f285(x57011,x57012))+~P1(f319(f319(f226(a1),f2(a1)),x57012))
% 28.25/28.11 [5721]P1(f319(f129(x57211),x57212))+~P1(f319(f129(x57211),f319(f159(x57211),x57212)))
% 28.25/28.11 [5722]P1(f319(f129(x57221),x57222))+~P1(f319(f129(x57221),f319(f160(x57221),x57222)))
% 28.25/28.11 [5747]P1(f319(f55(a925),x57471))+P1(f319(f319(f321(a925),f332(x57471,x57472)),x57471))
% 28.25/28.11 [5748]P1(f319(f55(a925),x57481))+P1(f319(f319(f321(a925),f351(x57481,x57482)),x57481))
% 28.25/28.11 [5751]P1(f319(f319(f227(a925),x57512),f319(a104,x57511)))+P1(f319(f319(f227(a925),x57511),x57512))
% 28.25/28.11 [5752]E(f39(a1,x57521,x57522),f284(x57521,x57522))+~P1(f319(f319(f226(a1),f2(a1)),x57522))
% 28.25/28.11 [5754]E(f131(a925,f319(f294(a925,x57541),x57542)),f105(a925))+~P1(f319(f319(f226(a925),x57542),x57541))
% 28.25/28.11 [5755]E(f131(a925,f319(f294(a925,x57551),x57552)),f105(a925))+~P1(f319(f319(f226(a925),x57552),x57551))
% 28.25/28.11 [5756]~P68(x57561)+E(f319(f302(x57561,x57561,f73(x57561)),f319(f296(x57561),x57562)),f319(f274(x57561),f319(f73(x57561),x57562)))
% 28.25/28.11 [5757]~P68(x57571)+E(f319(f302(x57571,x57571,f73(x57571)),f319(f274(x57571),x57572)),f319(f296(x57571),f319(f73(x57571),x57572)))
% 28.25/28.11 [5758]~P68(x57581)+E(f319(f302(x57581,x57581,f73(x57581)),f319(f275(x57581),x57582)),f319(f293(x57581),f319(f73(x57581),x57582)))
% 28.25/28.11 [5759]~P68(x57591)+E(f319(f302(x57591,x57591,f73(x57591)),f319(f293(x57591),x57592)),f319(f275(x57591),f319(f73(x57591),x57592)))
% 28.25/28.11 [5770]E(x57701,f180(f932(x57702,a923)))+P1(f319(f319(f321(x57702),f825(x57701,x57702)),x57701))
% 28.25/28.11 [5771]E(x57711,f180(f932(x57712,a923)))+P1(f319(f319(f321(x57712),f837(x57711,x57712)),x57711))
% 28.25/28.11 [5778]~P1(f319(f319(f227(a925),x57781),x57782))+P1(f319(f319(f226(a925),x57781),x57782))
% 28.25/28.11 [5779]~P1(f319(f319(f227(a925),x57791),x57792))+P1(f319(f319(f226(a925),x57791),x57792))
% 28.25/28.11 [5780]~P1(f319(f319(f227(a925),x57801),x57802))+P1(f319(f319(f226(a925),x57801),x57802))
% 28.25/28.11 [5781]~P1(f319(f319(f227(a925),x57811),x57812))+P1(f319(f319(f226(a925),x57811),x57812))
% 28.25/28.11 [5782]~P1(f319(f319(f227(a925),x57821),x57822))+P1(f319(f319(f226(a925),x57821),x57822))
% 28.25/28.11 [5783]~P1(f319(f319(f227(a1),x57831),x57832))+P1(f319(f319(f226(a1),x57831),x57832))
% 28.25/28.11 [5799]E(f41(x57991,x57992),f319(f319(f244(a1,a1),f2(a1)),x57991))+~P1(f319(f319(f227(a1),x57991),x57992))
% 28.25/28.11 [5801]E(f207(f319(f73(a1),x58011),f319(f73(a1),x58012)),f207(x58011,x58012))+~P1(f319(f319(f227(a1),x58012),f2(a1)))
% 28.25/28.11 [5812]E(x58121,x58122)+~E(f319(a3,f319(a104,f319(a20,x58121))),f319(a3,f319(a104,f319(a20,x58122))))
% 28.25/28.11 [5817]E(f41(x58171,x58172),f319(f319(f244(a1,a1),f2(a1)),x58171))+~P1(f319(f319(f226(a1),x58172),f2(a1)))
% 28.25/28.11 [5846]E(f39(a925,f319(f95(a925),x58461),f319(f95(a925),x58462)),f2(a925))+~P1(f319(a185,f319(f95(a1),x58461)))
% 28.25/28.11 [5861]P1(f319(f319(f226(a1),f2(a1)),f330(x58611)))+~P1(f319(x58611,f319(f92(a1),x58612)))
% 28.25/28.11 [5894]P42(f295(a1,x58941,x58942))+~P1(f319(f319(f226(a1),f2(a1)),x58941))
% 28.25/28.11 [5899]~P1(f319(f55(x58991),x58992))+P1(f319(f55(f932(x58991,a923)),f319(f300(x58991),x58992)))
% 28.25/28.11 [5912]E(f319(f319(f74(a1),x59121),f319(f92(a1),f365(x59122,x59121))),x59122)+~P1(f319(f319(f226(a1),x59121),x59122))
% 28.25/28.11 [5920]P1(f319(f319(f226(a925),x59201),x59202))+P1(f319(f319(f226(a925),f319(a104,x59202)),x59201))
% 28.25/28.11 [5964]E(f319(f319(f30(a925),f319(f95(a925),x59641)),f319(f95(a925),x59642)),f2(a925))+~P1(f319(a185,f319(f95(a1),x59641)))
% 28.25/28.11 [5965]E(f319(f319(f75(a925),f319(f95(a925),x59651)),f319(f95(a925),x59652)),f2(a925))+~P1(f319(f319(f227(a1),x59651),a77))
% 28.25/28.11 [5966]P1(f319(f319(f226(a925),x59661),f319(a104,x59662)))+~P1(f319(f319(f226(a925),x59661),x59662))
% 28.25/28.11 [5967]P1(f319(f319(f226(a925),x59671),f319(a104,x59672)))+~P1(f319(f319(f226(a925),x59671),x59672))
% 28.25/28.11 [5968]P1(f319(f319(f227(a925),x59681),f319(a104,x59682)))+~P1(f319(f319(f226(a925),x59681),x59682))
% 28.25/28.11 [5969]P1(f319(f319(f227(a925),x59691),f319(a104,x59692)))+~P1(f319(f319(f226(a925),x59691),x59692))
% 28.25/28.11 [5970]P1(f319(f319(f227(a925),x59701),f319(a104,x59702)))+~P1(f319(f319(f227(a925),x59701),x59702))
% 28.25/28.11 [5971]P1(f319(f319(f227(a925),x59711),f319(a104,x59712)))+~P1(f319(f319(f227(a925),x59711),x59712))
% 28.25/28.11 [5974]~E(x59741,x59742)+P1(f319(f319(f227(a1),x59741),f319(f319(f74(a1),x59742),f72(a1))))
% 28.25/28.11 [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))
% 28.25/28.11 [5986]E(x59861,f105(x59862))+P1(f319(f319(f321(x59862),f136(x59862,x59861)),f319(f164(x59862),x59861)))
% 28.25/28.11 [5997]E(f79(f931(a925,a925),f42(x59971,x59972)),f319(f319(f244(a925,a925),f2(a925)),x59971))+~P1(f319(f319(f227(a925),x59971),x59972))
% 28.25/28.11 [5998]E(f79(f931(a925,a925),f42(x59981,x59982)),f319(f319(f244(a925,a925),f2(a925)),x59981))+~P1(f319(f319(f227(a925),x59981),x59982))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [6041]E(f319(a104,f319(f319(f74(a925),x60411),f416(x60412,x60411))),x60412)+~P1(f319(f319(f227(a925),x60411),x60412))
% 28.25/28.11 [6066]P1(f319(x60661,x60662))+~P1(f319(x60661,f319(a83,f588(x60662,x60661))))
% 28.25/28.11 [6067]P1(f319(x60671,x60672))+~P1(f319(x60671,f319(a3,f838(x60672,x60671))))
% 28.25/28.11 [6077]~P1(f319(f319(f227(a925),x60771),f319(a104,x60772)))+P1(f319(f319(f226(a925),x60771),x60772))
% 28.25/28.11 [6114]P1(f319(x61141,x61142))+P1(f319(f319(f321(a925),f838(x61142,x61141)),f234(f932(a925,a923))))
% 28.25/28.11 [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))
% 28.25/28.11 [6129]E(x61291,f105(x61292))+E(f319(f319(f126(x61292),f106(x61292,x61291)),f319(f319(f143(x61292),f136(x61292,x61291)),f105(x61292))),x61291)
% 28.25/28.11 [6145]P1(f319(f55(x61451),x61452))+~P1(f319(f319(f227(a925),f2(a925)),f319(f29(x61451),x61452)))
% 28.25/28.11 [6146]P1(f319(f55(x61461),x61462))+~P1(f319(f319(f227(a925),f2(a925)),f319(f29(x61461),x61462)))
% 28.25/28.11 [6150]~E(x61501,f180(f932(x61502,a923)))+~P1(f319(f319(f227(a925),f2(a925)),f319(f29(x61502),x61501)))
% 28.25/28.11 [6160]~P1(f319(f319(f227(a925),x61601),x61602))+P1(f319(f319(f226(a925),f319(a104,x61601)),x61602))
% 28.25/28.11 [6161]~P1(f319(f319(f227(a925),x61611),x61612))+P1(f319(f319(f226(a925),f319(a104,x61611)),x61612))
% 28.25/28.11 [6162]~P1(f319(f319(f227(a925),x61621),x61622))+P1(f319(f319(f226(a925),f319(a104,x61621)),x61622))
% 28.25/28.11 [6166]~P4(x61661)+E(f142(x61661,x61661,f5(x61661),f144(x61661,x61662)),f131(x61661,f319(f164(x61661),x61662)))
% 28.25/28.11 [6169]E(x61691,f105(x61692))+P1(f319(f319(f321(x61692),f319(f133(x61692),x61691)),f319(f164(x61692),x61691)))
% 28.25/28.11 [6175]~P129(x61751)+P1(f319(f319(f227(x61751),x61752),f319(f319(f74(x61751),x61752),f72(x61751))))
% 28.25/28.11 [6177]~P92(x61771)+P1(f319(f319(f226(x61771),f319(f73(x61771),x61772)),f319(f69(x61771),x61772)))
% 28.25/28.11 [6191]~E(x61911,x61912)+E(f282(a925,f279(a925),x61911,x61912),f319(f319(f301(a925),x61911),f180(f932(a925,a923))))
% 28.25/28.11 [6211]P1(f319(f55(a925),x62111))+~P1(f319(f319(f226(a925),f332(x62111,x62112)),x62112))
% 28.25/28.11 [6212]P1(f319(f55(a925),x62121))+~P1(f319(f319(f227(a925),f351(x62121,x62122)),x62122))
% 28.25/28.11 [6216]~P1(f319(f55(f931(x62161,x62161)),x62162))+P1(f319(f55(x62161),f319(f273(x62161),x62162)))
% 28.25/28.11 [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)))
% 28.25/28.11 [6271]~P1(f319(f319(f227(a925),x62712),f319(a104,x62711)))+~P1(f319(f319(f227(a925),x62711),x62712))
% 28.25/28.11 [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))))
% 28.25/28.11 [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)))
% 28.25/28.11 [6284]P1(f319(f55(x62841),x62842))+~P1(f319(f55(f932(x62841,a923)),f319(f300(x62841),x62842)))
% 28.25/28.11 [6306]P1(f319(f319(f226(a925),f319(a104,x63061)),f319(a104,x63062)))+~P1(f319(f319(f226(a925),x63061),x63062))
% 28.25/28.11 [6307]P1(f319(f319(f226(a925),f319(a20,x63071)),f319(a20,x63072)))+~P1(f319(f319(f226(a91),x63071),x63072))
% 28.25/28.11 [6308]P1(f319(f319(f226(a91),f319(a3,x63081)),f319(a3,x63082)))+~P1(f319(f319(f226(a925),x63081),x63082))
% 28.25/28.11 [6309]P1(f319(f319(f227(a925),f319(a104,x63091)),f319(a104,x63092)))+~P1(f319(f319(f227(a925),x63091),x63092))
% 28.25/28.11 [6310]P1(f319(f319(f227(a925),f319(a104,x63101)),f319(a104,x63102)))+~P1(f319(f319(f227(a925),x63101),x63102))
% 28.25/28.11 [6311]P1(f319(f319(f227(a925),f319(a20,x63111)),f319(a20,x63112)))+~P1(f319(f319(f227(a91),x63111),x63112))
% 28.25/28.11 [6312]P1(f319(f319(f227(a91),f319(a3,x63121)),f319(a3,x63122)))+~P1(f319(f319(f227(a925),x63121),x63122))
% 28.25/28.11 [6317]E(x63171,x63172)+~E(f319(f302(a925,a1,f92(a1)),x63171),f319(f302(a925,a1,f92(a1)),x63172))
% 28.25/28.11 [6333]P1(f319(f319(f226(a925),x63331),x63332))+~P1(f319(f319(f226(a925),f319(a104,x63331)),x63332))
% 28.25/28.11 [6334]P1(f319(f319(f227(a925),x63341),x63342))+~P1(f319(f319(f226(a925),f319(a104,x63341)),x63342))
% 28.25/28.11 [6335]P1(f319(f319(f227(a925),x63351),x63352))+~P1(f319(f319(f226(a925),f319(a104,x63351)),x63352))
% 28.25/28.11 [6336]P1(f319(f319(f227(a925),x63361),x63362))+~P1(f319(f319(f226(a925),f319(a104,x63361)),x63362))
% 28.25/28.11 [6337]P1(f319(f319(f227(a925),x63371),x63372))+~P1(f319(f319(f227(a925),f319(a104,x63371)),x63372))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [6446]~P1(f319(f180(f932(x64461,a923)),x64462))+P1(f319(f319(f321(x64461),x64462),f180(f932(x64461,a923))))
% 28.25/28.11 [6475]~P1(f319(f55(x64751),f31(f932(x64751,a923),x64752)))+P1(f319(f55(f932(x64751,a923)),x64752))
% 28.25/28.11 [6497]P1(f319(f319(f226(a925),f319(f95(a925),x64971)),f319(f95(a925),x64972)))+~P1(f319(f319(f226(a1),x64971),a77))
% 28.25/28.11 [6518]~P1(f319(f319(f227(a1),x65181),x65182))+P1(f319(f319(f226(a1),x65181),f319(f319(f23(a1),x65182),f72(a1))))
% 28.25/28.11 [6519]~P1(f319(f319(f226(a1),x65191),x65192))+P1(f319(f319(f227(a1),x65191),f319(f319(f74(a1),x65192),f72(a1))))
% 28.25/28.11 [6520]~P1(f319(f319(f227(a1),x65201),x65202))+P1(f319(f319(f227(a1),x65201),f319(f319(f74(a1),x65202),f72(a1))))
% 28.25/28.11 [6522]~P1(f319(f319(f226(a1),x65221),x65222))+P1(f319(f319(f226(a925),f319(f95(a925),x65221)),f319(f95(a925),x65222)))
% 28.25/28.11 [6523]~P1(f319(f319(f226(a925),x65231),x65232))+P1(f319(f319(f226(a1),f319(f92(a1),x65231)),f319(f92(a1),x65232)))
% 28.25/28.11 [6524]~P1(f319(f319(f226(a925),x65241),x65242))+P1(f319(f319(f226(a1),f319(f92(a1),x65241)),f319(f92(a1),x65242)))
% 28.25/28.11 [6525]~P1(f319(f319(f226(a1),x65251),x65252))+P1(f319(f319(f226(a1),f319(f95(a1),x65251)),f319(f95(a1),x65252)))
% 28.25/28.11 [6526]~P1(f319(f319(f227(a925),x65261),x65262))+P1(f319(f319(f227(a1),f319(f92(a1),x65261)),f319(f92(a1),x65262)))
% 28.25/28.11 [6527]~P1(f319(f319(f227(a925),x65271),x65272))+P1(f319(f319(f227(a1),f319(f92(a1),x65271)),f319(f92(a1),x65272)))
% 28.25/28.11 [6528]~P1(f319(f319(f227(a1),x65281),x65282))+P1(f319(f319(f227(a1),f319(f95(a1),x65281)),f319(f95(a1),x65282)))
% 28.25/28.11 [6535]~E(x65352,f180(f932(x65351,a923)))+P1(f319(f319(f226(f932(x65351,a923)),x65352),f180(f932(x65351,a923))))
% 28.25/28.11 [6548]~P1(f319(f319(f226(a925),x65481),x65482))+~P1(f319(f319(f226(a925),f319(a104,x65482)),x65481))
% 28.25/28.11 [6591]~P1(f319(f319(f226(a925),f319(a104,x65911)),f319(a104,x65912)))+P1(f319(f319(f226(a925),x65911),x65912))
% 28.25/28.11 [6592]~P1(f319(f319(f226(a91),f319(a3,x65921)),f319(a3,x65922)))+P1(f319(f319(f226(a925),x65921),x65922))
% 28.25/28.11 [6593]~P1(f319(f319(f226(a925),f319(a20,x65931)),f319(a20,x65932)))+P1(f319(f319(f226(a91),x65931),x65932))
% 28.25/28.11 [6594]~P1(f319(f319(f227(a925),f319(a104,x65941)),f319(a104,x65942)))+P1(f319(f319(f227(a925),x65941),x65942))
% 28.25/28.11 [6595]~P1(f319(f319(f227(a925),f319(a104,x65951)),f319(a104,x65952)))+P1(f319(f319(f227(a925),x65951),x65952))
% 28.25/28.11 [6596]~P1(f319(f319(f227(a91),f319(a3,x65961)),f319(a3,x65962)))+P1(f319(f319(f227(a925),x65961),x65962))
% 28.25/28.11 [6597]~P1(f319(f319(f227(a925),f319(a96,x65971)),f319(a96,x65972)))+P1(f319(f319(f227(a1),x65971),x65972))
% 28.25/28.11 [6598]~P1(f319(f319(f227(a925),f319(a20,x65981)),f319(a20,x65982)))+P1(f319(f319(f227(a91),x65981),x65982))
% 28.25/28.11 [6620]~P1(f319(f319(f321(x66201),x66202),f180(f932(x66201,a923))))+P1(f319(f180(f932(x66201,a923)),x66202))
% 28.25/28.11 [6640]~P1(f319(f319(f227(a925),f319(a96,x66402)),f319(a96,x66401)))+P1(f319(f319(f227(a1),f2(a1)),x66401))
% 28.25/28.11 [6671]P1(f319(f319(f226(a1),f2(a1)),f39(a1,x66711,x66712)))+~P1(f319(f319(f227(a1),f2(a1)),x66712))
% 28.25/28.11 [6672]P1(f319(f319(f226(a1),f2(a1)),f39(a1,x66721,x66722)))+~P1(f319(f319(f227(a1),f2(a1)),x66722))
% 28.25/28.11 [6836]P38(x68361,x68362)+~E(f319(f319(f281(x68361,x68361,x68361),x68362),x68362),f180(f932(f931(x68361,x68361),a923)))
% 28.25/28.11 [6850]~P38(x68501,x68502)+P38(x68501,f319(f319(f281(x68501,x68501,x68501),x68502),x68502))
% 28.25/28.11 [6861]P1(f319(f319(f226(a1),x68611),x68612))+~P1(f319(f319(f227(a1),x68611),f319(f319(f74(a1),x68612),f72(a1))))
% 28.25/28.11 [6862]P1(f319(f319(f227(a1),x68621),x68622))+~P1(f319(f319(f226(a1),x68621),f319(f319(f23(a1),x68622),f72(a1))))
% 28.25/28.11 [6864]P1(f319(f319(f226(a925),x68641),x68642))+~P1(f319(f319(f226(a1),f319(f92(a1),x68641)),f319(f92(a1),x68642)))
% 28.25/28.11 [6865]P1(f319(f319(f226(a925),x68651),x68652))+~P1(f319(f319(f226(a1),f319(f92(a1),x68651)),f319(f92(a1),x68652)))
% 28.25/28.11 [6866]P1(f319(f319(f226(a1),x68661),x68662))+~P1(f319(f319(f226(a1),f319(f95(a1),x68661)),f319(f95(a1),x68662)))
% 28.25/28.11 [6867]P1(f319(f319(f227(a925),x68671),x68672))+~P1(f319(f319(f227(a1),f319(f92(a1),x68671)),f319(f92(a1),x68672)))
% 28.25/28.11 [6868]P1(f319(f319(f227(a925),x68681),x68682))+~P1(f319(f319(f227(a1),f319(f92(a1),x68681)),f319(f92(a1),x68682)))
% 28.25/28.11 [6869]P1(f319(f319(f227(a1),x68691),x68692))+~P1(f319(f319(f227(a925),f319(f95(a925),x68691)),f319(f95(a925),x68692)))
% 28.25/28.11 [6870]P1(f319(f319(f227(a1),x68701),x68702))+~P1(f319(f319(f227(a1),f319(f95(a1),x68701)),f319(f95(a1),x68702)))
% 28.25/28.11 [6969]~E(f717(x69692,x69691),f105(x69691))+E(f319(f134(f926(x69691),f926(x69691),f126(x69691),f105(x69691)),x69692),f105(x69691))
% 28.25/28.11 [6970]~E(f718(x69702,x69701),f105(x69701))+E(f319(f134(f926(x69701),f926(x69701),f126(x69701),f105(x69701)),x69702),f105(x69701))
% 28.25/28.11 [6974]~P6(x69741)+E(f319(f134(x69741,x69741,f93(x69741),f234(x69741)),x69742),f32(x69741,f319(f164(x69741),x69742)))
% 28.25/28.11 [6975]~P6(x69751)+E(f319(f134(x69751,x69751,f102(x69751),f180(x69751)),x69752),f31(x69751,f319(f164(x69751),x69752)))
% 28.25/28.11 [6989]E(x69891,f2(a91))+E(f319(f319(f74(a925),f319(a20,f319(f319(f23(a91),x69891),f72(a91)))),f319(a104,x69892)),f319(f319(f74(a925),f319(a20,x69891)),x69892))
% 28.25/28.11 [7038]P1(f319(f319(f227(a1),f319(f319(f23(a1),x70381),x70382)),f2(a1)))+~P1(f319(f319(f227(a1),x70381),x70382))
% 28.25/28.11 [7065]~P4(x70651)+E(f319(f319(f102(f932(x70651,a923)),f319(f319(f301(x70651),x70652),f180(f932(x70651,a923)))),f319(f296(x70651),x70652)),f319(f275(x70651),x70652))
% 28.25/28.11 [7141]~P64(x71411,x71412)+P38(x71411,f319(f254(f931(x71411,x71411)),f319(f249(x71411,x71411,a923),x71412)))
% 28.25/28.11 [7142]~P64(x71421,x71422)+P62(x71421,f319(f254(f931(x71421,x71421)),f319(f249(x71421,x71421,a923),x71422)))
% 28.25/28.11 [7143]~P54(x71431,x71432)+P39(x71431,f319(f254(f931(x71431,x71431)),f319(f249(x71431,x71431,a923),x71432)))
% 28.25/28.11 [7144]~P55(x71441,x71442)+P56(x71441,f319(f254(f931(x71441,x71441)),f319(f249(x71441,x71441,a923),x71442)))
% 28.25/28.11 [7145]E(x71451,f180(f932(x71452,a923)))+~P1(f319(f319(f226(f932(x71452,a923)),x71451),f180(f932(x71452,a923))))
% 28.25/28.11 [7226]~P1(f319(f319(f227(a925),f2(a925)),x72262))+P1(f319(f319(f226(a925),f39(a925,x72261,x72262)),x72262))
% 28.25/28.11 [7227]~P1(f319(f319(f226(a1),f2(a1)),x72271))+P1(f319(f319(f226(a1),f39(a1,x72271,x72272)),x72271))
% 28.25/28.11 [7228]~P1(f319(f319(f227(a925),f2(a925)),x72282))+P1(f319(f319(f227(a925),f39(a925,x72281,x72282)),x72282))
% 28.25/28.11 [7229]~P1(f319(f319(f227(a1),f2(a1)),x72292))+P1(f319(f319(f227(a1),f39(a1,x72291,x72292)),x72292))
% 28.25/28.11 [7230]~P1(f319(f319(f227(a1),f2(a1)),x72302))+P1(f319(f319(f227(a1),f39(a1,x72301,x72302)),x72302))
% 28.25/28.11 [7307]~P113(x73071)+E(f319(f319(f23(f932(x73071,a923)),f319(f319(f301(x73071),x73072),f180(f932(x73071,a923)))),f319(f274(x73071),x73072)),f319(f319(f301(x73071),x73072),f180(f932(x73071,a923))))
% 28.25/28.11 [7382]~P50(x73821,x73822)+P57(x73821,f234(f932(x73821,a923)),f319(f254(f931(x73821,x73821)),f319(f249(x73821,x73821,a923),x73822)))
% 28.25/28.11 [7383]P1(f319(x73831,x73832))+P1(f319(f319(f321(f932(f931(a925,a925),a923)),f588(x73832,x73831)),a90))
% 28.25/28.11 [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))
% 28.25/28.11 [7428]E(f319(f319(f126(a925),f131(a925,f319(f294(a925,x74281),x74282))),f319(f319(f143(a925),x74282),f105(a925))),f131(a925,f319(f294(a925,x74281),f319(a104,x74282))))+~P1(f319(f319(f226(a925),x74281),x74282))
% 28.25/28.11 [7577]E(x75771,f2(a925))+~E(f319(f134(a925,a925,f74(a925),x75771),x75772),f2(a925))
% 28.25/28.11 [7601]~P1(f319(f319(f227(a1),f319(f319(f23(a1),x76011),x76012)),f2(a1)))+P1(f319(f319(f227(a1),x76011),x76012))
% 28.25/28.11 [7629]P38(x76291,x76292)+~P38(x76291,f319(f319(f281(x76291,x76291,x76291),x76292),x76292))
% 28.25/28.11 [7654]~P1(f319(f319(f226(a925),f319(a104,x76541)),x76542))+P1(f177(a923,a231,f319(f226(a925),x76541),x76542))
% 28.25/28.11 [7806]P26(a925,a925,f319(f319(f7(a925,a925,a925),f23(a925)),x78061),x78062)+P1(f319(f319(f321(a925),f442(x78061,x78062)),x78062))
% 28.25/28.11 [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))
% 28.25/28.11 [7864]E(f319(f319(f319(f59(a925,x78641,f74(a925)),f319(f16(a925,x78641),f72(a925))),f2(a925)),x78642),f319(f29(x78641),x78642))+~P1(f319(f55(x78641),x78642))
% 28.25/28.11 [7906]P26(a925,a925,f319(f319(f7(a925,a925,a925),f23(a925)),x79061),x79062)+~P1(f319(f319(f226(a925),x79061),f442(x79061,x79062)))
% 28.25/28.11 [7961]P38(x79611,x79612)+P1(f319(f319(f226(f932(x79611,a923)),f597(x79612,x79611)),f319(f277(x79611,x79611,x79612),f597(x79612,x79611))))
% 28.25/28.11 [7966]P64(x79661,x79662)+~P38(x79661,f319(f254(f931(x79661,x79661)),f319(f249(x79661,x79661,a923),x79662)))
% 28.25/28.11 [7967]P54(x79671,x79672)+~P39(x79671,f319(f254(f931(x79671,x79671)),f319(f249(x79671,x79671,a923),x79672)))
% 28.25/28.11 [7968]P55(x79681,x79682)+~P56(x79681,f319(f254(f931(x79681,x79681)),f319(f249(x79681,x79681,a923),x79682)))
% 28.25/28.11 [8035]P1(f319(f319(f226(a925),f319(a104,x80351)),x80352))+~P1(f177(a923,a231,f319(f226(a925),x80351),x80352))
% 28.25/28.11 [8093]P1(f319(f319(f321(f931(a925,a925)),f319(f319(f244(a925,a925),x80931),x80932)),f299(a925,a309)))+~P1(f319(f319(f226(a925),x80931),x80932))
% 28.25/28.11 [8191]P50(x81911,x81912)+~P57(x81911,f234(f932(x81911,a923)),f319(f254(f931(x81911,x81911)),f319(f249(x81911,x81911,a923),x81912)))
% 28.25/28.11 [8247]~P1(f319(f129(x82471),x82472))+P1(f319(f129(f932(x82471,a923)),f319(f319(f146(f926(x82471),f932(x82471,a923)),f164(x82471)),f48(x82471,x82472))))
% 28.25/28.11 [8448]~P38(x84481,f319(f278(x84481,x84481),x84482))+P38(x84481,f319(f278(x84481,x84481),f319(f319(f281(x84481,x84481,x84481),x84482),f299(x84481,x84482))))
% 28.25/28.11 [8548]P27(x85481,a925,f515(x85482,x85481),x85482,f319(f294(a925,f2(a925)),f319(f29(x85481),x85482)))+~P1(f319(f55(x85481),x85482))
% 28.25/28.11 [8549]P27(a925,x85491,f458(x85492,x85491),f319(f294(a925,f2(a925)),f319(f29(x85491),x85492)),x85492)+~P1(f319(f55(x85491),x85492))
% 28.25/28.11 [8567]P27(a925,x85671,f451(x85672,x85671),f295(a925,f72(a925),f319(f29(x85671),x85672)),x85672)+~P1(f319(f55(x85671),x85672))
% 28.25/28.11 [8576]P1(f319(f55(f931(x85761,x85761)),f319(f319(f281(x85761,x85761,x85761),x85762),f299(x85761,x85762))))+~P1(f319(f55(f931(x85761,x85761)),x85762))
% 28.25/28.11 [8603]E(x86031,f2(a1))+P1(f319(f43(x86032,x86031),f319(f319(f244(a1,a1),f319(f319(f30(a1),x86032),x86031)),f39(a1,x86032,x86031))))
% 28.25/28.11 [8617]~P1(f319(f319(f321(f931(a925,a925)),f319(f319(f244(a925,a925),x86171),x86172)),f299(a925,a309)))+P1(f319(f319(f226(a925),x86171),x86172))
% 28.25/28.11 [8633]~P88(x86331)+E(f319(f134(x86331,x86331,f319(f7(x86331,x86331,x86331),f74(x86331)),f2(x86331)),f319(f160(x86331),x86332)),f319(f134(x86331,x86331,f74(x86331),f2(x86331)),x86332))
% 28.25/28.11 [8809]~P4(x88091)+E(f319(f134(f926(x88091),x88091,f319(f7(x88091,f926(x88091),f926(x88091)),f140(x88091,x88091,f5(x88091))),f105(x88091)),x88092),f142(x88091,x88091,f5(x88091),x88092))
% 28.25/28.11 [8920]~P62(x89201,f319(f254(f931(x89201,x89201)),f319(f249(x89201,x89201,a923),x89202)))+P62(x89201,f319(f254(f931(x89201,x89201)),f319(f249(x89201,x89201,a923),f235(x89201,x89201,x89202))))
% 28.25/28.11 [8934]P1(f319(f319(f321(f931(a925,a925)),f319(f319(f244(a925,a925),x89341),x89342)),f319(f319(f281(a925,a925,a925),a309),f299(a925,a309))))+~P1(f319(f319(f227(a925),x89341),x89342))
% 28.25/28.11 [8980]~P1(f319(f55(f931(x89801,x89801)),f319(f319(f281(x89801,x89801,x89801),x89802),f299(x89801,x89802))))+P1(f319(f55(f931(x89801,x89801)),x89802))
% 28.25/28.11 [9039]~P62(x90391,f319(f254(f931(x90391,x90391)),f319(f249(x90391,x90391,a923),f235(x90391,x90391,x90392))))+P62(x90391,f319(f254(f931(x90391,x90391)),f319(f249(x90391,x90391,a923),x90392)))
% 28.25/28.11 [9242]P62(x92421,x92422)+P1(f319(f319(f321(f931(x92421,x92421)),f319(f319(f244(x92421,x92421),f623(x92422,x92421)),f623(x92422,x92421))),f319(f319(f281(x92421,x92421,x92421),x92422),f299(x92421,x92422))))
% 28.25/28.11 [9243]P62(x92431,x92432)+P1(f319(f319(f321(f931(x92431,x92431)),f319(f319(f244(x92431,x92431),f633(x92432,x92431)),f633(x92432,x92431))),f319(f319(f281(x92431,x92431,x92431),x92432),f299(x92431,x92432))))
% 28.25/28.11 [9362]~P1(f319(f319(f321(f931(a925,a925)),f319(f319(f244(a925,a925),x93621),x93622)),f319(f319(f281(a925,a925,a925),a309),f299(a925,a309))))+P1(f319(f319(f227(a925),x93621),x93622))
% 28.25/28.11 [5286]~P99(x52861)+E(f319(f319(f74(x52861),f319(f95(x52861),a77)),x52862),x52862)
% 28.25/28.11 [5319]~P96(x53191)+E(f319(f319(f102(x53191),f319(f73(x53191),x53192)),x53192),f234(x53191))
% 28.25/28.11 [5320]~P96(x53201)+E(f319(f319(f93(x53201),f319(f73(x53201),x53202)),x53202),f180(x53201))
% 28.25/28.11 [5321]~P69(x53211)+E(f319(f319(f74(x53211),f319(f73(x53211),x53212)),x53212),f2(x53211))
% 28.25/28.11 [5322]~P70(x53221)+E(f319(f319(f74(x53221),f319(f73(x53221),x53222)),x53222),f2(x53221))
% 28.25/28.11 [5358]~P99(x53581)+E(f319(f319(f75(x53581),f319(f95(x53581),a89)),x53582),f319(f73(x53581),x53582))
% 28.25/28.11 [5513]~P118(x55131)+E(f319(f319(f75(x55131),f319(f73(x55131),f72(x55131))),x55132),f319(f73(x55131),x55132))
% 28.25/28.11 [5558]E(f319(f69(a1),x55581),f72(a1))+~E(f319(f69(a1),f319(f319(f75(a1),x55581),x55582)),f72(a1))
% 28.25/28.11 [5649]~P99(x56491)+E(f319(f319(f74(x56491),f72(x56491)),f319(f95(x56491),x56492)),f319(f95(x56491),f319(f319(f23(a1),x56492),a89)))
% 28.25/28.11 [5702]~P6(x57021)+E(f32(x57021,f319(f319(f301(x57021),x57022),f180(f932(x57021,a923)))),x57022)
% 28.25/28.11 [5703]~P6(x57031)+E(f31(x57031,f319(f319(f301(x57031),x57032),f180(f932(x57031,a923)))),x57032)
% 28.25/28.11 [5704]~P102(x57041)+E(f10(x57041,f319(f319(f301(x57041),x57042),f180(f932(x57041,a923)))),x57042)
% 28.25/28.11 [5705]~P102(x57051)+E(f13(x57051,f319(f319(f301(x57051),x57052),f180(f932(x57051,a923)))),x57052)
% 28.25/28.11 [5706]~P4(x57061)+E(f14(x57061,f319(f319(f301(x57061),x57062),f180(f932(x57061,a923)))),x57062)
% 28.25/28.11 [5707]~P4(x57071)+E(f15(x57071,f319(f319(f301(x57071),x57072),f180(f932(x57071,a923)))),x57072)
% 28.25/28.11 [5729]E(f319(f319(f74(a925),x57291),f319(f319(f23(a925),x57292),x57291)),x57292)+P1(f319(f319(f227(a925),x57292),x57291))
% 28.25/28.11 [5765]E(x57651,f105(x57652))+P1(f319(f319(f227(a925),f2(a925)),f319(f181(f926(x57652)),x57651)))
% 28.25/28.11 [5891]~P4(x58911)+E(f11(x58911,f224(x58911),f319(f319(f301(x58911),x58912),f180(f932(x58911,a923)))),x58912)
% 28.25/28.11 [5892]~P4(x58921)+E(f12(x58921,f225(x58921),f319(f319(f301(x58921),x58922),f180(f932(x58921,a923)))),x58922)
% 28.25/28.11 [5953]E(f319(f319(f23(a925),x59531),f319(f319(f23(a925),x59531),x59532)),x59532)+~P1(f319(f319(f226(a925),x59532),x59531))
% 28.25/28.11 [5954]E(f319(f319(f74(a925),x59541),f319(f319(f23(a925),x59542),x59541)),x59542)+~P1(f319(f319(f226(a925),x59541),x59542))
% 28.25/28.11 [5975]E(f39(a925,f319(f319(f23(a925),x59751),x59752),x59752),f39(a925,x59751,x59752))+P1(f319(f319(f227(a925),x59751),x59752))
% 28.25/28.11 [5976]E(f39(a925,f319(f319(f23(a925),x59761),x59762),x59762),f39(a925,x59761,x59762))+P1(f319(f319(f227(a925),x59761),x59762))
% 28.25/28.11 [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))
% 28.25/28.11 [5989]~E(x59892,f2(a925))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f236(a925),x59891),x59892)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [6154]E(f319(f133(a925),f131(a925,f319(f294(a925,x61541),x61542))),x61541)+~P1(f319(f319(f227(a925),x61541),x61542))
% 28.25/28.11 [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))
% 28.25/28.11 [6176]~P131(x61761)+P1(f319(f319(f226(x61761),f2(x61761)),f319(f319(f75(x61761),x61762),x61762)))
% 28.25/28.11 [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))
% 28.25/28.11 [6192]E(f39(a925,f319(f319(f23(a925),x61921),x61922),x61922),f39(a925,x61921,x61922))+~P1(f319(f319(f226(a925),x61922),x61921))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [6265]P1(f319(f129(x62651),x62652))+P1(f319(f319(f227(a925),f688(x62652,x62651)),f319(f181(f926(x62651)),x62652)))
% 28.25/28.11 [6266]P1(f319(f129(x62661),x62662))+P1(f319(f319(f227(a925),f694(x62662,x62661)),f319(f181(f926(x62661)),x62662)))
% 28.25/28.11 [6278]~E(x62781,f105(x62782))+~P1(f319(f319(f227(a925),f2(a925)),f319(f181(f926(x62782)),x62781)))
% 28.25/28.11 [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))
% 28.25/28.11 [6292]E(f319(f319(f74(a1),x62921),f319(f92(a1),f319(a104,f419(x62922,x62921)))),x62922)+~P1(f319(f319(f227(a1),x62921),x62922))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [6342]~P121(x63421)+E(f319(f319(f74(x63421),x63422),x63422),f319(f319(f75(x63421),f319(f319(f74(x63421),f72(x63421)),f72(x63421))),x63422))
% 28.25/28.11 [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))
% 28.25/28.11 [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)))
% 28.25/28.11 [6397]E(f171(x63971,x63972),f105(f926(x63971)))+P1(f319(f319(f321(f926(x63971)),f687(x63972,x63971)),f319(f164(f926(x63971)),x63972)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [6521]~P1(f319(f319(f227(a925),x65212),x65211))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f23(a925),x65211),x65212)))
% 28.25/28.11 [6553]~P1(f319(f319(f227(a925),x65531),f319(a96,x65532)))+P1(f319(f319(f227(a1),f319(f92(a1),x65531)),x65532))
% 28.25/28.11 [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))
% 28.25/28.11 [6583]~P1(f319(f319(f226(a1),f2(a1)),x65831))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f236(a1),x65831),x65832)))
% 28.25/28.11 [6584]~P1(f319(f319(f227(a925),f2(a925)),x65842))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f74(a925),x65841),x65842)))
% 28.25/28.11 [6585]~P1(f319(f319(f227(a925),f2(a925)),x65851))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f74(a925),x65851),x65852)))
% 28.25/28.11 [6586]~P1(f319(f319(f227(a925),f2(a925)),x65861))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f236(a925),x65861),x65862)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [6698]P1(f319(f319(f227(a925),x66981),f319(a96,x66982)))+~P1(f319(f319(f227(a1),f319(f92(a1),x66981)),x66982))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [6863]P1(f319(f319(f227(a925),x68631),x68632))+~P1(f319(f319(f227(a925),f2(a925)),f319(f319(f23(a925),x68632),x68631)))
% 28.25/28.11 [6908]P1(f319(f319(f227(a925),f2(a925)),x69081))+~P1(f319(f319(f227(a925),f2(a925)),f319(f319(f75(a925),x69082),x69081)))
% 28.25/28.11 [6909]P1(f319(f319(f227(a925),f2(a925)),x69091))+~P1(f319(f319(f227(a925),f2(a925)),f319(f319(f75(a925),x69091),x69092)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [6986]~E(x69862,f180(f932(x69861,a923)))+P1(f319(f319(f226(f932(x69861,a923)),x69862),f319(f73(f932(x69861,a923)),x69862)))
% 28.25/28.11 [7048]~P99(x70481)+E(f319(f319(f74(x70481),f319(f319(f74(x70481),f2(x70481)),f319(f95(x70481),x70482))),f319(f95(x70481),x70482)),f319(f95(x70481),f319(f319(f74(a1),x70482),x70482)))
% 28.25/28.11 [7105]~P1(f319(f319(f227(a1),x71051),x71052))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x71051),f72(a1))),x71052))
% 28.25/28.11 [7106]~P1(f319(f319(f227(a1),x71061),x71062))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x71061),f72(a1))),x71062))
% 28.25/28.11 [7172]E(x71721,f2(a925))+~P1(f319(f319(f226(a1),f319(f92(a1),x71722)),f319(f73(a1),f319(f92(a1),x71721))))
% 28.25/28.11 [7173]E(x71731,f2(a925))+~P1(f319(f319(f226(a1),f319(f92(a1),x71731)),f319(f73(a1),f319(f92(a1),x71732))))
% 28.25/28.11 [7274]E(f319(f319(f244(a1,a1),f319(f95(a1),a89)),f319(f319(f74(a1),x72741),x72742)),f44(x72741,x72742))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),x72741),x72742)))
% 28.25/28.11 [7319]~P28(x73191,x73192)+P38(x73191,f319(f243(f932(f931(x73191,x73191),a923),f932(f931(x73191,x73191),a923)),x73192))
% 28.25/28.11 [7338]~P1(f319(f319(f226(a925),f319(a104,f2(a925))),x73381))+P1(f319(f319(f226(a925),f319(a104,f2(a925))),f319(f319(f236(a925),x73381),x73382)))
% 28.25/28.11 [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)))
% 28.25/28.11 [7518]~P1(f319(f319(f226(a1),x75181),x75182))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x75181),x75181)),f319(f319(f74(a1),x75182),x75182)))
% 28.25/28.11 [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)))
% 28.25/28.11 [7523]~P1(f319(f319(f227(a1),x75231),x75232))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x75231),x75231)),f319(f319(f74(a1),x75232),x75232)))
% 28.25/28.11 [7578]~P1(f319(f319(f227(a925),f2(a925)),x75781))+P1(f319(f319(f227(a925),f319(f319(f23(a925),x75781),f319(a104,x75782))),x75781))
% 28.25/28.11 [7611]P1(f319(f319(f226(a925),f319(a104,f2(a925))),x76111))+~P1(f319(f319(f226(a925),f319(a104,f2(a925))),f319(f319(f75(a925),x76112),x76111)))
% 28.25/28.11 [7612]P1(f319(f319(f226(a925),f319(a104,f2(a925))),x76121))+~P1(f319(f319(f226(a925),f319(a104,f2(a925))),f319(f319(f75(a925),x76121),x76122)))
% 28.25/28.11 [7616]P1(f319(f319(f226(a925),f319(f319(f156(a925),x76161),x76162)),f319(f157(a925),x76161)))+~P1(f319(f319(f227(a925),x76162),f319(f181(f926(a925)),x76161)))
% 28.25/28.11 [7653]P1(f319(f319(f227(a1),x76531),x76532))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),x76531),f72(a1))),x76532))
% 28.25/28.11 [7662]~P1(f319(f319(f321(a925),x76621),x76622))+P1(f319(f319(f321(a1),f319(f92(a1),x76621)),f319(f302(a925,a1,f92(a1)),x76622)))
% 28.25/28.11 [7695]P1(f319(f55(x76951),f234(f932(x76951,a923))))+~P1(f319(f55(f932(x76952,x76951)),f234(f932(f932(x76952,x76951),a923))))
% 28.25/28.11 [7696]P1(f319(f55(x76961),f234(f932(x76961,a923))))+~P1(f319(f55(f933(x76962,x76961)),f234(f932(f933(x76962,x76961),a923))))
% 28.25/28.11 [7697]P1(f319(f55(x76971),f234(f932(x76971,a923))))+~P1(f319(f55(f933(x76971,x76972)),f234(f932(f933(x76971,x76972),a923))))
% 28.25/28.11 [7734]E(x77341,f180(f932(x77342,a923)))+~P1(f319(f319(f226(f932(x77342,a923)),x77341),f319(f73(f932(x77342,a923)),x77341)))
% 28.25/28.11 [7874]E(f319(f134(f926(x78741),f926(x78741),f126(x78741),f105(x78741)),x78742),f105(x78741))+P1(f319(f319(f321(f926(x78741)),f717(x78742,x78741)),f319(f164(f926(x78741)),x78742)))
% 28.25/28.11 [7875]E(f319(f134(f926(x78751),f926(x78751),f126(x78751),f105(x78751)),x78752),f105(x78751))+P1(f319(f319(f321(f926(x78751)),f718(x78752,x78751)),f319(f164(f926(x78751)),x78752)))
% 28.25/28.11 [8012]E(f171(x80121,f319(f319(f143(f926(x80121)),f105(x80121)),x80122)),f171(x80121,x80122))+~P1(f319(f307(f926(f926(x80121)),f172(x80121)),f319(f319(f143(f926(x80121)),f105(x80121)),x80122)))
% 28.25/28.11 [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)))
% 28.25/28.11 [8111]P1(f319(f319(f226(a1),x81111),x81112))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),x81111),x81111)),f319(f319(f74(a1),x81112),x81112)))
% 28.25/28.11 [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)))
% 28.25/28.11 [8116]P1(f319(f319(f227(a1),x81161),x81162))+~P1(f319(f319(f227(a1),f319(f319(f74(a1),x81161),x81161)),f319(f319(f74(a1),x81162),x81162)))
% 28.25/28.11 [8211]~P121(x82111)+E(f319(f319(f75(x82111),f319(f319(f74(x82111),f72(x82111)),f72(x82111))),f319(f319(f6(a925,x82111),f92(x82111)),f295(a925,f72(a925),x82112))),f319(f319(f75(x82111),f319(f92(x82111),x82112)),f319(f319(f74(x82111),f319(f92(x82111),x82112)),f72(x82111))))
% 28.25/28.11 [8246]E(f319(f319(f143(a1),f319(f95(a1),x82461)),f170(f319(f319(f74(a1),f319(f95(a1),x82461)),f72(a1)),f319(f95(a1),x82462))),f170(f319(f95(a1),x82461),f319(f95(a1),x82462)))+~P1(f319(f319(f226(a1),f319(f95(a1),x82461)),f319(f95(a1),x82462)))
% 28.25/28.11 [8261]P1(f319(f319(f321(a925),x82611),x82612))+~P1(f319(f319(f321(a1),f319(f92(a1),x82611)),f319(f302(a925,a1,f92(a1)),x82612)))
% 28.25/28.11 [8420]~P1(f319(f55(x84201),x84202))+E(f319(f302(a925,x84201,f456(x84202,x84201)),f319(f254(a925),f319(f319(f7(a925,a925,a923),f227(a925)),f457(x84202,x84201)))),x84202)
% 28.25/28.11 [8703]P58(x87031,x87032)+P1(f319(f319(f321(f931(x87031,x87031)),f319(f319(f244(x87031,x87031),f540(x87032,x87031)),f540(x87032,x87031))),x87032))
% 28.25/28.11 [8704]P39(x87041,x87042)+P1(f319(f319(f321(f931(x87041,x87041)),f319(f319(f244(x87041,x87041),f808(x87042,x87041)),f811(x87042,x87041))),x87042))
% 28.25/28.11 [8705]P39(x87051,x87052)+P1(f319(f319(f321(f931(x87051,x87051)),f319(f319(f244(x87051,x87051),f811(x87052,x87051)),f812(x87052,x87051))),x87052))
% 28.25/28.11 [8706]P40(x87061,x87062)+P1(f319(f319(f321(f931(x87061,x87061)),f319(f319(f244(x87061,x87061),f728(x87062,x87061)),f727(x87062,x87061))),x87062))
% 28.25/28.11 [8707]P40(x87071,x87072)+P1(f319(f319(f321(f931(x87071,x87071)),f319(f319(f244(x87071,x87071),f727(x87072,x87071)),f728(x87072,x87071))),x87072))
% 28.25/28.11 [8708]P56(x87081,x87082)+P1(f319(f319(f321(f931(x87081,x87081)),f319(f319(f244(x87081,x87081),f822(x87082,x87081)),f823(x87082,x87081))),x87082))
% 28.25/28.11 [8852]~P99(x88521)+E(f319(f319(f23(x88521),f72(x88521)),f319(f95(x88521),x88522)),f319(f95(x88521),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f73(a1),x88522))))
% 28.25/28.11 [8976]~P1(f319(f319(f226(f932(a925,a923)),x89761),x89762))+P1(f319(f319(f226(f932(a1,a923)),f319(f302(a925,a1,f92(a1)),x89761)),f319(f302(a925,a1,f92(a1)),x89762)))
% 28.25/28.11 [8977]~P1(f319(f319(f227(f932(a925,a923)),x89771),x89772))+P1(f319(f319(f227(f932(a1,a923)),f319(f302(a925,a1,f92(a1)),x89771)),f319(f302(a925,a1,f92(a1)),x89772)))
% 28.25/28.11 [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)))
% 28.25/28.11 [9012]~P1(f319(f319(f227(a1),x90121),x90122))+P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x90121),x90121)),a89)),f319(f319(f74(a1),x90122),x90122)))
% 28.25/28.11 [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)))
% 28.25/28.11 [9014]~P1(f319(f319(f227(a1),x90141),x90142))+P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x90141),x90141)),a89)),f319(f319(f74(a1),x90142),x90142)))
% 28.25/28.11 [9087]~P1(f319(f319(f321(a925),x90871),f319(f164(a925),x90872)))+P1(f319(f319(f226(a925),x90871),f319(f134(a925,a925,f74(a925),f2(a925)),x90872)))
% 28.25/28.11 [9181]P47(x91811,x91812)+~P1(f319(f319(f321(f931(x91811,x91811)),f319(f319(f244(x91811,x91811),f532(x91812,x91811)),f532(x91812,x91811))),x91812))
% 28.25/28.11 [9182]P39(x91821,x91822)+~P1(f319(f319(f321(f931(x91821,x91821)),f319(f319(f244(x91821,x91821),f808(x91822,x91821)),f812(x91822,x91821))),x91822))
% 28.25/28.11 [9183]P56(x91831,x91832)+~P1(f319(f319(f321(f931(x91831,x91831)),f319(f319(f244(x91831,x91831),f823(x91832,x91831)),f822(x91832,x91831))),x91832))
% 28.25/28.11 [9324]~P1(f319(f319(f226(f932(a1,a923)),f319(f302(a925,a1,f92(a1)),x93241)),f319(f302(a925,a1,f92(a1)),x93242)))+P1(f319(f319(f226(f932(a925,a923)),x93241),x93242))
% 28.25/28.11 [9325]~P1(f319(f319(f227(f932(a1,a923)),f319(f302(a925,a1,f92(a1)),x93251)),f319(f302(a925,a1,f92(a1)),x93252)))+P1(f319(f319(f227(f932(a925,a923)),x93251),x93252))
% 28.25/28.11 [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)))
% 28.25/28.11 [9412]P1(f319(f319(f227(a1),x94121),x94122))+~P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x94121),x94121)),a89)),f319(f319(f74(a1),x94122),x94122)))
% 28.25/28.11 [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)))
% 28.25/28.11 [9414]P1(f319(f319(f227(a1),x94141),x94142))+~P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x94141),x94141)),a89)),f319(f319(f74(a1),x94142),x94142)))
% 28.25/28.11 [10332]~P111(x103321)+E(f108(f926(x103321),f319(f121(f926(x103321)),f105(x103321)),f319(f319(f319(f86(f927(f926(x103321))),f319(f319(f227(a1),f2(a1)),x103322)),f319(f110(f931(x103321,f926(x103321)),f926(x103321),f123(x103321,f926(x103321),f124(x103321,f319(f319(f23(a1),x103322),f72(a1))),f124(f926(x103321),f319(f319(f23(a1),x103322),f72(a1))))),f319(f249(x103321,f926(x103321),f927(f926(x103321))),f319(f319(f8(f932(f926(x103321),f926(x103321)),f932(f926(x103321),f927(f926(x103321))),x103321),f319(f8(f926(x103321),f927(f926(x103321)),f926(x103321)),f121(f926(x103321)))),f143(x103321))))),f107(f926(x103321)))),f124(f926(x103321),x103322))
% 28.25/28.11 [10354]~P1(f319(f55(x103541),x103542))+E(f319(f181(f926(x103541)),f84(f926(x103541),f319(f319(f18(f926(x103541),a923,a923),f319(f319(f8(a923,f932(a923,a923),f926(x103541)),a317),f319(f319(f7(f926(x103541),f932(x103541,a923),a923),f319(f319(f8(f932(x103541,a923),f932(f932(x103541,a923),a923),f926(x103541)),a316),f164(x103541))),x103542))),f129(x103541)))),f206(x103541,x103542))
% 28.25/28.11 [6288]E(f319(f319(f74(a925),f319(f319(f23(a925),x62881),x62882)),x62882),x62881)+~P1(f319(f319(f226(a925),x62882),x62881))
% 28.25/28.11 [6359]E(f319(f319(f30(a925),f319(f319(f75(a925),x63591),x63592)),x63592),x63591)+~P1(f319(f319(f227(a925),f2(a925)),x63592))
% 28.25/28.11 [6360]E(f319(f319(f30(a925),f319(f319(f75(a925),x63601),x63602)),x63601),x63602)+~P1(f319(f319(f227(a925),f2(a925)),x63601))
% 28.25/28.11 [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))
% 28.25/28.11 [6473]E(f39(a925,f319(a104,f319(f319(f75(a925),x64731),x64732)),x64731),f72(a925))+~P1(f319(f319(f227(a925),f72(a925)),x64731))
% 28.25/28.11 [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)))
% 28.25/28.11 [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)))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [6876]E(x68761,f2(a1))+P1(f319(f319(f227(a1),f2(a1)),f319(f319(f236(a1),f319(f69(a1),x68761)),x68762)))
% 28.25/28.11 [6892]~E(x68922,f2(a925))+P1(f319(f319(f227(a1),f2(a1)),f319(f319(f236(a1),f319(f69(a1),x68921)),x68922)))
% 28.25/28.11 [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))
% 28.25/28.11 [6979]~P1(f319(f319(f226(a1),x69791),x69792))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x69791),a89)),x69792))
% 28.25/28.11 [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))
% 28.25/28.11 [7110]E(f319(f319(f143(a925),x71101),f131(a925,f319(f294(a925,f319(a104,x71101)),x71102))),f131(a925,f319(f294(a925,x71101),x71102)))+~P1(f319(f319(f227(a925),x71101),x71102))
% 28.25/28.11 [7310]E(x73101,x73102)+~E(f319(f319(f23(a1),f319(f319(f74(a1),x73101),x73101)),a89),f319(f319(f23(a1),f319(f319(f74(a1),x73102),x73102)),a89))
% 28.25/28.11 [7313]E(x73131,f105(x73132))+E(f258(x73132,f319(f319(f146(x73132,f931(a91,x73132)),f319(f244(a91,x73132),f72(a91))),x73131)),f267(x73132,x73131))
% 28.25/28.11 [7549]P1(f319(f319(f226(a1),x75491),x75492))+~P1(f319(f319(f227(a1),f319(f319(f74(a1),x75491),a89)),x75492))
% 28.25/28.11 [8014]~P1(f319(f319(f227(a925),x80141),x80142))+P1(f319(f319(f321(f931(a925,a925)),f319(f319(f244(a925,a925),x80141),x80142)),a232))
% 28.25/28.11 [8238]~P1(f319(f319(f227(a91),f2(a91)),x82381))+P1(f319(f319(f227(a91),f319(f243(a91,f931(a91,a91)),f319(f259(x82381),x82382))),x82381))
% 28.25/28.11 [8502]~P39(x85021,x85022)+P39(x85021,f319(f319(f102(f932(f931(x85021,x85021),a923)),x85022),f299(x85021,f180(f932(f931(x85021,x85021),a923)))))
% 28.25/28.11 [8503]~P40(x85031,x85032)+P40(x85031,f319(f319(f102(f932(f931(x85031,x85031),a923)),x85032),f299(x85031,f180(f932(f931(x85031,x85031),a923)))))
% 28.25/28.11 [8553]~P92(x85531)+P1(f319(f319(f226(x85531),f319(f69(x85531),f319(f157(x85531),x85532))),f319(f157(x85531),f319(f319(f146(x85531,x85531),f69(x85531)),x85532))))
% 28.25/28.11 [8578]P1(f319(f319(f227(a925),x85781),x85782))+~P1(f319(f319(f321(f931(a925,a925)),f319(f319(f244(a925,a925),x85781),x85782)),a232))
% 28.25/28.11 [8730]E(f319(f319(f244(x87301,x87301),f648(x87302,x87301)),f648(x87302,x87301)),x87302)+~P1(f319(f319(f321(f931(x87301,x87301)),x87302),f299(x87301,f180(f932(f931(x87301,x87301),a923)))))
% 28.25/28.11 [8773]E(f319(f294(a925,x87731),f319(f319(f74(a925),x87731),f319(f29(a925),x87732))),x87732)+~P1(f319(f319(f226(f932(a925,a923)),x87732),f319(f294(a925,x87731),f319(f319(f74(a925),x87731),f319(f29(a925),x87732)))))
% 28.25/28.11 [8794]E(f319(f319(f143(a925),f319(f95(a925),x87941)),f131(a925,f319(f294(a925,f319(a104,f319(f95(a925),x87941))),f319(f95(a925),x87942)))),f131(a925,f319(f294(a925,f319(f95(a925),x87941)),f319(f95(a925),x87942))))+~P1(f319(f319(f227(a925),f319(f95(a925),x87941)),f319(f95(a925),x87942)))
% 28.25/28.11 [9005]P40(x90051,x90052)+~P40(x90051,f319(f319(f102(f932(f931(x90051,x90051),a923)),x90052),f299(x90051,f180(f932(f931(x90051,x90051),a923)))))
% 28.25/28.11 [9132]E(f319(f319(f30(a1),f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),x91321),x91321)),a89))),f319(f95(a1),f319(f319(f74(a1),x91322),x91322))),f319(f319(f30(a1),f319(f95(a1),x91321)),f319(f95(a1),x91322)))+~P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x91322)))
% 28.25/28.11 [9227]~P39(x92271,x92272)+P1(f319(f319(f226(f932(f931(x92271,x92271),a923)),f319(f319(f281(x92271,x92271,x92271),x92272),x92272)),x92272))
% 28.25/28.11 [9253]E(f169(f926(x92531),f319(f319(f8(a923,a923,f926(x92531)),a314),f319(f319(f7(f926(x92531),f926(x92531),a923),a316),f105(x92531))),x92532),f171(x92531,f171(x92531,x92532)))+~P14(a925,f319(f160(a925),f319(f319(f146(f926(x92531),a925),f181(f926(x92531))),x92532)))
% 28.25/28.11 [9256]E(f319(f319(f30(a1),f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),x92561),x92561)),a89))),f319(f95(a1),f319(f319(f74(a1),x92562),x92562))),f319(f319(f30(a1),f319(f319(f74(a1),f319(f95(a1),x92561)),f72(a1))),f319(f95(a1),x92562)))+P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x92562)))
% 28.25/28.11 [10124]P1(f319(a185,x101242))+E(f319(f319(f80(a1,a925),f319(f319(f23(a1),x101241),x101242)),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,x101241)),f319(a96,x101242)))
% 28.25/28.11 [10132]E(f319(f319(f80(a1,a925),f319(f95(a1),f319(f319(f74(a1),x101321),f319(f73(a1),x101322)))),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),x101321)),f319(f95(a925),x101322)))+P1(f319(f319(f227(a1),x101322),a77))
% 28.25/28.11 [10133]~P28(x101331,x101332)+P1(f319(f319(f226(f932(f931(x101331,x101331),a923)),f319(f319(f281(x101331,x101331,x101331),f319(f243(f932(f931(x101331,x101331),a923),f932(f931(x101331,x101331),a923)),x101332)),f319(f248(f932(f931(x101331,x101331),a923),f932(f931(x101331,x101331),a923)),x101332))),f319(f243(f932(f931(x101331,x101331),a923),f932(f931(x101331,x101331),a923)),x101332)))
% 28.25/28.11 [10188]~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)),x101881))),f319(f319(f7(a925,a925,a923),f227(a925)),f319(a104,x101882))))),f2(a925))+~P1(f319(f319(f321(a925),f2(a925)),x101881))
% 28.25/28.11 [10202]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)))),x102021,x102022),f180(f932(a925,a923)))+~P1(f319(f319(f279(a925),x102022),x102021))
% 28.25/28.11 [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))
% 28.25/28.11 [10206]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)))),x102061,x102062),f180(f932(a925,a923)))+P1(f319(f319(f279(a925),x102061),x102062))
% 28.25/28.11 [10207]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)))),x102071,x102072),f180(f932(a925,a923)))+P1(f319(f319(f279(a925),x102071),x102072))
% 28.25/28.11 [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))
% 28.25/28.11 [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))
% 28.25/28.11 [10210]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)))),x102101,x102102),f180(f932(a925,a923)))+~P1(f319(f319(f279(a925),x102102),x102101))
% 28.25/28.11 [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))
% 28.25/28.11 [10212]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)))),x102121,x102122),f180(f932(a925,a923)))+~P1(f319(f319(f279(a925),x102122),x102121))
% 28.25/28.11 [10257]E(f39(a1,f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),x102571),x102571)),a89)),f319(f95(a1),f319(f319(f74(a1),x102572),x102572))),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),x102571),f319(f95(a1),x102572)))),f72(a1)))+~P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x102572)))
% 28.25/28.11 [10266]E(f39(a1,f319(f95(a1),f319(f319(f23(a1),f319(f319(f74(a1),x102661),x102661)),a89)),f319(f95(a1),f319(f319(f74(a1),x102662),x102662))),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),x102661)),f72(a1)),f319(f95(a1),x102662)))),f72(a1)))+P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x102662)))
% 28.25/28.11 [10322]~P6(x103221)+E(f31(x103221,f319(f254(x103221),f319(f319(f8(f932(x103221,a923),a923,x103221),f82(x103221)),f319(f319(f8(f932(x103221,a923),f932(x103221,a923),x103221),f319(f18(x103221,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103221),a322),f319(f319(f7(x103221,f932(x103221,a923),a923),f321(x103221)),x103222)))),f226(x103221))))),f32(x103221,x103222))
% 28.25/28.11 [10347]~P38(x103471,x103472)+P64(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))
% 28.25/28.11 [10348]~P9(x103481,f234(f932(x103481,a923)),x103482)+P8(x103481,f319(f319(f7(x103481,f932(f931(x103481,x103481),a923),f932(x103481,a923)),f319(f319(f8(f932(x103481,f932(f932(f931(x103481,x103481),a923),a923)),f932(f932(f931(x103481,x103481),a923),f932(x103481,a923)),x103481),f7(x103481,f932(f931(x103481,x103481),a923),a923)),f319(f319(f8(f932(x103481,f931(x103481,x103481)),f932(x103481,f932(f932(f931(x103481,x103481),a923),a923)),x103481),f319(f8(f931(x103481,x103481),f932(f932(f931(x103481,x103481),a923),a923),x103481),f321(f931(x103481,x103481)))),f244(x103481,x103481)))),x103482))
% 28.25/28.11 [10390]P38(x103901,x103902)+~P64(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))
% 28.25/28.11 [10391]P9(x103911,f234(f932(x103911,a923)),x103912)+~P8(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)))),x103912))
% 28.25/28.11 [7498]E(f319(f319(f74(a925),f319(f95(a925),f319(f319(f23(a1),x74981),a89))),x74982),f319(a104,f319(f319(f74(a925),f319(f95(a925),x74981)),x74982)))+P1(f319(a185,f319(f95(a1),x74981)))
% 28.25/28.11 [7932]~P99(x79321)+E(f319(f319(f74(x79321),f319(f319(f74(x79321),f72(x79321)),f319(f95(x79321),x79322))),f319(f95(x79321),x79322)),f319(f95(x79321),f319(f319(f23(a1),f319(f319(f74(a1),x79322),x79322)),a89)))
% 28.25/28.11 [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)))
% 28.25/28.11 [8580]~P1(f319(f319(f226(a1),x85801),x85802))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x85801),x85801)),f319(f319(f23(a1),f319(f319(f74(a1),x85802),x85802)),a89)))
% 28.25/28.11 [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)))
% 28.25/28.11 [8582]~P1(f319(f319(f226(a1),x85821),x85822))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x85821),x85821)),f319(f319(f23(a1),f319(f319(f74(a1),x85822),x85822)),a89)))
% 28.25/28.11 [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)))
% 28.25/28.11 [9016]P1(f319(f319(f226(a1),x90161),x90162))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),x90161),x90161)),f319(f319(f23(a1),f319(f319(f74(a1),x90162),x90162)),a89)))
% 28.25/28.11 [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)))
% 28.25/28.11 [9018]P1(f319(f319(f226(a1),x90181),x90182))+~P1(f319(f319(f227(a1),f319(f319(f74(a1),x90181),x90181)),f319(f319(f23(a1),f319(f319(f74(a1),x90182),x90182)),a89)))
% 28.25/28.11 [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)))
% 28.25/28.11 [9313]~P1(f319(f319(f226(a1),x93131),x93132))+P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x93131),x93131)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),x93132),x93132)),a89)))
% 28.25/28.11 [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)))
% 28.25/28.11 [9315]~P1(f319(f319(f227(a1),x93151),x93152))+P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x93151),x93151)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),x93152),x93152)),a89)))
% 28.25/28.11 [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)))
% 28.25/28.11 [9588]P1(f319(f319(f226(a1),x95881),x95882))+~P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),x95881),x95881)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),x95882),x95882)),a89)))
% 28.25/28.11 [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)))
% 28.25/28.11 [9590]P1(f319(f319(f227(a1),x95901),x95902))+~P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),x95901),x95901)),a89)),f319(f319(f23(a1),f319(f319(f74(a1),x95902),x95902)),a89)))
% 28.25/28.11 [9623]~P1(f319(f55(x96231),x96232))+P1(f319(f55(f932(x96231,a923)),f319(f254(f932(x96231,a923)),f319(f319(f7(f932(x96231,a923),f932(x96231,a923),a923),f226(f932(x96231,a923))),x96232))))
% 28.25/28.11 [9675]~E(f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),x96751),f180(f932(f931(a925,a925),a923)))),f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),x96752),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)),x96751),x96752)),a100))
% 28.25/28.11 [9762]E(f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),x97621),f180(f932(f931(a925,a925),a923)))),f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),x97622),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)),x97621),x97622)),a100))
% 28.25/28.11 [9800]P1(f319(f319(f226(a1),f2(a1)),f663(x98001,x98002)))+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)))
% 28.25/28.11 [10331]~P6(x103311)+E(f32(x103311,f319(f254(x103311),f319(f319(f8(f932(x103311,a923),a923,x103311),f82(x103311)),f319(f319(f8(f932(x103311,a923),f932(x103311,a923),x103311),f319(f18(x103311,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103311),a322),f319(f319(f7(x103311,f932(x103311,a923),a923),f321(x103311)),x103312)))),f319(f7(x103311,x103311,a923),f226(x103311)))))),f31(x103311,x103312))
% 28.25/28.11 [10353]P1(f319(f319(f321(a925),f2(a925)),x103531))+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)),x103531))),f319(f319(f7(a925,a925,a923),f227(a925)),x103532)))),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)),x103531))),f319(f319(f7(a925,a925,a923),f227(a925)),f319(a104,x103532))))))
% 28.25/28.11 [7800]~P99(x78001)+E(f319(f319(f75(x78001),x78002),f319(f95(x78001),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),x78002)
% 28.25/28.11 [8063]~P99(x80631)+E(f319(f319(f74(x80631),f319(f95(x80631),x80632)),f72(x80631)),f319(f95(x80631),f319(f319(f74(a1),x80632),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))))
% 28.25/28.11 [8209]P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x82092)))+E(f319(f319(f236(a1),x82091),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),x82092),x82092)),a89))),f72(a1))
% 28.25/28.11 [9650]~P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x96502)))+E(f319(f319(f236(a1),x96501),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),x96502),x96502)),a89))),f319(f319(f80(a1,a1),f319(f319(f236(a1),x96501),f319(f95(a925),x96502))),f319(f319(f18(a1,a1,a1),f319(f319(f8(a1,f932(a1,a1),a1),f75(a1)),f319(f75(a1),x96501))),f5(a1))))
% 28.25/28.11 [10038]~P1(f319(f319(f226(a925),f673(x100382,x100381)),f319(x100381,f673(x100382,x100381))))+P1(f319(f55(a925),f319(f254(a925),f319(f319(f7(a925,a925,a923),f319(f319(f8(a925,f932(a925,a923),a925),f226(a925)),x100381)),x100382))))
% 28.25/28.11 [10178]~P1(f319(f319(f226(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),f226(a925)),a96)),x101782))))
% 28.25/28.11 [10179]~P1(f319(f319(f227(a925),f319(f95(a925),x101791)),f319(a104,x101792)))+P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x101791),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)),x101792))))
% 28.25/28.11 [10241]P1(f319(f319(f226(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),f226(a925)),a96)),x102412))))
% 28.25/28.11 [10242]P1(f319(f319(f227(a925),f319(f95(a925),x102421)),f319(a104,x102422)))+~P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x102421),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)),x102422))))
% 28.25/28.11 [10272]~P1(f319(f319(f226(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(f226(a925),x102722)),a96)))))
% 28.25/28.11 [10273]~P1(f319(f319(f227(a925),f319(a104,x102732)),f319(f95(a925),x102731)))+P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x102731),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),x102732)),a96)))))
% 28.25/28.11 [10320]P1(f319(f319(f226(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(f226(a925),x103201)),a96)))))
% 28.25/28.11 [10321]P1(f319(f319(f227(a925),f319(a104,x103211)),f319(f95(a925),x103212)))+~P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x103212),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),x103211)),a96)))))
% 28.25/28.11 [10400]~P1(f319(f319(f321(a925),f2(a925)),x104001))+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)),x104001))),f319(f319(f7(a925,a925,a923),f227(a925)),x104002))))),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)),x104001))),f319(f319(f7(a925,a925,a923),f227(a925)),f319(a104,x104002))))))
% 28.25/28.11 [8756]~P99(x87561)+E(f319(f319(f75(x87561),f319(f95(x87561),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),x87562),x87562)
% 28.25/28.11 [8818]~P99(x88181)+E(f319(f319(f74(x88181),f72(x88181)),f319(f95(x88181),x88182)),f319(f95(x88181),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),x88182)))
% 28.25/28.11 [8880]~P99(x88801)+E(f319(f319(f23(x88801),f319(f95(x88801),x88802)),f72(x88801)),f319(f95(x88801),f319(f319(f74(a1),x88802),f319(f73(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))
% 28.25/28.11 [9035]~P1(f319(f319(f227(a925),f319(f95(a925),a77)),x90352))+E(f319(f319(f23(a925),x90351),f319(f319(f23(a925),x90352),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))),f319(f319(f23(a925),f319(a104,x90351)),x90352))
% 28.25/28.11 [9693]~P121(x96931)+E(f319(f319(f75(x96931),x96932),x96932),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)))))
% 28.25/28.11 [9694]~P87(x96941)+E(f319(f319(f236(x96941),x96942),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(x96941),x96942),x96942))
% 28.25/28.11 [9696]~P99(x96961)+E(f319(f319(f75(x96961),x96962),f319(f95(x96961),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(x96961),x96962),x96962))
% 28.25/28.11 [9944]~P145(x99441)+E(f319(f319(f236(x99441),f319(f73(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)))))
% 28.25/28.11 [9945]~P126(x99451)+E(f319(f319(f236(x99451),f319(f69(x99451),x99452)),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(x99451),x99452),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)))))
% 28.25/28.11 [9941]~P99(x99411)+E(f319(f319(f75(x99411),f319(f95(x99411),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)))),x99412),f319(f319(f74(x99411),x99412),x99412))
% 28.25/28.11 [10073]~P126(x100731)+E(f319(f69(x100731),f319(f319(f236(x100731),x100732),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(x100731),x100732),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)))))
% 28.25/28.11 [10140]~P126(x101401)+P1(f319(f319(f226(x101401),f2(x101401)),f319(f319(f236(x101401),x101402),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))))))
% 28.25/28.11 [10311]~E(f319(a104,x103112),f319(f95(a925),x103111))+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)))))
% 28.25/28.11 [10312]~E(f319(f95(a925),x103121),f319(a104,x103122))+P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x103121),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)),x103122)))))
% 28.25/28.11 [10356]E(f319(a104,x103561),f319(f95(a925),x103562))+~P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x103562),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)),x103561)))))
% 28.25/28.11 [10357]E(f319(f95(a925),x103571),f319(a104,x103572))+~P1(f319(f319(f80(a1,a923),f319(f95(a1),f319(f319(f74(a1),x103571),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)),x103572)))))
% 28.25/28.11 [10401]~P17(x104011,x104012)+P1(f319(f319(f321(f932(x104011,a923)),f830(x104012,x104011)),f319(f319(f8(f932(x104011,a923),a923,f932(x104011,a923)),f81(x104011)),f319(f319(f8(f932(x104011,a923),f932(x104011,a923),f932(x104011,a923)),f319(f18(x104011,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104011),a317),f319(f319(f18(x104011,x104011,a923),x104012),f5(x104011))))),f319(f319(f7(f932(x104011,a923),f932(x104011,f932(x104011,a923)),f932(x104011,a923)),f319(f319(f8(f932(f932(x104011,a923),a923),f932(f932(x104011,f932(x104011,a923)),f932(x104011,a923)),f932(x104011,a923)),f8(f932(x104011,a923),a923,x104011)),a316)),x104012)))))
% 28.25/28.11 [10138]~P99(x101381)+E(f319(f319(f236(x101381),f319(f95(x101381),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)))),x101382)),f72(x101381))
% 28.25/28.11 [10139]~P145(x101391)+E(f319(f319(f236(x101391),f319(f73(x101391),f72(x101391))),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)))),x101392)),f72(x101391))
% 28.25/28.11 [10142]~P87(x101421)+E(f319(f319(f236(x101421),x101422),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(x101421),f319(f319(f75(x101421),x101422),x101422)),x101422))
% 28.25/28.11 [10336]~P1(f319(f319(f226(a1),f2(a1)),x103362))+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)))),x103361)),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)))),x103362)),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,x103361,x103362))))
% 28.25/28.11 [10359]~P1(f319(f319(f226(a1),f2(a1)),x103592))+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)))),x103591))),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)))),x103592)),f319(f319(f30(a1),x103591),x103592))
% 28.25/28.11 [10361]~P1(f319(f319(f226(a1),x103612),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)))),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(f30(a1),f319(f319(f74(a1),x103611),f72(a1))),x103612))
% 28.25/28.11 [10362]~P1(f319(f319(f226(a1),x103622),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)))),x103621)),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)))),x103622)),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),x103621),f72(a1)),x103622))),f72(a1)))
% 28.25/28.11 [10232]~P99(x102321)+E(f319(f319(f236(x102321),f319(f95(x102321),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)))),x102322))),f319(f95(x102321),a89))
% 28.25/28.11 [10234]~P145(x102341)+E(f319(f319(f236(x102341),f319(f73(x102341),f72(x102341))),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)))),x102342))),f319(f73(x102341),f72(x102341)))
% 28.25/28.11 [5151]P39(x51511,x51512)+~P9(x51511,x51513,x51512)
% 28.25/28.11 [5152]P39(x51521,x51522)+~P9(x51521,x51523,x51522)
% 28.25/28.11 [5153]P56(x51531,x51532)+~P9(x51531,x51533,x51532)
% 28.25/28.11 [5154]P56(x51541,x51542)+~P9(x51541,x51543,x51542)
% 28.25/28.11 [5327]~P9(x53271,x53272,x53273)+P57(x53271,x53272,x53273)
% 28.25/28.11 [5328]~P9(x53281,x53282,x53283)+P57(x53281,x53282,x53283)
% 28.25/28.11 [8276]~E(x82762,x82763)+P35(x82761,x82761,a316,x82762,x82763)
% 28.25/28.11 [8831]E(x88311,x88312)+~P35(x88313,x88313,a316,x88311,x88312)
% 28.25/28.11 [4958]E(f161(x49581,x49582,x49583),f105(x49581))+~E(x49582,f2(a925))
% 28.25/28.11 [4959]E(f161(x49591,x49592,x49593),f105(x49591))+~E(x49592,f2(a925))
% 28.25/28.11 [5126]~E(f161(x51262,x51261,x51263),f105(x51262))+E(x51261,f2(a925))
% 28.25/28.11 [5127]~E(f161(x51272,x51271,x51273),f105(x51272))+E(x51271,f2(a925))
% 28.25/28.11 [5333]~P38(x53331,x53333)+P38(x53331,f313(x53331,x53332,x53333))
% 28.25/28.11 [5445]~P30(x54451,x54452,x54453)+P32(a1,x54451,f170(x54452,x54453))
% 28.25/28.11 [5511]P30(x55111,x55112,x55113)+~P32(a1,x55111,f170(x55112,x55113))
% 28.25/28.11 [5582]~P9(x55821,x55822,x55823)+P9(f926(x55821),f153(x55821,x55822),f150(x55821,x55823))
% 28.25/28.11 [5583]~P57(x55831,x55832,x55833)+P57(f926(x55831),f153(x55831,x55832),f150(x55831,x55833))
% 28.25/28.11 [5694]P59(x56941,x56942,x56943)+~E(f610(x56943,x56942,x56941),f611(x56943,x56942,x56941))
% 28.25/28.11 [5695]P60(x56951,x56952,x56953)+~E(f626(x56953,x56952,x56951),f627(x56953,x56952,x56951))
% 28.25/28.11 [8282]~E(x82822,x82823)+P27(x82821,x82821,f25(x82821),x82822,x82823)
% 28.25/28.11 [8839]E(x88391,x88392)+~P27(x88393,x88393,f25(x88393),x88391,x88392)
% 28.25/28.11 [4914]~E(f319(f160(x49142),x49141),x49143)+E(x49141,f319(f160(x49142),x49143))
% 28.25/28.11 [4915]~E(x49152,f319(f160(x49151),x49153))+E(f319(f160(x49151),x49152),x49153)
% 28.25/28.11 [4965]E(x49651,x49652)+~E(f319(f160(x49653),x49651),f319(f160(x49653),x49652))
% 28.25/28.11 [5178]~P8(x51783,x51781)+P1(f319(f319(x51781,x51782),x51782))
% 28.25/28.11 [5179]~P50(x51793,x51791)+P1(f319(f319(x51791,x51792),x51792))
% 28.25/28.11 [5180]~P64(x51801,x51802)+P1(f319(f307(x51801,x51802),x51803))
% 28.25/28.11 [5181]~P64(x51811,x51812)+P1(f319(f307(x51811,x51812),x51813))
% 28.25/28.11 [5245]~P38(x52451,x52452)+P38(f926(x52451),f319(f135(x52451,x52452),x52453))
% 28.25/28.11 [5250]~P1(f319(x52502,x52503))+~E(f319(f254(x52501),x52502),f180(f932(x52501,a923)))
% 28.25/28.11 [5251]~P1(f319(x52512,x52513))+~E(f180(f932(x52511,a923)),f319(f254(x52511),x52512))
% 28.25/28.11 [5263]E(x52631,f2(a925))+E(f136(x52632,f161(x52632,x52631,x52633)),x52633)
% 28.25/28.11 [5279]~P1(f319(x52791,x52793))+P1(f319(x52791,f84(x52792,x52791)))
% 28.25/28.11 [5280]~P1(f319(x52801,x52803))+P1(f319(x52801,f84(x52802,x52801)))
% 28.25/28.11 [5281]~P1(f319(x52811,x52813))+P1(f319(x52811,f84(x52812,x52811)))
% 28.25/28.11 [5282]~P1(f319(x52821,x52823))+P1(f319(x52821,f84(x52822,x52821)))
% 28.25/28.11 [5283]~P1(f319(x52831,x52833))+P1(f319(x52831,f756(x52831,x52832)))
% 28.25/28.11 [5295]E(x52951,f2(a925))+E(f319(f133(x52952),f161(x52952,x52951,x52953)),x52953)
% 28.25/28.11 [5408]~E(x54082,x54083)+P1(f319(f319(f321(x54081),x54082),f319(a316,x54083)))
% 28.25/28.11 [5423]~E(x54232,f2(a925))+E(f319(f164(x54231),f161(x54231,x54232,x54233)),f180(f932(x54231,a923)))
% 28.25/28.11 [5467]E(f319(f160(x54671),x54672),f319(f319(f143(x54671),x54673),f105(x54671)))+~E(x54672,f319(f319(f143(x54671),x54673),f105(x54671)))
% 28.25/28.11 [5468]~E(x54683,f319(f319(f143(x54681),x54682),f105(x54681)))+E(f319(f319(f143(x54681),x54682),f105(x54681)),f319(f160(x54681),x54683))
% 28.25/28.11 [5507]~P34(x55071,x55072,x55073)+P34(x55071,x55072,f319(f160(x55071),x55073))
% 28.25/28.11 [5508]~P32(x55081,x55082,x55083)+P32(x55081,x55082,f319(f160(x55081),x55083))
% 28.25/28.11 [5512]E(f319(f29(x55121),f328(x55122,x55123,x55121)),x55122)+~E(f319(f29(x55121),x55123),f319(a104,x55122))
% 28.25/28.11 [5518]~P38(x55181,x55183)+P1(f319(f319(f321(x55181),x55182),f308(x55181,x55183)))
% 28.25/28.11 [5519]~P38(x55191,x55193)+P1(f319(f319(f321(x55191),x55192),f308(x55191,x55193)))
% 28.25/28.11 [5523]~E(f319(f160(x55232),x55231),f319(f319(f143(x55232),x55233),f105(x55232)))+E(x55231,f319(f319(f143(x55232),x55233),f105(x55232)))
% 28.25/28.11 [5524]~E(f319(f319(f143(x55242),x55243),f105(x55242)),f319(f160(x55242),x55241))+E(x55241,f319(f319(f143(x55242),x55243),f105(x55242)))
% 28.25/28.11 [5547]E(f79(f931(a925,a925),f42(x55471,x55472)),x55473)+~P1(f319(f42(x55471,x55472),x55473))
% 28.25/28.11 [5586]P34(x55861,x55862,x55863)+~P34(x55861,x55862,f319(f160(x55861),x55863))
% 28.25/28.11 [5587]P32(x55871,x55872,x55873)+~P32(x55871,x55872,f319(f160(x55871),x55873))
% 28.25/28.11 [5625]P1(f319(f319(x56251,x56252),x56252))+~P1(f319(f262(x56253,x56251),x56252))
% 28.25/28.11 [5626]~P1(f319(f319(x56262,x56263),x56263))+P1(f319(f262(x56261,x56262),x56263))
% 28.25/28.11 [5648]~E(x56482,f105(x56481))+P1(f319(f319(f321(f926(x56481)),x56482),f153(x56481,x56483)))
% 28.25/28.11 [5657]~P57(x56571,x56572,x56573)+P57(x56571,x56572,f319(f278(x56571,x56571),x56573))
% 28.25/28.11 [5658]~P60(x56581,x56582,x56583)+P60(x56581,x56582,f319(f278(x56581,x56581),x56583))
% 28.25/28.11 [5675]~P65(x56751)+E(f39(x56751,f39(x56751,x56752,x56753),x56753),f39(x56751,x56752,x56753))
% 28.25/28.11 [5776]E(x57761,x57762)+~P1(f319(f319(f321(x57763),x57761),f319(a316,x57762)))
% 28.25/28.11 [5822]~P149(x58221)+E(f182(x58221,x58222,f2(a925),x58223),x58223)
% 28.25/28.11 [5844]P57(x58441,x58442,x58443)+~P57(x58441,x58442,f319(f278(x58441,x58441),x58443))
% 28.25/28.11 [5845]P60(x58451,x58452,x58453)+~P60(x58451,x58452,f319(f278(x58451,x58451),x58453))
% 28.25/28.11 [5849]~P4(x58492)+E(f142(x58491,x58492,x58493,f105(x58491)),f105(x58491))
% 28.25/28.11 [5862]E(f162(x58621,x58622,f144(x58621,x58623)),f144(x58621,f162(x58621,x58622,x58623)))+~P1(f319(f129(x58621),x58623))
% 28.25/28.11 [5961]~P1(f319(f319(x59613,x59612),x59612))+P1(f319(f319(f321(x59611),x59612),f262(x59611,x59613)))
% 28.25/28.11 [5963]E(f319(f128(x59631,x59632),x59633),f105(x59631))+P1(f319(x59632,f695(x59633,x59632,x59631)))
% 28.25/28.11 [6022]E(f62(x60221,x60222,x60223),x60222)+P1(f319(x60223,f757(x60222,x60221,x60223)))
% 28.25/28.11 [6120]~P1(f319(f129(x61201),x61202))+P1(f319(f129(x61201),f168(x61201,x61202,x61203)))
% 28.25/28.11 [6121]~P1(f319(f129(x61211),x61213))+P1(f319(f129(x61211),f162(x61211,x61212,x61213)))
% 28.25/28.11 [6122]~P1(f319(f129(x61221),x61223))+P1(f319(f129(x61221),f169(x61221,x61222,x61223)))
% 28.25/28.11 [6123]~P1(f319(f129(x61231),x61233))+P1(f319(f129(x61231),f132(x61231,x61232,x61233)))
% 28.25/28.11 [6124]~P151(x61241,x61243,x61242)+P1(f319(x61241,f39(a1,x61242,x61243)))
% 28.25/28.11 [6140]~P34(x61403,x61401,x61402)+P1(f319(x61401,f771(x61402,x61401,x61403)))
% 28.25/28.11 [6141]~P36(x61413,x61411,x61412)+P1(f319(x61411,f775(x61412,x61411,x61413)))
% 28.25/28.11 [6142]~P36(x61423,x61421,x61422)+P1(f319(x61421,f787(x61422,x61421,x61423)))
% 28.25/28.11 [6143]~P34(x61433,x61431,x61432)+P1(f319(x61431,f814(x61432,x61431,x61433)))
% 28.25/28.11 [6144]~P34(x61443,x61441,x61442)+P1(f319(x61441,f816(x61441,x61442,x61443)))
% 28.25/28.11 [6149]P1(f319(f319(x61491,x61492),x61492))+~P1(f319(f319(f321(x61493),x61492),f262(x61493,x61491)))
% 28.25/28.11 [6164]E(f319(f128(x61641,x61642),x61643),f169(x61641,x61642,x61643))+P1(f319(x61642,f743(x61643,x61642,x61641)))
% 28.25/28.11 [6206]~P1(f319(f129(x62061),x62063))+P1(f319(f129(f926(x62061)),f49(x62061,x62062,x62063)))
% 28.25/28.11 [6241]~P113(x62411)+E(f319(f319(f93(f932(x62411,a923)),f319(f274(x62411),x62412)),f295(x62411,x62412,x62413)),f180(f932(x62411,a923)))
% 28.25/28.11 [6242]~P113(x62421)+E(f319(f319(f93(f932(x62421,a923)),f319(f293(x62421),x62422)),f297(x62421,x62422,x62423)),f180(f932(x62421,a923)))
% 28.25/28.11 [6243]~P113(x62431)+E(f319(f319(f93(f932(x62431,a923)),f319(f293(x62431),x62432)),f298(x62431,x62432,x62433)),f180(f932(x62431,a923)))
% 28.25/28.11 [6469]E(f319(f128(x64691,x64692),x64693),x64693)+~P1(f319(x64692,f726(x64693,x64692,x64691)))
% 28.25/28.11 [6471]E(f319(f319(f301(x64711),f420(x64712,x64713,x64711)),f328(x64712,x64713,x64711)),x64713)+~E(f319(f29(x64711),x64713),f319(a104,x64712))
% 28.25/28.11 [6486]P151(x64861,x64862,x64863)+~P1(f319(x64861,f39(a1,x64863,x64862)))
% 28.25/28.11 [6536]P32(x65361,x65362,x65363)+~P1(f319(x65362,f776(x65363,x65362,x65361)))
% 28.25/28.11 [6537]P32(x65371,x65372,x65373)+~P1(f319(x65372,f785(x65372,x65373,x65371)))
% 28.25/28.11 [6538]P32(x65381,x65382,x65383)+~P1(f319(x65382,f786(x65383,x65382,x65381)))
% 28.25/28.11 [6539]P30(x65391,x65392,x65393)+~P1(f319(x65391,f801(x65393,x65392,x65391)))
% 28.25/28.11 [6540]P31(x65401,x65402,x65403)+~P1(f319(x65401,f857(x65403,x65402,x65401)))
% 28.25/28.11 [6542]E(f169(x65421,x65422,x65423),x65423)+~P1(f319(x65422,f739(x65423,x65422,x65421)))
% 28.25/28.11 [6623]~P1(f319(x66232,f598(x66233,x66232,x66231)))+P1(f319(f240(x66231,x66232),x66233))
% 28.25/28.11 [6624]~P1(f319(x66242,f696(x66243,x66242,x66241)))+P1(f319(f152(x66241,x66242),x66243))
% 28.25/28.11 [6877]~P1(f319(f307(x68771,x68772),f524(x68773,x68772,x68771)))+P1(f319(f307(x68771,x68772),x68773))
% 28.25/28.11 [6878]~P1(f319(f307(x68781,x68782),f539(x68783,x68782,x68781)))+P1(f319(f307(x68781,x68782),x68783))
% 28.25/28.11 [7499]~P65(x74991)+E(f319(f319(f74(x74991),f319(f319(f75(x74991),x74992),f319(f319(f30(x74991),x74993),x74992))),f39(x74991,x74993,x74992)),x74993)
% 28.25/28.11 [7529]P30(x75291,x75292,x75293)+P1(f319(f319(f321(a1),f801(x75293,x75292,x75291)),f295(a1,x75292,x75293)))
% 28.25/28.11 [7953]E(f319(f319(f244(x79531,x79531),f555(x79532,x79533,x79531)),f555(x79532,x79533,x79531)),x79533)+~P1(f319(f319(f321(f931(x79531,x79531)),x79533),f255(x79531,x79532)))
% 28.25/28.11 [8071]~P1(f319(f319(f321(x80711),f560(x80713,x80712,x80711)),f308(x80711,x80713)))+P1(f319(f319(f321(x80711),x80712),f308(x80711,x80713)))
% 28.25/28.11 [8072]~P1(f319(f319(f321(x80721),f612(x80723,x80722,x80721)),f308(x80721,x80723)))+P1(f319(f319(f321(x80721),x80722),f308(x80721,x80723)))
% 28.25/28.11 [8073]~P1(f319(f319(f321(x80731),f613(x80733,x80732,x80731)),f308(x80731,x80733)))+P1(f319(f319(f321(x80731),x80732),f308(x80731,x80733)))
% 28.25/28.11 [8167]P34(a1,x81671,f170(x81672,x81673))+P30(f319(f66(a923,a923,a1,a314),x81671),x81672,x81673)
% 28.25/28.11 [8256]~P65(x82561)+E(f319(f319(f74(x82561),f319(f319(f75(x82561),f319(f319(f30(x82561),x82562),x82563)),x82563)),f39(x82561,x82562,x82563)),x82562)
% 28.25/28.11 [8257]~P65(x82571)+E(f319(f319(f74(x82571),f319(f319(f75(x82571),f319(f319(f30(x82571),x82572),x82573)),x82573)),f39(x82571,x82572,x82573)),x82572)
% 28.25/28.11 [8304]~E(f319(f29(x83041),x83042),f319(a104,x83043))+~P1(f319(f319(f321(x83041),f420(x83043,x83042,x83041)),f328(x83043,x83042,x83041)))
% 28.25/28.11 [8748]~P34(a1,x87481,f170(x87482,x87483))+~P30(f319(f66(a923,a923,a1,a314),x87481),x87482,x87483)
% 28.25/28.11 [8936]P1(f319(f319(f226(f932(f931(x89361,x89361),a923)),f299(x89361,x89362)),f299(x89361,x89363)))+~P1(f319(f319(f226(f932(f931(x89361,x89361),a923)),x89362),f299(x89361,x89363)))
% 28.25/28.11 [9073]~P27(x90731,x90732,x90733,f234(f932(x90731,a923)),f234(f932(x90732,a923)))+P26(x90731,x90732,x90733,f234(f932(x90731,a923)))
% 28.25/28.11 [9074]~P27(x90741,x90742,x90743,f234(f932(x90741,a923)),f234(f932(x90742,a923)))+P26(x90741,x90742,x90743,f234(f932(x90741,a923)))
% 28.25/28.11 [9223]E(x92231,f105(x92232))+~P1(f319(f319(f321(f931(f926(x92232),f926(x92232))),f319(f319(f244(f926(x92232),f926(x92232)),x92231),f105(x92232))),f150(x92232,x92233)))
% 28.25/28.11 [9247]E(x92471,f105(x92472))+~P1(f319(f319(f321(f931(f926(x92472),f926(x92472))),f319(f319(f244(f926(x92472),f926(x92472)),f105(x92472)),x92471)),f150(x92472,x92473)))
% 28.25/28.11 [9374]E(f319(f319(f143(x93741),f712(x93742,x93743,x93741)),f713(x93742,x93743,x93741)),x93743)+~P1(f319(f319(f321(f931(f926(x93741),f926(x93741))),f319(f319(f244(f926(x93741),f926(x93741)),f105(x93741)),x93743)),f139(x93741,x93742)))
% 28.25/28.11 [9616]~P131(x96161)+~P1(f319(f319(f227(x96161),f319(f319(f74(x96161),f319(f319(f75(x96161),x96162),x96162)),f319(f319(f75(x96161),x96163),x96163))),f2(x96161)))
% 28.25/28.11 [9668]P1(f319(f55(x96681),x96682))+~P1(f319(f319(f321(f931(f932(x96681,a923),f932(x96681,a923))),f319(f319(f244(f932(x96681,a923),f932(x96681,a923)),x96683),x96682)),f306(x96681)))
% 28.25/28.11 [9976]~P48(x99761,x99762,x99763)+P1(f319(f319(f226(a1),f319(f319(f66(f931(a1,a1),a1,x99761,f243(a1,a1)),f204(x99761)),f222(x99761,x99762,f219(x99761,x99763)))),f2(a1)))
% 28.25/28.11 [9977]~P49(x99771,x99772,x99773)+P1(f319(f319(f227(a1),f319(f319(f66(f931(a1,a1),a1,x99771,f243(a1,a1)),f204(x99771)),f222(x99771,x99772,f219(x99771,x99773)))),f2(a1)))
% 28.25/28.11 [10106]P49(x101061,x101062,x101063)+~P1(f319(f319(f227(a1),f319(f319(f66(f931(a1,a1),a1,x101061,f243(a1,a1)),f204(x101061)),f222(x101061,x101062,f219(x101061,x101063)))),f2(a1)))
% 28.25/28.11 [10107]P48(x101071,x101072,x101073)+~P1(f319(f319(f226(a1),f319(f319(f66(f931(a1,a1),a1,x101071,f243(a1,a1)),f204(x101071)),f222(x101071,x101072,f219(x101071,x101073)))),f2(a1)))
% 28.25/28.11 [10461]~P126(x104611)+~P1(f319(f319(f227(x104611),f319(f319(f74(x104611),f319(f319(f236(x104611),x104612),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(x104611),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)))))),f2(x104611)))
% 28.25/28.11 [4942]~E(x49423,f105(x49421))+E(f319(f319(f126(x49421),x49422),x49423),x49422)
% 28.25/28.11 [4943]~E(x49432,f105(x49431))+E(f319(f319(f126(x49431),x49432),x49433),x49433)
% 28.25/28.11 [4944]~E(x49443,f105(x49441))+E(f319(f319(f126(x49441),x49442),x49443),x49442)
% 28.25/28.11 [4945]~E(x49452,f105(x49451))+E(f319(f319(f126(x49451),x49452),x49453),x49453)
% 28.25/28.11 [4951]~E(x49512,f2(a925))+E(f319(f319(f167(x49511),x49512),x49513),f105(x49511))
% 28.25/28.11 [4960]~E(x49603,f105(x49601))+E(f319(f319(f167(x49601),x49602),x49603),f105(x49601))
% 28.25/28.11 [4999]~E(x49991,x49993)+E(x49991,f319(f319(f126(x49992),f105(x49992)),x49993))
% 28.25/28.11 [5089]~P115(x50892)+E(f319(f234(f932(x50891,x50892)),x50893),f234(x50892))
% 28.25/28.11 [5090]~P109(x50902)+E(f319(f180(f932(x50901,x50902)),x50903),f180(x50902))
% 28.25/28.11 [5091]~P109(x50912)+E(f319(f180(f932(x50911,x50912)),x50913),f180(x50912))
% 28.25/28.11 [5107]E(x51071,f105(x51072))+~E(f319(f319(f126(x51072),x51071),x51073),x51073)
% 28.25/28.11 [5108]E(x51081,f105(x51082))+~E(f319(f319(f126(x51082),x51083),x51081),x51083)
% 28.25/28.11 [5109]E(x51091,f105(x51092))+~E(f319(f319(f126(x51092),x51093),x51091),x51093)
% 28.25/28.11 [5110]E(x51101,f105(x51102))+~E(f319(f319(f126(x51102),x51101),x51103),x51103)
% 28.25/28.11 [5116]E(x51161,f105(x51162))+~E(f319(f319(f126(x51162),x51163),x51161),f105(x51162))
% 28.25/28.11 [5117]E(x51171,f105(x51172))+~E(f319(f319(f126(x51172),x51171),x51173),f105(x51172))
% 28.25/28.11 [5118]E(x51181,f105(x51182))+~E(f319(f319(f126(x51182),x51183),x51181),f105(x51182))
% 28.25/28.11 [5119]E(x51191,f105(x51192))+~E(f319(f319(f126(x51192),x51191),x51193),f105(x51192))
% 28.25/28.11 [5144]~E(x51442,f2(a925))+E(f319(f319(f75(a925),x51441),x51442),f319(f319(f75(a925),x51443),x51442))
% 28.25/28.11 [5145]~E(x51451,f2(a925))+E(f319(f319(f75(a925),x51451),x51452),f319(f319(f75(a925),x51451),x51453))
% 28.25/28.11 [5146]~E(x51461,f2(a925))+E(f319(f319(f75(a925),x51461),x51462),f319(f319(f75(a925),x51461),x51463))
% 28.25/28.11 [5204]~P102(x52041)+E(f319(f319(f102(x52041),x52042),x52043),f319(f319(f102(x52041),x52043),x52042))
% 28.25/28.11 [5205]~P107(x52051)+E(f319(f319(f102(x52051),x52052),x52053),f319(f319(f102(x52051),x52053),x52052))
% 28.25/28.11 [5206]~P107(x52061)+E(f319(f319(f102(x52061),x52062),x52063),f319(f319(f102(x52061),x52063),x52062))
% 28.25/28.11 [5207]~P102(x52071)+E(f319(f319(f93(x52071),x52072),x52073),f319(f319(f93(x52071),x52073),x52072))
% 28.25/28.11 [5208]~P108(x52081)+E(f319(f319(f93(x52081),x52082),x52083),f319(f319(f93(x52081),x52083),x52082))
% 28.25/28.11 [5209]~P108(x52091)+E(f319(f319(f93(x52091),x52092),x52093),f319(f319(f93(x52091),x52093),x52092))
% 28.25/28.11 [5210]~P121(x52101)+E(f319(f319(f75(x52101),x52102),x52103),f319(f319(f75(x52101),x52103),x52102))
% 28.25/28.11 [5211]~P121(x52111)+E(f319(f319(f74(x52111),x52112),x52113),f319(f319(f74(x52111),x52113),x52112))
% 28.25/28.11 [5212]~P4(x52121)+E(f319(f319(f224(x52121),x52122),x52123),f319(f319(f224(x52121),x52123),x52122))
% 28.25/28.11 [5213]~P4(x52131)+E(f319(f319(f224(x52131),x52132),x52133),f319(f319(f224(x52131),x52133),x52132))
% 28.25/28.11 [5214]~P4(x52141)+E(f319(f319(f225(x52141),x52142),x52143),f319(f319(f225(x52141),x52143),x52142))
% 28.25/28.11 [5215]~P4(x52151)+E(f319(f319(f225(x52151),x52152),x52153),f319(f319(f225(x52151),x52153),x52152))
% 28.25/28.11 [5277]E(f39(a925,x52771,x52772),f2(a925))+~E(x52771,f319(f319(f75(a925),x52772),x52773))
% 28.25/28.11 [5278]E(f39(a1,x52781,x52782),f2(a1))+~E(x52781,f319(f319(f75(a1),x52782),x52783))
% 28.25/28.11 [5345]E(x53451,x53452)+~E(f319(f319(f74(a925),x53453),x53451),f319(f319(f74(a925),x53453),x53452))
% 28.25/28.11 [5346]E(x53461,x53462)+~E(f319(f319(f74(a925),x53461),x53463),f319(f319(f74(a925),x53462),x53463))
% 28.25/28.11 [5359]~P96(x53591)+E(f319(f319(f93(x53591),x53592),f319(f73(x53591),x53593)),f319(f319(f23(x53591),x53592),x53593))
% 28.25/28.11 [5360]~P69(x53601)+E(f319(f319(f74(x53601),x53602),f319(f73(x53601),x53603)),f319(f319(f23(x53601),x53602),x53603))
% 28.25/28.11 [5361]~P70(x53611)+E(f319(f319(f74(x53611),x53612),f319(f73(x53611),x53613)),f319(f319(f23(x53611),x53612),x53613))
% 28.25/28.11 [5362]~P118(x53621)+E(f319(f319(f74(x53621),x53622),f319(f73(x53621),x53623)),f319(f319(f23(x53621),x53622),x53623))
% 28.25/28.11 [5363]~P69(x53631)+E(f319(f319(f23(x53631),x53632),f319(f73(x53631),x53633)),f319(f319(f74(x53631),x53632),x53633))
% 28.25/28.11 [5401]~P1(f319(x54013,x54012))+P1(f319(f319(f321(x54011),x54012),x54013))
% 28.25/28.11 [5402]~P79(x54022)+E(f319(f319(f6(x54021,x54022),x54023),f180(f932(x54021,a923))),f2(x54022))
% 28.25/28.11 [5403]~P79(x54032)+E(f319(f319(f6(x54031,x54032),x54033),f180(f932(x54031,a923))),f2(x54032))
% 28.25/28.11 [5404]~P78(x54042)+E(f319(f319(f9(x54041,x54042),x54043),f180(f932(x54041,a923))),f72(x54042))
% 28.25/28.11 [5405]~P78(x54052)+E(f319(f319(f9(x54051,x54052),x54053),f180(f932(x54051,a923))),f72(x54052))
% 28.25/28.11 [5457]~E(x54572,f319(f319(f74(a925),x54571),x54573))+P1(f319(f319(f226(a925),x54571),x54572))
% 28.25/28.11 [5460]~E(x54602,f180(f932(x54601,a923)))+E(f319(f319(f54(x54601),x54602),x54603),f180(f932(f932(x54601,a923),a923)))
% 28.25/28.11 [5461]~E(x54612,f180(f932(x54611,a923)))+E(f180(f932(f932(x54611,a923),a923)),f319(f319(f54(x54611),x54612),x54613))
% 28.25/28.11 [5527]~E(f319(f276(x55272,x55273),x55271),f180(f932(x55273,a923)))+E(x55271,f180(f932(f931(x55272,x55273),a923)))
% 28.25/28.11 [5528]~E(f319(f256(x55282,x55283),x55281),f180(f932(x55282,a923)))+E(x55281,f180(f932(f931(x55282,x55283),a923)))
% 28.25/28.11 [5560]E(f319(f276(x55601,x55602),x55603),f180(f932(x55602,a923)))+~E(x55603,f180(f932(f931(x55601,x55602),a923)))
% 28.25/28.11 [5561]E(f319(f256(x55611,x55612),x55613),f180(f932(x55611,a923)))+~E(x55613,f180(f932(f931(x55611,x55612),a923)))
% 28.25/28.11 [5564]E(f266(x55641,x55642,x55643),f319(f319(f23(a91),x55642),x55643))+P1(f319(f319(f227(a91),x55642),x55643))
% 28.25/28.11 [5580]P1(f319(x55801,x55802))+~P1(f319(f319(f321(x55803),x55802),x55801))
% 28.25/28.11 [5618]E(x56181,x56182)+~E(f319(f73(f932(x56183,a923)),x56181),f319(f73(f932(x56183,a923)),x56182))
% 28.25/28.11 [5627]~E(x56271,f180(f932(x56272,a923)))+~P1(f319(f319(f321(x56272),x56273),x56271))
% 28.25/28.11 [5628]~E(x56281,f180(f932(x56282,a923)))+~P1(f319(f319(f321(x56282),x56283),x56281))
% 28.25/28.11 [5629]~E(x56291,f180(f932(x56292,a923)))+~P1(f319(f319(f321(x56292),x56293),x56291))
% 28.25/28.11 [5659]~E(x56592,f319(f319(f74(a1),x56591),f319(f92(a1),x56593)))+P1(f319(f319(f226(a1),x56591),x56592))
% 28.25/28.11 [5673]E(f319(f319(f301(x56731),x56732),x56733),x56733)+~P1(f319(f319(f321(x56731),x56732),x56733))
% 28.25/28.11 [5684]E(x56841,f180(f932(x56842,a923)))+~E(f319(f319(f54(x56842),x56841),x56843),f180(f932(f932(x56842,a923),a923)))
% 28.25/28.11 [5685]E(x56851,f180(f932(x56852,a923)))+~E(f180(f932(f932(x56852,a923),a923)),f319(f319(f54(x56852),x56851),x56853))
% 28.25/28.11 [5691]~P116(x56911)+E(f319(f319(f75(x56911),f319(f73(x56911),x56912)),f319(f73(x56911),x56913)),f319(f319(f75(x56911),x56912),x56913))
% 28.25/28.11 [5693]~P72(x56931)+E(f319(f319(f283(x56931),f319(f73(x56931),x56932)),f319(f73(x56931),x56933)),f319(f319(f283(x56931),x56932),x56933))
% 28.25/28.11 [5724]~P1(f319(x57243,x57242))+P1(f319(f319(f321(x57241),x57242),f319(f254(x57241),x57243)))
% 28.25/28.11 [5725]~P1(f319(x57253,x57252))+P1(f319(f319(f321(x57251),x57252),f319(f254(x57251),x57253)))
% 28.25/28.11 [5749]E(x57491,f2(a925))+E(f319(f164(x57492),f161(x57492,x57491,x57493)),f319(f319(f301(x57492),x57493),f180(f932(x57492,a923))))
% 28.25/28.11 [5750]E(x57501,f2(a925))+E(f319(f164(x57502),f161(x57502,x57501,x57503)),f319(f319(f301(x57502),x57503),f180(f932(x57502,a923))))
% 28.25/28.11 [5769]E(f162(x57691,x57692,x57693),x57693)+P1(f319(f319(f321(x57691),x57692),f319(f164(x57691),x57693)))
% 28.25/28.11 [5853]~P1(f319(f129(x58531),x58533))+P1(f319(f129(x58531),f319(f128(x58531,x58532),x58533)))
% 28.25/28.11 [5897]~P65(x58971)+E(f319(f319(f30(x58971),f39(x58971,x58972,x58973)),x58973),f2(x58971))
% 28.25/28.11 [5916]E(f168(x59161,f319(f319(f143(x59161),x59162),f105(x59161)),x59163),f105(x59161))+P1(f319(f319(f321(a925),f2(a925)),x59163))
% 28.25/28.11 [5922]E(x59221,f2(a925))+E(f319(f163(x59222),f161(x59222,x59221,x59223)),f161(x59222,f319(f319(f23(a925),x59221),f72(a925)),x59223))
% 28.25/28.11 [5972]E(f319(f319(f143(x59721),x59722),x59723),f132(x59721,x59722,x59723))+P1(f319(f319(f321(x59721),x59722),f319(f164(x59721),x59723)))
% 28.25/28.11 [5973]E(f319(f319(f143(x59731),x59732),x59733),f132(x59731,x59732,x59733))+P1(f319(f319(f321(x59731),x59732),f319(f164(x59731),x59733)))
% 28.25/28.11 [5982]E(x59821,x59822)+~E(f319(f319(f75(a925),f319(a104,x59823)),x59821),f319(f319(f75(a925),f319(a104,x59823)),x59822))
% 28.25/28.11 [5983]~E(x59832,f319(f319(f74(a1),x59831),f319(f92(a1),f319(a104,x59833))))+P1(f319(f319(f227(a1),x59831),x59832))
% 28.25/28.11 [6045]~P31(x60451,x60452,x60453)+P32(a925,x60451,f131(a925,f319(f294(a925,x60452),x60453)))
% 28.25/28.11 [6099]~E(x60993,f105(x60991))+E(f319(f319(f319(f175(f926(x60991),f926(x60991)),x60992),f159(x60991)),x60993),f105(x60991))
% 28.25/28.11 [6101]P1(f319(x61011,x61012))+~P1(f319(f319(f321(x61013),x61012),f319(f254(x61013),x61011)))
% 28.25/28.11 [6102]P1(f319(x61021,x61022))+~P1(f319(f319(f321(x61023),x61022),f319(f254(x61023),x61021)))
% 28.25/28.11 [6103]P1(f319(x61031,x61032))+~P1(f319(f319(f321(x61033),x61032),f319(f254(x61033),x61031)))
% 28.25/28.11 [6135]E(x61351,x61352)+~E(f319(f319(f301(x61353),x61351),f180(f932(x61353,a923))),f319(f319(f301(x61353),x61352),f180(f932(x61353,a923))))
% 28.25/28.11 [6151]~P113(x61511)+E(f319(f319(f93(f932(x61511,a923)),f319(f274(x61511),x61512)),f319(f294(x61511,x61512),x61513)),f180(f932(x61511,a923)))
% 28.25/28.11 [6189]E(f132(x61891,x61892,x61893),x61893)+~P1(f319(f319(f321(x61891),x61892),f319(f164(x61891),x61893)))
% 28.25/28.11 [6190]E(f132(x61901,x61902,x61903),x61903)+~P1(f319(f319(f321(x61901),x61902),f319(f164(x61901),x61903)))
% 28.25/28.11 [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)))
% 28.25/28.11 [6220]P1(f319(f319(f321(x62201),x62202),f319(f164(x62201),x62203)))+~P1(f319(f319(f164(x62201),x62203),x62202))
% 28.25/28.11 [6221]P1(f319(f319(f321(x62211),x62212),f319(f164(x62211),x62213)))+~P1(f319(f319(f164(x62211),x62213),x62212))
% 28.25/28.11 [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)))
% 28.25/28.11 [6244]P1(f319(x62441,x62442))+~P1(f319(f319(f321(x62443),x62442),f180(f932(x62443,a923))))
% 28.25/28.11 [6245]~P1(f319(x62452,x62453))+P1(f319(f319(f321(x62451),f756(x62452,x62451)),f234(f932(x62451,a923))))
% 28.25/28.11 [6277]~P113(x62771)+E(f319(f319(f93(f932(x62771,a923)),f319(f294(x62771,x62772),x62773)),f319(f275(x62771),x62773)),f180(f932(x62771,a923)))
% 28.25/28.11 [6297]~P68(x62971)+E(f319(f302(x62971,x62971,f73(x62971)),f295(x62971,x62972,x62973)),f295(x62971,f319(f73(x62971),x62973),f319(f73(x62971),x62972)))
% 28.25/28.11 [6298]~P68(x62981)+E(f319(f302(x62981,x62981,f73(x62981)),f298(x62981,x62982,x62983)),f298(x62981,f319(f73(x62981),x62983),f319(f73(x62981),x62982)))
% 28.25/28.11 [6303]~P1(f319(x63031,x63032))+~P1(f319(f319(f321(x63033),x63032),f180(f932(x63033,a923))))
% 28.25/28.11 [6356]~P1(f319(f319(f321(x63561),x63563),f319(f164(x63561),x63562)))+P1(f319(f319(f164(x63561),x63562),x63563))
% 28.25/28.11 [6357]~P1(f319(f319(f321(x63571),x63573),f319(f164(x63571),x63572)))+P1(f319(f319(f164(x63571),x63572),x63573))
% 28.25/28.11 [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))
% 28.25/28.11 [6366]P31(x63661,x63662,x63663)+~P32(a925,x63661,f131(a925,f319(f294(a925,x63662),x63663)))
% 28.25/28.11 [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)))
% 28.25/28.11 [6389]~P66(x63891)+E(f39(x63891,f319(f73(x63891),f39(x63891,x63892,x63893)),x63893),f39(x63891,f319(f73(x63891),x63892),x63893))
% 28.25/28.11 [6484]~P1(f319(f55(f931(x64842,x64841)),x64843))+P1(f319(f55(x64841),f319(f276(x64842,x64841),x64843)))
% 28.25/28.11 [6485]~P1(f319(f55(f931(x64851,x64852)),x64853))+P1(f319(f55(x64851),f319(f256(x64851,x64852),x64853)))
% 28.25/28.11 [6490]~P113(x64901)+E(f319(f319(f93(f932(x64901,a923)),f295(x64901,x64902,x64903)),f319(f296(x64901),x64903)),f180(f932(x64901,a923)))
% 28.25/28.11 [6491]~P113(x64911)+E(f319(f319(f93(f932(x64911,a923)),f297(x64911,x64912,x64913)),f319(f296(x64911),x64913)),f180(f932(x64911,a923)))
% 28.25/28.11 [6492]~P113(x64921)+E(f319(f319(f93(f932(x64921,a923)),f298(x64921,x64922,x64923)),f319(f275(x64921),x64923)),f180(f932(x64921,a923)))
% 28.25/28.11 [6563]E(f319(f319(f156(x65631),x65632),f658(x65632,x65633,x65631)),x65633)+~P1(f319(f319(f321(x65631),x65633),f319(f164(x65631),x65632)))
% 28.25/28.11 [6708]E(x67081,f105(x67082))+~E(f319(f319(f319(f175(f926(x67082),f926(x67082)),x67083),f159(x67082)),x67081),f105(x67082))
% 28.25/28.11 [6815]~P1(f319(f55(f931(x68152,x68151)),x68153))+P1(f319(f55(f931(x68151,x68152)),f319(f278(x68152,x68151),x68153)))
% 28.25/28.11 [6838]E(x68381,x68382)+~E(f282(a925,f279(a925),x68383,x68381),f319(f319(f301(a925),x68382),f180(f932(a925,a923))))
% 28.25/28.11 [6839]E(x68391,x68392)+~E(f282(a925,f279(a925),x68391,x68392),f319(f319(f301(a925),x68393),f180(f932(a925,a923))))
% 28.25/28.11 [6971]P60(x69711,x69712,x69713)+P1(f319(f319(f321(x69711),f627(x69713,x69712,x69711)),x69712))
% 28.25/28.11 [6972]P60(x69721,x69722,x69723)+P1(f319(f319(f321(x69721),f626(x69723,x69722,x69721)),x69722))
% 28.25/28.11 [6982]P1(f319(f307(x69821,x69822),x69823))+P1(f319(f319(x69822,f524(x69823,x69822,x69821)),x69823))
% 28.25/28.11 [6983]P1(f319(f307(x69831,x69832),x69833))+P1(f319(f319(x69832,f539(x69833,x69832,x69831)),x69833))
% 28.25/28.11 [7014]E(f319(f181(f926(x70141)),f162(x70141,x70142,x70143)),f319(f319(f23(a925),f319(f181(f926(x70141)),x70143)),f72(a925)))+~P1(f319(f319(f321(x70141),x70142),f319(f164(x70141),x70143)))
% 28.25/28.11 [7053]P1(f319(f240(x70531,x70532),x70533))+P1(f319(f319(f321(x70531),f598(x70533,x70532,x70531)),x70533))
% 28.25/28.11 [7064]~P1(f319(f55(f931(x70642,x70641)),f319(f278(x70641,x70642),x70643)))+P1(f319(f55(f931(x70641,x70642)),x70643))
% 28.25/28.11 [7122]~P1(f319(f319(f321(x71221),x71222),f319(f164(x71221),f106(x71221,x71223))))+P1(f319(f319(f321(x71221),x71222),f319(f164(x71221),x71223)))
% 28.25/28.11 [7156]E(f319(f128(x71561,x71562),x71563),x71563)+P1(f319(f319(f321(x71561),f726(x71563,x71562,x71561)),f319(f164(x71561),x71563)))
% 28.25/28.11 [7170]E(f319(f128(x71701,x71702),x71703),f105(x71701))+P1(f319(f319(f321(x71701),f695(x71703,x71702,x71701)),f319(f164(x71701),x71703)))
% 28.25/28.11 [7194]P32(x71941,x71942,x71943)+P1(f319(f319(f321(x71941),f776(x71943,x71942,x71941)),f319(f164(x71941),x71943)))
% 28.25/28.11 [7195]P32(x71951,x71952,x71953)+P1(f319(f319(f321(x71951),f786(x71953,x71952,x71951)),f319(f164(x71951),x71953)))
% 28.25/28.11 [7196]P32(x71961,x71962,x71963)+P1(f319(f319(f321(x71961),f785(x71962,x71963,x71961)),f319(f164(x71961),x71963)))
% 28.25/28.11 [7199]E(f169(x71991,x71992,x71993),x71993)+P1(f319(f319(f321(x71991),f739(x71993,x71992,x71991)),f319(f164(x71991),x71993)))
% 28.25/28.11 [7275]P1(f319(f152(x72751,x72752),x72753))+P1(f319(f319(f321(x72751),f696(x72753,x72752,x72751)),f319(f164(x72751),x72753)))
% 28.25/28.11 [7284]~P34(x72841,x72843,x72842)+P1(f319(f319(f321(x72841),f771(x72842,x72843,x72841)),f319(f164(x72841),x72842)))
% 28.25/28.12 [7285]~P36(x72851,x72853,x72852)+P1(f319(f319(f321(x72851),f775(x72852,x72853,x72851)),f319(f164(x72851),x72852)))
% 28.25/28.12 [7286]~P36(x72861,x72863,x72862)+P1(f319(f319(f321(x72861),f787(x72862,x72863,x72861)),f319(f164(x72861),x72862)))
% 28.25/28.12 [7287]~P34(x72871,x72873,x72872)+P1(f319(f319(f321(x72871),f814(x72872,x72873,x72871)),f319(f164(x72871),x72872)))
% 28.25/28.12 [7288]~P34(x72881,x72882,x72883)+P1(f319(f319(f321(x72881),f816(x72882,x72883,x72881)),f319(f164(x72881),x72883)))
% 28.25/28.12 [7323]P1(f319(f319(f321(x73231),x73232),f472(x73233,x73232,x73231)))+~P1(f319(f319(f321(x73231),x73232),f31(f932(x73231,a923),x73233)))
% 28.25/28.12 [7324]~P79(x73241)+E(f319(f319(f74(x73241),f319(f319(f6(a925,x73241),x73242),f319(f274(a925),x73243))),f319(x73242,x73243)),f319(f319(f6(a925,x73241),x73242),f319(f274(a925),f319(a104,x73243))))
% 28.25/28.12 [7336]P31(x73361,x73362,x73363)+P1(f319(f319(f321(a925),f857(x73363,x73362,x73361)),f319(f294(a925,x73362),x73363)))
% 28.25/28.12 [7416]~P34(x74162,x74161,x74163)+P1(f319(x74161,f319(f319(f156(x74162),x74163),f772(x74163,x74161,x74162))))
% 28.25/28.12 [7429]~P1(f319(f319(f321(x74291),x74292),f473(x74292,x74293,x74291)))+P1(f319(f319(f321(x74291),x74292),f32(f932(x74291,a923),x74293)))
% 28.25/28.12 [7462]~P79(x74621)+E(f319(f319(f74(x74621),f319(f319(f6(a925,x74621),x74622),f319(f293(a925),x74623))),f319(x74622,f319(a104,x74623))),f319(f319(f6(a925,x74621),x74622),f319(f293(a925),f319(a104,x74623))))
% 28.25/28.12 [7599]P1(f319(f319(f321(f926(x75991)),x75992),f153(x75991,x75993)))+P1(f319(f319(f321(x75991),f678(x75993,x75992,x75991)),f319(f164(x75991),x75992)))
% 28.25/28.12 [7614]~P1(f319(f319(f321(f926(x76141)),x76142),f153(x76141,f308(x76141,x76143))))+P1(f319(f319(f321(f926(x76141)),x76142),f308(f926(x76141),f149(x76141,x76143))))
% 28.25/28.12 [7638]~P1(f319(f319(f321(f926(x76381)),x76382),f308(f926(x76381),f149(x76381,x76383))))+P1(f319(f319(f321(f926(x76381)),x76382),f153(x76381,f308(x76381,x76383))))
% 28.25/28.12 [7671]E(f319(f319(f319(f175(f926(x76711),f926(x76711)),x76712),f159(x76711)),x76713),x76713)+~P1(f319(f319(f226(a925),f319(f181(f926(x76711)),x76713)),f72(a925)))
% 28.25/28.12 [7704]E(f319(f319(f126(x77041),f773(x77042,x77043,x77041)),f319(f319(f143(x77041),x77043),f774(x77042,x77043,x77041))),x77042)+~P1(f319(f319(f321(x77041),x77043),f319(f164(x77041),x77042)))
% 28.25/28.12 [7705]E(f319(f319(f126(x77051),f779(x77052,x77053,x77051)),f319(f319(f143(x77051),x77053),f780(x77052,x77053,x77051))),x77052)+~P1(f319(f319(f321(x77051),x77053),f319(f164(x77051),x77052)))
% 28.25/28.12 [7706]E(f319(f319(f126(x77061),f781(x77062,x77063,x77061)),f319(f319(f143(x77061),x77063),f782(x77062,x77063,x77061))),x77062)+~P1(f319(f319(f321(x77061),x77063),f319(f164(x77061),x77062)))
% 28.25/28.12 [7725]~P26(x77251,x77252,x77253,f234(f932(x77251,a923)))+P26(f926(x77251),f926(x77252),f319(f146(x77251,x77252),x77253),f234(f932(f926(x77251),a923)))
% 28.25/28.12 [7726]~P26(x77261,x77262,x77263,f234(f932(x77261,a923)))+P26(f926(x77261),f926(x77262),f319(f146(x77261,x77262),x77263),f234(f932(f926(x77261),a923)))
% 28.25/28.12 [7876]E(x78761,f319(f319(f74(a925),f319(f319(f75(a925),f319(f243(a925,a925),x78762)),x78763)),f319(f248(a925,a925),x78762)))+~P1(f319(f42(x78761,x78763),x78762))
% 28.25/28.12 [7883]P26(x78831,x78832,x78833,f234(f932(x78831,a923)))+~P26(f926(x78831),f926(x78832),f319(f146(x78831,x78832),x78833),f234(f932(f926(x78831),a923)))
% 28.25/28.12 [7884]P26(x78841,x78842,x78843,f234(f932(x78841,a923)))+~P26(f926(x78841),f926(x78842),f319(f146(x78841,x78842),x78843),f234(f932(f926(x78841),a923)))
% 28.25/28.12 [7928]P1(f319(f319(f321(f932(x79281,a923)),f473(x79282,x79283,x79281)),x79283))+P1(f319(f319(f321(x79281),x79282),f32(f932(x79281,a923),x79283)))
% 28.25/28.12 [8017]P1(f319(f319(f321(f926(x80171)),x80172),f153(x80171,x80173)))+~P1(f319(f319(f321(x80171),f678(x80173,x80172,x80171)),x80173))
% 28.25/28.12 [8120]P32(x81201,x81202,x81203)+~P1(f319(x81202,f319(f319(f156(x81201),x81203),f778(x81203,x81202,x81201))))
% 28.25/28.12 [8145]E(x81451,x81452)+~E(f319(f319(f7(x81453,f932(x81453,a923),a923),f321(x81453)),x81451),f319(f319(f7(x81453,f932(x81453,a923),a923),f321(x81453)),x81452))
% 28.25/28.12 [8153]~P1(f319(f319(f321(f931(x81531,x81531)),x81533),f255(x81531,x81532)))+P1(f319(f319(f321(x81531),f555(x81532,x81533,x81531)),x81532))
% 28.25/28.12 [8155]~P1(f319(f319(f321(x81551),x81553),f31(f932(x81551,a923),x81552)))+P1(f319(f319(f321(f932(x81551,a923)),f472(x81552,x81553,x81551)),x81552))
% 28.25/28.12 [8213]P1(f319(f319(f226(f932(x82131,a923)),x82132),f32(f932(x82131,a923),x82133)))+P1(f319(f319(f321(f932(x82131,a923)),f631(x82132,x82133,x82131)),x82133))
% 28.25/28.12 [8277]P26(x82771,x82772,f85(x82772,x82771,f234(f932(x82772,a923)),x82773),f234(f932(x82771,a923)))+~E(f319(f302(x82772,x82771,x82773),f234(f932(x82772,a923))),f234(f932(x82771,a923)))
% 28.25/28.12 [8303]~P1(f319(f319(f226(f932(x83031,a923)),x83032),f631(x83032,x83033,x83031)))+P1(f319(f319(f226(f932(x83031,a923)),x83032),f32(f932(x83031,a923),x83033)))
% 28.25/28.12 [8331]~P1(f319(f319(f321(x83311),x83312),f319(f164(x83311),f779(x83313,x83312,x83311))))+~P1(f319(f319(f321(x83311),x83312),f319(f164(x83311),x83313)))
% 28.25/28.12 [8332]~P1(f319(f319(f321(x83321),x83322),f319(f164(x83321),f782(x83323,x83322,x83321))))+~P1(f319(f319(f321(x83321),x83322),f319(f164(x83321),x83323)))
% 28.25/28.12 [8359]P31(f319(f66(a923,a923,a925,a314),x83591),x83592,x83593)+P34(a925,x83591,f131(a925,f319(f294(a925,x83592),x83593)))
% 28.25/28.12 [8523]E(x85231,f105(x85232))+P1(f319(f319(f321(x85232),f319(f243(x85232,f931(a91,a91)),f319(f267(x85232,x85231),x85233))),f319(f164(x85232),x85231)))
% 28.25/28.12 [8623]~P77(x86231)+E(f319(f134(x86231,x86231,f319(f7(x86231,x86231,x86231),f74(x86231)),x86232),f319(f160(x86231),x86233)),f319(f134(x86231,x86231,f74(x86231),x86232),x86233))
% 28.25/28.12 [8819]~P26(x88192,x88191,x88193,f234(f932(x88192,a923)))+E(f319(f302(x88191,x88192,f85(x88192,x88191,f234(f932(x88192,a923)),x88193)),f234(f932(x88191,a923))),f234(f932(x88192,a923)))
% 28.25/28.12 [8889]~P31(f319(f66(a923,a923,a925,a314),x88891),x88892,x88893)+~P34(a925,x88891,f131(a925,f319(f294(a925,x88892),x88893)))
% 28.25/28.12 [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)))
% 28.25/28.12 [9032]~P27(x90321,x90322,x90323,f234(f932(x90321,a923)),f234(f932(x90322,a923)))+E(f319(f302(x90321,x90322,x90323),f234(f932(x90321,a923))),f234(f932(x90322,a923)))
% 28.25/28.12 [9138]~P4(x91381)+E(f319(f164(x91381),f141(x91381,x91381,f5(x91381),x91382,x91383)),f319(f319(f301(x91381),x91382),f319(f164(x91381),x91383)))
% 28.25/28.12 [9149]~E(f319(x91493,f319(f85(x91491,x91492,f234(f932(x91491,a923)),x91493),f792(x91493,x91492,x91491))),f792(x91493,x91492,x91491))+E(f319(f302(x91491,x91492,x91493),f234(f932(x91491,a923))),f234(f932(x91492,a923)))
% 28.25/28.12 [9151]P1(f319(f319(f227(a925),f2(a925)),f634(x91511,x91512,x91513)))+~P1(f319(f319(f321(f931(x91513,x91513)),x91512),f319(f319(f281(x91513,x91513,x91513),x91511),f299(x91513,x91511))))
% 28.25/28.12 [9434]~P62(x94341,x94342)+~P1(f319(f319(f321(f931(x94341,x94341)),f319(f319(f244(x94341,x94341),x94343),x94343)),f319(f319(f281(x94341,x94341,x94341),x94342),f299(x94341,x94342))))
% 28.25/28.12 [9537]~P27(x95372,x95371,x95373,f234(f932(x95372,a923)),f234(f932(x95371,a923)))+P27(x95371,x95372,f85(x95372,x95371,f234(f932(x95372,a923)),x95373),f234(f932(x95371,a923)),f234(f932(x95372,a923)))
% 28.25/28.12 [9571]~E(f319(f319(f93(f932(f931(x95711,x95711),a923)),f319(f278(x95711,x95711),x95712)),f299(x95711,x95712)),f180(f932(f931(x95711,x95711),a923)))+~P1(f319(f319(f321(f931(x95711,x95711)),f319(f319(f244(x95711,x95711),x95713),x95713)),f319(f319(f281(x95711,x95711,x95711),x95712),f299(x95711,x95712))))
% 28.25/28.12 [9755]~P1(f319(f55(x97551),x97552))+P1(f319(f319(f226(a925),f319(f29(x97551),f319(f319(f23(f932(x97551,a923)),x97552),f319(f319(f301(x97551),x97553),f180(f932(x97551,a923)))))),f319(f29(x97551),x97552)))
% 28.25/28.12 [5264]~E(x52643,f105(x52641))+E(f136(x52641,f319(f319(f143(x52641),x52642),x52643)),x52642)
% 28.25/28.12 [5265]~E(x52653,f105(x52651))+E(f136(x52651,f319(f319(f143(x52651),x52652),x52653)),x52652)
% 28.25/28.12 [5274]~E(x52743,f105(x52741))+E(f106(x52741,f319(f319(f143(x52741),x52742),x52743)),f105(x52741))
% 28.25/28.12 [5305]E(x53051,f105(x53052))+E(f136(x53052,f319(f319(f143(x53052),x53053),x53051)),f136(x53052,x53051))
% 28.25/28.12 [5306]E(x53061,f105(x53062))+E(f136(x53062,f319(f319(f143(x53062),x53063),x53061)),f136(x53062,x53061))
% 28.25/28.12 [5307]E(x53071,f105(x53072))+E(f136(x53072,f319(f319(f126(x53072),x53073),x53071)),f136(x53072,x53071))
% 28.25/28.12 [5308]E(x53081,f105(x53082))+E(f136(x53082,f319(f319(f126(x53082),x53083),x53081)),f136(x53082,x53081))
% 28.25/28.12 [5315]~E(x53153,f105(x53151))+E(f106(x53151,f319(f319(f126(x53151),x53152),x53153)),f106(x53151,x53152))
% 28.25/28.12 [5316]~E(x53163,f105(x53161))+E(f136(x53161,f319(f319(f126(x53161),x53162),x53163)),f136(x53161,x53162))
% 28.25/28.12 [5317]~E(x53173,f105(x53171))+E(f136(x53171,f319(f319(f126(x53171),x53172),x53173)),f136(x53171,x53172))
% 28.25/28.12 [5352]E(x53521,f105(x53522))+E(f319(f133(x53522),f319(f319(f126(x53522),x53521),x53523)),f319(f133(x53522),x53521))
% 28.25/28.12 [5353]E(x53531,f105(x53532))+E(f319(f133(x53532),f319(f319(f126(x53532),x53531),x53533)),f319(f133(x53532),x53531))
% 28.25/28.12 [5381]~E(x53812,f105(x53811))+E(f319(f133(x53811),f319(f319(f126(x53811),x53812),x53813)),f319(f133(x53811),x53813))
% 28.25/28.12 [5433]~P102(x54331)+E(f319(f319(f102(x54331),x54332),f319(f319(f93(x54331),x54332),x54333)),x54332)
% 28.25/28.12 [5434]~P102(x54341)+E(f319(f319(f93(x54341),x54342),f319(f319(f102(x54341),x54342),x54343)),x54342)
% 28.25/28.12 [5435]~P4(x54351)+E(f319(f319(f224(x54351),x54352),f319(f319(f225(x54351),x54352),x54353)),x54352)
% 28.25/28.12 [5436]~P4(x54361)+E(f319(f319(f225(x54361),x54362),f319(f319(f224(x54361),x54362),x54363)),x54362)
% 28.25/28.12 [5455]~P65(x54551)+E(f39(x54551,f319(f319(f75(x54551),x54552),x54553),x54553),f2(x54551))
% 28.25/28.12 [5456]~P65(x54561)+E(f39(x54561,f319(f319(f75(x54561),x54562),x54563),x54562),f2(x54561))
% 28.25/28.12 [5522]~P70(x55221)+E(f319(f73(x55221),f319(f319(f23(x55221),x55222),x55223)),f319(f319(f23(x55221),x55223),x55222))
% 28.25/28.12 [5584]E(x55841,f105(x55842))+E(f106(x55842,f319(f319(f143(x55842),x55843),x55841)),f319(f319(f143(x55842),x55843),f106(x55842,x55841)))
% 28.25/28.12 [5585]E(x55851,f105(x55852))+E(f106(x55852,f319(f319(f126(x55852),x55853),x55851)),f319(f319(f126(x55852),x55853),f106(x55852,x55851)))
% 28.25/28.12 [5588]~P6(x55881)+E(f32(x55881,f319(f319(f301(x55881),x55882),x55883)),f319(f319(f93(x55881),x55882),f32(x55881,x55883)))
% 28.25/28.12 [5589]~P6(x55891)+E(f31(x55891,f319(f319(f301(x55891),x55892),x55893)),f319(f319(f102(x55891),x55892),f31(x55891,x55893)))
% 28.25/28.12 [5634]~P102(x56341)+E(f319(f319(f102(x56341),x56342),f319(f319(f102(x56341),x56342),x56343)),f319(f319(f102(x56341),x56342),x56343))
% 28.25/28.12 [5635]~P107(x56351)+E(f319(f319(f102(x56351),x56352),f319(f319(f102(x56351),x56352),x56353)),f319(f319(f102(x56351),x56352),x56353))
% 28.25/28.12 [5636]~P107(x56361)+E(f319(f319(f102(x56361),x56362),f319(f319(f102(x56361),x56362),x56363)),f319(f319(f102(x56361),x56362),x56363))
% 28.25/28.12 [5637]~P102(x56371)+E(f319(f319(f93(x56371),x56372),f319(f319(f93(x56371),x56372),x56373)),f319(f319(f93(x56371),x56372),x56373))
% 28.25/28.12 [5638]~P108(x56381)+E(f319(f319(f93(x56381),x56382),f319(f319(f93(x56381),x56382),x56383)),f319(f319(f93(x56381),x56382),x56383))
% 28.25/28.12 [5639]~P108(x56391)+E(f319(f319(f93(x56391),x56392),f319(f319(f93(x56391),x56392),x56393)),f319(f319(f93(x56391),x56392),x56393))
% 28.25/28.12 [5640]~P101(x56401)+E(f319(f319(f75(x56401),x56402),f319(f319(f75(x56401),x56402),x56403)),f319(f319(f75(x56401),x56402),x56403))
% 28.25/28.12 [5641]~P4(x56411)+E(f319(f319(f224(x56411),x56412),f319(f319(f224(x56411),x56412),x56413)),f319(f319(f224(x56411),x56412),x56413))
% 28.25/28.12 [5642]~P4(x56421)+E(f319(f319(f224(x56421),x56422),f319(f319(f224(x56421),x56422),x56423)),f319(f319(f224(x56421),x56422),x56423))
% 28.25/28.12 [5643]~P4(x56431)+E(f319(f319(f225(x56431),x56432),f319(f319(f225(x56431),x56432),x56433)),f319(f319(f225(x56431),x56432),x56433))
% 28.25/28.12 [5644]~P4(x56441)+E(f319(f319(f225(x56441),x56442),f319(f319(f225(x56441),x56442),x56443)),f319(f319(f225(x56441),x56442),x56443))
% 28.25/28.12 [5651]~P65(x56511)+E(f39(x56511,f319(f319(f74(x56511),x56512),x56513),x56513),f39(x56511,x56512,x56513))
% 28.25/28.12 [5652]~P65(x56521)+E(f39(x56521,f319(f319(f74(x56521),x56522),x56523),x56522),f39(x56521,x56523,x56522))
% 28.25/28.12 [5660]~P116(x56601)+E(f319(f319(f75(x56601),x56602),f319(f73(x56601),x56603)),f319(f73(x56601),f319(f319(f75(x56601),x56602),x56603)))
% 28.25/28.12 [5661]~P72(x56611)+E(f319(f319(f283(x56611),x56612),f319(f73(x56611),x56613)),f319(f73(x56611),f319(f319(f283(x56611),x56612),x56613)))
% 28.25/28.12 [5662]~P88(x56621)+E(f319(f319(f74(x56621),x56622),f319(f157(x56621),x56623)),f319(f157(x56621),f319(f319(f143(x56621),x56622),x56623)))
% 28.25/28.12 [5690]~P116(x56901)+E(f319(f319(f75(x56901),f319(f73(x56901),x56902)),x56903),f319(f319(f75(x56901),x56902),f319(f73(x56901),x56903)))
% 28.25/28.12 [5696]~P9(x56961,x56962,x56963)+E(f31(f932(x56961,a923),f319(f319(f54(x56961),x56962),x56963)),x56962)
% 28.25/28.12 [5760]~P121(x57601)+E(f319(f319(f75(x57601),x57602),f319(f319(f236(x57601),x57602),x57603)),f319(f319(f236(x57601),x57602),f319(a104,x57603)))
% 28.25/28.12 [5761]~P119(x57611)+E(f319(f319(f75(x57611),x57612),f319(f319(f236(x57611),x57612),x57613)),f319(f319(f236(x57611),x57612),f319(a104,x57613)))
% 28.25/28.12 [5762]~P121(x57621)+E(f319(f319(f75(x57621),x57622),f319(f319(f236(x57621),x57622),x57623)),f319(f319(f236(x57621),x57622),f319(a104,x57623)))
% 28.25/28.12 [5772]~P69(x57721)+E(f319(f319(f74(x57721),f319(f73(x57721),x57722)),f319(f319(f74(x57721),x57722),x57723)),x57723)
% 28.25/28.12 [5795]~P149(x57951)+E(f319(f319(f236(x57951),f319(f92(x57951),x57952)),x57953),f319(f92(x57951),f319(f319(f236(a925),x57952),x57953)))
% 28.25/28.12 [5796]~P145(x57961)+E(f319(f319(f236(x57961),f319(f94(x57961),x57962)),x57963),f319(f94(x57961),f319(f319(f236(a1),x57962),x57963)))
% 28.25/28.12 [5802]~P92(x58021)+E(f319(f69(x58021),f319(f319(f23(x58021),x58022),x58023)),f319(f69(x58021),f319(f319(f23(x58021),x58023),x58022)))
% 28.25/28.12 [5804]~P126(x58041)+E(f319(f319(f75(x58041),f76(x58041,x58042)),f76(x58041,x58043)),f76(x58041,f319(f319(f75(x58041),x58042),x58043)))
% 28.25/28.12 [5808]E(x58081,f105(x58082))+E(f319(f319(f126(x58082),f319(f163(x58082),x58081)),x58083),f319(f163(x58082),f319(f319(f126(x58082),x58081),x58083)))
% 28.25/28.12 [5813]~E(x58132,f319(a104,f319(f319(f74(a925),x58131),x58133)))+P1(f319(f319(f227(a925),x58131),x58132))
% 28.25/28.12 [5814]~P116(x58141)+E(f319(f319(f75(x58141),f319(f73(x58141),x58142)),x58143),f319(f73(x58141),f319(f319(f75(x58141),x58142),x58143)))
% 28.25/28.12 [5815]~P124(x58151)+E(f319(f319(f283(x58151),f319(f73(x58151),x58152)),x58153),f319(f73(x58151),f319(f319(f283(x58151),x58152),x58153)))
% 28.25/28.12 [5816]~P126(x58161)+E(f319(f319(f236(x58161),f319(f69(x58161),x58162)),x58163),f319(f69(x58161),f319(f319(f236(x58161),x58162),x58163)))
% 28.25/28.12 [5915]E(f845(x59151,x59152,x59153),f856(x59151,x59152,x59153))+E(f319(f319(f93(f932(x59153,a923)),x59152),x59151),f180(f932(x59153,a923)))
% 28.25/28.12 [5930]~P79(x59302)+E(f319(f319(f6(x59301,x59302),f319(f16(x59302,x59301),f2(x59302))),x59303),f2(x59302))
% 28.25/28.12 [5931]~P78(x59312)+E(f319(f319(f9(x59311,x59312),f319(f16(x59312,x59311),f72(x59312))),x59313),f72(x59312))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [5990]~E(x59903,x59902)+P1(f319(f319(f226(f932(x59901,a923)),x59902),x59903))
% 28.25/28.12 [5991]~E(x59912,x59913)+P1(f319(f319(f226(f932(x59911,a923)),x59912),x59913))
% 28.25/28.12 [5992]~E(x59922,x59923)+P1(f319(f319(f226(f932(x59921,a923)),x59922),x59923))
% 28.25/28.12 [5993]~E(x59932,x59933)+P1(f319(f319(f226(f932(x59931,a923)),x59932),x59933))
% 28.25/28.12 [5994]~E(x59942,x59943)+P1(f319(f319(f226(f932(x59941,a923)),x59942),x59943))
% 28.25/28.12 [5995]~E(x59952,x59953)+P1(f319(f319(f226(f932(x59951,a923)),x59952),x59953))
% 28.25/28.12 [5996]~E(x59962,x59963)+P1(f319(f319(f226(f932(x59961,a923)),x59962),x59963))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [6010]E(x60101,f180(f932(x60102,a923)))+~E(f319(f319(f102(f932(x60102,a923)),x60103),x60101),f180(f932(x60102,a923)))
% 28.25/28.12 [6011]E(x60111,f180(f932(x60112,a923)))+~E(f319(f319(f102(f932(x60112,a923)),x60111),x60113),f180(f932(x60112,a923)))
% 28.25/28.12 [6012]~P152(x60121,x60123,x60122)+P1(f319(x60121,f319(f319(f30(a1),x60122),x60123)))
% 28.25/28.12 [6068]~P1(f319(f55(x60681),x60683))+P1(f319(f55(x60681),f319(f319(f301(x60681),x60682),x60683)))
% 28.25/28.12 [6069]~P1(f319(f55(x60691),x60693))+P1(f319(f55(x60691),f319(f319(f301(x60691),x60692),x60693)))
% 28.25/28.12 [6070]~P1(f319(f129(x60701),x60703))+P1(f319(f129(x60701),f319(f319(f167(x60701),x60702),x60703)))
% 28.25/28.12 [6071]~P1(f319(f129(x60711),x60713))+P1(f319(f129(x60711),f319(f319(f130(x60711),x60712),x60713)))
% 28.25/28.12 [6104]~P102(x61041)+P1(f319(f319(f226(x61041),x61042),f319(f319(f102(x61041),x61043),x61042)))
% 28.25/28.12 [6105]~P107(x61051)+P1(f319(f319(f226(x61051),x61052),f319(f319(f102(x61051),x61053),x61052)))
% 28.25/28.12 [6106]~P102(x61061)+P1(f319(f319(f226(x61061),x61062),f319(f319(f102(x61061),x61062),x61063)))
% 28.25/28.12 [6107]~P107(x61071)+P1(f319(f319(f226(x61071),x61072),f319(f319(f102(x61071),x61072),x61073)))
% 28.25/28.12 [6108]~P4(x61081)+P1(f319(f319(f226(x61081),x61082),f319(f319(f225(x61081),x61083),x61082)))
% 28.25/28.12 [6109]~P4(x61091)+P1(f319(f319(f226(x61091),x61092),f319(f319(f225(x61091),x61092),x61093)))
% 28.25/28.12 [6110]~P121(x61101)+P1(f319(f319(f279(x61101),x61102),f319(f319(f75(x61101),x61103),x61102)))
% 28.25/28.12 [6111]~P121(x61111)+P1(f319(f319(f279(x61111),x61112),f319(f319(f75(x61111),x61112),x61113)))
% 28.25/28.12 [6125]~E(x61251,f2(a925))+E(f319(f319(f30(a925),f319(f319(f75(a925),x61251),x61252)),f319(f319(f75(a925),x61251),x61253)),f2(a925))
% 28.25/28.12 [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))))
% 28.25/28.12 [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))
% 28.25/28.12 [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)))
% 28.25/28.12 [6331]P152(x63311,x63312,x63313)+~P1(f319(x63311,f319(f319(f30(a1),x63313),x63312)))
% 28.25/28.12 [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))
% 28.25/28.12 [6409]E(f319(f319(f23(f932(x64091,a923)),x64092),x64093),x64092)+~E(f319(f319(f93(f932(x64091,a923)),x64092),x64093),f180(f932(x64091,a923)))
% 28.25/28.12 [6424]E(f144(x64241,f319(f319(f143(x64241),x64242),x64243)),f144(x64241,x64243))+~P1(f319(f319(f321(x64241),x64242),f319(f164(x64241),x64243)))
% 28.25/28.12 [6453]~P1(f319(f319(f226(a925),x64531),x64533))+P1(f319(f319(f226(a925),x64531),f319(f319(f74(a925),x64532),x64533)))
% 28.25/28.12 [6454]~P1(f319(f319(f226(a925),x64541),x64543))+P1(f319(f319(f226(a925),x64541),f319(f319(f74(a925),x64542),x64543)))
% 28.25/28.12 [6455]~P1(f319(f319(f226(a925),x64551),x64552))+P1(f319(f319(f226(a925),x64551),f319(f319(f74(a925),x64552),x64553)))
% 28.25/28.12 [6456]~P1(f319(f319(f226(a925),x64561),x64562))+P1(f319(f319(f226(a925),x64561),f319(f319(f74(a925),x64562),x64563)))
% 28.25/28.12 [6457]~P1(f319(f319(f227(a925),x64571),x64573))+P1(f319(f319(f227(a925),x64571),f319(f319(f74(a925),x64572),x64573)))
% 28.25/28.12 [6458]~P1(f319(f319(f227(a925),x64581),x64583))+P1(f319(f319(f227(a925),x64581),f319(f319(f74(a925),x64582),x64583)))
% 28.25/28.12 [6459]~P1(f319(f319(f227(a925),x64591),x64592))+P1(f319(f319(f227(a925),x64591),f319(f319(f74(a925),x64592),x64593)))
% 28.25/28.12 [6460]~P1(f319(f319(f227(a925),x64601),x64602))+P1(f319(f319(f227(a925),x64601),f319(f319(f74(a925),x64602),x64603)))
% 28.25/28.12 [6498]P1(f319(f55(x64981),x64982))+~P1(f319(f55(x64981),f319(f319(f301(x64981),x64983),x64982)))
% 28.25/28.12 [6499]P1(f319(f129(x64991),x64992))+~P1(f319(f129(x64991),f319(f319(f143(x64991),x64993),x64992)))
% 28.25/28.12 [6500]P1(f319(f129(x65001),x65002))+~P1(f319(f129(x65001),f319(f319(f126(x65001),x65003),x65002)))
% 28.25/28.12 [6501]P1(f319(f129(x65011),x65012))+~P1(f319(f129(x65011),f319(f319(f126(x65011),x65012),x65013)))
% 28.25/28.12 [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))
% 28.25/28.12 [6599]~E(x65991,x65992)+~P1(f319(f319(f227(f932(x65993,a923)),x65991),x65992))
% 28.25/28.12 [6645]P1(f319(f319(f321(x66451),x66452),x66453))+P1(f319(f319(f321(x66451),x66452),f319(f73(f932(x66451,a923)),x66453)))
% 28.25/28.12 [6646]P1(f319(f319(f321(x66461),x66462),x66463))+P1(f319(f319(f321(x66461),x66462),f319(f73(f932(x66461,a923)),x66463)))
% 28.25/28.12 [6652]E(f136(x66521,f319(f319(f130(x66521),x66522),x66523)),f136(x66521,x66523))+~P1(f319(f319(f227(a925),x66522),f319(f181(f926(x66521)),x66523)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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))
% 28.25/28.12 [6717]~P9(x67171,x67173,x67172)+E(f319(f319(f281(x67171,x67171,x67171),f319(f278(x67171,x67171),x67172)),x67172),x67172)
% 28.25/28.12 [6759]~E(f319(f319(f102(f932(x67591,a923)),x67592),x67593),x67593)+P1(f319(f319(f226(f932(x67591,a923)),x67592),x67593))
% 28.25/28.12 [6764]~P59(x67641,x67641,x67643)+P59(x67641,x67641,f319(f319(f175(f931(x67641,x67641),a923),x67642),x67643))
% 28.25/28.12 [6768]~P1(f319(f319(f321(x67681),x67683),f319(f164(x67681),x67682)))+P1(f319(f319(f227(a925),f2(a925)),f319(f181(f926(x67681)),x67682)))
% 28.25/28.12 [6783]~E(x67832,x67833)+P1(f319(f319(f321(x67831),x67832),f319(f319(f301(x67831),x67833),f180(f932(x67831,a923)))))
% 28.25/28.12 [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)))
% 28.25/28.12 [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))
% 28.25/28.12 [6951]~P1(f319(f55(x69511),x69513))+E(f319(f319(f58(x69511,f932(x69511,a923),f301(x69511)),x69512),x69513),f319(f319(f102(f932(x69511,a923)),x69513),x69512))
% 28.25/28.12 [7007]E(f319(f319(f102(f932(x70071,a923)),x70072),x70073),x70072)+~P1(f319(f319(f226(f932(x70071,a923)),x70073),x70072))
% 28.25/28.12 [7008]E(f319(f319(f102(f932(x70081,a923)),x70082),x70083),x70083)+~P1(f319(f319(f226(f932(x70081,a923)),x70082),x70083))
% 28.25/28.12 [7009]E(f319(f319(f102(f932(x70091,a923)),x70092),x70093),x70093)+~P1(f319(f319(f226(f932(x70091,a923)),x70092),x70093))
% 28.25/28.12 [7010]E(f319(f319(f93(f932(x70101,a923)),x70102),x70103),x70103)+~P1(f319(f319(f226(f932(x70101,a923)),x70103),x70102))
% 28.25/28.12 [7011]E(f319(f319(f93(f932(x70111,a923)),x70112),x70113),x70112)+~P1(f319(f319(f226(f932(x70111,a923)),x70112),x70113))
% 28.25/28.12 [7062]~P1(f319(f129(x70621),x70622))+E(f319(f319(f23(f932(x70621,a923)),f319(f164(x70621),x70622)),f319(f319(f301(x70621),x70623),f180(f932(x70621,a923)))),f319(f164(x70621),f162(x70621,x70623,x70622)))
% 28.25/28.12 [7117]P38(x71171,x71172)+~P38(x71171,f319(f319(f175(f931(x71171,x71171),a923),x71173),x71172))
% 28.25/28.12 [7133]~E(x71331,f2(a925))+P1(f319(f319(f279(a925),f319(f319(f75(a925),x71331),x71332)),f319(f319(f75(a925),x71331),x71333)))
% 28.25/28.12 [7182]P1(f319(f43(x71821,x71822),f319(a45,x71823)))+~P1(f319(f43(f319(f73(a1),x71821),f319(f73(a1),x71822)),x71823))
% 28.25/28.12 [7187]E(f319(f319(f23(f932(x71871,a923)),f319(f319(f301(x71871),x71872),x71873)),f319(f319(f301(x71871),x71872),f180(f932(x71871,a923)))),x71873)+P1(f319(f319(f321(x71871),x71872),x71873))
% 28.25/28.12 [7209]E(f319(f319(f93(f932(x72091,a923)),f319(f164(x72091),x72092)),f319(f164(x72091),x72093)),f180(f932(x72091,a923)))+~P1(f319(f129(x72091),f319(f319(f126(x72091),x72092),x72093)))
% 28.25/28.12 [7224]~P1(f319(f319(f321(x72241),x72242),f319(f164(x72241),x72243)))+~P1(f319(f129(x72241),f319(f319(f143(x72241),x72242),x72243)))
% 28.25/28.12 [7295]P32(x72951,x72952,x72953)+P1(f319(f319(f227(a925),f778(x72953,x72952,x72951)),f319(f181(f926(x72951)),x72953)))
% 28.25/28.12 [7305]E(f319(f319(f93(f932(x73051,a923)),x73052),x73053),f180(f932(x73051,a923)))+P1(f319(f319(f321(x73051),f845(x73053,x73052,x73051)),x73052))
% 28.25/28.12 [7306]E(f319(f319(f93(f932(x73061,a923)),x73062),x73063),f180(f932(x73061,a923)))+P1(f319(f319(f321(x73061),f856(x73063,x73062,x73061)),x73063))
% 28.25/28.12 [7309]E(f106(x73091,f319(f319(f167(x73091),x73092),x73093)),f319(f319(f167(x73091),f319(f319(f23(a925),x73092),f72(a925))),x73093))+~P1(f319(f319(f226(a925),x73092),f319(f181(f926(x73091)),x73093)))
% 28.25/28.12 [7369]~P34(x73693,x73692,x73691)+P1(f319(f319(f227(a925),f772(x73691,x73692,x73693)),f319(f181(f926(x73693)),x73691)))
% 28.25/28.12 [7389]P1(f319(f319(f227(a925),f2(a925)),x73891))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x73892),x73891)),f319(f319(f75(a925),x73893),x73891)))
% 28.25/28.12 [7390]P1(f319(f319(f227(a925),f2(a925)),x73901))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x73901),x73902)),f319(f319(f75(a925),x73901),x73903)))
% 28.25/28.12 [7391]~P1(f319(f319(f321(x73911),x73912),x73913))+~P1(f319(f319(f321(x73911),x73912),f319(f73(f932(x73911,a923)),x73913)))
% 28.25/28.12 [7392]~P1(f319(f319(f321(x73921),x73922),x73923))+~P1(f319(f319(f321(x73921),x73922),f319(f73(f932(x73921,a923)),x73923)))
% 28.25/28.12 [7393]~P1(f319(f319(f321(x73931),x73932),x73933))+~P1(f319(f319(f321(x73931),x73932),f319(f73(f932(x73931,a923)),x73933)))
% 28.25/28.12 [7397]~P1(f319(f319(f227(f932(x73971,a923)),x73972),x73973))+P1(f319(f319(f226(f932(x73971,a923)),x73972),x73973))
% 28.25/28.12 [7398]~P1(f319(f319(f227(f932(x73981,a923)),x73982),x73983))+P1(f319(f319(f226(f932(x73981,a923)),x73982),x73983))
% 28.25/28.12 [7399]~P1(f319(f319(f227(f932(x73991,a923)),x73992),x73993))+P1(f319(f319(f226(f932(x73991,a923)),x73992),x73993))
% 28.25/28.12 [7507]~P1(f319(f319(f226(a925),x75073),x75072))+P1(f319(f319(f226(a925),f319(f319(f23(a925),x75071),x75072)),f319(f319(f23(a925),x75071),x75073)))
% 28.25/28.12 [7508]~P1(f319(f319(f226(a925),x75081),x75083))+P1(f319(f319(f226(a925),f319(f319(f23(a925),x75081),x75082)),f319(f319(f23(a925),x75083),x75082)))
% 28.25/28.12 [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)))
% 28.25/28.12 [7510]~P1(f319(f319(f226(a925),x75102),x75103))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x75101),x75102)),f319(f319(f75(a925),x75101),x75103)))
% 28.25/28.12 [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)))
% 28.25/28.12 [7512]~P1(f319(f319(f226(a925),x75121),x75123))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x75121),x75122)),f319(f319(f75(a925),x75123),x75122)))
% 28.25/28.12 [7513]~P1(f319(f319(f226(a925),x75132),x75133))+P1(f319(f319(f226(a925),f319(f319(f74(a925),x75131),x75132)),f319(f319(f74(a925),x75131),x75133)))
% 28.25/28.12 [7514]~P1(f319(f319(f226(a925),x75141),x75143))+P1(f319(f319(f226(a925),f319(f319(f74(a925),x75141),x75142)),f319(f319(f74(a925),x75143),x75142)))
% 28.25/28.12 [7515]~P1(f319(f319(f226(a925),x75151),x75153))+P1(f319(f319(f226(a925),f319(f319(f30(a925),x75151),x75152)),f319(f319(f30(a925),x75153),x75152)))
% 28.25/28.12 [7516]~P1(f319(f319(f226(a1),x75162),x75163))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x75161),x75162)),f319(f319(f74(a1),x75161),x75163)))
% 28.25/28.12 [7519]~P1(f319(f319(f227(a925),x75192),x75193))+P1(f319(f319(f227(a925),f319(f319(f74(a925),x75191),x75192)),f319(f319(f74(a925),x75191),x75193)))
% 28.25/28.12 [7520]~P1(f319(f319(f227(a925),x75201),x75203))+P1(f319(f319(f227(a925),f319(f319(f74(a925),x75201),x75202)),f319(f319(f74(a925),x75203),x75202)))
% 28.25/28.12 [7521]~P1(f319(f319(f227(a1),x75211),x75213))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x75211),x75212)),f319(f319(f74(a1),x75213),x75212)))
% 28.25/28.12 [7524]~P1(f319(f319(f279(a925),x75242),x75243))+P1(f319(f319(f279(a925),f319(f319(f75(a925),x75241),x75242)),f319(f319(f75(a925),x75241),x75243)))
% 28.25/28.12 [7597]E(x75971,x75972)+~P1(f319(f319(f321(x75973),x75971),f319(f319(f301(x75973),x75972),f180(f932(x75973,a923)))))
% 28.25/28.12 [7598]E(x75981,x75982)+~P1(f319(f319(f321(x75983),x75981),f319(f319(f301(x75983),x75982),f180(f932(x75983,a923)))))
% 28.25/28.12 [7600]~E(f319(f319(f93(f932(x76001,a923)),x76002),x76003),f180(f932(x76001,a923)))+P1(f319(f319(f226(f932(x76001,a923)),x76002),f319(f73(f932(x76001,a923)),x76003)))
% 28.25/28.12 [7604]P1(f319(f319(f321(f932(x76041,a923)),x76042),f319(f300(x76041),x76043)))+~P1(f319(f319(f226(f932(x76041,a923)),x76042),x76043))
% 28.25/28.12 [7605]P1(f319(f319(f321(f932(x76051,a923)),x76052),f319(f300(x76051),x76053)))+~P1(f319(f319(f226(f932(x76051,a923)),x76052),x76053))
% 28.25/28.12 [7610]P1(f319(f319(f321(x76101),f737(x76102,x76103,x76101)),x76103))+P1(f319(f319(f226(f932(x76101,a923)),x76103),x76102))
% 28.25/28.12 [7655]E(f319(f319(f143(x76551),f319(f319(f156(x76551),x76552),x76553)),f319(f319(f130(x76551),f319(a104,x76553)),x76552)),f319(f319(f130(x76551),x76553),x76552))+~P1(f319(f319(f227(a925),x76553),f319(f181(f926(x76551)),x76552)))
% 28.25/28.12 [7681]P1(f319(f319(f321(f931(x76811,x76811)),x76812),f299(x76811,x76813)))+~P1(f319(f319(f321(f931(x76811,x76811)),x76812),x76813))
% 28.25/28.12 [7689]~P1(f319(f319(f321(f932(x76891,a923)),x76892),f319(f300(x76891),x76893)))+P1(f319(f319(f226(f932(x76891,a923)),x76892),x76893))
% 28.25/28.12 [7690]~P1(f319(f319(f321(f932(x76901,a923)),x76902),f319(f300(x76901),x76903)))+P1(f319(f319(f226(f932(x76901,a923)),x76902),x76903))
% 28.25/28.12 [7732]P1(f319(f319(f226(f932(x77321,a923)),x77322),f31(f932(x77321,a923),x77323)))+~P1(f319(f319(f321(f932(x77321,a923)),x77322),x77323))
% 28.25/28.12 [7756]~P145(x77561)+E(f319(f319(f75(x77561),f319(f319(f236(x77561),f319(f73(x77561),f72(x77561))),x77562)),f319(f319(f236(x77561),x77563),x77562)),f319(f319(f236(x77561),f319(f73(x77561),x77563)),x77562))
% 28.25/28.12 [7778]E(f319(f319(f156(x77781),x77782),f319(f319(f23(a925),f319(f181(f926(x77781)),x77782)),f319(a104,x77783))),f319(f319(f156(x77781),f319(f160(x77781),x77782)),x77783))+~P1(f319(f319(f227(a925),x77783),f319(f181(f926(x77781)),x77782)))
% 28.25/28.12 [7795]~E(f319(f319(f93(f932(x77951,a923)),f880(x77953,x77952,x77951)),x77953),f180(f932(x77951,a923)))+E(f319(f319(f93(f932(x77951,a923)),f31(f932(x77951,a923),x77952)),x77953),f180(f932(x77951,a923)))
% 28.25/28.12 [7859]~P1(f319(f319(f321(x78593),x78592),f319(f164(x78593),x78591)))+P1(f319(f319(f227(a925),f658(x78591,x78592,x78593)),f319(f181(f926(x78593)),x78591)))
% 28.25/28.12 [7867]P1(f319(f319(f321(x78671),f319(f319(f156(x78671),x78672),x78673)),f319(f164(x78671),x78672)))+~P1(f319(f319(f227(a925),x78673),f319(f181(f926(x78671)),x78672)))
% 28.25/28.12 [7964]~P1(f319(x79642,f740(x79643,x79642,x79641)))+E(f319(f319(f130(x79641),f319(f181(f926(x79641)),f169(x79641,x79642,x79643))),x79643),f105(x79641))
% 28.25/28.12 [7977]P1(f319(f319(f226(f932(f926(x79771),a923)),f153(x79771,x79772)),f153(x79771,x79773)))+~P1(f319(f319(f226(f932(x79771,a923)),x79772),x79773))
% 28.25/28.12 [7978]P1(f319(f319(f226(f932(f926(x79781),a923)),f152(x79781,x79782)),f152(x79781,x79783)))+~P1(f319(f319(f226(f932(x79781,a923)),x79782),x79783))
% 28.25/28.12 [8004]E(f319(f319(f93(f932(x80041,a923)),f31(f932(x80041,a923),x80042)),x80043),f180(f932(x80041,a923)))+P1(f319(f319(f321(f932(x80041,a923)),f880(x80043,x80042,x80041)),x80042))
% 28.25/28.12 [8006]~P1(f319(f319(f321(f932(x80061,a923)),x80063),x80062))+P1(f319(f319(f226(f932(x80061,a923)),f32(f932(x80061,a923),x80062)),x80063))
% 28.25/28.12 [8008]E(f319(f319(f93(f932(x80081,a923)),x80082),x80083),f180(f932(x80081,a923)))+~P1(f319(f319(f226(f932(x80081,a923)),x80082),f319(f73(f932(x80081,a923)),x80083)))
% 28.25/28.12 [8058]E(f319(f319(f23(a925),f319(f319(f74(a925),f319(f157(a925),x80581)),x80582)),f319(f319(f156(a925),x80581),x80583)),f319(f157(a925),f319(f319(f151(a925,x80581),x80583),x80582)))+~P1(f319(f319(f227(a925),x80583),f319(f181(f926(a925)),x80581)))
% 28.25/28.12 [8109]P1(f319(f319(f226(a925),x81091),x81092))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),x81093),x81091)),f319(f319(f74(a925),x81093),x81092)))
% 28.25/28.12 [8112]P1(f319(f319(f227(a925),x81121),x81122))+~P1(f319(f319(f227(a925),f319(f319(f74(a925),x81123),x81121)),f319(f319(f74(a925),x81123),x81122)))
% 28.25/28.12 [8113]P1(f319(f319(f227(a925),x81131),x81132))+~P1(f319(f319(f227(a925),f319(f319(f75(a925),x81133),x81131)),f319(f319(f75(a925),x81133),x81132)))
% 28.25/28.12 [8114]P1(f319(f319(f227(a925),x81141),x81142))+~P1(f319(f319(f227(a925),f319(f319(f75(a925),x81141),x81143)),f319(f319(f75(a925),x81142),x81143)))
% 28.25/28.12 [8143]P1(f319(f319(f227(a925),f2(a925)),x81431))+~P1(f319(f319(f227(a925),f319(f319(f75(a925),x81432),x81431)),f319(f319(f75(a925),x81433),x81431)))
% 28.25/28.12 [8144]P1(f319(f319(f227(a925),f2(a925)),x81441))+~P1(f319(f319(f227(a925),f319(f319(f75(a925),x81441),x81442)),f319(f319(f75(a925),x81441),x81443)))
% 28.25/28.12 [8183]~P1(f319(f319(f321(x81831),f737(x81833,x81832,x81831)),x81833))+P1(f319(f319(f226(f932(x81831,a923)),x81832),x81833))
% 28.25/28.12 [8220]E(f239(x82201,x82202,x82203),x82202)+~P1(f319(f319(f226(f932(x82201,a923)),x82203),f319(f319(f301(x82201),x82202),f180(f932(x82201,a923)))))
% 28.25/28.12 [8270]~P1(f319(f129(x82701),x82703))+E(f319(f128(x82701,f319(f319(f8(a923,a923,x82701),a314),f319(a316,x82702))),x82703),f162(x82701,x82702,x82703))
% 28.25/28.12 [8295]E(f319(f319(f130(x82951),f319(f181(f926(x82951)),f169(x82951,x82952,x82953))),x82953),f105(x82951))+P1(f319(f319(f321(x82951),f740(x82953,x82952,x82951)),f319(f164(x82951),x82953)))
% 28.25/28.12 [8299]E(f319(f319(f126(x82991),f319(f319(f167(x82991),x82992),x82993)),f319(f319(f143(x82991),f319(f319(f156(x82991),x82993),x82992)),f105(x82991))),f319(f319(f167(x82991),f319(a104,x82992)),x82993))+~P1(f319(f319(f227(a925),x82992),f319(f181(f926(x82991)),x82993)))
% 28.25/28.12 [8364]E(f319(f128(x83641,f319(f319(f8(a923,a923,x83641),a314),f319(a316,x83642))),x83643),x83643)+P1(f319(f319(f321(x83641),x83642),f319(f164(x83641),x83643)))
% 28.25/28.12 [8370]P1(f319(f319(f226(f932(f932(x83701,a923),a923)),f240(x83701,x83702)),f240(x83701,x83703)))+~P1(f319(f319(f226(f932(x83701,a923)),x83702),x83703))
% 28.25/28.12 [8390]P1(f319(f319(f321(f932(x83901,a923)),f656(x83902,x83903,x83901)),x83903))+P1(f319(f319(f226(f932(x83901,a923)),f31(f932(x83901,a923),x83903)),x83902))
% 28.25/28.12 [8411]~P1(f319(f129(x84111),x84113))+P1(f319(f129(x84111),f319(f319(f319(f175(f926(x84111),f926(x84111)),x84112),f159(x84111)),x84113)))
% 28.25/28.12 [8416]~P1(f319(f319(f226(a925),x84162),x84163))+P1(f319(f319(f226(a925),f319(f319(f75(a925),f319(a104,x84161)),x84162)),f319(f319(f75(a925),f319(a104,x84161)),x84163)))
% 28.25/28.12 [8417]~P1(f319(f319(f227(a925),x84172),x84173))+P1(f319(f319(f227(a925),f319(f319(f75(a925),f319(a104,x84171)),x84172)),f319(f319(f75(a925),f319(a104,x84171)),x84173)))
% 28.25/28.12 [8437]P1(f319(f319(f226(f932(f932(x84371,a923),a923)),f319(f300(x84371),x84372)),f319(f300(x84371),x84373)))+~P1(f319(f319(f226(f932(x84371,a923)),x84372),x84373))
% 28.25/28.12 [8507]~E(f319(f302(x85071,x85072,x85073),f234(f932(x85071,a923))),f234(f932(x85072,a923)))+E(f319(f66(x85071,x85072,x85072,x85073),f85(x85071,x85072,f234(f932(x85071,a923)),x85073)),f25(x85072))
% 28.25/28.12 [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)))
% 28.25/28.12 [8602]~P1(f319(f319(f226(f932(x86021,a923)),x86023),x86022))+P1(f319(f319(f226(f932(x86021,a923)),f319(f73(f932(x86021,a923)),x86022)),f319(f73(f932(x86021,a923)),x86023)))
% 28.25/28.12 [8636]E(f319(f302(a925,a925,f319(f319(f7(a925,a925,a925),f23(a925)),x86361)),f319(f294(a925,x86362),x86363)),f319(f294(a925,f319(f319(f23(a925),x86362),x86361)),f319(f319(f23(a925),x86363),x86361)))+~P1(f319(f319(f227(a925),x86361),x86363))
% 28.25/28.12 [8662]~P88(x86621)+E(f319(f319(f74(x86621),x86622),f319(f134(x86621,x86621,f74(x86621),f2(x86621)),x86623)),f319(f134(x86621,x86621,f74(x86621),x86622),x86623))
% 28.25/28.12 [8721]~P1(f319(f319(f226(f932(x87211,a923)),f656(x87213,x87212,x87211)),x87213))+P1(f319(f319(f226(f932(x87211,a923)),f31(f932(x87211,a923),x87212)),x87213))
% 28.25/28.12 [8742]~P92(x87421)+P1(f319(f319(f226(x87421),f319(f69(x87421),f319(f319(f23(x87421),x87422),x87423))),f319(f319(f74(x87421),f319(f69(x87421),x87422)),f319(f69(x87421),x87423))))
% 28.25/28.12 [8743]~P92(x87431)+P1(f319(f319(f226(x87431),f319(f69(x87431),f319(f319(f74(x87431),x87432),x87433))),f319(f319(f74(x87431),f319(f69(x87431),x87432)),f319(f69(x87431),x87433))))
% 28.25/28.12 [8754]E(f319(f319(f74(a1),f319(f319(f75(a1),x87541),f39(a1,f319(f319(f30(a1),x87542),x87541),x87543))),f39(a1,x87542,x87541)),f39(a1,x87542,f319(f319(f75(a1),x87541),x87543)))+~P1(f319(f319(f227(a1),f2(a1)),x87543))
% 28.25/28.12 [8760]E(f319(f319(f126(x87601),f319(f319(f167(x87601),x87602),x87603)),f319(f319(f143(x87601),f319(f133(x87601),f319(f319(f130(x87601),x87602),x87603))),f105(x87601))),f319(f319(f167(x87601),f319(a104,x87602)),x87603))+~P1(f319(f319(f227(a925),x87602),f319(f181(f926(x87601)),x87603)))
% 28.25/28.12 [8780]E(f319(f260(x87801,f319(f319(f146(x87801,f931(a91,x87801)),f319(f244(a91,x87801),f72(a91))),x87802)),f319(a3,x87803)),f319(f319(f156(x87801),x87802),x87803))+~P1(f319(f319(f227(a925),x87803),f319(f181(f926(x87801)),x87802)))
% 28.25/28.12 [8849]P1(f319(f319(f321(f931(x88491,x88491)),x88492),f319(f319(f281(x88491,x88491,x88491),x88493),f299(x88491,x88493))))+~P1(f319(f319(f321(f931(x88491,x88491)),x88492),x88493))
% 28.25/28.12 [8860]E(f319(f302(x88601,x88602,x88603),f234(f932(x88601,a923))),f234(f932(x88602,a923)))+~E(f319(f66(x88601,x88602,x88602,x88603),f85(x88601,x88602,f234(f932(x88601,a923)),x88603)),f25(x88602))
% 28.25/28.12 [8869]P1(f319(f319(f226(a925),x88691),x88692))+~P1(f319(f319(f226(a925),f319(f319(f75(a925),f319(a104,x88693)),x88691)),f319(f319(f75(a925),f319(a104,x88693)),x88692)))
% 28.25/28.12 [8870]P1(f319(f319(f227(a925),x88701),x88702))+~P1(f319(f319(f227(a925),f319(f319(f75(a925),f319(a104,x88703)),x88701)),f319(f319(f75(a925),f319(a104,x88703)),x88702)))
% 28.25/28.12 [8885]P1(f319(f319(f226(f932(x88851,a923)),x88852),x88853))+~P1(f319(f319(f226(f932(x88851,a923)),f319(f73(f932(x88851,a923)),x88853)),f319(f73(f932(x88851,a923)),x88852)))
% 28.25/28.12 [8908]P1(f319(f129(x89081),x89082))+~P1(f319(f129(x89081),f319(f319(f319(f175(f926(x89081),f926(x89081)),x89083),f159(x89081)),x89082)))
% 28.25/28.12 [8981]E(f319(f277(x89811,x89811,f299(x89811,x89812)),x89813),x89813)+~P1(f319(f319(f226(f932(x89811,a923)),f319(f277(x89811,x89811,x89812),x89813)),x89813))
% 28.25/28.12 [9030]~P4(x90301)+P14(x90301,f319(f128(x90301,f319(f319(f7(x90301,x90301,a923),a316),f319(x90302,x90303))),x90303))
% 28.25/28.12 [9037]~P1(f319(f319(f226(a925),x90371),x90372))+P1(f319(f319(f226(a925),x90371),f319(f134(a925,a925,f74(a925),x90372),x90373)))
% 28.25/28.12 [9124]~P1(f319(f319(f321(f931(x91241,x91241)),x91242),f299(x91241,x91243)))+P1(f319(f319(f321(f931(x91241,x91241)),x91242),f319(f319(f175(f931(x91241,x91241),a923),f632(x91243,x91242,x91241)),x91243)))
% 28.25/28.12 [9209]~P88(x92091)+E(f319(f319(f74(x92091),x92092),f319(f134(x92091,x92091,f319(f7(x92091,x92091,x92091),f74(x92091)),f2(x92091)),f319(f160(x92091),x92093))),f319(f134(x92091,x92091,f74(x92091),x92092),x92093))
% 28.25/28.12 [9328]~P27(x93282,x93281,x93283,f234(f932(x93282,a923)),f234(f932(x93281,a923)))+E(f85(x93281,x93282,f234(f932(x93281,a923)),f85(x93282,x93281,f234(f932(x93282,a923)),x93283)),x93283)
% 28.25/28.12 [9484]P59(x94841,x94842,x94843)+P1(f319(f319(f321(f931(x94841,x94842)),f319(f319(f244(x94841,x94842),f625(x94843,x94842,x94841)),f611(x94843,x94842,x94841))),x94843))
% 28.25/28.12 [9485]P59(x94851,x94852,x94853)+P1(f319(f319(f321(f931(x94851,x94852)),f319(f319(f244(x94851,x94852),f625(x94853,x94852,x94851)),f610(x94853,x94852,x94851))),x94853))
% 28.25/28.12 [9556]~P1(f319(f319(f321(f931(x95561,x95561)),x95562),f319(f319(f281(x95561,x95561,x95561),x95563),f299(x95561,x95563))))+P1(f319(f319(f321(f931(x95561,x95561)),x95562),f319(f319(f175(f931(x95561,x95561),a923),f634(x95563,x95562,x95561)),x95563)))
% 28.25/28.12 [9557]~P1(f319(x95571,f319(f319(f156(x95572),x95573),f319(f181(f926(x95572)),f169(x95572,x95571,x95573)))))+~P1(f319(f319(f227(a925),f319(f181(f926(x95572)),f169(x95572,x95571,x95573))),f319(f181(f926(x95572)),x95573)))
% 28.25/28.12 [9648]~P1(f319(f319(f226(f932(x96481,a923)),x96482),x96483))+P1(f319(f319(f226(f932(x96481,a923)),f319(f319(f7(x96481,f932(x96481,a923),a923),f321(x96481)),x96482)),f319(f319(f7(x96481,f932(x96481,a923),a923),f321(x96481)),x96483)))
% 28.25/28.12 [9707]~P1(f319(f319(f321(f931(f932(x97071,a923),f932(x97071,a923))),f319(f319(f244(f932(x97071,a923),f932(x97071,a923)),x97072),x97073)),f306(x97071)))+P1(f319(f319(f227(f932(x97071,a923)),x97072),x97073))
% 28.25/28.12 [9731]P60(x97311,x97312,x97313)+~P1(f319(f319(f321(f931(x97311,x97311)),f319(f319(f244(x97311,x97311),f627(x97313,x97312,x97311)),f626(x97313,x97312,x97311))),x97313))
% 28.25/28.12 [9732]P60(x97321,x97322,x97323)+~P1(f319(f319(f321(f931(x97321,x97321)),f319(f319(f244(x97321,x97321),f626(x97323,x97322,x97321)),f627(x97323,x97322,x97321))),x97323))
% 28.25/28.12 [9769]~P1(f319(f319(f321(f931(f926(x97691),f926(x97691))),f319(f319(f244(f926(x97691),f926(x97691)),x97692),x97692)),f139(x97691,x97693)))+P1(f319(f319(f321(f931(x97691,x97691)),f319(f319(f244(x97691,x97691),f677(x97692,x97693,x97691)),f677(x97692,x97693,x97691))),x97693))
% 28.25/28.12 [9821]P1(f319(f319(f226(f932(x98211,a923)),x98212),x98213))+~P1(f319(f319(f226(f932(x98211,a923)),f319(f319(f7(x98211,f932(x98211,a923),a923),f321(x98211)),x98212)),f319(f319(f7(x98211,f932(x98211,a923),a923),f321(x98211)),x98213)))
% 28.25/28.12 [9903]E(f319(f319(f23(a925),f319(f319(f6(a925,a925),x99031),f319(f274(a925),x99032))),f319(f319(f6(a925,a925),x99033),f319(f274(a925),x99032))),f319(f319(f6(a925,a925),f319(f319(f18(a925,a925,a925),f319(f319(f8(a925,f932(a925,a925),a925),f23(a925)),x99031)),x99033)),f319(f274(a925),x99032)))+~P1(f319(f319(f226(a925),f319(x99033,f436(x99032,x99031,x99033))),f319(x99031,f436(x99032,x99031,x99033))))
% 28.25/28.12 [5850]~P69(x58501)+E(f319(f319(f23(x58501),f319(f319(f74(x58501),x58502),x58503)),x58503),x58502)
% 28.25/28.12 [5851]~P69(x58511)+E(f319(f319(f74(x58511),f319(f319(f23(x58511),x58512),x58513)),x58513),x58512)
% 28.25/28.12 [6079]~P69(x60791)+E(f319(f319(f74(x60791),x60792),f319(f319(f74(x60791),f319(f73(x60791),x60792)),x60793)),x60793)
% 28.25/28.12 [6167]~P87(x61671)+E(f319(f319(f75(x61671),f319(f319(f236(x61671),x61672),x61673)),x61672),f319(f319(f236(x61671),x61672),f319(a104,x61673)))
% 28.25/28.12 [6168]~P121(x61681)+E(f319(f319(f75(x61681),f319(f319(f236(x61681),x61682),x61683)),x61682),f319(f319(f236(x61681),x61682),f319(a104,x61683)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [6489]E(f319(f319(f23(a91),f319(f319(f74(a91),x64891),x64892)),x64893),f266(x64891,x64892,x64893))+~P1(f319(f319(f227(a91),x64892),x64893))
% 28.25/28.12 [6513]~E(f319(f319(f130(x65131),x65133),x65132),f105(x65131))+P1(f319(f319(f226(a925),f319(f181(f926(x65131)),x65132)),x65133))
% 28.25/28.12 [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))
% 28.25/28.12 [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)))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [6785]~P102(x67851)+P1(f319(f319(f226(x67851),f319(f319(f93(x67851),x67852),x67853)),x67853))
% 28.25/28.12 [6786]~P108(x67861)+P1(f319(f319(f226(x67861),f319(f319(f93(x67861),x67862),x67863)),x67863))
% 28.25/28.12 [6787]~P102(x67871)+P1(f319(f319(f226(x67871),f319(f319(f93(x67871),x67872),x67873)),x67872))
% 28.25/28.12 [6788]~P108(x67881)+P1(f319(f319(f226(x67881),f319(f319(f93(x67881),x67882),x67883)),x67882))
% 28.25/28.12 [6789]~P4(x67891)+P1(f319(f319(f226(x67891),f319(f319(f224(x67891),x67892),x67893)),x67893))
% 28.25/28.12 [6790]~P4(x67901)+P1(f319(f319(f226(x67901),f319(f319(f224(x67901),x67902),x67903)),x67902))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [6935]~P88(x69351)+E(f319(f157(x69351),f319(f319(f146(x69352,x69351),f319(f16(x69351,x69352),f2(x69351))),x69353)),f2(x69351))
% 28.25/28.12 [6952]E(f319(f319(f74(a925),f319(f95(a925),x69521)),f319(f319(f74(a925),f319(f95(a925),x69522)),x69523)),f319(f319(f74(a925),f319(f95(a925),x69522)),x69523))+~P1(f319(a185,f319(f95(a1),x69521)))
% 28.25/28.12 [6967]~P6(x69671)+E(f32(x69671,f319(f319(f301(x69671),x69672),f319(f319(f301(x69671),x69673),f180(f932(x69671,a923))))),f319(f319(f93(x69671),x69672),x69673))
% 28.25/28.12 [6968]~P6(x69681)+E(f31(x69681,f319(f319(f301(x69681),x69682),f319(f319(f301(x69681),x69683),f180(f932(x69681,a923))))),f319(f319(f102(x69681),x69682),x69683))
% 28.25/28.12 [6990]E(f319(f319(f167(x69901),x69902),x69903),x69903)+~P1(f319(f319(f226(a925),f319(f181(f926(x69901)),x69903)),x69902))
% 28.25/28.12 [7001]E(f319(f319(f130(x70011),x70012),x70013),f105(x70011))+~P1(f319(f319(f226(a925),f319(f181(f926(x70011)),x70013)),x70012))
% 28.25/28.12 [7002]E(f319(f319(f130(x70021),x70022),x70023),f105(x70021))+~P1(f319(f319(f226(a925),f319(f181(f926(x70021)),x70023)),x70022))
% 28.25/28.12 [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))
% 28.25/28.12 [7013]E(f319(f319(f74(a925),f319(f319(f23(a925),x70131),x70132)),x70133),f319(f319(f23(a925),f319(f319(f74(a925),x70131),x70133)),x70132))+~P1(f319(f319(f226(a925),x70132),x70131))
% 28.25/28.12 [7027]~P1(f319(f319(f227(a925),x70271),x70273))+P1(f319(f319(f227(a925),f319(f319(f23(a925),x70271),x70272)),x70273))
% 28.25/28.12 [7054]~P4(x70541)+E(f162(x70541,x70542,f319(f319(f140(x70541,x70541,f5(x70541)),x70542),x70543)),x70543)
% 28.25/28.12 [7146]E(f319(f319(f23(a925),f319(f319(f74(a925),x71461),x71462)),f319(a104,x71463)),f319(f319(f23(a925),x71461),f319(a104,f319(f319(f23(a925),x71463),x71462))))+~P1(f319(f319(f226(a925),x71462),x71463))
% 28.25/28.12 [7147]~P126(x71471)+P1(f319(f319(f226(x71471),f2(x71471)),f319(f319(f236(x71471),f319(f69(x71471),x71472)),x71473)))
% 28.25/28.12 [7192]P15(x71921,x71922,x71923)+~P1(f319(f319(f226(f932(f924(x71921),a923)),x71923),x71922))
% 28.25/28.12 [7235]~P1(f319(f55(x72351),x72353))+P1(f319(f55(x72351),f319(f319(f93(f932(x72351,a923)),x72352),x72353)))
% 28.25/28.12 [7236]~P1(f319(f55(x72361),x72362))+P1(f319(f55(x72361),f319(f319(f93(f932(x72361,a923)),x72362),x72363)))
% 28.25/28.12 [7237]~P1(f319(f55(x72371),x72372))+P1(f319(f55(x72371),f319(f319(f23(f932(x72371,a923)),x72372),x72373)))
% 28.25/28.12 [7379]~P38(x73791,x73793)+P38(x73791,f319(f319(f93(f932(f931(x73791,x73791),a923)),x73792),x73793))
% 28.25/28.12 [7380]~P38(x73801,x73802)+P38(x73801,f319(f319(f93(f932(f931(x73801,x73801),a923)),x73802),x73803))
% 28.25/28.12 [7503]~P102(x75031)+E(f10(x75031,f319(f164(x75031),f319(f319(f143(x75031),x75032),x75033))),f319(f134(x75031,x75031,f93(x75031),x75032),x75033))
% 28.25/28.12 [7504]~P102(x75041)+E(f13(x75041,f319(f164(x75041),f319(f319(f143(x75041),x75042),x75043))),f319(f134(x75041,x75041,f102(x75041),x75042),x75043))
% 28.25/28.12 [7505]~P4(x75051)+E(f14(x75051,f319(f164(x75051),f319(f319(f143(x75051),x75052),x75053))),f319(f134(x75051,x75051,f224(x75051),x75052),x75053))
% 28.25/28.12 [7506]~P4(x75061)+E(f15(x75061,f319(f164(x75061),f319(f319(f143(x75061),x75062),x75063))),f319(f134(x75061,x75061,f225(x75061),x75062),x75063))
% 28.25/28.12 [7567]~P1(f319(f55(x75671),x75672))+P1(f319(f319(f226(a925),f319(f29(x75671),x75672)),f319(f29(x75671),f319(f319(f301(x75671),x75673),x75672))))
% 28.25/28.12 [7574]E(f319(f319(f102(f932(a925,a923)),f319(f294(a925,x75741),x75742)),f319(f294(a925,x75742),f319(f319(f74(a925),x75742),x75743))),f319(f294(a925,x75741),f319(f319(f74(a925),x75742),x75743)))+~P1(f319(f319(f226(a925),x75741),x75742))
% 28.25/28.12 [7581]P1(f319(f319(f226(a925),x75811),x75812))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),x75813),x75811)),x75812))
% 28.25/28.12 [7582]P1(f319(f319(f226(a925),x75821),x75822))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),x75821),x75823)),x75822))
% 28.25/28.12 [7583]P1(f319(f319(f226(a925),x75831),x75832))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),x75833),x75831)),x75832))
% 28.25/28.12 [7584]P1(f319(f319(f226(a925),x75841),x75842))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),x75841),x75843)),x75842))
% 28.25/28.12 [7585]P1(f319(f319(f227(a925),x75851),x75852))+~P1(f319(f319(f227(a925),f319(f319(f74(a925),x75851),x75853)),x75852))
% 28.25/28.12 [7623]~P4(x76231)+E(f11(x76231,f224(x76231),f319(f164(x76231),f319(f319(f143(x76231),x76232),x76233))),f319(f134(x76231,x76231,f224(x76231),x76232),x76233))
% 28.25/28.12 [7624]~P4(x76241)+E(f12(x76241,f225(x76241),f319(f164(x76241),f319(f319(f143(x76241),x76242),x76243))),f319(f134(x76241,x76241,f225(x76241),x76242),x76243))
% 28.25/28.12 [7628]~E(x76282,f180(f932(f931(x76281,x76281),a923)))+P1(f319(f319(f226(f932(f931(x76281,x76281),a923)),x76282),x76283))
% 28.25/28.12 [7727]E(f319(f319(f102(f932(x77271,a923)),x77272),f319(f319(f23(f932(x77271,a923)),x77273),x77272)),x77273)+~P1(f319(f319(f226(f932(x77271,a923)),x77272),x77273))
% 28.25/28.12 [7728]~P1(f319(f319(f226(a925),x77281),f319(f319(f74(a925),x77283),x77282)))+P1(f319(f319(f226(a925),f319(f319(f23(a925),x77281),x77282)),x77283))
% 28.25/28.12 [7729]~P1(f319(f319(f227(a925),x77291),f319(f319(f23(a925),x77293),x77292)))+P1(f319(f319(f227(a925),f319(f319(f74(a925),x77291),x77292)),x77293))
% 28.25/28.12 [7785]E(x77851,f105(x77852))+E(f319(f133(x77852),f319(f319(f319(f175(f926(x77852),f926(x77852)),x77853),f159(x77852)),x77851)),f319(f319(f156(x77852),x77851),f39(a925,x77853,f319(f181(f926(x77852)),x77851))))
% 28.25/28.12 [7794]E(f319(f319(f301(x77941),x77942),f319(f319(f23(f932(x77941,a923)),x77943),f319(f319(f301(x77941),x77942),f180(f932(x77941,a923))))),x77943)+~P1(f319(f319(f321(x77941),x77942),x77943))
% 28.25/28.12 [7955]P1(f319(f319(f226(a925),x79551),f319(f319(f74(a925),x79552),x79553)))+~P1(f319(f319(f226(a925),f319(f319(f23(a925),x79551),x79553)),x79552))
% 28.25/28.12 [7956]P1(f319(f319(f227(a925),x79561),f319(f319(f23(a925),x79562),x79563)))+~P1(f319(f319(f227(a925),f319(f319(f74(a925),x79561),x79563)),x79562))
% 28.25/28.12 [7981]P1(f319(f55(x79811),x79812))+~P1(f319(f55(x79811),f319(f319(f102(f932(x79811,a923)),x79813),x79812)))
% 28.25/28.12 [7982]P1(f319(f55(x79821),x79822))+~P1(f319(f55(x79821),f319(f319(f102(f932(x79821,a923)),x79822),x79823)))
% 28.25/28.12 [8056]~P47(x80561,x80563)+P1(f319(f319(f321(f931(x80561,x80561)),f319(f319(f244(x80561,x80561),x80562),x80562)),x80563))
% 28.25/28.12 [8192]E(f319(f319(f156(a925),f131(a925,f319(f294(a925,x81921),x81922))),x81923),f319(f319(f74(a925),x81921),x81923))+~P1(f319(f319(f227(a925),f319(f319(f74(a925),x81921),x81923)),x81922))
% 28.25/28.12 [8259]E(f319(f319(f167(a925),x82591),f131(a925,f319(f294(a925,x82592),x82593))),f131(a925,f319(f294(a925,x82592),f319(f319(f74(a925),x82592),x82591))))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),x82592),x82591)),x82593))
% 28.25/28.12 [8316]~P99(x83161)+E(f319(f319(f236(x83161),x83162),f319(f95(a925),f319(f319(f74(a1),x83163),x83163))),f319(f319(f80(x83161,x83161),f319(f319(f236(x83161),x83162),f319(f95(a925),x83163))),f319(f319(f18(x83161,x83161,x83161),f75(x83161)),f5(x83161))))
% 28.25/28.12 [8583]E(f319(f319(f126(x85831),f319(f319(f167(x85831),x85832),x85833)),f319(f319(f143(x85831),f319(f319(f156(x85831),x85833),x85832)),f319(f319(f130(x85831),f319(a104,x85832)),x85833))),x85833)+~P1(f319(f319(f227(a925),x85832),f319(f181(f926(x85831)),x85833)))
% 28.25/28.12 [8590]P1(f319(f319(f226(f932(x85901,a923)),f307(x85901,x85902)),f307(x85901,x85903)))+~P1(f319(f319(f226(f932(x85901,f932(x85901,a923))),x85903),x85902))
% 28.25/28.12 [8591]~P60(x85911,x85912,x85913)+P60(x85911,x85912,f319(f319(f23(f932(f931(x85911,x85911),a923)),x85913),f299(x85911,f180(f932(f931(x85911,x85911),a923)))))
% 28.25/28.12 [8610]P1(f319(f319(f226(f932(x86101,a923)),f308(x86101,x86102)),f308(x86101,x86103)))+~P1(f319(f319(f226(f932(f931(x86101,x86101),a923)),x86103),x86102))
% 28.25/28.12 [8616]~P1(f319(f319(f227(f932(x86161,a923)),x86163),x86162))+P1(f319(f319(f321(x86161),f904(x86162,x86163,x86161)),f319(f319(f23(f932(x86161,a923)),x86162),x86163)))
% 28.25/28.12 [8618]~P131(x86181)+P1(f319(f319(f226(x86181),f2(x86181)),f319(f319(f74(x86181),f319(f319(f75(x86181),x86182),x86182)),f319(f319(f75(x86181),x86183),x86183))))
% 28.25/28.12 [8646]~P99(x86461)+E(f319(f319(f236(x86461),f319(f95(x86461),x86462)),f319(f95(a925),f319(f319(f74(a1),x86463),x86463))),f319(f319(f80(x86461,x86461),f319(f319(f236(x86461),f319(f95(x86461),x86462)),f319(f95(a925),x86463))),f319(f319(f18(x86461,x86461,x86461),f75(x86461)),f5(x86461))))
% 28.25/28.12 [8651]P1(f319(f319(f226(f932(x86511,a923)),f319(f273(x86511),x86512)),f319(f273(x86511),x86513)))+~P1(f319(f319(f226(f932(f931(x86511,x86511),a923)),x86512),x86513))
% 28.25/28.12 [8682]~P58(x86821,x86822)+~P1(f319(f319(f321(f931(x86821,x86821)),f319(f319(f244(x86821,x86821),x86823),x86823)),x86822))
% 28.25/28.12 [8683]~P38(x86831,x86832)+~P1(f319(f319(f321(f931(x86831,x86831)),f319(f319(f244(x86831,x86831),x86833),x86833)),x86832))
% 28.25/28.12 [8684]~P38(x86841,x86842)+~P1(f319(f319(f321(f931(x86841,x86841)),f319(f319(f244(x86841,x86841),x86843),x86843)),x86842))
% 28.25/28.12 [8727]~E(x87272,x87273)+P1(f319(f319(f321(f931(x87271,x87271)),f319(f319(f244(x87271,x87271),x87272),x87273)),f299(x87271,f180(f932(f931(x87271,x87271),a923)))))
% 28.25/28.12 [8744]P1(f319(f319(f226(f932(x87441,a923)),f32(f932(x87441,a923),x87442)),f32(f932(x87441,a923),x87443)))+~P1(f319(f319(f226(f932(f932(x87441,a923),a923)),x87443),x87442))
% 28.25/28.12 [8745]P1(f319(f319(f226(f932(x87451,a923)),f31(f932(x87451,a923),x87452)),f31(f932(x87451,a923),x87453)))+~P1(f319(f319(f226(f932(f932(x87451,a923),a923)),x87452),x87453))
% 28.25/28.12 [8799]~P9(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))))
% 28.25/28.12 [8800]~P57(x88001,x88003,x88002)+P1(f319(f319(f226(f932(f931(x88001,x88001),a923)),x88002),f319(f319(f246(x88001,x88001),x88003),f319(f16(f932(x88001,a923),x88001),x88003))))
% 28.25/28.12 [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),x88503),x88502))))
% 28.25/28.12 [8851]~P92(x88511)+P1(f319(f319(f226(x88511),f319(f319(f23(x88511),f319(f69(x88511),x88512)),f319(f69(x88511),x88513))),f319(f69(x88511),f319(f319(f23(x88511),x88512),x88513))))
% 28.25/28.12 [8883]P1(f319(f319(f226(f932(f931(x88831,x88831),a923)),f299(x88831,x88832)),f299(x88831,x88833)))+~P1(f319(f319(f226(f932(f931(x88831,x88831),a923)),x88832),x88833))
% 28.25/28.12 [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))
% 28.25/28.12 [8994]~P26(x89942,x89941,x89943,f234(f932(x89942,a923)))+E(f319(f66(x89941,x89942,x89942,f85(x89942,x89941,f234(f932(x89942,a923)),x89943)),x89943),f25(x89942))
% 28.25/28.12 [9055]P60(x90551,x90552,x90553)+~P60(x90551,x90552,f319(f319(f23(f932(f931(x90551,x90551),a923)),x90553),f299(x90551,f180(f932(f931(x90551,x90551),a923)))))
% 28.25/28.12 [9075]P1(f319(f319(f226(f932(f931(f926(x90751),f926(x90751)),a923)),f149(x90751,x90752)),f149(x90751,x90753)))+~P1(f319(f319(f226(f932(f931(x90751,x90751),a923)),x90752),x90753))
% 28.25/28.12 [9076]P1(f319(f319(f226(f932(f931(f926(x90761),f926(x90761)),a923)),f150(x90761,x90762)),f150(x90761,x90763)))+~P1(f319(f319(f226(f932(f931(x90761,x90761),a923)),x90762),x90763))
% 28.25/28.12 [9097]~P57(x90971,x90973,x90972)+P1(f319(f319(f226(f932(f931(x90971,x90971),a923)),x90972),f319(f319(f281(x90971,x90971,x90971),f319(f278(x90971,x90971),x90972)),x90972)))
% 28.25/28.12 [9133]~P1(f319(f129(x91331),x91333))+P1(f319(f129(x91331),f319(f319(f130(x91331),f319(f181(f926(x91331)),f169(x91331,x91332,x91333))),x91333)))
% 28.25/28.12 [9152]~P1(f319(f129(x91521),x91522))+E(f319(f128(x91521,f319(f319(f7(x91521,f932(x91521,a923),a923),f321(x91521)),f319(f164(x91521),f168(x91521,x91522,x91523)))),x91522),f168(x91521,x91522,x91523))
% 28.25/28.12 [9207]E(x92071,x92072)+~P1(f319(f319(f321(f931(x92073,x92073)),f319(f319(f244(x92073,x92073),x92071),x92072)),f299(x92073,f180(f932(f931(x92073,x92073),a923)))))
% 28.25/28.12 [9291]P1(f319(f319(f321(x92911),x92912),f308(x92911,x92913)))+P1(f319(f319(f321(f931(x92911,x92911)),f319(f319(f244(x92911,x92911),f560(x92913,x92912,x92911)),x92912)),x92913))
% 28.25/28.12 [9292]P1(f319(f319(f321(x92921),x92922),f308(x92921,x92923)))+P1(f319(f319(f321(f931(x92921,x92921)),f319(f319(f244(x92921,x92921),f612(x92923,x92922,x92921)),x92922)),x92923))
% 28.25/28.12 [9293]P1(f319(f319(f321(x92931),x92932),f308(x92931,x92933)))+P1(f319(f319(f321(f931(x92931,x92931)),f319(f319(f244(x92931,x92931),f613(x92933,x92932,x92931)),x92932)),x92933))
% 28.25/28.12 [9329]P26(x93291,x93292,x93293,f234(f932(x93291,a923)))+~E(f319(f66(x93292,x93291,x93291,f85(x93291,x93292,f234(f932(x93291,a923)),x93293)),x93293),f25(x93291))
% 28.25/28.12 [9383]~P1(f319(f319(f321(f926(x93831)),x93833),f153(x93831,x93832)))+P1(f319(f152(x93831,f319(f319(f7(x93831,f932(x93831,a923),a923),f321(x93831)),x93832)),x93833))
% 28.25/28.12 [9408]P1(f319(x94083,x94082))+E(f319(f254(x94081),f319(f319(f18(x94081,a923,a923),f319(f319(f8(a923,f932(a923,a923),x94081),a317),f319(a316,x94082))),x94083)),f180(f932(x94081,a923)))
% 28.25/28.12 [9424]~P92(x94241)+P1(f319(f319(f226(x94241),f319(f69(x94241),f319(f319(f23(x94241),f319(f69(x94241),x94242)),f319(f69(x94241),x94243)))),f319(f69(x94241),f319(f319(f23(x94241),x94242),x94243))))
% 28.25/28.12 [9439]~P1(f319(x94393,x94392))+E(f319(f254(x94391),f319(f319(f18(x94391,a923,a923),f319(f319(f8(a923,f932(a923,a923),x94391),a317),f319(a316,x94392))),x94393)),f319(f319(f301(x94391),x94392),f180(f932(x94391,a923))))
% 28.25/28.12 [9448]~P1(f319(f319(f321(f932(x94481,a923)),x94483),f319(f300(x94481),x94482)))+P1(f319(f240(x94481,f319(f319(f7(x94481,f932(x94481,a923),a923),f321(x94481)),x94482)),x94483))
% 28.25/28.12 [9483]P38(x94831,x94832)+P1(f319(f319(f321(f931(x94831,x94831)),f319(f319(f244(x94831,x94831),f319(f568(x94832,x94831),f319(a104,x94833))),f319(f568(x94832,x94831),x94833))),x94832))
% 28.25/28.12 [9581]~P1(f319(f129(x95811),x95813))+P1(f319(f129(x95811),f319(f128(x95811,f319(f319(f8(a923,a923,x95811),a314),f319(a316,x95812))),x95813)))
% 28.25/28.12 [9625]P1(f319(f319(f321(f926(x96251)),x96252),f153(x96251,x96253)))+~P1(f319(f152(x96251,f319(f319(f7(x96251,f932(x96251,a923),a923),f321(x96251)),x96253)),x96252))
% 28.25/28.12 [9640]P1(f319(f319(f321(f932(x96401,a923)),x96402),f319(f300(x96401),x96403)))+~P1(f319(f240(x96401,f319(f319(f7(x96401,f932(x96401,a923),a923),f321(x96401)),x96403)),x96402))
% 28.25/28.12 [9702]P1(f319(f319(f321(x97021),f319(f260(x97021,x97022),x97023)),f319(f164(x97021),f319(f319(f146(f931(a91,x97021),x97021),f248(a91,x97021)),x97022))))+~P1(f319(f319(f227(a91),x97023),f319(f157(a91),f319(f319(f146(f931(a91,x97021),a91),f243(a91,x97021)),x97022))))
% 28.25/28.12 [9748]P1(f319(f319(f226(f932(f931(f926(x97481),f926(x97481)),a923)),f150(x97481,x97482)),f319(f319(f246(f926(x97481),f926(x97481)),f153(x97481,x97483)),f319(f16(f932(f926(x97481),a923),f926(x97481)),f153(x97481,x97483)))))+~P1(f319(f319(f226(f932(f931(x97481,x97481),a923)),x97482),f319(f319(f246(x97481,x97481),x97483),f319(f16(f932(x97481,a923),x97481),x97483))))
% 28.25/28.12 [9772]P1(f319(f319(f321(x97721),f319(f243(x97721,f931(a91,a91)),f319(f258(x97721,x97722),x97723))),f319(f164(x97721),f319(f319(f146(f931(a91,x97721),x97721),f248(a91,x97721)),x97722))))+~P1(f319(f319(f227(a91),f2(a91)),f319(f157(a91),f319(f319(f146(f931(a91,x97721),a91),f243(a91,x97721)),x97722))))
% 28.25/28.12 [9789]~P1(f319(f319(f226(f932(f931(x97891,x97891),a923)),x97892),f319(f319(f246(x97891,x97891),x97893),f319(f16(f932(x97891,a923),x97891),x97893))))+P1(f319(f319(f226(f932(f931(x97891,x97891),a923)),f319(f319(f281(x97891,x97891,x97891),x97892),f299(x97891,x97892))),f319(f319(f246(x97891,x97891),x97893),f319(f16(f932(x97891,a923),x97891),x97893))))
% 28.25/28.12 [10109]~P38(x101091,x101092)+~P1(f319(f319(f321(f931(x101091,x101091)),f319(f319(f244(x101091,x101091),f319(x101093,f319(a104,f569(x101092,x101091,x101093)))),f319(x101093,f569(x101092,x101091,x101093)))),x101092))
% 28.25/28.12 [10110]~P38(x101101,x101102)+~P1(f319(f319(f321(f931(x101101,x101101)),f319(f319(f244(x101101,x101101),f319(x101103,f319(a104,f620(x101103,x101102,x101101)))),f319(x101103,f620(x101103,x101102,x101101)))),x101102))
% 28.25/28.12 [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)),f310(x103711,x103712)),f319(f319(f102(f932(f931(f932(x103711,a923),f932(x103711,a923)),a923)),f310(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)))))),f310(x103711,x103712)))+~P1(f319(f319(f226(f932(f931(x103711,x103711),a923)),f319(f319(f281(x103711,x103711,x103711),x103712),x103713)),x103712))
% 28.25/28.12 [10372]P1(f319(f319(f226(f932(f931(f932(x103721,a923),f932(x103721,a923)),a923)),f319(f319(f281(f932(x103721,a923),f932(x103721,a923),f932(x103721,a923)),f311(x103721,x103722)),f319(f319(f102(f932(f931(f932(x103721,a923),f932(x103721,a923)),a923)),f311(x103721,x103723)),f319(f319(f301(f931(f932(x103721,a923),f932(x103721,a923))),f319(f319(f244(f932(x103721,a923),f932(x103721,a923)),f180(f932(x103721,a923))),f180(f932(x103721,a923)))),f180(f932(f931(f932(x103721,a923),f932(x103721,a923)),a923)))))),f311(x103721,x103722)))+~P1(f319(f319(f226(f932(f931(x103721,x103721),a923)),f319(f319(f281(x103721,x103721,x103721),x103722),x103723)),x103722))
% 28.25/28.12 [7502]~P1(f319(f319(f226(a925),x75022),x75021))+E(f319(f319(f23(a925),f319(a104,f319(f319(f23(a925),x75021),x75022))),x75023),f319(f319(f23(a925),f319(a104,x75021)),f319(f319(f74(a925),x75022),x75023)))
% 28.25/28.12 [7542]~P65(x75421)+E(f319(f319(f74(x75421),f39(x75421,x75422,x75423)),f319(f319(f75(x75421),f319(f319(f30(x75421),x75422),x75423)),x75423)),x75422)
% 28.25/28.12 [7733]E(f319(f319(f75(a925),f319(f95(a925),x77331)),f319(f319(f75(a925),f319(f95(a925),x77332)),x77333)),f319(f319(f75(a925),f319(f95(a925),f319(f319(f75(a1),x77331),x77332))),x77333))+P1(f319(f319(f227(a1),x77331),a77))
% 28.25/28.12 [8201]~P1(f319(f319(f226(a925),x82013),x82012))+P1(f319(f319(f226(a925),x82011),f319(f319(f23(a925),f319(f319(f74(a925),x82012),x82011)),x82013)))
% 28.25/28.12 [8402]~P1(f319(f319(f226(a925),x84021),x84022))+E(f319(f319(f126(a925),f131(a925,f319(f294(a925,x84021),x84022))),f131(a925,f319(f294(a925,x84022),f319(f319(f74(a925),x84022),x84023)))),f131(a925,f319(f294(a925,x84021),f319(f319(f74(a925),x84022),x84023))))
% 28.25/28.12 [8659]~P1(f319(f55(x86591),x86592))+E(f319(a104,f319(f29(x86591),f319(f319(f23(f932(x86591,a923)),x86592),f319(f319(f301(x86591),x86593),f180(f932(x86591,a923)))))),f319(f29(x86591),f319(f319(f301(x86591),x86593),x86592)))
% 28.25/28.12 [8700]~P1(f319(f55(x87001),x87002))+E(f319(f319(f74(a925),f72(a925)),f319(f29(x87001),f319(f319(f23(f932(x87001,a923)),x87002),f319(f319(f301(x87001),x87003),f180(f932(x87001,a923)))))),f319(f29(x87001),f319(f319(f301(x87001),x87003),x87002)))
% 28.25/28.12 [8892]E(f319(f319(f23(a925),f319(f29(x88921),x88922)),f319(f29(x88921),f319(f319(f93(f932(x88921,a923)),x88922),x88923))),f319(f29(x88921),f319(f319(f23(f932(x88921,a923)),x88922),x88923)))+~P1(f319(f55(x88921),f319(f319(f93(f932(x88921,a923)),x88922),x88923)))
% 28.25/28.12 [9147]~P7(f319(x91472,f432(x91472,x91473,x91471)))+E(f319(f92(a1),f319(f319(f6(x91471,a925),f319(f319(f8(a1,a925,x91471),a96),x91472)),x91473)),f319(f319(f6(x91471,a1),x91472),x91473))
% 28.25/28.12 [9148]~P7(f319(x91482,f479(x91482,x91483,x91481)))+E(f319(f92(a1),f319(f319(f9(x91481,a925),f319(f319(f8(a1,a925,x91481),a96),x91482)),x91483)),f319(f319(f9(x91481,a1),x91482),x91483))
% 28.25/28.12 [9190]~P1(f319(f55(x91901),x91903))+P1(f319(f319(f226(a925),f319(f319(f23(a925),f319(f29(x91901),x91902)),f319(f29(x91901),x91903))),f319(f29(x91901),f319(f319(f23(f932(x91901,a923)),x91902),x91903))))
% 28.25/28.12 [9218]P1(f319(f319(f321(x92181),f432(x92182,x92183,x92181)),x92183))+E(f319(f92(a1),f319(f319(f6(x92181,a925),f319(f319(f8(a1,a925,x92181),a96),x92182)),x92183)),f319(f319(f6(x92181,a1),x92182),x92183))
% 28.25/28.12 [9219]P1(f319(f319(f321(x92191),f479(x92192,x92193,x92191)),x92193))+E(f319(f92(a1),f319(f319(f9(x92191,a925),f319(f319(f8(a1,a925,x92191),a96),x92192)),x92193)),f319(f319(f9(x92191,a1),x92192),x92193))
% 28.25/28.12 [9283]E(f79(x92831,f319(f319(f7(x92831,f932(x92831,a923),a923),f321(x92831)),f319(f319(f23(f932(x92831,a923)),x92832),f319(f319(f301(x92831),x92833),f180(f932(x92831,a923)))))),f239(x92831,x92833,x92832))+P1(f319(f319(f226(f932(x92831,a923)),x92832),f319(f319(f301(x92831),x92833),f180(f932(x92831,a923)))))
% 28.25/28.12 [9641]E(f319(f319(f146(f926(x96411),x96411),f319(f319(f7(f926(x96411),a925,x96411),f156(x96411)),x96412)),f319(f128(f926(x96411),f319(f319(f8(a925,a923,f926(x96411)),f319(f227(a925),x96412)),f181(f926(x96411)))),x96413)),f319(f319(f156(f926(x96411)),f171(x96411,x96413)),x96412))+~P1(f319(f319(f227(a925),x96412),f319(f181(f926(f926(x96411))),f171(x96411,x96413))))
% 28.25/28.12 [9722]E(f319(f128(x97221,x97222),x97223),f169(x97221,x97222,x97223))+P1(f319(f319(f321(x97221),f743(x97223,x97222,x97221)),f319(f164(x97221),f319(f319(f130(x97221),f319(f181(f926(x97221)),f169(x97221,x97222,x97223))),x97223))))
% 28.25/28.12 [9863]E(f319(f319(f130(x98631),f319(f181(f926(x98631)),f169(x98631,x98632,x98633))),x98633),f105(x98631))+~P1(f319(x98632,f319(f133(x98631),f319(f319(f130(x98631),f319(f181(f926(x98631)),f169(x98631,x98632,x98633))),x98633))))
% 28.25/28.12 [9963]~P1(f319(f319(f321(f931(x99631,x99631)),x99632),f299(x99631,x99633)))+P1(f319(f319(f321(f931(x99631,x99631)),x99632),f319(f319(f33(a925,f932(f931(x99631,x99631),a923)),f234(f932(a925,a923))),f319(f319(f7(a925,f932(f931(x99631,x99631),a923),f932(f931(x99631,x99631),a923)),f175(f931(x99631,x99631),a923)),x99633))))
% 28.25/28.12 [10030]~P1(f319(f319(f226(f932(x100301,a923)),f319(f319(f33(a925,f932(x100301,a923)),f319(f294(a925,f2(a925)),f411(x100303,x100302,x100301))),x100302)),x100303))+P1(f319(f319(f226(f932(x100301,a923)),f319(f319(f33(a925,f932(x100301,a923)),f234(f932(a925,a923))),x100302)),x100303))
% 28.25/28.12 [10080]~P1(f319(f319(f227(a1),f2(a1)),x100803))+P1(f319(f319(f227(a1),x100801),f319(f319(f74(a1),x100802),f319(f319(f75(a1),f319(f319(f74(a1),f319(f69(a1),f319(f319(f23(a1),x100802),x100801))),f72(a1))),x100803))))
% 28.25/28.12 [10096]~P38(x100961,f319(f319(f102(f932(f931(x100961,x100961),a923)),x100962),x100963))+P38(x100961,f319(f319(f102(f932(f931(x100961,x100961),a923)),f319(f319(f102(f932(f931(x100961,x100961),a923)),f319(f319(f281(x100961,x100961,x100961),x100962),x100962)),f319(f319(f281(x100961,x100961,x100961),x100963),x100962))),x100963))
% 28.25/28.12 [10171]P38(x101711,f319(f319(f102(f932(f931(x101711,x101711),a923)),x101712),x101713))+~P38(x101711,f319(f319(f102(f932(f931(x101711,x101711),a923)),f319(f319(f102(f932(f931(x101711,x101711),a923)),f319(f319(f281(x101711,x101711,x101711),x101712),x101712)),f319(f319(f281(x101711,x101711,x101711),x101713),x101712))),x101713))
% 28.25/28.12 [9725]~P145(x97251)+E(f319(f94(x97251),f319(a83,f319(f277(f931(a925,a925),f931(a925,a925),a100),f319(f319(f301(f931(a925,a925)),f319(f319(f244(a925,a925),x97252),x97253)),f180(f932(f931(a925,a925),a923)))))),f319(f319(f23(x97251),f319(f92(x97251),x97252)),f319(f92(x97251),x97253)))
% 28.25/28.12 [9809]P1(f319(x98093,x98092))+E(f319(f254(x98091),f319(f319(f18(x98091,a923,a923),f319(f319(f8(a923,f932(a923,a923),x98091),a317),f319(f319(f7(x98091,x98091,a923),a316),x98092))),x98093)),f180(f932(x98091,a923)))
% 28.25/28.12 [9811]~P1(f319(x98113,x98112))+E(f319(f254(x98111),f319(f319(f18(x98111,a923,a923),f319(f319(f8(a923,f932(a923,a923),x98111),a317),f319(f319(f7(x98111,x98111,a923),a316),x98112))),x98113)),f319(f319(f301(x98111),x98112),f180(f932(x98111,a923))))
% 28.25/28.12 [10059]E(x100591,x100592)+P1(f319(f319(f235(x100593,x100593,f319(f319(f8(f932(x100593,a923),f932(x100593,a923),x100593),f319(f8(a923,a923,x100593),a314)),a316)),x100591),x100592))
% 28.25/28.12 [10151]~E(x101511,x101512)+~P1(f319(f319(f235(x101513,x101513,f319(f319(f8(f932(x101513,a923),f932(x101513,a923),x101513),f319(f8(a923,a923,x101513),a314)),a316)),x101511),x101512))
% 28.25/28.12 [10163]~P1(f319(f55(x101631),x101633))+E(f319(f319(f58(x101631,f932(x101631,a923),f319(f319(f8(f932(x101631,a923),f932(f932(x101631,a923),f932(x101631,a923)),x101631),f319(f7(f932(x101631,a923),f932(x101631,a923),f932(x101631,a923)),f23(f932(x101631,a923)))),f319(f319(f7(x101631,f932(x101631,a923),f932(x101631,a923)),f301(x101631)),f180(f932(x101631,a923))))),x101632),x101633),f319(f319(f23(f932(x101631,a923)),x101632),x101633))
% 28.25/28.12 [10194]~P1(f319(f319(f227(a1),f2(a1)),x101943))+P1(f319(f319(f227(a1),f319(f319(f23(a1),x101941),f319(f319(f75(a1),f319(f319(f74(a1),f319(f69(a1),f319(f319(f23(a1),x101941),x101942))),f72(a1))),x101943))),x101942))
% 28.25/28.12 [10457]~P1(f319(f319(f321(x104571),x104573),f308(x104571,x104572)))+P1(f319(f307(x104571,f319(f319(f7(x104571,f932(f931(x104571,x104571),a923),f932(x104571,a923)),f319(f319(f8(f932(x104571,f932(f932(f931(x104571,x104571),a923),a923)),f932(f932(f931(x104571,x104571),a923),f932(x104571,a923)),x104571),f7(x104571,f932(f931(x104571,x104571),a923),a923)),f319(f319(f8(f932(x104571,f931(x104571,x104571)),f932(x104571,f932(f932(f931(x104571,x104571),a923),a923)),x104571),f319(f8(f931(x104571,x104571),f932(f932(f931(x104571,x104571),a923),a923),x104571),f321(f931(x104571,x104571)))),f244(x104571,x104571)))),x104572)),x104573))
% 28.25/28.12 [10470]P1(f319(f319(f321(x104701),x104702),f308(x104701,x104703)))+~P1(f319(f307(x104701,f319(f319(f7(x104701,f932(f931(x104701,x104701),a923),f932(x104701,a923)),f319(f319(f8(f932(x104701,f932(f932(f931(x104701,x104701),a923),a923)),f932(f932(f931(x104701,x104701),a923),f932(x104701,a923)),x104701),f7(x104701,f932(f931(x104701,x104701),a923),a923)),f319(f319(f8(f932(x104701,f931(x104701,x104701)),f932(x104701,f932(f932(f931(x104701,x104701),a923),a923)),x104701),f319(f8(f931(x104701,x104701),f932(f932(f931(x104701,x104701),a923),a923),x104701),f321(f931(x104701,x104701)))),f244(x104701,x104701)))),x104703)),x104702))
% 28.25/28.12 [10028]~P1(f319(f55(x100281),f319(f254(x100281),x100283)))+P1(f319(f55(x100281),f319(f254(x100281),f319(f319(f18(x100281,a923,a923),f319(f319(f8(a923,f932(a923,a923),x100281),a317),x100282)),x100283))))
% 28.25/28.12 [10029]~P1(f319(f55(x100291),f319(f254(x100291),x100292)))+P1(f319(f55(x100291),f319(f254(x100291),f319(f319(f18(x100291,a923,a923),f319(f319(f8(a923,f932(a923,a923),x100291),a317),x100292)),x100293))))
% 28.25/28.12 [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),x101303)),x101302))))
% 28.25/28.12 [10131]P1(f319(f55(x101311),f319(f254(x101311),x101312)))+~P1(f319(f55(x101311),f319(f254(x101311),f319(f319(f18(x101311,a923,a923),f319(f319(f8(a923,f932(a923,a923),x101311),a318),x101312)),x101313))))
% 28.25/28.12 [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)),a316),f181(f926(x104351)))),x104353)))))
% 28.25/28.12 [10436]~P1(f319(f55(x104361),x104362))+P1(f319(f55(f926(x104361)),f319(f254(f926(x104361)),f319(f319(f18(f926(x104361),a923,a923),f319(f319(f8(a923,f932(a923,a923),f926(x104361)),a317),f319(f319(f7(f926(x104361),f932(x104361,a923),a923),f319(f319(f8(f932(x104361,a923),f932(f932(x104361,a923),a923),f926(x104361)),f226(f932(x104361,a923))),f164(x104361))),x104362))),f319(f319(f7(f926(x104361),a925,a923),f319(f319(f8(a925,f932(a925,a923),f926(x104361)),f226(a925)),f181(f926(x104361)))),x104363)))))
% 28.25/28.12 [10144]~P121(x101441)+E(f319(f319(f236(x101441),x101442),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)))),x101443)),f319(f319(f75(x101441),f319(f319(f236(x101441),x101442),x101443)),f319(f319(f236(x101441),x101442),x101443)))
% 28.25/28.12 [10174]~P87(x101741)+E(f319(f319(f236(x101741),f319(f319(f236(x101741),x101742),x101743)),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(x101741),x101742),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)))),x101743)))
% 28.25/28.12 [10233]~P145(x102331)+E(f319(f319(f236(x102331),f319(f73(x102331),x102332)),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)))),x102333)),f319(f319(f236(x102331),x102332),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)))),x102333)))
% 28.25/28.12 [10379]~P126(x103791)+P1(f319(f319(f226(x103791),f2(x103791)),f319(f319(f74(x103791),f319(f319(f236(x103791),x103792),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(x103791),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)))))))
% 28.25/28.12 [10243]~P121(x102431)+E(f319(f319(f236(x102431),x102432),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)))),x102433))),f319(f319(f75(x102431),x102432),f319(f319(f75(x102431),f319(f319(f236(x102431),x102432),x102433)),f319(f319(f236(x102431),x102432),x102433))))
% 28.25/28.12 [10296]~P87(x102961)+E(f319(f319(f75(x102961),x102962),f319(f319(f236(x102961),f319(f319(f236(x102961),x102962),x102963)),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(x102961),x102962),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)))),x102963))))
% 28.25/28.12 [10335]~P126(x103351)+P1(f319(f319(f226(x103351),f2(x103351)),f319(f319(f236(x103351),x103352),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)))),x103353))))
% 28.25/28.12 [10410]~P99(x104101)+E(f319(f319(f23(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(f23(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)))))
% 28.25/28.12 [10411]~P99(x104111)+E(f319(f319(f74(x104111),f319(f319(f74(x104111),f319(f319(f236(x104111),x104112),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(x104111),x104113),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(x104111),f319(f319(f75(x104111),f319(f95(x104111),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)))),x104112)),x104113)),f319(f319(f236(x104111),f319(f319(f74(x104111),x104112),x104113)),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)))))
% 28.25/28.12 [7998]P26(x79981,x79982,x79983,x79984)+~E(f889(x79984,x79983,x79982,x79981),f890(x79984,x79983,x79982,x79981))
% 28.25/28.12 [8293]P35(x82931,x82932,x82933,x82934,f105(x82932))+~E(x82934,f105(x82931))
% 28.25/28.12 [8294]P35(x82941,x82942,x82943,f105(x82941),x82944)+~E(x82944,f105(x82942))
% 28.25/28.12 [8840]~P35(x88402,x88403,x88404,x88401,f105(x88403))+E(x88401,f105(x88402))
% 28.25/28.12 [8841]~P35(x88413,x88412,x88414,f105(x88413),x88411)+E(x88411,f105(x88412))
% 28.25/28.12 [5270]~P19(x52703,x52701,x52704)+E(f319(f319(x52701,x52702),x52702),x52702)
% 28.25/28.12 [5520]P1(f319(x55202,x55204))+E(f319(f128(x55201,x55202),f161(x55201,x55203,x55204)),f105(x55201))
% 28.25/28.12 [5556]~E(x55564,f180(f932(x55561,a923)))+E(f319(f302(x55561,x55562,x55563),x55564),f180(f932(x55562,a923)))
% 28.25/28.12 [5557]~E(x55574,f180(f932(x55571,a923)))+E(f319(f302(x55571,x55572,x55573),x55574),f180(f932(x55572,a923)))
% 28.25/28.12 [5800]~P1(f319(x58002,x58004))+E(f319(f128(x58001,x58002),f161(x58001,x58003,x58004)),f161(x58001,x58003,x58004))
% 28.25/28.12 [5828]~E(f319(f302(x58282,x58283,x58284),x58281),f180(f932(x58283,a923)))+E(x58281,f180(f932(x58282,a923)))
% 28.25/28.12 [5829]~E(f319(f302(x58292,x58293,x58294),x58291),f180(f932(x58293,a923)))+E(x58291,f180(f932(x58292,a923)))
% 28.25/28.12 [6017]~P8(x60171,x60173)+E(f263(x60171,x60172,f262(x60171,x60173),x60174),x60174)
% 28.25/28.12 [6126]~P4(x61262)+E(f319(f319(f140(x61261,x61262,x61263),x61264),f105(x61261)),f319(f319(f143(x61261),x61264),f105(x61261)))
% 28.25/28.12 [6483]~E(x64831,f180(f932(x64832,a923)))+~P1(f319(f56(x64832,x64833,x64831),x64834))
% 28.25/28.12 [6504]~P63(x65041,x65043,x65044,x65042)+P1(f319(f55(x65041),x65042))
% 28.25/28.12 [6505]~P63(x65051,x65053,x65054,x65052)+P1(f319(f55(x65051),x65052))
% 28.25/28.12 [6506]~P63(x65061,x65063,x65062,x65064)+P1(f319(f55(x65061),x65062))
% 28.25/28.12 [6507]~P63(x65071,x65073,x65072,x65074)+P1(f319(f55(x65071),x65072))
% 28.25/28.12 [6514]~P63(x65142,x65143,x65144,x65141)+~E(x65141,f180(f932(x65142,a923)))
% 28.25/28.12 [6515]~P63(x65152,x65153,x65154,x65151)+~E(x65151,f180(f932(x65152,a923)))
% 28.25/28.12 [6547]~P113(x65471)+E(f319(f319(f93(f932(x65471,a923)),f319(f294(x65471,x65472),x65473)),f295(x65471,x65473,x65474)),f180(f932(x65471,a923)))
% 28.25/28.12 [6574]~P1(f319(f319(x65743,x65744),x65742))+P1(f319(f319(f321(x65741),x65742),f287(x65741,x65743,x65744)))
% 28.25/28.12 [6575]~P1(f319(f319(x65753,x65754),x65752))+P1(f319(f319(f321(x65751),x65752),f286(x65751,x65753,x65754)))
% 28.25/28.12 [6576]~P1(f319(f319(x65763,x65762),x65764))+P1(f319(f319(f321(x65761),x65762),f290(x65761,x65763,x65764)))
% 28.25/28.12 [6577]~P1(f319(f319(x65773,x65772),x65774))+P1(f319(f319(f321(x65771),x65772),f288(x65771,x65773,x65774)))
% 28.25/28.12 [6642]~P52(x66424,x66421,x66422,x66423)+P1(f319(f319(x66421,x66422),x66423))
% 28.25/28.12 [6721]~P113(x67211)+E(f319(f319(f93(f932(x67211,a923)),f295(x67211,x67212,x67213)),f297(x67211,x67213,x67214)),f180(f932(x67211,a923)))
% 28.25/28.12 [6722]~P113(x67221)+E(f319(f319(f93(f932(x67221,a923)),f295(x67221,x67222,x67223)),f298(x67221,x67223,x67224)),f180(f932(x67221,a923)))
% 28.25/28.12 [6723]~P113(x67231)+E(f319(f319(f93(f932(x67231,a923)),f297(x67231,x67232,x67233)),f297(x67231,x67233,x67234)),f180(f932(x67231,a923)))
% 28.25/28.12 [6724]~P113(x67241)+E(f319(f319(f93(f932(x67241,a923)),f297(x67241,x67242,x67243)),f298(x67241,x67243,x67244)),f180(f932(x67241,a923)))
% 28.25/28.12 [6725]~P113(x67251)+E(f319(f319(f93(f932(x67251,a923)),f298(x67251,x67252,x67253)),f295(x67251,x67253,x67254)),f180(f932(x67251,a923)))
% 28.25/28.12 [6762]P1(f319(f319(x67621,x67622),f564(x67622,x67621)))+~P1(f319(f241(x67623,x67624,x67621),x67622))
% 28.25/28.12 [6766]~P52(x67661,x67662,x67663,x67664)+~P1(f319(f319(x67662,x67664),x67663))
% 28.25/28.12 [6846]~P4(x68462)+E(f319(f164(x68461),f142(x68461,x68462,x68463,x68464)),f319(f164(x68461),x68464))
% 28.25/28.12 [6897]~P149(x68971)+E(f182(x68971,x68972,f319(a104,x68973),x68974),f182(x68971,x68972,x68973,f319(x68972,x68974)))
% 28.25/28.12 [6961]~P1(f319(f319(f321(x69614),x69613),f287(x69614,x69611,x69612)))+P1(f319(f319(x69611,x69612),x69613))
% 28.25/28.12 [6962]~P1(f319(f319(f321(x69624),x69623),f286(x69624,x69621,x69622)))+P1(f319(f319(x69621,x69622),x69623))
% 28.25/28.12 [6963]~P1(f319(f319(f321(x69634),x69632),f290(x69634,x69631,x69633)))+P1(f319(f319(x69631,x69632),x69633))
% 28.25/28.12 [6964]~P1(f319(f319(f321(x69644),x69642),f288(x69644,x69641,x69643)))+P1(f319(f319(x69641,x69642),x69643))
% 28.25/28.12 [7039]E(f319(f29(f933(x70391,x70392)),f305(x70391,x70392,x70393,x70394)),f2(a925))+P1(f319(f55(x70392),x70394))
% 28.25/28.12 [7040]E(f319(f29(f933(x70401,x70402)),f305(x70401,x70402,x70403,x70404)),f2(a925))+P1(f319(f55(x70401),x70403))
% 28.25/28.12 [7243]~P16(x72434,x72431,x72432)+E(f319(f66(x72431,x72431,x72431,f319(x72432,x72433)),f319(x72432,x72433)),f319(x72432,x72433))
% 28.25/28.12 [7487]E(f269(x74871,x74872,x74873,x74874),f319(f244(f932(a91,f932(a923,f929(f927(x74871)))),f931(a91,a91)),f35(x74871)))+~P1(f319(f319(f226(a91),x74873),f2(a91)))
% 28.25/28.12 [8122]~E(x81222,x81223)+P1(f319(f319(f321(f931(x81221,x81221)),f319(f319(f244(x81221,x81221),x81222),x81223)),f299(x81221,x81224)))
% 28.25/28.12 [8151]~P26(x81511,x81512,x81513,f234(f932(x81511,a923)))+E(f319(f71(x81511,x81512,f234(f932(x81511,a923)),x81513),f319(x81513,x81514)),x81514)
% 28.25/28.12 [8152]~P26(x81521,x81522,x81523,f234(f932(x81521,a923)))+E(f319(f85(x81521,x81522,f234(f932(x81521,a923)),x81523),f319(x81523,x81524)),x81524)
% 28.25/28.12 [8242]~P1(f319(f319(f321(f926(x82421)),f319(f319(f143(x82421),x82424),x82422)),f153(x82421,x82423)))+P1(f319(f319(f321(f926(x82421)),x82422),f153(x82421,x82423)))
% 28.25/28.12 [8243]~P1(f319(f319(f321(f926(x82431)),f319(f319(f126(x82431),x82434),x82432)),f153(x82431,x82433)))+P1(f319(f319(f321(f926(x82431)),x82432),f153(x82431,x82433)))
% 28.25/28.12 [8244]~P1(f319(f319(f321(f926(x82441)),f319(f319(f126(x82441),x82442),x82444)),f153(x82441,x82443)))+P1(f319(f319(f321(f926(x82441)),x82442),f153(x82441,x82443)))
% 28.25/28.12 [8255]~P4(x82551)+P14(x82551,f319(f319(f146(x82552,x82551),x82553),f142(x82552,x82551,x82553,x82554)))
% 28.25/28.12 [8358]P26(x83584,x83583,x83581,x83582)+E(f319(x83581,f889(x83582,x83581,x83583,x83584)),f319(x83581,f890(x83582,x83581,x83583,x83584)))
% 28.25/28.12 [8467]~P26(x84672,x84671,x84674,x84673)+P26(x84671,x84672,f71(x84672,x84671,x84673,x84674),f319(f302(x84672,x84671,x84674),x84673))
% 28.25/28.12 [8608]P38(f931(x86082,x86084),f272(x86082,x86084,x86081,x86083))+P1(f319(x86081,f566(x86082,x86083,x86084,x86081)))
% 28.25/28.12 [8728]E(x87281,x87282)+~P1(f319(f319(f321(f931(x87283,x87283)),f319(f319(f244(x87283,x87283),x87281),x87282)),f255(x87283,x87284)))
% 28.25/28.12 [8789]~P1(f319(f55(f933(x87893,x87891)),f305(x87893,x87891,x87894,x87892)))+P1(f319(f55(x87891),x87892))
% 28.25/28.12 [8790]~P1(f319(f55(f933(x87901,x87903)),f305(x87901,x87903,x87902,x87904)))+P1(f319(f55(x87901),x87902))
% 28.25/28.12 [8791]~P1(f319(f55(f933(x87913,x87911)),f305(x87913,x87911,x87914,x87912)))+P1(f319(f55(x87911),x87912))
% 28.25/28.12 [8792]~P1(f319(f55(f933(x87921,x87923)),f305(x87921,x87923,x87922,x87924)))+P1(f319(f55(x87921),x87922))
% 28.25/28.12 [8801]~P26(x88011,x88012,x88013,x88014)+P27(x88011,x88012,x88013,x88014,f319(f302(x88011,x88012,x88013),x88014))
% 28.25/28.12 [8803]P12(x88031,x88032,x88033,x88034)+~E(f319(x88034,f858(x88032,x88034,x88033,x88031)),f319(x88034,f859(x88032,x88034,x88033,x88031)))
% 28.25/28.12 [8893]~P27(x88932,x88933,x88934,x88931,f180(f932(x88933,a923)))+E(x88931,f180(f932(x88932,a923)))
% 28.25/28.12 [8894]~P27(x88943,x88942,x88944,f180(f932(x88943,a923)),x88941)+E(x88941,f180(f932(x88942,a923)))
% 28.25/28.12 [8986]P38(f931(x89861,x89862),f272(x89861,x89862,x89863,x89864))+~P38(x89862,f319(x89864,f566(x89861,x89864,x89862,x89863)))
% 28.25/28.12 [9561]E(f319(f319(f151(x95611,x95612),f692(x95613,x95614,x95612,x95611)),f693(x95613,x95614,x95612,x95611)),x95614)+~P1(f319(f319(f321(f931(f926(x95611),f926(x95611))),f319(f319(f244(f926(x95611),f926(x95611)),x95612),x95614)),f149(x95611,x95613)))
% 28.25/28.12 [9566]~P1(f319(f319(f321(f931(f926(x95661),f926(x95661))),f319(f319(f244(f926(x95661),f926(x95661)),x95662),x95663)),f137(x95661,x95664)))+P1(f319(f319(f321(f931(f926(x95661),f926(x95661))),f319(f319(f244(f926(x95661),f926(x95661)),x95662),x95663)),f139(x95661,x95664)))
% 28.25/28.12 [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)),x96783),x96782)),f311(x96781,x96784)))
% 28.25/28.12 [9679]P1(f319(f55(x96791),x96792))+~P1(f319(f319(f321(f931(f932(x96791,a923),f932(x96791,a923))),f319(f319(f244(f932(x96791,a923),f932(x96791,a923)),x96792),x96793)),f311(x96791,x96794)))
% 28.25/28.12 [9682]~E(x96821,f180(f932(x96822,a923)))+~P1(f319(f319(f321(f931(f932(x96822,a923),f932(x96822,a923))),f319(f319(f244(f932(x96822,a923),f932(x96822,a923)),x96823),x96821)),f311(x96822,x96824)))
% 28.25/28.12 [10346]P12(x103461,x103462,x103463,x103464)+~P1(f319(f319(f249(x103461,x103461,a923),f319(f319(f7(x103461,f932(x103461,x103462),f932(x103461,a923)),f319(f319(f8(f932(x103462,a923),f932(f932(x103461,x103462),f932(x103461,a923)),x103461),f8(x103462,a923,x103461)),f319(f319(f8(x103462,f932(x103462,a923),x103461),a316),x103464))),x103464)),f601(x103464,x103463,x103462,x103461)))
% 28.25/28.12 [5169]~E(x51694,f105(x51691))+E(f319(f319(f146(x51691,x51692),x51693),x51694),f105(x51692))
% 28.25/28.12 [5170]~E(x51702,f105(x51701))+E(f319(f319(f151(x51701,x51702),x51703),x51704),f105(x51701))
% 28.25/28.12 [5171]~E(x51714,f105(x51711))+E(f319(f319(f146(x51711,x51712),x51713),x51714),f105(x51712))
% 28.25/28.12 [5409]E(x54091,f105(x54092))+~E(f319(f319(f146(x54092,x54093),x54094),x54091),f105(x54093))
% 28.25/28.12 [5410]E(x54101,f105(x54102))+~E(f319(f319(f146(x54102,x54103),x54104),x54101),f105(x54103))
% 28.25/28.12 [5411]E(x54111,f105(x54112))+~E(f319(f319(f151(x54112,x54111),x54113),x54114),f105(x54112))
% 28.25/28.12 [5447]E(x54471,x54472)+~E(f319(f319(f126(x54473),x54474),x54471),f319(f319(f126(x54473),x54474),x54472))
% 28.25/28.12 [5448]E(x54481,x54482)+~E(f319(f319(f126(x54483),x54481),x54484),f319(f319(f126(x54483),x54482),x54484))
% 28.25/28.12 [5594]P1(f319(x55943,x55942))+E(f162(x55941,x55942,f319(f128(x55941,x55943),x55944)),f319(f128(x55941,x55943),x55944))
% 28.25/28.12 [5596]~P1(f319(x55962,x55963))+P34(x55961,x55962,f319(f319(f143(x55961),x55963),x55964))
% 28.25/28.12 [5605]E(x56051,x56052)+~E(f131(a925,f319(f294(a925,x56051),x56053)),f319(f319(f143(a925),x56052),x56054))
% 28.25/28.12 [5653]~P28(x56532,x56533)+P28(x56531,f319(f319(f67(x56532,x56531),x56533),x56534))
% 28.25/28.12 [5654]~P38(x56542,x56543)+P38(x56541,f319(f319(f280(x56542,x56541),x56543),x56544))
% 28.25/28.12 [5655]~P39(x56552,x56553)+P39(x56551,f319(f319(f280(x56552,x56551),x56553),x56554))
% 28.25/28.12 [5656]~P56(x56562,x56563)+P56(x56561,f319(f319(f280(x56562,x56561),x56563),x56564))
% 28.25/28.12 [5784]~P34(x57841,x57842,x57844)+P34(x57841,x57842,f319(f319(f143(x57841),x57843),x57844))
% 28.25/28.12 [5785]~P34(x57851,x57852,x57854)+P34(x57851,x57852,f319(f319(f126(x57851),x57853),x57854))
% 28.25/28.12 [5786]~P34(x57861,x57862,x57863)+P34(x57861,x57862,f319(f319(f126(x57861),x57863),x57864))
% 28.25/28.12 [5873]~E(x58731,f105(x58732))+~E(f319(f319(f126(x58732),x58733),f319(f319(f143(x58732),x58734),f105(x58732))),x58731)
% 28.25/28.12 [5898]~P32(x58983,x58981,f319(f319(f143(x58983),x58982),x58984))+P1(f319(x58981,x58982))
% 28.25/28.12 [5908]E(f106(x59081,x59082),x59083)+~E(f319(f319(f126(x59081),x59083),f319(f319(f143(x59081),x59084),f105(x59081))),x59082)
% 28.25/28.12 [5909]E(f136(x59091,x59092),x59093)+~E(f319(f319(f126(x59091),x59094),f319(f319(f143(x59091),x59093),f105(x59091))),x59092)
% 28.25/28.12 [6019]~E(f131(a925,f319(f294(a925,x60191),x60192)),f319(f319(f143(a925),x60193),x60194))+P1(f319(f319(f227(a925),x60191),x60192))
% 28.25/28.12 [6028]P32(x60281,x60282,x60283)+~P32(x60281,x60282,f319(f319(f143(x60281),x60284),x60283))
% 28.25/28.12 [6029]P32(x60291,x60292,x60293)+~P32(x60291,x60292,f319(f319(f126(x60291),x60294),x60293))
% 28.25/28.12 [6030]P32(x60301,x60302,x60303)+~P32(x60301,x60302,f319(f319(f126(x60301),x60303),x60304))
% 28.25/28.12 [6116]~E(f319(f95(a925),x61164),f2(a925))+E(f319(f319(f156(x61161),f319(f319(f143(x61161),x61162),x61163)),f319(f95(a925),x61164)),x61162)
% 28.25/28.12 [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))
% 28.25/28.12 [6404]~P113(x64041)+E(f319(f319(f93(f932(x64041,a923)),f319(f294(x64041,x64042),x64043)),f319(f294(x64041,x64043),x64044)),f180(f932(x64041,a923)))
% 28.25/28.12 [6416]E(f319(f319(f156(x64161),f161(x64161,x64162,x64163)),x64164),x64163)+~P1(f319(f319(f227(a925),x64164),x64162))
% 28.25/28.12 [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))))
% 28.25/28.12 [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))))
% 28.25/28.12 [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))
% 28.25/28.12 [6605]~P21(x66052,x66053,x66054,x66051)+E(f319(x66051,f180(f932(x66052,a923))),f25(x66053))
% 28.25/28.12 [6631]~P113(x66311)+E(f319(f319(f93(f932(x66311,a923)),f298(x66311,x66312,x66313)),f319(f294(x66311,x66313),x66314)),f180(f932(x66311,a923)))
% 28.25/28.12 [6847]E(x68471,f180(f932(x68472,a923)))+~E(f305(x68473,x68472,x68474,x68471),f180(f932(f933(x68473,x68472),a923)))
% 28.25/28.12 [6848]E(x68481,f180(f932(x68482,a923)))+~E(f305(x68482,x68483,x68481,x68484),f180(f932(f933(x68482,x68483),a923)))
% 28.25/28.12 [6920]~P4(x69202)+E(f319(f181(f926(x69201)),f142(x69201,x69202,x69203,x69204)),f319(f181(f926(x69201)),x69204))
% 28.25/28.12 [6931]~P1(f319(f242(x69313,x69314,x69311),x69312))+P1(f319(f319(x69311,f565(x69312,x69311)),x69312))
% 28.25/28.12 [6957]E(f319(f95(a925),x69571),f2(a925))+E(f319(f319(f156(x69572),f319(f319(f143(x69572),x69573),x69574)),f319(f95(a925),x69571)),f319(f319(f156(x69572),x69574),f319(f319(f23(a925),f319(f95(a925),x69571)),f72(a925))))
% 28.25/28.12 [6973]~P1(f319(f55(x69732),x69734))+P1(f319(f55(x69731),f319(f302(x69732,x69731,x69733),x69734)))
% 28.25/28.12 [7205]~P26(x72052,x72051,x72053,x72054)+E(f319(f29(x72051),f319(f302(x72052,x72051,x72053),x72054)),f319(f29(x72052),x72054))
% 28.25/28.12 [7223]E(f319(f302(x72231,x72232,x72233),f319(f303(x72231,x72232,x72233),x72234)),x72234)+~E(f319(f302(x72231,x72232,x72233),f234(f932(x72231,a923))),f234(f932(x72232,a923)))
% 28.25/28.12 [7636]~P26(x76361,x76362,x76363,f234(f932(x76361,a923)))+E(f319(f303(x76361,x76362,x76363),f319(f302(x76361,x76362,x76363),x76364)),x76364)
% 28.25/28.12 [7916]E(x79161,x79162)+~P1(f319(f319(f321(x79163),x79161),f319(f164(x79163),f161(x79163,x79164,x79162))))
% 28.25/28.12 [7925]~E(x79251,f2(a925))+~P1(f319(f319(f321(x79252),x79253),f319(f164(x79252),f161(x79252,x79251,x79254))))
% 28.25/28.12 [7958]P1(f319(x79581,x79582))+~P1(f319(f319(f321(x79583),x79582),f319(f164(x79583),f169(x79583,x79581,x79584))))
% 28.25/28.12 [8068]~P1(f319(f319(f321(f926(x80681)),f319(f319(f143(x80681),x80682),x80684)),f153(x80681,x80683)))+P1(f319(f319(f321(x80681),x80682),x80683))
% 28.25/28.12 [8197]~P1(f319(f319(f321(x81971),x81972),f319(f164(x81971),f168(x81971,x81973,x81974))))+P1(f319(f319(f321(x81971),x81972),f319(f164(x81971),x81973)))
% 28.25/28.12 [8198]~P1(f319(f319(f321(x81981),x81982),f319(f164(x81981),f168(x81981,x81983,x81984))))+P1(f319(f319(f321(x81981),x81982),f319(f164(x81981),x81983)))
% 28.25/28.12 [8199]~P1(f319(f319(f321(x81991),x81992),f319(f164(x81991),f162(x81991,x81994,x81993))))+P1(f319(f319(f321(x81991),x81992),f319(f164(x81991),x81993)))
% 28.25/28.12 [8200]~P1(f319(f319(f321(x82001),x82002),f319(f164(x82001),f169(x82001,x82004,x82003))))+P1(f319(f319(f321(x82001),x82002),f319(f164(x82001),x82003)))
% 28.25/28.12 [8210]E(f319(f181(f926(x82101)),x82102),x82103)+~P1(f319(f319(f321(f926(x82101)),x82102),f319(f164(f926(x82101)),f49(x82101,x82103,x82104))))
% 28.25/28.12 [8307]P1(f319(x83073,x83072))+E(f319(f128(x83071,f319(f319(f8(a923,a923,x83071),a314),f319(a316,x83072))),f319(f128(x83071,x83073),x83074)),f319(f128(x83071,x83073),x83074))
% 28.25/28.12 [8418]E(f319(f319(f156(x84181),f169(x84181,x84182,x84183)),x84184),f319(f319(f156(x84181),x84183),x84184))+~P1(f319(f319(f227(a925),x84184),f319(f181(f926(x84181)),f169(x84181,x84182,x84183))))
% 28.25/28.12 [8505]~P79(x85051)+E(f319(f319(f6(a925,x85051),f319(f319(f8(a925,x85051,a925),x85052),a104)),f319(f294(a925,x85053),x85054)),f319(f319(f6(a925,x85051),x85052),f319(f294(a925,f319(a104,x85053)),f319(a104,x85054))))
% 28.25/28.12 [8515]~P79(x85151)+E(f319(f319(f6(a925,x85151),f319(f319(f8(a925,x85151,a925),x85152),a104)),f295(a925,x85153,x85154)),f319(f319(f6(a925,x85151),x85152),f295(a925,f319(a104,x85153),f319(a104,x85154))))
% 28.25/28.12 [8644]~P26(x86441,x86443,x86444,f234(f932(x86441,a923)))+P26(x86441,f932(x86442,x86443),f319(f319(f8(x86443,f932(x86442,x86443),x86441),f16(x86443,x86442)),x86444),f234(f932(x86441,a923)))
% 28.25/28.12 [8733]~P26(x87332,x87331,x87334,x87333)+E(f319(f302(x87331,x87332,f71(x87332,x87331,x87333,x87334)),f319(f302(x87332,x87331,x87334),x87333)),x87333)
% 28.25/28.12 [8793]~P1(f319(f319(f321(f931(x87931,x87931)),f319(f319(f244(x87931,x87931),x87932),x87934)),f255(x87931,x87933)))+P1(f319(f319(f321(x87931),x87932),x87933))
% 28.25/28.12 [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)
% 28.25/28.12 [8917]~P26(x89172,x89171,x89173,f234(f932(x89172,a923)))+E(f319(f302(x89171,x89172,f85(x89172,x89171,f234(f932(x89172,a923)),x89173)),f319(f302(x89172,x89171,x89173),x89174)),x89174)
% 28.25/28.12 [8992]~P27(x89921,x89922,x89923,x89924,f234(f932(x89922,a923)))+E(f319(f302(x89921,x89922,x89923),f234(f932(x89921,a923))),f234(f932(x89922,a923)))
% 28.25/28.12 [9026]~E(f319(f319(f6(x90261,a925),x90264),x90263),f319(a104,x90262))+P1(f319(f319(f321(x90261),f466(x90262,x90263,x90264,x90261)),x90263))
% 28.25/28.12 [9047]~E(f319(f319(f6(x90474,a925),x90471),x90473),f319(a104,x90472))+P1(f319(f319(f227(a925),f2(a925)),f319(x90471,f466(x90472,x90473,x90471,x90474))))
% 28.25/28.12 [9058]~P1(f319(f55(x90582),x90584))+P1(f319(f319(f226(a925),f319(f29(x90581),f319(f302(x90582,x90581,x90583),x90584))),f319(f29(x90582),x90584)))
% 28.25/28.12 [9059]E(f319(f319(f244(x90591,x90592),f661(x90593,x90594,x90592,x90591)),f662(x90593,x90594,x90592,x90591)),x90594)+~P1(f319(f319(f321(f931(x90591,x90592)),x90594),f319(f278(x90592,x90591),x90593)))
% 28.25/28.12 [9067]P26(x90671,x90672,x90673,x90674)+P1(f319(f319(f321(x90671),f889(x90674,x90673,x90672,x90671)),x90674))
% 28.25/28.12 [9068]P26(x90681,x90682,x90683,x90684)+P1(f319(f319(f321(x90681),f890(x90684,x90683,x90682,x90681)),x90684))
% 28.25/28.12 [9137]P12(x91371,x91372,x91373,x91374)+P1(f319(f319(f321(f931(x91371,x91371)),f601(x91374,x91373,x91372,x91371)),x91373))
% 28.25/28.12 [9195]P1(f319(x91951,x91952))+~P1(f319(x91951,f319(f319(f244(x91953,x91954),f533(x91954,x91953,x91951)),f534(x91954,x91953,x91951))))
% 28.25/28.12 [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)),f137(x92121,x92124)))
% 28.25/28.12 [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)),f149(x92131,x92134)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [9216]E(f319(f181(f926(x92161)),x92162),f319(f181(f926(x92161)),x92163))+~P1(f319(f319(f321(f931(f926(x92161),f926(x92161))),f319(f319(f244(f926(x92161),f926(x92161)),x92162),x92163)),f150(x92161,x92164)))
% 28.25/28.12 [9287]P1(f319(f319(f226(a925),f147(x92871,x92872,x92873)),f147(x92871,x92874,x92873)))+P1(f319(f319(f321(x92871),f690(x92874,x92872,x92873,x92871)),f319(f164(x92871),x92873)))
% 28.25/28.12 [9290]E(f319(f181(f926(x92901)),x92902),f319(f181(f926(x92901)),x92903))+~P1(f319(f319(f321(f931(f926(x92901),f926(x92901))),f319(f319(f244(f926(x92901),f926(x92901)),x92902),x92903)),f299(f926(x92901),f149(x92901,x92904))))
% 28.25/28.12 [9531]~P26(x95311,x95312,x95313,x95314)+~P1(f319(f319(f227(a925),f319(f29(x95312),f319(f302(x95311,x95312,x95313),x95314))),f319(f29(x95311),x95314)))
% 28.25/28.12 [9579]~P1(f319(f319(f321(f931(f926(x95791),f926(x95791))),f319(f319(f244(f926(x95791),f926(x95791)),x95792),x95793)),f149(x95791,x95794)))+P1(f319(f319(f321(f931(f926(x95791),f926(x95791))),f319(f319(f244(f926(x95791),f926(x95791)),x95792),x95793)),f150(x95791,f299(x95791,x95794))))
% 28.25/28.12 [9583]~P1(f319(f319(f321(f931(f926(x95831),f926(x95831))),f319(f319(f244(f926(x95831),f926(x95831)),x95832),x95833)),f150(x95831,x95834)))+P1(f319(f319(f321(f931(f926(x95831),f926(x95831))),f319(f319(f244(f926(x95831),f926(x95831)),x95832),x95833)),f299(f926(x95831),f149(x95831,x95834))))
% 28.25/28.12 [9599]P1(f319(f319(f321(f931(x95991,x95991)),f319(f319(f244(x95991,x95991),x95992),x95993)),f299(x95991,x95994)))+~P1(f319(f319(f321(f931(x95991,x95991)),f319(f319(f244(x95991,x95991),x95992),x95993)),f319(f319(f281(x95991,x95991,x95991),x95994),f299(x95991,x95994))))
% 28.25/28.12 [9790]E(f319(f319(f126(x97901),f705(x97902,x97903,x97904,x97901)),f319(f319(f143(x97901),f706(x97902,x97903,x97904,x97901)),f708(x97902,x97903,x97904,x97901))),x97904)+~P1(f319(f319(f321(f931(f926(x97901),f926(x97901))),f319(f319(f244(f926(x97901),f926(x97901)),x97904),x97903)),f149(x97901,x97902)))
% 28.25/28.12 [9791]E(f319(f319(f126(x97911),f705(x97912,x97913,x97914,x97911)),f319(f319(f143(x97911),f707(x97912,x97913,x97914,x97911)),f708(x97912,x97913,x97914,x97911))),x97913)+~P1(f319(f319(f321(f931(f926(x97911),f926(x97911))),f319(f319(f244(f926(x97911),f926(x97911)),x97914),x97913)),f149(x97911,x97912)))
% 28.25/28.12 [9870]P1(f319(f319(f321(f931(x98701,x98701)),f319(f319(f244(x98701,x98701),x98702),f640(x98703,x98704,x98702,x98701))),f299(x98701,x98703)))+~P1(f319(f319(f321(f931(x98701,x98701)),f319(f319(f244(x98701,x98701),x98702),x98704)),f319(f319(f281(x98701,x98701,x98701),x98703),f299(x98701,x98703))))
% 28.25/28.12 [9942]P1(f319(f319(f226(a925),f147(x99421,x99422,x99423)),f147(x99421,x99424,x99423)))+~P1(f319(f319(f227(a925),f319(x99422,f690(x99424,x99422,x99423,x99421))),f319(x99424,f690(x99424,x99422,x99423,x99421))))
% 28.25/28.12 [10024]P1(f319(f319(f321(f931(x100241,x100241)),f319(f319(f244(x100241,x100241),f649(x100242,x100243,x100244,x100241)),x100243)),f299(x100241,x100242)))+~P1(f319(f319(f321(f931(x100241,x100241)),f319(f319(f244(x100241,x100241),x100244),x100243)),f319(f319(f281(x100241,x100241,x100241),x100242),f299(x100241,x100242))))
% 28.25/28.12 [5429]~E(x54292,x54293)+E(f162(x54291,x54292,f319(f319(f143(x54291),x54293),x54294)),x54294)
% 28.25/28.12 [5441]~E(x54412,f2(a925))+E(f319(f319(f167(x54411),x54412),f319(f319(f143(x54411),x54413),x54414)),f105(x54411))
% 28.25/28.12 [5550]P1(f319(x55502,x55503))+E(f169(x55501,x55502,f319(f319(f143(x55501),x55503),x55504)),f105(x55501))
% 28.25/28.12 [5616]~P67(x56162)+E(f319(f319(f73(f932(x56161,x56162)),x56163),x56164),f319(f73(x56162),f319(x56163,x56164)))
% 28.25/28.12 [5617]~P67(x56172)+E(f319(f319(f73(f932(x56171,x56172)),x56173),x56174),f319(f73(x56172),f319(x56173,x56174)))
% 28.25/28.12 [5630]~E(x56302,f2(a925))+E(f319(f319(f130(x56301),x56302),f319(f319(f143(x56301),x56303),x56304)),f319(f319(f143(x56301),x56303),x56304))
% 28.25/28.12 [5631]P1(f319(x56312,x56313))+E(f319(f128(x56311,x56312),f319(f319(f143(x56311),x56313),x56314)),f319(f128(x56311,x56312),x56314))
% 28.25/28.12 [5767]~E(x57672,x57674)+P1(f319(f319(f319(f301(x57671),x57672),x57673),x57674))
% 28.25/28.12 [5775]E(x57751,f105(x57752))+E(f136(x57753,f319(f319(f146(x57752,x57753),x57754),x57751)),f319(x57754,f136(x57752,x57751)))
% 28.25/28.12 [5789]~E(x57891,f57(x57892,x57894))+E(f319(x57891,f319(f319(f301(x57892),x57893),f180(f932(x57892,a923)))),x57893)
% 28.25/28.12 [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))
% 28.25/28.12 [5824]E(x58241,f105(x58242))+E(f319(f133(x58243),f319(f319(f146(x58242,x58243),x58244),x58241)),f319(x58244,f319(f133(x58242),x58241)))
% 28.25/28.12 [5928]~P1(f319(x59283,x59284))+P1(f319(f319(f319(f301(x59281),x59282),x59283),x59284))
% 28.25/28.12 [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))
% 28.25/28.12 [6048]~P20(x60482,x60484,x60481)+E(f319(x60481,f319(f319(f301(x60482),x60483),f180(f932(x60482,a923)))),x60483)
% 28.25/28.12 [6074]~E(x60742,x60743)+P1(f319(f319(f321(x60741),x60742),f319(f319(f301(x60741),x60743),x60744)))
% 28.25/28.12 [6075]~E(x60752,x60753)+P1(f319(f319(f321(x60751),x60752),f319(f319(f301(x60751),x60753),x60754)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [6098]E(x60981,x60982)+E(f162(x60983,x60981,f319(f319(f143(x60983),x60982),x60984)),f319(f319(f143(x60983),x60982),f162(x60983,x60981,x60984)))
% 28.25/28.12 [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)))
% 28.25/28.12 [6207]~E(x62074,f180(f932(x62071,a923)))+E(f319(f302(x62071,x62072,f319(f16(x62072,x62071),x62073)),x62074),f180(f932(x62072,a923)))
% 28.25/28.12 [6253]~P1(f319(x62532,x62533))+E(f169(x62531,x62532,f319(f319(f143(x62531),x62533),x62534)),f319(f319(f143(x62531),x62533),f169(x62531,x62532,x62534)))
% 28.25/28.12 [6315]E(x63151,f180(f932(x63152,a923)))+E(f319(f319(f33(x63152,f932(x63153,a923)),x63151),f319(f16(f932(x63153,a923),x63152),x63154)),x63154)
% 28.25/28.12 [6316]E(x63161,f180(f932(x63162,a923)))+E(f319(f319(f34(x63162,f932(x63163,a923)),x63161),f319(f16(f932(x63163,a923),x63162),x63164)),x63164)
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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))
% 28.25/28.12 [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))))
% 28.25/28.12 [6401]E(f319(f303(x64011,x64012,f319(f16(x64012,x64011),x64013)),x64014),f180(f932(x64011,a923)))+P1(f319(f319(f321(x64012),x64013),x64014))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [6641]E(f319(f303(x66411,x66412,f319(f16(x66412,x66411),x66413)),x66414),f234(f932(x66411,a923)))+~P1(f319(f319(f321(x66412),x66413),x66414))
% 28.25/28.12 [6663]~P1(f319(f319(f321(x66631),x66632),x66634))+P1(f319(f319(f321(x66631),x66632),f319(f319(f301(x66631),x66633),x66634)))
% 28.25/28.12 [6664]~P1(f319(f319(f321(x66641),x66642),x66644))+P1(f319(f319(f321(x66641),x66642),f319(f319(f301(x66641),x66643),x66644)))
% 28.25/28.12 [6665]~P1(f319(f319(f321(x66651),x66652),x66654))+P1(f319(f319(f321(x66651),x66652),f319(f319(f301(x66651),x66653),x66654)))
% 28.25/28.12 [6670]P1(f319(x66701,x66702))+~P1(f319(f152(x66703,x66701),f319(f319(f143(x66703),x66702),x66704)))
% 28.25/28.12 [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))
% 28.25/28.12 [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)))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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))
% 28.25/28.12 [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)
% 28.25/28.12 [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)
% 28.25/28.12 [6819]P1(f319(f152(x68191,x68192),x68193))+~P1(f319(f152(x68191,x68192),f319(f319(f143(x68191),x68194),x68193)))
% 28.25/28.12 [6820]P1(f319(f152(x68201,x68202),x68203))+~P1(f319(f152(x68201,x68202),f319(f319(f126(x68201),x68204),x68203)))
% 28.25/28.12 [6821]P1(f319(f152(x68211,x68212),x68213))+~P1(f319(f152(x68211,x68212),f319(f319(f126(x68211),x68213),x68214)))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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)))
% 28.25/28.12 [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))
% 28.25/28.12 [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)))
% 28.25/28.12 [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))
% 28.25/28.12 [6944]~P1(f319(f129(x69442),x69444))+P1(f319(f129(f931(x69441,x69442)),f319(f319(f173(x69441,x69442),x69443),x69444)))
% 28.25/28.12 [6945]~P1(f319(f129(x69451),x69453))+P1(f319(f129(f931(x69451,x69452)),f319(f319(f173(x69451,x69452),x69453),x69454)))
% 28.25/28.12 [7208]E(f319(f319(f30(a925),x72081),x72082),x72083)+~P1(f319(f42(x72081,x72082),f319(f319(f244(a925,a925),x72083),x72084)))
% 28.25/28.12 [7231]E(f39(a925,x72311,x72312),x72313)+~P1(f319(f42(x72311,x72312),f319(f319(f244(a925,a925),x72314),x72313)))
% 28.25/28.12 [7234]P1(f319(f129(x72341),x72342))+~P1(f319(f129(x72343),f319(f319(f146(x72341,x72343),x72344),x72342)))
% 28.25/28.12 [7318]E(f162(x73181,x73182,f319(f319(f126(x73181),x73183),x73184)),f319(f319(f126(x73181),f162(x73181,x73182,x73183)),x73184))+~P1(f319(f319(f321(x73181),x73182),f319(f164(x73181),x73183)))
% 28.25/28.12 [7384]E(f319(f95(a925),x73841),f2(a925))+E(f319(f319(f130(x73842),f319(f95(a925),x73841)),f319(f319(f143(x73842),x73843),x73844)),f319(f319(f130(x73842),f319(f319(f23(a925),f319(f95(a925),x73841)),f72(a925))),x73844))
% 28.25/28.12 [7411]~P66(x74111)+E(f39(x74111,f319(f319(f23(x74111),f39(x74111,x74112,x74113)),x74114),x74113),f39(x74111,f319(f319(f23(x74111),x74112),x74114),x74113))
% 28.25/28.12 [7412]~P65(x74121)+E(f39(x74121,f319(f319(f75(x74121),f39(x74121,x74122,x74123)),x74124),x74123),f39(x74121,f319(f319(f75(x74121),x74122),x74124),x74123))
% 28.25/28.12 [7413]~P65(x74131)+E(f39(x74131,f319(f319(f74(x74131),f39(x74131,x74132,x74133)),x74134),x74133),f39(x74131,f319(f319(f74(x74131),x74132),x74134),x74133))
% 28.25/28.12 [7414]~P65(x74141)+E(f39(x74141,f319(f319(f75(x74141),f39(x74141,x74142,x74143)),x74144),x74143),f39(x74141,f319(f319(f75(x74141),x74142),x74144),x74143))
% 28.25/28.12 [7415]~P65(x74151)+E(f39(x74151,f319(f319(f74(x74151),f39(x74151,x74152,x74153)),x74154),x74153),f39(x74151,f319(f319(f74(x74151),x74152),x74154),x74153))
% 28.25/28.12 [7607]~E(x76071,f319(f319(f143(x76072),x76073),x76074))+~P1(f319(f319(f226(a925),f319(f181(f926(x76072)),x76071)),f319(f181(f926(x76072)),x76074)))
% 28.25/28.12 [7807]P26(x78071,x78072,x78073,f319(f164(x78071),x78074))+~P1(f319(f129(x78072),f319(f319(f146(x78071,x78072),x78073),x78074)))
% 28.25/28.12 [7882]~P1(f319(f319(f226(f932(x78821,a923)),x78822),x78824))+P1(f319(f319(f226(f932(x78821,a923)),x78822),f319(f319(f301(x78821),x78823),x78824)))
% 28.25/28.12 [7917]~P66(x79171)+E(f39(x79171,f319(f319(f23(x79171),f39(x79171,x79172,x79173)),f39(x79171,x79174,x79173)),x79173),f39(x79171,f319(f319(f23(x79171),x79172),x79174),x79173))
% 28.25/28.12 [7918]~P65(x79181)+E(f39(x79181,f319(f319(f75(x79181),f39(x79181,x79182,x79183)),f39(x79181,x79184,x79183)),x79183),f39(x79181,f319(f319(f75(x79181),x79182),x79184),x79183))
% 28.25/28.12 [7919]~P65(x79191)+E(f39(x79191,f319(f319(f74(x79191),f39(x79191,x79192,x79193)),f39(x79191,x79194,x79193)),x79193),f39(x79191,f319(f319(f74(x79191),x79192),x79194),x79193))
% 28.25/28.12 [8021]~E(f319(x80214,f783(x80214,x80213,x80211,x80212)),f234(f932(x80212,a923)))+E(f319(f319(f34(x80211,f932(x80212,a923)),x80213),x80214),f234(f932(x80212,a923)))
% 28.25/28.12 [8022]~E(f319(x80224,f881(x80224,x80223,x80221,x80222)),f180(f932(x80222,a923)))+E(f319(f319(f33(x80221,f932(x80222,a923)),x80223),x80224),f180(f932(x80222,a923)))
% 28.25/28.12 [8023]~E(f319(x80234,f877(x80234,x80233,x80232,x80231)),f180(f932(x80232,a923)))+E(f319(f319(f33(x80231,f932(x80232,a923)),x80233),x80234),f180(f932(x80232,a923)))
% 28.25/28.12 [8024]~E(f319(x80244,f790(x80244,x80243,x80242,x80241)),f234(f932(x80242,a923)))+E(f319(f319(f34(x80241,f932(x80242,a923)),x80243),x80244),f234(f932(x80242,a923)))
% 28.25/28.12 [8419]P1(f319(x84191,x84192))+~P1(f319(f319(f321(x84193),x84192),f319(f319(f93(f932(x84193,a923)),x84194),f319(f254(x84193),x84191))))
% 28.25/28.12 [8456]~P1(f319(f319(f226(f932(x84561,a923)),x84563),x84564))+P1(f319(f319(f226(f932(x84561,a923)),f319(f319(f301(x84561),x84562),x84563)),f319(f319(f301(x84561),x84562),x84564)))
% 28.25/28.12 [8466]E(f319(x84661,f895(x84661,x84662,x84663)),x84663)+~P1(f319(f319(f321(x84664),x84663),f319(f302(x84662,x84664,x84661),f234(f932(x84662,a923)))))
% 28.25/28.12 [8501]P1(f319(f319(f321(x85011),x85012),x85013))+~P1(f319(f319(f321(x85011),x85012),f319(f319(f93(f932(x85011,a923)),x85013),f319(f254(x85011),x85014))))
% 28.25/28.12 [8637]P1(f319(x86372,x86373))+E(f319(f319(f130(x86371),f319(f181(f926(x86371)),f169(x86371,x86372,f319(f319(f143(x86371),x86373),x86374)))),f319(f319(f143(x86371),x86373),x86374)),f319(f319(f143(x86371),x86373),x86374))
% 28.25/28.12 [8747]~P1(f319(f319(f227(a925),f319(x87474,x87472)),f319(x87474,x87473)))+P1(f319(f319(f321(f931(x87471,x87471)),f319(f319(f244(x87471,x87471),x87472),x87473)),f319(f319(f280(a925,x87471),a232),x87474)))
% 28.25/28.12 [8844]~P1(f319(x88442,f761(x88444,x88442,x88443,x88441)))+E(f169(x88441,x88442,f319(f319(f126(x88441),x88443),x88444)),f319(f319(f126(x88441),x88443),f169(x88441,x88442,x88444)))
% 28.25/28.12 [8921]P26(f926(x89211),f926(x89212),f319(f146(x89211,x89212),x89213),x89214)+~P26(x89211,x89212,x89213,f31(f932(x89211,a923),f319(f302(f926(x89211),f932(x89211,a923),f164(x89211)),x89214)))
% 28.25/28.12 [8996]~P1(f319(x89962,x89963))+E(f319(f319(f130(x89961),f319(f181(f926(x89961)),f169(x89961,x89962,f319(f319(f143(x89961),x89963),x89964)))),f319(f319(f143(x89961),x89963),x89964)),f319(f319(f130(x89961),f319(f181(f926(x89961)),f169(x89961,x89962,x89964))),x89964))
% 28.25/28.12 [9038]~E(x90382,x90383)+E(f319(f128(x90381,f319(f319(f8(a923,a923,x90381),a314),f319(a316,x90382))),f319(f319(f143(x90381),x90383),x90384)),f319(f128(x90381,f319(f319(f8(a923,a923,x90381),a314),f319(a316,x90382))),x90384))
% 28.25/28.12 [9048]E(f319(f319(f34(x90481,f932(x90482,a923)),x90483),x90484),f234(f932(x90482,a923)))+P1(f319(f319(f321(x90481),f783(x90484,x90483,x90481,x90482)),x90483))
% 28.25/28.12 [9049]E(f319(f319(f33(x90491,f932(x90492,a923)),x90493),x90494),f180(f932(x90492,a923)))+P1(f319(f319(f321(x90491),f881(x90494,x90493,x90491,x90492)),x90493))
% 28.25/28.12 [9050]E(f319(f319(f33(x90501,f932(x90502,a923)),x90503),x90504),f180(f932(x90502,a923)))+P1(f319(f319(f321(x90501),f877(x90504,x90503,x90502,x90501)),x90503))
% 28.25/28.12 [9051]E(f319(f319(f34(x90511,f932(x90512,a923)),x90513),x90514),f234(f932(x90512,a923)))+P1(f319(f319(f321(x90511),f790(x90514,x90513,x90512,x90511)),x90513))
% 28.25/28.12 [9089]P1(f319(f319(f227(a925),f319(x90891,x90892)),f319(x90891,x90893)))+~P1(f319(f319(f321(f931(x90894,x90894)),f319(f319(f244(x90894,x90894),x90892),x90893)),f319(f319(f280(a925,x90894),a232),x90891)))
% 28.25/28.12 [9116]E(f169(x91161,x91162,f319(f319(f126(x91161),x91163),x91164)),f319(f319(f126(x91161),x91163),f169(x91161,x91162,x91164)))+P1(f319(f319(f321(x91161),f761(x91164,x91162,x91163,x91161)),f319(f164(x91161),x91163)))
% 28.25/28.12 [9171]~P27(x91711,x91712,x91713,f234(f932(x91711,a923)),f234(f932(x91712,a923)))+E(f319(f302(x91711,x91712,x91713),f319(f73(f932(x91711,a923)),x91714)),f319(f73(f932(x91712,a923)),f319(f302(x91711,x91712,x91713),x91714)))
% 28.25/28.12 [9276]P1(f319(f319(f321(x92761),f522(x92762,x92763,x92764,x92761)),x92763))+~P1(f319(f319(f321(f932(x92761,a923)),x92764),f319(f319(f54(x92761),x92763),x92762)))
% 28.25/28.12 [9279]E(x92791,x92792)+~P1(f319(f319(f321(f931(x92793,x92793)),f319(f319(f244(x92793,x92793),x92791),x92792)),f319(f319(f175(f931(x92793,x92793),a923),f2(a925)),x92794)))
% 28.25/28.12 [9361]E(f319(f277(x93611,x93611,x93612),f319(f319(f301(x93611),f522(x93612,x93613,x93614,x93611)),f180(f932(x93611,a923)))),x93614)+~P1(f319(f319(f321(f932(x93611,a923)),x93614),f319(f319(f54(x93611),x93613),x93612)))
% 28.25/28.12 [9366]~P1(f319(f319(f321(f931(x93661,x93661)),f319(f319(f244(x93661,x93661),x93663),x93662)),f299(x93661,x93664)))+P1(f319(f319(f321(f931(x93661,x93661)),f319(f319(f244(x93661,x93661),x93662),x93663)),f299(x93661,f319(f278(x93661,x93661),x93664))))
% 28.25/28.12 [9379]~P65(x93791)+E(f319(f319(f74(x93791),f319(f319(f74(x93791),f319(f319(f75(x93791),x93792),f319(f319(f30(x93791),x93793),x93792))),f39(x93791,x93793,x93792))),x93794),f319(f319(f74(x93791),x93793),x93794))
% 28.25/28.12 [9392]~P1(f319(f319(f321(x93921),x93923),x93924))+P1(f319(f319(f321(f932(x93921,a923)),f319(f277(x93921,x93921,x93922),f319(f319(f301(x93921),x93923),f180(f932(x93921,a923))))),f319(f319(f54(x93921),x93924),x93922)))
% 28.25/28.12 [9404]P1(f319(f319(f321(f931(x94041,x94041)),f319(f319(f244(x94041,x94041),x94042),x94043)),f299(x94041,x94044)))+~P1(f319(f319(f321(f931(x94041,x94041)),f319(f319(f244(x94041,x94041),x94043),x94042)),f299(x94041,f319(f278(x94041,x94041),x94044))))
% 28.25/28.12 [9490]E(f319(f319(f151(x94901,f319(f160(x94901),x94902)),f319(f319(f23(a925),f319(f319(f23(a925),f319(f181(f926(x94901)),x94902)),x94903)),f72(a925))),x94904),f319(f160(x94901),f319(f319(f151(x94901,x94902),x94903),x94904)))+~P1(f319(f319(f227(a925),x94903),f319(f181(f926(x94901)),x94902)))
% 28.25/28.12 [9494]~P1(f319(x94942,f753(x94944,x94942,x94943,x94941)))+E(f319(f319(f130(x94941),f319(f181(f926(x94941)),f169(x94941,x94942,f319(f319(f126(x94941),x94943),x94944)))),f319(f319(f126(x94941),x94943),x94944)),f319(f319(f130(x94941),f319(f181(f926(x94941)),f169(x94941,x94942,x94944))),x94944))
% 28.25/28.12 [9539]~P26(x95392,x95391,x95393,f234(f932(x95392,a923)))+P1(f319(f319(f226(f932(x95391,a923)),f319(f302(x95392,x95391,x95393),f319(f73(f932(x95392,a923)),x95394))),f319(f73(f932(x95391,a923)),f319(f302(x95392,x95391,x95393),x95394))))
% 28.25/28.12 [9552]~P6(x95521)+E(f319(f134(x95521,x95522,f319(f7(x95522,x95521,x95521),f319(f319(f8(x95521,f932(x95521,x95521),x95522),f102(x95521)),x95523)),f180(x95521)),x95524),f319(f319(f33(x95522,x95521),f319(f164(x95522),x95524)),x95523))
% 28.25/28.12 [9553]~P6(x95531)+E(f319(f134(x95531,x95532,f319(f7(x95532,x95531,x95531),f319(f319(f8(x95531,f932(x95531,x95531),x95532),f93(x95531)),x95533)),f234(x95531)),x95534),f319(f319(f34(x95532,x95531),f319(f164(x95532),x95534)),x95533))
% 28.25/28.12 [9563]E(f319(f319(f130(x95631),f319(f181(f926(x95631)),f169(x95631,x95632,f319(f319(f126(x95631),x95633),x95634)))),f319(f319(f126(x95631),x95633),x95634)),f319(f319(f130(x95631),f319(f181(f926(x95631)),f169(x95631,x95632,x95634))),x95634))+P1(f319(f319(f321(x95631),f753(x95634,x95632,x95633,x95631)),f319(f164(x95631),x95633)))
% 28.25/28.12 [9633]~P1(f319(f319(f321(f931(f926(x96334),f926(x96334))),f319(f319(f244(f926(x96334),f926(x96334)),x96333),x96332)),f149(x96334,x96331)))+P1(f319(f319(f227(a925),f692(x96331,x96332,x96333,x96334)),f319(f181(f926(x96334)),x96333)))
% 28.25/28.12 [9634]~P65(x96341)+E(f319(f319(f74(x96341),f319(f319(f74(x96341),f319(f319(f75(x96341),f319(f319(f30(x96341),x96342),x96343)),x96343)),f39(x96341,x96342,x96343))),x96344),f319(f319(f74(x96341),x96342),x96344))
% 28.25/28.12 [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))))
% 28.25/28.12 [9665]P1(f319(f319(f321(f931(f926(x96651),f926(x96651))),f319(f319(f244(f926(x96651),f926(x96651)),x96652),x96653)),f319(f278(f926(x96651),f926(x96651)),f149(x96651,x96654))))+~P1(f319(f319(f321(f931(f926(x96651),f926(x96651))),f319(f319(f244(f926(x96651),f926(x96651)),x96652),x96653)),f149(x96651,f319(f278(x96651,x96651),x96654))))
% 28.25/28.12 [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),f573(x97054,x97052,x97053,x97051))),x97054))
% 28.25/28.12 [9706]~P1(f319(f319(f321(x97061),x97063),f319(f256(x97061,x97062),x97064)))+P1(f319(f319(f321(f931(x97061,x97062)),f319(f319(f244(x97061,x97062),x97063),f575(x97064,x97062,x97063,x97061))),x97064))
% 28.25/28.12 [9865]~P1(f319(f319(f321(f931(x98651,x98651)),f319(f319(f244(x98651,x98651),x98652),x98654)),f319(f319(f281(x98651,x98651,x98651),x98653),f299(x98651,x98653))))+P1(f319(f319(f321(f931(x98651,x98651)),f319(f319(f244(x98651,x98651),x98652),f649(x98653,x98654,x98652,x98651))),x98653))
% 28.25/28.12 [10039]P12(x100391,x100392,x100393,x100394)+P1(f319(f319(f321(f931(x100391,x100391)),f319(f319(f244(x100391,x100391),f859(x100392,x100394,x100393,x100391)),f858(x100392,x100394,x100393,x100391))),x100393))
% 28.25/28.12 [10047]~P1(f319(f319(f321(f931(x100472,x100471)),x100474),f319(f278(x100471,x100472),x100473)))+P1(f319(f319(f321(f931(x100471,x100472)),f319(f319(f244(x100471,x100472),f662(x100473,x100474,x100471,x100472)),f661(x100473,x100474,x100471,x100472))),x100473))
% 28.25/28.12 [10072]~P1(f319(f319(f321(f931(f926(x100721),f926(x100721))),f319(f319(f244(f926(x100721),f926(x100721)),x100724),x100723)),f149(x100721,x100722)))+P1(f319(f319(f321(f931(x100721,x100721)),f319(f319(f244(x100721,x100721),f706(x100722,x100723,x100724,x100721)),f707(x100722,x100723,x100724,x100721))),x100722))
% 28.25/28.12 [10165]~P1(f319(f319(f321(f931(f926(x101651),f926(x101651))),f319(f319(f244(f926(x101651),f926(x101651)),x101652),x101654)),f149(x101651,x101653)))+P1(f319(f319(f321(f931(x101651,x101651)),f319(f319(f244(x101651,x101651),f319(f319(f156(x101651),x101652),f692(x101653,x101654,x101652,x101651))),f693(x101653,x101654,x101652,x101651))),x101653))
% 28.25/28.12 [10185]~P1(f319(f55(x101852),x101854))+E(f319(f319(f319(f59(f932(x101851,a923),x101852,f102(f932(x101851,a923))),f319(f319(f7(x101852,f932(x101851,a923),f932(x101851,a923)),f319(f319(f8(x101851,f932(f932(x101851,a923),f932(x101851,a923)),x101852),f301(x101851)),x101853)),f180(f932(x101851,a923)))),f180(f932(x101851,a923))),x101854),f319(f302(x101852,x101851,x101853),x101854))
% 28.25/28.12 [10300]~P26(x103001,x103002,x103003,f234(f932(x103001,a923)))+P1(f319(f319(f226(f932(x103001,a923)),f319(f303(x103001,x103002,x103003),f319(f319(f301(x103002),x103004),f180(f932(x103002,a923))))),f319(f319(f301(x103001),f79(x103001,f319(f319(f7(x103001,x103002,a923),f319(f319(f8(x103002,f932(x103002,a923),x103001),a316),x103003)),x103004))),f180(f932(x103001,a923)))))
% 28.25/28.12 [5835]~E(f319(f319(f126(x58351),x58352),x58354),x58353)+E(f319(f319(f167(x58351),f319(f181(f926(x58351)),x58352)),x58353),x58352)
% 28.25/28.12 [5836]~E(f319(f319(f126(x58362),x58363),x58361),x58364)+E(x58361,f319(f319(f130(x58362),f319(f181(f926(x58362)),x58363)),x58364))
% 28.25/28.12 [5847]~E(x58474,f2(a925))+E(f319(f319(f156(x58471),f319(f319(f143(x58471),x58472),x58473)),x58474),x58472)
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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))))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [6451]~P65(x64511)+E(f39(x64511,f319(f319(f74(x64511),x64512),f319(f319(f75(x64511),x64513),x64514)),x64514),f39(x64511,x64512,x64514))
% 28.25/28.12 [6452]~P65(x64521)+E(f39(x64521,f319(f319(f74(x64521),x64522),f319(f319(f75(x64521),x64523),x64524)),x64523),f39(x64521,x64522,x64523))
% 28.25/28.12 [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))
% 28.25/28.12 [6767]~E(x67672,x67674)+P1(f319(f319(f164(x67671),f319(f319(f143(x67671),x67672),x67673)),x67674))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [7005]E(f319(f319(f93(f932(x70051,a923)),f319(f319(f301(x70051),x70052),x70053)),x70054),f319(f319(f93(f932(x70051,a923)),x70053),x70054))+P1(f319(f319(f321(x70051),x70052),x70054))
% 28.25/28.12 [7076]~P106(x70761)+E(f319(f319(f93(x70761),f319(f319(f102(x70761),x70762),x70763)),f319(f319(f102(x70761),x70764),x70763)),f319(f319(f102(x70761),f319(f319(f93(x70761),x70762),x70764)),x70763))
% 28.25/28.12 [7077]~P106(x70771)+E(f319(f319(f102(x70771),f319(f319(f93(x70771),x70772),x70773)),f319(f319(f93(x70771),x70774),x70773)),f319(f319(f93(x70771),f319(f319(f102(x70771),x70772),x70774)),x70773))
% 28.25/28.12 [7078]~P68(x70781)+E(f319(f319(f224(x70781),f319(f319(f23(x70781),x70782),x70783)),f319(f319(f23(x70781),x70784),x70783)),f319(f319(f23(x70781),f319(f319(f224(x70781),x70782),x70784)),x70783))
% 28.25/28.12 [7079]~P68(x70791)+E(f319(f319(f225(x70791),f319(f319(f23(x70791),x70792),x70793)),f319(f319(f23(x70791),x70794),x70793)),f319(f319(f23(x70791),f319(f319(f225(x70791),x70792),x70794)),x70793))
% 28.25/28.12 [7080]~P121(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))
% 28.25/28.12 [7081]~P122(x70811)+E(f319(f319(f74(x70811),f319(f319(f75(x70811),x70812),x70813)),f319(f319(f75(x70811),x70814),x70813)),f319(f319(f75(x70811),f319(f319(f74(x70811),x70812),x70814)),x70813))
% 28.25/28.12 [7082]~P90(x70821)+E(f319(f319(f224(x70821),f319(f319(f74(x70821),x70822),x70823)),f319(f319(f74(x70821),x70824),x70823)),f319(f319(f74(x70821),f319(f319(f224(x70821),x70822),x70824)),x70823))
% 28.25/28.12 [7083]~P90(x70831)+E(f319(f319(f225(x70831),f319(f319(f74(x70831),x70832),x70833)),f319(f319(f74(x70831),x70834),x70833)),f319(f319(f74(x70831),f319(f319(f225(x70831),x70832),x70834)),x70833))
% 28.25/28.12 [7084]~P4(x70841)+E(f319(f319(f225(x70841),f319(f319(f224(x70841),x70842),x70843)),f319(f319(f224(x70841),x70844),x70843)),f319(f319(f224(x70841),f319(f319(f225(x70841),x70842),x70844)),x70843))
% 28.25/28.12 [7085]~P4(x70851)+E(f319(f319(f224(x70851),f319(f319(f225(x70851),x70852),x70853)),f319(f319(f225(x70851),x70854),x70853)),f319(f319(f225(x70851),f319(f319(f224(x70851),x70852),x70854)),x70853))
% 28.25/28.12 [7086]~P78(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))
% 28.25/28.12 [7087]~P121(x70871)+E(f319(f319(f75(x70871),f319(f319(f236(x70871),x70872),x70873)),f319(f319(f236(x70871),x70874),x70873)),f319(f319(f236(x70871),f319(f319(f75(x70871),x70872),x70874)),x70873))
% 28.25/28.12 [7088]~P72(x70881)+E(f319(f319(f283(x70881),f319(f319(f236(x70881),x70882),x70883)),f319(f319(f236(x70881),x70884),x70883)),f319(f319(f236(x70881),f319(f319(f283(x70881),x70882),x70884)),x70883))
% 28.25/28.12 [7089]~P124(x70891)+E(f319(f319(f23(x70891),f319(f319(f283(x70891),x70892),x70893)),f319(f319(f283(x70891),x70894),x70893)),f319(f319(f283(x70891),f319(f319(f23(x70891),x70892),x70894)),x70893))
% 28.25/28.12 [7090]~P124(x70901)+E(f319(f319(f74(x70901),f319(f319(f283(x70901),x70902),x70903)),f319(f319(f283(x70901),x70904),x70903)),f319(f319(f283(x70901),f319(f319(f74(x70901),x70902),x70904)),x70903))
% 28.25/28.12 [7091]~P121(x70911)+E(f319(f319(f74(x70911),f319(f319(f75(x70911),x70912),x70913)),f319(f319(f75(x70911),x70914),x70913)),f319(f319(f75(x70911),f319(f319(f74(x70911),x70912),x70914)),x70913))
% 28.25/28.12 [7123]E(f319(f319(f151(x71231,x71232),x71233),x71234),x71232)+~P1(f319(f319(f226(a925),f319(f181(f926(x71231)),x71232)),x71233))
% 28.25/28.12 [7148]~P1(f319(x71483,x71484))+P1(f319(f319(f319(f102(f932(x71481,a923)),x71482),x71483),x71484))
% 28.25/28.12 [7149]~P1(f319(x71493,x71494))+P1(f319(f319(f319(f102(f932(x71491,a923)),x71492),x71493),x71494))
% 28.25/28.12 [7150]~P1(f319(x71502,x71504))+P1(f319(f319(f319(f102(f932(x71501,a923)),x71502),x71503),x71504))
% 28.25/28.12 [7151]~P1(f319(x71512,x71514))+P1(f319(f319(f319(f102(f932(x71511,a923)),x71512),x71513),x71514))
% 28.25/28.12 [7169]E(f319(f319(f156(x71691),f319(f319(f126(x71691),x71692),x71693)),x71694),f319(f319(f156(x71691),x71692),x71694))+~P1(f319(f319(f227(a925),x71694),f319(f181(f926(x71691)),x71692)))
% 28.25/28.12 [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))
% 28.25/28.12 [7180]E(f319(f319(f23(f932(x71801,a923)),f319(f319(f301(x71801),x71802),x71803)),x71804),f319(f319(f23(f932(x71801,a923)),x71803),x71804))+~P1(f319(f319(f321(x71801),x71802),x71804))
% 28.25/28.12 [7221]~E(f131(a925,f319(f294(a925,x72211),x72212)),f319(f319(f143(a925),x72214),x72213))+E(f131(a925,f319(f294(a925,f319(f319(f74(a925),x72211),f72(a925))),x72212)),x72213)
% 28.25/28.12 [7242]~P1(f319(f319(f164(x72421),x72423),x72424))+P1(f319(f319(f164(x72421),f319(f319(f143(x72421),x72422),x72423)),x72424))
% 28.25/28.12 [7292]E(x72921,f2(a925))+E(f319(f319(f143(x72922),x72923),f319(f319(f167(x72922),f319(f319(f23(a925),x72921),f72(a925))),x72924)),f319(f319(f167(x72922),x72921),f319(f319(f143(x72922),x72923),x72924)))
% 28.25/28.12 [7395]E(f319(f319(f156(x73951),x73952),f319(f319(f23(a925),x73953),f319(f181(f926(x73951)),x73954))),f319(f319(f156(x73951),f319(f319(f126(x73951),x73954),x73952)),x73953))+P1(f319(f319(f227(a925),x73953),f319(f181(f926(x73951)),x73954)))
% 28.25/28.12 [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))
% 28.25/28.12 [7424]E(f319(f319(f93(f932(x74241,a923)),x74242),f319(f319(f301(x74241),x74243),x74244)),f319(f319(f301(x74241),x74243),f319(f319(f93(f932(x74241,a923)),x74242),x74244)))+~P1(f319(f319(f321(x74241),x74243),x74242))
% 28.25/28.12 [7463]E(f319(f319(f156(x74631),f319(f319(f151(x74631,x74632),x74633),x74634)),x74633),x74634)+~P1(f319(f319(f227(a925),x74633),f319(f181(f926(x74631)),x74632)))
% 28.25/28.12 [7485]E(x74851,f180(f932(x74852,a923)))+E(f319(f302(f931(x74853,x74852),x74853,f243(x74853,x74852)),f319(f319(f246(x74853,x74852),x74854),f319(f16(f932(x74852,a923),x74853),x74851))),x74854)
% 28.25/28.12 [7486]E(x74861,f180(f932(x74862,a923)))+E(f319(f302(f931(x74862,x74863),x74863,f248(x74862,x74863)),f319(f319(f246(x74862,x74863),x74861),f319(f16(f932(x74863,a923),x74862),x74864))),x74864)
% 28.25/28.12 [7558]E(f319(f319(f23(f932(x75581,a923)),f319(f319(f301(x75581),x75582),x75583)),x75584),f319(f319(f301(x75581),x75582),f319(f319(f23(f932(x75581,a923)),x75583),x75584)))+P1(f319(f319(f321(x75581),x75582),x75584))
% 28.25/28.12 [7593]~E(x75934,f180(f932(x75932,a923)))+E(f319(f302(f931(x75931,x75932),x75931,f243(x75931,x75932)),f319(f319(f246(x75931,x75932),x75933),f319(f16(f932(x75932,a923),x75931),x75934))),f180(f932(x75931,a923)))
% 28.25/28.12 [7594]~E(x75943,f180(f932(x75941,a923)))+E(f319(f302(f931(x75941,x75942),x75942,f248(x75941,x75942)),f319(f319(f246(x75941,x75942),x75943),f319(f16(f932(x75942,a923),x75941),x75944))),f180(f932(x75942,a923)))
% 28.25/28.12 [7643]~P1(f319(f319(f321(x76431),x76432),x76434))+P1(f319(f319(f321(x76431),x76432),f319(f319(f102(f932(x76431,a923)),x76433),x76434)))
% 28.25/28.12 [7644]~P1(f319(f319(f321(x76441),x76442),x76444))+P1(f319(f319(f321(x76441),x76442),f319(f319(f102(f932(x76441,a923)),x76443),x76444)))
% 28.25/28.12 [7645]~P1(f319(f319(f321(x76451),x76452),x76454))+P1(f319(f319(f321(x76451),x76452),f319(f319(f102(f932(x76451,a923)),x76453),x76454)))
% 28.25/28.12 [7646]~P1(f319(f319(f321(x76461),x76462),x76463))+P1(f319(f319(f321(x76461),x76462),f319(f319(f102(f932(x76461,a923)),x76463),x76464)))
% 28.25/28.12 [7647]~P1(f319(f319(f321(x76471),x76472),x76473))+P1(f319(f319(f321(x76471),x76472),f319(f319(f102(f932(x76471,a923)),x76473),x76474)))
% 28.25/28.12 [7648]~P1(f319(f319(f321(x76481),x76482),x76483))+P1(f319(f319(f321(x76481),x76482),f319(f319(f102(f932(x76481,a923)),x76483),x76484)))
% 28.25/28.12 [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))
% 28.25/28.12 [7666]E(f319(f319(f93(f932(x76661,a923)),f319(f319(f301(x76661),x76662),x76663)),x76664),f319(f319(f301(x76661),x76662),f319(f319(f93(f932(x76661,a923)),x76663),x76664)))+~P1(f319(f319(f321(x76661),x76662),x76664))
% 28.25/28.12 [7937]P1(f319(x79371,x79372))+~P1(f319(f319(f319(f93(f932(x79373,a923)),x79374),x79371),x79372))
% 28.25/28.12 [7938]P1(f319(x79381,x79382))+~P1(f319(f319(f319(f93(f932(x79383,a923)),x79381),x79384),x79382))
% 28.25/28.12 [7939]P1(f319(x79391,x79392))+~P1(f319(f319(f319(f93(f932(x79393,a923)),x79394),x79391),x79392))
% 28.25/28.12 [7940]P1(f319(x79401,x79402))+~P1(f319(f319(f319(f93(f932(x79403,a923)),x79401),x79404),x79402))
% 28.25/28.12 [7941]E(f319(f319(f6(x79411,a925),x79412),f319(f319(f23(f932(x79411,a923)),x79413),f319(f319(f301(x79411),x79414),f180(f932(x79411,a923))))),f319(f319(f6(x79411,a925),x79412),x79413))+P1(f319(f319(f321(x79411),x79414),x79413))
% 28.25/28.12 [7946]~P79(x79461)+E(f319(f157(x79461),f319(f319(f146(a925,x79461),x79462),f131(a925,f319(f294(a925,x79463),x79464)))),f319(f319(f6(a925,x79461),x79462),f319(f164(a925),f131(a925,f319(f294(a925,x79463),x79464)))))
% 28.25/28.12 [7947]~P79(x79471)+E(f319(f319(f6(a925,x79471),x79472),f319(f164(a925),f131(a925,f319(f294(a925,x79473),x79474)))),f319(f157(x79471),f319(f319(f146(a925,x79471),x79472),f131(a925,f319(f294(a925,x79473),x79474)))))
% 28.25/28.12 [8061]~E(x80613,x80614)+P1(f319(f56(x80611,x80612,f319(f319(f301(x80611),x80613),f180(f932(x80611,a923)))),x80614))
% 28.25/28.12 [8158]P1(f319(f319(f321(x81581),x81582),f319(f164(x81581),x81583)))+~P1(f319(f319(f321(x81581),x81582),f319(f164(x81581),f319(f319(f167(x81581),x81584),x81583))))
% 28.25/28.12 [8159]P1(f319(f319(f321(x81591),x81592),f319(f164(x81591),x81593)))+~P1(f319(f319(f321(x81591),x81592),f319(f164(x81591),f319(f319(f130(x81591),x81594),x81593))))
% 28.25/28.12 [8229]P1(f319(f319(f321(x82291),x82292),x82293))+~P1(f319(f319(f321(x82291),x82292),f319(f319(f93(f932(x82291,a923)),x82294),x82293)))
% 28.25/28.12 [8230]P1(f319(f319(f321(x82301),x82302),x82303))+~P1(f319(f319(f321(x82301),x82302),f319(f319(f93(f932(x82301,a923)),x82304),x82303)))
% 28.25/28.12 [8231]P1(f319(f319(f321(x82311),x82312),x82313))+~P1(f319(f319(f321(x82311),x82312),f319(f319(f93(f932(x82311,a923)),x82314),x82313)))
% 28.25/28.12 [8232]P1(f319(f319(f321(x82321),x82322),x82323))+~P1(f319(f319(f321(x82321),x82322),f319(f319(f93(f932(x82321,a923)),x82323),x82324)))
% 28.25/28.12 [8233]P1(f319(f319(f321(x82331),x82332),x82333))+~P1(f319(f319(f321(x82331),x82332),f319(f319(f93(f932(x82331,a923)),x82333),x82334)))
% 28.25/28.12 [8234]P1(f319(f319(f321(x82341),x82342),x82343))+~P1(f319(f319(f321(x82341),x82342),f319(f319(f93(f932(x82341,a923)),x82343),x82344)))
% 28.25/28.12 [8235]P1(f319(f319(f321(x82351),x82352),x82353))+~P1(f319(f319(f321(x82351),x82352),f319(f319(f23(f932(x82351,a923)),x82353),x82354)))
% 28.25/28.12 [8236]P1(f319(f319(f321(x82361),x82362),x82363))+~P1(f319(f319(f321(x82361),x82362),f319(f319(f23(f932(x82361,a923)),x82363),x82364)))
% 28.25/28.12 [8237]P1(f319(f319(f321(x82371),x82372),x82373))+~P1(f319(f319(f321(x82371),x82372),f319(f319(f23(f932(x82371,a923)),x82373),x82374)))
% 28.25/28.12 [8252]E(f319(f319(f126(x82521),f319(f319(f167(x82521),x82522),x82523)),f319(f319(f143(x82521),x82524),f319(f319(f130(x82521),f319(a104,x82522)),x82523))),f319(f319(f151(x82521,x82523),x82522),x82524))+~P1(f319(f319(f227(a925),x82522),f319(f181(f926(x82521)),x82523)))
% 28.25/28.12 [8275]P1(f319(f319(f321(x82751),x82752),x82753))+~P1(f319(f319(f226(f932(x82751,a923)),f319(f319(f301(x82751),x82752),x82754)),x82753))
% 28.25/28.12 [8310]~P1(f319(f319(f321(x83101),x83102),x83103))+~P1(f319(f319(f321(x83101),x83102),f319(f319(f23(f932(x83101,a923)),x83104),x83103)))
% 28.25/28.12 [8311]~P1(f319(f319(f321(x83111),x83112),x83113))+~P1(f319(f319(f321(x83111),x83112),f319(f319(f23(f932(x83111,a923)),x83114),x83113)))
% 28.25/28.12 [8312]~P1(f319(f319(f321(x83121),x83122),x83123))+~P1(f319(f319(f321(x83121),x83122),f319(f319(f23(f932(x83121,a923)),x83124),x83123)))
% 28.25/28.12 [8345]~P1(f319(f319(f227(a925),x83454),f319(f181(f926(x83451)),x83453)))+P1(f319(f319(f321(x83451),x83452),f319(f164(x83451),f319(f319(f151(x83451,x83453),x83454),x83452))))
% 28.25/28.12 [8388]E(f319(f95(a925),x83881),f2(a925))+E(f319(f319(f143(x83882),x83883),f319(f319(f167(x83882),f319(f319(f23(a925),f319(f95(a925),x83881)),f72(a925))),x83884)),f319(f319(f167(x83882),f319(f95(a925),x83881)),f319(f319(f143(x83882),x83883),x83884)))
% 28.25/28.12 [8398]E(f319(f319(f156(x83981),f319(f319(f130(x83981),x83982),x83983)),x83984),f319(f319(f156(x83981),x83983),f319(f319(f74(a925),x83982),x83984)))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),x83982),x83984)),f319(f181(f926(x83981)),x83983)))
% 28.25/28.12 [8407]~P149(x84072)+E(f319(f319(f6(x84071,x84072),f319(f319(f8(a925,x84072,x84071),f92(x84072)),x84073)),x84074),f319(f92(x84072),f319(f319(f6(x84071,a925),x84073),x84074)))
% 28.25/28.12 [8408]~P145(x84082)+E(f319(f319(f6(x84081,x84082),f319(f319(f8(a1,x84082,x84081),f94(x84082)),x84083)),x84084),f319(f94(x84082),f319(f319(f6(x84081,a1),x84083),x84084)))
% 28.25/28.12 [8458]~P75(x84582)+E(f319(f319(f9(x84581,x84582),f319(f319(f8(x84582,x84582,x84581),f69(x84582)),x84583)),x84584),f319(f69(x84582),f319(f319(f9(x84581,x84582),x84583),x84584)))
% 28.25/28.12 [8459]~P70(x84592)+E(f319(f319(f6(x84591,x84592),f319(f319(f8(x84592,x84592,x84591),f73(x84592)),x84593)),x84594),f319(f73(x84592),f319(f319(f6(x84591,x84592),x84593),x84594)))
% 28.25/28.12 [8461]E(f319(f319(f6(x84611,a925),x84612),f319(f319(f23(f932(x84611,a923)),x84613),f319(f319(f301(x84611),x84614),f180(f932(x84611,a923))))),f319(f319(f23(a925),f319(f319(f6(x84611,a925),x84612),x84613)),f319(x84612,x84614)))+~P1(f319(f319(f321(x84611),x84614),x84613))
% 28.25/28.12 [8481]P1(f319(f319(f226(f932(x84811,a923)),x84812),x84813))+~P1(f319(f319(f226(f932(x84811,a923)),f319(f319(f301(x84811),x84814),x84812)),x84813))
% 28.25/28.12 [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)
% 28.25/28.12 [8606]~E(f319(f302(x86062,x86063,x86061),f234(f932(x86062,a923))),f234(f932(x86063,a923)))+E(f319(x86061,f319(f85(x86062,x86063,f234(f932(x86062,a923)),x86061),x86064)),x86064)
% 28.25/28.12 [8691]P38(x86911,x86912)+~P38(x86911,f319(f319(f301(f931(x86911,x86911)),f319(f319(f244(x86911,x86911),x86913),x86914)),x86912))
% 28.25/28.12 [8692]P62(x86921,x86922)+~P62(x86921,f319(f319(f301(f931(x86921,x86921)),f319(f319(f244(x86921,x86921),x86923),x86924)),x86922))
% 28.25/28.12 [8697]~P4(x86971)+E(f319(f319(f140(x86971,x86971,f5(x86971)),x86972),f319(f319(f140(x86971,x86971,f5(x86971)),x86973),x86974)),f319(f319(f140(x86971,x86971,f5(x86971)),x86973),f319(f319(f140(x86971,x86971,f5(x86971)),x86972),x86974)))
% 28.25/28.12 [8712]E(x87121,x87122)+~P1(f319(f56(x87123,x87124,f319(f319(f301(x87123),x87121),f180(f932(x87123,a923)))),x87122))
% 28.25/28.12 [8724]E(f319(f319(f126(x87241),f319(f319(f167(x87241),x87242),x87243)),f319(f319(f167(x87241),x87244),f319(f319(f130(x87241),x87242),x87243))),f319(f319(f167(x87241),f319(f319(f74(a925),x87242),x87244)),x87243))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),x87242),x87244)),f319(f181(f926(x87241)),x87243)))
% 28.25/28.12 [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))))
% 28.25/28.12 [8763]P1(f319(f55(x87631),x87632))+~E(x87632,f319(f302(a925,x87631,x87633),f319(f254(a925),f319(f319(f7(a925,a925,a923),f227(a925)),x87634))))
% 28.25/28.12 [8783]~P95(x87831)+E(f319(f134(x87831,x87831,f74(x87831),f319(f319(f74(x87831),x87832),x87833)),x87834),f319(f319(f74(x87831),x87832),f319(f134(x87831,x87831,f74(x87831),x87833),x87834)))
% 28.25/28.12 [8820]P1(f319(f319(f226(f932(x88201,a923)),f319(f256(x88201,x88202),x88203)),f319(f256(x88201,x88202),x88204)))+~P1(f319(f319(f226(f932(f931(x88201,x88202),a923)),x88203),x88204))
% 28.25/28.12 [8832]~P1(f319(f319(f226(a925),x88322),x88324))+P1(f319(f319(f226(f932(x88321,a923)),f319(f164(x88321),f319(f319(f167(x88321),x88322),x88323))),f319(f164(x88321),f319(f319(f167(x88321),x88324),x88323))))
% 28.25/28.12 [8833]~P1(f319(f319(f226(a925),x88334),x88332))+P1(f319(f319(f226(f932(x88331,a923)),f319(f164(x88331),f319(f319(f130(x88331),x88332),x88333))),f319(f164(x88331),f319(f319(f130(x88331),x88334),x88333))))
% 28.25/28.12 [8890]~P1(f319(f55(x88901),f319(f319(f23(f932(x88901,a923)),x88902),x88904)))+P1(f319(f55(x88901),f319(f319(f23(f932(x88901,a923)),x88902),f319(f319(f301(x88901),x88903),x88904))))
% 28.25/28.12 [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)))
% 28.25/28.12 [8932]P1(f319(f319(f321(f931(x89321,x89321)),x89322),f299(x89321,x89323)))+~P1(f319(f319(f321(f931(x89321,x89321)),x89322),f319(f319(f175(f931(x89321,x89321),a923),x89324),x89323)))
% 28.25/28.12 [9019]~P1(f319(f55(x90191),f319(f319(f23(f932(x90191,a923)),x90192),f319(f319(f301(x90191),x90194),x90193))))+P1(f319(f55(x90191),f319(f319(f23(f932(x90191,a923)),x90192),x90193)))
% 28.25/28.12 [9094]P1(f319(f319(f321(f931(x90941,x90942)),f319(f319(f244(x90941,x90942),x90943),x90944)),f180(f932(f931(x90941,x90942),a923))))+~P1(f319(f319(f180(f932(x90941,f932(x90942,a923))),x90943),x90944))
% 28.25/28.12 [9236]~P102(x92361)+P1(f319(f319(f226(x92361),f319(f319(f102(x92361),x92362),f319(f319(f93(x92361),x92363),x92364))),f319(f319(f93(x92361),f319(f319(f102(x92361),x92362),x92363)),f319(f319(f102(x92361),x92362),x92364))))
% 28.25/28.12 [9237]~P4(x92371)+P1(f319(f319(f226(x92371),f319(f319(f225(x92371),x92372),f319(f319(f224(x92371),x92373),x92374))),f319(f319(f224(x92371),f319(f319(f225(x92371),x92372),x92373)),f319(f319(f225(x92371),x92372),x92374))))
% 28.25/28.12 [9254]~P1(f319(f319(f321(f931(x92541,x92542)),f319(f319(f244(x92541,x92542),x92543),x92544)),f180(f932(f931(x92541,x92542),a923))))+P1(f319(f319(f180(f932(x92541,f932(x92542,a923))),x92543),x92544))
% 28.25/28.12 [9387]E(x93871,x93872)+~P1(f319(f319(f321(f931(x93873,x93873)),f319(f319(f244(x93873,x93873),x93871),x93872)),f319(f164(f931(x93873,x93873)),f319(f319(f173(x93873,x93873),x93874),x93874))))
% 28.25/28.12 [9418]~P1(f319(f319(f321(f931(x94181,x94181)),f319(f319(f244(x94181,x94181),x94183),x94182)),f299(x94181,x94184)))+~P38(x94181,f319(f319(f301(f931(x94181,x94181)),f319(f319(f244(x94181,x94181),x94182),x94183)),x94184))
% 28.25/28.12 [9419]~P1(f319(f319(f321(f931(x94191,x94191)),f319(f319(f244(x94191,x94191),x94193),x94192)),f299(x94191,x94194)))+~P62(x94191,f319(f319(f301(f931(x94191,x94191)),f319(f319(f244(x94191,x94191),x94192),x94193)),x94194))
% 28.25/28.12 [9423]E(x94231,x94232)+E(f319(f128(x94233,f319(f319(f8(a923,a923,x94233),a314),f319(a316,x94231))),f319(f319(f143(x94233),x94232),x94234)),f319(f319(f143(x94233),x94232),f319(f128(x94233,f319(f319(f8(a923,a923,x94233),a314),f319(a316,x94231))),x94234)))
% 28.25/28.12 [9433]P1(f319(f319(f321(x94331),x94332),f319(f164(x94331),x94333)))+~P1(f319(f319(f321(f931(x94331,x94331)),f319(f319(f244(x94331,x94331),x94332),x94334)),f319(f164(f931(x94331,x94331)),f319(f319(f173(x94331,x94331),x94333),x94333))))
% 28.25/28.12 [9454]~P27(x94542,x94541,x94543,f234(f932(x94542,a923)),f234(f932(x94541,a923)))+E(f319(f302(x94541,x94542,f85(x94542,x94541,f234(f932(x94542,a923)),x94543)),x94544),f319(f303(x94542,x94541,x94543),x94544))
% 28.25/28.12 [9469]~P102(x94691)+P1(f319(f319(f226(x94691),f319(f319(f102(x94691),f319(f319(f93(x94691),x94692),x94693)),f319(f319(f93(x94691),x94692),x94694))),f319(f319(f93(x94691),x94692),f319(f319(f102(x94691),x94693),x94694))))
% 28.25/28.12 [9470]~P4(x94701)+P1(f319(f319(f226(x94701),f319(f319(f225(x94701),f319(f319(f224(x94701),x94702),x94703)),f319(f319(f224(x94701),x94702),x94704))),f319(f319(f224(x94701),x94702),f319(f319(f225(x94701),x94703),x94704))))
% 28.25/28.12 [9508]P1(f319(f319(f321(f931(x95081,x95081)),f319(f319(f244(x95081,x95081),x95082),x95083)),f319(f319(f281(x95081,x95081,x95081),x95084),f299(x95081,x95084))))+~P1(f319(f319(f321(f931(x95081,x95081)),f319(f319(f244(x95081,x95081),x95082),x95083)),x95084))
% 28.25/28.12 [9533]~P27(x95332,x95331,x95334,f234(f932(x95332,a923)),f234(f932(x95331,a923)))+E(f319(f254(x95331),f319(f319(f8(x95332,a923,x95331),x95333),f85(x95332,x95331,f234(f932(x95332,a923)),x95334))),f319(f302(x95332,x95331,x95334),f319(f254(x95332),x95333)))
% 28.25/28.12 [9547]~E(f319(f302(x95472,x95471,x95473),f234(f932(x95472,a923))),f234(f932(x95471,a923)))+P1(f319(f319(f226(f932(x95471,a923)),f319(f73(f932(x95471,a923)),f319(f302(x95472,x95471,x95473),x95474))),f319(f302(x95472,x95471,x95473),f319(f73(f932(x95472,a923)),x95474))))
% 28.25/28.12 [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)))))
% 28.25/28.12 [9879]~P1(f319(f319(f321(f931(x98791,x98791)),f319(f319(f244(x98791,x98791),x98792),x98793)),f319(f278(x98791,x98791),f319(f319(f281(x98791,x98791,x98791),x98794),f299(x98791,x98794)))))+P1(f319(f319(f321(f931(x98791,x98791)),f319(f319(f244(x98791,x98791),x98792),x98793)),f319(f319(f281(x98791,x98791,x98791),f319(f278(x98791,x98791),x98794)),f299(x98791,f319(f278(x98791,x98791),x98794)))))
% 28.25/28.12 [9900]~P1(f319(f319(f321(x99002),x99004),f319(f276(x99001,x99002),x99003)))+P1(f319(f319(f321(f931(x99001,x99002)),f319(f319(f244(x99001,x99002),f572(x99003,x99001,x99004,x99002)),x99004)),x99003))
% 28.25/28.12 [9901]~P1(f319(f319(f321(x99012),x99014),f319(f276(x99011,x99012),x99013)))+P1(f319(f319(f321(f931(x99011,x99012)),f319(f319(f244(x99011,x99012),f574(x99013,x99011,x99014,x99012)),x99014)),x99013))
% 28.25/28.12 [9929]~P1(f319(f319(f321(x99291),x99294),f319(f319(f102(f932(x99291,a923)),x99292),x99293)))+P1(f319(f319(f319(f102(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))
% 28.25/28.12 [9930]~P1(f319(f319(f321(x99301),x99304),f319(f319(f93(f932(x99301,a923)),x99302),x99303)))+P1(f319(f319(f319(f93(f932(x99301,a923)),f319(f319(f7(x99301,f932(x99301,a923),a923),f321(x99301)),x99302)),f319(f319(f7(x99301,f932(x99301,a923),a923),f321(x99301)),x99303)),x99304))
% 28.25/28.12 [10022]~P1(f319(f319(f321(f931(x100221,x100221)),f319(f319(f244(x100221,x100221),x100224),x100223)),f319(f319(f281(x100221,x100221,x100221),x100222),f299(x100221,x100222))))+P1(f319(f319(f321(f931(x100221,x100221)),f319(f319(f244(x100221,x100221),f640(x100222,x100223,x100224,x100221)),x100223)),x100222))
% 28.25/28.12 [10060]P1(f319(f319(f321(x100601),x100602),f319(f319(f102(f932(x100601,a923)),x100603),x100604)))+~P1(f319(f319(f319(f102(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))
% 28.25/28.12 [10061]P1(f319(f319(f321(x100611),x100612),f319(f319(f93(f932(x100611,a923)),x100613),x100614)))+~P1(f319(f319(f319(f93(f932(x100611,a923)),f319(f319(f7(x100611,f932(x100611,a923),a923),f321(x100611)),x100613)),f319(f319(f7(x100611,f932(x100611,a923),a923),f321(x100611)),x100614)),x100612))
% 28.25/28.12 [10351]P33(x103511,f319(f319(f7(x103511,f932(f931(x103511,x103511),a923),f932(x103511,a923)),f319(f319(f8(f932(x103511,f932(f932(f931(x103511,x103511),a923),a923)),f932(f932(f931(x103511,x103511),a923),f932(x103511,a923)),x103511),f7(x103511,f932(f931(x103511,x103511),a923),a923)),f319(f319(f8(f932(x103511,f931(x103511,x103511)),f932(x103511,f932(f932(f931(x103511,x103511),a923),a923)),x103511),f319(f8(f931(x103511,x103511),f932(f932(f931(x103511,x103511),a923),a923),x103511),f321(f931(x103511,x103511)))),f244(x103511,x103511)))),x103512),x103513,x103514)+~P1(f319(f319(f321(f931(f926(x103511),f926(x103511))),f319(f319(f244(f926(x103511),f926(x103511)),x103513),x103514)),f150(x103511,x103512)))
% 28.25/28.12 [10355]P63(x103551,f319(f319(f7(x103551,f932(f931(x103551,x103551),a923),f932(x103551,a923)),f319(f319(f8(f932(x103551,f932(f932(f931(x103551,x103551),a923),a923)),f932(f932(f931(x103551,x103551),a923),f932(x103551,a923)),x103551),f7(x103551,f932(f931(x103551,x103551),a923),a923)),f319(f319(f8(f932(x103551,f931(x103551,x103551)),f932(x103551,f932(f932(f931(x103551,x103551),a923),a923)),x103551),f319(f8(f931(x103551,x103551),f932(f932(f931(x103551,x103551),a923),a923),x103551),f321(f931(x103551,x103551)))),f244(x103551,x103551)))),x103552),x103553,x103554)+~P1(f319(f319(f321(f931(f932(x103551,a923),f932(x103551,a923))),f319(f319(f244(f932(x103551,a923),f932(x103551,a923)),x103553),x103554)),f311(x103551,x103552)))
% 28.25/28.12 [10389]E(x103891,x103892)+~E(f319(f319(f7(x103893,f932(f931(x103893,x103894),a923),f932(x103894,a923)),f319(f319(f8(f932(x103894,f932(f932(f931(x103893,x103894),a923),a923)),f932(f932(f931(x103893,x103894),a923),f932(x103894,a923)),x103893),f7(x103894,f932(f931(x103893,x103894),a923),a923)),f319(f319(f8(f932(x103894,f931(x103893,x103894)),f932(x103894,f932(f932(f931(x103893,x103894),a923),a923)),x103893),f319(f8(f931(x103893,x103894),f932(f932(f931(x103893,x103894),a923),a923),x103894),f321(f931(x103893,x103894)))),f244(x103893,x103894)))),x103891),f319(f319(f7(x103893,f932(f931(x103893,x103894),a923),f932(x103894,a923)),f319(f319(f8(f932(x103894,f932(f932(f931(x103893,x103894),a923),a923)),f932(f932(f931(x103893,x103894),a923),f932(x103894,a923)),x103893),f7(x103894,f932(f931(x103893,x103894),a923),a923)),f319(f319(f8(f932(x103894,f931(x103893,x103894)),f932(x103894,f932(f932(f931(x103893,x103894),a923),a923)),x103893),f319(f8(f931(x103893,x103894),f932(f932(f931(x103893,x103894),a923),a923),x103894),f321(f931(x103893,x103894)))),f244(x103893,x103894)))),x103892))
% 28.25/28.12 [10392]~P33(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(f926(x103921),f926(x103921))),f319(f319(f244(f926(x103921),f926(x103921)),x103922),x103923)),f150(x103921,x103924)))
% 28.25/28.12 [10393]~P63(x103931,f319(f319(f7(x103931,f932(f931(x103931,x103931),a923),f932(x103931,a923)),f319(f319(f8(f932(x103931,f932(f932(f931(x103931,x103931),a923),a923)),f932(f932(f931(x103931,x103931),a923),f932(x103931,a923)),x103931),f7(x103931,f932(f931(x103931,x103931),a923),a923)),f319(f319(f8(f932(x103931,f931(x103931,x103931)),f932(x103931,f932(f932(f931(x103931,x103931),a923),a923)),x103931),f319(f8(f931(x103931,x103931),f932(f932(f931(x103931,x103931),a923),a923),x103931),f321(f931(x103931,x103931)))),f244(x103931,x103931)))),x103934),x103932,x103933)+P1(f319(f319(f321(f931(f932(x103931,a923),f932(x103931,a923))),f319(f319(f244(f932(x103931,a923),f932(x103931,a923)),x103932),x103933)),f311(x103931,x103934)))
% 28.25/28.12 [7715]~P99(x77151)+E(f319(f319(f75(x77151),f319(f95(x77151),x77152)),f319(f319(f75(x77151),f319(f95(x77151),x77153)),x77154)),f319(f319(f75(x77151),f319(f95(x77151),f319(f319(f75(a1),x77152),x77153))),x77154))
% 28.25/28.12 [7716]~P99(x77161)+E(f319(f319(f74(x77161),f319(f95(x77161),x77162)),f319(f319(f23(x77161),f319(f95(x77161),x77163)),x77164)),f319(f319(f23(x77161),f319(f95(x77161),f319(f319(f74(a1),x77162),x77163))),x77164))
% 28.25/28.12 [7717]~P99(x77171)+E(f319(f319(f74(x77171),f319(f95(x77171),x77172)),f319(f319(f74(x77171),f319(f95(x77171),x77173)),x77174)),f319(f319(f74(x77171),f319(f95(x77171),f319(f319(f74(a1),x77172),x77173))),x77174))
% 28.25/28.12 [7757]~P149(x77571)+E(f319(f157(x77571),f319(f319(f146(x77572,x77571),f319(f16(x77571,x77572),x77573)),x77574)),f319(f319(f75(x77571),f319(f92(x77571),f319(f181(f926(x77572)),x77574))),x77573))
% 28.25/28.12 [7995]E(f319(f260(x79951,f319(f319(f143(f931(a91,x79951)),x79952),x79953)),x79954),f319(f248(a91,x79951),x79952))+~P1(f319(f319(f227(a91),x79954),f319(f243(a91,x79951),x79952)))
% 28.25/28.12 [8036]~P99(x80361)+E(f319(f319(f74(x80361),f319(f95(x80361),x80362)),f319(f319(f23(x80361),x80363),f319(f95(x80361),x80364))),f319(f319(f74(x80361),f319(f95(x80361),f319(f319(f74(a1),x80362),f319(f73(a1),x80364)))),x80363))
% 28.25/28.12 [8172]E(f319(f260(x81721,x81722),f319(f319(f23(a91),x81723),f319(f243(a91,x81721),x81724))),f319(f260(x81721,f319(f319(f143(f931(a91,x81721)),x81724),x81722)),x81723))+P1(f319(f319(f227(a91),x81723),f319(f243(a91,x81721),x81724)))
% 28.25/28.12 [8612]~P1(f319(f319(f321(x86121),x86122),f319(f164(x86121),f106(x86121,x86124))))+P1(f319(f319(f321(x86121),x86122),f319(f164(x86121),f106(x86121,f319(f319(f126(x86121),x86123),x86124)))))
% 28.25/28.12 [8613]~P1(f319(f319(f321(x86131),x86132),f319(f164(x86131),f106(x86131,x86133))))+P1(f319(f319(f321(x86131),x86132),f319(f164(x86131),f106(x86131,f319(f319(f126(x86131),x86133),x86134)))))
% 28.25/28.12 [8632]E(f319(f319(f102(f932(x86321,a923)),f319(f319(f93(f932(x86321,a923)),x86322),x86323)),x86324),f319(f319(f93(f932(x86321,a923)),x86322),f319(f319(f102(f932(x86321,a923)),x86323),x86324)))+~P1(f319(f319(f226(f932(x86321,a923)),x86324),x86322))
% 28.25/28.12 [8946]~E(f319(f319(f102(f932(x89461,a923)),f319(f319(f93(f932(x89461,a923)),x89463),x89464)),x89462),f319(f319(f93(f932(x89461,a923)),x89463),f319(f319(f102(f932(x89461,a923)),x89464),x89462)))+P1(f319(f319(f226(f932(x89461,a923)),x89462),x89463))
% 28.25/28.12 [9241]~P1(f319(f319(f226(f932(x92411,a923)),x92412),f319(f319(f102(f932(x92411,a923)),x92413),x92414)))+P1(f319(f319(f226(f932(x92411,a923)),f319(f319(f23(f932(x92411,a923)),x92412),x92413)),x92414))
% 28.25/28.12 [9358]~E(f319(f302(x93581,x93582,x93583),f234(f932(x93581,a923))),f234(f932(x93582,a923)))+E(f319(f302(x93581,x93582,x93583),f319(f302(x93582,x93581,f85(x93581,x93582,f234(f932(x93581,a923)),x93583)),x93584)),x93584)
% 28.25/28.12 [9363]P1(f319(f319(f226(f932(x93631,a923)),x93632),f319(f319(f102(f932(x93631,a923)),x93633),x93634)))+~P1(f319(f319(f226(f932(x93631,a923)),f319(f319(f23(f932(x93631,a923)),x93632),x93633)),x93634))
% 28.25/28.12 [9450]~P92(x94501)+E(f319(f69(x94501),f319(f319(f6(x94502,x94501),f319(f319(f8(x94501,x94501,x94502),f69(x94501)),x94503)),x94504)),f319(f319(f6(x94502,x94501),f319(f319(f8(x94501,x94501,x94502),f69(x94501)),x94503)),x94504))
% 28.25/28.12 [9624]~P92(x96241)+P1(f319(f319(f226(x96241),f2(x96241)),f319(f319(f6(x96242,x96241),f319(f319(f8(x96241,x96241,x96242),f69(x96241)),x96243)),x96244)))
% 28.25/28.12 [9628]~P70(x96281)+E(f319(f157(x96281),f319(f319(f146(x96282,x96281),f319(f66(x96281,x96281,x96282,f73(x96281)),x96283)),x96284)),f319(f73(x96281),f319(f157(x96281),f319(f319(f146(x96282,x96281),x96283),x96284))))
% 28.25/28.12 [9771]~P92(x97711)+P1(f319(f319(f226(x97711),f319(f69(x97711),f319(f319(f6(x97712,x97711),x97713),x97714))),f319(f319(f6(x97712,x97711),f319(f319(f8(x97711,x97711,x97712),f69(x97711)),x97713)),x97714)))
% 28.25/28.12 [9802]~E(f319(f319(f74(a925),x98021),x98024),f319(f319(f74(a925),x98023),x98022))+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))),a100))
% 28.25/28.12 [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))),a26))
% 28.25/28.12 [9804]~P1(f319(f319(f227(a925),x98041),x98043))+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),x98041),x98042)),f319(f319(f244(a925,a925),x98043),x98044))),a64))
% 28.25/28.12 [9959]E(f319(f319(f74(a925),x99591),x99592),f319(f319(f74(a925),x99593),x99594))+~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),x99591),x99594)),f319(f319(f244(a925,a925),x99593),x99592))),a100))
% 28.25/28.12 [9995]E(f319(f319(f156(x99951),f319(f319(f130(x99951),f319(f181(f926(x99951)),f169(x99951,x99952,x99953))),x99953)),x99954),f319(f319(f156(x99951),x99953),f319(f319(f74(a925),x99954),f319(f181(f926(x99951)),f169(x99951,x99952,x99953)))))+~P1(f319(f319(f227(a925),x99954),f319(f181(f926(x99951)),f319(f319(f130(x99951),f319(f181(f926(x99951)),f169(x99951,x99952,x99953))),x99953))))
% 28.25/28.12 [10013]~P1(f319(f319(f321(x100132),x100134),f319(f319(f33(x100131,f932(x100132,a923)),f234(f932(x100131,a923))),x100133)))+P1(f319(f319(f319(f33(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))
% 28.25/28.12 [10014]~P1(f319(f319(f321(x100142),x100144),f319(f319(f34(x100141,f932(x100142,a923)),f234(f932(x100141,a923))),x100143)))+P1(f319(f319(f319(f34(x100141,f932(x100142,a923)),f234(f932(x100141,a923))),f319(f319(f8(f932(x100142,a923),f932(x100142,a923),x100141),f319(f7(x100142,f932(x100142,a923),a923),f321(x100142))),x100143)),x100144))
% 28.25/28.12 [10089]~P1(f319(f43(x100891,x100892),f319(f319(f244(a1,a1),x100894),x100893)))+P1(f319(f43(f319(f73(a1),x100891),x100892),f319(f319(f244(a1,a1),f319(f319(f319(f86(a1),f319(f319(a316,x100893),f2(a1))),f319(f73(a1),x100894)),f319(f319(f23(a1),f319(f73(a1),x100894)),f72(a1)))),f319(f319(f319(f86(a1),f319(f319(a316,x100893),f2(a1))),f2(a1)),f319(f319(f23(a1),x100892),x100893)))))
% 28.25/28.12 [10101]P1(f319(f319(f321(x101011),x101012),f319(f319(f33(x101013,f932(x101011,a923)),f234(f932(x101013,a923))),x101014)))+~P1(f319(f319(f319(f33(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))
% 28.25/28.12 [10102]P1(f319(f319(f321(x101021),x101022),f319(f319(f34(x101023,f932(x101021,a923)),f234(f932(x101023,a923))),x101024)))+~P1(f319(f319(f319(f34(x101023,f932(x101021,a923)),f234(f932(x101023,a923))),f319(f319(f8(f932(x101021,a923),f932(x101021,a923),x101023),f319(f7(x101021,f932(x101021,a923),a923),f321(x101021))),x101024)),x101022))
% 28.25/28.12 [10114]E(f319(f319(f33(a925,f932(x101141,a923)),f234(f932(a925,a923))),x101142),f319(f319(f33(a925,f932(x101141,a923)),f234(f932(a925,a923))),x101143))+~E(f319(f319(f33(a925,f932(x101141,a923)),f319(f294(a925,f2(a925)),f412(x101142,x101144,x101143,x101141))),x101143),f319(f319(f33(a925,f932(x101141,a923)),f319(f294(a925,f2(a925)),f319(f319(f74(a925),f412(x101142,x101144,x101143,x101141)),x101144))),x101142))
% 28.25/28.12 [10468]~P1(f319(f319(f226(f932(f931(x104681,x104682),a923)),x104683),x104684))+P1(f319(f319(f226(f932(x104681,f932(x104682,a923))),f319(f319(f7(x104681,f932(f931(x104681,x104682),a923),f932(x104682,a923)),f319(f319(f8(f932(x104682,f932(f932(f931(x104681,x104682),a923),a923)),f932(f932(f931(x104681,x104682),a923),f932(x104682,a923)),x104681),f7(x104682,f932(f931(x104681,x104682),a923),a923)),f319(f319(f8(f932(x104682,f931(x104681,x104682)),f932(x104682,f932(f932(f931(x104681,x104682),a923),a923)),x104681),f319(f8(f931(x104681,x104682),f932(f932(f931(x104681,x104682),a923),a923),x104682),f321(f931(x104681,x104682)))),f244(x104681,x104682)))),x104683)),f319(f319(f7(x104681,f932(f931(x104681,x104682),a923),f932(x104682,a923)),f319(f319(f8(f932(x104682,f932(f932(f931(x104681,x104682),a923),a923)),f932(f932(f931(x104681,x104682),a923),f932(x104682,a923)),x104681),f7(x104682,f932(f931(x104681,x104682),a923),a923)),f319(f319(f8(f932(x104682,f931(x104681,x104682)),f932(x104682,f932(f932(f931(x104681,x104682),a923),a923)),x104681),f319(f8(f931(x104681,x104682),f932(f932(f931(x104681,x104682),a923),a923),x104682),f321(f931(x104681,x104682)))),f244(x104681,x104682)))),x104684)))
% 28.25/28.12 [10484]P1(f319(f319(f226(f932(f931(x104841,x104842),a923)),x104843),x104844))+~P1(f319(f319(f226(f932(x104841,f932(x104842,a923))),f319(f319(f7(x104841,f932(f931(x104841,x104842),a923),f932(x104842,a923)),f319(f319(f8(f932(x104842,f932(f932(f931(x104841,x104842),a923),a923)),f932(f932(f931(x104841,x104842),a923),f932(x104842,a923)),x104841),f7(x104842,f932(f931(x104841,x104842),a923),a923)),f319(f319(f8(f932(x104842,f931(x104841,x104842)),f932(x104842,f932(f932(f931(x104841,x104842),a923),a923)),x104841),f319(f8(f931(x104841,x104842),f932(f932(f931(x104841,x104842),a923),a923),x104842),f321(f931(x104841,x104842)))),f244(x104841,x104842)))),x104843)),f319(f319(f7(x104841,f932(f931(x104841,x104842),a923),f932(x104842,a923)),f319(f319(f8(f932(x104842,f932(f932(f931(x104841,x104842),a923),a923)),f932(f932(f931(x104841,x104842),a923),f932(x104842,a923)),x104841),f7(x104842,f932(f931(x104841,x104842),a923),a923)),f319(f319(f8(f932(x104842,f931(x104841,x104842)),f932(x104842,f932(f932(f931(x104841,x104842),a923),a923)),x104841),f319(f8(f931(x104841,x104842),f932(f932(f931(x104841,x104842),a923),a923),x104842),f321(f931(x104841,x104842)))),f244(x104841,x104842)))),x104844)))
% 28.25/28.12 [9497]~P1(f319(f319(f321(f931(x94971,x94971)),x94972),f299(x94971,x94974)))+P1(f319(f319(f321(f931(x94971,x94971)),x94972),f299(x94971,f319(f319(f102(f932(f931(x94971,x94971),a923)),x94973),x94974))))
% 28.25/28.12 [9498]~P1(f319(f319(f321(f931(x94981,x94981)),x94982),f299(x94981,x94983)))+P1(f319(f319(f321(f931(x94981,x94981)),x94982),f299(x94981,f319(f319(f102(f932(f931(x94981,x94981),a923)),x94983),x94984))))
% 28.25/28.12 [10203]~P1(f319(f319(f226(a925),f319(f319(f74(a925),x102031),x102034)),f319(f319(f74(a925),x102033),x102032)))+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),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)))))))
% 28.25/28.12 [10204]~P1(f319(f319(f227(a925),f319(f319(f74(a925),x102041),x102044)),f319(f319(f74(a925),x102043),x102042)))+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),x102041),x102042)),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),x102043),x102044)),f180(f932(f931(a925,a925),a923)))))))
% 28.25/28.12 [10294]P1(f319(f319(f226(a925),f319(f319(f74(a925),x102941),x102942)),f319(f319(f74(a925),x102943),x102944)))+~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),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)))))))
% 28.25/28.12 [10295]P1(f319(f319(f227(a925),f319(f319(f74(a925),x102951),x102952)),f319(f319(f74(a925),x102953),x102954)))+~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),x102951),x102954)),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),x102953),x102952)),f180(f932(f931(a925,a925),a923)))))))
% 28.25/28.12 [10337]P1(f319(f319(f226(f932(x103371,a923)),f319(f319(f33(a925,f932(x103371,a923)),f234(f932(a925,a923))),x103372)),f319(f319(f33(a925,f932(x103371,a923)),f234(f932(a925,a923))),x103373)))+~P1(f319(f319(f226(f932(x103371,a923)),f319(f319(f33(a925,f932(x103371,a923)),f319(f294(a925,f2(a925)),f369(x103373,x103374,x103372,x103371))),x103372)),f319(f319(f33(a925,f932(x103371,a923)),f319(f294(a925,f2(a925)),f319(f319(f74(a925),f369(x103373,x103374,x103372,x103371)),x103374))),x103373)))
% 28.25/28.12 [10396]P1(f319(f319(f226(a91),x103964),f2(a91)))+E(f319(f319(f251(f931(a91,a91),f931(x103961,f932(a928,a315)),f931(a91,a91),f931(f932(a91,f932(a923,f929(f927(x103961)))),f931(a91,a91))),f319(x103962,x103963)),f319(f319(f8(f932(f932(a91,f932(a923,f929(f927(x103961)))),f932(f931(a91,a91),f931(f932(a91,f932(a923,f929(f927(x103961)))),f931(a91,a91)))),f932(f931(a91,a91),f931(f932(a91,f932(a923,f929(f927(x103961)))),f931(a91,a91))),f931(x103961,f932(a928,a315))),f319(f251(f931(a91,a91),f932(a91,f932(a923,f929(f927(x103961)))),f931(a91,a91),f931(f932(a91,f932(a923,f929(f927(x103961)))),f931(a91,a91))),f269(x103961,x103962,f319(f319(f23(a91),x103964),f72(a91)),x103963))),f319(f319(f8(f932(f932(a91,f932(a923,f929(f927(x103961)))),f932(a91,f932(a923,f929(f927(x103961))))),f932(f932(a91,f932(a923,f929(f927(x103961)))),f932(f931(a91,a91),f931(f932(a91,f932(a923,f929(f927(x103961)))),f931(a91,a91)))),f931(x103961,f932(a928,a315))),f319(f8(f932(a91,f932(a923,f929(f927(x103961)))),f932(f931(a91,a91),f931(f932(a91,f932(a923,f929(f927(x103961)))),f931(a91,a91))),f932(a91,f932(a923,f929(f927(x103961))))),f244(f932(a91,f932(a923,f929(f927(x103961)))),f931(a91,a91)))),f319(f319(f8(f932(a91,f932(a923,f929(f927(x103961)))),f932(f932(a91,f932(a923,f929(f927(x103961)))),f932(a91,f932(a923,f929(f927(x103961))))),f931(x103961,f932(a928,a315))),f38(x103961)),f319(f319(f8(x103961,f932(a91,f932(a923,f929(f927(x103961)))),f931(x103961,f932(a928,a315))),f36(x103961)),f243(x103961,f932(a928,a315))))))),f269(x103961,x103962,x103964,x103963))
% 28.25/28.12 [10458]~P1(f319(f319(f321(x104582),x104584),f319(f276(x104581,x104582),x104583)))+P1(f319(f242(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))
% 28.25/28.12 [10459]~P1(f319(f319(f321(x104591),x104594),f319(f256(x104591,x104592),x104593)))+P1(f319(f241(x104591,x104592,f319(f319(f7(x104591,f932(f931(x104591,x104592),a923),f932(x104592,a923)),f319(f319(f8(f932(x104592,f932(f932(f931(x104591,x104592),a923),a923)),f932(f932(f931(x104591,x104592),a923),f932(x104592,a923)),x104591),f7(x104592,f932(f931(x104591,x104592),a923),a923)),f319(f319(f8(f932(x104592,f931(x104591,x104592)),f932(x104592,f932(f932(f931(x104591,x104592),a923),a923)),x104591),f319(f8(f931(x104591,x104592),f932(f932(f931(x104591,x104592),a923),a923),x104592),f321(f931(x104591,x104592)))),f244(x104591,x104592)))),x104593)),x104594))
% 28.25/28.12 [10471]P1(f319(f319(f321(x104711),x104712),f319(f276(x104713,x104711),x104714)))+~P1(f319(f242(x104713,x104711,f319(f319(f7(x104713,f932(f931(x104713,x104711),a923),f932(x104711,a923)),f319(f319(f8(f932(x104711,f932(f932(f931(x104713,x104711),a923),a923)),f932(f932(f931(x104713,x104711),a923),f932(x104711,a923)),x104713),f7(x104711,f932(f931(x104713,x104711),a923),a923)),f319(f319(f8(f932(x104711,f931(x104713,x104711)),f932(x104711,f932(f932(f931(x104713,x104711),a923),a923)),x104713),f319(f8(f931(x104713,x104711),f932(f932(f931(x104713,x104711),a923),a923),x104711),f321(f931(x104713,x104711)))),f244(x104713,x104711)))),x104714)),x104712))
% 28.25/28.12 [10472]P1(f319(f319(f321(x104721),x104722),f319(f256(x104721,x104723),x104724)))+~P1(f319(f241(x104721,x104723,f319(f319(f7(x104721,f932(f931(x104721,x104723),a923),f932(x104723,a923)),f319(f319(f8(f932(x104723,f932(f932(f931(x104721,x104723),a923),a923)),f932(f932(f931(x104721,x104723),a923),f932(x104723,a923)),x104721),f7(x104723,f932(f931(x104721,x104723),a923),a923)),f319(f319(f8(f932(x104723,f931(x104721,x104723)),f932(x104723,f932(f932(f931(x104721,x104723),a923),a923)),x104721),f319(f8(f931(x104721,x104723),f932(f932(f931(x104721,x104723),a923),a923),x104723),f321(f931(x104721,x104723)))),f244(x104721,x104723)))),x104724)),x104722))
% 28.25/28.12 [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),x101254)),x101252)),x101253))
% 28.25/28.12 [10126]P1(f319(f152(x101261,x101262),x101263))+~P1(f319(f152(x101261,f319(f319(f18(x101261,a923,a923),f319(f319(f8(a923,f932(a923,a923),x101261),a317),x101262)),x101264)),x101263))
% 28.25/28.12 [10213]~P121(x102131)+E(f319(f319(f75(x102131),f319(f319(f74(x102131),f72(x102131)),f72(x102131))),f319(f319(f6(a925,x102131),f319(f319(f8(x102131,x102131,a925),f319(f74(x102131),x102132)),f319(f319(f7(a925,x102131,x102131),f319(f319(f8(x102131,f932(x102131,x102131),a925),f75(x102131)),f92(x102131))),x102133))),f319(f274(a925),x102134))),f319(f319(f75(x102131),f319(f92(x102131),x102134)),f319(f319(f74(x102131),x102132),f319(f319(f74(x102131),x102132),f319(f319(f75(x102131),f319(f92(x102131),f319(f319(f23(a925),x102134),f72(a925)))),x102133)))))
% 28.25/28.12 [10358]P1(f319(x103581,f570(x103582,x103583,x103584,x103581)))+P38(x103582,f319(f254(f931(x103582,x103582)),f319(f249(x103582,x103582,a923),f319(f319(f8(f932(x103582,a923),f932(x103582,a923),x103582),f319(f18(x103582,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103582),a317),x103581))),f319(f319(f7(x103582,f932(x103582,x103582),f932(x103582,a923)),f319(f319(f8(f932(x103582,a923),f932(f932(x103582,x103582),f932(x103582,a923)),x103582),f8(x103582,a923,x103582)),a316)),x103583)))))
% 28.25/28.12 [10373]~P1(f319(f319(f227(a925),f319(x103734,f319(x103733,f570(x103731,x103733,x103734,x103732)))),f319(x103734,f570(x103731,x103733,x103734,x103732))))+P38(x103731,f319(f254(f931(x103731,x103731)),f319(f249(x103731,x103731,a923),f319(f319(f8(f932(x103731,a923),f932(x103731,a923),x103731),f319(f18(x103731,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103731),a317),x103732))),f319(f319(f7(x103731,f932(x103731,x103731),f932(x103731,a923)),f319(f319(f8(f932(x103731,a923),f932(f932(x103731,x103731),f932(x103731,a923)),x103731),f8(x103731,a923,x103731)),a316)),x103733)))))
% 28.25/28.12 [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))
% 28.25/28.12 [10445]~P6(x104451)+E(f32(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(f32(f932(x104452,x104451),x104453),x104454))
% 28.25/28.12 [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))
% 28.25/28.12 [10447]~P6(x104471)+E(f31(x104471,f319(f254(x104471),f319(f319(f8(f932(f932(x104472,x104471),a923),a923,x104471),f81(f932(x104472,x104471))),f319(f319(f8(f932(f932(x104472,x104471),a923),f932(f932(x104472,x104471),a923),x104471),f319(f18(f932(x104472,x104471),a923,a923),f319(f319(f8(a923,f932(a923,a923),f932(x104472,x104471)),a317),f319(f319(f7(f932(x104472,x104471),f932(f932(x104472,x104471),a923),a923),f321(f932(x104472,x104471))),x104473)))),f319(f319(f7(x104471,f932(f932(x104472,x104471),x104471),f932(f932(x104472,x104471),a923)),f319(f319(f8(f932(x104471,a923),f932(f932(f932(x104472,x104471),x104471),f932(f932(x104472,x104471),a923)),x104471),f8(x104471,a923,f932(x104472,x104471))),a316)),f319(f319(f7(f932(x104472,x104471),x104472,x104471),f5(f932(x104472,x104471))),x104474)))))),f319(f31(f932(x104472,x104471),x104473),x104474))
% 28.25/28.12 [10499]~P1(f319(f319(f321(f931(x104991,x104991)),f319(f319(f244(x104991,x104991),x104993),x104994)),f319(f319(f102(f932(f931(x104991,x104991),a923)),x104992),f299(x104991,f180(f932(f931(x104991,x104991),a923))))))+P1(f319(f319(f319(f319(f102(f932(x104991,f932(x104991,a923))),f319(f319(f7(x104991,f932(f931(x104991,x104991),a923),f932(x104991,a923)),f319(f319(f8(f932(x104991,f932(f932(f931(x104991,x104991),a923),a923)),f932(f932(f931(x104991,x104991),a923),f932(x104991,a923)),x104991),f7(x104991,f932(f931(x104991,x104991),a923),a923)),f319(f319(f8(f932(x104991,f931(x104991,x104991)),f932(x104991,f932(f932(f931(x104991,x104991),a923),a923)),x104991),f319(f8(f931(x104991,x104991),f932(f932(f931(x104991,x104991),a923),a923),x104991),f321(f931(x104991,x104991)))),f244(x104991,x104991)))),x104992)),a316),x104993),x104994))
% 28.25/28.12 [10510]P1(f319(f319(f321(f931(x105101,x105101)),f319(f319(f244(x105101,x105101),x105102),x105103)),f319(f319(f102(f932(f931(x105101,x105101),a923)),x105104),f299(x105101,f180(f932(f931(x105101,x105101),a923))))))+~P1(f319(f319(f319(f319(f102(f932(x105101,f932(x105101,a923))),f319(f319(f7(x105101,f932(f931(x105101,x105101),a923),f932(x105101,a923)),f319(f319(f8(f932(x105101,f932(f932(f931(x105101,x105101),a923),a923)),f932(f932(f931(x105101,x105101),a923),f932(x105101,a923)),x105101),f7(x105101,f932(f931(x105101,x105101),a923),a923)),f319(f319(f8(f932(x105101,f931(x105101,x105101)),f932(x105101,f932(f932(f931(x105101,x105101),a923),a923)),x105101),f319(f8(f931(x105101,x105101),f932(f932(f931(x105101,x105101),a923),a923),x105101),f321(f931(x105101,x105101)))),f244(x105101,x105101)))),x105104)),a316),x105102),x105103))
% 28.25/28.12 [10455]E(f319(f319(f143(f926(x104551)),f319(f319(f143(x104551),x104552),f319(f134(f926(x104551),f926(x104551),f126(x104551),f105(x104551)),f319(f319(f146(f926(x104551),f926(x104551)),f148(f926(x104551),x104551,f105(x104551),f319(f319(f8(f926(x104551),f932(f926(x104551),f926(x104551)),x104551),f16(f926(x104551),f926(x104551))),f319(f319(f7(x104551,f926(x104551),f926(x104551)),f143(x104551)),f105(x104551))))),x104553)))),f171(x104551,f319(f319(f143(f926(x104551)),x104554),f319(f134(f926(f926(x104551)),f926(f926(x104551)),f126(f926(x104551)),f105(f926(x104551))),f319(f319(f146(f926(x104551),f926(f926(x104551))),f148(f926(f926(x104551)),x104551,f105(f926(x104551)),f319(f16(f932(f926(x104551),f926(f926(x104551))),x104551),f319(f319(f7(f926(x104551),f926(f926(x104551)),f926(f926(x104551))),f143(f926(x104551))),f105(f926(x104551)))))),x104553))))),f171(x104551,f319(f319(f143(f926(x104551)),f319(f319(f143(x104551),x104552),x104554)),x104553)))+~P1(f319(f307(f926(f926(x104551)),f172(x104551)),f319(f319(f143(f926(x104551)),f319(f319(f143(x104551),x104552),x104554)),x104553)))
% 28.25/28.12 [10498]~P1(f319(f55(x104982),f319(f254(x104982),x104984)))+P1(f319(f55(x104981),f319(f254(x104981),f319(f319(f8(f932(x104982,a923),a923,x104981),f81(x104982)),f319(f319(f7(x104981,f932(x104982,a923),f932(x104982,a923)),f319(f319(f8(f932(x104982,f932(a923,a923)),f932(f932(x104982,a923),f932(x104982,a923)),x104981),f18(x104982,a923,a923)),f319(f319(f8(f932(x104982,a923),f932(x104982,f932(a923,a923)),x104981),f319(f8(a923,f932(a923,a923),x104982),a317)),f319(f319(f7(x104981,f932(x104982,x104981),f932(x104982,a923)),f319(f319(f8(f932(x104981,a923),f932(f932(x104982,x104981),f932(x104982,a923)),x104981),f8(x104981,a923,x104982)),a316)),x104983)))),x104984)))))
% 28.25/28.12 [8983]P26(x89831,x89832,x89833,x89834)+~P27(x89831,x89832,x89833,x89834,x89835)
% 28.25/28.12 [8984]P26(x89841,x89842,x89843,x89844)+~P27(x89841,x89842,x89843,x89844,x89845)
% 28.25/28.12 [5475]E(x54751,x54752)+~E(f161(x54753,x54751,x54754),f161(x54753,x54752,x54755))
% 28.25/28.12 [5476]E(x54761,x54762)+~E(f118(x54763,x54764,x54761),f118(x54763,x54765,x54762))
% 28.25/28.12 [5477]E(x54771,x54772)+~E(f118(x54773,x54771,x54774),f118(x54773,x54772,x54775))
% 28.25/28.12 [8305]~E(f319(x83053,x83054),x83055)+E(f68(x83051,x83052,x83053,x83054,x83055),x83053)
% 28.25/28.12 [8306]~E(f319(x83063,x83064),x83065)+E(f68(x83061,x83062,x83063,x83064,x83065),x83063)
% 28.25/28.12 [8842]~E(f68(x88424,x88425,x88421,x88422,x88423),x88421)+E(f319(x88421,x88422),x88423)
% 28.25/28.12 [9467]~P27(x94672,x94671,x94674,x94673,x94675)+P27(x94671,x94672,f71(x94672,x94671,x94673,x94674),x94675,x94673)
% 28.25/28.12 [9468]~P27(x94682,x94681,x94684,x94683,x94685)+P27(x94681,x94682,f85(x94682,x94681,x94683,x94684),x94685,x94683)
% 28.25/28.12 [6280]P1(f319(f242(x62801,x62802,x62803),x62804))+~P1(f319(f319(x62803,x62805),x62804))
% 28.25/28.12 [6281]P1(f319(f242(x62811,x62812,x62813),x62814))+~P1(f319(f319(x62813,x62815),x62814))
% 28.25/28.12 [6282]P1(f319(f241(x62821,x62822,x62823),x62824))+~P1(f319(f319(x62823,x62824),x62825))
% 28.25/28.12 [6283]P1(f319(f241(x62831,x62832,x62833),x62834))+~P1(f319(f319(x62833,x62834),x62835))
% 28.25/28.12 [6757]~E(x67575,f2(a91))+E(f319(f188(x67571,x67572,x67573,x67574),x67575),f116(x67572))
% 28.25/28.12 [6758]~E(x67585,f2(a91))+E(f319(f190(x67581,x67582,x67583,x67584),x67585),f107(x67582))
% 28.25/28.12 [6899]~E(x68993,f2(a91))+E(f319(f265(x68991,x68992,x68993,x68994),x68995),f319(f244(x68991,x68992),x68995))
% 28.25/28.12 [7951]~P22(x79514,x79511,x79512,x79515)+E(f319(f66(x79511,x79511,x79511,f319(x79512,x79513)),f319(x79512,x79513)),f319(x79512,x79513))
% 28.25/28.12 [8346]~P18(x83465,x83461,x83462)+E(f319(f66(x83461,x83461,x83461,f319(x83462,x83463)),f319(x83462,x83464)),f319(f66(x83461,x83461,x83461,f319(x83462,x83464)),f319(x83462,x83463)))
% 28.25/28.12 [8674]P1(f319(f319(f321(f931(x86741,x86741)),f319(f319(f244(x86741,x86741),x86742),x86743)),f313(x86741,x86744,x86745)))+~P1(f319(f319(f227(a925),f319(x86744,x86742)),f319(x86744,x86743)))
% 28.25/28.12 [8769]~P1(f319(f319(f321(x87694),x87693),f291(x87694,x87691,x87692,x87695)))+P1(f319(f319(x87691,x87692),x87693))
% 28.25/28.12 [8770]~P1(f319(f319(f321(x87704),x87703),f282(x87704,x87701,x87702,x87705)))+P1(f319(f319(x87701,x87702),x87703))
% 28.25/28.12 [8771]~P1(f319(f319(f321(x87714),x87712),f291(x87714,x87711,x87715,x87713)))+P1(f319(f319(x87711,x87712),x87713))
% 28.25/28.12 [8772]~P1(f319(f319(f321(x87724),x87722),f282(x87724,x87721,x87725,x87723)))+P1(f319(f319(x87721,x87722),x87723))
% 28.25/28.12 [8854]~P27(x88541,x88543,x88545,x88542,x88544)+E(f319(f29(x88541),x88542),f319(f29(x88543),x88544))
% 28.25/28.12 [8902]~P27(x89021,x89022,x89023,x89024,x89025)+E(f319(f302(x89021,x89022,x89023),x89024),x89025)
% 28.25/28.12 [8922]~P61(x89222,x89221,x89225,x89223,x89224)+E(f319(f302(x89221,x89222,x89223),x89224),f234(f932(x89222,a923)))
% 28.25/28.12 [9375]~P35(x93751,x93752,x93753,x93754,x93755)+P35(x93751,x93752,x93753,f319(f160(x93751),x93754),f319(f160(x93752),x93755))
% 28.25/28.12 [9377]~P35(x93771,x93772,x93773,f319(f160(x93771),x93774),x93775)+P35(x93771,x93772,x93773,x93774,f319(f160(x93772),x93775))
% 28.25/28.12 [9378]~P35(x93781,x93782,x93783,x93784,f319(f160(x93782),x93785))+P35(x93781,x93782,x93783,f319(f160(x93781),x93784),x93785)
% 28.25/28.12 [9384]P35(x93841,x93842,x93843,x93844,x93845)+~P35(x93841,x93842,x93843,f319(f160(x93841),x93844),f319(f160(x93842),x93845))
% 28.25/28.12 [9792]P1(f319(f319(f321(f931(f926(x97921),f926(x97921))),f319(f319(f244(f926(x97921),f926(x97921)),f319(f319(f143(x97921),x97922),x97923)),f319(f319(f143(x97921),x97922),x97924))),f149(x97921,x97925)))+~P1(f319(f319(f321(f931(f926(x97921),f926(x97921))),f319(f319(f244(f926(x97921),f926(x97921)),x97923),x97924)),f149(x97921,x97925)))
% 28.25/28.12 [9793]P1(f319(f319(f321(f931(f926(x97931),f926(x97931))),f319(f319(f244(f926(x97931),f926(x97931)),f319(f319(f126(x97931),x97932),x97933)),f319(f319(f126(x97931),x97932),x97934))),f139(x97931,x97935)))+~P1(f319(f319(f321(f931(f926(x97931),f926(x97931))),f319(f319(f244(f926(x97931),f926(x97931)),x97933),x97934)),f139(x97931,x97935)))
% 28.25/28.12 [10002]E(f319(f319(f143(x100021),f672(x100022,x100023,x100024,x100025,x100021)),f674(x100022,x100023,x100024,x100025,x100021)),x100025)+~P1(f319(f319(f321(f931(f926(x100021),f926(x100021))),f319(f319(f244(f926(x100021),f926(x100021)),x100025),f319(f319(f143(x100021),x100024),x100023))),f150(x100021,x100022)))
% 28.25/28.12 [10025]E(f319(f319(f143(x100251),f675(x100252,x100253,x100254,x100255,x100251)),f676(x100252,x100253,x100254,x100255,x100251)),x100253)+~P1(f319(f319(f321(f931(f926(x100251),f926(x100251))),f319(f319(f244(f926(x100251),f926(x100251)),f319(f319(f143(x100251),x100255),x100254)),x100253)),f150(x100251,x100252)))
% 28.25/28.12 [10175]~P1(f319(f319(f321(f931(f926(x101751),f926(x101751))),f319(f319(f244(f926(x101751),f926(x101751)),f319(f319(f143(x101751),x101755),x101752)),x101754)),f150(x101751,x101753)))+P1(f319(f319(f321(f931(f926(x101751),f926(x101751))),f319(f319(f244(f926(x101751),f926(x101751)),x101752),f676(x101753,x101754,x101752,x101755,x101751))),f150(x101751,x101753)))
% 28.25/28.12 [10258]~P1(f319(f319(f321(f931(f926(x102581),f926(x102581))),f319(f319(f244(f926(x102581),f926(x102581)),x102585),f319(f319(f143(x102581),x102584),x102583))),f150(x102581,x102582)))+P1(f319(f319(f321(f931(f926(x102581),f926(x102581))),f319(f319(f244(f926(x102581),f926(x102581)),f674(x102582,x102583,x102584,x102585,x102581)),x102583)),f150(x102581,x102582)))
% 28.25/28.12 [10449]P1(f319(f319(f321(f931(x104491,x104491)),f319(f319(f244(x104491,x104491),f319(x104492,f319(f319(f74(a925),x104493),x104494))),f319(x104492,x104493))),f299(x104491,x104495)))+~P1(f319(f319(f321(f931(x104491,x104491)),f319(f319(f244(x104491,x104491),f319(x104492,f319(a104,f624(x104494,x104493,x104495,x104492,x104491)))),f319(x104492,f624(x104494,x104493,x104495,x104492,x104491)))),f299(x104491,x104495)))
% 28.25/28.12 [5449]E(x54491,x54492)+~E(f319(f319(f143(x54493),x54494),x54491),f319(f319(f143(x54493),x54495),x54492))
% 28.25/28.12 [5450]E(x54501,x54502)+~E(f319(f319(f143(x54503),x54501),x54504),f319(f319(f143(x54503),x54502),x54505))
% 28.25/28.12 [5492]P1(f319(x54921,x54922))+~E(f319(f128(x54923,x54921),x54924),f319(f319(f143(x54923),x54922),x54925))
% 28.25/28.12 [5493]P1(f319(x54931,x54932))+~E(f319(f319(f143(x54933),x54932),x54934),f319(f128(x54933,x54931),x54935))
% 28.25/28.12 [5650]~E(f319(f319(f130(x56501),x56503),x56502),f319(f319(f143(x56501),x56504),x56505))+E(f319(f319(f156(x56501),x56502),x56503),x56504)
% 28.25/28.12 [5788]~P16(x57884,x57885,x57881)+E(f319(f319(x57881,x57882),f319(f319(x57881,x57882),x57883)),f319(f319(x57881,x57882),x57883))
% 28.25/28.12 [6339]~E(x63394,f2(a91))+E(f319(f319(f109(x63391,x63392,x63393),x63394),x63395),f319(f319(f244(f926(x63392),x63391),f105(x63392)),x63395))
% 28.25/28.12 [6408]~P4(x64082)+~E(f319(f319(f140(x64081,x64082,x64083),x64084),x64085),f105(x64081))
% 28.25/28.12 [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))))
% 28.25/28.12 [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))))
% 28.25/28.12 [7121]E(f319(f319(f301(x71211),f319(x71212,x71213)),f319(f302(x71214,x71211,x71212),x71215)),f319(f302(x71214,x71211,x71212),x71215))+~P1(f319(f319(f321(x71214),x71213),x71215))
% 28.25/28.12 [7127]~P1(f319(x71274,f319(x71273,x71275)))+P1(f319(f319(f303(x71271,x71272,x71273),x71274),x71275))
% 28.25/28.12 [7128]~P1(f319(f319(x71283,x71285),x71284))+P1(f319(f319(f235(x71281,x71282,x71283),x71284),x71285))
% 28.25/28.12 [7129]~P1(f319(f319(x71293,x71295),x71294))+P1(f319(f319(f235(x71291,x71292,x71293),x71294),x71295))
% 28.25/28.12 [7130]~P1(f319(f319(x71303,x71305),x71304))+P1(f319(f319(f235(x71301,x71302,x71303),x71304),x71305))
% 28.25/28.12 [7225]~E(f319(f302(x72251,x72252,x72253),x72254),x72255)+E(f319(f302(f932(x72251,a923),f932(x72252,a923),f302(x72251,x72252,x72253)),f319(f300(x72251),x72254)),f319(f300(x72252),x72255))
% 28.25/28.12 [7252]E(f319(f263(x72521,x72522,x72523,x72524),x72525),f319(x72524,x72525))+~P1(f319(f319(f321(x72521),x72525),x72523))
% 28.25/28.12 [7566]P26(x75661,x75662,x75663,x75664)+~P26(x75661,x75662,x75663,f319(f319(f301(x75661),x75665),x75664))
% 28.25/28.12 [7670]~P1(f319(f319(f321(x76704),x76703),x76705))+P1(f319(f319(f321(x76701),f319(x76702,x76703)),f319(f302(x76704,x76701,x76702),x76705)))
% 28.25/28.12 [7691]~P4(x76912)+E(f142(x76911,x76912,x76913,f319(f128(x76911,x76914),x76915)),f319(f128(x76911,x76914),f142(x76911,x76912,x76913,x76915)))
% 28.25/28.12 [7721]P1(f319(x77211,f319(x77212,x77213)))+~P1(f319(f319(f303(x77214,x77215,x77212),x77211),x77213))
% 28.25/28.12 [7722]P1(f319(f319(x77221,x77222),x77223))+~P1(f319(f319(f235(x77224,x77225,x77221),x77223),x77222))
% 28.25/28.12 [7723]P1(f319(f319(x77231,x77232),x77233))+~P1(f319(f319(f235(x77234,x77235,x77231),x77233),x77232))
% 28.25/28.12 [7724]P1(f319(f319(x77241,x77242),x77243))+~P1(f319(f319(f235(x77244,x77245,x77241),x77243),x77242))
% 28.25/28.12 [7786]~P1(f319(f319(f321(x77863),f319(x77864,x77862)),x77865))+P1(f319(f319(f321(x77861),x77862),f319(f303(x77861,x77863,x77864),x77865)))
% 28.25/28.12 [7787]~P1(f319(f319(f321(x77873),f319(x77874,x77872)),x77875))+P1(f319(f319(f321(x77871),x77872),f319(f303(x77871,x77873,x77874),x77875)))
% 28.25/28.12 [8185]~P1(f319(f319(f321(x81855),x81853),f319(f303(x81855,x81851,x81852),x81854)))+P1(f319(f319(f321(x81851),f319(x81852,x81853)),x81854))
% 28.25/28.12 [8186]~P1(f319(f319(f321(x81865),x81863),f319(f303(x81865,x81861,x81862),x81864)))+P1(f319(f319(f321(x81861),f319(x81862,x81863)),x81864))
% 28.25/28.12 [8486]~P18(x84862,x84861,x84863)+E(f319(f134(x84861,x84862,f319(f7(x84862,x84861,x84861),x84863),x84864),f144(x84862,x84865)),f319(f319(f58(x84862,x84861,x84863),x84864),f319(f164(x84862),x84865)))
% 28.25/28.12 [8508]E(f319(x85081,f760(x85082,x85081,x85083,x85084)),x85084)+~P1(f319(f319(f321(x85085),x85084),f319(f302(x85083,x85085,x85081),x85082)))
% 28.25/28.12 [8509]E(f319(x85091,f813(x85092,x85091,x85093,x85094)),x85094)+~P1(f319(f319(f321(x85095),x85094),f319(f302(x85093,x85095,x85091),x85092)))
% 28.25/28.12 [8817]~E(x88172,f319(f319(f143(x88171),x88174),x88175))+P1(f319(f319(f321(f931(f926(x88171),f926(x88171))),f319(f319(f244(f926(x88171),f926(x88171)),f105(x88171)),x88172)),f139(x88171,x88173)))
% 28.25/28.12 [8863]E(f319(x88631,f319(f85(x88632,x88633,x88634,x88631),x88635)),x88635)+~P1(f319(f319(f321(x88633),x88635),f319(f302(x88632,x88633,x88631),x88634)))
% 28.25/28.12 [8866]P26(x88661,x88662,f85(x88662,x88661,x88663,x88664),x88665)+~P1(f319(f319(f226(f932(x88661,a923)),x88665),f319(f302(x88662,x88661,x88664),x88663)))
% 28.25/28.12 [8871]~P35(x88711,x88713,x88715,x88712,x88714)+E(f319(f181(f926(x88711)),x88712),f319(f181(f926(x88713)),x88714))
% 28.25/28.12 [8872]~P35(x88721,x88723,x88725,x88722,x88724)+E(f319(f181(f926(x88721)),x88722),f319(f181(f926(x88723)),x88724))
% 28.25/28.12 [8873]~P35(x88731,x88733,x88735,x88732,x88734)+E(f319(f181(f926(x88731)),x88732),f319(f181(f926(x88733)),x88734))
% 28.25/28.12 [8884]P1(f319(f319(f226(f932(x88841,a923)),f319(f319(f34(x88842,f932(x88841,a923)),x88843),x88844)),f319(x88844,x88845)))+~P1(f319(f319(f321(x88842),x88845),x88843))
% 28.25/28.12 [8938]~P61(x89381,x89382,x89383,x89385,x89384)+E(f319(f302(x89381,x89382,x89383),f234(f932(x89381,a923))),x89384)
% 28.25/28.12 [9167]E(f319(f128(x91671,x91672),f763(x91673,x91674,x91675,x91672,x91671)),x91673)+~E(f319(f128(x91671,x91672),x91675),f319(f319(f143(x91671),x91674),x91673))
% 28.25/28.12 [9168]E(f319(f128(x91681,x91682),f764(x91683,x91682,x91684,x91685,x91681)),x91684)+~E(f319(f319(f143(x91681),x91685),x91684),f319(f128(x91681,x91682),x91683))
% 28.25/28.12 [9263]E(f319(f181(f926(x92631)),x92632),x92633)+~P1(f319(f319(f321(f931(f926(x92631),f926(x92631))),f319(f319(f244(f926(x92631),f926(x92631)),x92634),x92632)),f319(f135(x92631,x92635),x92633)))
% 28.25/28.12 [9264]E(f319(f181(f926(x92641)),x92642),x92643)+~P1(f319(f319(f321(f931(f926(x92641),f926(x92641))),f319(f319(f244(f926(x92641),f926(x92641)),x92642),x92644)),f319(f135(x92641,x92645),x92643)))
% 28.25/28.12 [9333]P1(f319(f319(f321(x93331),f760(x93332,x93333,x93331,x93334)),x93332))+~P1(f319(f319(f321(x93335),x93334),f319(f302(x93331,x93335,x93333),x93332)))
% 28.25/28.12 [9334]P1(f319(f319(f321(x93341),f813(x93342,x93343,x93341,x93344)),x93342))+~P1(f319(f319(f321(x93345),x93344),f319(f302(x93341,x93345,x93343),x93342)))
% 28.25/28.12 [9493]~P41(f932(x94933,a923),f932(x94931,a923),x94932)+P1(f319(f319(f226(f932(x94931,a923)),f319(x94932,f319(f319(f93(f932(x94933,a923)),x94934),x94935))),f319(f319(f93(f932(x94931,a923)),f319(x94932,x94934)),f319(x94932,x94935))))
% 28.25/28.12 [9495]E(f319(f302(x94951,x94952,x94953),f770(x94954,x94953,x94951,x94955,x94952)),x94955)+~P1(f319(f319(f226(f932(x94952,a923)),x94955),f319(f302(x94951,x94952,x94953),x94954)))
% 28.25/28.12 [9810]P1(f319(f319(f321(f931(f926(x98101),f926(x98101))),f319(f319(f244(f926(x98101),f926(x98101)),f319(f319(f143(x98101),x98102),x98103)),f319(f319(f143(x98101),x98102),x98104))),f299(f926(x98101),f149(x98101,x98105))))+~P1(f319(f319(f321(f931(f926(x98101),f926(x98101))),f319(f319(f244(f926(x98101),f926(x98101)),x98103),x98104)),f299(f926(x98101),f149(x98101,x98105))))
% 28.25/28.12 [9841]~E(f319(x98413,f715(x98415,x98414,x98413,x98412,x98411)),f319(x98415,f715(x98415,x98414,x98413,x98412,x98411)))+E(f319(f319(f146(x98411,x98412),x98413),x98414),f319(f319(f146(x98411,x98412),x98415),x98414))
% 28.25/28.12 [9919]~E(f319(f128(x99191,x99195),x99194),f319(f319(f143(x99191),x99193),x99192))+E(f319(f319(f126(x99191),f767(x99192,x99193,x99194,x99195,x99191)),f319(f319(f143(x99191),x99193),f763(x99192,x99193,x99194,x99195,x99191))),x99194)
% 28.25/28.12 [9920]~E(f319(f319(f143(x99201),x99205),x99204),f319(f128(x99201,x99203),x99202))+E(f319(f319(f126(x99201),f765(x99202,x99203,x99204,x99205,x99201)),f319(f319(f143(x99201),x99205),f764(x99202,x99203,x99204,x99205,x99201))),x99202)
% 28.25/28.12 [9924]E(f319(f319(f146(x99241,x99242),x99243),x99244),f319(f319(f146(x99241,x99242),x99245),x99244))+P1(f319(f319(f321(x99241),f715(x99243,x99244,x99245,x99242,x99241)),f319(f164(x99241),x99244)))
% 28.25/28.12 [9960]~P1(f319(f319(f321(x99605),x99604),f319(f277(x99601,x99605,x99603),x99602)))+P1(f319(f319(f321(x99601),f530(x99602,x99603,x99601,x99604,x99605)),x99602))
% 28.25/28.12 [9961]~P1(f319(f319(f321(x99615),x99614),f319(f277(x99611,x99615,x99613),x99612)))+P1(f319(f319(f321(x99611),f556(x99612,x99613,x99611,x99614,x99615)),x99612))
% 28.25/28.12 [9996]~P1(f319(f319(f226(f932(x99965,a923)),x99964),f319(f302(x99961,x99965,x99963),x99962)))+P1(f319(f319(f226(f932(x99961,a923)),f770(x99962,x99963,x99961,x99964,x99965)),x99962))
% 28.25/28.12 [10450]E(x104501,f2(a91))+E(f215(f931(f926(x104502),x104503),f931(x104502,x104503),f319(f319(f244(f926(x104502),x104503),f105(x104502)),x104504),f319(f249(x104502,x104503,f931(f926(x104502),x104503)),f319(f319(f7(x104502,f932(x104503,f931(f926(x104502),x104503)),f932(x104503,f931(f926(x104502),x104503))),f319(f319(f8(f932(f931(f926(x104502),x104503),f931(f926(x104502),x104503)),f932(f932(x104503,f931(f926(x104502),x104503)),f932(x104503,f931(f926(x104502),x104503))),x104502),f8(f931(f926(x104502),x104503),f931(f926(x104502),x104503),x104503)),f319(f319(f8(f932(f926(x104502),f932(x104503,f931(f926(x104502),x104503))),f932(f931(f926(x104502),x104503),f931(f926(x104502),x104503)),x104502),f249(f926(x104502),x104503,f931(f926(x104502),x104503))),f319(f319(f8(f932(f926(x104502),f926(x104502)),f932(f926(x104502),f932(x104503,f931(f926(x104502),x104503))),x104502),f319(f8(f926(x104502),f932(x104503,f931(f926(x104502),x104503)),f926(x104502)),f244(f926(x104502),x104503))),f143(x104502))))),f319(f109(x104503,x104502,x104505),f319(f319(f23(a91),x104501),f72(a91))))),f319(x104505,x104504)),f319(f319(f109(x104503,x104502,x104505),x104501),x104504))
% 28.25/28.12 [6222]E(x62221,x62222)+~E(f319(f248(x62223,x62224),f319(f319(f244(x62223,x62224),x62225),x62221)),x62222)
% 28.25/28.12 [6223]E(x62231,x62232)+~E(f319(f243(x62233,x62234),f319(f319(f244(x62233,x62234),x62231),x62235)),x62232)
% 28.25/28.12 [6482]~E(x64823,f319(f319(f126(x64821),x64824),f319(f319(f143(x64821),x64822),x64825)))+P1(f319(f319(f321(x64821),x64822),f319(f164(x64821),x64823)))
% 28.25/28.12 [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))
% 28.25/28.12 [6960]E(f319(f319(f102(f932(x69601,a923)),f319(f164(x69601),x69602)),f319(f164(x69601),x69603)),f319(f164(x69601),x69604))+~E(f158(x69601,x69605,x69604),f319(f319(f244(f926(x69601),f926(x69601)),x69602),x69603))
% 28.25/28.12 [7059]~P4(x70592)+E(f319(f181(f926(x70591)),f319(f319(f140(x70591,x70592,x70593),x70594),x70595)),f319(a104,f319(f181(f926(x70591)),x70595)))
% 28.25/28.12 [7075]~P4(x70752)+E(f319(f164(x70751),f319(f319(f140(x70751,x70752,x70753),x70754),x70755)),f319(f319(f301(x70751),x70754),f319(f164(x70751),x70755)))
% 28.25/28.12 [7347]~P121(x73471)+E(f319(f319(f75(x73471),f319(f319(f75(x73471),x73472),x73473)),f319(f319(f75(x73471),x73474),x73475)),f319(f319(f75(x73471),f319(f319(f75(x73471),x73472),x73474)),f319(f319(f75(x73471),x73473),x73475)))
% 28.25/28.12 [7348]~P121(x73481)+E(f319(f319(f74(x73481),f319(f319(f74(x73481),x73482),x73483)),f319(f319(f74(x73481),x73484),x73485)),f319(f319(f74(x73481),f319(f319(f74(x73481),x73482),x73484)),f319(f319(f74(x73481),x73483),x73485)))
% 28.25/28.12 [7349]~P72(x73491)+E(f319(f319(f283(x73491),f319(f319(f75(x73491),x73492),x73493)),f319(f319(f75(x73491),x73494),x73495)),f319(f319(f75(x73491),f319(f319(f283(x73491),x73492),x73494)),f319(f319(f283(x73491),x73493),x73495)))
% 28.25/28.12 [7363]~P4(x73631)+E(f295(x73631,f319(f319(f225(x73631),x73632),x73633),f319(f319(f224(x73631),x73634),x73635)),f319(f319(f93(f932(x73631,a923)),f295(x73631,x73632,x73634)),f295(x73631,x73633,x73635)))
% 28.25/28.12 [7364]~P4(x73641)+E(f297(x73641,f319(f319(f225(x73641),x73642),x73643),f319(f319(f224(x73641),x73644),x73645)),f319(f319(f93(f932(x73641,a923)),f297(x73641,x73642,x73644)),f297(x73641,x73643,x73645)))
% 28.25/28.12 [7365]~P4(x73651)+E(f298(x73651,f319(f319(f225(x73651),x73652),x73653),f319(f319(f224(x73651),x73654),x73655)),f319(f319(f93(f932(x73651,a923)),f298(x73651,x73652,x73654)),f298(x73651,x73653,x73655)))
% 28.25/28.12 [7366]~P4(x73661)+E(f319(f319(f93(f932(x73661,a923)),f319(f294(x73661,x73662),x73663)),f319(f294(x73661,x73664),x73665)),f319(f294(x73661,f319(f319(f225(x73661),x73662),x73664)),f319(f319(f224(x73661),x73663),x73665)))
% 28.25/28.12 [7488]~P1(f319(x74881,f529(x74883,x74882,x74881)))+P1(f319(x74881,f319(f319(f244(x74882,x74883),x74884),x74885)))
% 28.25/28.12 [7596]~E(x75962,f319(x75964,x75965))+P1(f319(f319(f321(x75961),x75962),f319(f302(x75963,x75961,x75964),f234(f932(x75963,a923)))))
% 28.25/28.12 [7667]~P16(x76673,x76672,x76674)+P16(x76671,x76672,f319(f319(f8(x76673,f932(x76672,x76672),x76671),x76674),x76675))
% 28.25/28.12 [7668]~P18(x76683,x76682,x76684)+P18(x76681,x76682,f319(f319(f8(x76683,f932(x76682,x76682),x76681),x76684),x76685))
% 28.25/28.12 [7804]~P26(x78041,x78042,x78043,x78044)+P26(x78041,x78042,x78043,f319(f319(f23(f932(x78041,a923)),x78044),x78045))
% 28.25/28.12 [7959]~P1(f319(f319(x79593,x79594),x79595))+P1(f319(f319(f249(x79591,x79592,a923),x79593),f319(f319(f244(x79591,x79592),x79594),x79595)))
% 28.25/28.12 [7960]~P1(f319(f319(x79603,x79604),x79605))+P1(f319(f319(f249(x79601,x79602,a923),x79603),f319(f319(f244(x79601,x79602),x79604),x79605)))
% 28.25/28.12 [8074]~P1(f319(x80742,x80744))+~E(f319(f319(f130(x80741),f319(f181(f926(x80741)),f169(x80741,x80742,x80743))),x80743),f319(f319(f143(x80741),x80744),x80745))
% 28.25/28.12 [8094]P26(x80941,x80942,x80943,x80944)+~P26(x80941,x80942,x80943,f319(f319(f102(f932(x80941,a923)),x80945),x80944))
% 28.25/28.12 [8095]P26(x80951,x80952,x80953,x80954)+~P26(x80951,x80952,x80953,f319(f319(f102(f932(x80951,a923)),x80954),x80955))
% 28.25/28.12 [8142]~P4(x81422)+E(f319(f319(f140(x81421,x81422,x81423),x81424),f142(x81421,x81422,x81423,x81425)),f142(x81421,x81422,x81423,f319(f319(f143(x81421),x81424),x81425)))
% 28.25/28.12 [8462]~P16(x84622,x84621,x84623)+E(f319(f134(x84621,x84622,f319(f7(x84622,x84621,x84621),x84623),x84624),x84625),f319(f319(f58(x84622,x84621,x84623),x84624),f319(f164(x84622),x84625)))
% 28.25/28.12 [8491]~E(f319(f319(f130(x84911),f319(f181(f926(x84911)),f169(x84911,x84912,x84913))),x84913),f319(f319(f143(x84911),x84914),x84915))+E(f319(f319(f126(x84911),f169(x84911,x84912,x84913)),f319(f319(f143(x84911),x84914),x84915)),x84913)
% 28.25/28.12 [8519]P1(f319(f319(x85191,x85192),x85193))+~P1(f319(f319(f249(x85194,x85195,a923),x85191),f319(f319(f244(x85194,x85195),x85192),x85193)))
% 28.25/28.12 [9002]P1(f319(f319(f226(f932(x90021,a923)),f319(f302(x90022,x90021,x90023),x90024)),f319(f302(x90022,x90021,x90023),x90025)))+~P1(f319(f319(f226(f932(x90022,a923)),x90024),x90025))
% 28.25/28.12 [9003]P1(f319(f319(f226(f932(x90031,a923)),f319(f303(x90031,x90032,x90033),x90034)),f319(f303(x90031,x90032,x90033),x90035)))+~P1(f319(f319(f226(f932(x90032,a923)),x90034),x90035))
% 28.25/28.12 [9082]E(x90821,f2(a91))+E(f319(f319(f251(x90822,x90823,x90822,f931(x90823,x90822)),f319(x90824,x90825)),f265(x90823,x90822,f319(f319(f23(a91),x90821),f72(a91)),x90824)),f319(f265(x90823,x90822,x90821,x90824),x90825))
% 28.25/28.12 [9194]P1(f319(f319(f247(x91941,x91942,a923,x91943),x91944),x91945))+~P1(f319(x91943,f319(f319(f244(x91941,x91942),x91944),x91945)))
% 28.25/28.12 [9472]~P1(f319(f319(f247(x94722,x94723,a923,x94721),x94724),x94725))+P1(f319(x94721,f319(f319(f244(x94722,x94723),x94724),x94725)))
% 28.25/28.12 [9473]~P1(f319(f319(f247(x94732,x94733,a923,x94731),x94734),x94735))+P1(f319(x94731,f319(f319(f244(x94732,x94733),x94734),x94735)))
% 28.25/28.12 [9659]~P1(f319(f319(f321(x96592),x96595),f319(f302(x96591,x96592,x96594),x96593)))+P1(f319(f319(f321(x96591),f319(f85(x96591,x96592,x96593,x96594),x96595)),x96593))
% 28.25/28.12 [9750]~P1(f319(f55(x97503),f319(f302(x97502,x97503,x97505),f234(f932(x97502,a923)))))+P1(f319(f55(x97501),f319(f302(x97502,x97501,f319(f319(f8(x97503,x97501,x97502),x97504),x97505)),f234(f932(x97502,a923)))))
% 28.25/28.12 [9777]P1(f319(f319(f226(f932(f932(x97771,a923),a923)),f319(f302(f932(x97772,a923),f932(x97771,a923),f302(x97772,x97771,x97773)),f319(f300(x97772),x97774))),f319(f300(x97771),x97775)))+~P1(f319(f319(f226(f932(x97771,a923)),f319(f302(x97772,x97771,x97773),x97774)),x97775))
% 28.25/28.12 [9849]E(x98491,x98492)+~P1(f319(f60(x98493,x98494,x98495,x98491,f180(f932(x98493,a923))),x98492))
% 28.25/28.12 [9866]E(f319(f319(f244(x98661,x98662),f584(x98663,x98664,x98665,x98662,x98661)),f585(x98663,x98664,x98665,x98662,x98661)),x98665)+~P1(f319(f319(f321(f931(x98661,x98662)),x98665),f319(f319(f246(x98661,x98662),x98664),x98663)))
% 28.25/28.12 [9966]P1(f319(f319(f321(x99661),f584(x99662,x99663,x99664,x99665,x99661)),x99663))+~P1(f319(f319(f321(f931(x99661,x99665)),x99664),f319(f319(f246(x99661,x99665),x99663),x99662)))
% 28.25/28.12 [9978]P1(f319(f319(f321(x99781),f824(x99782,x99783,x99784,x99785,x99781)),x99785))+P1(f319(f319(f226(f932(x99784,a923)),f319(f302(x99781,x99784,x99783),x99785)),x99782))
% 28.25/28.12 [10134]P1(f319(f319(f321(x101341),f585(x101342,x101343,x101344,x101341,x101345)),f319(x101342,f584(x101342,x101343,x101344,x101341,x101345))))+~P1(f319(f319(f321(f931(x101345,x101341)),x101344),f319(f319(f246(x101345,x101341),x101343),x101342)))
% 28.25/28.12 [10154]P1(f319(f319(f321(f931(x101541,x101541)),f319(f319(f244(x101541,x101541),x101542),f645(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)))
% 28.25/28.12 [10155]P1(f319(f319(f321(f931(x101551,x101551)),f319(f319(f244(x101551,x101551),x101552),f647(x101553,x101554,x101555,x101552,x101551))),x101553))+~P1(f319(f319(f321(f931(x101551,x101551)),f319(f319(f244(x101551,x101551),x101552),x101555)),f319(f319(f175(f931(x101551,x101551),a923),f319(a104,x101554)),x101553)))
% 28.25/28.12 [10172]~P1(f319(f319(f321(f931(f926(x101721),f926(x101721))),f319(f319(f244(f926(x101721),f926(x101721)),f319(f319(f143(x101721),x101722),x101725)),x101724)),f150(x101721,x101723)))+P1(f319(f319(f321(f931(x101721,x101721)),f319(f319(f244(x101721,x101721),x101722),f675(x101723,x101724,x101725,x101722,x101721))),x101723))
% 28.25/28.12 [10195]~P1(f319(f319(f321(x101951),f319(x101953,f824(x101955,x101953,x101951,x101954,x101952))),x101955))+P1(f319(f319(f226(f932(x101951,a923)),f319(f302(x101952,x101951,x101953),x101954)),x101955))
% 28.25/28.12 [6560]P1(f319(x65602,x65604))+E(f169(x65601,x65602,f319(f319(f126(x65601),x65603),f319(f319(f143(x65601),x65604),x65605))),f169(x65601,x65602,x65603))
% 28.25/28.12 [6610]~P102(x66102)+E(f319(f319(f319(f102(f932(x66101,x66102)),x66103),x66104),x66105),f319(f319(f102(x66102),f319(x66103,x66105)),f319(x66104,x66105)))
% 28.25/28.12 [6611]~P102(x66112)+E(f319(f319(f319(f102(f932(x66111,x66112)),x66113),x66114),x66115),f319(f319(f102(x66112),f319(x66113,x66115)),f319(x66114,x66115)))
% 28.25/28.12 [6612]~P102(x66122)+E(f319(f319(f319(f93(f932(x66121,x66122)),x66123),x66124),x66125),f319(f319(f93(x66122),f319(x66123,x66125)),f319(x66124,x66125)))
% 28.25/28.12 [6613]~P102(x66132)+E(f319(f319(f319(f93(f932(x66131,x66132)),x66133),x66134),x66135),f319(f319(f93(x66132),f319(x66133,x66135)),f319(x66134,x66135)))
% 28.25/28.12 [6614]~P83(x66142)+E(f319(f319(f319(f23(f932(x66141,x66142)),x66143),x66144),x66145),f319(f319(f23(x66142),f319(x66143,x66145)),f319(x66144,x66145)))
% 28.25/28.12 [6615]~P83(x66152)+E(f319(f319(f319(f23(f932(x66151,x66152)),x66153),x66154),x66155),f319(f319(f23(x66152),f319(x66153,x66155)),f319(x66154,x66155)))
% 28.25/28.12 [6632]E(x66321,x66322)+E(f319(f319(f156(x66323),f319(f319(f151(x66323,x66324),x66321),x66325)),x66322),f319(f319(f156(x66323),x66324),x66322))
% 28.25/28.12 [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)
% 28.25/28.12 [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)
% 28.25/28.12 [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)
% 28.25/28.12 [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))))
% 28.25/28.12 [7346]~P121(x73461)+E(f319(f319(f75(x73461),f319(f319(f75(x73461),x73462),x73463)),f319(f319(f75(x73461),x73464),x73465)),f319(f319(f75(x73461),x73462),f319(f319(f75(x73461),x73463),f319(f319(f75(x73461),x73464),x73465))))
% 28.25/28.12 [7713]E(f319(f319(f156(x77131),f319(f319(f146(x77132,x77131),x77133),x77134)),x77135),f319(x77133,f319(f319(f156(x77132),x77134),x77135)))+~P1(f319(f319(f227(a925),x77135),f319(f181(f926(x77132)),x77134)))
% 28.25/28.12 [7775]E(f319(f319(f102(f932(x77751,a923)),f319(x77752,x77753)),f319(f319(f33(x77754,f932(x77751,a923)),x77755),x77752)),f319(f319(f33(x77754,f932(x77751,a923)),x77755),x77752))+~P1(f319(f319(f321(x77754),x77753),x77755))
% 28.25/28.12 [7776]E(f319(f319(f93(f932(x77761,a923)),f319(x77762,x77763)),f319(f319(f34(x77764,f932(x77761,a923)),x77765),x77762)),f319(f319(f34(x77764,f932(x77761,a923)),x77765),x77762))+~P1(f319(f319(f321(x77764),x77763),x77765))
% 28.25/28.12 [8384]~E(x83843,f180(f932(x83841,a923)))+E(f319(f319(f33(x83841,f932(x83842,a923)),x83843),f319(f319(f8(f932(x83842,a923),f932(x83842,a923),x83841),f319(f301(x83842),x83844)),x83845)),f180(f932(x83842,a923)))
% 28.25/28.12 [8389]~P1(f319(f319(f321(x83894),x83893),x83895))+P1(f319(f319(f226(f932(x83891,a923)),f319(x83892,x83893)),f319(f319(f33(x83894,f932(x83891,a923)),x83895),x83892)))
% 28.25/28.12 [8518]~E(f319(x85184,x85182),x85185)+P1(f319(f319(f321(x85181),x85182),f319(f303(x85181,x85183,x85184),f319(f319(f301(x85183),x85185),f180(f932(x85183,a923))))))
% 28.25/28.12 [8566]~P59(x85661,x85662,f319(f278(x85662,x85661),x85663))+E(f319(f319(f93(f932(x85661,a923)),f319(f277(x85662,x85661,x85663),x85664)),f319(f277(x85662,x85661,x85663),x85665)),f319(f277(x85662,x85661,x85663),f319(f319(f93(f932(x85662,a923)),x85664),x85665)))
% 28.25/28.12 [8641]E(x86411,f2(a91))+E(f319(f110(x86412,x86413,f319(x86414,f319(f319(f23(a91),x86411),f72(a91)))),f319(f319(f7(x86412,a91,f927(x86413)),x86415),x86411)),f319(f190(x86412,x86413,x86414,x86415),x86411))
% 28.25/28.12 [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)))
% 28.25/28.12 [8681]E(x86811,f180(f932(x86812,a923)))+E(f319(f319(f33(x86812,f932(x86813,a923)),x86811),f319(f319(f8(f932(x86813,a923),f932(x86813,a923),x86812),f319(f301(x86813),x86814)),x86815)),f319(f319(f301(x86813),x86814),f319(f319(f33(x86812,f932(x86813,a923)),x86811),x86815)))
% 28.25/28.12 [8734]~P26(x87342,x87341,x87343,f234(f932(x87342,a923)))+E(f319(f319(f93(f932(x87341,a923)),f319(f302(x87342,x87341,x87343),x87344)),f319(f302(x87342,x87341,x87343),x87345)),f319(f302(x87342,x87341,x87343),f319(f319(f93(f932(x87342,a923)),x87344),x87345)))
% 28.25/28.12 [8735]~P26(x87352,x87351,x87353,f234(f932(x87352,a923)))+E(f319(f319(f23(f932(x87351,a923)),f319(f302(x87352,x87351,x87353),x87354)),f319(f302(x87352,x87351,x87353),x87355)),f319(f302(x87352,x87351,x87353),f319(f319(f23(f932(x87352,a923)),x87354),x87355)))
% 28.25/28.12 [8804]~P1(f319(f319(f61(x88041,x88042,x88045),x88043),x88044))+P1(f319(f319(f321(f931(x88041,x88042)),f319(f319(f244(x88041,x88042),x88043),x88044)),x88045))
% 28.25/28.12 [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))
% 28.25/28.12 [8836]P1(f319(f319(f321(x88361),x88362),f319(f276(x88363,x88361),x88364)))+~P1(f319(f319(f321(f931(x88363,x88361)),f319(f319(f244(x88363,x88361),x88365),x88362)),x88364))
% 28.25/28.12 [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))
% 28.25/28.12 [8838]P1(f319(f319(f321(x88381),x88382),f319(f256(x88381,x88383),x88384)))+~P1(f319(f319(f321(f931(x88381,x88383)),f319(f319(f244(x88381,x88383),x88382),x88385)),x88384))
% 28.25/28.12 [8985]P1(f319(f319(f61(x89851,x89852,x89853),x89854),x89855))+~P1(f319(f319(f321(f931(x89851,x89852)),f319(f319(f244(x89851,x89852),x89854),x89855)),x89853))
% 28.25/28.12 [9025]E(f319(x90251,x90252),x90253)+~P1(f319(f319(f321(x90254),x90252),f319(f303(x90254,x90255,x90251),f319(f319(f301(x90255),x90253),f180(f932(x90255,a923))))))
% 28.25/28.12 [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))
% 28.25/28.12 [9260]P1(f319(f319(f321(f931(x92601,x92602)),f319(f319(f244(x92601,x92602),x92603),x92604)),f319(f278(x92602,x92601),x92605)))+~P1(f319(f319(f321(f931(x92602,x92601)),f319(f319(f244(x92602,x92601),x92604),x92603)),x92605))
% 28.25/28.12 [9278]~P1(f319(f319(x92781,x92785),x92784))+P1(f319(f319(x92781,f319(f248(x92782,x92783),f319(f319(f244(x92782,x92783),x92784),x92785))),f319(f243(x92782,x92783),f319(f319(f244(x92782,x92783),x92784),x92785))))
% 28.25/28.12 [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))
% 28.25/28.12 [9308]~P1(f319(f319(f321(f931(x93082,x93081)),f319(f319(f244(x93082,x93081),x93084),x93083)),f319(f278(x93081,x93082),x93085)))+P1(f319(f319(f321(f931(x93081,x93082)),f319(f319(f244(x93081,x93082),x93083),x93084)),x93085))
% 28.25/28.12 [9341]~P1(f319(f319(f321(f931(x93413,x93411)),f319(f319(f244(x93413,x93411),x93415),x93412)),x93414))+P1(f319(f319(f321(x93411),x93412),f319(f277(x93413,x93411,x93414),f319(f319(f301(x93413),x93415),f180(f932(x93413,a923))))))
% 28.25/28.12 [9390]P1(f319(f319(f321(f931(x93901,x93902)),f319(f319(f244(x93901,x93902),x93903),x93904)),x93905))+~P1(f319(f319(f321(x93902),x93904),f319(f277(x93901,x93902,x93905),f319(f319(f301(x93901),x93903),f180(f932(x93901,a923))))))
% 28.25/28.12 [9480]~P79(x94801)+E(f319(f319(f6(a925,x94801),x94802),f295(a925,f319(f319(f74(a925),x94803),x94804),f319(f319(f74(a925),x94805),x94804))),f319(f319(f6(a925,x94801),f319(f319(f8(a925,x94801,a925),x94802),f319(f319(f7(a925,a925,a925),f74(a925)),x94804))),f295(a925,x94803,x94805)))
% 28.25/28.12 [9500]~P79(x95001)+E(f319(f319(f6(a925,x95001),x95002),f319(f294(a925,f319(f319(f74(a925),x95003),x95004)),f319(f319(f74(a925),x95005),x95004))),f319(f319(f6(a925,x95001),f319(f319(f8(a925,x95001,a925),x95002),f319(f319(f7(a925,a925,a925),f74(a925)),x95004))),f319(f294(a925,x95003),x95005)))
% 28.25/28.12 [9558]~P26(x95581,x95582,x95583,f234(f932(x95581,a923)))+E(f319(f319(f146(x95581,x95582),x95583),f319(f128(x95581,f319(f319(f8(a923,a923,x95581),a314),f319(a316,x95584))),x95585)),f319(f128(x95582,f319(f319(f8(a923,a923,x95582),a314),f319(a316,f319(x95583,x95584)))),f319(f319(f146(x95581,x95582),x95583),x95585)))
% 28.25/28.12 [9576]~P26(x95761,x95762,x95763,f319(f319(f301(x95761),x95764),f319(f164(x95761),x95765)))+E(f319(f319(f146(x95761,x95762),x95763),f319(f128(x95761,f319(f319(f8(a923,a923,x95761),a314),f319(a316,x95764))),x95765)),f319(f128(x95762,f319(f319(f8(a923,a923,x95762),a314),f319(a316,f319(x95763,x95764)))),f319(f319(f146(x95761,x95762),x95763),x95765)))
% 28.25/28.12 [9738]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),x97383))),f149(x97381,x97385)))+~P1(f319(f319(f321(f931(x97381,x97381)),f319(f319(f244(x97381,x97381),x97382),x97384)),x97385))
% 28.25/28.12 [9861]E(f319(f319(f301(x98611),f906(x98612,x98613,x98614,x98615,x98611)),f908(x98612,x98613,x98614,x98615,x98611)),f319(f319(f301(x98611),x98614),x98613))+~P1(f319(f56(x98611,x98615,f319(f319(f301(x98611),x98614),x98613)),x98612))
% 28.25/28.12 [9862]E(f319(f319(f301(x98621),f909(x98622,x98623,x98624,x98625,x98621)),f910(x98622,x98623,x98624,x98625,x98621)),f319(f319(f301(x98621),x98624),x98623))+~P1(f319(f56(x98621,x98625,f319(f319(f301(x98621),x98624),x98623)),x98622))
% 28.25/28.12 [9947]P1(f319(f319(f321(x99471),f392(x99472,x99473,x99474,x99475,x99471)),x99474))+P1(f319(f319(f319(f34(x99471,f932(x99475,a923)),x99474),x99473),x99472))
% 28.25/28.12 [9948]P1(f319(f319(f321(x99481),f670(x99482,x99483,x99484,x99485,x99481)),x99485))+P1(f319(f319(f319(f34(x99481,f932(x99482,a923)),x99485),x99484),x99483))
% 28.25/28.12 [9953]P1(f319(f319(f321(x99531),f409(x99532,x99533,x99531,x99534,x99535)),x99533))+P1(f319(f319(f321(x99535),x99534),f319(f319(f34(x99531,f932(x99535,a923)),x99533),x99532)))
% 28.25/28.12 [9954]P1(f319(f319(f321(x99541),f682(x99542,x99543,x99544,x99545,x99541)),x99545))+P1(f319(f319(f321(x99544),x99543),f319(f319(f34(x99541,f932(x99544,a923)),x99545),x99542)))
% 28.25/28.12 [9964]P1(f319(f319(f321(x99641),f891(x99642,x99643,x99641,x99644,x99645)),x99643))+P1(f319(f319(f226(f932(x99645,a923)),x99644),f319(f319(f34(x99641,f932(x99645,a923)),x99643),x99642)))
% 28.25/28.12 [9965]P1(f319(f319(f321(x99651),f514(x99652,x99653,x99654,x99655,x99651)),x99655))+P1(f319(f319(f226(f932(x99654,a923)),x99653),f319(f319(f34(x99651,f932(x99654,a923)),x99655),x99652)))
% 28.25/28.12 [9967]P1(f319(f319(x99671,f402(x99672,x99671,x99673,x99674,x99675)),x99672))+~P1(f319(f319(f319(f33(x99675,f932(x99674,a923)),x99673),x99671),x99672))
% 28.25/28.12 [9968]P1(f319(f319(x99681,f691(x99682,x99681,x99683,x99684,x99685)),x99682))+~P1(f319(f319(f319(f33(x99685,f932(x99684,a923)),x99683),x99681),x99682))
% 28.25/28.12 [9972]P1(f319(f319(f321(x99721),f402(x99722,x99723,x99724,x99725,x99721)),x99724))+~P1(f319(f319(f319(f33(x99721,f932(x99725,a923)),x99724),x99723),x99722))
% 28.25/28.12 [9973]P1(f319(f319(f321(x99731),f691(x99732,x99733,x99734,x99735,x99731)),x99734))+~P1(f319(f319(f319(f33(x99731,f932(x99735,a923)),x99734),x99733),x99732))
% 28.25/28.12 [9974]P57(x99744,f319(f319(f34(x99741,f932(x99744,a923)),x99745),x99743),f319(f319(f34(x99741,f932(f931(x99744,x99744),a923)),x99745),x99742))+P1(f319(f319(f321(x99741),f797(x99742,x99743,x99744,x99745,x99741)),x99745))
% 28.25/28.12 [9975]P57(x99754,f319(f319(f33(x99751,f932(x99754,a923)),x99755),x99753),f319(f319(f33(x99751,f932(f931(x99754,x99754),a923)),x99755),x99752))+P1(f319(f319(f321(x99751),f842(x99752,x99753,x99754,x99755,x99751)),x99755))
% 28.25/28.12 [9986]P1(f319(f319(f321(x99861),f417(x99862,x99863,x99861,x99864,x99865)),x99863))+~P1(f319(f319(f321(x99865),x99864),f319(f319(f33(x99861,f932(x99865,a923)),x99863),x99862)))
% 28.25/28.12 [9987]P1(f319(f319(f321(x99871),f704(x99872,x99873,x99871,x99874,x99875)),x99873))+~P1(f319(f319(f321(x99875),x99874),f319(f319(f33(x99871,f932(x99875,a923)),x99873),x99872)))
% 28.25/28.12 [9993]P1(f319(f319(f321(x99931),x99932),f319(x99933,f417(x99933,x99934,x99935,x99932,x99931))))+~P1(f319(f319(f321(x99931),x99932),f319(f319(f33(x99935,f932(x99931,a923)),x99934),x99933)))
% 28.25/28.12 [9994]P1(f319(f319(f321(x99941),x99942),f319(x99943,f704(x99943,x99944,x99945,x99942,x99941))))+~P1(f319(f319(f321(x99941),x99942),f319(f319(f33(x99945,f932(x99941,a923)),x99944),x99943)))
% 28.25/28.12 [10081]~P1(f319(f319(x100814,f392(x100815,x100814,x100813,x100812,x100811)),x100815))+P1(f319(f319(f319(f34(x100811,f932(x100812,a923)),x100813),x100814),x100815))
% 28.25/28.12 [10082]~P1(f319(f319(x100824,f670(x100822,x100825,x100824,x100823,x100821)),x100825))+P1(f319(f319(f319(f34(x100821,f932(x100822,a923)),x100823),x100824),x100825))
% 28.25/28.12 [10085]~P1(f319(f319(f321(x100851),x100852),f319(x100855,f409(x100855,x100854,x100853,x100852,x100851))))+P1(f319(f319(f321(x100851),x100852),f319(f319(f34(x100853,f932(x100851,a923)),x100854),x100855)))
% 28.25/28.12 [10086]~P1(f319(f319(f321(x100861),x100862),f319(x100865,f682(x100865,x100862,x100861,x100864,x100863))))+P1(f319(f319(f321(x100861),x100862),f319(f319(f34(x100863,f932(x100861,a923)),x100864),x100865)))
% 28.25/28.12 [10090]~P57(x100901,f319(x100904,f842(x100905,x100904,x100901,x100903,x100902)),f319(x100905,f842(x100905,x100904,x100901,x100903,x100902)))+P57(x100901,f319(f319(f33(x100902,f932(x100901,a923)),x100903),x100904),f319(f319(f33(x100902,f932(f931(x100901,x100901),a923)),x100903),x100905))
% 28.25/28.12 [10091]~P57(x100911,f319(x100914,f797(x100915,x100914,x100911,x100913,x100912)),f319(x100915,f797(x100915,x100914,x100911,x100913,x100912)))+P57(x100911,f319(f319(f34(x100912,f932(x100911,a923)),x100913),x100914),f319(f319(f34(x100912,f932(f931(x100911,x100911),a923)),x100913),x100915))
% 28.25/28.12 [10092]~P1(f319(f319(f226(f932(x100921,a923)),x100922),f319(x100925,f891(x100925,x100924,x100923,x100922,x100921))))+P1(f319(f319(f226(f932(x100921,a923)),x100922),f319(f319(f34(x100923,f932(x100921,a923)),x100924),x100925)))
% 28.25/28.12 [10093]~P1(f319(f319(f226(f932(x100931,a923)),x100932),f319(x100935,f514(x100935,x100932,x100931,x100934,x100933))))+P1(f319(f319(f226(f932(x100931,a923)),x100932),f319(f319(f34(x100933,f932(x100931,a923)),x100934),x100935)))
% 28.25/28.12 [10158]~P1(f319(f319(f321(x101581),f906(x101585,x101584,x101583,x101582,x101581)),f908(x101585,x101584,x101583,x101582,x101581)))+~P1(f319(f56(x101581,x101582,f319(f319(f301(x101581),x101583),x101584)),x101585))
% 28.25/28.12 [10159]~P1(f319(f319(f321(x101591),f909(x101595,x101594,x101593,x101592,x101591)),f910(x101595,x101594,x101593,x101592,x101591)))+~P1(f319(f56(x101591,x101592,f319(f319(f301(x101591),x101593),x101594)),x101595))
% 28.25/28.12 [10160]~P1(f319(f319(f321(f931(x101601,x101601)),f319(f319(f244(x101601,x101601),x101602),x101605)),f319(f319(f175(f931(x101601,x101601),a923),f319(a104,x101604)),x101603)))+P1(f319(f319(f321(f931(x101601,x101601)),f319(f319(f244(x101601,x101601),x101602),f646(x101603,x101604,x101605,x101602,x101601))),f319(f319(f175(f931(x101601,x101601),a923),x101604),x101603)))
% 28.25/28.12 [10166]P1(f319(f60(x101661,x101661,x101662,f906(x101663,x101664,x101665,x101662,x101661),f908(x101663,x101664,x101665,x101662,x101661)),x101663))+~P1(f319(f56(x101661,x101662,f319(f319(f301(x101661),x101665),x101664)),x101663))
% 28.25/28.12 [10167]P1(f319(f60(x101671,x101671,x101672,f909(x101673,x101674,x101675,x101672,x101671),f910(x101673,x101674,x101675,x101672,x101671)),x101673))+~P1(f319(f56(x101671,x101672,f319(f319(f301(x101671),x101675),x101674)),x101673))
% 28.25/28.12 [10177]~P4(x101771)+P14(x101771,f319(f319(f146(x101772,x101771),x101773),f319(f128(x101772,f319(f319(f7(x101772,x101771,a923),f319(f319(f8(x101771,f932(x101771,a923),x101772),a316),x101773)),f319(x101774,x101775))),x101775)))
% 28.25/28.12 [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),f530(x102303,x102304,x102301,x102305,x102302)),x102305)),x102304))
% 28.25/28.12 [10231]~P1(f319(f319(f321(x102312),x102315),f319(f277(x102311,x102312,x102314),x102313)))+P1(f319(f319(f321(f931(x102311,x102312)),f319(f319(f244(x102311,x102312),f556(x102313,x102314,x102311,x102315,x102312)),x102315)),x102314))
% 28.25/28.12 [10251]~P1(f319(f319(f321(f931(x102511,x102511)),f319(f319(f244(x102511,x102511),x102515),x102514)),f319(f319(f175(f931(x102511,x102511),a923),f319(a104,x102513)),x102512)))+P1(f319(f319(f321(f931(x102511,x102511)),f319(f319(f244(x102511,x102511),f646(x102512,x102513,x102514,x102515,x102511)),x102514)),x102512))
% 28.25/28.12 [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),f645(x102542,x102543,x102544,x102545,x102541)),x102544)),f319(f319(f175(f931(x102541,x102541),a923),x102543),x102542)))
% 28.25/28.12 [10255]~P1(f319(f319(f321(f931(x102551,x102551)),f319(f319(f244(x102551,x102551),x102555),x102554)),f319(f319(f175(f931(x102551,x102551),a923),f319(a104,x102553)),x102552)))+P1(f319(f319(f321(f931(x102551,x102551)),f319(f319(f244(x102551,x102551),f647(x102552,x102553,x102554,x102555,x102551)),x102554)),f319(f319(f175(f931(x102551,x102551),a923),x102553),x102552)))
% 28.25/28.12 [10256]~P1(f319(f319(f321(f931(f926(x102561),f926(x102561))),f319(f319(f244(f926(x102561),f926(x102561)),x102565),f319(f319(f143(x102561),x102564),x102563))),f150(x102561,x102562)))+P1(f319(f319(f321(f931(x102561,x102561)),f319(f319(f244(x102561,x102561),f672(x102562,x102563,x102564,x102565,x102561)),x102564)),x102562))
% 28.25/28.12 [7796]~E(x77963,f180(f932(x77962,a923)))+E(f319(f319(f102(f932(x77961,a923)),f319(f319(f33(x77962,f932(x77961,a923)),x77963),x77964)),x77965),x77965)
% 28.25/28.12 [7797]~E(x77973,f180(f932(x77972,a923)))+E(f319(f319(f93(f932(x77971,a923)),f319(f319(f34(x77972,f932(x77971,a923)),x77973),x77974)),x77975),x77975)
% 28.25/28.12 [7850]~P121(x78501)+E(f319(f319(f75(x78501),f319(f319(f75(x78501),x78502),x78503)),f319(f319(f75(x78501),x78504),x78505)),f319(f319(f75(x78501),x78504),f319(f319(f75(x78501),f319(f319(f75(x78501),x78502),x78503)),x78505)))
% 28.25/28.12 [8226]~E(x82263,f180(f932(x82262,a923)))+E(f319(f319(f23(f932(x82261,a923)),f319(f319(f34(x82262,f932(x82261,a923)),x82263),x82264)),x82265),f319(f319(f23(f932(x82261,a923)),f234(f932(x82261,a923))),x82265))
% 28.25/28.12 [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)))
% 28.25/28.12 [8357]E(f319(f319(f151(x83571,f319(f319(f126(x83571),x83572),x83573)),x83574),x83575),f319(f319(f126(x83571),f319(f319(f151(x83571,x83572),x83574),x83575)),x83573))+~P1(f319(f319(f227(a925),x83574),f319(f181(f926(x83571)),x83572)))
% 28.25/28.12 [8631]E(f319(f319(f156(x86311),f319(f319(f146(a925,x86311),x86312),f131(a925,f319(f294(a925,x86313),x86314)))),x86315),f319(x86312,f319(f319(f74(a925),x86313),x86315)))+~P1(f319(f319(f227(a925),x86315),f319(f319(f23(a925),x86314),x86313)))
% 28.25/28.12 [8645]E(x86451,f2(a91))+E(f114(x86452,x86453,f319(x86454,f319(f319(f23(a91),x86451),f72(a91))),f319(f319(f7(x86452,a91,f927(f929(x86453))),x86455),x86451)),f319(f188(x86452,x86453,x86454,x86455),x86451))
% 28.25/28.12 [8671]~E(x86713,f180(f932(x86711,a923)))+E(f319(f319(f33(x86711,f932(x86712,a923)),x86713),f319(f319(f8(f932(x86712,a923),f932(x86712,a923),x86711),f319(f102(f932(x86712,a923)),x86714)),x86715)),f180(f932(x86712,a923)))
% 28.25/28.12 [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(f93(f932(x86722,a923)),x86724)),x86725)),f234(f932(x86722,a923)))
% 28.25/28.12 [8673]~E(x86733,f180(f932(x86731,a923)))+E(f319(f319(f34(x86731,f932(x86732,a923)),x86733),f319(f319(f8(f932(x86732,a923),f932(x86732,a923),x86731),f319(f23(f932(x86732,a923)),x86734)),x86735)),f234(f932(x86732,a923)))
% 28.25/28.12 [8675]~P143(x86752)+E(f319(f319(f6(x86751,x86752),f319(f319(f8(x86752,x86752,x86751),f319(f75(x86752),x86753)),x86754)),x86755),f319(f319(f75(x86752),x86753),f319(f319(f6(x86751,x86752),x86754),x86755)))
% 28.25/28.12 [8966]E(x89661,f180(f932(x89662,a923)))+E(f319(f319(f33(x89662,f932(x89663,a923)),x89661),f319(f319(f8(f932(x89663,a923),f932(x89663,a923),x89662),f319(f102(f932(x89663,a923)),x89664)),x89665)),f319(f319(f102(f932(x89663,a923)),x89664),f319(f319(f33(x89662,f932(x89663,a923)),x89661),x89665)))
% 28.25/28.12 [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(f93(f932(x89673,a923)),x89674)),x89675)),f319(f319(f93(f932(x89673,a923)),x89674),f319(f319(f34(x89672,f932(x89673,a923)),x89671),x89675)))
% 28.25/28.12 [8968]E(x89681,f180(f932(x89682,a923)))+E(f319(f319(f34(x89682,f932(x89683,a923)),x89681),f319(f319(f8(f932(x89683,a923),f932(x89683,a923),x89682),f319(f23(f932(x89683,a923)),x89684)),x89685)),f319(f319(f23(f932(x89683,a923)),x89684),f319(f319(f33(x89682,f932(x89683,a923)),x89681),x89685)))
% 28.25/28.12 [8969]E(x89691,f180(f932(x89692,a923)))+E(f319(f319(f33(x89692,f932(x89693,a923)),x89691),f319(f319(f8(f932(x89693,a923),f932(x89693,a923),x89692),f319(f102(f932(x89693,a923)),x89694)),x89695)),f319(f319(f102(f932(x89693,a923)),x89694),f319(f319(f33(x89692,f932(x89693,a923)),x89691),x89695)))
% 28.25/28.12 [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(f93(f932(x89703,a923)),x89704)),x89705)),f319(f319(f93(f932(x89703,a923)),x89704),f319(f319(f34(x89702,f932(x89703,a923)),x89701),x89705)))
% 28.25/28.12 [8971]E(x89711,f180(f932(x89712,a923)))+E(f319(f319(f34(x89712,f932(x89713,a923)),x89711),f319(f319(f8(f932(x89713,a923),f932(x89713,a923),x89712),f319(f23(f932(x89713,a923)),x89714)),x89715)),f319(f319(f23(f932(x89713,a923)),x89714),f319(f319(f33(x89712,f932(x89713,a923)),x89711),x89715)))
% 28.25/28.12 [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))))
% 28.25/28.12 [9176]~P1(f319(f319(f227(a925),f319(x91764,x91762)),f319(x91764,x91763)))+P1(f319(f319(f321(f931(x91761,x91761)),f319(f319(f244(x91761,x91761),x91762),x91763)),f145(x91761,f319(f319(f143(f932(x91761,a925)),x91764),x91765))))
% 28.25/28.12 [9427]~P41(f932(x94275,a923),f932(x94271,a923),x94272)+P1(f319(f319(f226(f932(x94271,a923)),f319(f319(f102(f932(x94271,a923)),f319(x94272,x94273)),f319(x94272,x94274))),f319(x94272,f319(f319(f102(f932(x94275,a923)),x94273),x94274))))
% 28.25/28.12 [9446]~P26(x94462,x94461,x94463,f319(f319(f102(f932(x94462,a923)),x94464),x94465))+E(f319(f319(f93(f932(x94461,a923)),f319(f302(x94462,x94461,x94463),f319(f319(f23(f932(x94462,a923)),x94464),x94465))),f319(f302(x94462,x94461,x94463),f319(f319(f23(f932(x94462,a923)),x94465),x94464))),f180(f932(x94461,a923)))
% 28.25/28.12 [9704]~P26(x97043,x97041,x97045,f234(f932(x97043,a923)))+E(f319(f66(x97041,x97042,x97043,f319(f66(x97043,x97042,x97041,x97044),f85(x97043,x97041,f234(f932(x97043,a923)),x97045))),x97045),x97044)
% 28.25/28.12 [9734]~P1(f319(f319(f226(f932(x97343,a923)),f319(f277(x97341,x97343,x97344),x97342)),x97345))+P1(f319(f319(f226(f932(x97341,a923)),x97342),f319(f73(f932(x97341,a923)),f319(f277(x97343,x97341,f319(f278(x97341,x97343),x97344)),f319(f73(f932(x97343,a923)),x97345)))))
% 28.25/28.12 [9759]~P26(x97591,x97592,x97593,f319(f319(f301(x97591),x97594),x97595))+~P1(f319(f319(f321(x97592),f319(x97593,x97594)),f319(f302(x97591,x97592,x97593),f319(f319(f23(f932(x97591,a923)),x97595),f319(f319(f301(x97591),x97594),f180(f932(x97591,a923)))))))
% 28.25/28.12 [9814]P1(f319(f319(f226(f932(x98141,a923)),f319(f277(x98142,x98141,x98143),x98144)),x98145))+~P1(f319(f319(f226(f932(x98142,a923)),x98144),f319(f73(f932(x98142,a923)),f319(f277(x98141,x98142,f319(f278(x98142,x98141),x98143)),f319(f73(f932(x98141,a923)),x98145)))))
% 28.25/28.12 [9888]~P92(x98881)+P1(f319(f319(f226(x98881),f319(f69(x98881),f319(f319(f23(x98881),f319(f319(f74(x98881),x98882),x98883)),f319(f319(f74(x98881),x98884),x98885)))),f319(f319(f74(x98881),f319(f69(x98881),f319(f319(f23(x98881),x98882),x98884))),f319(f69(x98881),f319(f319(f23(x98881),x98883),x98885)))))
% 28.25/28.12 [10009]P1(f319(f319(f321(x100091),f900(x100092,x100093,x100094,x100091,x100095)),x100094))+P1(f319(f319(f226(f932(x100095,a923)),f319(f319(f33(x100091,f932(x100095,a923)),x100094),x100093)),x100092))
% 28.25/28.12 [10010]P1(f319(f319(f321(x100101),f537(x100102,x100103,x100104,x100105,x100101)),x100105))+P1(f319(f319(f226(f932(x100104,a923)),f319(f319(f33(x100101,f932(x100104,a923)),x100105),x100103)),x100102))
% 28.25/28.12 [10197]~P1(f319(f319(f226(f932(x101971,a923)),f319(x101974,f900(x101975,x101974,x101973,x101972,x101971))),x101975))+P1(f319(f319(f226(f932(x101971,a923)),f319(f319(f33(x101972,f932(x101971,a923)),x101973),x101974)),x101975))
% 28.25/28.12 [10198]~P1(f319(f319(f226(f932(x101981,a923)),f319(x101984,f537(x101985,x101984,x101981,x101983,x101982))),x101985))+P1(f319(f319(f226(f932(x101981,a923)),f319(f319(f33(x101982,f932(x101981,a923)),x101983),x101984)),x101985))
% 28.25/28.12 [8782]E(f319(f319(f126(x87821),x87822),f319(f319(f151(x87821,x87823),f319(f319(f23(a925),x87824),f319(f181(f926(x87821)),x87822))),x87825)),f319(f319(f151(x87821,f319(f319(f126(x87821),x87822),x87823)),x87824),x87825))+P1(f319(f319(f227(a925),x87824),f319(f181(f926(x87821)),x87822)))
% 28.25/28.12 [8811]~P146(x88111)+E(f319(f319(f74(x88111),f319(f319(f75(x88111),x88112),x88113)),f319(f319(f74(x88111),f319(f319(f75(x88111),x88114),x88113)),x88115)),f319(f319(f74(x88111),f319(f319(f75(x88111),f319(f319(f74(x88111),x88112),x88114)),x88113)),x88115))
% 28.25/28.12 [9399]~P143(x93991)+E(f319(f157(x93991),f319(f319(f146(x93992,x93991),f319(f319(f8(x93991,x93991,x93992),f319(f75(x93991),x93993)),x93994)),x93995)),f319(f319(f75(x93991),x93993),f319(f157(x93991),f319(f319(f146(x93992,x93991),x93994),x93995))))
% 28.25/28.12 [9575]E(f319(f181(f926(x95751)),f319(f319(f167(x95751),f319(f319(f224(a925),f319(f181(f926(x95751)),x95752)),f319(f181(f926(x95753)),x95754))),x95752)),f319(f181(f926(x95753)),f319(f319(f167(x95753),f319(f319(f224(a925),f319(f181(f926(x95751)),x95752)),f319(f181(f926(x95753)),x95754))),x95754)))+P1(f319(x95755,f319(f319(f173(x95751,x95753),x95752),x95754)))
% 28.25/28.12 [9824]~P143(x98242)+E(f319(f319(f6(x98241,x98242),f319(f319(f7(x98241,x98242,x98242),f319(f319(f8(x98242,f932(x98242,x98242),x98241),f75(x98242)),x98243)),x98244)),x98245),f319(f319(f75(x98242),f319(f319(f6(x98241,x98242),x98243),x98245)),x98244))
% 28.25/28.12 [9825]~P73(x98252)+E(f319(f319(f6(x98251,x98252),f319(f319(f7(x98251,x98252,x98252),f319(f319(f8(x98252,f932(x98252,x98252),x98251),f283(x98252)),x98253)),x98254)),x98255),f319(f319(f283(x98252),f319(f319(f6(x98251,x98252),x98253),x98255)),x98254))
% 28.25/28.12 [9832]~P70(x98322)+E(f319(f319(f6(x98321,x98322),f319(f319(f18(x98321,x98322,x98322),f319(f319(f8(x98322,f932(x98322,x98322),x98321),f23(x98322)),x98323)),x98324)),x98325),f319(f319(f23(x98322),f319(f319(f6(x98321,x98322),x98323),x98325)),f319(f319(f6(x98321,x98322),x98324),x98325)))
% 28.25/28.12 [9833]~P79(x98332)+E(f319(f319(f6(x98331,x98332),f319(f319(f18(x98331,x98332,x98332),f319(f319(f8(x98332,f932(x98332,x98332),x98331),f74(x98332)),x98333)),x98334)),x98335),f319(f319(f74(x98332),f319(f319(f6(x98331,x98332),x98333),x98335)),f319(f319(f6(x98331,x98332),x98334),x98335)))
% 28.25/28.12 [9834]~P78(x98342)+E(f319(f319(f9(x98341,x98342),f319(f319(f18(x98341,x98342,x98342),f319(f319(f8(x98342,f932(x98342,x98342),x98341),f75(x98342)),x98343)),x98344)),x98345),f319(f319(f75(x98342),f319(f319(f9(x98341,x98342),x98343),x98345)),f319(f319(f9(x98341,x98342),x98344),x98345)))
% 28.25/28.12 [9873]~E(x98733,f180(f932(x98731,a923)))+E(f319(f319(f33(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),f102(f932(x98732,a923))),x98734)),x98735)),f180(f932(x98732,a923)))
% 28.25/28.12 [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),f93(f932(x98742,a923))),x98744)),x98745)),f234(f932(x98742,a923)))
% 28.25/28.12 [9875]~E(x98753,f180(f932(x98751,a923)))+E(f319(f319(f34(x98751,f932(x98752,a923)),x98753),f319(f319(f7(x98751,f932(x98752,a923),f932(x98752,a923)),f319(f319(f8(f932(x98752,a923),f932(f932(x98752,a923),f932(x98752,a923)),x98751),f23(f932(x98752,a923))),x98754)),x98755)),f234(f932(x98752,a923)))
% 28.25/28.12 [9893]E(x98931,f180(f932(x98932,a923)))+E(f319(f319(f33(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),f102(f932(x98933,a923))),x98934)),x98935)),f319(f319(f102(f932(x98933,a923)),f319(f319(f33(x98932,f932(x98933,a923)),x98931),x98934)),x98935))
% 28.25/28.12 [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),f93(f932(x98943,a923))),x98944)),x98945)),f319(f319(f93(f932(x98943,a923)),f319(f319(f34(x98942,f932(x98943,a923)),x98941),x98944)),x98945))
% 28.25/28.12 [9895]E(x98951,f180(f932(x98952,a923)))+E(f319(f319(f34(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),f23(f932(x98953,a923))),x98954)),x98955)),f319(f319(f23(f932(x98953,a923)),f319(f319(f34(x98952,f932(x98953,a923)),x98951),x98954)),x98955))
% 28.25/28.12 [9896]E(x98961,f180(f932(x98962,a923)))+E(f319(f319(f33(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),f102(f932(x98963,a923))),x98964)),x98965)),f319(f319(f102(f932(x98963,a923)),f319(f319(f33(x98962,f932(x98963,a923)),x98961),x98964)),x98965))
% 28.25/28.12 [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),f93(f932(x98973,a923))),x98974)),x98975)),f319(f319(f93(f932(x98973,a923)),f319(f319(f34(x98972,f932(x98973,a923)),x98971),x98974)),x98975))
% 28.25/28.12 [9898]E(x98981,f180(f932(x98982,a923)))+E(f319(f319(f34(x98982,f932(x98983,a923)),x98981),f319(f319(f7(x98982,f932(x98983,a923),f932(x98983,a923)),f319(f319(f8(f932(x98983,a923),f932(f932(x98983,a923),f932(x98983,a923)),x98982),f23(f932(x98983,a923))),x98984)),x98985)),f319(f319(f23(f932(x98983,a923)),f319(f319(f34(x98982,f932(x98983,a923)),x98981),x98984)),x98985))
% 28.25/28.12 [9451]~P1(f319(f319(f226(a925),x94511),x94514))+E(f319(f319(f23(a925),f319(f319(f74(a925),f319(f319(f75(a925),x94511),x94512)),x94513)),f319(f319(f74(a925),f319(f319(f75(a925),x94514),x94512)),x94515)),f319(f319(f23(a925),x94513),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x94514),x94511)),x94512)),x94515)))
% 28.25/28.12 [10063]~P143(x100631)+E(f319(f157(x100631),f319(f319(f146(x100632,x100631),f319(f319(f7(x100632,x100631,x100631),f319(f319(f8(x100631,f932(x100631,x100631),x100632),f75(x100631)),x100633)),x100634)),x100635)),f319(f319(f75(x100631),f319(f157(x100631),f319(f319(f146(x100632,x100631),x100633),x100635))),x100634))
% 28.25/28.12 [10069]~P70(x100691)+E(f319(f157(x100691),f319(f319(f146(x100692,x100691),f319(f319(f18(x100692,x100691,x100691),f319(f319(f8(x100691,f932(x100691,x100691),x100692),f23(x100691)),x100693)),x100694)),x100695)),f319(f319(f23(x100691),f319(f157(x100691),f319(f319(f146(x100692,x100691),x100693),x100695))),f319(f157(x100691),f319(f319(f146(x100692,x100691),x100694),x100695))))
% 28.25/28.12 [10070]~P79(x100701)+E(f319(f157(x100701),f319(f319(f146(x100702,x100701),f319(f319(f18(x100702,x100701,x100701),f319(f319(f8(x100701,f932(x100701,x100701),x100702),f74(x100701)),x100703)),x100704)),x100705)),f319(f319(f74(x100701),f319(f157(x100701),f319(f319(f146(x100702,x100701),x100703),x100705))),f319(f157(x100701),f319(f319(f146(x100702,x100701),x100704),x100705))))
% 28.25/28.12 [10221]P1(f319(x102211,f319(f319(f173(x102212,x102213),x102214),x102215)))+~P1(f319(x102211,f319(f319(f173(x102212,x102213),f319(f319(f167(x102212),f319(f319(f224(a925),f319(f181(f926(x102212)),x102214)),f319(f181(f926(x102213)),x102215))),x102214)),f319(f319(f167(x102213),f319(f319(f224(a925),f319(f181(f926(x102212)),x102214)),f319(f181(f926(x102213)),x102215))),x102215))))
% 28.25/28.12 [10483]~P1(f319(f319(f321(f931(x104832,x104831)),f319(f319(f244(x104832,x104831),x104834),x104835)),f319(f278(x104831,x104832),x104833)))+P1(f319(f319(f235(x104831,x104832,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)),x104834),x104835))
% 28.25/28.12 [10495]P1(f319(f319(f321(f931(x104951,x104952)),f319(f319(f244(x104951,x104952),x104953),x104954)),f319(f278(x104952,x104951),x104955)))+~P1(f319(f319(f235(x104952,x104951,f319(f319(f7(x104952,f932(f931(x104952,x104951),a923),f932(x104951,a923)),f319(f319(f8(f932(x104951,f932(f932(f931(x104952,x104951),a923),a923)),f932(f932(f931(x104952,x104951),a923),f932(x104951,a923)),x104952),f7(x104951,f932(f931(x104952,x104951),a923),a923)),f319(f319(f8(f932(x104951,f931(x104952,x104951)),f932(x104951,f932(f932(f931(x104952,x104951),a923),a923)),x104952),f319(f8(f931(x104952,x104951),f932(f932(f931(x104952,x104951),a923),a923),x104951),f321(f931(x104952,x104951)))),f244(x104952,x104951)))),x104955)),x104953),x104954))
% 28.25/28.12 [9703]~P1(f319(f319(f226(a925),x97034),x97031))+E(f319(f319(f23(a925),f319(f319(f74(a925),f319(f319(f75(a925),x97031),x97032)),x97033)),f319(f319(f74(a925),f319(f319(f75(a925),x97034),x97032)),x97035)),f319(f319(f23(a925),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x97031),x97034)),x97032)),x97033)),x97035))
% 28.25/28.12 [7496]E(x74961,x74962)+~E(f212(x74963,x74964,x74965,x74961),f212(x74963,x74964,x74966,x74962))
% 28.25/28.12 [7497]E(x74971,x74972)+~E(f212(x74973,x74974,x74971,x74975),f212(x74973,x74974,x74972,x74976))
% 28.25/28.12 [8615]~P21(x86155,x86151,x86152,x86156)+E(f319(f66(x86151,x86151,x86151,f319(x86152,x86153)),f319(x86152,x86154)),f319(f66(x86151,x86151,x86151,f319(x86152,x86154)),f319(x86152,x86153)))
% 28.25/28.12 [8855]~P61(x88554,x88555,x88552,x88551,x88556)+E(f319(x88551,f319(x88552,x88553)),x88553)
% 28.25/28.12 [9023]P26(x90231,x90232,x90233,x90234)+~P26(x90231,x90235,f319(f66(x90232,x90235,x90231,x90236),x90233),x90234)
% 28.25/28.12 [9095]~E(x90956,x90954)+E(f319(f68(x90951,x90952,x90953,x90954,x90955),x90956),x90955)
% 28.25/28.12 [9096]~E(x90966,x90964)+E(f319(f68(x90961,x90962,x90963,x90964,x90965),x90966),x90965)
% 28.25/28.12 [9101]E(x91011,x91012)+E(f319(f68(x91013,x91014,x91015,x91012,x91016),x91011),f319(x91015,x91011))
% 28.25/28.12 [9102]E(x91021,x91022)+E(f319(f68(x91023,x91024,x91025,x91022,x91026),x91021),f319(x91025,x91021))
% 28.25/28.12 [9103]E(x91031,x91032)+E(f319(f68(x91033,x91034,x91035,x91032,x91036),x91031),f319(x91035,x91031))
% 28.25/28.12 [9115]~P26(x91154,x91152,f319(f66(x91151,x91152,x91154,x91153),x91155),x91156)+P26(x91151,x91152,x91153,f319(f302(x91154,x91151,x91155),x91156))
% 28.25/28.12 [9773]P53(x97731,x97732,x97733,x97734,x97735,x97736)+~P1(f319(f319(x97733,f319(x97734,x97735)),f319(x97734,x97736)))
% 28.25/28.12 [9774]P53(x97741,x97742,x97743,x97744,x97745,x97746)+~P1(f319(f319(x97743,f319(x97744,x97745)),f319(x97744,x97746)))
% 28.25/28.12 [9835]P1(f319(f55(x98351),x98352))+~P1(f319(f60(x98351,x98353,x98354,x98355,x98352),x98356))
% 28.25/28.12 [9844]~P1(f319(f319(f321(x98444),x98443),f292(x98444,x98445,x98441,x98442,x98446)))+P1(f319(f319(x98441,x98442),x98443))
% 28.25/28.12 [9845]~P1(f319(f319(f321(x98454),x98453),f289(x98454,x98451,x98455,x98452,x98456)))+P1(f319(f319(x98451,x98452),x98453))
% 28.25/28.12 [9846]~P1(f319(f319(f321(x98464),x98462),f292(x98464,x98461,x98465,x98466,x98463)))+P1(f319(f319(x98461,x98462),x98463))
% 28.25/28.12 [9847]~P1(f319(f319(f321(x98474),x98472),f289(x98474,x98475,x98471,x98476,x98473)))+P1(f319(f319(x98471,x98472),x98473))
% 28.25/28.12 [9909]~P53(x99095,x99096,x99091,x99092,x99093,x99094)+P1(f319(f319(x99091,f319(x99092,x99093)),f319(x99092,x99094)))
% 28.25/28.12 [9910]~P53(x99105,x99106,x99101,x99102,x99103,x99104)+P1(f319(f319(x99101,f319(x99102,x99103)),f319(x99102,x99104)))
% 28.25/28.12 [10374]P13(x103741,x103742,x103743,x103744,x103745,x103746)+~E(f319(f319(x103746,f860(x103743,x103746,x103745,x103742,x103744,x103741)),f864(x103743,x103746,x103745,x103742,x103744,x103741)),f319(f319(x103746,f861(x103743,x103746,x103745,x103742,x103744,x103741)),f865(x103743,x103746,x103745,x103742,x103744,x103741)))
% 28.25/28.12 [5978]E(x59781,x59782)+~E(f319(f319(f244(x59783,x59784),x59785),x59781),f319(f319(f244(x59783,x59784),x59786),x59782))
% 28.25/28.12 [5979]E(x59791,x59792)+~E(f319(f319(f244(x59793,x59794),x59795),x59791),f319(f319(f244(x59793,x59794),x59796),x59792))
% 28.25/28.12 [5980]E(x59801,x59802)+~E(f319(f319(f244(x59803,x59804),x59801),x59805),f319(f319(f244(x59803,x59804),x59802),x59806))
% 28.25/28.12 [5981]E(x59811,x59812)+~E(f319(f319(f244(x59813,x59814),x59811),x59815),f319(f319(f244(x59813,x59814),x59812),x59816))
% 28.25/28.12 [6119]~P18(x61195,x61196,x61191)+E(f319(f319(x61191,x61192),f319(f319(x61191,x61193),x61194)),f319(f319(x61191,x61193),f319(f319(x61191,x61192),x61194)))
% 28.25/28.12 [7560]~P33(x75604,x75601,f319(f319(f143(x75604),x75602),x75605),f319(f319(f143(x75604),x75603),x75606))+P1(f319(f319(x75601,x75602),x75603))
% 28.25/28.12 [7913]P33(x79131,x79132,x79133,x79134)+~P33(x79131,x79132,f319(f319(f143(x79131),x79135),x79133),f319(f319(f143(x79131),x79136),x79134))
% 28.25/28.12 [8959]~P61(x89595,x89591,x89592,x89596,x89594)+P1(f319(f319(f321(x89591),f319(x89592,x89593)),x89594))
% 28.25/28.12 [9142]E(f319(f70(x91421,x91422,x91423,x91424,x91425),x91426),f319(x91423,x91426))+P1(f319(f319(f321(x91421),x91426),x91425))
% 28.25/28.12 [9143]E(f319(f70(x91431,x91432,x91433,x91434,x91435),x91436),f319(x91433,x91436))+P1(f319(f319(f321(x91431),x91436),x91435))
% 28.25/28.12 [9165]~E(x91653,f319(f319(f143(x91651),x91655),x91656))+P1(f319(f319(f321(f931(f926(x91651),f926(x91651))),f319(f319(f244(f926(x91651),f926(x91651)),x91652),f319(f319(f126(x91651),x91652),x91653))),f139(x91651,x91654)))
% 28.25/28.12 [9169]E(f319(f70(x91691,x91692,x91693,x91694,x91695),x91696),f319(x91694,x91696))+~P1(f319(f319(f321(x91691),x91696),x91695))
% 28.25/28.12 [9170]E(f319(f70(x91701,x91702,x91703,x91704,x91705),x91706),f319(x91704,x91706))+~P1(f319(f319(f321(x91701),x91706),x91705))
% 28.25/28.12 [9405]~P35(x94051,x94052,x94053,x94055,x94056)+P35(x94051,x94052,x94053,f319(f319(f167(x94051),x94054),x94055),f319(f319(f167(x94052),x94054),x94056))
% 28.25/28.12 [9406]~P35(x94061,x94062,x94063,x94065,x94066)+P35(x94061,x94062,x94063,f319(f319(f130(x94061),x94064),x94065),f319(f319(f130(x94062),x94064),x94066))
% 28.25/28.12 [9669]E(f319(f302(x96691,x96692,f68(x96691,x96692,x96693,x96694,x96695)),x96696),f319(f302(x96691,x96692,x96693),x96696))+P1(f319(f319(f321(x96691),x96694),x96696))
% 28.25/28.12 [9672]E(f319(f319(f146(x96721,x96722),f68(x96721,x96722,x96723,x96724,x96725)),x96726),f319(f319(f146(x96721,x96722),x96723),x96726))+P1(f319(f319(f321(x96721),x96724),f319(f164(x96721),x96726)))
% 28.25/28.12 [9908]~P25(x99084,x99082,x99085,x99083,x99086,x99081)+E(f319(x99081,f180(f932(x99082,a923))),x99083)
% 28.25/28.12 [10161]~E(f319(x101614,f319(f243(x101611,x101613),x101615)),f319(x101616,f319(f243(x101611,x101613),x101615)))+E(f319(f250(x101611,x101612,x101613,x101613,x101614,f25(x101613)),x101615),f319(f250(x101611,x101612,x101613,x101613,x101616,f25(x101613)),x101615))
% 28.25/28.12 [10162]~E(f319(x101624,f319(f248(x101621,x101622),x101625)),f319(x101626,f319(f248(x101621,x101622),x101625)))+E(f319(f250(x101621,x101621,x101622,x101623,f25(x101621),x101624),x101625),f319(f250(x101621,x101621,x101622,x101623,f25(x101621),x101626),x101625))
% 28.25/28.12 [10216]~E(f319(f250(x102162,x102166,x102163,x102163,x102161,f25(x102163)),x102164),f319(f250(x102162,x102166,x102163,x102163,x102165,f25(x102163)),x102164))+E(f319(x102161,f319(f243(x102162,x102163),x102164)),f319(x102165,f319(f243(x102162,x102163),x102164)))
% 28.25/28.12 [10217]~E(f319(f250(x102172,x102172,x102173,x102176,f25(x102172),x102171),x102174),f319(f250(x102172,x102172,x102173,x102176,f25(x102172),x102175),x102174))+E(f319(x102171,f319(f248(x102172,x102173),x102174)),f319(x102175,f319(f248(x102172,x102173),x102174)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [9063]P1(f319(f319(f321(x90631),x90632),x90633))+~P1(f319(f319(f321(f931(x90631,x90634)),f319(f319(f244(x90631,x90634),x90632),x90635)),f319(f319(f246(x90631,x90634),x90633),x90636)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [9079]P1(f319(f319(f321(x90791),x90792),f319(x90793,x90794)))+~P1(f319(f319(f321(f931(x90795,x90791)),f319(f319(f244(x90795,x90791),x90794),x90792)),f319(f319(f246(x90795,x90791),x90796),x90793)))
% 28.25/28.12 [9524]P1(f319(f319(f321(f931(x95241,x95241)),f319(f319(f244(x95241,x95241),f319(x95242,x95243)),f319(x95242,x95244))),x95245))+~P1(f319(f319(f321(f931(x95246,x95246)),f319(f319(f244(x95246,x95246),x95243),x95244)),f319(f319(f280(x95241,x95246),x95245),x95242)))
% 28.25/28.12 [9544]~P1(f319(f319(f321(f931(x95444,x95444)),f319(f319(f244(x95444,x95444),f319(x95446,x95442)),f319(x95446,x95443))),x95445))+P1(f319(f319(f321(f931(x95441,x95441)),f319(f319(f244(x95441,x95441),x95442),x95443)),f319(f319(f280(x95444,x95441),x95445),x95446)))
% 28.25/28.12 [10220]E(f319(f319(f244(x102201,x102202),f666(x102203,x102204,x102205,x102206,x102202,x102201)),f667(x102203,x102204,x102205,x102206,x102202,x102201)),x102206)+~P1(f319(f319(f321(f931(x102201,x102202)),x102206),f319(f319(f281(x102201,x102205,x102202),x102204),x102203)))
% 28.25/28.12 [10225]~E(f319(x102253,f907(x102254,x102252,x102256,x102253,x102255,x102251)),f319(x102256,f907(x102254,x102252,x102256,x102253,x102255,x102251)))+E(f319(f319(f93(f932(x102251,a923)),f319(f303(x102251,x102252,x102253),x102254)),x102255),f319(f319(f93(f932(x102251,a923)),f319(f303(x102251,x102252,x102256),x102254)),x102255))
% 28.25/28.12 [10287]E(f319(f319(f93(f932(x102871,a923)),f319(f303(x102871,x102872,x102873),x102874)),x102875),f319(f319(f93(f932(x102871,a923)),f319(f303(x102871,x102872,x102876),x102874)),x102875))+P1(f319(f319(f321(x102871),f907(x102874,x102872,x102873,x102876,x102875,x102871)),x102875))
% 28.25/28.12 [10440]~P1(f319(f319(f321(f931(x104401,x104406)),x104405),f319(f319(f281(x104401,x104402,x104406),x104404),x104403)))+P1(f319(f319(f321(f931(x104401,x104402)),f319(f319(f244(x104401,x104402),f666(x104403,x104404,x104402,x104405,x104406,x104401)),f668(x104403,x104404,x104402,x104405,x104406,x104401))),x104404))
% 28.25/28.12 [10441]~P1(f319(f319(f321(f931(x104416,x104412)),x104415),f319(f319(f281(x104416,x104411,x104412),x104414),x104413)))+P1(f319(f319(f321(f931(x104411,x104412)),f319(f319(f244(x104411,x104412),f668(x104413,x104414,x104411,x104415,x104412,x104416)),f667(x104413,x104414,x104411,x104415,x104412,x104416))),x104413))
% 28.25/28.12 [10442]P13(x104421,x104422,x104423,x104424,x104425,x104426)+P1(f319(f319(f321(f931(x104422,x104422)),f319(f319(f244(x104422,x104422),f865(x104423,x104426,x104425,x104422,x104424,x104421)),f864(x104423,x104426,x104425,x104422,x104424,x104421))),x104425))
% 28.25/28.12 [10443]P13(x104431,x104432,x104433,x104434,x104435,x104436)+P1(f319(f319(f321(f931(x104431,x104431)),f319(f319(f244(x104431,x104431),f861(x104433,x104436,x104435,x104432,x104434,x104431)),f860(x104433,x104436,x104435,x104432,x104434,x104431))),x104434))
% 28.25/28.12 [7983]~P6(x79832)+E(f319(f319(f33(x79831,x79832),x79833),f319(f319(f7(x79831,x79834,x79832),x79835),x79836)),f319(f319(f319(f33(x79831,f932(x79834,x79832)),x79833),x79835),x79836))
% 28.25/28.12 [7984]~P6(x79842)+E(f319(f319(f34(x79841,x79842),x79843),f319(f319(f7(x79841,x79844,x79842),x79845),x79846)),f319(f319(f319(f34(x79841,f932(x79844,x79842)),x79843),x79845),x79846))
% 28.25/28.12 [8764]E(f319(f319(f33(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(f33(x87641,f932(x87642,a923)),x87643),x87645)))+~P1(f319(f319(f321(x87641),x87646),x87643))
% 28.25/28.12 [8765]E(f319(f319(f34(x87651,f932(x87652,a923)),x87653),f319(f319(f8(f932(x87652,a923),f932(x87652,a923),x87651),f319(f301(x87652),x87654)),x87655)),f319(f319(f301(x87652),x87654),f319(f319(f34(x87651,f932(x87652,a923)),x87653),x87655)))+~P1(f319(f319(f321(x87651),x87656),x87653))
% 28.25/28.12 [9221]~P6(x92212)+E(f319(f319(f33(x92211,x92212),x92213),f319(f319(f8(f932(x92214,x92212),x92212,x92211),f319(f33(x92214,x92212),x92215)),f319(f7(x92214,x92211,x92212),x92216))),f319(f319(f33(x92214,x92212),x92215),f319(f319(f8(f932(x92211,x92212),x92212,x92214),f319(f33(x92211,x92212),x92213)),x92216)))
% 28.25/28.12 [9222]~P6(x92222)+E(f319(f319(f34(x92221,x92222),x92223),f319(f319(f8(f932(x92224,x92222),x92222,x92221),f319(f34(x92224,x92222),x92225)),f319(f7(x92224,x92221,x92222),x92226))),f319(f319(f34(x92224,x92222),x92225),f319(f319(f8(f932(x92221,x92222),x92222,x92224),f319(f34(x92221,x92222),x92223)),x92226)))
% 28.25/28.12 [9429]P1(f319(f319(f321(x94291),x94292),f319(f164(x94291),x94293)))+~P1(f319(f319(f321(f931(x94294,x94291)),f319(f319(f244(x94294,x94291),x94295),x94292)),f319(f164(f931(x94294,x94291)),f319(f319(f173(x94294,x94291),x94296),x94293))))
% 28.25/28.12 [9430]P1(f319(f319(f321(x94301),x94302),f319(f164(x94301),x94303)))+~P1(f319(f319(f321(f931(x94301,x94304)),f319(f319(f244(x94301,x94304),x94302),x94305)),f319(f164(f931(x94301,x94304)),f319(f319(f173(x94301,x94304),x94303),x94306))))
% 28.25/28.12 [9431]P1(f319(f319(f321(x94311),x94312),f319(f164(x94311),x94313)))+~P1(f319(f319(f321(f931(x94314,x94311)),f319(f319(f244(x94314,x94311),x94315),x94312)),f319(f164(f931(x94314,x94311)),f319(f319(f173(x94314,x94311),x94316),x94313))))
% 28.25/28.12 [9432]P1(f319(f319(f321(x94321),x94322),f319(f164(x94321),x94323)))+~P1(f319(f319(f321(f931(x94321,x94324)),f319(f319(f244(x94321,x94324),x94322),x94325)),f319(f164(f931(x94321,x94324)),f319(f319(f173(x94321,x94324),x94323),x94326))))
% 28.25/28.12 [9540]P1(f319(f319(f226(f932(x95401,a923)),f319(f277(x95402,x95401,x95403),x95404)),x95405))+~P1(f319(f319(f226(f932(f931(x95402,x95401),a923)),x95403),f319(f319(f246(x95402,x95401),x95406),f319(f16(f932(x95401,a923),x95402),x95405))))
% 28.25/28.12 [9545]~P27(x95454,x95452,x95455,f234(f932(x95454,a923)),f234(f932(x95452,a923)))+E(f319(f319(f34(x95451,f932(x95452,a923)),x95453),f319(f319(f8(f932(x95454,a923),f932(x95452,a923),x95451),f302(x95454,x95452,x95455)),x95456)),f319(f302(x95454,x95452,x95455),f319(f319(f34(x95451,f932(x95454,a923)),x95453),x95456)))
% 28.25/28.12 [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),x97375))),f139(x97371,x97376)))+~P1(f319(f319(f321(f931(x97371,x97371)),f319(f319(f244(x97371,x97371),x97372),x97374)),x97376))
% 28.25/28.12 [10215]E(f319(f319(f244(x102151,x102152),f604(x102153,x102154,x102155,x102152,x102151,x102156)),f607(x102153,x102154,x102155,x102152,x102151,x102156)),x102156)+P1(f319(f319(f321(x102155),x102154),f319(f319(f249(x102151,x102152,f932(x102155,a923)),x102153),x102156)))
% 28.25/28.12 [10222]E(f319(f319(f244(x102221,x102222),f605(x102223,x102224,x102222,x102221,x102225,x102226)),f606(x102223,x102224,x102222,x102221,x102225,x102226)),x102223)+~P1(f319(f319(f321(x102226),x102225),f319(f319(f249(x102221,x102222,f932(x102226,a923)),x102224),x102223)))
% 28.25/28.12 [10387]P1(f319(f319(f321(x103871),x103872),f319(f319(x103873,f605(x103874,x103873,x103875,x103876,x103872,x103871)),f606(x103874,x103873,x103875,x103876,x103872,x103871))))+~P1(f319(f319(f321(x103871),x103872),f319(f319(f249(x103876,x103875,f932(x103871,a923)),x103873),x103874)))
% 28.25/28.12 [10412]~P1(f319(f319(f321(x104121),x104122),f319(f319(x104125,f604(x104125,x104122,x104121,x104124,x104123,x104126)),f607(x104125,x104122,x104121,x104124,x104123,x104126))))+P1(f319(f319(f321(x104121),x104122),f319(f319(f249(x104123,x104124,f932(x104121,a923)),x104125),x104126)))
% 28.25/28.12 [8661]E(x86611,x86612)+E(f319(f319(f151(x86613,f319(f319(f151(x86613,x86614),x86611),x86615)),x86612),x86616),f319(f319(f151(x86613,f319(f319(f151(x86613,x86614),x86612),x86616)),x86611),x86615))
% 28.25/28.12 [9799]~P1(f319(f319(f321(x97993),x97996),x97995))+E(f319(f319(f301(x97991),x97992),f319(f302(x97993,x97991,x97994),f319(f319(f23(f932(x97993,a923)),x97995),f319(f319(f301(x97993),x97996),f180(f932(x97993,a923)))))),f319(f302(x97993,x97991,f68(x97993,x97991,x97994,x97996,x97992)),x97995))
% 28.25/28.12 [9300]~P1(f319(f319(x93004,x93005),x93006))+P1(f319(f319(f319(f319(f102(f932(x93001,f932(x93002,a923))),x93003),x93004),x93005),x93006))
% 28.25/28.12 [9301]~P1(f319(f319(x93014,x93015),x93016))+P1(f319(f319(f319(f319(f102(f932(x93011,f932(x93012,a923))),x93013),x93014),x93015),x93016))
% 28.25/28.12 [9302]~P1(f319(f319(x93023,x93025),x93026))+P1(f319(f319(f319(f319(f102(f932(x93021,f932(x93022,a923))),x93023),x93024),x93025),x93026))
% 28.25/28.12 [9303]~P1(f319(f319(x93033,x93035),x93036))+P1(f319(f319(f319(f319(f102(f932(x93031,f932(x93032,a923))),x93033),x93034),x93035),x93036))
% 28.25/28.12 [9594]P1(f319(f319(x95941,x95942),x95943))+~P1(f319(f319(f319(f319(f93(f932(x95944,f932(x95945,a923))),x95946),x95941),x95942),x95943))
% 28.25/28.12 [9595]P1(f319(f319(x95951,x95952),x95953))+~P1(f319(f319(f319(f319(f93(f932(x95954,f932(x95955,a923))),x95951),x95956),x95952),x95953))
% 28.25/28.12 [9596]P1(f319(f319(x95961,x95962),x95963))+~P1(f319(f319(f319(f319(f93(f932(x95964,f932(x95965,a923))),x95966),x95961),x95962),x95963))
% 28.25/28.12 [9597]P1(f319(f319(x95971,x95972),x95973))+~P1(f319(f319(f319(f319(f93(f932(x95974,f932(x95975,a923))),x95971),x95976),x95972),x95973))
% 28.25/28.12 [10051]~P79(x100512)+E(f319(f319(f6(x100511,x100512),f319(f319(f7(x100511,f932(x100513,a923),x100512),f319(f319(f8(f932(x100513,x100512),f932(f932(x100513,a923),x100512),x100511),f6(x100513,x100512)),x100514)),x100515)),x100516),f319(f319(f6(f931(x100511,x100513),x100512),f319(f249(x100511,x100513,x100512),x100514)),f319(f319(f246(x100511,x100513),x100516),f319(f16(f932(x100513,a923),x100511),x100515))))
% 28.25/28.12 [10052]~P78(x100522)+E(f319(f319(f9(x100521,x100522),f319(f319(f7(x100521,f932(x100523,a923),x100522),f319(f319(f8(f932(x100523,x100522),f932(f932(x100523,a923),x100522),x100521),f9(x100523,x100522)),x100524)),x100525)),x100526),f319(f319(f9(f931(x100521,x100523),x100522),f319(f249(x100521,x100523,x100522),x100524)),f319(f319(f246(x100521,x100523),x100526),f319(f16(f932(x100523,a923),x100521),x100525))))
% 28.25/28.12 [10186]~P79(x101862)+E(f319(f319(f6(x101861,x101862),f319(f319(f7(x101861,f932(x101863,a923),x101862),f319(f319(f8(f932(x101863,x101862),f932(f932(x101863,a923),x101862),x101861),f6(x101863,x101862)),f319(f7(x101863,x101861,x101862),x101864))),x101865)),x101866),f319(f319(f6(x101863,x101862),f319(f319(f7(x101863,f932(x101861,a923),x101862),f319(f319(f8(f932(x101861,x101862),f932(f932(x101861,a923),x101862),x101863),f6(x101861,x101862)),x101864)),x101866)),x101865))
% 28.25/28.12 [10507]~P1(f319(f319(f321(f931(x105071,x105072)),f319(f319(f244(x105071,x105072),x105075),x105076)),f319(f319(f102(f932(f931(x105071,x105072),a923)),x105073),x105074)))+P1(f319(f319(f319(f319(f102(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))
% 28.25/28.12 [10508]~P1(f319(f319(f321(f931(x105081,x105082)),f319(f319(f244(x105081,x105082),x105085),x105086)),f319(f319(f93(f932(f931(x105081,x105082),a923)),x105083),x105084)))+P1(f319(f319(f319(f319(f93(f932(x105081,f932(x105082,a923))),f319(f319(f7(x105081,f932(f931(x105081,x105082),a923),f932(x105082,a923)),f319(f319(f8(f932(x105082,f932(f932(f931(x105081,x105082),a923),a923)),f932(f932(f931(x105081,x105082),a923),f932(x105082,a923)),x105081),f7(x105082,f932(f931(x105081,x105082),a923),a923)),f319(f319(f8(f932(x105082,f931(x105081,x105082)),f932(x105082,f932(f932(f931(x105081,x105082),a923),a923)),x105081),f319(f8(f931(x105081,x105082),f932(f932(f931(x105081,x105082),a923),a923),x105082),f321(f931(x105081,x105082)))),f244(x105081,x105082)))),x105083)),f319(f319(f7(x105081,f932(f931(x105081,x105082),a923),f932(x105082,a923)),f319(f319(f8(f932(x105082,f932(f932(f931(x105081,x105082),a923),a923)),f932(f932(f931(x105081,x105082),a923),f932(x105082,a923)),x105081),f7(x105082,f932(f931(x105081,x105082),a923),a923)),f319(f319(f8(f932(x105082,f931(x105081,x105082)),f932(x105082,f932(f932(f931(x105081,x105082),a923),a923)),x105081),f319(f8(f931(x105081,x105082),f932(f932(f931(x105081,x105082),a923),a923),x105082),f321(f931(x105081,x105082)))),f244(x105081,x105082)))),x105084)),x105085),x105086))
% 28.25/28.12 [10518]P1(f319(f319(f321(f931(x105181,x105182)),f319(f319(f244(x105181,x105182),x105183),x105184)),f319(f319(f102(f932(f931(x105181,x105182),a923)),x105185),x105186)))+~P1(f319(f319(f319(f319(f102(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))
% 28.25/28.12 [10519]P1(f319(f319(f321(f931(x105191,x105192)),f319(f319(f244(x105191,x105192),x105193),x105194)),f319(f319(f93(f932(f931(x105191,x105192),a923)),x105195),x105196)))+~P1(f319(f319(f319(f319(f93(f932(x105191,f932(x105192,a923))),f319(f319(f7(x105191,f932(f931(x105191,x105192),a923),f932(x105192,a923)),f319(f319(f8(f932(x105192,f932(f932(f931(x105191,x105192),a923),a923)),f932(f932(f931(x105191,x105192),a923),f932(x105192,a923)),x105191),f7(x105192,f932(f931(x105191,x105192),a923),a923)),f319(f319(f8(f932(x105192,f931(x105191,x105192)),f932(x105192,f932(f932(f931(x105191,x105192),a923),a923)),x105191),f319(f8(f931(x105191,x105192),f932(f932(f931(x105191,x105192),a923),a923),x105192),f321(f931(x105191,x105192)))),f244(x105191,x105192)))),x105195)),f319(f319(f7(x105191,f932(f931(x105191,x105192),a923),f932(x105192,a923)),f319(f319(f8(f932(x105192,f932(f932(f931(x105191,x105192),a923),a923)),f932(f932(f931(x105191,x105192),a923),f932(x105192,a923)),x105191),f7(x105192,f932(f931(x105191,x105192),a923),a923)),f319(f319(f8(f932(x105192,f931(x105191,x105192)),f932(x105192,f932(f932(f931(x105191,x105192),a923),a923)),x105191),f319(f8(f931(x105191,x105192),f932(f932(f931(x105191,x105192),a923),a923),x105192),f321(f931(x105191,x105192)))),f244(x105191,x105192)))),x105196)),x105193),x105194))
% 28.25/28.12 [10501]~P1(f319(f319(f321(f931(x105012,x105013)),f319(f319(f244(x105012,x105013),x105015),x105016)),f319(f319(f33(x105011,f932(f931(x105012,x105013),a923)),f234(f932(x105011,a923))),x105014)))+P1(f319(f319(f319(f319(f33(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))
% 28.25/28.12 [10502]~P1(f319(f319(f321(f931(x105022,x105023)),f319(f319(f244(x105022,x105023),x105025),x105026)),f319(f319(f34(x105021,f932(f931(x105022,x105023),a923)),f234(f932(x105021,a923))),x105024)))+P1(f319(f319(f319(f319(f34(x105021,f932(x105022,f932(x105023,a923))),f234(f932(x105021,a923))),f319(f319(f8(f932(f931(x105022,x105023),a923),f932(x105022,f932(x105023,a923)),x105021),f319(f7(x105022,f932(f931(x105022,x105023),a923),f932(x105023,a923)),f319(f319(f8(f932(x105023,f932(f932(f931(x105022,x105023),a923),a923)),f932(f932(f931(x105022,x105023),a923),f932(x105023,a923)),x105022),f7(x105023,f932(f931(x105022,x105023),a923),a923)),f319(f319(f8(f932(x105023,f931(x105022,x105023)),f932(x105023,f932(f932(f931(x105022,x105023),a923),a923)),x105022),f319(f8(f931(x105022,x105023),f932(f932(f931(x105022,x105023),a923),a923),x105023),f321(f931(x105022,x105023)))),f244(x105022,x105023))))),x105024)),x105025),x105026))
% 28.25/28.12 [10512]P1(f319(f319(f321(f931(x105121,x105122)),f319(f319(f244(x105121,x105122),x105123),x105124)),f319(f319(f33(x105125,f932(f931(x105121,x105122),a923)),f234(f932(x105125,a923))),x105126)))+~P1(f319(f319(f319(f319(f33(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))
% 28.25/28.12 [10513]P1(f319(f319(f321(f931(x105131,x105132)),f319(f319(f244(x105131,x105132),x105133),x105134)),f319(f319(f34(x105135,f932(f931(x105131,x105132),a923)),f234(f932(x105135,a923))),x105136)))+~P1(f319(f319(f319(f319(f34(x105135,f932(x105131,f932(x105132,a923))),f234(f932(x105135,a923))),f319(f319(f8(f932(f931(x105131,x105132),a923),f932(x105131,f932(x105132,a923)),x105135),f319(f7(x105131,f932(f931(x105131,x105132),a923),f932(x105132,a923)),f319(f319(f8(f932(x105132,f932(f932(f931(x105131,x105132),a923),a923)),f932(f932(f931(x105131,x105132),a923),f932(x105132,a923)),x105131),f7(x105132,f932(f931(x105131,x105132),a923),a923)),f319(f319(f8(f932(x105132,f931(x105131,x105132)),f932(x105132,f932(f932(f931(x105131,x105132),a923),a923)),x105131),f319(f8(f931(x105131,x105132),f932(f932(f931(x105131,x105132),a923),a923),x105132),f321(f931(x105131,x105132)))),f244(x105131,x105132))))),x105136)),x105133),x105134))
% 28.25/28.12 [7663]E(f319(x76631,f319(x76632,x76633)),f319(x76634,x76633))+~E(f319(f66(x76635,x76636,x76637,x76631),x76632),x76634)
% 28.25/28.12 [9815]E(x98151,x98152)+E(f68(x98153,x98154,f68(x98153,x98154,x98155,x98151,x98156),x98152,x98157),f68(x98153,x98154,f68(x98153,x98154,x98155,x98152,x98157),x98151,x98156))
% 28.25/28.12 [9907]~P24(x99073,x99074,x99071,x99075,x99076,x99077)+E(f319(f319(x99071,x99072),x99072),x99072)
% 28.25/28.12 [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))
% 28.25/28.12 [8694]E(f319(x86941,f319(x86942,x86943)),f319(x86944,x86943))+~E(f319(f66(x86945,x86946,x86947,x86941),x86942),f319(f66(x86946,x86946,x86947,f25(x86946)),x86944))
% 28.25/28.12 [9052]~P35(x90524,x90525,x90521,f319(f319(f143(x90524),x90522),x90526),f319(f319(f143(x90525),x90523),x90527))+P1(f319(f319(x90521,x90522),x90523))
% 28.25/28.12 [9438]P35(x94381,x94382,x94383,x94384,x94385)+~P35(x94381,x94382,x94383,f319(f319(f143(x94381),x94386),x94384),f319(f319(f143(x94382),x94387),x94385))
% 28.25/28.12 [10087]P1(f319(f319(x100871,x100872),f563(x100873,x100872,x100874,x100871)))+~P1(f319(f319(f245(x100875,x100876,x100877,x100871,x100874),x100872),x100873))
% 28.25/28.12 [10111]P1(f319(f319(x101111,f563(x101112,x101113,x101111,x101114)),x101112))+~P1(f319(f319(f245(x101115,x101116,x101117,x101114,x101111),x101113),x101112))
% 28.25/28.12 [9174]~P22(x91746,x91741,x91743,x91747)+E(f319(f66(x91741,x91741,x91742,f319(x91743,x91744)),f319(f66(x91741,x91741,x91742,f319(x91743,x91744)),x91745)),f319(f66(x91741,x91741,x91742,f319(x91743,x91744)),x91745))
% 28.25/28.12 [9548]~P35(x95483,x95482,x95484,f319(f319(f146(x95481,x95483),x95485),x95486),x95487)+P35(x95481,x95482,f319(f319(f8(x95483,f932(x95482,a923),x95481),x95484),x95485),x95486,x95487)
% 28.25/28.12 [9572]P35(x95721,x95722,x95723,f319(f319(f146(x95724,x95721),x95725),x95726),x95727)+~P35(x95724,x95722,f319(f319(f8(x95721,f932(x95722,a923),x95724),x95723),x95725),x95726,x95727)
% 28.25/28.12 [9173]~P1(f319(f319(f321(x91731),x91732),f319(f319(x91735,x91736),x91737)))+P1(f319(f319(f321(x91731),x91732),f319(f319(f249(x91733,x91734,f932(x91731,a923)),x91735),f319(f319(f244(x91733,x91734),x91736),x91737))))
% 28.25/28.12 [9463]P1(f319(f319(f319(x94631,x94632),x94633),x94634))+~P1(f319(f319(f319(f249(x94635,x94636,f932(x94637,a923)),x94631),f319(f319(f244(x94635,x94636),x94632),x94633)),x94634))
% 28.25/28.12 [9611]P1(f319(f319(f321(x96111),f319(f319(x96112,x96113),x96114)),f319(f302(f931(x96115,x96116),x96111,f319(f249(x96115,x96116,x96111),x96112)),x96117)))+~P1(f319(f319(f321(f931(x96115,x96116)),f319(f319(f244(x96115,x96116),x96113),x96114)),x96117))
% 28.25/28.12 [9962]P1(f319(f319(f321(f931(f926(x99621),f926(x99621))),f319(f319(f244(f926(x99621),f926(x99621)),f319(f319(f126(x99621),x99622),f319(f319(f143(x99621),x99623),x99624))),f319(f319(f126(x99621),x99622),f319(f319(f143(x99621),x99625),x99626)))),f139(x99621,x99627)))+~P1(f319(f319(f321(f931(x99621,x99621)),f319(f319(f244(x99621,x99621),x99623),x99625)),x99627))
% 28.25/28.12 [10034]~P35(x100341,x100343,x100344,x100346,f319(f319(f146(x100342,x100343),x100345),x100347))+P35(x100341,x100342,f319(f319(f7(x100341,f932(x100342,x100343),f932(x100342,a923)),f319(f319(f8(f932(x100343,a923),f932(f932(x100342,x100343),f932(x100342,a923)),x100341),f8(x100343,a923,x100342)),x100344)),x100345),x100346,x100347)
% 28.25/28.12 [10115]P35(x101151,x101152,x101153,x101154,f319(f319(f146(x101155,x101152),x101156),x101157))+~P35(x101151,x101155,f319(f319(f7(x101151,f932(x101155,x101152),f932(x101155,a923)),f319(f319(f8(f932(x101152,a923),f932(f932(x101155,x101152),f932(x101155,a923)),x101151),f8(x101152,a923,x101155)),x101153)),x101156),x101154,x101157)
% 28.25/28.12 [10427]P1(f319(f319(f321(x104271),f465(x104272,x104273,x104274,x104275,x104276,x104277,x104271)),x104275))+P1(f319(f319(f319(f319(f34(x104271,f932(x104277,f932(x104276,a923))),x104275),x104274),x104273),x104272))
% 28.25/28.12 [10428]P1(f319(f319(f321(x104281),f507(x104282,x104283,x104284,x104285,x104286,x104287,x104281)),x104287))+P1(f319(f319(f319(f319(f34(x104281,f932(x104283,f932(x104282,a923))),x104287),x104286),x104285),x104284))
% 28.25/28.12 [10429]P1(f319(f319(f321(x104291),f450(x104292,x104293,x104294,x104295,x104296,x104297,x104291)),x104295))+~P1(f319(f319(f319(f319(f33(x104291,f932(x104297,f932(x104296,a923))),x104295),x104294),x104293),x104292))
% 28.25/28.12 [10430]P1(f319(f319(f321(x104301),f497(x104302,x104303,x104304,x104305,x104306,x104307,x104301)),x104305))+~P1(f319(f319(f319(f319(f33(x104301,f932(x104307,f932(x104306,a923))),x104305),x104304),x104303),x104302))
% 28.25/28.12 [10464]P1(f319(f319(f319(x104641,f450(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))
% 28.25/28.12 [10465]P1(f319(f319(f319(x104651,f497(x104652,x104653,x104651,x104654,x104655,x104656,x104657)),x104653),x104652))+~P1(f319(f319(f319(f319(f33(x104657,f932(x104656,f932(x104655,a923))),x104654),x104651),x104653),x104652))
% 28.25/28.12 [10480]~P1(f319(f319(f319(x104805,f465(x104807,x104806,x104805,x104804,x104803,x104802,x104801)),x104806),x104807))+P1(f319(f319(f319(f319(f34(x104801,f932(x104802,f932(x104803,a923))),x104804),x104805),x104806),x104807))
% 28.25/28.12 [10481]~P1(f319(f319(f319(x104815,f507(x104813,x104812,x104817,x104816,x104815,x104814,x104811)),x104816),x104817))+P1(f319(f319(f319(f319(f34(x104811,f932(x104812,f932(x104813,a923))),x104814),x104815),x104816),x104817))
% 28.25/28.12 [10500]~P1(f319(f319(f321(f931(x105001,x105003)),f319(f319(f244(x105001,x105003),x105006),x105007)),f319(f319(f281(x105001,x105002,x105003),x105004),x105005)))+P1(f319(f319(f245(x105001,x105002,x105003,f319(f319(f7(x105001,f932(f931(x105001,x105002),a923),f932(x105002,a923)),f319(f319(f8(f932(x105002,f932(f932(f931(x105001,x105002),a923),a923)),f932(f932(f931(x105001,x105002),a923),f932(x105002,a923)),x105001),f7(x105002,f932(f931(x105001,x105002),a923),a923)),f319(f319(f8(f932(x105002,f931(x105001,x105002)),f932(x105002,f932(f932(f931(x105001,x105002),a923),a923)),x105001),f319(f8(f931(x105001,x105002),f932(f932(f931(x105001,x105002),a923),a923),x105002),f321(f931(x105001,x105002)))),f244(x105001,x105002)))),x105004),f319(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)))),x105005)),x105006),x105007))
% 28.25/28.12 [10511]P1(f319(f319(f321(f931(x105111,x105112)),f319(f319(f244(x105111,x105112),x105113),x105114)),f319(f319(f281(x105111,x105115,x105112),x105116),x105117)))+~P1(f319(f319(f245(x105111,x105115,x105112,f319(f319(f7(x105111,f932(f931(x105111,x105115),a923),f932(x105115,a923)),f319(f319(f8(f932(x105115,f932(f932(f931(x105111,x105115),a923),a923)),f932(f932(f931(x105111,x105115),a923),f932(x105115,a923)),x105111),f7(x105115,f932(f931(x105111,x105115),a923),a923)),f319(f319(f8(f932(x105115,f931(x105111,x105115)),f932(x105115,f932(f932(f931(x105111,x105115),a923),a923)),x105111),f319(f8(f931(x105111,x105115),f932(f932(f931(x105111,x105115),a923),a923),x105115),f321(f931(x105111,x105115)))),f244(x105111,x105115)))),x105116),f319(f319(f7(x105115,f932(f931(x105115,x105112),a923),f932(x105112,a923)),f319(f319(f8(f932(x105112,f932(f932(f931(x105115,x105112),a923),a923)),f932(f932(f931(x105115,x105112),a923),f932(x105112,a923)),x105115),f7(x105112,f932(f931(x105115,x105112),a923),a923)),f319(f319(f8(f932(x105112,f931(x105115,x105112)),f932(x105112,f932(f932(f931(x105115,x105112),a923),a923)),x105115),f319(f8(f931(x105115,x105112),f932(f932(f931(x105115,x105112),a923),a923),x105112),f321(f931(x105115,x105112)))),f244(x105115,x105112)))),x105117)),x105113),x105114))
% 28.25/28.12 [10439]~P143(x104392)+E(f319(f319(f6(x104391,x104392),f319(f319(f7(x104391,f932(x104393,a923),x104392),f319(f319(f8(f932(x104393,x104392),f932(f932(x104393,a923),x104392),x104391),f6(x104393,x104392)),f319(f319(f7(x104391,f932(x104393,x104392),f932(x104393,x104392)),f319(f319(f8(f932(x104392,x104392),f932(f932(x104393,x104392),f932(x104393,x104392)),x104391),f8(x104392,x104392,x104393)),f319(f319(f8(x104392,f932(x104392,x104392),x104391),f75(x104392)),x104394))),x104395))),x104396)),x104397),f319(f319(f75(x104392),f319(f319(f6(x104391,x104392),x104394),x104397)),f319(f319(f6(x104393,x104392),x104395),x104396)))
% 28.25/28.12 [9496]~P21(x94967,x94961,x94963,x94968)+E(f319(f66(x94961,x94961,x94962,f319(x94963,x94964)),f319(f66(x94961,x94961,x94962,f319(x94963,x94965)),x94966)),f319(f66(x94961,x94961,x94962,f319(x94963,x94965)),f319(f66(x94961,x94961,x94962,f319(x94963,x94964)),x94966)))
% 28.25/28.12 [10505]E(f319(f319(f244(x105051,x105052),f319(x105053,f586(x105054,x105055,x105053,x105056,x105057,x105058,x105052,x105051))),f319(x105055,f587(x105054,x105055,x105053,x105056,x105057,x105058,x105052,x105051))),x105058)+~P1(f319(f319(f321(f931(x105051,x105052)),x105058),f319(f302(f931(x105057,x105056),f931(x105051,x105052),f250(x105057,x105051,x105056,x105052,x105053,x105055)),x105054)))
% 28.25/28.12 [10524]~P1(f319(f319(f321(f931(x105248,x105247)),x105246),f319(f302(f931(x105241,x105242),f931(x105248,x105247),f250(x105241,x105248,x105242,x105247,x105245,x105244)),x105243)))+P1(f319(f319(f321(f931(x105241,x105242)),f319(f319(f244(x105241,x105242),f586(x105243,x105244,x105245,x105242,x105241,x105246,x105247,x105248)),f587(x105243,x105244,x105245,x105242,x105241,x105246,x105247,x105248))),x105243))
% 28.25/28.12 [9949]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(x99491,x99491)),f319(f319(f244(x99491,x99491),x99493),x99495)),x99497))
% 28.25/28.12 [10494]E(f319(f134(x104941,x104942,f319(f7(x104942,x104941,x104941),x104943),f319(x104944,x104945)),x104946),f319(x104944,f319(f134(x104947,x104942,f319(f7(x104942,x104947,x104947),x104948),x104945),x104946)))+P1(f319(f319(f321(x104942),f754(x104945,x104948,x104944,x104943,x104947,x104941,x104946,x104942)),f319(f164(x104942),x104946)))
% 28.25/28.12 [10514]~E(f319(f66(x105141,x105141,x105147,f319(x105143,f754(x105145,x105148,x105144,x105143,x105147,x105141,x105146,x105142))),x105144),f319(f66(x105147,x105141,x105147,x105144),f319(x105148,f754(x105145,x105148,x105144,x105143,x105147,x105141,x105146,x105142))))+E(f319(f134(x105141,x105142,f319(f7(x105142,x105141,x105141),x105143),f319(x105144,x105145)),x105146),f319(x105144,f319(f134(x105147,x105142,f319(f7(x105142,x105147,x105147),x105148),x105145),x105146)))
% 28.25/28.12 [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))
% 28.25/28.12 [8699]E(f319(x86991,f319(x86992,x86993)),f319(x86994,f319(x86995,x86993)))+~E(f319(f66(x86996,x86997,x86998,x86991),x86992),f319(f66(x86999,x86997,x86998,x86994),x86995))
% 28.25/28.12 [10352]P1(f319(f319(f321(f931(x103521,x103522)),f319(f319(f244(x103521,x103522),f319(x103523,x103524)),f319(x103525,x103526))),f319(f302(f931(x103527,x103528),f931(x103521,x103522),f250(x103527,x103521,x103528,x103522,x103523,x103525)),x103529)))+~P1(f319(f319(f321(f931(x103527,x103528)),f319(f319(f244(x103527,x103528),x103524),x103526)),x103529))
% 28.25/28.12 [8997]~E(f319(x89974,f319(x89975,x89976)),f319(x89979,f319(x899710,x899711)))+E(f319(f319(f66(x89971,x89972,x89973,x89974),x89975),x89976),f319(f319(f66(x89977,x89972,x89978,x89979),x899710),x899711))
% 28.25/28.12 [9582]~P21(x95828,x95829,x958210,x958211)+E(f319(f66(x95821,x95822,x95823,x95824),f319(f66(x95825,x95821,x95823,x95826),x95827)),f319(f66(x95825,x95822,x95823,f319(f66(x95821,x95822,x95825,x95824),x95826)),x95827))
% 28.25/28.12 [4793]~P4(x47931)+~P108(x47931)+E(f93(x47931),f224(x47931))
% 28.25/28.12 [4794]~P4(x47941)+~P107(x47941)+E(f102(x47941),f225(x47941))
% 28.25/28.12 [5039]~P126(x50391)+~P99(x50391)+E(f319(f69(x50391),f319(f95(x50391),a89)),f72(x50391))
% 28.25/28.12 [5330]E(x53301,f2(a1))+E(f76(a1,x53301),f319(f73(a1),f72(a1)))+P1(f319(f319(f227(a1),f2(a1)),x53301))
% 28.25/28.12 [5535]E(x55351,f2(a1))+E(f76(a1,x55351),f72(a1))+~P1(f319(f319(f227(a1),f2(a1)),x55351))
% 28.25/28.12 [6856]~P42(x68561)+~P1(f319(f55(a1),x68561))+P1(f319(f55(a925),f319(f302(a1,a925,a96),x68561)))
% 28.25/28.12 [7222]E(f41(f72(a1),f319(f95(a1),x72221)),f319(f319(f244(a1,a1),f2(a1)),f72(a1)))+~P1(f319(f319(f227(a1),f2(a1)),f319(f95(a1),x72221)))+~P1(f319(f319(f227(a1),f72(a1)),f319(f95(a1),x72221)))
% 28.25/28.12 [7564]~P42(x75641)+P1(f319(f55(a1),x75641))+~P1(f319(f55(a925),f319(f302(a1,a925,a96),x75641)))
% 28.25/28.12 [8400]E(f319(f319(f244(a1,a1),f319(f95(a1),a89)),f319(f319(f74(a1),f72(a1)),f319(f95(a1),x84001))),f44(f72(a1),f319(f95(a1),x84001)))+~P1(f319(f319(f227(a1),f2(a1)),f319(f95(a1),x84001)))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),f72(a1)),f319(f95(a1),x84001))))
% 28.25/28.12 [10240]E(f319(f37(f319(f95(a1),x102401)),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),x102401)))),f41(f72(a1),f319(f95(a1),x102401)))+~P1(f319(f319(f227(a1),f2(a1)),f319(f95(a1),x102401)))+P1(f319(f319(f227(a1),f72(a1)),f319(f95(a1),x102401)))
% 28.25/28.12 [10246]E(f319(f37(f319(f95(a1),x102461)),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),x102461)))),f44(f72(a1),f319(f95(a1),x102461)))+~P1(f319(f319(f227(a1),f2(a1)),f319(f95(a1),x102461)))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),f72(a1)),f319(f95(a1),x102461))))
% 28.25/28.12 [9906]E(x99061,f180(f932(f931(a925,a925),a923)))+~P1(f319(f55(f931(a925,a925)),x99061))+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))),x99061)),a28))
% 28.25/28.12 [10088]E(x100881,f2(a925))+E(x100881,f319(a104,f2(a925)))+~P1(f319(f319(f227(a925),x100881),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)))))
% 28.25/28.12 [10382]E(x103821,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),x103821),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,x103821))+E(f39(a91,x103821,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))
% 28.25/28.12 [10227]E(x102271,f2(a91))+~E(f39(a91,x102271,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),x102271),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,x102271))
% 28.25/28.12 [4874]~P62(x48741,x48742)+P45(x48741,x48742)+~P46(a923)
% 28.25/28.12 [4803]~P149(x48031)+P29(x48031,x48032)+~E(x48032,f2(x48031))
% 28.25/28.12 [4804]~P4(x48041)+P14(x48041,x48042)+~E(x48042,f105(x48041))
% 28.25/28.12 [4813]~P126(x48131)+~E(x48132,f2(x48131))+E(f76(x48131,x48132),f2(x48131))
% 28.25/28.12 [4814]~P94(x48141)+~E(x48142,f2(x48141))+E(f76(x48141,x48142),f2(x48141))
% 28.25/28.12 [4822]~P149(x48222)+~P29(x48222,x48221)+E(x48221,f2(x48222))
% 28.25/28.12 [4867]~P126(x48672)+~E(f76(x48672,x48671),f2(x48672))+E(x48671,f2(x48672))
% 28.25/28.12 [4881]~P5(x48812)+~P5(x48811)+P5(f932(x48811,x48812))
% 28.25/28.12 [4882]~P5(x48822)+~P5(x48821)+P5(f931(x48821,x48822))
% 28.25/28.12 [4883]~P5(x48832)+~P5(x48831)+P5(f933(x48831,x48832))
% 28.25/28.12 [4884]~P71(x48842)+~P71(x48841)+P71(f932(x48841,x48842))
% 28.25/28.12 [4885]~P71(x48852)+~P71(x48851)+P71(f931(x48851,x48852))
% 28.25/28.12 [4886]~P71(x48862)+~P71(x48861)+P71(f933(x48861,x48862))
% 28.25/28.12 [4887]~P7(x48872)+~P7(x48871)+P7(f186(x48871,x48872))
% 28.25/28.12 [4888]~P111(x48882)+~P111(x48881)+P111(f931(x48881,x48882))
% 28.25/28.12 [5011]~P4(x50111)+~P14(x50111,x50112)+P14(x50111,f144(x50111,x50112))
% 28.25/28.12 [5254]~P7(x52542)+~P7(x52541)+P7(f39(a1,x52541,x52542))
% 28.25/28.12 [4823]~P84(x48231)+~E(x48232,f2(x48231))+E(f319(f73(x48231),x48232),x48232)
% 28.25/28.12 [4824]~P84(x48241)+~E(x48242,f2(x48241))+E(f319(f73(x48241),x48242),x48242)
% 28.25/28.12 [4838]~P98(x48381)+~E(x48382,f2(a1))+E(f319(f94(x48381),x48382),f2(x48381))
% 28.25/28.12 [4839]~P145(x48391)+~E(x48392,f2(a1))+E(f319(f94(x48391),x48392),f2(x48391))
% 28.25/28.12 [4840]~P98(x48401)+~E(x48402,f2(a1))+E(f319(f94(x48401),x48402),f2(x48401))
% 28.25/28.12 [4864]~P69(x48641)+~E(f2(x48641),x48642)+E(f319(f73(x48641),x48642),f2(x48641))
% 28.25/28.12 [4865]~P69(x48651)+~E(x48652,f2(x48651))+E(f319(f73(x48651),x48652),f2(x48651))
% 28.25/28.12 [4866]~P92(x48661)+~E(x48662,f2(x48661))+E(f319(f69(x48661),x48662),f2(x48661))
% 28.25/28.12 [4889]~P84(x48892)+E(x48891,f2(x48892))+~E(f319(f73(x48892),x48891),x48891)
% 28.25/28.12 [4890]~P84(x48902)+E(x48901,f2(x48902))+~E(f319(f73(x48902),x48901),x48901)
% 28.25/28.12 [4892]E(x48921,f319(a96,x48922))+~E(x48921,f2(a925))+~E(x48922,f319(f92(a1),x48921))
% 28.25/28.12 [4893]E(f319(a96,x48931),x48932)+~E(x48932,f2(a925))+~E(x48931,f319(f92(a1),x48932))
% 28.25/28.12 [4896]~P98(x48962)+E(x48961,f2(a1))+~E(f319(f94(x48962),x48961),f2(x48962))
% 28.25/28.12 [4897]~P98(x48972)+E(x48971,f2(a1))+~E(f319(f94(x48972),x48971),f2(x48972))
% 28.25/28.12 [4901]~P69(x49012)+E(x49011,f2(x49012))+~E(f319(f73(x49012),x49011),f2(x49012))
% 28.25/28.12 [4902]~P92(x49022)+E(x49021,f2(x49022))+~E(f319(f69(x49022),x49021),f2(x49022))
% 28.25/28.12 [4903]~P69(x49031)+E(f2(x49031),x49032)+~E(f319(f73(x49031),x49032),f2(x49031))
% 28.25/28.12 [5086]~P4(x50861)+~P14(x50861,x50862)+P14(x50861,f319(f163(x50861),x50862))
% 28.25/28.12 [5113]~P1(x51132)+~P1(x51131)+P1(f319(f319(a317,x51131),x51132))
% 28.25/28.12 [5147]~E(f72(a925),f2(a925))+E(f319(f29(x51471),x51472),f2(a925))+~P1(f319(f55(x51471),x51472))
% 28.25/28.12 [5184]~P143(x51841)+~P119(x51841)+E(f319(f319(f236(x51841),f2(x51841)),f319(a104,x51842)),f2(x51841))
% 28.25/28.12 [5222]~P4(x52221)+P14(x52221,f131(x52221,x52222))+~P1(f319(f55(x52221),x52222))
% 28.25/28.12 [5223]~P4(x52231)+P14(x52231,f747(x52232,x52231))+~P1(f319(f55(x52231),x52232))
% 28.25/28.12 [5246]~P4(x52461)+E(f319(f164(x52461),f131(x52461,x52462)),x52462)+~P1(f319(f55(x52461),x52462))
% 28.25/28.12 [5247]~P4(x52471)+E(f319(f164(x52471),f747(x52472,x52471)),x52472)+~P1(f319(f55(x52471),x52472))
% 28.25/28.12 [5276]P1(x52761)+P1(x52762)+~P1(f319(f319(a318,x52762),x52761))
% 28.25/28.12 [5289]E(x52891,f180(f932(x52892,a923)))+~E(f319(f29(x52892),x52891),f2(a925))+~P1(f319(f55(x52892),x52891))
% 28.25/28.12 [5294]P1(x52941)+~P1(x52942)+~P1(f319(f319(a322,x52942),x52941))
% 28.25/28.12 [5349]~P82(x53491)+E(f319(f69(x53491),x53492),x53492)+P1(f319(f319(f227(x53491),x53492),f2(x53491)))
% 28.25/28.12 [5350]~P6(x53502)+~P41(x53502,x53502,x53501)+E(f319(x53501,f88(x53502,x53501)),f88(x53502,x53501))
% 28.25/28.12 [5351]~P6(x53512)+~P41(x53512,x53512,x53511)+E(f319(x53511,f87(x53512,x53511)),f87(x53512,x53511))
% 28.25/28.12 [5412]~P5(x54122)+~P1(f319(f50(x54122),x54121))+P1(f319(x54121,f835(x54121,x54122)))
% 28.25/28.12 [5413]~P5(x54132)+~P1(f319(f50(x54132),x54131))+P1(f319(x54131,f902(x54131,x54132)))
% 28.25/28.12 [5453]E(x54531,f105(x54532))+P1(f319(f129(x54532),f106(x54532,x54531)))+~P1(f319(f129(x54532),x54531))
% 28.25/28.12 [5458]~P4(x54581)+~P1(f319(f55(x54581),x54582))+P1(f319(f129(x54581),f131(x54581,x54582)))
% 28.25/28.12 [5459]~P4(x54591)+~P1(f319(f55(x54591),x54592))+P1(f319(f129(x54591),f747(x54592,x54591)))
% 28.25/28.12 [5464]~P145(x54641)+E(f319(f92(x54641),f319(a96,x54642)),f319(f94(x54641),x54642))+P1(f319(f319(f227(a1),x54642),f2(a1)))
% 28.25/28.12 [5485]P8(x54852,x54851)+E(f319(x54851,f516(x54851)),f319(x54851,f554(x54851)))+P1(f319(f319(x54851,f516(x54851)),f554(x54851)))
% 28.25/28.12 [5497]E(f319(f92(a1),f430(x54971,x54972)),x54971)+P1(f319(x54972,f319(a96,x54971)))+~P1(f319(x54972,f2(a925)))
% 28.25/28.12 [5509]~P5(x55091)+~P1(f319(x55092,f758(x55092,x55091)))+P1(f319(f51(x55091),x55092))
% 28.25/28.12 [5510]~P5(x55101)+~P1(f319(x55102,f836(x55102,x55101)))+P1(f319(f51(x55101),x55102))
% 28.25/28.12 [5545]~P126(x55451)+~E(f76(x55451,x55452),f319(f73(x55451),f72(x55451)))+P1(f319(f319(f227(x55451),x55452),f2(x55451)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [5672]E(f319(f92(a1),f430(x56721,x56722)),x56721)+P1(f319(x56722,f319(a96,x56721)))+P1(f319(f319(f227(a1),x56721),f2(a1)))
% 28.25/28.12 [5738]~P126(x57381)+E(f76(x57381,x57382),f319(f73(x57381),f72(x57381)))+~P1(f319(f319(f227(x57381),x57382),f2(x57381)))
% 28.25/28.12 [5739]~P126(x57391)+E(f76(x57391,x57392),f319(f73(x57391),f72(x57391)))+~P1(f319(f319(f227(x57391),x57392),f2(x57391)))
% 28.25/28.12 [5740]~P92(x57401)+E(f319(f69(x57401),x57402),f319(f73(x57401),x57402))+~P1(f319(f319(f226(x57401),x57402),f2(x57401)))
% 28.25/28.12 [5741]~P92(x57411)+E(f319(f69(x57411),x57412),f319(f73(x57411),x57412))+~P1(f319(f319(f227(x57411),x57412),f2(x57411)))
% 28.25/28.12 [5742]~P82(x57421)+E(f319(f69(x57421),x57422),f319(f73(x57421),x57422))+~P1(f319(f319(f227(x57421),x57422),f2(x57421)))
% 28.25/28.12 [5841]~P1(f319(x58411,f430(x58412,x58411)))+P1(f319(x58411,f319(a96,x58412)))+~P1(f319(x58411,f2(a925)))
% 28.25/28.12 [5848]E(x58481,f2(a925))+E(f319(a104,f372(x58482,x58481)),x58481)+~P1(f319(f319(f227(a925),x58481),f319(a104,x58482)))
% 28.25/28.12 [5852]P8(x58521,x58522)+~E(f319(x58522,f516(x58522)),f319(x58522,f554(x58522)))+~P1(f319(f319(x58522,f516(x58522)),f554(x58522)))
% 28.25/28.12 [5871]~P4(x58711)+P14(x58711,x58712)+P1(f319(f319(f226(a925),f730(x58712,x58711)),f731(x58712,x58711)))
% 28.25/28.12 [5872]~P4(x58721)+P14(x58721,x58722)+P1(f319(f319(f226(a925),f738(x58722,x58721)),f742(x58722,x58721)))
% 28.25/28.12 [5958]~P92(x59581)+~E(x59582,f2(x59581))+P1(f319(f319(f226(x59581),f319(f69(x59581),x59582)),f2(x59581)))
% 28.25/28.12 [6047]~P1(f319(x60471,f430(x60472,x60471)))+P1(f319(x60471,f319(a96,x60472)))+P1(f319(f319(f227(a1),x60472),f2(a1)))
% 28.25/28.12 [6073]~P1(f319(x60731,f319(a96,x60732)))+P1(f319(x60731,f2(a925)))+~P1(f319(f319(f227(a1),x60732),f2(a1)))
% 28.25/28.12 [6419]~P126(x64191)+~P1(f319(f319(f227(x64191),x64192),f2(x64191)))+P1(f319(f319(f227(x64191),f76(x64191,x64192)),f2(x64191)))
% 28.25/28.12 [6533]~P126(x65331)+P1(f319(f319(f226(x65331),f319(f94(x65331),x65332)),f2(x65331)))+~P1(f319(f319(f226(a1),x65332),f2(a1)))
% 28.25/28.12 [6534]~P126(x65341)+P1(f319(f319(f227(x65341),f319(f94(x65341),x65342)),f2(x65341)))+~P1(f319(f319(f227(a1),x65342),f2(a1)))
% 28.25/28.12 [6543]~P92(x65432)+E(x65431,f2(x65432))+~P1(f319(f319(f226(x65432),f319(f69(x65432),x65431)),f2(x65432)))
% 28.25/28.12 [6621]~P145(x66211)+~P1(f319(f319(f321(x66211),x66212),f101(x66211)))+P1(f319(f319(f321(x66211),f319(f73(x66211),x66212)),f101(x66211)))
% 28.25/28.12 [6654]~P126(x66541)+~P1(f319(f319(f227(x66541),f76(x66541,x66542)),f2(x66541)))+P1(f319(f319(f227(x66541),x66542),f2(x66541)))
% 28.25/28.12 [6830]~P126(x68302)+~P1(f319(f319(f226(x68302),f319(f94(x68302),x68301)),f2(x68302)))+P1(f319(f319(f226(a1),x68301),f2(a1)))
% 28.25/28.12 [6831]~P126(x68312)+~P1(f319(f319(f227(x68312),f319(f94(x68312),x68311)),f2(x68312)))+P1(f319(f319(f227(a1),x68311),f2(a1)))
% 28.25/28.12 [6917]~P6(x69171)+~P41(x69171,x69171,x69172)+P1(f319(f319(f226(x69171),f319(x69172,f88(x69171,x69172))),f88(x69171,x69172)))
% 28.25/28.12 [6918]~P6(x69181)+~P41(x69181,x69181,x69182)+P1(f319(f319(f226(x69181),f319(x69182,f87(x69181,x69182))),f87(x69181,x69182)))
% 28.25/28.12 [7339]~P84(x73391)+~P1(f319(f319(f226(x73391),x73392),f2(x73391)))+P1(f319(f319(f226(x73391),f319(f319(f74(x73391),x73392),x73392)),f2(x73391)))
% 28.25/28.12 [7341]~P126(x73411)+~P1(f319(f319(f227(x73411),x73412),f2(x73411)))+P1(f319(f319(f227(x73411),f319(f319(f74(x73411),x73412),x73412)),f2(x73411)))
% 28.25/28.12 [7342]~P84(x73421)+~P1(f319(f319(f227(x73421),x73422),f2(x73421)))+P1(f319(f319(f227(x73421),f319(f319(f74(x73421),x73422),x73422)),f2(x73421)))
% 28.25/28.12 [7907]~P84(x79071)+~P1(f319(f319(f226(x79071),f319(f319(f74(x79071),x79072),x79072)),f2(x79071)))+P1(f319(f319(f226(x79071),x79072),f2(x79071)))
% 28.25/28.12 [7908]~P126(x79081)+~P1(f319(f319(f227(x79081),f319(f319(f74(x79081),x79082),x79082)),f2(x79081)))+P1(f319(f319(f227(x79081),x79082),f2(x79081)))
% 28.25/28.12 [7909]~P84(x79091)+~P1(f319(f319(f227(x79091),f319(f319(f74(x79091),x79092),x79092)),f2(x79091)))+P1(f319(f319(f227(x79091),x79092),f2(x79091)))
% 28.25/28.12 [4937]~E(x49372,f72(a925))+~E(x49371,f72(a925))+E(f319(f319(f75(a925),x49371),x49372),f72(a925))
% 28.25/28.12 [4938]~E(x49382,f72(a925))+~E(x49381,f72(a925))+E(f319(f319(f75(a925),x49381),x49382),f72(a925))
% 28.25/28.12 [4939]~E(x49392,f72(a1))+~E(x49391,f72(a1))+E(f319(f319(f75(a1),x49391),x49392),f72(a1))
% 28.25/28.12 [4940]~E(x49402,f2(a925))+~E(x49401,f2(a925))+E(f319(f319(f74(a925),x49401),x49402),f2(a925))
% 28.25/28.12 [4995]~P124(x49952)+E(x49951,f2(x49952))+E(f319(f319(f283(x49952),x49951),x49951),f72(x49952))
% 28.25/28.12 [4996]~P65(x49962)+E(x49961,f2(x49962))+E(f319(f319(f30(x49962),x49961),x49961),f72(x49962))
% 28.25/28.12 [4997]~P125(x49972)+E(x49971,f2(x49972))+E(f319(f319(f283(x49972),x49971),x49971),f72(x49972))
% 28.25/28.12 [5014]~P84(x50141)+~E(x50142,f2(x50141))+E(f319(f319(f74(x50141),x50142),x50142),f2(x50141))
% 28.25/28.12 [5017]~P144(x50171)+~E(x50172,f72(x50171))+E(f319(f319(f75(x50171),x50172),x50172),f72(x50171))
% 28.25/28.12 [5018]~P84(x50181)+~E(x50182,f2(x50181))+E(f319(f319(f74(x50181),x50182),x50182),f2(x50181))
% 28.25/28.12 [5019]~P125(x50191)+~E(x50192,f2(x50191))+E(f319(f319(f283(x50191),x50192),x50192),f2(x50191))
% 28.25/28.12 [5064]~E(x50642,f2(a925))+~E(x50641,f2(a925))+E(f319(f73(a1),f319(f92(a1),x50641)),f319(f92(a1),x50642))
% 28.25/28.12 [5083]E(x50831,f72(a925))+E(x50832,f2(a925))+~E(f319(f319(f75(a925),x50832),x50831),x50832)
% 28.25/28.12 [5095]E(x50951,f2(a925))+E(x50952,f2(a925))+~E(f319(f319(f75(a925),x50952),x50951),f2(a925))
% 28.25/28.12 [5120]~E(x51202,f2(a925))+~E(x51201,f319(a104,f2(a925)))+E(f319(f319(f74(a925),x51201),x51202),f319(a104,f2(a925)))
% 28.25/28.12 [5121]~E(x51211,f2(a925))+~E(x51212,f319(a104,f2(a925)))+E(f319(f319(f74(a925),x51211),x51212),f319(a104,f2(a925)))
% 28.25/28.12 [5122]~E(x51222,f2(a925))+~E(x51221,f319(a104,f2(a925)))+E(f319(f319(f74(a925),x51221),x51222),f319(a104,f2(a925)))
% 28.25/28.12 [5123]~E(x51231,f2(a925))+~E(x51232,f319(a104,f2(a925)))+E(f319(f319(f74(a925),x51231),x51232),f319(a104,f2(a925)))
% 28.25/28.12 [5130]E(x51301,f72(a1))+E(x51302,f319(f95(a1),a89))+~E(f319(f319(f75(a1),x51301),x51302),f72(a1))
% 28.25/28.12 [5131]E(x51311,f72(a1))+E(x51312,f319(f95(a1),a89))+~E(f319(f319(f75(a1),x51312),x51311),f72(a1))
% 28.25/28.12 [5132]E(x51321,f72(a1))+E(x51321,f319(f95(a1),a89))+~E(f319(f319(f75(a1),x51322),x51321),f72(a1))
% 28.25/28.12 [5133]E(x51331,f72(a1))+E(x51331,f319(f95(a1),a89))+~E(f319(f319(f75(a1),x51331),x51332),f72(a1))
% 28.25/28.12 [5134]E(x51341,f72(a1))+E(x51341,f319(f95(a1),a89))+~E(f319(f319(f75(a1),x51341),x51342),f72(a1))
% 28.25/28.12 [5155]~P84(x51552)+E(x51551,f2(x51552))+~E(f319(f319(f74(x51552),x51551),x51551),f2(x51552))
% 28.25/28.12 [5156]~P84(x51562)+E(x51561,f2(x51562))+~E(f319(f319(f74(x51562),x51561),x51561),f2(x51562))
% 28.25/28.12 [5162]~E(x51621,f319(f95(a1),a89))+~E(x51622,f319(f95(a1),a89))+E(f319(f319(f75(a1),x51621),x51622),f72(a1))
% 28.25/28.12 [5172]E(x51721,f2(a925))+E(x51722,f2(a925))+~E(f319(f319(f74(a925),x51722),x51721),f319(a104,f2(a925)))
% 28.25/28.12 [5173]E(x51731,f2(a925))+E(x51732,f2(a925))+~E(f319(f319(f74(a925),x51732),x51731),f319(a104,f2(a925)))
% 28.25/28.12 [5183]~P72(x51831)+~P99(x51831)+E(f319(f319(f283(x51831),x51832),f319(f95(x51831),a77)),f2(x51831))
% 28.25/28.12 [5189]~P144(x51891)+~E(x51892,f319(f73(x51891),f72(x51891)))+E(f319(f319(f75(x51891),x51892),x51892),f72(x51891))
% 28.25/28.12 [5194]~P7(x51942)+~P7(x51941)+P7(f319(f319(f75(a1),x51941),x51942))
% 28.25/28.12 [5195]~P7(x51952)+~P7(x51951)+P7(f319(f319(f74(a1),x51951),x51952))
% 28.25/28.12 [5196]~P7(x51962)+~P7(x51961)+P7(f319(f319(f30(a1),x51961),x51962))
% 28.25/28.12 [5197]~E(x51972,f2(a1))+E(x51971,f2(a1))+E(f40(x51971,x51972),f319(f319(f244(a1,a1),f2(a1)),x51971))
% 28.25/28.12 [5198]~E(x51982,f2(a1))+E(x51981,f2(a1))+E(f40(x51981,x51982),f319(f319(f244(a1,a1),f2(a1)),x51981))
% 28.25/28.12 [5220]~E(x52202,f319(a104,f2(a925)))+~E(x52201,f319(a104,f2(a925)))+E(f319(f319(f75(a925),x52201),x52202),f319(a104,f2(a925)))
% 28.25/28.12 [5235]E(x52351,f2(a925))+E(x52351,f319(a104,f2(a925)))+~E(f319(f319(f74(a925),x52352),x52351),f319(a104,f2(a925)))
% 28.25/28.12 [5236]E(x52361,f2(a925))+E(x52361,f319(a104,f2(a925)))+~E(f319(f319(f74(a925),x52361),x52362),f319(a104,f2(a925)))
% 28.25/28.12 [5237]E(x52371,f2(a925))+E(x52372,f319(a104,f2(a925)))+~E(f319(f319(f236(a925),x52372),x52371),f319(a104,f2(a925)))
% 28.25/28.12 [5238]E(x52381,f2(a925))+E(x52381,f319(a104,f2(a925)))+~E(f319(f319(f74(a925),x52382),x52381),f319(a104,f2(a925)))
% 28.25/28.12 [5239]E(x52391,f2(a925))+E(x52391,f319(a104,f2(a925)))+~E(f319(f319(f74(a925),x52391),x52392),f319(a104,f2(a925)))
% 28.25/28.12 [5248]~P72(x52481)+~P99(x52481)+E(f319(f319(f283(x52481),x52482),f319(f95(x52481),a89)),f319(f73(x52481),x52482))
% 28.25/28.12 [5268]E(x52681,f319(a96,x52682))+~E(x52681,f2(a925))+P1(f319(f319(f226(a1),f2(a1)),x52682))
% 28.25/28.12 [5269]E(f319(a96,x52691),x52692)+~E(x52692,f2(a925))+P1(f319(f319(f226(a1),f2(a1)),x52691))
% 28.25/28.12 [5284]E(x52841,f319(a104,f2(a925)))+E(x52842,f319(a104,f2(a925)))+~E(f319(f319(f74(a925),x52841),x52842),f319(a104,f2(a925)))
% 28.25/28.12 [5285]E(x52851,f319(a104,f2(a925)))+E(x52852,f319(a104,f2(a925)))+~E(f319(f319(f74(a925),x52851),x52852),f319(a104,f2(a925)))
% 28.25/28.12 [5296]~E(x52961,f319(a96,x52962))+E(x52961,f2(a925))+P1(f319(f319(f226(a1),f2(a1)),x52962))
% 28.25/28.12 [5297]~E(f319(a96,x52972),x52971)+E(x52971,f2(a925))+P1(f319(f319(f226(a1),f2(a1)),x52972))
% 28.25/28.12 [5323]~P102(x53231)+E(f319(f57(x53231,f93(x53231)),x53232),f10(x53231,x53232))+~P1(f319(f55(x53231),x53232))
% 28.25/28.12 [5324]~P102(x53241)+E(f319(f57(x53241,f102(x53241)),x53242),f13(x53241,x53242))+~P1(f319(f55(x53241),x53242))
% 28.25/28.12 [5325]~P4(x53251)+E(f319(f57(x53251,f224(x53251)),x53252),f14(x53251,x53252))+~P1(f319(f55(x53251),x53252))
% 28.25/28.12 [5326]~P4(x53261)+E(f319(f57(x53261,f225(x53261)),x53262),f15(x53261,x53262))+~P1(f319(f55(x53261),x53262))
% 28.25/28.12 [5407]E(x54071,x54072)+~E(f319(f319(f23(a925),x54072),x54071),f2(a925))+~E(f319(f319(f23(a925),x54071),x54072),f2(a925))
% 28.25/28.12 [5424]P7(x54241)+~P42(x54242)+~P1(f319(f319(f321(a1),x54241),x54242))
% 28.25/28.12 [5454]~P126(x54541)+~E(f76(x54541,x54542),f72(x54541))+P1(f319(f319(f227(x54541),f2(x54541)),x54542))
% 28.25/28.12 [5465]~P99(x54651)+E(f319(f92(x54651),f319(f95(a925),x54652)),f319(f95(x54651),x54652))+P1(f319(a185,f319(f95(a1),x54652)))
% 28.25/28.12 [5470]~P45(x54701,x54702)+P46(a923)+P1(f319(f55(f931(x54701,x54701)),x54702))
% 28.25/28.12 [5537]~P4(x55371)+E(f319(f57(x55371,f224(x55371)),x55372),f11(x55371,f224(x55371),x55372))+~P1(f319(f55(x55371),x55372))
% 28.25/28.12 [5538]~P4(x55381)+E(f319(f57(x55381,f225(x55381)),x55382),f12(x55381,f225(x55381),x55382))+~P1(f319(f55(x55381),x55382))
% 28.25/28.12 [5551]E(x55511,x55512)+P1(f319(f319(f227(a925),x55512),x55511))+P1(f319(f319(f227(a925),x55511),x55512))
% 28.25/28.12 [5552]E(x55521,x55522)+P1(f319(f319(f227(a925),x55522),x55521))+P1(f319(f319(f227(a925),x55521),x55522))
% 28.25/28.12 [5553]E(x55531,x55532)+P1(f319(f319(f227(a1),x55532),x55531))+P1(f319(f319(f227(a1),x55531),x55532))
% 28.25/28.12 [5606]~P99(x56061)+E(f319(f92(x56061),f319(f95(a925),x56062)),f2(x56061))+~P1(f319(a185,f319(f95(a1),x56062)))
% 28.25/28.12 [5609]~E(x56092,f319(a96,x56091))+E(x56091,f319(f92(a1),x56092))+~P1(f319(f319(f226(a1),f2(a1)),x56091))
% 28.25/28.12 [5610]~E(f319(a96,x56101),x56102)+E(x56101,f319(f92(a1),x56102))+~P1(f319(f319(f226(a1),f2(a1)),x56101))
% 28.25/28.12 [5611]~E(x56111,f319(a96,x56112))+E(f319(f92(a1),x56111),x56112)+~P1(f319(f319(f226(a1),f2(a1)),x56112))
% 28.25/28.12 [5621]E(x56211,f319(a96,x56212))+~E(x56212,f319(f92(a1),x56211))+~P1(f319(f319(f226(a1),f2(a1)),x56212))
% 28.25/28.12 [5622]E(f319(a96,x56221),x56222)+~E(x56221,f319(f92(a1),x56222))+~P1(f319(f319(f226(a1),f2(a1)),x56221))
% 28.25/28.12 [5663]~P92(x56632)+E(x56631,f2(x56632))+P1(f319(f319(f227(x56632),f2(x56632)),f319(f69(x56632),x56631)))
% 28.25/28.12 [5727]~P126(x57271)+E(f76(x57271,x57272),f72(x57271))+~P1(f319(f319(f227(x57271),f2(x57271)),x57272))
% 28.25/28.12 [5728]~P126(x57281)+E(f76(x57281,x57282),f72(x57281))+~P1(f319(f319(f227(x57281),f2(x57281)),x57282))
% 28.25/28.12 [5732]~P99(x57321)+E(f319(f92(x57321),f319(f95(a925),x57322)),f2(x57321))+P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x57322)))
% 28.25/28.12 [5743]~P92(x57431)+E(f319(f69(x57431),x57432),x57432)+~P1(f319(f319(f226(x57431),f2(x57431)),x57432))
% 28.25/28.12 [5744]~P92(x57441)+E(f319(f69(x57441),x57442),x57442)+~P1(f319(f319(f227(x57441),f2(x57441)),x57442))
% 28.25/28.12 [5753]E(x57531,f2(a925))+~E(f131(a925,f319(f294(a925,x57532),x57531)),f105(a925))+P1(f319(f319(f226(a925),x57531),x57532))
% 28.25/28.12 [5763]~P79(x57631)+E(f319(f319(f6(x57631,x57631),f5(x57631)),f319(f164(x57631),x57632)),f319(f157(x57631),x57632))+~P1(f319(f129(x57631),x57632))
% 28.25/28.12 [5766]~P145(x57661)+E(f319(f92(x57661),f319(a96,x57662)),f319(f94(x57661),x57662))+~P1(f319(f319(f226(a1),f2(a1)),x57662))
% 28.25/28.12 [5768]~E(x57681,x57682)+P1(f319(f319(f227(a925),x57681),f319(a104,x57682)))+P1(f319(f319(f227(a925),x57681),x57682))
% 28.25/28.12 [5791]E(x57911,x57912)+P1(f319(f319(f227(a925),x57911),x57912))+~P1(f319(f319(f226(a925),x57911),x57912))
% 28.25/28.12 [5792]E(x57921,x57922)+P1(f319(f319(f227(a925),x57921),x57922))+~P1(f319(f319(f226(a925),x57921),x57922))
% 28.25/28.12 [5793]E(x57931,x57932)+P1(f319(f319(f227(a925),x57931),x57932))+~P1(f319(f319(f226(a925),x57931),x57932))
% 28.25/28.12 [5794]E(x57941,x57942)+P1(f319(f319(f227(a1),x57941),x57942))+~P1(f319(f319(f226(a1),x57941),x57942))
% 28.25/28.12 [5797]E(x57971,f72(a1))+~E(f319(f319(f75(a1),x57972),x57971),f72(a1))+~P1(f319(f319(f227(a1),f2(a1)),x57972))
% 28.25/28.12 [5798]E(x57981,f72(a1))+~E(f319(f319(f75(a1),x57981),x57982),f72(a1))+~P1(f319(f319(f227(a1),f2(a1)),x57981))
% 28.25/28.12 [5837]~P42(x58372)+P1(f319(f319(f226(a1),f2(a1)),x58371))+~P1(f319(f319(f321(a1),x58371),x58372))
% 28.25/28.12 [5838]~P42(x58382)+P1(f319(f319(f226(a1),f2(a1)),x58381))+~P1(f319(f319(f321(a1),x58381),x58382))
% 28.25/28.12 [5857]~P62(x58571,x58572)+P38(x58571,x58572)+~P1(f319(f55(f931(x58571,x58571)),x58572))
% 28.25/28.12 [5858]~P62(x58581,x58582)+P38(x58581,x58582)+~P1(f319(f55(f931(x58581,x58581)),x58582))
% 28.25/28.12 [5859]~P38(x58591,x58592)+P62(x58591,x58592)+~P1(f319(f55(f931(x58591,x58591)),x58592))
% 28.25/28.12 [5860]~P62(x58601,x58602)+P45(x58601,x58602)+~P1(f319(f55(f931(x58601,x58601)),x58602))
% 28.25/28.12 [5902]E(x59021,f180(f932(x59022,a923)))+~P1(f319(f55(x59022),x59021))+P1(f319(f319(f227(a925),f2(a925)),f319(f29(x59022),x59021)))
% 28.25/28.12 [5929]~P1(f319(x59291,x59292))+P1(f319(x59291,f2(a925)))+P1(f319(f319(f227(a925),f440(x59292,x59291)),x59292))
% 28.25/28.12 [5952]E(x59521,f2(a925))+~E(f319(f157(a925),x59522),f2(a925))+~P1(f319(f319(f321(a925),x59521),f319(f164(a925),x59522)))
% 28.25/28.12 [5988]~E(x59881,x59882)+P1(f319(f319(f227(a925),x59881),f319(a104,x59882)))+~P1(f319(f319(f226(a925),x59882),x59881))
% 28.25/28.12 [6020]E(x60201,x60202)+~P1(f319(f319(f226(a925),x60202),x60201))+~P1(f319(f319(f226(a925),x60201),x60202))
% 28.25/28.12 [6021]E(x60211,x60212)+~P1(f319(f319(f226(a1),x60212),x60211))+~P1(f319(f319(f226(a1),x60211),x60212))
% 28.25/28.12 [6023]E(f319(f29(x60231),x60232),f2(a925))+~P1(f319(f55(x60231),x60232))+P1(f319(f319(f321(x60231),f517(x60232,x60231)),x60232))
% 28.25/28.12 [6032]E(f44(x60321,x60322),f40(x60321,x60322))+P1(f319(f319(f226(a1),f2(a1)),x60321))+~P1(f319(f319(f227(a1),f2(a1)),x60322))
% 28.25/28.12 [6059]~P1(f319(x60591,f427(x60591)))+P1(f319(x60591,f319(a96,x60592)))+~P1(f319(f319(f226(a1),f2(a1)),x60592))
% 28.25/28.12 [6062]P1(f319(f319(f226(a925),x60621),f333(x60622)))+~P1(f319(f55(a925),x60622))+~P1(f319(f319(f321(a925),x60621),x60622))
% 28.25/28.12 [6063]P1(f319(f319(f227(a925),x60631),f352(x60632)))+~P1(f319(f55(a925),x60632))+~P1(f319(f319(f321(a925),x60631),x60632))
% 28.25/28.12 [6092]E(x60921,x60922)+~P1(f319(f319(f227(a925),x60921),f319(a104,x60922)))+P1(f319(f319(f227(a925),x60921),x60922))
% 28.25/28.12 [6093]E(x60931,x60932)+~P1(f319(f319(f227(a925),x60931),f319(a104,x60932)))+P1(f319(f319(f227(a925),x60931),x60932))
% 28.25/28.12 [6094]E(x60941,x60942)+~P1(f319(f319(f227(a925),x60941),f319(a104,x60942)))+P1(f319(f319(f227(a925),x60941),x60942))
% 28.25/28.12 [6095]E(x60951,x60952)+~P1(f319(f319(f227(a925),x60951),f319(a104,x60952)))+P1(f319(f319(f227(a925),x60951),x60952))
% 28.25/28.12 [6130]E(x61301,f319(a104,x61302))+~P1(f319(f319(f226(a925),x61301),f319(a104,x61302)))+P1(f319(f319(f226(a925),x61301),x61302))
% 28.25/28.12 [6131]E(x61311,f319(a104,x61312))+~P1(f319(f319(f226(a925),x61311),f319(a104,x61312)))+P1(f319(f319(f226(a925),x61311),x61312))
% 28.25/28.12 [6147]P1(f319(x61471,f431(x61471)))+~P1(f319(x61471,f319(a96,x61472)))+~P1(f319(f319(f226(a1),f2(a1)),x61472))
% 28.25/28.12 [6163]~P1(f319(x61631,x61632))+~P1(f319(f319(f226(a1),f2(a1)),x61632))+P1(f319(x61631,f319(f92(a1),f370(x61631))))
% 28.25/28.12 [6174]~P92(x61742)+~E(x61741,f2(x61742))+~P1(f319(f319(f227(x61742),f2(x61742)),f319(f69(x61742),x61741)))
% 28.25/28.12 [6199]~P62(x61991,x61992)+P38(x61991,f319(f278(x61991,x61991),x61992))+~P1(f319(f55(f931(x61991,x61991)),x61992))
% 28.25/28.12 [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)))
% 28.25/28.12 [6213]E(f319(a104,x62131),x62132)+~P1(f319(f319(f227(a925),x62131),x62132))+P1(f319(f319(f227(a925),f319(a104,x62131)),x62132))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [6240]E(f39(a1,x62401,x62402),x62401)+~P1(f319(f319(f226(a1),x62401),f2(a1)))+~P1(f319(f319(f227(a1),x62402),x62401))
% 28.25/28.12 [6254]E(f41(x62541,x62542),f40(x62541,x62542))+~P1(f319(f319(f226(a1),f2(a1)),x62541))+~P1(f319(f319(f226(a1),f2(a1)),x62542))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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)))
% 28.25/28.12 [6275]E(f39(a1,x62751,x62752),x62751)+~P1(f319(f319(f226(a1),f2(a1)),x62751))+~P1(f319(f319(f227(a1),x62751),x62752))
% 28.25/28.12 [6276]E(x62761,x62762)+~P1(f319(f319(f227(a925),x62761),f319(a104,x62762)))+~P1(f319(f319(f226(a925),x62762),x62761))
% 28.25/28.12 [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)))
% 28.25/28.12 [6290]~P84(x62901)+~P1(f319(f319(f226(x62901),x62902),f2(x62901)))+P1(f319(f319(f226(x62901),x62902),f319(f73(x62901),x62902)))
% 28.25/28.12 [6291]~P126(x62911)+~P1(f319(f319(f227(x62911),x62912),f2(x62911)))+P1(f319(f319(f227(x62911),x62912),f319(f73(x62911),x62912)))
% 28.25/28.12 [6300]~P6(x63001)+E(f319(f319(f58(x63001,x63001,f93(x63001)),f234(x63001)),x63002),f32(x63001,x63002))+~P1(f319(f55(x63001),x63002))
% 28.25/28.12 [6301]~P6(x63011)+E(f319(f319(f58(x63011,x63011,f102(x63011)),f180(x63011)),x63012),f31(x63011,x63012))+~P1(f319(f55(x63011),x63012))
% 28.25/28.12 [6318]~P126(x63181)+~P1(f319(f319(f226(a1),f2(a1)),x63182))+P1(f319(f319(f226(x63181),f2(x63181)),f319(f94(x63181),x63182)))
% 28.25/28.12 [6319]~P129(x63191)+~P1(f319(f319(f227(a925),f2(a925)),x63192))+P1(f319(f319(f227(x63191),f2(x63191)),f319(f92(x63191),x63192)))
% 28.25/28.12 [6320]~P126(x63201)+~P1(f319(f319(f227(a1),f2(a1)),x63202))+P1(f319(f319(f227(x63201),f2(x63201)),f319(f94(x63201),x63202)))
% 28.25/28.12 [6323]~P7(x63232)+~P7(x63231)+E(f319(f302(a925,a1,f92(a1)),f295(a925,f319(a96,x63231),f319(a96,x63232))),f295(a1,x63231,x63232))
% 28.25/28.12 [6329]P1(f319(x63291,x63292))+~P1(f319(f319(f226(a1),f2(a1)),x63292))+~P1(f319(x63291,f319(f92(a1),f373(x63291))))
% 28.25/28.12 [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))
% 28.25/28.12 [6362]~P126(x63621)+P1(f319(f319(f227(x63621),f2(x63621)),f76(x63621,x63622)))+~P1(f319(f319(f227(x63621),f2(x63621)),x63622))
% 28.25/28.12 [6374]~P68(x63741)+~P1(f319(f319(f226(x63741),x63742),f2(x63741)))+P1(f319(f319(f226(x63741),f2(x63741)),f319(f73(x63741),x63742)))
% 28.25/28.12 [6375]~P68(x63751)+~P1(f319(f319(f227(x63751),x63752),f2(x63751)))+P1(f319(f319(f227(x63751),f2(x63751)),f319(f73(x63751),x63752)))
% 28.25/28.12 [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))))
% 28.25/28.12 [6410]~P84(x64101)+P1(f319(f319(f226(x64101),x64102),f2(x64101)))+~P1(f319(f319(f226(x64101),x64102),f319(f73(x64101),x64102)))
% 28.25/28.12 [6411]~P126(x64111)+P1(f319(f319(f227(x64111),x64112),f2(x64111)))+~P1(f319(f319(f227(x64111),x64112),f319(f73(x64111),x64112)))
% 28.25/28.12 [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))
% 28.25/28.12 [6421]~P99(x64211)+P1(f319(f319(f321(x64211),f319(f95(x64211),x64212)),f178(x64211)))+~P1(f319(f319(f226(a1),a77),x64212))
% 28.25/28.12 [6450]E(x64501,f2(a925))+~P1(f319(f319(f227(a925),x64501),f319(a104,x64502)))+P1(f319(f319(f227(a925),f372(x64502,x64501)),x64502))
% 28.25/28.12 [6472]~P126(x64721)+~P1(f319(f319(f227(x64721),f2(x64721)),f76(x64721,x64722)))+P1(f319(f319(f227(x64721),f2(x64721)),x64722))
% 28.25/28.12 [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)))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [6544]~P126(x65442)+~P1(f319(f319(f226(x65442),f2(x65442)),f319(f94(x65442),x65441)))+P1(f319(f319(f226(a1),f2(a1)),x65441))
% 28.25/28.12 [6545]~P129(x65452)+~P1(f319(f319(f227(x65452),f2(x65452)),f319(f92(x65452),x65451)))+P1(f319(f319(f227(a925),f2(a925)),x65451))
% 28.25/28.12 [6546]~P126(x65462)+~P1(f319(f319(f227(x65462),f2(x65462)),f319(f94(x65462),x65461)))+P1(f319(f319(f227(a1),f2(a1)),x65461))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [6579]~P68(x65791)+P1(f319(f319(f226(x65791),x65792),f2(x65791)))+~P1(f319(f319(f226(x65791),f2(x65791)),f319(f73(x65791),x65792)))
% 28.25/28.12 [6580]~P68(x65801)+P1(f319(f319(f227(x65801),x65802),f2(x65801)))+~P1(f319(f319(f227(x65801),f2(x65801)),f319(f73(x65801),x65802)))
% 28.25/28.12 [6603]~P6(x66031)+~P41(x66031,x66031,x66032)+P1(f319(f319(f226(x66031),f88(x66031,x66032)),f319(x66032,f88(x66031,x66032))))
% 28.25/28.12 [6604]~P6(x66041)+~P41(x66041,x66041,x66042)+P1(f319(f319(f226(x66041),f87(x66041,x66042)),f319(x66042,f87(x66041,x66042))))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [6677]~P68(x66771)+P1(f319(f319(f226(x66771),f319(f73(x66771),x66772)),f2(x66771)))+~P1(f319(f319(f226(x66771),f2(x66771)),x66772))
% 28.25/28.12 [6678]~P68(x66781)+P1(f319(f319(f227(x66781),f319(f73(x66781),x66782)),f2(x66781)))+~P1(f319(f319(f227(x66781),f2(x66781)),x66782))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [6751]~P1(f319(x67511,x67512))+P1(f319(x67511,f2(a925)))+P1(f319(x67511,f319(f319(f74(a925),f440(x67512,x67511)),f72(a925))))
% 28.25/28.12 [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)))
% 28.25/28.12 [6849]~E(x68491,f2(a925))+~E(f697(x68492,x68491),f2(a925))+E(f319(f134(a925,a925,f74(a925),x68491),x68492),f2(a925))
% 28.25/28.12 [6873]~P1(f319(f55(x68731),f903(x68732,x68731)))+~P1(f319(f55(f932(x68731,a923)),x68732))+P1(f319(f55(x68731),f31(f932(x68731,a923),x68732)))
% 28.25/28.12 [6879]E(x68791,x68792)+P1(f319(f319(f227(a1),x68791),x68792))+~P1(f319(f319(f227(a1),x68791),f319(f319(f74(a1),x68792),f72(a1))))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [6922]~P68(x69221)+~P1(f319(f319(f226(x69221),f319(f73(x69221),x69222)),f2(x69221)))+P1(f319(f319(f226(x69221),f2(x69221)),x69222))
% 28.25/28.12 [6923]~P68(x69231)+~P1(f319(f319(f227(x69231),f319(f73(x69231),x69232)),f2(x69231)))+P1(f319(f319(f227(x69231),f2(x69231)),x69232))
% 28.25/28.12 [6939]~P1(f319(f319(f227(a1),a77),x69392))+~P1(f319(f319(f227(a1),x69391),x69392))+P1(f319(f319(f227(a925),f319(f95(a925),x69391)),f319(f95(a925),x69392)))
% 28.25/28.12 [7028]~P1(f319(f319(f226(a1),f2(a1)),x70281))+P1(f319(f319(f227(a925),f319(a96,x70281)),x70282))+~P1(f319(f319(f227(a1),x70281),f319(f92(a1),x70282)))
% 28.25/28.12 [7033]P1(f319(x70331,x70332))+~P1(f319(x70331,f319(a20,f834(x70331,x70332))))+~P1(f319(f319(f321(a925),x70332),f234(f932(a925,a923))))
% 28.25/28.12 [7044]E(x70441,f2(a1))+E(f39(a1,x70442,x70441),f2(a1))+E(f319(f319(f23(a1),f319(f73(a1),f319(f319(f30(a1),x70442),x70441))),f72(a1)),f319(f319(f30(a1),x70442),f319(f73(a1),x70441)))
% 28.25/28.12 [7058]~P1(f319(f319(f226(a1),f2(a1)),x70581))+~P1(f319(f319(f227(a925),f319(a96,x70581)),x70582))+P1(f319(f319(f227(a1),x70581),f319(f92(a1),x70582)))
% 28.25/28.12 [7096]~P1(f319(f319(f226(a925),f319(a96,x70961)),f319(a96,x70962)))+~P1(f319(f319(f226(a1),f2(a1)),x70962))+P1(f319(f319(f226(a1),x70961),x70962))
% 28.25/28.12 [7097]~P1(f319(f319(f226(a925),f319(a96,x70971)),f319(a96,x70972)))+~P1(f319(f319(f227(a1),f2(a1)),x70971))+P1(f319(f319(f226(a1),x70971),x70972))
% 28.25/28.12 [7098]~P1(f319(f319(f227(a925),f319(a96,x70981)),f319(a96,x70982)))+~P1(f319(f319(f226(a1),f2(a1)),x70981))+P1(f319(f319(f227(a1),x70981),x70982))
% 28.25/28.12 [7099]~P1(f319(f319(f227(a925),f319(a96,x70991)),f319(a96,x70992)))+~P1(f319(f319(f227(a1),f2(a1)),x70992))+P1(f319(f319(f227(a1),x70991),x70992))
% 28.25/28.12 [7126]P1(f319(f319(f226(a1),x71261),x71262))+~P1(f319(f319(f226(a925),f319(f95(a925),x71261)),f319(f95(a925),x71262)))+P1(f319(f319(f226(a1),x71261),a77))
% 28.25/28.12 [7152]P1(f319(f319(f226(a1),f2(a1)),f39(a1,x71521,x71522)))+~P1(f319(f319(f226(a1),f2(a1)),x71522))+~P1(f319(f319(f226(a1),f2(a1)),x71521))
% 28.25/28.12 [7247]P1(f319(f319(f227(a1),a77),x72471))+~P1(f319(f319(f227(a1),x72472),x72471))+~P1(f319(f319(f227(a925),f319(f95(a925),x72472)),f319(f95(a925),x72471)))
% 28.25/28.12 [7302]E(f319(f319(f244(a1,a1),f319(f319(f30(a1),x73021),x73022)),f39(a1,x73021,x73022)),f44(x73021,x73022))+~P1(f319(f319(f227(a1),x73021),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x73022))
% 28.25/28.12 [7322]E(f319(f319(f244(a1,a1),f319(f319(f30(a1),x73221),x73222)),f39(a1,x73221,x73222)),f41(x73221,x73222))+~P1(f319(f319(f226(a1),f2(a1)),x73222))+~P1(f319(f319(f226(a1),f2(a1)),x73221))
% 28.25/28.12 [7376]~P101(x73762)+E(x73761,f105(x73762))+E(f319(f134(x73762,x73762,f75(x73762),f319(f133(x73762),x73761)),f319(f163(x73762),x73761)),f319(f57(x73762,f75(x73762)),f319(f164(x73762),x73761)))
% 28.25/28.12 [7493]~E(x74931,f2(a925))+E(f319(f134(a925,a925,f74(a925),x74931),x74932),f2(a925))+P1(f319(f319(f321(a925),f697(x74932,x74931)),f319(f164(a925),x74932)))
% 28.25/28.12 [7544]~P1(f319(f319(f226(a1),x75441),f2(a1)))+P1(f319(f319(f226(a1),f319(f319(f30(a1),x75441),x75442)),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x75442))
% 28.25/28.12 [7545]~P1(f319(f319(f227(a1),x75452),f2(a1)))+P1(f319(f319(f226(a1),f319(f319(f30(a1),x75451),x75452)),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x75451))
% 28.25/28.12 [7546]~P1(f319(f319(f227(a1),x75462),f2(a1)))+P1(f319(f319(f227(a1),f319(f319(f30(a1),x75461),x75462)),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x75461))
% 28.25/28.12 [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))
% 28.25/28.12 [7548]~P1(f319(f319(f227(a1),x75481),f2(a1)))+P1(f319(f319(f227(a1),f319(f319(f30(a1),x75481),x75482)),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x75482))
% 28.25/28.12 [7554]P1(f319(f319(f321(f932(x75541,a923)),f903(x75542,x75541)),x75542))+~P1(f319(f55(f932(x75541,a923)),x75542))+P1(f319(f55(x75541),f31(f932(x75541,a923),x75542)))
% 28.25/28.12 [7642]P26(x76421,x76421,x76422,f234(f932(x76421,a923)))+~E(f319(f302(x76421,x76421,x76422),f234(f932(x76421,a923))),f234(f932(x76421,a923)))+~P1(f319(f55(x76421),f234(f932(x76421,a923))))
% 28.25/28.12 [7761]~P26(x77611,x77611,x77612,f234(f932(x77611,a923)))+E(f319(f302(x77611,x77611,x77612),f234(f932(x77611,a923))),f234(f932(x77611,a923)))+~P1(f319(f55(x77611),f234(f932(x77611,a923))))
% 28.25/28.12 [7784]E(f41(f319(f95(a1),x77841),f319(f95(a1),x77842)),f319(f319(f244(a1,a1),f2(a1)),f319(f95(a1),x77841)))+~P1(f319(f319(f227(a1),f2(a1)),f319(f95(a1),x77842)))+~P1(f319(f319(f227(a1),f319(f95(a1),x77841)),f319(f95(a1),x77842)))
% 28.25/28.12 [7900]E(f319(f319(f30(a1),x79001),x79002),f319(f95(a1),a89))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),x79001),x79002)),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x79001))
% 28.25/28.12 [7957]~P1(f319(f319(f227(a1),x79572),f2(a1)))+~P1(f319(f319(f227(a1),f319(f319(f30(a1),x79571),x79572)),f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x79571))
% 28.25/28.12 [7962]E(f319(f319(f74(a1),x79621),x79622),f39(a1,x79621,x79622))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),x79621),x79622)),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x79621))
% 28.25/28.12 [7965]P1(f319(f319(f227(a1),x79651),f2(a1)))+~P1(f319(f319(f227(a1),f319(f319(f30(a1),x79651),x79652)),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x79652))
% 28.25/28.12 [8666]~P4(x86661)+P14(x86661,x86662)+~P1(f319(f319(f226(x86661),f319(f319(f156(x86661),x86662),f730(x86662,x86661))),f319(f319(f156(x86661),x86662),f731(x86662,x86661))))
% 28.25/28.12 [8667]~P4(x86671)+P14(x86671,x86672)+~P1(f319(f319(f226(x86671),f319(f319(f156(x86671),x86672),f738(x86672,x86671))),f319(f319(f156(x86671),x86672),f742(x86672,x86671))))
% 28.25/28.12 [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)))
% 28.25/28.12 [5913]~P42(x59132)+~P42(x59131)+P42(f319(f319(f102(f932(a1,a923)),x59131),x59132))
% 28.25/28.12 [5914]~P42(x59142)+~P42(x59141)+P42(f319(f319(f93(f932(a1,a923)),x59141),x59142))
% 28.25/28.12 [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))
% 28.25/28.12 [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)))
% 28.25/28.12 [6193]~P4(x61931)+P14(x61931,x61932)+P1(f319(f319(f227(a925),f731(x61932,x61931)),f319(f181(f926(x61931)),x61932)))
% 28.25/28.12 [6194]~P4(x61941)+P14(x61941,x61942)+P1(f319(f319(f227(a925),f742(x61942,x61941)),f319(f181(f926(x61941)),x61942)))
% 28.25/28.12 [6352]~P99(x63521)+~E(f319(f95(x63521),x63522),f2(x63521))+P29(x63521,f319(f95(x63521),f319(f319(f74(a1),x63522),f319(f73(a1),a77))))
% 28.25/28.12 [6353]~P99(x63531)+~E(f319(f95(x63531),x63532),f2(x63531))+P29(x63531,f319(f95(x63531),f319(f319(f74(a1),a77),f319(f73(a1),x63532))))
% 28.25/28.12 [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))
% 28.25/28.12 [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))))
% 28.25/28.12 [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))
% 28.25/28.12 [6643]~P84(x66431)+~P1(f319(f319(f226(x66431),f2(x66431)),x66432))+P1(f319(f319(f226(x66431),f319(f73(x66431),x66432)),x66432))
% 28.25/28.12 [6644]~P84(x66441)+~P1(f319(f319(f227(x66441),f2(x66441)),x66442))+P1(f319(f319(f227(x66441),f319(f73(x66441),x66442)),x66442))
% 28.25/28.12 [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))
% 28.25/28.12 [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)))
% 28.25/28.12 [6874]~P84(x68741)+P1(f319(f319(f226(x68741),f2(x68741)),x68742))+~P1(f319(f319(f226(x68741),f319(f73(x68741),x68742)),x68742))
% 28.25/28.12 [6875]~P84(x68751)+P1(f319(f319(f227(x68751),f2(x68751)),x68752))+~P1(f319(f319(f227(x68751),f319(f73(x68751),x68752)),x68752))
% 28.25/28.12 [6888]~P84(x68881)+~P1(f319(f319(f226(x68881),f2(x68881)),x68882))+P1(f319(f319(f226(x68881),f2(x68881)),f319(f319(f74(x68881),x68882),x68882)))
% 28.25/28.12 [6890]~P84(x68901)+~P1(f319(f319(f227(x68901),f2(x68901)),x68902))+P1(f319(f319(f227(x68901),f2(x68901)),f319(f319(f74(x68901),x68902),x68902)))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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)))
% 28.25/28.12 [6949]~P99(x69491)+E(f319(f95(x69491),x69492),f2(x69491))+~P29(x69491,f319(f95(x69491),f319(f319(f74(a1),a77),f319(f73(a1),x69492))))
% 28.25/28.12 [6950]~P99(x69501)+E(f319(f95(x69501),x69502),f2(x69501))+~P29(x69501,f319(f95(x69501),f319(f319(f74(a1),x69502),f319(f73(a1),a77))))
% 28.25/28.12 [7006]~P1(f319(f55(x70061),x70062))+~P1(f319(f55(x70061),f234(f932(x70061,a923))))+P1(f319(f55(x70061),f319(f73(f932(x70061,a923)),x70062)))
% 28.25/28.12 [7029]~P1(f319(f319(f227(a1),f2(a1)),x70292))+~P1(f319(f319(f226(a1),x70292),x70291))+P1(f319(f319(f227(a1),f2(a1)),f319(f319(f30(a1),x70291),x70292)))
% 28.25/28.12 [7030]~P1(f319(f319(f226(a1),x70301),f2(a1)))+~P1(f319(f319(f227(a1),x70302),f2(a1)))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f30(a1),x70301),x70302)))
% 28.25/28.12 [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(f75(a1),x70701),x70702)))
% 28.25/28.12 [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(f74(a1),x70711),x70712)))
% 28.25/28.12 [7072]~P1(f319(f319(f226(a1),f2(a1)),x70722))+~P1(f319(f319(f226(a1),f2(a1)),x70721))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f30(a1),x70721),x70722)))
% 28.25/28.12 [7073]~P1(f319(f319(f226(a1),f2(a1)),x70731))+~P1(f319(f319(f227(a1),f2(a1)),x70732))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f30(a1),x70731),x70732)))
% 28.25/28.12 [7074]~P1(f319(f319(f227(a925),f2(a925)),x70742))+~P1(f319(f319(f227(a925),f2(a925)),x70741))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f75(a925),x70741),x70742)))
% 28.25/28.12 [7139]E(x71391,f2(a1))+E(f39(a1,x71392,x71391),f2(a1))+E(f319(f319(f23(a1),f319(f73(a1),f319(f319(f30(a1),x71392),x71391))),f72(a1)),f319(f319(f30(a1),f319(f73(a1),x71392)),x71391))
% 28.25/28.12 [7193]P1(f319(f319(f227(a925),f2(a925)),x71931))+P1(f319(f319(f227(a925),f2(a925)),x71932))+~P1(f319(f319(f227(a925),f2(a925)),f319(f319(f74(a925),x71932),x71931)))
% 28.25/28.12 [7197]~P84(x71971)+P1(f319(f319(f226(x71971),f2(x71971)),x71972))+~P1(f319(f319(f226(x71971),f2(x71971)),f319(f319(f74(x71971),x71972),x71972)))
% 28.25/28.12 [7198]~P84(x71981)+P1(f319(f319(f227(x71981),f2(x71981)),x71982))+~P1(f319(f319(f227(x71981),f2(x71981)),f319(f319(f74(x71981),x71982),x71982)))
% 28.25/28.12 [7248]~P1(f319(f55(x72481),x72482))+P1(f319(f55(x72481),f234(f932(x72481,a923))))+~P1(f319(f55(x72481),f319(f73(f932(x72481,a923)),x72482)))
% 28.25/28.12 [7314]P1(f319(f319(f226(a1),x73141),f2(a1)))+~P1(f319(f319(f227(a1),x73142),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f30(a1),x73141),x73142)))
% 28.25/28.12 [7320]~P1(f319(f319(f227(a1),f2(a1)),x73201))+P1(f319(f319(f226(a1),x73201),x73202))+~P1(f319(f319(f227(a1),f2(a1)),f319(f319(f30(a1),x73202),x73201)))
% 28.25/28.12 [7321]~P1(f319(f319(f226(a1),f2(a1)),x73212))+P1(f319(f319(f226(a1),x73211),x73212))+~P1(f319(f319(f227(a1),f2(a1)),f319(f319(f30(a1),x73212),x73211)))
% 28.25/28.12 [7351]P1(f319(f319(f226(a1),f2(a1)),x73511))+~P1(f319(f319(f227(a1),f2(a1)),x73512))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f30(a1),x73511),x73512)))
% 28.25/28.12 [7352]P1(f319(f319(f227(a1),f2(a1)),x73521))+~P1(f319(f319(f226(a1),f2(a1)),x73522))+~P1(f319(f319(f227(a1),f2(a1)),f319(f319(f30(a1),x73522),x73521)))
% 28.25/28.12 [7455]E(f208(x74551,x74552),x74551)+~E(x74552,f2(a925))+~P1(f319(f307(f931(a925,a925),a211),f319(f319(f244(a925,a925),x74551),x74552)))
% 28.25/28.12 [7661]E(f170(x76611,x76612),f105(a1))+P1(f319(f319(f226(a1),x76611),x76612))+~P1(f319(f307(f931(a1,a1),a174),f319(f319(f244(a1,a1),x76611),x76612)))
% 28.25/28.12 [7682]E(f319(f319(f244(a1,a1),f319(f95(a1),a89)),f319(f319(f74(a1),x76821),x76822)),f44(x76821,x76822))+~P1(f319(f319(f227(a1),f2(a1)),x76822))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),x76821),x76822)))
% 28.25/28.12 [7712]E(x77121,f2(a925))+E(f208(x77121,f39(a925,x77122,x77121)),f208(x77122,x77121))+~P1(f319(f307(f931(a925,a925),a211),f319(f319(f244(a925,a925),x77122),x77121)))
% 28.25/28.12 [7763]E(f120(x77631,x77632),f107(a1))+~P1(f319(f319(f227(a1),x77631),x77632))+~P1(f319(f307(f931(a1,a1),a125),f319(f319(f244(a1,a1),x77631),x77632)))
% 28.25/28.12 [7792]~P1(f319(f55(x77922),f234(f932(x77922,a923))))+~P1(f319(f55(x77921),f234(f932(x77921,a923))))+P1(f319(f55(f931(x77921,x77922)),f234(f932(f931(x77921,x77922),a923))))
% 28.25/28.12 [7793]~P1(f319(f55(x77932),f234(f932(x77932,a923))))+~P1(f319(f55(x77931),f234(f932(x77931,a923))))+P1(f319(f55(f933(x77931,x77932)),f234(f932(f933(x77931,x77932),a923))))
% 28.25/28.12 [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),x78652),x78651)))
% 28.25/28.12 [7866]~P1(f319(f319(f227(a925),f319(a104,f2(a925))),x78661))+~P1(f319(f319(f227(a925),f319(a104,f2(a925))),x78662))+P1(f319(f319(f227(a925),x78661),f319(f319(f75(a925),x78661),x78662)))
% 28.25/28.12 [7899]E(f319(f29(x78991),f234(f932(x78991,a923))),f319(a104,f2(a925)))+P1(f319(f55(x78992),f234(f932(x78992,a923))))+~P1(f319(f55(f932(x78992,x78991)),f234(f932(f932(x78992,x78991),a923))))
% 28.25/28.12 [7950]E(f41(x79501,x79502),f319(f319(f244(a1,a1),f2(a1)),x79501))+~P1(f319(f319(f227(a1),x79501),x79502))+~P1(f319(f307(f931(a1,a1),a52),f319(f319(f244(a1,a1),x79501),x79502)))
% 28.25/28.12 [7954]E(f207(f319(f73(a1),x79541),f319(f73(a1),x79542)),f207(x79541,x79542))+~P1(f319(f319(f227(a1),x79542),f2(a1)))+~P1(f319(f307(f931(a1,a1),a213),f319(f319(f244(a1,a1),x79541),x79542)))
% 28.25/28.12 [7975]E(f41(x79751,x79752),f319(f319(f244(a1,a1),f2(a1)),x79751))+~P1(f319(f319(f226(a1),x79752),f2(a1)))+~P1(f319(f307(f931(a1,a1),a52),f319(f319(f244(a1,a1),x79751),x79752)))
% 28.25/28.12 [8025]~P1(f319(f319(f226(a925),f319(a104,f2(a925))),x80251))+~P1(f319(f319(f226(a925),f319(a104,f2(a925))),x80252))+P1(f319(f319(f226(a925),f319(a104,f2(a925))),f319(f319(f75(a925),x80251),x80252)))
% 28.25/28.12 [8026]~P1(f319(f319(f227(a925),f319(a104,f2(a925))),x80262))+~P1(f319(f319(f227(a925),f319(a104,f2(a925))),x80261))+P1(f319(f319(f227(a925),f319(a104,f2(a925))),f319(f319(f75(a925),x80261),x80262)))
% 28.25/28.12 [8190]E(f319(f319(f244(a1,a1),f319(f95(a1),a89)),f319(f319(f74(a1),x81901),x81902)),f44(x81901,x81902))+~P1(f319(f319(f226(a1),x81902),f2(a1)))+~P1(f319(f307(f931(a1,a1),a46),f319(f319(f244(a1,a1),x81901),x81902)))
% 28.25/28.12 [8214]E(f108(a1,f319(f121(a1),x82141),f120(x82142,f319(f319(f74(a1),x82141),f72(a1)))),f120(x82142,x82141))+P1(f319(f319(f227(a1),x82142),x82141))+~P1(f319(f307(f931(a1,a1),a125),f319(f319(f244(a1,a1),x82142),x82141)))
% 28.25/28.12 [8227]E(f319(f319(f143(a1),x82271),f170(f319(f319(f74(a1),x82271),f72(a1)),x82272)),f170(x82271,x82272))+~P1(f319(f319(f226(a1),x82271),x82272))+~P1(f319(f307(f931(a1,a1),a174),f319(f319(f244(a1,a1),x82271),x82272)))
% 28.25/28.12 [8373]~P113(x83731)+P41(a925,x83731,x83732)+~P1(f319(f319(f226(x83731),f319(x83732,f374(x83732,x83731))),f319(x83732,f319(a104,f374(x83732,x83731)))))
% 28.25/28.12 [8511]E(f319(f319(f244(a1,a1),f319(f95(a1),a89)),f319(f319(f74(a1),x85111),x85112)),f44(x85111,x85112))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),x85111),x85112)))+~P1(f319(f307(f931(a1,a1),a46),f319(f319(f244(a1,a1),x85111),x85112)))
% 28.25/28.12 [8715]E(x87151,f105(x87152))+~P1(f319(f129(x87152),x87151))+E(f169(x87152,f319(f319(f8(a923,a923,x87152),a314),f319(f319(f7(x87152,x87152,a923),a316),f136(x87152,x87151))),x87151),f106(x87152,x87151))
% 28.25/28.12 [8788]E(f319(f319(f244(a1,a1),f319(f95(a1),a89)),f319(f319(f74(a1),f319(f95(a1),x87881)),f319(f95(a1),x87882))),f44(f319(f95(a1),x87881),f319(f95(a1),x87882)))+~P1(f319(f319(f227(a1),f2(a1)),f319(f95(a1),x87882)))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),f319(f95(a1),x87881)),f319(f95(a1),x87882))))
% 28.25/28.12 [8813]~P42(x88132)+~P42(x88131)+E(f319(f302(a925,a1,f92(a1)),f319(f319(f102(f932(a925,a923)),f319(f302(a1,a925,a96),x88131)),f319(f302(a1,a925,a96),x88132))),f319(f319(f102(f932(a1,a923)),x88131),x88132))
% 28.25/28.12 [8814]~P42(x88142)+~P42(x88141)+E(f319(f302(a925,a1,f92(a1)),f319(f319(f93(f932(a925,a923)),f319(f302(a1,a925,a96),x88141)),f319(f302(a1,a925,a96),x88142))),f319(f319(f93(f932(a1,a923)),x88141),x88142))
% 28.25/28.12 [9489]~P99(x94891)+~E(f319(f95(x94891),x94892),f72(x94891))+P29(x94891,f319(f95(x94891),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f73(a1),x94892))))
% 28.25/28.12 [9735]~P99(x97351)+E(f319(f95(x97351),x97352),f72(x97351))+~P29(x97351,f319(f95(x97351),f319(f319(f74(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),f319(f73(a1),x97352))))
% 28.25/28.12 [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(a316,f76(a1,x105211)),f76(a1,x105212))),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))
% 28.25/28.12 [10522]E(x105221,f2(a1))+E(x105222,f2(a1))+E(f319(f250(a1,a1,a1,a1,f25(a1),f319(f75(a1),f76(a1,x105222))),f319(f319(f319(f86(f931(a1,a1)),f319(f319(a318,f319(f319(a317,f319(f319(f227(a1),f2(a1)),x105222)),f319(f319(f226(a1),f2(a1)),x105221))),f319(f319(a317,f319(f319(f227(a1),x105222),f2(a1))),f319(f319(f227(a1),x105221),f2(a1))))),f47(x105221,x105222)),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),x105222))))),f47(x105221,x105222)))),f40(x105221,x105222))
% 28.25/28.12 [5921]~P126(x59211)+~P99(x59211)+E(f319(f69(x59211),f319(f319(f236(x59211),f319(f95(x59211),a89)),x59212)),f72(x59211))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [7238]~P98(x72381)+~P1(f319(f319(f321(x72381),x72382),f101(x72381)))+~E(f319(f319(f74(x72381),f319(f319(f74(x72381),f72(x72381)),x72382)),x72382),f2(x72381))
% 28.25/28.12 [7353]~P1(f319(f319(f226(a1),x73532),f2(a1)))+~P1(f319(f319(f227(a1),x73531),f2(a1)))+E(f319(f243(a1,a1),f319(a45,f41(f319(f73(a1),x73531),f319(f73(a1),x73532)))),f319(f319(f30(a1),x73531),x73532))
% 28.25/28.12 [7370]~P1(f319(f319(f226(a1),x73702),f2(a1)))+~P1(f319(f319(f227(a1),x73701),f2(a1)))+E(f319(f248(a1,a1),f319(a45,f41(f319(f73(a1),x73701),f319(f73(a1),x73702)))),f39(a1,x73701,x73702))
% 28.25/28.12 [7378]~P1(f319(f319(f227(a1),x73782),f2(a1)))+E(f319(f243(a1,a1),f319(a45,f44(f319(f73(a1),x73781),f319(f73(a1),x73782)))),f319(f319(f30(a1),x73781),x73782))+~P1(f319(f319(f227(a1),f2(a1)),x73781))
% 28.25/28.12 [7396]~P1(f319(f319(f227(a1),x73962),f2(a1)))+E(f319(f248(a1,a1),f319(a45,f44(f319(f73(a1),x73961),f319(f73(a1),x73962)))),f39(a1,x73961,x73962))+~P1(f319(f319(f227(a1),f2(a1)),x73961))
% 28.25/28.12 [7449]E(f319(f319(f30(a1),f319(f319(f236(a1),x74491),x74492)),x74491),f319(f319(f236(a1),x74491),f319(f319(f23(a925),x74492),f319(a104,f2(a925)))))+~P1(f319(f319(f227(a925),f2(a925)),x74492))+~P1(f319(f319(f227(a1),f2(a1)),x74491))
% 28.25/28.12 [7551]~P1(f319(f319(f227(a925),f2(a925)),x75511))+~P1(f319(f319(f227(a925),f2(a925)),x75512))+P1(f319(f319(f227(a925),f319(f319(f23(a925),x75511),x75512)),x75511))
% 28.25/28.12 [7552]~P1(f319(f319(f227(a925),f2(a925)),x75521))+~P1(f319(f319(f227(a925),f72(a925)),x75522))+P1(f319(f319(f227(a925),f319(f319(f30(a925),x75521),x75522)),x75521))
% 28.25/28.12 [7553]~P1(f319(f319(f227(a1),f2(a1)),x75531))+~P1(f319(f319(f227(a1),f72(a1)),x75532))+P1(f319(f319(f227(a1),f319(f319(f30(a1),x75531),x75532)),x75531))
% 28.25/28.12 [7688]E(x76881,f2(a925))+~E(x76882,f2(a1))+~P1(f319(f319(f227(a1),f2(a1)),f319(f319(f236(a1),f319(f69(a1),x76882)),x76881)))
% 28.25/28.12 [8057]~P1(f319(x80571,x80572))+P1(f319(x80571,f2(a925)))+E(f319(a104,f230(a925,f319(f319(f8(a925,a923,a925),x80571),a104))),f230(a925,x80571))
% 28.25/28.12 [8106]~E(x81062,f105(f926(x81061)))+E(f319(f181(f926(f926(x81061))),f171(x81061,x81062)),f2(a925))+~P14(a925,f319(f160(a925),f319(f319(f146(f926(x81061),a925),f181(f926(x81061))),x81062)))
% 28.25/28.12 [8360]P1(f319(x83601,x83602))+~P1(f319(x83601,f319(a99,f590(x83601,x83602))))+~P1(f319(f319(f321(f932(f931(a925,a925),a923)),x83602),a90))
% 28.25/28.12 [8377]E(x83771,f105(f926(x83772)))+E(f319(f181(f926(x83772)),f319(f319(f156(f926(x83772)),x83771),f2(a925))),f319(f181(f926(f926(x83772))),f171(x83772,x83771)))+~P14(a925,f319(f160(a925),f319(f319(f146(f926(x83772),a925),f181(f926(x83772))),x83771)))
% 28.25/28.12 [8520]~P39(x85201,x85202)+~P40(x85201,x85202)+P39(x85201,f319(f319(f23(f932(f931(x85201,x85201),a923)),x85202),f299(x85201,f180(f932(f931(x85201,x85201),a923)))))
% 28.25/28.12 [9100]~P1(f319(f55(x91001),f319(f254(x91001),x91002)))+~P1(f319(f55(x91001),f234(f932(x91001,a923))))+P1(f319(f55(x91001),f319(f254(x91001),f319(f319(f8(a923,a923,x91001),a314),x91002))))
% 28.25/28.12 [9166]E(f319(f319(f244(a925,a925),f319(a104,f319(f319(f30(a925),f319(f319(f23(a925),x91661),x91662)),x91662))),f39(a925,f319(f319(f23(a925),x91661),x91662),x91662)),f79(f931(a925,a925),f42(x91661,x91662)))+~P1(f319(f319(f227(a925),f2(a925)),x91662))+~P1(f319(f319(f226(a925),x91662),x91661))
% 28.25/28.12 [9455]~P1(f319(f55(x94551),f319(f254(x94551),x94552)))+P1(f319(f55(x94551),f234(f932(x94551,a923))))+~P1(f319(f55(x94551),f319(f254(x94551),f319(f319(f8(a923,a923,x94551),a314),x94552))))
% 28.25/28.12 [10200]P28(x102001,x102002)+~P38(x102001,f319(f243(f932(f931(x102001,x102001),a923),f932(f931(x102001,x102001),a923)),x102002))+~P1(f319(f319(f226(f932(f931(x102001,x102001),a923)),f319(f319(f281(x102001,x102001,x102001),f319(f243(f932(f931(x102001,x102001),a923),f932(f931(x102001,x102001),a923)),x102002)),f319(f248(f932(f931(x102001,x102001),a923),f932(f931(x102001,x102001),a923)),x102002))),f319(f243(f932(f931(x102001,x102001),a923),f932(f931(x102001,x102001),a923)),x102002)))
% 28.25/28.12 [10244]E(f319(f37(f319(f95(a1),x102441)),f41(f319(f95(a1),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)))),f319(f95(a1),x102441)))),f41(f319(f95(a1),x102442),f319(f95(a1),x102441)))+~P1(f319(f319(f227(a1),f2(a1)),f319(f95(a1),x102441)))+P1(f319(f319(f227(a1),f319(f95(a1),x102442)),f319(f95(a1),x102441)))
% 28.25/28.12 [10250]E(f319(f37(f319(f95(a1),x102501)),f44(f319(f95(a1),x102502),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),x102501)))),f44(f319(f95(a1),x102502),f319(f95(a1),x102501)))+~P1(f319(f319(f227(a1),f2(a1)),f319(f95(a1),x102501)))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),f319(f95(a1),x102502)),f319(f95(a1),x102501))))
% 28.25/28.12 [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))
% 28.25/28.12 [10298]~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)))),x102982,x102981),f180(f932(a925,a923)))+~P1(f319(f319(f279(a925),x102982),x102981))+P1(f319(f319(f279(a925),x102981),x102982))
% 28.25/28.12 [10299]~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)))),x102992,x102991),f180(f932(a925,a923)))+~P1(f319(f319(f279(a925),x102992),x102991))+P1(f319(f319(f279(a925),x102991),x102992))
% 28.25/28.12 [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))
% 28.25/28.12 [7479]~P1(f319(f319(f227(a925),f2(a925)),x74792))+P1(f319(f319(f227(a925),x74791),x74792))+E(f319(a104,f319(f319(f30(a925),f319(f319(f23(a925),x74791),x74792)),x74792)),f319(f319(f30(a925),x74791),x74792))
% 28.25/28.12 [7615]~P1(f319(f319(f227(a925),f2(a925)),x76152))+~P1(f319(f319(f226(a925),x76152),x76151))+E(f319(a104,f319(f319(f30(a925),f319(f319(f23(a925),x76151),x76152)),x76152)),f319(f319(f30(a925),x76151),x76152))
% 28.25/28.12 [8584]~P99(x85841)+~P98(x85841)+~P29(x85841,f319(f95(x85841),f319(f319(f23(a1),f319(f319(f74(a1),x85842),x85842)),a89)))
% 28.25/28.12 [9360]E(x93601,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),x93602),x93601),x93601))),f79(f931(a925,a925),f42(x93602,x93601)))+P1(f319(f319(f227(a925),x93602),x93601))
% 28.25/28.12 [9543]~P39(x95431,x95432)+~P56(x95431,x95432)+P1(f319(f319(f226(f932(f931(x95431,x95431),a923)),f319(f319(f281(x95431,x95431,x95431),f319(f278(x95431,x95431),x95432)),x95432)),x95432))
% 28.25/28.12 [9801]P1(f319(x98012,f663(x98012,x98011)))+P1(f319(x98011,f663(x98012,x98011)))+E(f319(f254(a1),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f226(a1),f2(a1)))),x98011)),f319(f254(a1),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f226(a1),f2(a1)))),x98012)))
% 28.25/28.12 [9805]~P1(f319(x98052,f663(x98052,x98051)))+~P1(f319(x98051,f663(x98052,x98051)))+E(f319(f254(a1),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f226(a1),f2(a1)))),x98051)),f319(f254(a1),f319(f319(f18(a1,a923,a923),f319(f319(f8(a923,f932(a923,a923),a1),a317),f319(f226(a1),f2(a1)))),x98052)))
% 28.25/28.12 [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)
% 28.25/28.12 [7823]~P73(x78231)+~P99(x78231)+E(f319(f319(f283(x78231),x78232),f319(f95(x78231),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89))),x78232)
% 28.25/28.12 [9488]~P99(x94881)+~E(f319(f95(x94881),x94882),f72(x94881))+P29(x94881,f319(f95(x94881),f319(f319(f74(a1),x94882),f319(f73(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))
% 28.25/28.12 [9676]~P144(x96761)+~E(x96762,f72(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)))),f72(x96761))
% 28.25/28.12 [9677]~P144(x96771)+~E(x96772,f2(x96771))+E(f319(f319(f236(x96771),x96772),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(x96771))
% 28.25/28.12 [9692]~P144(x96921)+~E(x96922,f319(f73(x96921),f72(x96921)))+E(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)))),f72(x96921))
% 28.25/28.12 [9712]~P87(x97121)+~P100(x97121)+E(f319(f319(f236(x97121),f319(f95(x97121),x97122)),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(x97121),f319(f95(x97121),x97122)),f319(f95(x97121),x97122)))
% 28.25/28.12 [9736]~P99(x97361)+E(f319(f95(x97361),x97362),f72(x97361))+~P29(x97361,f319(f95(x97361),f319(f319(f74(a1),x97362),f319(f73(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))))
% 28.25/28.12 [9857]~P144(x98572)+E(x98571,f2(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)))),f2(x98572))
% 28.25/28.12 [10141]~P126(x101412)+E(x101411,f2(x101412))+P1(f319(f319(f227(x101412),f2(x101412)),f319(f319(f236(x101412),x101411),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))))))
% 28.25/28.12 [10199]~P126(x101992)+~E(x101991,f2(x101992))+~P1(f319(f319(f227(x101992),f2(x101992)),f319(f319(f236(x101992),x101991),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))))))
% 28.25/28.12 [10235]P1(f319(f319(f226(a1),x102351),f2(a1)))+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))
% 28.25/28.12 [10236]~P1(f319(f319(f227(a1),f2(a1)),x102361))+P1(f319(f319(f227(a1),x102362),x102361))+E(f319(f37(x102361),f41(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))),f41(x102362,x102361))
% 28.25/28.12 [10237]P1(f319(f319(f226(a1),x102371),f2(a1)))+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))
% 28.25/28.12 [10238]~P1(f319(f319(f227(a1),f2(a1)),x102381))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),x102382),x102381)))+E(f319(f37(x102381),f44(x102382,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)))),x102381))),f44(x102382,x102381))
% 28.25/28.12 [10239]~P149(x102391)+~P1(f319(f319(f226(a1),f2(a1)),x102392))+E(f319(f92(x102391),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)))),x102392))),f319(f319(f74(x102391),f319(f92(x102391),f319(a96,x102392))),f319(f92(x102391),f319(a96,x102392))))
% 28.25/28.12 [5255]~P151(x52551,x52553,x52552)+~E(x52553,f2(a1))+P1(f319(x52551,x52552))
% 28.25/28.12 [5385]~P4(x53851)+~P14(x53851,x53853)+P14(x53851,f162(x53851,x53852,x53853))
% 28.25/28.12 [5386]~P4(x53861)+~P14(x53861,x53863)+P14(x53861,f169(x53861,x53862,x53863))
% 28.25/28.12 [4947]~P69(x49472)+~E(x49473,f319(f73(x49472),x49471))+E(x49471,f319(f73(x49472),x49473))
% 28.25/28.12 [4948]~P69(x49482)+~E(x49483,f319(f73(x49482),x49481))+E(x49481,f319(f73(x49482),x49483))
% 28.25/28.12 [4949]~P69(x49491)+~E(f319(f73(x49491),x49493),x49492)+E(f319(f73(x49491),x49492),x49493)
% 28.25/28.12 [4950]~P69(x49501)+~E(f319(f73(x49501),x49503),x49502)+E(f319(f73(x49501),x49502),x49503)
% 28.25/28.12 [5029]~P4(x50293)+E(x50291,x50292)+~E(f319(f296(x50293),x50291),f319(f296(x50293),x50292))
% 28.25/28.12 [5030]~P4(x50303)+E(x50301,x50302)+~E(f319(f274(x50303),x50301),f319(f274(x50303),x50302))
% 28.25/28.12 [5031]~P4(x50313)+E(x50311,x50312)+~E(f319(f275(x50313),x50311),f319(f275(x50313),x50312))
% 28.25/28.12 [5032]~P4(x50323)+E(x50321,x50322)+~E(f319(f293(x50323),x50321),f319(f293(x50323),x50322))
% 28.25/28.12 [5033]~P96(x50333)+E(x50331,x50332)+~E(f319(f73(x50333),x50331),f319(f73(x50333),x50332))
% 28.25/28.12 [5034]~P69(x50343)+E(x50341,x50342)+~E(f319(f73(x50343),x50341),f319(f73(x50343),x50342))
% 28.25/28.12 [5035]~P110(x50353)+E(x50351,x50352)+~E(f319(f92(x50353),x50351),f319(f92(x50353),x50352))
% 28.25/28.12 [5036]~P98(x50363)+E(x50361,x50362)+~E(f319(f94(x50363),x50361),f319(f94(x50363),x50362))
% 28.25/28.12 [5137]~P5(x51371)+~P1(f319(x51372,x51373))+P1(f319(f50(x51371),x51372))
% 28.25/28.12 [5138]~P5(x51381)+~P1(f319(x51382,x51383))+P1(f319(f50(x51381),x51382))
% 28.25/28.12 [5174]~P5(x51743)+P1(f319(x51741,x51742))+~P1(f319(f51(x51743),x51741))
% 28.25/28.12 [5175]~P5(x51753)+P1(f319(x51751,x51752))+~P1(f319(f51(x51753),x51751))
% 28.25/28.12 [5275]~P152(x52751,x52752,x52753)+~E(x52752,f2(a1))+P1(f319(x52751,f2(a1)))
% 28.25/28.12 [5310]~P114(x53102)+~P1(f319(x53101,x53103))+P1(f319(x53101,f230(x53102,x53101)))
% 28.25/28.12 [5311]~P114(x53112)+~P1(f319(x53111,x53113))+P1(f319(x53111,f230(x53112,x53111)))
% 28.25/28.12 [5318]~E(x53181,f2(a925))+E(f328(x53181,x53182,x53183),f180(f932(x53183,a923)))+~E(f319(f29(x53183),x53182),f319(a104,x53181))
% 28.25/28.12 [5469]~E(x54692,f2(a925))+E(f319(f243(a925,a925),x54691),f2(a925))+~P1(f319(f42(x54693,x54692),x54691))
% 28.25/28.12 [5506]P1(f319(x55061,x55062))+~E(x55063,f319(f92(a1),x55062))+~P1(f319(x55061,f319(a96,x55063)))
% 28.25/28.12 [5985]~E(x59853,f2(a925))+~P1(f319(x59851,x59852))+P1(f319(x59851,f39(a925,x59852,x59853)))
% 28.25/28.12 [6042]~P114(x60421)+~P1(f319(x60422,x60423))+~P1(f319(f319(f227(x60421),x60423),f230(x60421,x60422)))
% 28.25/28.12 [6225]~P111(x62252)+~P111(x62251)+E(f123(x62251,x62252,f124(x62251,x62253),f124(x62252,x62253)),f124(f931(x62251,x62252),x62253))
% 28.25/28.12 [6403]~E(x64033,f2(a925))+P1(f319(x64031,x64032))+~P1(f319(x64031,f39(a925,x64032,x64033)))
% 28.25/28.12 [6415]~P6(x64151)+~P1(f319(f319(f226(x64151),x64152),f319(x64153,x64152)))+P1(f319(f319(f226(x64151),x64152),f88(x64151,x64153)))
% 28.25/28.12 [6900]E(x69001,f180(f932(x69002,a923)))+~P1(f319(f55(x69002),x69001))+P1(f319(f56(x69002,x69003,x69001),f870(x69003,x69001,x69002)))
% 28.25/28.12 [7095]E(x70951,f2(a925))+~P1(f319(x70952,f518(x70951,x70953,x70952)))+P1(f319(x70952,f39(a925,x70953,x70951)))
% 28.25/28.12 [7203]~P6(x72031)+~P1(f319(f319(f226(x72031),x72032),f434(x72033,x72032,x72031)))+P1(f319(f319(f226(x72031),x72032),f32(x72031,x72033)))
% 28.25/28.12 [7204]~P6(x72041)+~P1(f319(f319(f226(x72041),x72042),f710(x72042,x72043,x72041)))+P1(f319(f319(f226(x72041),x72042),f32(x72041,x72043)))
% 28.25/28.12 [7206]~P1(f319(x72061,x72062))+~P1(f319(x72061,f518(x72063,x72062,x72061)))+P1(f319(x72061,f39(a925,x72062,x72063)))
% 28.25/28.12 [7308]E(x73081,f105(x73082))+E(f319(f319(f143(x73082),f711(x73083,x73081,x73082)),f714(x73083,x73081,x73082)),x73081)+~P1(f319(f319(f321(f926(x73082)),x73081),f153(x73082,x73083)))
% 28.25/28.12 [7340]~P145(x73401)+~P1(f319(f319(f321(x73401),x73402),f101(x73401)))+P1(f319(f319(f321(x73401),f319(f319(f236(x73401),x73402),x73403)),f101(x73401)))
% 28.25/28.12 [7660]P38(x76601,x76602)+~P1(f319(f319(f321(x76601),x76603),f629(x76602,x76601)))+P1(f319(f319(f321(x76601),f660(x76602,x76601,x76603)),f629(x76602,x76601)))
% 28.25/28.12 [7927]E(x79271,f105(x79272))+~P1(f319(f319(f321(f926(x79272)),x79271),f153(x79272,x79273)))+P1(f319(f319(f321(f926(x79272)),f714(x79273,x79271,x79272)),f153(x79272,x79273)))
% 28.25/28.12 [7979]E(x79791,f2(a925))+E(f319(f319(f74(a925),f319(f319(f75(a925),x79791),f519(x79791,x79792,x79793))),f518(x79791,x79792,x79793)),x79792)+P1(f319(x79793,f39(a925,x79792,x79791)))
% 28.25/28.12 [8020]~P1(f319(x80203,x80202))+E(f319(f319(f74(a925),f319(f319(f75(a925),x80201),f519(x80201,x80202,x80203))),f518(x80201,x80202,x80203)),x80202)+P1(f319(x80203,f39(a925,x80202,x80201)))
% 28.25/28.12 [8163]P1(f319(f319(f227(a1),x81631),f508(x81632,x81633,x81631)))+P1(f319(f319(x81633,f319(f319(f30(a1),x81632),x81631)),f39(a1,x81632,x81631)))+~P1(f319(f319(f227(a1),x81631),f2(a1)))
% 28.25/28.12 [8433]P1(f319(f319(x84332,f319(f319(f30(a1),x84331),x84333)),f39(a1,x84331,x84333)))+~P1(f319(f319(f227(a1),x84333),f2(a1)))+P1(f319(f319(f226(a1),f508(x84331,x84332,x84333)),f2(a1)))
% 28.25/28.12 [8619]E(f319(f319(f74(a1),f319(f319(f75(a1),x86191),f509(x86192,x86193,x86191))),f508(x86192,x86193,x86191)),x86192)+P1(f319(f319(x86193,f319(f319(f30(a1),x86192),x86191)),f39(a1,x86192,x86191)))+~P1(f319(f319(f227(a1),x86191),f2(a1)))
% 28.25/28.12 [8861]~P1(f319(f319(x88611,f509(x88612,x88611,x88613)),f508(x88612,x88611,x88613)))+P1(f319(f319(x88611,f319(f319(f30(a1),x88612),x88613)),f39(a1,x88612,x88613)))+~P1(f319(f319(f227(a1),x88613),f2(a1)))
% 28.25/28.12 [9113]~P4(x91131)+~P14(x91131,x91133)+P14(x91131,f141(x91131,x91131,f5(x91131),x91132,x91133))
% 28.25/28.12 [9621]~P130(x96212)+E(x96211,f2(x96212))+~P1(f319(f319(f226(x96212),f319(f319(f74(x96212),f319(f319(f75(x96212),x96213),x96213)),f319(f319(f75(x96212),x96211),x96211))),f2(x96212)))
% 28.25/28.12 [9622]~P130(x96222)+E(x96221,f2(x96222))+~P1(f319(f319(f226(x96222),f319(f319(f74(x96222),f319(f319(f75(x96222),x96221),x96221)),f319(f319(f75(x96222),x96223),x96223))),f2(x96222)))
% 28.25/28.12 [10453]~P126(x104531)+~P1(f319(f319(f227(x104531),x104532),f2(x104531)))+P1(f319(f319(f227(x104531),f319(f319(f236(x104531),x104532),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)))),x104533)))),f2(x104531)))
% 28.25/28.12 [10462]~P126(x104622)+E(x104621,f2(x104622))+~P1(f319(f319(f226(x104622),f319(f319(f74(x104622),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))))),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)))))),f2(x104622)))
% 28.25/28.12 [10463]~P126(x104632)+E(x104631,f2(x104632))+~P1(f319(f319(f226(x104632),f319(f319(f74(x104632),f319(f319(f236(x104632),x104631),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(x104632),x104633),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(x104632)))
% 28.25/28.12 [4984]~E(x49842,x49843)+~P69(x49841)+E(f319(f319(f23(x49841),x49842),x49843),f2(x49841))
% 28.25/28.12 [4985]~E(x49852,x49853)+~P70(x49851)+E(f319(f319(f23(x49851),x49852),x49853),f2(x49851))
% 28.25/28.12 [4998]~P148(x49981)+~E(x49983,f2(x49981))+E(f319(f319(f74(x49981),x49982),x49983),x49982)
% 28.25/28.12 [5015]~P147(x50151)+~E(x50153,f2(x50151))+E(f319(f319(f75(x50151),x50152),x50153),f2(x50151))
% 28.25/28.12 [5016]~P147(x50161)+~E(x50162,f2(x50161))+E(f319(f319(f75(x50161),x50162),x50163),f2(x50161))
% 28.25/28.12 [5037]~E(x50373,f105(x50371))+~E(x50372,f105(x50371))+E(f319(f319(f126(x50371),x50372),x50373),f105(x50371))
% 28.25/28.12 [5038]~E(x50383,f105(x50381))+~E(x50382,f105(x50381))+E(f319(f319(f126(x50381),x50382),x50383),f105(x50381))
% 28.25/28.12 [5128]~P148(x51282)+E(x51281,f2(x51282))+~E(f319(f319(f74(x51282),x51283),x51281),x51283)
% 28.25/28.12 [5129]~P69(x51291)+~E(x51292,f319(f73(x51291),x51293))+E(f319(f319(f74(x51291),x51292),x51293),f2(x51291))
% 28.25/28.12 [5136]E(x51361,f105(x51362))+E(x51363,f2(a925))+~E(f319(f319(f167(x51362),x51363),x51361),f105(x51362))
% 28.25/28.12 [5142]~P69(x51423)+E(x51421,x51422)+~E(f319(f319(f23(x51423),x51421),x51422),f2(x51423))
% 28.25/28.12 [5143]~P70(x51433)+E(x51431,x51432)+~E(f319(f319(f23(x51433),x51431),x51432),f2(x51433))
% 28.25/28.12 [5157]~P144(x51572)+E(x51571,f2(x51572))+~E(f319(f319(f236(x51572),x51571),x51573),f2(x51572))
% 28.25/28.12 [5158]~P103(x51582)+E(x51581,f234(x51582))+~E(f319(f319(f93(x51582),x51583),x51581),f234(x51582))
% 28.25/28.12 [5159]~P103(x51592)+E(x51591,f234(x51592))+~E(f319(f319(f93(x51592),x51591),x51593),f234(x51592))
% 28.25/28.12 [5160]~P104(x51602)+E(x51601,f180(x51602))+~E(f319(f319(f102(x51602),x51603),x51601),f180(x51602))
% 28.25/28.12 [5161]~P104(x51612)+E(x51611,f180(x51612))+~E(f319(f319(f102(x51612),x51611),x51613),f180(x51612))
% 28.25/28.12 [5229]~P69(x52292)+E(x52291,f319(f73(x52292),x52293))+~E(f319(f319(f74(x52292),x52291),x52293),f2(x52292))
% 28.25/28.12 [5230]~P69(x52301)+E(f319(f73(x52301),x52302),x52303)+~E(f319(f319(f74(x52301),x52302),x52303),f2(x52301))
% 28.25/28.12 [5231]~E(x52312,x52313)+~P113(x52311)+P1(f319(f319(f226(x52311),x52312),x52313))
% 28.25/28.12 [5232]~E(x52322,x52323)+~P2(x52321)+P1(f319(f319(f226(x52321),x52322),x52323))
% 28.25/28.12 [5233]~E(x52332,x52333)+~P113(x52331)+P1(f319(f319(f226(x52331),x52332),x52333))
% 28.25/28.12 [5234]~E(x52342,x52343)+~P113(x52341)+P1(f319(f319(f226(x52341),x52342),x52343))
% 28.25/28.12 [5335]~P117(x53351)+~E(x53352,f319(f73(x53351),x53353))+E(f319(f319(f75(x53351),x53352),x53352),f319(f319(f75(x53351),x53353),x53353))
% 28.25/28.12 [5343]~P4(x53431)+~P14(x53431,x53433)+P14(x53431,f319(f319(f167(x53431),x53432),x53433))
% 28.25/28.12 [5344]~P4(x53441)+~P14(x53441,x53443)+P14(x53441,f319(f319(f130(x53441),x53442),x53443))
% 28.25/28.12 [5382]E(x53821,x53822)+E(x53823,f2(a925))+~E(f319(f319(f75(a925),x53823),x53821),f319(f319(f75(a925),x53823),x53822))
% 28.25/28.12 [5383]E(x53831,x53832)+E(x53833,f2(a925))+~E(f319(f319(f75(a925),x53833),x53831),f319(f319(f75(a925),x53833),x53832))
% 28.25/28.12 [5384]E(x53841,x53842)+E(x53843,f2(a925))+~E(f319(f319(f75(a925),x53841),x53843),f319(f319(f75(a925),x53842),x53843))
% 28.25/28.12 [5462]~E(x54622,x54623)+~P113(x54621)+E(f295(x54621,x54622,x54623),f319(f319(f301(x54621),x54622),f180(f932(x54621,a923))))
% 28.25/28.12 [5499]~E(x54991,x54992)+~P4(x54993)+~P1(f319(f319(f227(x54993),x54991),x54992))
% 28.25/28.12 [5500]~E(x55001,x55002)+~P4(x55003)+~P1(f319(f319(f227(x55003),x55001),x55002))
% 28.25/28.12 [5501]~E(x55011,x55012)+~P113(x55013)+~P1(f319(f319(f227(x55013),x55011),x55012))
% 28.25/28.12 [5502]~E(x55021,x55022)+~P113(x55023)+~P1(f319(f319(f227(x55023),x55021),x55022))
% 28.25/28.12 [5503]~E(x55031,x55032)+~P113(x55033)+~P1(f319(f319(f227(x55033),x55031),x55032))
% 28.25/28.12 [5504]~E(x55041,x55042)+~P4(x55043)+~P1(f319(f319(f227(x55043),x55041),x55042))
% 28.25/28.12 [5505]~E(x55051,x55052)+~P113(x55053)+~P1(f319(f319(f227(x55053),x55051),x55052))
% 28.25/28.12 [5516]~P113(x55161)+E(f319(f294(x55161,x55162),x55163),f180(f932(x55161,a923)))+P1(f319(f319(f227(x55161),x55162),x55163))
% 28.25/28.12 [5517]~P113(x55171)+E(f319(f294(x55171,x55172),x55173),f180(f932(x55171,a923)))+P1(f319(f319(f227(x55171),x55172),x55173))
% 28.25/28.12 [5565]~P113(x55651)+E(f295(x55651,x55652,x55653),f180(f932(x55651,a923)))+P1(f319(f319(f226(x55651),x55652),x55653))
% 28.25/28.12 [5566]~P113(x55661)+E(f297(x55661,x55662,x55663),f180(f932(x55661,a923)))+P1(f319(f319(f227(x55661),x55662),x55663))
% 28.25/28.12 [5567]~P113(x55671)+E(f180(f932(x55671,a923)),f295(x55671,x55672,x55673))+P1(f319(f319(f226(x55671),x55672),x55673))
% 28.25/28.12 [5568]~P113(x55681)+E(f180(f932(x55681,a923)),f297(x55681,x55682,x55683))+P1(f319(f319(f227(x55681),x55682),x55683))
% 28.25/28.12 [5576]~P107(x55761)+~E(f319(f319(f102(x55761),x55762),x55763),x55763)+P1(f319(f319(f226(x55761),x55762),x55763))
% 28.25/28.12 [5577]~P108(x55771)+~E(f319(f319(f93(x55771),x55772),x55773),x55772)+P1(f319(f319(f226(x55771),x55772),x55773))
% 28.25/28.12 [5578]~P4(x55781)+~E(f319(f319(f224(x55781),x55782),x55783),x55782)+P1(f319(f319(f226(x55781),x55782),x55783))
% 28.25/28.12 [5579]~P4(x55791)+~E(f319(f319(f225(x55791),x55792),x55793),x55793)+P1(f319(f319(f226(x55791),x55792),x55793))
% 28.25/28.12 [5597]~P4(x55971)+P14(x55971,x55972)+~P14(x55971,f319(f319(f143(x55971),x55973),x55972))
% 28.25/28.12 [5598]~P4(x55981)+P14(x55981,x55982)+~P14(x55981,f319(f319(f143(x55981),x55983),x55982))
% 28.25/28.12 [5599]~P4(x55991)+P14(x55991,x55992)+~P14(x55991,f319(f319(f126(x55991),x55993),x55992))
% 28.25/28.12 [5600]~P4(x56001)+P14(x56001,x56002)+~P14(x56001,f319(f319(f126(x56001),x56002),x56003))
% 28.25/28.12 [5664]~P4(x56641)+P1(f319(f319(f226(x56641),x56643),x56642))+P1(f319(f319(f226(x56641),x56642),x56643))
% 28.25/28.12 [5665]~P4(x56651)+P1(f319(f319(f226(x56651),x56653),x56652))+P1(f319(f319(f226(x56651),x56652),x56653))
% 28.25/28.12 [5666]~P4(x56661)+P1(f319(f319(f227(x56661),x56663),x56662))+P1(f319(f319(f226(x56661),x56662),x56663))
% 28.25/28.12 [5667]~P4(x56671)+P1(f319(f319(f227(x56671),x56673),x56672))+P1(f319(f319(f226(x56671),x56672),x56673))
% 28.25/28.12 [5668]~P4(x56681)+P1(f319(f319(f227(x56681),x56683),x56682))+P1(f319(f319(f226(x56681),x56682),x56683))
% 28.25/28.12 [5669]~P4(x56691)+P1(f319(f319(f227(x56691),x56693),x56692))+P1(f319(f319(f226(x56691),x56692),x56693))
% 28.25/28.12 [5670]~P4(x56701)+P1(f319(f319(f227(x56701),x56703),x56702))+P1(f319(f319(f226(x56701),x56702),x56703))
% 28.25/28.12 [5708]~P107(x57081)+E(f319(f319(f102(x57081),x57082),x57083),x57082)+~P1(f319(f319(f226(x57081),x57083),x57082))
% 28.25/28.12 [5709]~P107(x57091)+E(f319(f319(f102(x57091),x57092),x57093),x57093)+~P1(f319(f319(f226(x57091),x57092),x57093))
% 28.25/28.12 [5710]~P107(x57101)+E(f319(f319(f102(x57101),x57102),x57103),x57103)+~P1(f319(f319(f226(x57101),x57102),x57103))
% 28.25/28.12 [5711]~P108(x57111)+E(f319(f319(f93(x57111),x57112),x57113),x57113)+~P1(f319(f319(f226(x57111),x57113),x57112))
% 28.25/28.12 [5712]~P108(x57121)+E(f319(f319(f93(x57121),x57122),x57123),x57122)+~P1(f319(f319(f226(x57121),x57122),x57123))
% 28.25/28.12 [5713]~P108(x57131)+E(f319(f319(f93(x57131),x57132),x57133),x57132)+~P1(f319(f319(f226(x57131),x57132),x57133))
% 28.25/28.12 [5714]~P4(x57141)+E(f319(f319(f224(x57141),x57142),x57143),x57143)+~P1(f319(f319(f226(x57141),x57143),x57142))
% 28.25/28.12 [5715]~P4(x57151)+E(f319(f319(f224(x57151),x57152),x57153),x57152)+~P1(f319(f319(f226(x57151),x57152),x57153))
% 28.25/28.12 [5716]~P4(x57161)+E(f319(f319(f224(x57161),x57162),x57163),x57162)+~P1(f319(f319(f226(x57161),x57162),x57163))
% 28.25/28.12 [5717]~P4(x57171)+E(f319(f319(f225(x57171),x57172),x57173),x57172)+~P1(f319(f319(f226(x57171),x57173),x57172))
% 28.25/28.12 [5718]~P4(x57181)+E(f319(f319(f225(x57181),x57182),x57183),x57183)+~P1(f319(f319(f226(x57181),x57182),x57183))
% 28.25/28.12 [5719]~P4(x57191)+E(f319(f319(f225(x57191),x57192),x57193),x57193)+~P1(f319(f319(f226(x57191),x57192),x57193))
% 28.25/28.12 [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))
% 28.25/28.12 [5777]~P113(x57771)+E(f319(f294(x57771,x57772),x57773),f180(f932(x57771,a923)))+~P1(f319(f319(f226(x57771),x57773),x57772))
% 28.25/28.12 [5809]~P113(x58091)+E(f295(x58091,x58092,x58093),f180(f932(x58091,a923)))+~P1(f319(f319(f227(x58091),x58093),x58092))
% 28.25/28.12 [5810]~P113(x58101)+E(f297(x58101,x58102,x58103),f180(f932(x58101,a923)))+~P1(f319(f319(f226(x58101),x58103),x58102))
% 28.25/28.12 [5811]~P113(x58111)+E(f298(x58111,x58112,x58113),f180(f932(x58111,a923)))+~P1(f319(f319(f226(x58111),x58113),x58112))
% 28.25/28.12 [5854]~P114(x58541)+~P1(f319(x58542,x58543))+P1(f319(f319(f226(x58541),f230(x58541,x58542)),x58543))
% 28.25/28.12 [5864]~E(f319(f319(f23(a925),x58641),x58643),x58642)+E(x58641,f319(f319(f74(a925),x58642),x58643))+~P1(f319(f319(f226(a925),x58643),x58641))
% 28.25/28.12 [5865]~E(x58651,f319(f319(f74(a925),x58653),x58652))+E(f319(f319(f23(a925),x58651),x58652),x58653)+~P1(f319(f319(f226(a925),x58652),x58651))
% 28.25/28.12 [5910]~P1(f319(x59101,x59103))+P1(f319(x59101,f354(x59101,x59102)))+~P1(f319(f319(f226(a925),x59103),x59102))
% 28.25/28.12 [5911]~P1(f319(x59111,x59113))+P1(f319(x59111,f360(x59111,x59112)))+~P1(f319(f319(f227(a925),x59113),x59112))
% 28.25/28.12 [5918]~P113(x59181)+~E(f319(f294(x59181,x59182),x59183),f180(f932(x59181,a923)))+~P1(f319(f319(f227(x59181),x59182),x59183))
% 28.25/28.12 [5919]~P113(x59191)+~E(f319(f294(x59191,x59192),x59193),f180(f932(x59191,a923)))+~P1(f319(f319(f227(x59191),x59192),x59193))
% 28.25/28.12 [5923]~P2(x59231)+~P1(f319(f319(f227(x59231),x59232),x59233))+P1(f319(f319(f226(x59231),x59232),x59233))
% 28.25/28.12 [5924]~P2(x59241)+~P1(f319(f319(f227(x59241),x59242),x59243))+P1(f319(f319(f226(x59241),x59242),x59243))
% 28.25/28.12 [5925]~P113(x59251)+~P1(f319(f319(f227(x59251),x59252),x59253))+P1(f319(f319(f226(x59251),x59252),x59253))
% 28.25/28.12 [5926]~P113(x59261)+~P1(f319(f319(f227(x59261),x59262),x59263))+P1(f319(f319(f226(x59261),x59262),x59263))
% 28.25/28.12 [6035]~P113(x60351)+~E(f295(x60351,x60352,x60353),f180(f932(x60351,a923)))+~P1(f319(f319(f226(x60351),x60352),x60353))
% 28.25/28.12 [6036]~P113(x60361)+~E(f297(x60361,x60362,x60363),f180(f932(x60361,a923)))+~P1(f319(f319(f227(x60361),x60362),x60363))
% 28.25/28.12 [6037]~P113(x60371)+~E(f180(f932(x60371,a923)),f295(x60371,x60372,x60373))+~P1(f319(f319(f226(x60371),x60372),x60373))
% 28.25/28.12 [6038]~P113(x60381)+~E(f180(f932(x60381,a923)),f297(x60381,x60382,x60383))+~P1(f319(f319(f227(x60381),x60382),x60383))
% 28.25/28.12 [6049]P1(f319(x60491,x60492))+~P1(f319(x60491,f361(x60491,x60493)))+~P1(f319(f319(f226(a925),x60492),x60493))
% 28.25/28.12 [6050]P1(f319(x60501,x60502))+~P1(f319(x60501,f366(x60501,x60503)))+~P1(f319(f319(f227(a925),x60502),x60503))
% 28.25/28.12 [6058]~E(x60581,f319(a104,x60583))+P1(f319(f319(f227(a925),x60581),f319(a104,x60582)))+~P1(f319(f319(f227(a925),x60583),x60582))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [6155]~P6(x61551)+P1(f319(f319(f226(x61551),x61552),f31(x61551,x61553)))+~P1(f319(f319(f321(x61551),x61552),x61553))
% 28.25/28.12 [6178]~P2(x61781)+~P1(f319(f319(f227(x61781),x61783),x61782))+~P1(f319(f319(f226(x61781),x61782),x61783))
% 28.25/28.12 [6179]~P2(x61791)+~P1(f319(f319(f227(x61791),x61793),x61792))+~P1(f319(f319(f227(x61791),x61792),x61793))
% 28.25/28.12 [6180]~P2(x61801)+~P1(f319(f319(f227(x61801),x61803),x61802))+~P1(f319(f319(f227(x61801),x61802),x61803))
% 28.25/28.12 [6181]~P2(x61811)+~P1(f319(f319(f227(x61811),x61813),x61812))+~P1(f319(f319(f227(x61811),x61812),x61813))
% 28.25/28.12 [6182]~P2(x61821)+~P1(f319(f319(f227(x61821),x61823),x61822))+~P1(f319(f319(f227(x61821),x61822),x61823))
% 28.25/28.12 [6183]~P4(x61831)+~P1(f319(f319(f227(x61831),x61833),x61832))+~P1(f319(f319(f226(x61831),x61832),x61833))
% 28.25/28.12 [6184]~P4(x61841)+~P1(f319(f319(f227(x61841),x61843),x61842))+~P1(f319(f319(f226(x61841),x61842),x61843))
% 28.25/28.12 [6185]~P4(x61851)+~P1(f319(f319(f227(x61851),x61853),x61852))+~P1(f319(f319(f226(x61851),x61852),x61853))
% 28.25/28.12 [6186]~P4(x61861)+~P1(f319(f319(f227(x61861),x61863),x61862))+~P1(f319(f319(f227(x61861),x61862),x61863))
% 28.25/28.12 [6187]~P113(x61871)+~P1(f319(f319(f227(x61871),x61873),x61872))+~P1(f319(f319(f227(x61871),x61872),x61873))
% 28.25/28.12 [6209]~E(x62092,x62093)+~E(x62091,x62092)+E(f282(a925,f279(a925),x62091,x62092),f319(f319(f301(a925),x62093),f180(f932(a925,a923))))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [6234]~P3(x62341)+~P1(f319(f319(f227(x62341),x62343),x62342))+P1(f319(f319(f321(x62341),x62342),f319(f296(x62341),x62343)))
% 28.25/28.12 [6235]~P3(x62351)+~P1(f319(f319(f226(x62351),x62353),x62352))+P1(f319(f319(f321(x62351),x62352),f319(f275(x62351),x62353)))
% 28.25/28.12 [6236]~P3(x62361)+~P1(f319(f319(f227(x62361),x62362),x62363))+P1(f319(f319(f321(x62361),x62362),f319(f274(x62361),x62363)))
% 28.25/28.12 [6237]~P3(x62371)+~P1(f319(f319(f226(x62371),x62372),x62373))+P1(f319(f319(f321(x62371),x62372),f319(f293(x62371),x62373)))
% 28.25/28.12 [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))
% 28.25/28.12 [6330]~P6(x63301)+~P1(f319(f319(f321(x63301),x63303),x63302))+P1(f319(f319(f226(x63301),f32(x63301,x63302)),x63303))
% 28.25/28.12 [6349]~P1(f319(f319(f226(a925),x63491),x63493))+P1(f319(f319(f226(a925),x63491),x63492))+~P1(f319(f319(f226(a925),x63493),x63492))
% 28.25/28.12 [6350]~P1(f319(f319(f226(a1),x63501),x63503))+P1(f319(f319(f226(a1),x63501),x63502))+~P1(f319(f319(f226(a1),x63503),x63502))
% 28.25/28.12 [6370]~P3(x63701)+~P1(f319(f319(f321(x63701),x63703),f319(f275(x63701),x63702)))+P1(f319(f319(f226(x63701),x63702),x63703))
% 28.25/28.12 [6371]~P3(x63711)+~P1(f319(f319(f321(x63711),x63712),f319(f293(x63711),x63713)))+P1(f319(f319(f226(x63711),x63712),x63713))
% 28.25/28.12 [6372]~P3(x63721)+~P1(f319(f319(f321(x63721),x63723),f319(f296(x63721),x63722)))+P1(f319(f319(f227(x63721),x63722),x63723))
% 28.25/28.12 [6373]~P3(x63731)+~P1(f319(f319(f321(x63731),x63732),f319(f274(x63731),x63733)))+P1(f319(f319(f227(x63731),x63732),x63733))
% 28.25/28.12 [6447]~P1(f319(x64471,x64472))+P1(f319(x64471,f800(x64471)))+~P1(f319(f319(f321(x64473),x64472),f234(f932(x64473,a923))))
% 28.25/28.12 [6555]~P113(x65551)+~P41(a925,x65551,x65552)+P1(f319(f319(f226(x65551),f319(x65552,x65553)),f319(x65552,f319(a104,x65553))))
% 28.25/28.12 [6589]~P74(x65891)+P1(f319(f319(f227(x65891),f2(x65891)),f469(x65893,x65892,x65891)))+P1(f319(f319(f226(x65891),x65892),x65893))
% 28.25/28.12 [6590]~P75(x65901)+P1(f319(f319(f227(x65901),f2(x65901)),f788(x65903,x65902,x65901)))+P1(f319(f319(f226(x65901),x65902),x65903))
% 28.25/28.12 [6659]~P68(x66591)+~P1(f319(f319(f226(x66591),x66593),f319(f73(x66591),x66592)))+P1(f319(f319(f226(x66591),x66592),f319(f73(x66591),x66593)))
% 28.25/28.12 [6660]~P68(x66601)+~P1(f319(f319(f226(x66601),x66603),f319(f73(x66601),x66602)))+P1(f319(f319(f226(x66601),x66602),f319(f73(x66601),x66603)))
% 28.25/28.12 [6661]~P68(x66611)+~P1(f319(f319(f227(x66611),x66613),f319(f73(x66611),x66612)))+P1(f319(f319(f227(x66611),x66612),f319(f73(x66611),x66613)))
% 28.25/28.12 [6662]~P68(x66621)+~P1(f319(f319(f227(x66621),x66623),f319(f73(x66621),x66622)))+P1(f319(f319(f227(x66621),x66622),f319(f73(x66621),x66623)))
% 28.25/28.12 [6674]~P1(f319(f319(f227(a925),x66741),x66743))+~P1(f319(f319(f227(a925),x66743),x66742))+P1(f319(f319(f227(a925),f319(a104,x66741)),x66742))
% 28.25/28.12 [6702]~P129(x67021)+P1(f319(f319(f226(x67021),f319(f92(x67021),x67022)),f319(f92(x67021),x67023)))+~P1(f319(f319(f226(a925),x67022),x67023))
% 28.25/28.12 [6703]~P126(x67031)+P1(f319(f319(f226(x67031),f319(f94(x67031),x67032)),f319(f94(x67031),x67033)))+~P1(f319(f319(f226(a1),x67032),x67033))
% 28.25/28.12 [6704]~P129(x67041)+P1(f319(f319(f227(x67041),f319(f92(x67041),x67042)),f319(f92(x67041),x67043)))+~P1(f319(f319(f227(a925),x67042),x67043))
% 28.25/28.12 [6705]~P126(x67051)+P1(f319(f319(f227(x67051),f319(f94(x67051),x67052)),f319(f94(x67051),x67053)))+~P1(f319(f319(f227(a1),x67052),x67053))
% 28.25/28.12 [6706]~P129(x67061)+P1(f319(f319(f227(x67061),f319(f92(x67061),x67062)),f319(f92(x67061),x67063)))+~P1(f319(f319(f227(a925),x67062),x67063))
% 28.25/28.12 [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))
% 28.25/28.12 [6741]~P96(x67411)+~P1(f319(f319(f226(x67411),x67413),x67412))+P1(f319(f319(f226(x67411),f319(f73(x67411),x67412)),f319(f73(x67411),x67413)))
% 28.25/28.12 [6742]~P96(x67421)+~P1(f319(f319(f226(x67421),x67423),x67422))+P1(f319(f319(f226(x67421),f319(f73(x67421),x67422)),f319(f73(x67421),x67423)))
% 28.25/28.12 [6743]~P68(x67431)+~P1(f319(f319(f226(x67431),x67433),x67432))+P1(f319(f319(f226(x67431),f319(f73(x67431),x67432)),f319(f73(x67431),x67433)))
% 28.25/28.12 [6744]~P68(x67441)+~P1(f319(f319(f226(x67441),x67443),x67442))+P1(f319(f319(f226(x67441),f319(f73(x67441),x67442)),f319(f73(x67441),x67443)))
% 28.25/28.12 [6745]~P68(x67451)+~P1(f319(f319(f227(x67451),x67453),x67452))+P1(f319(f319(f227(x67451),f319(f73(x67451),x67452)),f319(f73(x67451),x67453)))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [6886]~P6(x68861)+~P1(f319(f319(f226(x68861),f319(x68862,x68863)),x68863))+P1(f319(f319(f226(x68861),f87(x68861,x68862)),x68863))
% 28.25/28.12 [6976]~P4(x69761)+E(f319(f319(f102(f932(x69761,a923)),f295(x69761,x69762,x69763)),f319(f296(x69761),x69763)),f319(f275(x69761),x69762))+~P1(f319(f319(f226(x69761),x69762),x69763))
% 28.25/28.12 [6977]~P4(x69771)+E(f319(f319(f102(f932(x69771,a923)),f297(x69771,x69772,x69773)),f319(f296(x69771),x69773)),f319(f296(x69771),x69772))+~P1(f319(f319(f226(x69771),x69772),x69773))
% 28.25/28.12 [6978]~P4(x69781)+E(f319(f319(f102(f932(x69781,a923)),f298(x69781,x69782,x69783)),f319(f275(x69781),x69783)),f319(f296(x69781),x69782))+~P1(f319(f319(f227(x69781),x69782),x69783))
% 28.25/28.12 [6997]P1(f319(x69971,x69972))+~P1(f319(f319(f226(a925),x69972),x69973))+P1(f319(f319(f321(a925),f361(x69971,x69973)),f295(a925,f2(a925),x69973)))
% 28.25/28.12 [7031]E(x70311,x70312)+~E(f319(f319(f156(x70313),x70311),f659(x70313,x70312,x70311)),f319(f319(f156(x70313),x70312),f659(x70313,x70312,x70311)))+~E(f319(f181(f926(x70313)),x70311),f319(f181(f926(x70313)),x70312))
% 28.25/28.12 [7036]~E(x70363,f319(f319(f30(a925),x70361),x70362))+~P1(f319(f319(f227(a925),f2(a925)),x70362))+P1(f319(f319(f227(a925),x70361),f319(f319(f75(a925),x70362),f319(a104,x70363))))
% 28.25/28.12 [7052]~P1(f319(x70521,x70523))+~P1(f319(f319(f226(a925),x70523),x70522))+P1(f319(f319(f321(a925),f354(x70521,x70522)),f295(a925,f2(a925),x70522)))
% 28.25/28.12 [7093]~P1(f319(x70931,x70933))+P1(f319(x70931,f362(x70931,x70932)))+~P1(f319(f319(f321(a925),x70933),f295(a925,f2(a925),x70932)))
% 28.25/28.12 [7112]~P129(x71123)+~P1(f319(f319(f226(x71123),f319(f92(x71123),x71121)),f319(f92(x71123),x71122)))+P1(f319(f319(f226(a925),x71121),x71122))
% 28.25/28.12 [7113]~P126(x71133)+~P1(f319(f319(f226(x71133),f319(f94(x71133),x71131)),f319(f94(x71133),x71132)))+P1(f319(f319(f226(a1),x71131),x71132))
% 28.25/28.12 [7114]~P129(x71143)+~P1(f319(f319(f227(x71143),f319(f92(x71143),x71141)),f319(f92(x71143),x71142)))+P1(f319(f319(f227(a925),x71141),x71142))
% 28.25/28.12 [7115]~P129(x71153)+~P1(f319(f319(f227(x71153),f319(f92(x71153),x71151)),f319(f92(x71153),x71152)))+P1(f319(f319(f227(a925),x71151),x71152))
% 28.25/28.12 [7116]~P126(x71163)+~P1(f319(f319(f227(x71163),f319(f94(x71163),x71161)),f319(f94(x71163),x71162)))+P1(f319(f319(f227(a1),x71161),x71162))
% 28.25/28.12 [7132]~P129(x71321)+~P1(f319(f319(f227(x71321),f72(x71321)),x71322))+P1(f319(f319(f227(x71321),f72(x71321)),f319(f319(f236(x71321),x71322),f319(a104,x71323))))
% 28.25/28.12 [7135]~P96(x71351)+~P1(f319(f319(f226(x71351),f319(f73(x71351),x71353)),f319(f73(x71351),x71352)))+P1(f319(f319(f226(x71351),x71352),x71353))
% 28.25/28.12 [7136]~P68(x71361)+~P1(f319(f319(f226(x71361),f319(f73(x71361),x71363)),f319(f73(x71361),x71362)))+P1(f319(f319(f226(x71361),x71362),x71363))
% 28.25/28.12 [7137]~P68(x71371)+~P1(f319(f319(f227(x71371),f319(f73(x71371),x71373)),f319(f73(x71371),x71372)))+P1(f319(f319(f227(x71371),x71372),x71373))
% 28.25/28.12 [7161]P1(f319(x71611,x71612))+~P1(f319(x71611,f363(x71611,x71613)))+~P1(f319(f319(f321(a925),x71612),f295(a925,f2(a925),x71613)))
% 28.25/28.12 [7181]~P74(x71811)+P1(f319(f319(f227(x71811),f469(x71813,x71812,x71811)),f72(x71811)))+P1(f319(f319(f226(x71811),x71812),x71813))
% 28.25/28.12 [7200]~E(f39(a925,x72003,x72002),f39(a925,x72001,x72002))+E(f319(f319(f74(a925),x72001),f319(f319(f75(a925),x72002),f520(x72001,x72002,x72003))),x72003)+~P1(f319(f319(f226(a925),x72001),x72003))
% 28.25/28.12 [7255]E(f319(f319(f6(x72551,a925),x72552),x72553),f2(a925))+~P1(f319(f55(x72551),x72553))+P1(f319(f319(f321(x72551),f356(x72552,x72553,x72551)),x72553))
% 28.25/28.12 [7256]E(f319(f319(f9(x72561,a925),x72562),x72563),f72(a925))+~P1(f319(f55(x72561),x72563))+P1(f319(f319(f321(x72561),f454(x72562,x72563,x72561)),x72563))
% 28.25/28.12 [7278]~P4(x72781)+~P1(f319(f319(f226(x72781),x72783),x72782))+P1(f319(f319(f226(f932(x72781,a923)),f319(f296(x72781),x72782)),f319(f296(x72781),x72783)))
% 28.25/28.12 [7279]~P4(x72791)+~P1(f319(f319(f226(x72791),x72792),x72793))+P1(f319(f319(f226(f932(x72791,a923)),f319(f274(x72791),x72792)),f319(f274(x72791),x72793)))
% 28.25/28.12 [7280]~P113(x72801)+~P1(f319(f319(f226(x72801),x72803),x72802))+P1(f319(f319(f226(f932(x72801,a923)),f319(f275(x72801),x72802)),f319(f275(x72801),x72803)))
% 28.25/28.12 [7281]~P113(x72811)+~P1(f319(f319(f226(x72811),x72812),x72813))+P1(f319(f319(f226(f932(x72811,a923)),f319(f293(x72811),x72812)),f319(f293(x72811),x72813)))
% 28.25/28.12 [7282]~P4(x72821)+~P1(f319(f319(f227(x72821),x72822),x72823))+P1(f319(f319(f227(f932(x72821,a923)),f319(f274(x72821),x72822)),f319(f274(x72821),x72823)))
% 28.25/28.12 [7293]~P6(x72931)+P1(f319(f319(f226(x72931),x72932),f32(x72931,x72933)))+P1(f319(f319(f321(x72931),f434(x72933,x72932,x72931)),x72933))
% 28.25/28.12 [7294]~P6(x72941)+P1(f319(f319(f226(x72941),x72942),f32(x72941,x72943)))+P1(f319(f319(f321(x72941),f710(x72942,x72943,x72941)),x72943))
% 28.25/28.12 [7300]~P68(x73001)+P1(f319(f319(f226(x73001),f319(f319(f23(x73001),x73002),x73003)),f2(x73001)))+~P1(f319(f319(f226(x73001),x73002),x73003))
% 28.25/28.12 [7301]~P68(x73011)+P1(f319(f319(f227(x73011),f319(f319(f23(x73011),x73012),x73013)),f2(x73011)))+~P1(f319(f319(f227(x73011),x73012),x73013))
% 28.25/28.12 [7343]P1(f319(x73431,x73432))+P1(f319(f319(f226(a925),f363(x73431,x73433)),x73433))+~P1(f319(f319(f321(a925),x73432),f295(a925,f2(a925),x73433)))
% 28.25/28.12 [7385]~E(f319(f319(f6(x73851,a925),x73852),x73853),f72(a925))+~P1(f319(f55(x73851),x73853))+P1(f319(f319(f321(x73851),f355(x73852,x73853,x73851)),x73853))
% 28.25/28.12 [7386]~P1(f319(x73861,x73863))+P1(f319(f319(f226(a925),f362(x73861,x73862)),x73862))+~P1(f319(f319(f321(a925),x73863),f295(a925,f2(a925),x73862)))
% 28.25/28.12 [7425]~P6(x74251)+P1(f319(f319(f321(x74251),f428(x74253,x74252,x74251)),x74252))+P1(f319(f319(f226(x74251),f31(x74251,x74252)),x74253))
% 28.25/28.12 [7426]~P6(x74261)+P1(f319(f319(f321(x74261),f723(x74263,x74262,x74261)),x74262))+P1(f319(f319(f226(x74261),f31(x74261,x74262)),x74263))
% 28.25/28.12 [7460]~E(f319(f319(f6(x74601,a925),x74602),x74603),f319(a104,f2(a925)))+~P1(f319(f55(x74601),x74603))+P1(f319(f319(f321(x74601),f418(x74602,x74603,x74601)),x74603))
% 28.25/28.12 [7471]E(x74711,f2(a925))+P1(f319(x74712,f39(a925,x74713,x74711)))+P1(f319(f319(f227(a925),f518(x74711,x74713,x74712)),x74711))
% 28.25/28.12 [7580]~P1(f319(x75801,x75802))+P1(f319(x75801,f39(a925,x75802,x75803)))+P1(f319(f319(f227(a925),f518(x75803,x75802,x75801)),x75803))
% 28.25/28.12 [7692]E(x76921,f105(x76922))+~P1(f319(f319(f321(f926(x76922)),x76921),f153(x76922,x76923)))+P1(f319(f319(f321(x76922),f711(x76923,x76921,x76922)),x76923))
% 28.25/28.12 [7714]~P4(x77141)+E(f319(f319(f102(f932(x77141,a923)),f319(f319(f301(x77141),x77142),f180(f932(x77141,a923)))),f298(x77141,x77142,x77143)),f319(f294(x77141,x77142),x77143))+~P1(f319(f319(f227(x77141),x77142),x77143))
% 28.25/28.12 [7735]~P4(x77351)+E(f319(f319(f102(f932(x77351,a923)),f319(f319(f301(x77351),x77352),f180(f932(x77351,a923)))),f297(x77351,x77352,x77353)),f295(x77351,x77352,x77353))+~P1(f319(f319(f226(x77351),x77352),x77353))
% 28.25/28.12 [7845]~P4(x78451)+P1(f319(f319(f226(x78451),x78452),x78453))+~P1(f319(f319(f226(f932(x78451,a923)),f319(f296(x78451),x78453)),f319(f296(x78451),x78452)))
% 28.25/28.12 [7846]~P113(x78461)+P1(f319(f319(f226(x78461),x78462),x78463))+~P1(f319(f319(f226(f932(x78461,a923)),f319(f275(x78461),x78463)),f319(f275(x78461),x78462)))
% 28.25/28.12 [7847]~P4(x78471)+P1(f319(f319(f226(x78471),x78472),x78473))+~P1(f319(f319(f226(f932(x78471,a923)),f319(f274(x78471),x78472)),f319(f274(x78471),x78473)))
% 28.25/28.12 [7848]~P113(x78481)+P1(f319(f319(f226(x78481),x78482),x78483))+~P1(f319(f319(f226(f932(x78481,a923)),f319(f293(x78481),x78482)),f319(f293(x78481),x78483)))
% 28.25/28.12 [7849]~P4(x78491)+P1(f319(f319(f227(x78491),x78492),x78493))+~P1(f319(f319(f227(f932(x78491,a923)),f319(f274(x78491),x78492)),f319(f274(x78491),x78493)))
% 28.25/28.12 [7872]~P68(x78721)+~P1(f319(f319(f226(x78721),f319(f319(f23(x78721),x78722),x78723)),f2(x78721)))+P1(f319(f319(f226(x78721),x78722),x78723))
% 28.25/28.12 [7873]~P68(x78731)+~P1(f319(f319(f227(x78731),f319(f319(f23(x78731),x78732),x78733)),f2(x78731)))+P1(f319(f319(f227(x78731),x78732),x78733))
% 28.25/28.12 [8027]E(x80271,f2(a925))+~E(f319(f134(a925,a925,f74(a925),x80272),x80273),f2(a925))+~P1(f319(f319(f321(a925),x80271),f319(f164(a925),x80273)))
% 28.25/28.12 [8031]~P6(x80311)+~P1(f319(f319(f226(x80311),f428(x80313,x80312,x80311)),x80313))+P1(f319(f319(f226(x80311),f31(x80311,x80312)),x80313))
% 28.25/28.12 [8032]~P6(x80321)+~P1(f319(f319(f226(x80321),f723(x80323,x80322,x80321)),x80323))+P1(f319(f319(f226(x80321),f31(x80321,x80322)),x80323))
% 28.25/28.12 [8189]P1(f319(f319(f226(a1),f2(a1)),f512(x81891,x81892,x81893)))+P1(f319(f319(x81892,f319(f319(f30(a1),x81891),x81893)),f39(a1,x81891,x81893)))+~P1(f319(f319(f227(a1),f2(a1)),x81893))
% 28.25/28.12 [8278]E(x82781,x82782)+~E(f319(f181(f926(x82783)),x82781),f319(f181(f926(x82783)),x82782))+~P1(f319(f319(f249(x82783,x82783,a923),a316),f685(x82783,x82781,x82782)))
% 28.25/28.12 [8349]~P38(x83492,x83493)+E(x83491,f180(f932(x83492,a923)))+~P1(f319(f319(f226(f932(x83492,a923)),x83491),f319(f277(x83492,x83492,x83493),x83491)))
% 28.25/28.12 [8379]~P75(x83791)+~P1(f319(f319(f226(x83791),x83792),f319(f319(f74(x83791),x83793),f788(x83793,x83792,x83791))))+P1(f319(f319(f226(x83791),x83792),x83793))
% 28.25/28.12 [8415]P57(x84151,x84152,x84153)+P1(f319(f319(f321(x84151),f593(x84153,x84152,x84151)),x84152))+P1(f319(f319(f321(f931(x84151,x84151)),f594(x84153,x84152,x84151)),x84153))
% 28.25/28.12 [8436]P1(f319(f319(x84362,f319(f319(f30(a1),x84361),x84363)),f39(a1,x84361,x84363)))+~P1(f319(f319(f227(a1),f2(a1)),x84363))+P1(f319(f319(f227(a1),f512(x84361,x84362,x84363)),x84363))
% 28.25/28.12 [8460]E(f319(f302(a925,a925,f319(f319(f7(a925,a925,a925),f23(a925)),x84601)),f319(f294(a925,x84602),x84603)),f180(f932(a925,a923)))+P1(f319(f319(f227(a925),x84601),x84603))+P1(f319(f319(f227(a925),x84602),x84603))
% 28.25/28.12 [8573]E(f319(f302(a925,a925,f319(f319(f7(a925,a925,a925),f23(a925)),x85731)),f319(f294(a925,x85732),x85733)),f319(f319(f301(a925),f2(a925)),f180(f932(a925,a923))))+P1(f319(f319(f227(a925),x85731),x85733))+~P1(f319(f319(f227(a925),x85732),x85733))
% 28.25/28.12 [8587]~P4(x85871)+E(f141(x85871,x85871,f5(x85871),x85872,x85873),x85873)+~P1(f319(f319(f321(x85871),x85872),f319(f164(x85871),x85873)))
% 28.25/28.12 [8600]P26(x86001,x86001,x86002,x86003)+~P1(f319(f55(x86001),x86003))+~P1(f319(f319(f226(f932(x86001,a923)),x86003),f319(f302(x86001,x86001,x86002),x86003)))
% 28.25/28.12 [8627]E(f319(f319(f74(a1),f319(f319(f75(a1),x86271),f513(x86272,x86273,x86271))),f512(x86272,x86273,x86271)),x86272)+P1(f319(f319(x86273,f319(f319(f30(a1),x86272),x86271)),f39(a1,x86272,x86271)))+~P1(f319(f319(f227(a1),f2(a1)),x86271))
% 28.25/28.12 [8868]~P1(f319(f319(x88681,f513(x88682,x88681,x88683)),f512(x88682,x88681,x88683)))+P1(f319(f319(x88681,f319(f319(f30(a1),x88682),x88683)),f39(a1,x88682,x88683)))+~P1(f319(f319(f227(a1),f2(a1)),x88683))
% 28.25/28.12 [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)))
% 28.25/28.12 [8951]P27(x89511,x89512,x89513,f234(f932(x89511,a923)),f234(f932(x89512,a923)))+~P26(x89511,x89512,x89513,f234(f932(x89511,a923)))+~E(f319(f302(x89511,x89512,x89513),f234(f932(x89511,a923))),f234(f932(x89512,a923)))
% 28.25/28.12 [9767]~P1(f319(f55(x97671),x97672))+~P1(f319(f319(f321(x97671),x97673),x97672))+P1(f319(f319(f227(a925),f319(f29(x97671),f319(f319(f23(f932(x97671,a923)),x97672),f319(f319(f301(x97671),x97673),f180(f932(x97671,a923)))))),f319(f29(x97671),x97672)))
% 28.25/28.12 [10395]P57(x103951,x103952,x103953)+~P1(f319(f319(f249(x103951,x103951,a923),f319(f319(f7(x103951,f932(x103951,a923),f932(x103951,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x103951,a923),f932(x103951,a923)),x103951),f8(a923,a923,x103951)),f319(f319(f8(a923,f932(a923,a923),x103951),a317),f319(f319(f7(x103951,f932(x103951,a923),a923),f321(x103951)),x103952)))),f319(f319(f7(x103951,f932(x103951,a923),a923),f321(x103951)),x103952))),f594(x103953,x103952,x103951)))+P1(f319(f319(f321(x103951),f593(x103953,x103952,x103951)),x103952))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [5883]~E(x58833,f2(a925))+~P1(f319(x58831,f2(a925)))+P1(f319(x58831,f319(f319(f30(a925),x58832),x58833)))
% 28.25/28.12 [5884]~E(x58843,f2(a925))+~P1(f319(x58841,f2(a925)))+P1(f319(x58841,f319(f319(f30(a925),x58842),x58843)))
% 28.25/28.12 [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)))
% 28.25/28.12 [6148]~P65(x61481)+E(f319(f319(f75(x61481),x61482),f319(f319(f30(x61481),x61483),x61482)),x61483)+~P1(f319(f319(f279(x61481),x61482),x61483))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [6279]~E(x62792,f2(a925))+P1(f319(x62791,f2(a925)))+~P1(f319(x62791,f319(f319(f30(a925),x62793),x62792)))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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))))
% 28.25/28.12 [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))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [6676]E(x66761,f105(x66762))+~E(f171(x66762,x66763),f105(f926(x66762)))+~P1(f319(f319(f321(f926(x66762)),x66761),f319(f164(f926(x66762)),x66763)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [6755]P1(f319(x67551,f2(a925)))+~P1(f319(f319(f227(a925),x67552),x67553))+~P1(f319(x67551,f319(f319(f23(a925),x67552),x67553)))
% 28.25/28.12 [6756]P1(f319(x67561,f2(a925)))+~P1(f319(f319(f227(a925),x67562),x67563))+~P1(f319(x67561,f319(f319(f23(a925),x67562),x67563)))
% 28.25/28.12 [6776]~P92(x67761)+P1(f319(f319(f226(x67761),x67762),x67763))+~P1(f319(f319(f226(x67761),f319(f69(x67761),x67762)),x67763))
% 28.25/28.12 [6777]~P92(x67771)+P1(f319(f319(f226(x67771),x67772),x67773))+~P1(f319(f319(f226(x67771),f319(f69(x67771),x67772)),x67773))
% 28.25/28.12 [6778]~P126(x67781)+P1(f319(f319(f227(x67781),x67782),x67783))+~P1(f319(f319(f227(x67781),f319(f69(x67781),x67782)),x67783))
% 28.25/28.12 [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)))
% 28.25/28.12 [6851]~P1(f319(x68511,x68513))+P1(f319(x68511,f367(x68511,x68512)))+~P1(f319(f319(f321(a925),x68513),f319(f294(a925,f2(a925)),x68512)))
% 28.25/28.12 [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)))
% 28.25/28.12 [6887]~P129(x68871)+~P1(f319(f319(f226(x68871),f72(x68871)),x68872))+P1(f319(f319(f226(x68871),f72(x68871)),f319(f319(f236(x68871),x68872),x68873)))
% 28.25/28.12 [6889]~P129(x68891)+~P1(f319(f319(f226(x68891),f2(x68891)),x68892))+P1(f319(f319(f226(x68891),f2(x68891)),f319(f319(f236(x68891),x68892),x68893)))
% 28.25/28.12 [6891]~P129(x68911)+~P1(f319(f319(f227(x68911),f2(x68911)),x68912))+P1(f319(f319(f227(x68911),f2(x68911)),f319(f319(f236(x68911),x68912),x68913)))
% 28.25/28.12 [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)))
% 28.25/28.12 [6925]P1(f319(f55(x69251),x69252))+~P1(f319(f55(x69251),x69253))+~P1(f319(f319(f226(f932(x69251,a923)),x69252),x69253))
% 28.25/28.12 [6926]P1(f319(f55(x69261),x69262))+~P1(f319(f55(x69261),x69263))+~P1(f319(f319(f226(f932(x69261,a923)),x69262),x69263))
% 28.25/28.12 [6933]P1(f319(x69331,x69332))+~P1(f319(x69331,f368(x69331,x69333)))+~P1(f319(f319(f321(a925),x69332),f319(f294(a925,f2(a925)),x69333)))
% 28.25/28.12 [6946]E(x69461,f2(a925))+P1(f319(x69462,f470(x69461,x69463,x69462)))+~P1(f319(x69462,f319(f319(f30(a925),x69463),x69461)))
% 28.25/28.12 [6953]~P130(x69532)+E(x69531,f2(x69532))+~E(f319(f319(f74(x69532),f319(f319(f75(x69532),x69533),x69533)),f319(f319(f75(x69532),x69531),x69531)),f2(x69532))
% 28.25/28.12 [6954]~P130(x69542)+E(x69541,f2(x69542))+~E(f319(f319(f74(x69542),f319(f319(f75(x69542),x69541),x69541)),f319(f319(f75(x69542),x69543),x69543)),f2(x69542))
% 28.25/28.12 [6998]E(x69981,f2(a925))+~P1(f319(x69982,f471(x69981,x69983,x69982)))+P1(f319(x69982,f319(f319(f30(a925),x69983),x69981)))
% 28.25/28.12 [7003]~P4(x70031)+~P14(x70031,x70033)+P14(x70031,f319(f319(f140(x70031,x70031,f5(x70031)),x70032),x70033))
% 28.25/28.12 [7045]P1(f319(x70451,f470(x70452,x70453,x70451)))+P1(f319(x70451,f2(a925)))+~P1(f319(x70451,f319(f319(f30(a925),x70453),x70452)))
% 28.25/28.12 [7051]~P99(x70511)+E(f319(f95(x70511),x70512),f319(f95(x70511),x70513))+~P29(x70511,f319(f95(x70511),f319(f319(f74(a1),x70512),f319(f73(a1),x70513))))
% 28.25/28.12 [7119]E(x71191,f2(a1))+E(x71192,f2(a1))+~P1(f319(f43(x71192,x71192),f319(f319(f244(a1,a1),x71193),x71191)))
% 28.25/28.12 [7120]E(x71201,f72(a1))+E(x71202,f2(a1))+~P1(f319(f43(x71202,x71202),f319(f319(f244(a1,a1),x71201),x71203)))
% 28.25/28.12 [7134]P1(f319(x71341,x71342))+P1(f319(f319(f227(a925),f368(x71341,x71343)),x71343))+~P1(f319(f319(f321(a925),x71342),f319(f294(a925,f2(a925)),x71343)))
% 28.25/28.12 [7157]~P1(f319(x71571,f357(x71573,x71572,x71571)))+~P1(f319(x71571,f2(a925)))+P1(f319(x71571,f319(f319(f23(a925),x71572),x71573)))
% 28.25/28.12 [7158]~P1(f319(x71581,f358(x71583,x71582,x71581)))+~P1(f319(x71581,f2(a925)))+P1(f319(x71581,f319(f319(f23(a925),x71582),x71583)))
% 28.25/28.12 [7159]~P1(f319(x71591,f471(x71593,x71592,x71591)))+~P1(f319(x71591,f2(a925)))+P1(f319(x71591,f319(f319(f30(a925),x71592),x71593)))
% 28.25/28.12 [7177]~P1(f319(x71771,x71773))+P1(f319(f319(f227(a925),f367(x71771,x71772)),x71772))+~P1(f319(f319(f321(a925),x71773),f319(f294(a925,f2(a925)),x71772)))
% 28.25/28.12 [7178]E(f319(f319(f23(a925),f319(f319(f23(a925),x71781),x71782)),f319(f319(f23(a925),x71783),x71782)),f319(f319(f23(a925),x71781),x71783))+~P1(f319(f319(f226(a925),x71782),x71781))+~P1(f319(f319(f226(a925),x71782),x71783))
% 28.25/28.12 [7213]~P68(x72131)+~P1(f319(f319(f226(x72131),f319(f73(x72131),x72133)),x72132))+P1(f319(f319(f226(x72131),f319(f73(x72131),x72132)),x72133))
% 28.25/28.12 [7214]~P68(x72141)+~P1(f319(f319(f226(x72141),f319(f73(x72141),x72143)),x72142))+P1(f319(f319(f226(x72141),f319(f73(x72141),x72142)),x72143))
% 28.25/28.12 [7215]~P92(x72151)+~P1(f319(f319(f226(x72151),f319(f69(x72151),x72152)),x72153))+P1(f319(f319(f226(x72151),f319(f73(x72151),x72152)),x72153))
% 28.25/28.12 [7216]~P92(x72161)+~P1(f319(f319(f226(x72161),f319(f69(x72161),x72162)),x72163))+P1(f319(f319(f226(x72161),f319(f73(x72161),x72162)),x72163))
% 28.25/28.12 [7217]~P68(x72171)+~P1(f319(f319(f227(x72171),f319(f73(x72171),x72173)),x72172))+P1(f319(f319(f227(x72171),f319(f73(x72171),x72172)),x72173))
% 28.25/28.12 [7218]~P68(x72181)+~P1(f319(f319(f227(x72181),f319(f73(x72181),x72183)),x72182))+P1(f319(f319(f227(x72181),f319(f73(x72181),x72182)),x72183))
% 28.25/28.12 [7219]~P126(x72191)+~P1(f319(f319(f227(x72191),f319(f69(x72191),x72192)),x72193))+P1(f319(f319(f227(x72191),f319(f73(x72191),x72192)),x72193))
% 28.25/28.12 [7250]~P1(f319(x72503,f357(x72502,x72501,x72503)))+P1(f319(f319(f227(a925),x72501),x72502))+P1(f319(x72503,f319(f319(f23(a925),x72501),x72502)))
% 28.25/28.12 [7251]~P1(f319(x72513,f358(x72512,x72511,x72513)))+P1(f319(f319(f227(a925),x72511),x72512))+P1(f319(x72513,f319(f319(f23(a925),x72511),x72512)))
% 28.25/28.12 [7304]~E(f883(x73043,x73042,x73041),f884(x73043,x73042,x73041))+E(f319(f319(f93(f932(x73041,a923)),x73042),f31(f932(x73041,a923),x73043)),f180(f932(x73041,a923)))+P1(f319(f319(f321(f932(x73041,a923)),x73042),x73043))
% 28.25/28.12 [7312]~P1(f319(f55(x73121),x73123))+P1(f319(f55(x73121),f32(f932(x73121,a923),x73122)))+~P1(f319(f319(f321(f932(x73121,a923)),x73123),x73122))
% 28.25/28.12 [7372]~P4(x73721)+E(f319(f319(f102(f932(x73721,a923)),f319(f294(x73721,x73722),x73723)),f319(f319(f301(x73721),x73723),f180(f932(x73721,a923)))),f295(x73721,x73722,x73723))+~P1(f319(f319(f226(x73721),x73722),x73723))
% 28.25/28.12 [7375]E(x73751,f2(a925))+P1(f319(f319(f227(a925),f501(x73751,x73753,x73752)),x73751))+P1(f319(x73752,f319(f319(f30(a925),x73753),x73751)))
% 28.25/28.12 [7404]P1(f319(f319(f227(a925),f319(f181(f926(x74041)),x74042)),f802(x74043,x74041)))+~P1(f319(f55(f926(x74041)),x74043))+~P1(f319(f319(f321(f926(x74041)),x74042),x74043))
% 28.25/28.12 [7409]E(x74091,x74092)+~P1(f319(f319(f226(f932(x74093,a923)),x74091),x74092))+P1(f319(f319(f227(f932(x74093,a923)),x74091),x74092))
% 28.25/28.12 [7410]E(x74101,x74102)+~P1(f319(f319(f226(f932(x74103,a923)),x74101),x74102))+P1(f319(f319(f227(f932(x74103,a923)),x74101),x74102))
% 28.25/28.12 [7422]E(x74221,x74222)+~E(f319(f181(f926(x74223)),x74221),f319(f181(f926(x74223)),x74222))+P1(f319(f319(f227(a925),f659(x74223,x74221,x74222)),f319(f181(f926(x74223)),x74222)))
% 28.25/28.12 [7472]P9(x74721,x74722,x74723)+~E(f319(f256(x74721,x74721),x74723),x74722)+~E(f319(f319(f281(x74721,x74721,x74721),f319(f278(x74721,x74721),x74723)),x74723),x74723)
% 28.25/28.12 [7550]~P1(f319(x75501,f2(a925)))+P1(f319(f319(f227(a925),f501(x75503,x75502,x75501)),x75503))+P1(f319(x75501,f319(f319(f30(a925),x75502),x75503)))
% 28.25/28.12 [7559]~P4(x75591)+E(f319(f319(f102(f932(x75591,a923)),f298(x75591,x75592,x75593)),f319(f319(f301(x75591),x75593),f180(f932(x75591,a923)))),f297(x75591,x75592,x75593))+~P1(f319(f319(f227(x75591),x75592),x75593))
% 28.25/28.12 [7649]~P1(f319(f55(x76491),x76493))+P1(f319(f319(f226(a925),f319(f29(x76491),x76492)),f319(f29(x76491),x76493)))+~P1(f319(f319(f226(f932(x76491,a923)),x76492),x76493))
% 28.25/28.12 [7650]~P1(f319(f55(x76501),x76503))+P1(f319(f319(f227(a925),f319(f29(x76501),x76502)),f319(f29(x76501),x76503)))+~P1(f319(f319(f227(f932(x76501,a923)),x76502),x76503))
% 28.25/28.12 [7779]E(x77791,x77792)+~P1(f319(f319(f226(f932(x77793,a923)),x77792),x77791))+~P1(f319(f319(f226(f932(x77793,a923)),x77791),x77792))
% 28.25/28.12 [7780]E(x77801,x77802)+~P1(f319(f319(f226(f932(x77803,a923)),x77802),x77801))+~P1(f319(f319(f226(f932(x77803,a923)),x77801),x77802))
% 28.25/28.12 [7783]~P4(x77831)+P14(x77831,x77832)+~P14(x77831,f319(f319(f140(x77831,x77831,f5(x77831)),x77833),x77832))
% 28.25/28.12 [7854]~P1(f319(f319(f227(a925),x78543),x78542))+~P1(f319(f319(f227(a925),x78543),x78541))+P1(f319(f319(f227(a925),f319(f319(f23(a925),x78541),x78542)),f319(f319(f23(a925),x78541),x78543)))
% 28.25/28.12 [7855]~P1(f319(f319(f226(a925),x78552),x78551))+~P1(f319(f319(f227(a925),x78551),x78553))+P1(f319(f319(f227(a925),f319(f319(f23(a925),x78551),x78552)),f319(f319(f23(a925),x78553),x78552)))
% 28.25/28.12 [7870]~P1(f319(f319(f227(a1),x78702),f2(a1)))+~P1(f319(f319(f226(a1),x78703),x78701))+P1(f319(f319(f226(a1),f319(f319(f30(a1),x78701),x78702)),f319(f319(f30(a1),x78703),x78702)))
% 28.25/28.12 [7886]~P1(f319(f319(f227(a925),f2(a925)),x78861))+~P1(f319(f319(f226(a925),x78862),x78863))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x78861),x78862)),f319(f319(f75(a925),x78861),x78863)))
% 28.25/28.12 [7887]~P1(f319(f319(f227(a925),f2(a925)),x78873))+~P1(f319(f319(f226(a925),x78873),x78872))+P1(f319(f319(f226(a925),f319(f319(f30(a925),x78871),x78872)),f319(f319(f30(a925),x78871),x78873)))
% 28.25/28.12 [7888]~P1(f319(f319(f227(a1),f2(a1)),x78882))+~P1(f319(f319(f226(a1),x78881),x78883))+P1(f319(f319(f226(a1),f319(f319(f30(a1),x78881),x78882)),f319(f319(f30(a1),x78883),x78882)))
% 28.25/28.12 [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)))
% 28.25/28.12 [7890]~P1(f319(f319(f227(a925),f2(a925)),x78901))+~P1(f319(f319(f227(a925),x78902),x78903))+P1(f319(f319(f227(a925),f319(f319(f75(a925),x78901),x78902)),f319(f319(f75(a925),x78901),x78903)))
% 28.25/28.12 [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)))
% 28.25/28.12 [7892]~P1(f319(f319(f227(a925),f2(a925)),x78922))+~P1(f319(f319(f227(a925),x78921),x78923))+P1(f319(f319(f227(a925),f319(f319(f75(a925),x78921),x78922)),f319(f319(f75(a925),x78923),x78922)))
% 28.25/28.12 [7893]~P1(f319(f319(f227(a925),f2(a925)),x78931))+~P1(f319(f319(f227(a925),x78932),x78933))+P1(f319(f319(f227(a925),f319(f319(f75(a925),x78931),x78932)),f319(f319(f75(a925),x78931),x78933)))
% 28.25/28.12 [7894]~P1(f319(f319(f227(a1),f2(a1)),x78941))+~P1(f319(f319(f227(a1),x78942),x78943))+P1(f319(f319(f227(a1),f319(f319(f75(a1),x78941),x78942)),f319(f319(f75(a1),x78941),x78943)))
% 28.25/28.12 [7942]E(x79421,f2(a925))+E(f319(f319(f74(a925),f319(f319(f75(a925),x79421),f471(x79421,x79422,x79423))),f501(x79421,x79422,x79423)),x79422)+P1(f319(x79423,f319(f319(f30(a925),x79422),x79421)))
% 28.25/28.12 [8001]E(f319(f319(f74(a925),f319(f319(f75(a925),x80011),f471(x80011,x80012,x80013))),f501(x80011,x80012,x80013)),x80012)+~P1(f319(x80013,f2(a925)))+P1(f319(x80013,f319(f319(f30(a925),x80012),x80011)))
% 28.25/28.12 [8018]~P1(f319(f55(x80181),x80183))+P1(f319(f319(f321(x80181),f474(x80182,x80183,x80181)),x80183))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f9(x80181,a925),x80182),x80183)))
% 28.25/28.12 [8019]~P1(f319(f55(x80191),x80193))+P1(f319(f319(f321(x80191),f511(x80192,x80193,x80191)),x80193))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f9(x80191,a925),x80192),x80193)))
% 28.25/28.12 [8121]E(x81211,f2(a925))+P1(f319(f319(f279(a925),x81212),x81213))+~P1(f319(f319(f279(a925),f319(f319(f75(a925),x81211),x81212)),f319(f319(f75(a925),x81211),x81213)))
% 28.25/28.12 [8314]E(x83141,f180(f932(x83142,a923)))+E(x83141,f319(f319(f301(x83142),x83143),f180(f932(x83142,a923))))+~P1(f319(f319(f226(f932(x83142,a923)),x83141),f319(f319(f301(x83142),x83143),f180(f932(x83142,a923)))))
% 28.25/28.12 [8338]~P4(x83381)+~P14(x83381,x83383)+P14(x83381,f319(f319(f130(x83381),f319(f181(f926(x83381)),f169(x83381,x83382,x83383))),x83383))
% 28.25/28.12 [8350]~P1(f319(f319(f227(a925),f72(a925)),x83503))+P1(f319(f319(f226(a925),x83501),x83502))+~P1(f319(f319(f279(a925),f319(f319(f236(a925),x83503),x83501)),f319(f319(f236(a925),x83503),x83502)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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),x83523),x83521)),f319(f319(f75(a925),x83523),x83522)))
% 28.25/28.12 [8353]~P1(f319(f319(f227(a925),f2(a925)),x83533))+P1(f319(f319(f226(a925),x83531),x83532))+~P1(f319(f319(f226(a925),f319(f319(f75(a925),x83531),x83533)),f319(f319(f75(a925),x83532),x83533)))
% 28.25/28.12 [8354]~P1(f319(f319(f227(a925),f2(a925)),x83543))+P1(f319(f319(f227(a925),x83541),x83542))+~P1(f319(f319(f227(a925),f319(f319(f75(a925),x83543),x83541)),f319(f319(f75(a925),x83543),x83542)))
% 28.25/28.12 [8355]~P1(f319(f319(f227(a925),f2(a925)),x83553))+P1(f319(f319(f227(a925),x83551),x83552))+~P1(f319(f319(f227(a925),f319(f319(f236(a925),x83553),x83551)),f319(f319(f236(a925),x83553),x83552)))
% 28.25/28.12 [8396]~E(f319(f319(f93(f932(x83961,a923)),f884(x83963,x83962,x83961)),f883(x83963,x83962,x83961)),f180(f932(x83961,a923)))+E(f319(f319(f93(f932(x83961,a923)),x83962),f31(f932(x83961,a923),x83963)),f180(f932(x83961,a923)))+P1(f319(f319(f321(f932(x83961,a923)),x83962),x83963))
% 28.25/28.12 [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)))
% 28.25/28.12 [8410]E(x84101,f105(x84102))+~E(f319(f134(f926(x84102),f926(x84102),f126(x84102),f105(x84102)),x84103),f105(x84102))+~P1(f319(f319(f321(f926(x84102)),x84101),f319(f164(f926(x84102)),x84103)))
% 28.25/28.12 [8465]E(x84651,f180(f932(f932(x84652,a923),a923)))+P1(f319(f319(f321(f932(x84652,a923)),f882(x84653,x84651,x84652)),x84651))+P1(f319(f319(f226(f932(x84652,a923)),f32(f932(x84652,a923),x84651)),x84653))
% 28.25/28.12 [8472]~P78(x84721)+~P79(x84721)+E(f319(f319(f6(a1,x84721),f319(f319(f8(a925,x84721,a1),x84722),a96)),f319(f302(a925,a1,f92(a1)),x84723)),f319(f319(f6(a925,x84721),x84722),x84723))
% 28.25/28.12 [8473]~P78(x84731)+~P79(x84731)+E(f319(f319(f9(a1,x84731),f319(f319(f8(a925,x84731,a1),x84732),a96)),f319(f302(a925,a1,f92(a1)),x84733)),f319(f319(f9(a925,x84731),x84732),x84733))
% 28.25/28.12 [8516]~P1(f319(f55(x85161),x85163))+~P1(f319(f319(f227(a925),f2(a925)),f319(x85162,f474(x85162,x85163,x85161))))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f9(x85161,a925),x85162),x85163)))
% 28.25/28.12 [8517]~P1(f319(f55(x85171),x85173))+~P1(f319(f319(f227(a925),f2(a925)),f319(x85172,f511(x85172,x85173,x85171))))+P1(f319(f319(f227(a925),f2(a925)),f319(f319(f9(x85171,a925),x85172),x85173)))
% 28.25/28.12 [8554]~P73(x85542)+E(x85541,f72(x85542))+E(f319(f319(f283(x85542),f319(f319(f23(x85542),f319(f319(f236(x85542),x85541),x85543)),f72(x85542))),f319(f319(f23(x85542),x85541),f72(x85542))),f319(f319(f6(a925,x85542),f319(f236(x85542),x85541)),f319(f294(a925,f2(a925)),x85543)))
% 28.25/28.12 [8611]E(x86111,f2(a925))+~P1(f319(x86113,f319(f319(f30(a925),x86112),x86111)))+P1(f319(f319(f227(a925),x86112),f319(f319(f75(a925),x86111),f319(a104,f470(x86111,x86112,x86113)))))
% 28.25/28.12 [8630]P1(f319(x86301,f2(a925)))+~P1(f319(x86301,f319(f319(f30(a925),x86302),x86303)))+P1(f319(f319(f227(a925),x86302),f319(f319(f75(a925),x86303),f319(a104,f470(x86303,x86302,x86301)))))
% 28.25/28.12 [8668]E(x86681,f2(a925))+~P1(f319(x86683,f319(f319(f30(a925),x86682),x86681)))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x86681),f470(x86681,x86682,x86683))),x86682))
% 28.25/28.12 [8701]P1(f319(x87011,f2(a925)))+~P1(f319(x87011,f319(f319(f30(a925),x87013),x87012)))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x87012),f470(x87012,x87013,x87011))),x87013))
% 28.25/28.12 [8709]~P4(x87091)+E(f319(f319(f140(x87091,x87091,f5(x87091)),x87092),x87093),f141(x87091,x87091,f5(x87091),x87092,x87093))+P1(f319(f319(f321(x87091),x87092),f319(f164(x87091),x87093)))
% 28.25/28.12 [8746]~E(f319(x87463,f599(x87462,x87463,x87461)),f319(x87463,f603(x87462,x87463,x87461)))+~P64(x87461,f319(x87463,f600(x87462,x87463,x87461)))+P64(x87461,f319(f319(f33(x87462,f932(x87461,f932(x87461,a923))),f234(f932(x87462,a923))),x87463))
% 28.25/28.12 [8755]E(x87551,f180(f932(f932(x87552,a923),a923)))+~P1(f319(f319(f226(f932(x87552,a923)),f882(x87553,x87551,x87552)),x87553))+P1(f319(f319(f226(f932(x87552,a923)),f32(f932(x87552,a923),x87551)),x87553))
% 28.25/28.12 [8816]~P75(x88161)+~P1(f319(f319(f227(x88161),x88162),x88163))+P1(f319(f319(f227(x88161),x88162),f319(f319(f283(x88161),f319(f319(f74(x88161),x88162),x88163)),f319(f319(f74(x88161),f72(x88161)),f72(x88161)))))
% 28.25/28.12 [8874]~P1(f319(f319(x88741,f531(x88741,x88743,x88742)),f535(x88741,x88743,x88742)))+P1(f319(f319(x88741,x88742),x88743))+~P1(f319(f307(f931(a1,a1),a46),f319(f319(f244(a1,a1),x88742),x88743)))
% 28.25/28.12 [8875]~P1(f319(f319(x88751,f536(x88751,x88753,x88752)),f538(x88751,x88753,x88752)))+P1(f319(f319(x88751,x88752),x88753))+~P1(f319(f307(f931(a1,a1),a52),f319(f319(f244(a1,a1),x88752),x88753)))
% 28.25/28.12 [8876]~P1(f319(f319(x88761,f541(x88761,x88763,x88762)),f542(x88761,x88763,x88762)))+P1(f319(f319(x88761,x88762),x88763))+~P1(f319(f307(f931(a1,a1),a213),f319(f319(f244(a1,a1),x88762),x88763)))
% 28.25/28.12 [8877]~P1(f319(f319(x88771,f543(x88771,x88773,x88772)),f544(x88771,x88773,x88772)))+P1(f319(f319(x88771,x88772),x88773))+~P1(f319(f307(f931(a925,a925),a211),f319(f319(f244(a925,a925),x88772),x88773)))
% 28.25/28.12 [8878]~P1(f319(f319(x88781,f698(x88781,x88783,x88782)),f699(x88781,x88783,x88782)))+P1(f319(f319(x88781,x88782),x88783))+~P1(f319(f307(f931(a1,a1),a174),f319(f319(f244(a1,a1),x88782),x88783)))
% 28.25/28.12 [8879]~P1(f319(f319(x88791,f795(x88791,x88793,x88792)),f796(x88791,x88793,x88792)))+P1(f319(f319(x88791,x88792),x88793))+~P1(f319(f307(f931(a1,a1),a125),f319(f319(f244(a1,a1),x88792),x88793)))
% 28.25/28.12 [9156]P1(f319(f319(x91561,x91562),x91563))+P1(f319(f307(f931(a925,a925),a211),f319(f319(f244(a925,a925),f543(x91561,x91563,x91562)),f544(x91561,x91563,x91562))))+~P1(f319(f307(f931(a925,a925),a211),f319(f319(f244(a925,a925),x91562),x91563)))
% 28.25/28.12 [9157]P1(f319(f319(x91571,x91572),x91573))+P1(f319(f307(f931(a1,a1),a46),f319(f319(f244(a1,a1),f531(x91571,x91573,x91572)),f535(x91571,x91573,x91572))))+~P1(f319(f307(f931(a1,a1),a46),f319(f319(f244(a1,a1),x91572),x91573)))
% 28.25/28.12 [9158]P1(f319(f319(x91581,x91582),x91583))+P1(f319(f307(f931(a1,a1),a52),f319(f319(f244(a1,a1),f536(x91581,x91583,x91582)),f538(x91581,x91583,x91582))))+~P1(f319(f307(f931(a1,a1),a52),f319(f319(f244(a1,a1),x91582),x91583)))
% 28.25/28.12 [9159]P1(f319(f319(x91591,x91592),x91593))+P1(f319(f307(f931(a1,a1),a213),f319(f319(f244(a1,a1),f541(x91591,x91593,x91592)),f542(x91591,x91593,x91592))))+~P1(f319(f307(f931(a1,a1),a213),f319(f319(f244(a1,a1),x91592),x91593)))
% 28.25/28.12 [9160]P1(f319(f319(x91601,x91602),x91603))+P1(f319(f307(f931(a1,a1),a174),f319(f319(f244(a1,a1),f698(x91601,x91603,x91602)),f699(x91601,x91603,x91602))))+~P1(f319(f307(f931(a1,a1),a174),f319(f319(f244(a1,a1),x91602),x91603)))
% 28.25/28.12 [9161]P1(f319(f319(x91611,x91612),x91613))+P1(f319(f307(f931(a1,a1),a125),f319(f319(f244(a1,a1),f795(x91611,x91613,x91612)),f796(x91611,x91613,x91612))))+~P1(f319(f307(f931(a1,a1),a125),f319(f319(f244(a1,a1),x91612),x91613)))
% 28.25/28.12 [9502]~P1(f319(f55(x95021),x95023))+P1(f319(f319(f321(f931(f932(x95021,a923),f932(x95021,a923))),f319(f319(f244(f932(x95021,a923),f932(x95021,a923)),x95022),x95023)),f306(x95021)))+~P1(f319(f319(f227(f932(x95021,a923)),x95022),x95023))
% 28.25/28.12 [9577]~P64(x95771,f319(x95773,f600(x95772,x95773,x95771)))+P64(x95771,f319(f319(f33(x95772,f932(x95771,f932(x95771,a923))),f234(f932(x95772,a923))),x95773))+~E(f319(f319(f93(f932(x95771,a923)),f241(x95771,x95771,f319(x95773,f599(x95772,x95773,x95771)))),f242(x95771,x95771,f319(x95773,f603(x95772,x95773,x95771)))),f180(f932(x95771,a923)))
% 28.25/28.12 [9782]P57(x97821,x97822,x97823)+P1(f319(f319(f321(f931(x97821,x97821)),f594(x97823,x97822,x97821)),x97823))+~P1(f319(f319(f321(f931(x97821,x97821)),f319(f319(f244(x97821,x97821),f593(x97823,x97822,x97821)),f593(x97823,x97822,x97821))),x97823))
% 28.25/28.12 [10398]P57(x103981,x103982,x103983)+~P1(f319(f319(f249(x103981,x103981,a923),f319(f319(f7(x103981,f932(x103981,a923),f932(x103981,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x103981,a923),f932(x103981,a923)),x103981),f8(a923,a923,x103981)),f319(f319(f8(a923,f932(a923,a923),x103981),a317),f319(f319(f7(x103981,f932(x103981,a923),a923),f321(x103981)),x103982)))),f319(f319(f7(x103981,f932(x103981,a923),a923),f321(x103981)),x103982))),f594(x103983,x103982,x103981)))+~P1(f319(f319(f321(f931(x103981,x103981)),f319(f319(f244(x103981,x103981),f593(x103983,x103982,x103981)),f593(x103983,x103982,x103981))),x103983))
% 28.25/28.12 [5866]~P65(x58662)+E(x58661,f2(x58662))+E(f319(f319(f30(x58662),f319(f319(f75(x58662),x58663),x58661)),x58661),x58663)
% 28.25/28.12 [5867]~P65(x58672)+E(x58671,f2(x58672))+E(f319(f319(f30(x58672),f319(f319(f75(x58672),x58671),x58673)),x58671),x58673)
% 28.25/28.12 [6512]~P65(x65121)+E(f319(f319(f75(x65121),f319(f319(f30(x65121),x65122),x65123)),x65123),x65122)+~P1(f319(f319(f279(x65121),x65123),x65122))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [7034]~P1(f319(x70343,f2(a1)))+P1(f319(f319(f226(a925),x70341),x70342))+P1(f319(x70343,f319(f92(a1),f319(f319(f23(a925),x70342),x70341))))
% 28.25/28.12 [7140]P1(f319(f319(f227(a925),x71402),x71401))+P1(f319(f319(f226(a925),x71401),x71402))+P1(f319(x71403,f319(f92(a1),f319(f319(f23(a925),x71402),x71401))))
% 28.25/28.12 [7212]E(f319(f319(f74(a925),f319(f95(a925),x72121)),f319(f319(f74(a925),f319(f95(a925),x72122)),x72123)),f319(f319(f74(a925),f319(f95(a925),x72121)),x72123))+P1(f319(a185,f319(f95(a1),x72121)))+~P1(f319(a185,f319(f95(a1),x72122)))
% 28.25/28.12 [7290]~E(x72902,f319(f319(f30(a925),x72903),x72901))+~P1(f319(f319(f227(a925),f2(a925)),x72901))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x72901),x72902)),x72903))
% 28.25/28.12 [7406]~P1(f319(f55(x74061),x74063))+~P1(f319(f55(x74061),x74062))+P1(f319(f55(x74061),f319(f319(f102(f932(x74061,a923)),x74062),x74063)))
% 28.25/28.12 [7407]~P1(f319(f55(x74071),x74073))+~P1(f319(f55(x74071),x74072))+P1(f319(f55(x74071),f319(f319(f102(f932(x74071,a923)),x74072),x74073)))
% 28.25/28.12 [7408]~P1(f319(f55(x74081),x74083))+~P1(f319(f55(x74081),x74082))+P1(f319(f55(x74081),f319(f319(f23(f932(x74081,a923)),x74082),x74083)))
% 28.25/28.12 [7457]~P39(x74571,x74573)+~P39(x74571,x74572)+P39(x74571,f319(f319(f93(f932(f931(x74571,x74571),a923)),x74572),x74573))
% 28.25/28.12 [7458]~P56(x74581,x74583)+~P56(x74581,x74582)+P56(x74581,f319(f319(f102(f932(f931(x74581,x74581),a923)),x74582),x74583))
% 28.25/28.12 [7459]~P56(x74591,x74593)+~P56(x74591,x74592)+P56(x74591,f319(f319(f93(f932(f931(x74591,x74591),a923)),x74592),x74593))
% 28.25/28.12 [7698]~P4(x76981)+~P1(f319(f55(x76981),x76982))+E(f131(x76981,f319(f319(f23(f932(x76981,a923)),x76982),f319(f319(f301(x76981),x76983),f180(f932(x76981,a923))))),f162(x76981,x76983,f131(x76981,x76982)))
% 28.25/28.12 [7759]P1(f319(x77591,f2(a1)))+~P1(f319(f319(f227(a925),x77592),x77593))+~P1(f319(x77591,f319(f92(a1),f319(f319(f23(a925),x77592),x77593))))
% 28.25/28.12 [7777]~P1(f319(f55(x77771),x77772))+E(f319(f29(x77771),f319(f319(f23(f932(x77771,a923)),x77772),f319(f319(f301(x77771),x77773),f180(f932(x77771,a923))))),f319(f29(x77771),x77772))+P1(f319(f319(f321(x77771),x77773),x77772))
% 28.25/28.12 [7910]~P129(x79101)+~P1(f319(f319(f227(x79101),f72(x79101)),x79102))+P1(f319(f319(f227(x79101),f72(x79101)),f319(f319(f75(x79101),x79102),f319(f319(f236(x79101),x79102),x79103))))
% 28.25/28.12 [7952]~P1(f319(f55(x79521),x79523))+E(f319(f319(f23(a925),f319(f29(x79521),x79522)),f319(f29(x79521),x79523)),f319(f29(x79521),f319(f319(f23(f932(x79521,a923)),x79522),x79523)))+~P1(f319(f319(f226(f932(x79521,a923)),x79523),x79522))
% 28.25/28.12 [8009]~P1(f319(f319(f226(a925),x80092),x80093))+~P1(f319(f319(f226(a925),x80091),f319(f319(f23(a925),x80093),x80092)))+P1(f319(f319(f226(a925),f319(f319(f74(a925),x80091),x80092)),x80093))
% 28.25/28.12 [8064]P1(f319(f55(x80641),x80642))+~P1(f319(f55(x80641),x80643))+~P1(f319(f55(x80641),f319(f319(f23(f932(x80641,a923)),x80642),x80643)))
% 28.25/28.12 [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))
% 28.25/28.12 [8070]~P1(f319(f55(x80701),x80702))+E(f319(f29(x80701),f319(f319(f23(f932(x80701,a923)),x80702),f319(f319(f301(x80701),x80703),f180(f932(x80701,a923))))),f319(f319(f23(a925),f319(f29(x80701),x80702)),f72(a925)))+~P1(f319(f319(f321(x80701),x80703),x80702))
% 28.25/28.12 [8146]P64(x81461,x81462)+~P64(x81461,x81463)+~P1(f319(f319(f226(f932(x81461,f932(x81461,a923))),x81462),x81463))
% 28.25/28.12 [8188]~P1(f319(f319(f226(a925),x81883),x81882))+P1(f319(f319(f226(a925),x81881),f319(f319(f23(a925),x81882),x81883)))+~P1(f319(f319(f226(a925),f319(f319(f74(a925),x81881),x81883)),x81882))
% 28.25/28.12 [8206]P38(x82061,x82062)+~P38(x82061,x82063)+~P1(f319(f319(f226(f932(f931(x82061,x82061),a923)),x82062),x82063))
% 28.25/28.12 [8207]P62(x82071,x82072)+~P62(x82071,x82073)+~P1(f319(f319(f226(f932(f931(x82071,x82071),a923)),x82072),x82073))
% 28.25/28.12 [8208]P40(x82081,x82082)+~P40(x82081,x82083)+~P1(f319(f319(f226(f932(f931(x82081,x82081),a923)),x82082),x82083))
% 28.25/28.12 [8443]~P129(x84431)+~P1(f319(f319(f227(x84431),f72(x84431)),x84432))+P1(f319(f319(f227(x84431),f319(f319(f236(x84431),x84432),x84433)),f319(f319(f75(x84431),x84432),f319(f319(f236(x84431),x84432),x84433))))
% 28.25/28.12 [8535]~P1(f319(x85351,f2(a1)))+~P1(f319(x85351,f319(f319(f23(a1),f319(f92(a1),x85352)),f319(f92(a1),x85353))))+P1(f319(x85351,f319(f92(a1),f319(f319(f23(a925),x85352),x85353))))
% 28.25/28.12 [8550]~P1(f319(f319(f226(a925),x85503),x85502))+P1(f319(x85501,f319(f319(f23(a1),f319(f92(a1),x85502)),f319(f92(a1),x85503))))+~P1(f319(x85501,f319(f92(a1),f319(f319(f23(a925),x85502),x85503))))
% 28.25/28.12 [8570]P1(f319(f319(f227(a925),x85701),x85702))+~P1(f319(x85703,f319(f319(f23(a1),f319(f92(a1),x85701)),f319(f92(a1),x85702))))+P1(f319(x85703,f319(f92(a1),f319(f319(f23(a925),x85701),x85702))))
% 28.25/28.12 [8624]~P130(x86242)+E(x86241,f2(x86242))+P1(f319(f319(f227(x86242),f2(x86242)),f319(f319(f74(x86242),f319(f319(f75(x86242),x86243),x86243)),f319(f319(f75(x86242),x86241),x86241))))
% 28.25/28.12 [8625]~P130(x86252)+E(x86251,f2(x86252))+P1(f319(f319(f227(x86252),f2(x86252)),f319(f319(f74(x86252),f319(f319(f75(x86252),x86251),x86251)),f319(f319(f75(x86252),x86253),x86253))))
% 28.25/28.12 [8729]~P1(f319(f319(f227(a925),f2(a925)),x87291))+~P1(f319(f319(f227(a1),x87292),x87293))+P1(f319(f319(f227(a1),f319(f319(f75(a1),f319(f92(a1),x87291)),x87292)),f319(f319(f75(a1),f319(f92(a1),x87291)),x87293)))
% 28.25/28.12 [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)),f884(x87843,x87842,x87841)),f319(f319(f301(f932(x87841,a923)),x87842),x87843)))
% 28.25/28.12 [8785]E(f319(f319(f93(f932(x87851,a923)),x87852),f31(f932(x87851,a923),x87853)),f180(f932(x87851,a923)))+P1(f319(f319(f321(f932(x87851,a923)),x87852),x87853))+P1(f319(f319(f321(f932(x87851,a923)),f883(x87853,x87852,x87851)),f319(f319(f301(f932(x87851,a923)),x87852),x87853)))
% 28.25/28.12 [8815]E(x88151,x88152)+~E(f319(f181(f926(x88153)),x88151),f319(f181(f926(x88153)),x88152))+P1(f319(f319(f321(f931(x88153,x88153)),f685(x88153,x88151,x88152)),f319(f164(f931(x88153,x88153)),f319(f319(f173(x88153,x88153),x88152),x88151))))
% 28.25/28.12 [9066]E(f299(x90661,x90662),f299(x90661,x90663))+~P1(f319(f319(f226(f932(f931(x90661,x90661),a923)),x90663),f299(x90661,x90662)))+~P1(f319(f319(f226(f932(f931(x90661,x90661),a923)),x90662),x90663))
% 28.25/28.12 [9134]~P57(x91341,f234(f932(x91341,a923)),x91343)+P1(f319(f319(f226(f932(f931(f926(x91341),f926(x91341)),a923)),f149(x91341,x91342)),f150(x91341,x91343)))+~P1(f319(f319(f226(f932(f931(x91341,x91341),a923)),x91342),x91343))
% 28.25/28.12 [9336]P38(x93361,x93362)+~P1(f319(f319(f321(x93361),x93363),f629(x93362,x93361)))+P1(f319(f319(f321(f931(x93361,x93361)),f319(f319(f244(x93361,x93361),f660(x93362,x93361,x93363)),x93363)),x93362))
% 28.25/28.12 [9371]~P1(f319(f55(x93711),x93712))+P1(f319(f55(f932(x93711,a923)),f319(f319(f54(x93711),x93712),x93713)))+~P1(f319(f319(f226(f932(f931(x93711,x93711),a923)),x93713),f319(f319(f246(x93711,x93711),x93712),f319(f16(f932(x93711,a923),x93711),x93712))))
% 28.25/28.12 [9409]P57(x94091,x94092,x94093)+P1(f319(f319(f321(x94091),f583(x94093,x94092,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))))
% 28.25/28.12 [9410]P57(x94101,x94102,x94103)+P1(f319(f319(f321(x94101),f591(x94102,x94103,x94101)),x94102))+~P1(f319(f319(f226(f932(f931(x94101,x94101),a923)),x94103),f319(f319(f246(x94101,x94101),x94102),f319(f16(f932(x94101,a923),x94101),x94102))))
% 28.25/28.12 [9445]~P75(x94451)+~P1(f319(f319(f227(x94451),x94452),x94453))+P1(f319(f319(f227(x94451),f319(f319(f283(x94451),f319(f319(f74(x94451),x94452),x94453)),f319(f319(f74(x94451),f72(x94451)),f72(x94451)))),x94453))
% 28.25/28.12 [9474]~P74(x94741)+P1(f319(f319(f226(x94741),x94742),x94743))+~P1(f319(f319(f226(x94741),f319(f319(f75(x94741),f469(x94743,x94742,x94741)),x94742)),x94743))
% 28.25/28.12 [9612]E(f319(f181(f926(f926(x96121))),f319(f128(f926(x96121),f319(f319(f8(a925,a923,f926(x96121)),f319(f227(a925),x96122)),f181(f926(x96121)))),f171(x96121,x96123))),f319(f181(f926(x96121)),f319(f319(f156(f926(x96121)),x96123),x96122)))+~P14(a925,f319(f160(a925),f319(f319(f146(f926(x96121),a925),f181(f926(x96121))),x96123)))+~P1(f319(f319(f227(a925),x96122),f319(f181(f926(f926(x96121))),x96123)))
% 28.25/28.12 [9728]~P38(x97281,x97282)+P28(x97281,f319(f319(f244(f932(f931(x97281,x97281),a923),f932(f931(x97281,x97281),a923)),x97282),x97283))+~P1(f319(f319(f226(f932(f931(x97281,x97281),a923)),f319(f319(f281(x97281,x97281,x97281),x97282),x97283)),x97282))
% 28.25/28.12 [9733]E(f319(f319(f146(f926(x97331),x97331),f319(f319(f7(f926(x97331),a925,x97331),f156(x97331)),x97332)),f319(f128(f926(x97331),f319(f319(f8(a925,a923,f926(x97331)),f319(f227(a925),x97332)),f181(f926(x97331)))),f171(x97331,x97333))),f319(f319(f156(f926(x97331)),x97333),x97332))+~P14(a925,f319(f160(a925),f319(f319(f146(f926(x97331),a925),f181(f926(x97331))),x97333)))+~P1(f319(f319(f227(a925),x97332),f319(f181(f926(f926(x97331))),x97333)))
% 28.25/28.12 [9871]P57(x98711,x98712,x98713)+~P1(f319(f319(f321(f931(x98711,x98711)),f319(f319(f244(x98711,x98711),f583(x98713,x98712,x98711)),f583(x98713,x98712,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))))
% 28.25/28.12 [9872]P57(x98721,x98722,x98723)+~P1(f319(f319(f321(f931(x98721,x98721)),f319(f319(f244(x98721,x98721),f591(x98722,x98723,x98721)),f591(x98722,x98723,x98721))),x98723))+~P1(f319(f319(f226(f932(f931(x98721,x98721),a923)),x98723),f319(f319(f246(x98721,x98721),x98722),f319(f16(f932(x98721,a923),x98721),x98722))))
% 28.25/28.12 [10058]~P145(x100581)+~P128(x100581)+E(f319(f319(f283(x100581),f319(f94(x100581),f319(f319(f66(f931(a1,a1),a1,x100582,f243(a1,a1)),f204(x100582)),x100583))),f319(f94(x100581),f319(f319(f66(f931(a1,a1),a1,x100582,f248(a1,a1)),f204(x100582)),x100583))),f214(x100582,x100581,x100583))
% 28.25/28.12 [10267]~E(x102673,f2(a925))+~E(f319(f181(f926(x102671)),f319(f319(f156(f926(x102671)),x102672),f733(x102673,x102671,x102672))),x102673)+E(f319(f319(f146(a925,f926(x102671)),f319(f319(f7(a925,f926(a925),f926(x102671)),f319(f319(f8(f932(a925,x102671),f932(f926(a925),f926(x102671)),a925),f146(a925,x102671)),f319(f7(a925,a925,x102671),f319(f319(f8(f926(x102671),f932(a925,x102671),a925),f156(x102671)),f319(f156(f926(x102671)),x102672))))),f131(a925,f319(f294(a925,f2(a925)),f319(f181(f926(f926(x102671))),x102672))))),f131(a925,f319(f294(a925,f2(a925)),x102673))),f171(x102671,x102672))
% 28.25/28.12 [10268]E(x102681,f105(f926(x102682)))+~E(f319(f181(f926(x102682)),f319(f319(f156(f926(x102682)),x102681),f733(x102683,x102682,x102681))),x102683)+E(f319(f319(f146(a925,f926(x102682)),f319(f319(f7(a925,f926(a925),f926(x102682)),f319(f319(f8(f932(a925,x102682),f932(f926(a925),f926(x102682)),a925),f146(a925,x102682)),f319(f7(a925,a925,x102682),f319(f319(f8(f926(x102682),f932(a925,x102682),a925),f156(x102682)),f319(f156(f926(x102682)),x102681))))),f131(a925,f319(f294(a925,f2(a925)),f319(f181(f926(f926(x102682))),x102681))))),f131(a925,f319(f294(a925,f2(a925)),x102683))),f171(x102682,x102681))
% 28.25/28.12 [10269]~E(x102693,f2(a925))+E(f319(f319(f146(a925,f926(x102691)),f319(f319(f7(a925,f926(a925),f926(x102691)),f319(f319(f8(f932(a925,x102691),f932(f926(a925),f926(x102691)),a925),f146(a925,x102691)),f319(f7(a925,a925,x102691),f319(f319(f8(f926(x102691),f932(a925,x102691),a925),f156(x102691)),f319(f156(f926(x102691)),x102692))))),f131(a925,f319(f294(a925,f2(a925)),f319(f181(f926(f926(x102691))),x102692))))),f131(a925,f319(f294(a925,f2(a925)),x102693))),f171(x102691,x102692))+P1(f319(f319(f227(a925),f733(x102693,x102691,x102692)),f319(f181(f926(f926(x102691))),x102692)))
% 28.25/28.12 [10270]E(x102701,f105(f926(x102702)))+E(f319(f319(f146(a925,f926(x102702)),f319(f319(f7(a925,f926(a925),f926(x102702)),f319(f319(f8(f932(a925,x102702),f932(f926(a925),f926(x102702)),a925),f146(a925,x102702)),f319(f7(a925,a925,x102702),f319(f319(f8(f926(x102702),f932(a925,x102702),a925),f156(x102702)),f319(f156(f926(x102702)),x102701))))),f131(a925,f319(f294(a925,f2(a925)),f319(f181(f926(f926(x102702))),x102701))))),f131(a925,f319(f294(a925,f2(a925)),x102703))),f171(x102702,x102701))+P1(f319(f319(f227(a925),f733(x102703,x102702,x102701)),f319(f181(f926(f926(x102702))),x102701)))
% 28.25/28.12 [7949]E(f319(f319(f74(a925),f319(f95(a925),x79491)),f319(f319(f74(a925),f319(f95(a925),x79492)),x79493)),f319(f319(f74(a925),f319(f95(a925),f319(f319(f74(a1),x79491),x79492))),x79493))+P1(f319(a185,f319(f95(a1),x79491)))+P1(f319(a185,f319(f95(a1),x79492)))
% 28.25/28.12 [8720]~P1(f319(f55(x87201),x87202))+~P1(f319(f319(f321(x87201),x87203),x87202))+E(f319(a104,f319(f29(x87201),f319(f319(f23(f932(x87201,a923)),x87202),f319(f319(f301(x87201),x87203),f180(f932(x87201,a923)))))),f319(f29(x87201),x87202))
% 28.25/28.12 [8736]~P1(f319(f55(x87361),x87362))+~P1(f319(f319(f321(x87361),x87363),x87362))+E(f319(f319(f74(a925),f72(a925)),f319(f29(x87361),f319(f319(f23(f932(x87361,a923)),x87362),f319(f319(f301(x87361),x87363),f180(f932(x87361,a923)))))),f319(f29(x87361),x87362))
% 28.25/28.12 [8824]~P4(x88241)+~P1(f319(f55(x88241),x88243))+E(f319(f319(f140(x88241,x88241,f5(x88241)),x88242),f131(x88241,f319(f319(f23(f932(x88241,a923)),x88243),f319(f319(f301(x88241),x88242),f180(f932(x88241,a923)))))),f131(x88241,f319(f319(f301(x88241),x88242),x88243)))
% 28.25/28.12 [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)))
% 28.25/28.12 [8990]~P1(f319(f55(x89901),x89903))+~P1(f319(f55(x89901),x89902))+E(f319(f319(f74(a925),f319(f29(x89901),f319(f319(f102(f932(x89901,a923)),x89902),x89903))),f319(f29(x89901),f319(f319(f93(f932(x89901,a923)),x89902),x89903))),f319(f319(f74(a925),f319(f29(x89901),x89902)),f319(f29(x89901),x89903)))
% 28.25/28.12 [10214]~P26(x102141,f932(f932(x102141,a923),a923),f319(f319(f7(x102141,f932(f931(x102141,x102141),a923),f932(f932(x102141,a923),a923)),f319(f319(f8(f932(x102141,a923),f932(f932(f931(x102141,x102141),a923),f932(f932(x102141,a923),a923)),x102141),f54(x102141)),f319(f319(f7(x102141,f932(x102141,a923),f932(x102141,a923)),f301(x102141)),f180(f932(x102141,a923))))),x102143),x102142)+~P1(f319(f55(x102141),x102142))+E(f319(f29(f932(x102141,a923)),f319(f319(f54(x102141),x102142),x102143)),f319(f29(x102141),x102142))
% 28.25/28.12 [10509]~P41(f932(x105091,a923),f932(x105091,a923),x105092)+~P1(f319(f319(f226(f932(x105091,a923)),x105093),f319(x105092,f87(f932(x105091,a923),f319(f319(f7(f932(x105091,a923),f932(x105091,a923),f932(x105091,a923)),f319(f319(f8(f932(x105091,a923),f932(f932(x105091,a923),f932(x105091,a923)),f932(x105091,a923)),f102(f932(x105091,a923))),f319(f319(f7(f932(x105091,a923),f932(x105091,a923),f932(x105091,a923)),f319(f319(f8(f932(x105091,a923),f932(f932(x105091,a923),f932(x105091,a923)),f932(x105091,a923)),f102(f932(x105091,a923))),x105092)),x105093))),f88(f932(x105091,a923),x105092))))))+P1(f319(f319(f226(f932(x105091,a923)),f87(f932(x105091,a923),f319(f319(f7(f932(x105091,a923),f932(x105091,a923),f932(x105091,a923)),f319(f319(f8(f932(x105091,a923),f932(f932(x105091,a923),f932(x105091,a923)),f932(x105091,a923)),f102(f932(x105091,a923))),f319(f319(f7(f932(x105091,a923),f932(x105091,a923),f932(x105091,a923)),f319(f319(f8(f932(x105091,a923),f932(f932(x105091,a923),f932(x105091,a923)),f932(x105091,a923)),f102(f932(x105091,a923))),x105092)),x105093))),f88(f932(x105091,a923),x105092)))),f319(x105092,f87(f932(x105091,a923),f319(f319(f7(f932(x105091,a923),f932(x105091,a923),f932(x105091,a923)),f319(f319(f8(f932(x105091,a923),f932(f932(x105091,a923),f932(x105091,a923)),f932(x105091,a923)),f102(f932(x105091,a923))),f319(f319(f7(f932(x105091,a923),f932(x105091,a923),f932(x105091,a923)),f319(f319(f8(f932(x105091,a923),f932(f932(x105091,a923),f932(x105091,a923)),f932(x105091,a923)),f102(f932(x105091,a923))),x105092)),x105093))),f88(f932(x105091,a923),x105092))))))
% 28.25/28.12 [8221]~P99(x82211)+P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x82213)))+E(f319(f319(f236(x82211),x82212),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),x82213),x82213)),a89))),f72(x82211))
% 28.25/28.12 [8315]~P99(x83151)+P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x83153)))+E(f319(f319(f236(x83151),f319(f95(x83151),x83152)),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),x83153),x83153)),a89))),f72(x83151))
% 28.25/28.12 [9713]~P99(x97131)+~P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x97133)))+E(f319(f319(f236(x97131),x97132),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),x97133),x97133)),a89))),f319(f319(f80(x97131,x97131),f319(f319(f236(x97131),x97132),f319(f95(a925),x97133))),f319(f319(f18(x97131,x97131,x97131),f319(f319(f8(x97131,f932(x97131,x97131),x97131),f75(x97131)),f319(f75(x97131),x97132))),f5(x97131))))
% 28.25/28.12 [9781]~P99(x97811)+~P1(f319(f319(f226(a1),f2(a1)),f319(f95(a1),x97813)))+E(f319(f319(f236(x97811),f319(f95(x97811),x97812)),f319(f95(a925),f319(f319(f23(a1),f319(f319(f74(a1),x97813),x97813)),a89))),f319(f319(f80(x97811,x97811),f319(f319(f236(x97811),f319(f95(x97811),x97812)),f319(f95(a925),x97813))),f319(f319(f18(x97811,x97811,x97811),f319(f319(f8(x97811,f932(x97811,x97811),x97811),f75(x97811)),f319(f75(x97811),f319(f95(x97811),x97812)))),f5(x97811))))
% 28.25/28.12 [10123]~P1(f319(f129(x101231),x101233))+~P1(f319(f319(f321(x101231),x101232),f319(f164(x101231),x101233)))+E(f319(f319(f130(x101231),f319(f181(f926(x101231)),f169(x101231,f319(f319(f8(a923,a923,x101231),a314),f319(f319(f7(x101231,x101231,a923),a316),x101232)),f319(f160(x101231),x101233)))),f319(f160(x101231),x101233)),f319(f319(f143(x101231),x101232),f319(f160(x101231),f169(x101231,f319(f319(f8(a923,a923,x101231),a314),f319(f319(f7(x101231,x101231,a923),a316),x101232)),x101233))))
% 28.25/28.12 [10183]P1(f319(f319(f226(f932(f931(x101831,x101831),a923)),f299(x101831,x101832)),x101833))+~P1(f319(f319(f226(f932(f931(x101831,x101831),a923)),f299(x101831,f180(f932(f931(x101831,x101831),a923)))),x101833))+~P1(f319(f319(f226(f932(f931(x101831,x101831),a923)),f319(f319(f281(x101831,x101831,x101831),f319(f319(f93(f932(f931(x101831,x101831),a923)),f299(x101831,x101832)),x101833)),x101832)),x101833))
% 28.25/28.12 [10036]~P1(f319(f55(x100361),f319(f254(x100361),x100363)))+~P1(f319(f55(x100361),f319(f254(x100361),x100362)))+P1(f319(f55(x100361),f319(f254(x100361),f319(f319(f18(x100361,a923,a923),f319(f319(f8(a923,f932(a923,a923),x100361),a318),x100362)),x100363))))
% 28.25/28.12 [10334]P1(f319(f319(f226(f932(f931(x103341,x103341),a923)),f319(f319(f281(x103341,x103341,x103341),x103342),f299(x103341,x103342))),x103343))+~P1(f319(f319(f226(f932(f931(x103341,x103341),a923)),x103342),x103343))+~P1(f319(f319(f226(f932(f931(x103341,x103341),a923)),f319(f319(f281(x103341,x103341,x103341),f319(f319(f93(f932(f931(x103341,x103341),a923)),f319(f319(f281(x103341,x103341,x103341),x103342),f299(x103341,x103342))),x103343)),x103342)),x103343))
% 28.25/28.12 [10284]~P126(x102842)+E(x102841,f2(x102842))+~E(f319(f319(f74(x102842),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))))),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))))),f2(x102842))
% 28.25/28.12 [10285]~P126(x102852)+E(x102851,f2(x102852))+~E(f319(f319(f74(x102852),f319(f319(f236(x102852),x102851),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(x102852),x102853),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(x102852))
% 28.25/28.12 [10291]~P1(f319(f129(x102911),x102913))+~P1(f319(f319(f321(x102911),x102912),f319(f164(x102911),x102913)))+E(f319(f160(x102911),f319(f163(x102911),f319(f319(f130(x102911),f319(f181(f926(x102911)),f169(x102911,f319(f319(f8(a923,a923,x102911),a314),f319(f319(f7(x102911,x102911,a923),a316),x102912)),x102913))),x102913))),f169(x102911,f319(f319(f8(a923,a923,x102911),a314),f319(f319(f7(x102911,x102911,a923),a316),x102912)),f319(f160(x102911),x102913)))
% 28.25/28.12 [10380]~P126(x103802)+E(x103801,f2(x103802))+P1(f319(f319(f227(x103802),f2(x103802)),f319(f319(f74(x103802),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))))),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)))))))
% 28.25/28.12 [10381]~P126(x103812)+E(x103811,f2(x103812))+P1(f319(f319(f227(x103812),f2(x103812)),f319(f319(f74(x103812),f319(f319(f236(x103812),x103811),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(x103812),x103813),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)))))))
% 28.25/28.12 [10437]~P126(x104371)+P1(f319(f319(f226(x104371),f2(x104371)),x104372))+~P1(f319(f319(f226(x104371),f2(x104371)),f319(f319(f236(x104371),x104372),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)))),x104373)))))
% 28.25/28.12 [5700]~P15(x57001,x57004,x57003)+P15(x57001,x57002,x57003)+~P15(x57001,x57002,x57004)
% 28.25/28.12 [5167]~E(x51672,f84(x51673,x51671))+P1(f319(x51671,x51672))+~P1(f319(x51671,x51674))
% 28.25/28.12 [5418]E(f62(x54183,x54182,x54184),x54182)+E(x54181,f757(x54182,x54183,x54184))+~P1(f319(x54184,x54181))
% 28.25/28.12 [6732]E(f62(x67321,x67322,x67323),f79(x67321,x67323))+~E(f798(x67322,x67321,x67323,x67324),x67324)+~P1(f319(x67323,x67324))
% 28.25/28.12 [6947]~P38(x69472,x69474)+~P38(x69471,x69473)+P38(f931(x69471,x69472),f312(x69471,x69472,x69473,x69474))
% 28.25/28.12 [6948]~P39(x69482,x69484)+~P39(x69481,x69483)+P39(f931(x69481,x69482),f312(x69481,x69482,x69483,x69484))
% 28.25/28.12 [5357]~P8(x53574,x53571)+~E(f319(x53571,x53572),f319(x53571,x53573))+P1(f319(f319(x53571,x53572),x53573))
% 28.25/28.12 [5514]~P8(x55144,x55141)+E(f319(x55141,x55142),f319(x55141,x55143))+~P1(f319(f319(x55141,x55142),x55143))
% 28.25/28.12 [5515]~P17(x55154,x55151)+E(f319(x55151,x55152),f319(x55151,x55153))+~P1(f319(f319(x55151,x55152),x55153))
% 28.25/28.12 [5607]~P20(x56073,x56074,x56071)+E(f319(x56071,x56072),f319(f57(x56073,x56074),x56072))+~P1(f319(f55(x56073),x56072))
% 28.25/28.12 [5608]~P10(x56083,x56084,x56081)+E(f319(x56081,x56082),f319(f57(x56083,x56084),x56082))+~P1(f319(f55(x56083),x56082))
% 28.25/28.12 [5733]~P8(x57334,x57331)+~P1(f319(f319(x57331,x57333),x57332))+P1(f319(f319(x57331,x57332),x57333))
% 28.25/28.12 [5734]~P55(x57344,x57341)+~P1(f319(f319(x57341,x57343),x57342))+P1(f319(f319(x57341,x57342),x57343))
% 28.25/28.12 [5735]~P17(x57354,x57351)+~P1(f319(f319(x57351,x57353),x57352))+P1(f319(f319(x57351,x57352),x57353))
% 28.25/28.12 [5736]~P17(x57363,x57361)+P1(f319(f319(x57361,x57362),x57362))+~P1(f319(f319(x57361,x57364),x57362))
% 28.25/28.12 [5737]~P17(x57373,x57371)+P1(f319(f319(x57371,x57372),x57372))+~P1(f319(f319(x57371,x57372),x57374))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [5834]E(x58341,x58342)+~P1(f319(f42(x58343,x58344),x58342))+~P1(f319(f42(x58343,x58344),x58341))
% 28.25/28.12 [6026]~P79(x60262)+E(f223(x60261,x60262,x60263,x60264),f2(x60262))+P1(f319(f55(x60261),x60264))
% 28.25/28.12 [6076]~P8(x60763,x60762)+~P1(f319(x60761,x60764))+P1(f319(x60761,f839(x60761,x60762,x60763)))
% 28.25/28.12 [6171]~P1(f319(f307(x61711,x61712),x61714))+P1(f319(f307(x61711,x61712),x61713))+~P1(f319(f319(x61712,x61713),x61714))
% 28.25/28.12 [6172]~P1(f319(f307(x61721,x61722),x61724))+P1(f319(f307(x61721,x61722),x61723))+~P1(f319(f319(x61722,x61723),x61724))
% 28.25/28.12 [6173]~P1(f319(f307(x61731,x61732),x61734))+P1(f319(f307(x61731,x61732),x61733))+~P1(f319(f319(x61732,x61733),x61734))
% 28.25/28.12 [6606]P52(x66061,x66062,x66063,x66064)+P1(f319(f319(x66062,x66064),x66063))+~P1(f319(f319(x66062,x66063),x66064))
% 28.25/28.12 [6981]~P30(x69811,x69813,x69814)+P1(f319(x69811,x69812))+~P1(f319(f319(f321(a1),x69812),f295(a1,x69813,x69814)))
% 28.25/28.12 [7174]~P8(x71741,x71743)+~P1(f319(x71742,x71744))+P1(f319(f319(f321(x71741),f839(x71742,x71743,x71741)),f262(x71741,x71743)))
% 28.25/28.12 [8059]E(x80591,f2(a925))+~P1(f319(x80592,x80593))+P1(f319(x80592,f791(x80592,x80593,x80591,x80594)))
% 28.25/28.12 [8141]~P4(x81412)+~P1(f319(f129(x81411),x81414))+P1(f319(f129(x81411),f142(x81411,x81412,x81413,x81414)))
% 28.25/28.12 [8187]E(f62(x81871,x81872,x81873),f79(x81871,x81873))+~P1(f319(x81873,x81874))+P1(f319(x81873,f798(x81872,x81871,x81873,x81874)))
% 28.25/28.12 [8367]~P1(f319(f55(x83672),x83674))+~P1(f319(f55(x83671),x83673))+P1(f319(f55(f933(x83671,x83672)),f305(x83671,x83672,x83673,x83674)))
% 28.25/28.12 [8368]~P1(f319(f55(x83682),x83684))+~P1(f319(f55(x83681),x83683))+P1(f319(f55(f933(x83681,x83682)),f305(x83681,x83682,x83683,x83684)))
% 28.25/28.12 [8369]~P1(f319(f129(x83692),x83694))+~P1(f319(f129(x83691),x83693))+P1(f319(f129(f931(x83691,x83692)),f53(x83691,x83692,x83693,x83694)))
% 28.25/28.12 [8372]P1(f319(f319(f321(f926(x83721)),f319(f319(f126(x83721),x83722),x83723)),f153(x83721,x83724)))+~P1(f319(f319(f321(f926(x83721)),x83723),f153(x83721,x83724)))+~P1(f319(f319(f321(f926(x83721)),x83722),f153(x83721,x83724)))
% 28.25/28.12 [8654]E(x86541,f2(a925))+P1(f319(x86542,x86543))+~P1(f319(x86542,f794(x86542,x86543,x86541,x86544)))
% 28.25/28.12 [8693]~P4(x86933)+~P1(f319(f129(x86931),f142(x86931,x86933,x86934,x86932)))+P1(f319(f129(x86931),x86932))
% 28.25/28.12 [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)))
% 28.25/28.12 [8979]~P1(f319(f319(f321(f931(x89791,x89791)),f319(f319(f244(x89791,x89791),x89792),x89794)),f299(x89791,x89793)))+P1(f319(f319(f321(x89791),x89792),f308(x89791,x89793)))+~P1(f319(f319(f321(x89791),x89794),f308(x89791,x89793)))
% 28.25/28.12 [5336]~P79(x53362)+E(f319(f319(f6(x53361,x53362),x53363),x53364),f2(x53362))+P1(f319(f55(x53361),x53364))
% 28.25/28.12 [5337]~P79(x53372)+E(f319(f319(f6(x53371,x53372),x53373),x53374),f2(x53372))+P1(f319(f55(x53371),x53374))
% 28.25/28.12 [5338]~P79(x53382)+E(f319(f319(f6(x53381,x53382),x53383),x53384),f2(x53382))+P1(f319(f55(x53381),x53384))
% 28.25/28.12 [5339]~P78(x53392)+E(f319(f319(f9(x53391,x53392),x53393),x53394),f72(x53392))+P1(f319(f55(x53391),x53394))
% 28.25/28.12 [5340]~P78(x53402)+E(f319(f319(f9(x53401,x53402),x53403),x53404),f72(x53402))+P1(f319(f55(x53401),x53404))
% 28.25/28.12 [5341]~P78(x53412)+E(f319(f319(f9(x53411,x53412),x53413),x53414),f72(x53412))+P1(f319(f55(x53411),x53414))
% 28.25/28.12 [5478]~P80(x54783)+E(x54781,x54782)+~E(f319(f319(f74(x54783),x54784),x54781),f319(f319(f74(x54783),x54784),x54782))
% 28.25/28.12 [5479]~P80(x54793)+E(x54791,x54792)+~E(f319(f319(f74(x54793),x54794),x54791),f319(f319(f74(x54793),x54794),x54792))
% 28.25/28.12 [5480]~P81(x54803)+E(x54801,x54802)+~E(f319(f319(f74(x54803),x54804),x54801),f319(f319(f74(x54803),x54804),x54802))
% 28.25/28.12 [5481]~P80(x54813)+E(x54811,x54812)+~E(f319(f319(f74(x54813),x54811),x54814),f319(f319(f74(x54813),x54812),x54814))
% 28.25/28.12 [5482]~P80(x54823)+E(x54821,x54822)+~E(f319(f319(f74(x54823),x54821),x54824),f319(f319(f74(x54823),x54822),x54824))
% 28.25/28.12 [5575]~P123(x55751)+~E(x55753,f319(f319(f75(x55751),x55752),x55754))+P1(f319(f319(f279(x55751),x55752),x55753))
% 28.25/28.12 [5603]~P6(x56033)+E(x56031,f180(f932(x56032,a923)))+E(f319(f319(f33(x56032,x56033),x56031),f319(f16(x56033,x56032),x56034)),x56034)
% 28.25/28.12 [5604]~P6(x56043)+E(x56041,f180(f932(x56042,a923)))+E(f319(f319(f34(x56042,x56043),x56041),f319(f16(x56043,x56042),x56044)),x56044)
% 28.25/28.12 [5820]~P113(x58203)+E(x58201,x58202)+~E(f295(x58203,x58204,x58201),f319(f319(f301(x58203),x58202),f180(f932(x58203,a923))))
% 28.25/28.12 [5821]~P113(x58213)+E(x58211,x58212)+~E(f295(x58213,x58211,x58212),f319(f319(f301(x58213),x58214),f180(f932(x58213,a923))))
% 28.25/28.12 [5882]~P36(x58823,x58821,x58824)+P36(x58823,x58821,f319(f319(f143(x58823),x58822),x58824))+P1(f319(x58821,x58822))
% 28.25/28.12 [5984]~P32(x59841,x59842,x59844)+~P1(f319(x59842,x59843))+P32(x59841,x59842,f319(f319(f143(x59841),x59843),x59844))
% 28.25/28.12 [6128]P1(f319(x61281,x61282))+~P1(f319(f240(x61283,x61281),x61284))+~P1(f319(f319(f321(x61283),x61282),x61284))
% 28.25/28.12 [6137]~P32(x61371,x61372,x61374)+~P32(x61371,x61372,x61373)+P32(x61371,x61372,f319(f319(f126(x61371),x61373),x61374))
% 28.25/28.12 [6152]P34(x61521,x61522,x61523)+~P34(x61521,x61522,f319(f319(f143(x61521),x61524),x61523))+P1(f319(x61522,x61524))
% 28.25/28.12 [6153]P36(x61531,x61532,x61533)+~P36(x61531,x61532,f319(f319(f143(x61531),x61534),x61533))+P1(f319(x61532,x61534))
% 28.25/28.12 [6231]P34(x62311,x62312,x62313)+P34(x62311,x62312,x62314)+~P34(x62311,x62312,f319(f319(f126(x62311),x62314),x62313))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [6321]P1(f319(x63211,x63212))+~E(f319(f128(x63213,x63211),x63214),x63214)+~P1(f319(f319(f321(x63213),x63212),f319(f164(x63213),x63214)))
% 28.25/28.12 [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))
% 28.25/28.12 [6344]P34(x63441,x63442,x63443)+~P1(f319(x63442,x63444))+~P1(f319(f319(f321(x63441),x63444),f319(f164(x63441),x63443)))
% 28.25/28.12 [6345]P34(x63451,x63452,x63453)+~P1(f319(x63452,x63454))+~P1(f319(f319(f321(x63451),x63454),f319(f164(x63451),x63453)))
% 28.25/28.12 [6346]P34(x63461,x63462,x63463)+~P1(f319(x63462,x63464))+~P1(f319(f319(f321(x63461),x63464),f319(f164(x63461),x63463)))
% 28.25/28.12 [6383]~P32(x63833,x63831,x63834)+P1(f319(x63831,x63832))+~P1(f319(f319(f321(x63833),x63832),f319(f164(x63833),x63834)))
% 28.25/28.12 [6384]~P32(x63843,x63841,x63844)+P1(f319(x63841,x63842))+~P1(f319(f319(f321(x63843),x63842),f319(f164(x63843),x63844)))
% 28.25/28.12 [6385]~P32(x63853,x63851,x63854)+P1(f319(x63851,x63852))+~P1(f319(f319(f321(x63853),x63852),f319(f164(x63853),x63854)))
% 28.25/28.12 [6387]~E(f319(f128(x63871,x63872),x63873),f105(x63871))+~P1(f319(x63872,x63874))+~P1(f319(f319(f321(x63871),x63874),f319(f164(x63871),x63873)))
% 28.25/28.12 [6388]~E(f169(x63883,x63881,x63884),x63884)+P1(f319(x63881,x63882))+~P1(f319(f319(f321(x63883),x63882),f319(f164(x63883),x63884)))
% 28.25/28.12 [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)))
% 28.25/28.12 [6562]P1(f319(x65621,x65622))+~P1(f319(f152(x65623,x65621),x65624))+~P1(f319(f319(f321(x65623),x65622),f319(f164(x65623),x65624)))
% 28.25/28.12 [6701]~P31(x67011,x67013,x67014)+P1(f319(x67011,x67012))+~P1(f319(f319(f321(a925),x67012),f319(f294(a925,x67013),x67014)))
% 28.25/28.12 [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))
% 28.25/28.12 [6984]~P4(x69841)+E(f319(f319(f23(f932(x69841,a923)),f319(f294(x69841,x69842),x69843)),f319(f294(x69841,x69842),x69844)),f319(f294(x69841,x69844),x69843))+~P1(f319(f319(f226(x69841),x69842),x69844))
% 28.25/28.12 [7055]~E(x70553,x70554)+E(x70551,f2(a925))+P1(f319(f319(f321(x70552),x70553),f319(f164(x70552),f161(x70552,x70551,x70554))))
% 28.25/28.12 [7337]~P1(f319(f319(f321(f926(x73371)),x73374),f153(x73371,x73373)))+P1(f319(f319(f321(x73371),x73372),x73373))+~P1(f319(f319(f321(x73371),x73372),f319(f164(x73371),x73374)))
% 28.25/28.12 [7344]~P38(x73441,x73442)+P1(f319(f319(f321(x73441),f630(x73442,x73441,x73443)),x73443))+~P1(f319(f319(f321(x73441),x73444),x73443))
% 28.25/28.12 [7377]~P26(x73772,x73771,x73773,x73774)+E(f319(f29(x73771),f319(f302(x73772,x73771,x73773),x73774)),f319(f29(x73772),x73774))+~P1(f319(f55(x73772),x73774))
% 28.25/28.12 [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))
% 28.25/28.12 [7401]~P79(x74011)+E(f319(f319(f319(f59(x74011,x74012,f74(x74011)),x74013),f2(x74011)),x74014),f319(f319(f6(x74012,x74011),x74013),x74014))+~P1(f319(f55(x74012),x74014))
% 28.25/28.12 [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))
% 28.25/28.12 [7403]~P78(x74031)+E(f319(f319(f319(f59(x74031,x74032,f75(x74031)),x74033),f72(x74031)),x74034),f319(f319(f9(x74032,x74031),x74033),x74034))+~P1(f319(f55(x74032),x74034))
% 28.25/28.12 [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))
% 28.25/28.12 [7432]P26(x74321,x74322,x74323,x74324)+~E(f319(f29(x74322),f319(f302(x74321,x74322,x74323),x74324)),f319(f29(x74321),x74324))+~P1(f319(f55(x74321),x74324))
% 28.25/28.12 [7621]~P79(x76211)+E(f319(f319(f74(x76211),f319(x76212,x76213)),f319(f319(f6(a925,x76211),x76212),f297(a925,x76213,x76214))),f319(f319(f6(a925,x76211),x76212),f295(a925,x76213,x76214)))+~P1(f319(f319(f226(a925),x76213),x76214))
% 28.25/28.12 [7630]~P79(x76301)+~P26(x76302,x76301,x76303,x76304)+E(f319(f319(f6(x76301,x76301),f25(x76301)),f319(f302(x76302,x76301,x76303),x76304)),f319(f319(f6(x76302,x76301),x76303),x76304))
% 28.25/28.12 [7631]~P78(x76311)+~P26(x76312,x76311,x76313,x76314)+E(f319(f319(f9(x76311,x76311),f25(x76311)),f319(f302(x76312,x76311,x76313),x76314)),f319(f319(f9(x76312,x76311),x76313),x76314))
% 28.25/28.12 [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))
% 28.25/28.12 [7680]E(f319(f29(f933(x76801,x76802)),f305(x76801,x76802,x76803,x76804)),f319(f319(f74(a925),f319(f29(x76801),x76803)),f319(f29(x76802),x76804)))+~P1(f319(f55(x76802),x76804))+~P1(f319(f55(x76801),x76803))
% 28.25/28.12 [7760]E(x77601,x77602)+P1(f319(f319(f321(x77603),x77601),f319(f164(x77603),f162(x77603,x77602,x77604))))+~P1(f319(f319(f321(x77603),x77601),f319(f164(x77603),x77604)))
% 28.25/28.12 [7903]~P1(f319(f319(f226(f932(x79031,a923)),x79034),f319(x79033,x79034)))+~P1(f319(f319(f321(x79031),x79032),x79034))+P1(f319(f319(f321(x79031),x79032),f88(f932(x79031,a923),x79033)))
% 28.25/28.12 [7988]~P79(x79881)+E(f319(f319(f74(x79881),f319(f319(f6(a925,x79881),x79882),f319(f294(a925,x79883),x79884))),f319(x79882,x79884)),f319(f319(f6(a925,x79881),x79882),f319(f294(a925,x79883),f319(a104,x79884))))+P1(f319(f319(f227(a925),x79884),x79883))
% 28.25/28.12 [8038]~P26(x80381,x80382,x80383,f234(f932(x80381,a923)))+~P1(f319(f55(x80382),x80384))+P1(f319(f55(x80381),f319(f303(x80381,x80382,x80383),x80384)))
% 28.25/28.12 [8156]P1(f319(f319(f321(f926(x81561)),f319(f319(f143(x81561),x81562),x81563)),f153(x81561,x81564)))+~P1(f319(f319(f321(f926(x81561)),x81563),f153(x81561,x81564)))+~P1(f319(f319(f321(x81561),x81562),x81564))
% 28.25/28.12 [8205]E(x82051,x82052)+~P1(f319(f319(f321(x82053),x82051),f319(f164(x82053),f162(x82053,x82052,x82054))))+P1(f319(f319(f321(x82053),x82051),f319(f164(x82053),x82054)))
% 28.25/28.12 [8245]~E(f319(f302(x82453,x82451,x82454),f234(f932(x82453,a923))),f234(f932(x82451,a923)))+P1(f319(f55(x82451),x82452))+~P1(f319(f55(x82453),f319(f303(x82453,x82451,x82454),x82452)))
% 28.25/28.12 [8340]~P26(x83401,x83403,x83404,x83402)+P1(f319(f55(x83401),x83402))+~P1(f319(f55(x83403),f319(f302(x83401,x83403,x83404),x83402)))
% 28.25/28.12 [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))
% 28.25/28.12 [8362]~E(x83622,x83623)+P1(f319(f319(f321(f931(x83621,x83621)),f319(f319(f244(x83621,x83621),x83622),x83623)),f255(x83621,x83624)))+~P1(f319(f319(f321(x83621),x83622),x83624))
% 28.25/28.12 [8397]~P79(x83971)+E(f319(f319(f74(x83971),f319(f319(f6(a925,x83971),x83972),f295(a925,x83973,x83974))),f319(x83972,f319(a104,x83974))),f319(f319(f6(a925,x83971),x83972),f295(a925,x83973,f319(a104,x83974))))+P1(f319(f319(f227(a925),f319(a104,x83974)),x83973))
% 28.25/28.12 [8455]~E(x84552,x84554)+P1(f319(f319(f321(f931(x84551,x84551)),f319(f319(f244(x84551,x84551),x84552),x84554)),f299(x84551,x84553)))+P1(f319(f319(f321(x84551),x84552),f319(f256(x84551,x84551),x84553)))
% 28.25/28.12 [8457]P1(f319(x84571,x84572))+~P1(f319(x84571,f319(f319(f156(x84573),x84574),f684(x84571,x84574,x84573))))+~P1(f319(f319(f321(x84573),x84572),f319(f164(x84573),x84574)))
% 28.25/28.12 [8599]~P1(f319(f319(f321(x85991),x85992),f308(x85991,x85994)))+P1(f319(f319(f321(f926(x85991)),f319(f319(f143(x85991),x85992),x85993)),f308(f926(x85991),f149(x85991,x85994))))+~P1(f319(f319(f321(f926(x85991)),x85993),f308(f926(x85991),f149(x85991,x85994))))
% 28.25/28.12 [8614]~P26(x86142,x86143,x86144,f896(x86144,x86143,x86142,x86141))+P26(x86142,x86143,x86144,f32(f932(x86142,a923),x86141))+E(x86141,f180(f932(f932(x86142,a923),a923)))
% 28.25/28.12 [8888]E(x88881,x88882)+~P1(f319(f319(f321(f931(x88883,x88883)),f319(f319(f244(x88883,x88883),x88881),x88882)),f299(x88883,x88884)))+P1(f319(f319(f321(x88883),x88881),f319(f256(x88883,x88883),x88884)))
% 28.25/28.12 [9172]E(x91721,f2(a925))+P1(f319(x91722,x91723))+P1(f319(f319(f321(x91724),f794(x91722,x91723,x91721,x91724)),f319(f164(x91724),f161(x91724,x91721,x91723))))
% 28.25/28.12 [9184]E(x91841,f2(a925))+~P1(f319(x91843,x91844))+P1(f319(f319(f321(x91842),f791(x91843,x91844,x91841,x91842)),f319(f164(x91842),f161(x91842,x91841,x91844))))
% 28.25/28.12 [9186]~P27(x91861,x91862,x91863,f234(f932(x91861,a923)),f234(f932(x91862,a923)))+~P1(f319(f55(x91862),x91864))+P1(f319(f55(x91861),f319(f303(x91861,x91862,x91863),x91864)))
% 28.25/28.12 [9189]P26(x91892,x91893,x91894,f32(f932(x91892,a923),x91891))+E(x91891,f180(f932(f932(x91892,a923),a923)))+P1(f319(f319(f321(f932(x91892,a923)),f896(x91894,x91893,x91892,x91891)),x91891))
% 28.25/28.12 [9306]~P27(x93063,x93061,x93064,f234(f932(x93063,a923)),f234(f932(x93061,a923)))+P1(f319(f55(x93061),x93062))+~P1(f319(f55(x93063),f319(f303(x93063,x93061,x93064),x93062)))
% 28.25/28.12 [9323]P1(f319(f55(x93231),x93232))+~P1(f319(f55(x93234),f319(f302(x93231,x93234,x93233),x93232)))+P1(f319(f319(f321(x93231),f467(x93233,x93234,x93232,x93231)),x93232))
% 28.25/28.12 [9420]~P6(x94202)+E(f319(f319(f58(x94201,x94202,f319(f319(f8(x94202,f932(x94202,x94202),x94201),f102(x94202)),x94203)),f180(x94202)),x94204),f319(f319(f33(x94201,x94202),x94204),x94203))+~P1(f319(f55(x94201),x94204))
% 28.25/28.12 [9421]~P6(x94212)+E(f319(f319(f58(x94211,x94212,f319(f319(f8(x94212,f932(x94212,x94212),x94211),f93(x94212)),x94213)),f234(x94212)),x94214),f319(f319(f34(x94211,x94212),x94214),x94213))+~P1(f319(f55(x94211),x94214))
% 28.25/28.12 [9505]P1(f319(x95051,x95052))+~P1(f319(x95051,f319(f319(f156(x95053),x95054),f719(x95052,x95051,x95054,x95053))))+~P1(f319(f319(f321(x95053),x95052),f319(f164(x95053),x95054)))
% 28.25/28.12 [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))))
% 28.25/28.12 [9527]E(x95271,x95272)+~P1(f319(f319(f321(f931(x95273,x95273)),f319(f319(f244(x95273,x95273),x95271),x95272)),f299(x95273,x95274)))+P1(f319(f319(f321(f931(x95273,x95273)),f319(f319(f244(x95273,x95273),x95271),x95272)),f319(f319(f281(x95273,x95273,x95273),x95274),f299(x95273,x95274))))
% 28.25/28.12 [9578]~E(f319(f181(f926(x95781)),x95782),f319(f181(f926(x95781)),x95783))+~P1(f319(f319(f321(f931(f926(x95781),f926(x95781))),f319(f319(f244(f926(x95781),f926(x95781)),x95782),x95783)),f139(x95781,x95784)))+P1(f319(f319(f321(f931(f926(x95781),f926(x95781))),f319(f319(f244(f926(x95781),f926(x95781)),x95782),x95783)),f137(x95781,x95784)))
% 28.25/28.12 [9600]E(x96001,x96002)+P1(f319(f319(f321(f931(x96003,x96003)),f319(f319(f244(x96003,x96003),x96001),x96002)),f299(x96003,x96004)))+~P1(f319(f319(f321(f931(x96003,x96003)),f319(f319(f244(x96003,x96003),x96001),x96002)),f319(f319(f281(x96003,x96003,x96003),x96004),f299(x96003,x96004))))
% 28.25/28.12 [9818]P32(x98181,f319(f319(f18(x98181,a923,a923),f319(f319(f8(a923,f932(a923,a923),x98181),a318),f319(f319(f8(a923,a923,x98181),a314),x98182))),f319(a316,x98183)),x98184)+~P1(f319(x98182,x98183))+~P36(x98181,x98182,f319(f319(f143(x98181),x98183),x98184))
% 28.25/28.12 [9997]~P32(x99971,f319(f319(f18(x99971,a923,a923),f319(f319(f8(a923,f932(a923,a923),x99971),a318),f319(f319(f8(a923,a923,x99971),a314),x99972))),f319(a316,x99973)),x99974)+~P1(f319(x99972,x99973))+P36(x99971,x99972,f319(f319(f143(x99971),x99973),x99974))
% 28.25/28.12 [10001]~P36(x100011,x100012,x100014)+~P32(x100011,f319(f319(f18(x100011,a923,a923),f319(f319(f8(a923,f932(a923,a923),x100011),a318),f319(f319(f8(a923,a923,x100011),a314),x100012))),f319(a316,x100013)),x100014)+P36(x100011,x100012,f319(f319(f143(x100011),x100013),x100014))
% 28.25/28.12 [10037]~P70(x100371)+E(f319(f319(f6(a925,x100371),f319(f319(f18(a925,x100371,x100371),f319(f319(f8(x100371,f932(x100371,x100371),a925),f23(x100371)),x100372)),f319(f319(f8(a925,x100371,a925),x100372),f319(f319(f7(a925,a925,a925),f74(a925)),f72(a925))))),f295(a925,x100373,x100374)),f2(x100371))+P1(f319(f319(f226(a925),x100373),x100374))
% 28.25/28.12 [10283]~P38(x102832,x102834)+~P26(x102832,x102831,x102833,f234(f932(x102832,a923)))+P38(x102831,f319(f302(f931(x102832,x102832),f931(x102831,x102831),f250(x102832,x102831,x102832,x102831,x102833,x102833)),x102834))
% 28.25/28.12 [10473]~E(f319(f181(f926(x104731)),x104733),f319(f181(f926(x104731)),x104732))+P1(f319(f319(f321(f931(f926(x104731),f926(x104731))),f319(f319(f244(f926(x104731),f926(x104731)),x104732),x104733)),f150(x104731,x104734)))+~P1(f319(f319(f249(x104731,x104731,a923),f319(f319(f7(x104731,f932(f931(x104731,x104731),a923),f932(x104731,a923)),f319(f319(f8(f932(x104731,f932(f932(f931(x104731,x104731),a923),a923)),f932(f932(f931(x104731,x104731),a923),f932(x104731,a923)),x104731),f7(x104731,f932(f931(x104731,x104731),a923),a923)),f319(f319(f8(f932(x104731,f931(x104731,x104731)),f932(x104731,f932(f932(f931(x104731,x104731),a923),a923)),x104731),f319(f8(f931(x104731,x104731),f932(f932(f931(x104731,x104731),a923),a923),x104731),f321(f931(x104731,x104731)))),f244(x104731,x104731)))),x104734)),f686(x104734,x104733,x104732,x104731)))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [6376]E(x63761,x63762)+P1(f319(x63763,x63762))+~P1(f319(f319(f319(f301(x63764),x63761),x63763),x63762))
% 28.25/28.12 [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)))
% 28.25/28.12 [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)))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [6529]P1(f319(x65291,x65292))+~E(x65293,f319(f319(f74(a925),x65294),x65292))+~P1(f319(x65291,f319(f319(f23(a925),x65293),x65294)))
% 28.25/28.12 [6530]P1(f319(x65301,x65302))+~E(x65303,f319(f319(f74(a925),x65304),x65302))+~P1(f319(x65301,f319(f319(f23(a925),x65303),x65304)))
% 28.25/28.12 [6617]~P1(f319(x66172,x66173))+~P1(f319(f152(x66171,x66172),x66174))+P1(f319(f152(x66171,x66172),f319(f319(f143(x66171),x66173),x66174)))
% 28.25/28.12 [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)
% 28.25/28.12 [6681]~P107(x66811)+~P1(f319(f319(f226(x66811),x66812),x66814))+P1(f319(f319(f226(x66811),x66812),f319(f319(f102(x66811),x66813),x66814)))
% 28.25/28.12 [6682]~P107(x66821)+~P1(f319(f319(f226(x66821),x66822),x66823))+P1(f319(f319(f226(x66821),x66822),f319(f319(f102(x66821),x66823),x66824)))
% 28.25/28.12 [6683]~P4(x66831)+~P1(f319(f319(f226(x66831),x66832),x66834))+P1(f319(f319(f226(x66831),x66832),f319(f319(f225(x66831),x66833),x66834)))
% 28.25/28.12 [6684]~P4(x66841)+~P1(f319(f319(f226(x66841),x66842),x66844))+P1(f319(f319(f226(x66841),x66842),f319(f319(f225(x66841),x66843),x66844)))
% 28.25/28.12 [6685]~P4(x66851)+~P1(f319(f319(f226(x66851),x66852),x66853))+P1(f319(f319(f226(x66851),x66852),f319(f319(f225(x66851),x66853),x66854)))
% 28.25/28.12 [6686]~P4(x66861)+~P1(f319(f319(f226(x66861),x66862),x66863))+P1(f319(f319(f226(x66861),x66862),f319(f319(f225(x66861),x66863),x66864)))
% 28.25/28.12 [6687]~P107(x66871)+~P1(f319(f319(f227(x66871),x66872),x66874))+P1(f319(f319(f227(x66871),x66872),f319(f319(f102(x66871),x66873),x66874)))
% 28.25/28.12 [6688]~P107(x66881)+~P1(f319(f319(f227(x66881),x66882),x66883))+P1(f319(f319(f227(x66881),x66882),f319(f319(f102(x66881),x66883),x66884)))
% 28.25/28.12 [6689]~P4(x66891)+~P1(f319(f319(f227(x66891),x66892),x66894))+P1(f319(f319(f227(x66891),x66892),f319(f319(f225(x66891),x66893),x66894)))
% 28.25/28.12 [6690]~P4(x66901)+~P1(f319(f319(f227(x66901),x66902),x66904))+P1(f319(f319(f227(x66901),x66902),f319(f319(f225(x66901),x66903),x66904)))
% 28.25/28.12 [6691]~P4(x66911)+~P1(f319(f319(f227(x66911),x66912),x66913))+P1(f319(f319(f227(x66911),x66912),f319(f319(f225(x66911),x66913),x66914)))
% 28.25/28.12 [6692]~P4(x66921)+~P1(f319(f319(f227(x66921),x66922),x66923))+P1(f319(f319(f227(x66921),x66922),f319(f319(f225(x66921),x66923),x66924)))
% 28.25/28.12 [6693]~P121(x66931)+~P1(f319(f319(f279(x66931),x66932),x66934))+P1(f319(f319(f279(x66931),x66932),f319(f319(f75(x66931),x66933),x66934)))
% 28.25/28.12 [6694]~P121(x66941)+~P1(f319(f319(f279(x66941),x66942),x66943))+P1(f319(f319(f279(x66941),x66942),f319(f319(f75(x66941),x66943),x66944)))
% 28.25/28.12 [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)))
% 28.25/28.12 [6824]P1(f319(x68241,x68242))+~P1(f319(x68243,x68242))+~P1(f319(f319(f226(f932(x68244,a923)),x68243),x68241))
% 28.25/28.12 [6825]P1(f319(x68251,x68252))+~P1(f319(x68253,x68252))+~P1(f319(f319(f226(f932(x68254,a923)),x68253),x68251))
% 28.25/28.12 [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)))
% 28.25/28.12 [6872]~P1(f319(f152(x68721,x68722),x68724))+~P1(f319(f152(x68721,x68722),x68723))+P1(f319(f152(x68721,x68722),f319(f319(f126(x68721),x68723),x68724)))
% 28.25/28.12 [6980]E(x69801,f180(f932(x69802,a923)))+E(x69803,f180(f932(x69804,a923)))+~E(f319(f319(f246(x69804,x69802),x69803),f319(f16(f932(x69802,a923),x69804),x69801)),f180(f932(f931(x69804,x69802),a923)))
% 28.25/28.12 [6999]E(x69991,x69992)+P1(f319(f319(f321(x69993),x69991),x69994))+~P1(f319(f319(f321(x69993),x69991),f319(f319(f301(x69993),x69992),x69994)))
% 28.25/28.12 [7000]E(x70001,x70002)+P1(f319(f319(f321(x70003),x70001),x70004))+~P1(f319(f319(f321(x70003),x70001),f319(f319(f301(x70003),x70002),x70004)))
% 28.25/28.12 [7016]~P4(x70161)+P1(f319(f319(f226(x70161),x70162),x70163))+~P1(f319(f319(f226(x70161),x70162),f319(f319(f224(x70161),x70164),x70163)))
% 28.25/28.12 [7017]~P4(x70171)+P1(f319(f319(f226(x70171),x70172),x70173))+~P1(f319(f319(f226(x70171),x70172),f319(f319(f224(x70171),x70174),x70173)))
% 28.25/28.12 [7018]~P4(x70181)+P1(f319(f319(f226(x70181),x70182),x70183))+~P1(f319(f319(f226(x70181),x70182),f319(f319(f224(x70181),x70183),x70184)))
% 28.25/28.12 [7019]~P4(x70191)+P1(f319(f319(f226(x70191),x70192),x70193))+~P1(f319(f319(f226(x70191),x70192),f319(f319(f224(x70191),x70193),x70194)))
% 28.25/28.12 [7020]~P108(x70201)+P1(f319(f319(f226(x70201),x70202),x70203))+~P1(f319(f319(f226(x70201),x70202),f319(f319(f93(x70201),x70204),x70203)))
% 28.25/28.12 [7021]~P108(x70211)+P1(f319(f319(f226(x70211),x70212),x70213))+~P1(f319(f319(f226(x70211),x70212),f319(f319(f93(x70211),x70214),x70213)))
% 28.25/28.12 [7022]~P108(x70221)+P1(f319(f319(f226(x70221),x70222),x70223))+~P1(f319(f319(f226(x70221),x70222),f319(f319(f93(x70221),x70223),x70224)))
% 28.25/28.12 [7023]~P108(x70231)+P1(f319(f319(f226(x70231),x70232),x70233))+~P1(f319(f319(f226(x70231),x70232),f319(f319(f93(x70231),x70233),x70234)))
% 28.25/28.12 [7024]~P4(x70241)+P1(f319(f319(f227(x70241),x70242),x70243))+~P1(f319(f319(f227(x70241),x70242),f319(f319(f224(x70241),x70244),x70243)))
% 28.25/28.12 [7025]~P4(x70251)+P1(f319(f319(f227(x70251),x70252),x70253))+~P1(f319(f319(f227(x70251),x70252),f319(f319(f224(x70251),x70253),x70254)))
% 28.25/28.12 [7046]~E(f319(f319(f156(x70461),x70463),x70464),x70462)+P1(f319(f319(f321(x70461),x70462),f319(f164(x70461),x70463)))+~P1(f319(f319(f227(a925),x70464),f319(f181(f926(x70461)),x70463)))
% 28.25/28.12 [7056]~P4(x70561)+~P14(x70561,f319(f319(f143(x70561),x70562),f319(f319(f143(x70561),x70563),x70564)))+P1(f319(f319(f226(x70561),x70562),x70563))
% 28.25/28.12 [7111]~P4(x71111)+P14(x71111,f319(f319(f143(x71111),x71112),x71113))+~P14(x71111,f319(f319(f143(x71111),x71114),f319(f319(f143(x71111),x71112),x71113)))
% 28.25/28.12 [7201]~P32(x72012,x72011,x72013)+P1(f319(x72011,f319(f319(f156(x72012),x72013),x72014)))+~P1(f319(f319(f227(a925),x72014),f319(f181(f926(x72012)),x72013)))
% 28.25/28.12 [7220]E(x72201,f2(a1))+E(f319(f319(f30(a1),x72202),x72201),x72203)+~P1(f319(f43(x72202,x72201),f319(f319(f244(a1,a1),x72203),x72204)))
% 28.25/28.12 [7241]E(f39(a1,x72412,x72411),x72413)+E(x72411,f2(a1))+~P1(f319(f43(x72412,x72411),f319(f319(f244(a1,a1),x72414),x72413)))
% 28.25/28.12 [7358]P1(f319(f319(f321(x73581),x73582),x73583))+~P1(f319(f319(f321(x73581),x73582),x73584))+~P1(f319(f319(f226(f932(x73581,a923)),x73584),x73583))
% 28.25/28.12 [7359]P1(f319(f319(f321(x73591),x73592),x73593))+~P1(f319(f319(f321(x73591),x73592),x73594))+~P1(f319(f319(f226(f932(x73591,a923)),x73594),x73593))
% 28.25/28.12 [7360]P1(f319(f319(f321(x73601),x73602),x73603))+~P1(f319(f319(f321(x73601),x73602),x73604))+~P1(f319(f319(f226(f932(x73601,a923)),x73604),x73603))
% 28.25/28.12 [7361]P1(f319(f319(f321(x73611),x73612),x73613))+~P1(f319(f319(f321(x73611),x73612),x73614))+~P1(f319(f319(f227(f932(x73611,a923)),x73614),x73613))
% 28.25/28.12 [7362]P1(f319(f319(f321(x73621),x73622),x73623))+~P1(f319(f319(f321(x73621),x73622),x73624))+~P1(f319(f319(f226(f932(x73621,a923)),x73624),x73623))
% 28.25/28.12 [7373]~P117(x73731)+~E(x73733,f2(x73731))+P1(f319(f319(f279(x73731),f319(f319(f75(x73731),x73732),x73733)),f319(f319(f75(x73731),x73734),x73733)))
% 28.25/28.12 [7374]~P117(x73741)+~E(x73742,f2(x73741))+P1(f319(f319(f279(x73741),f319(f319(f75(x73741),x73742),x73743)),f319(f319(f75(x73741),x73742),x73744)))
% 28.25/28.12 [7476]P34(x74761,x74762,x74763)+~P1(f319(x74762,f319(f319(f156(x74761),x74763),x74764)))+~P1(f319(f319(f227(a925),x74764),f319(f181(f926(x74761)),x74763)))
% 28.25/28.12 [7588]~P3(x75882)+~P1(f319(f319(f227(f932(x75881,x75882)),x75883),x75884))+P1(f319(f319(f226(f932(x75881,x75882)),x75883),x75884))
% 28.25/28.12 [7669]~P15(x76691,x76692,x76694)+P15(x76691,x76692,f319(f319(f301(f924(x76691)),x76693),x76694))+~P15(x76691,x76692,f319(f319(f301(f924(x76691)),x76693),f180(f932(f924(x76691),a923))))
% 28.25/28.12 [7711]~P1(f319(f319(f321(x77111),x77112),x77114))+P1(f319(f319(f321(x77111),x77112),f31(f932(x77111,a923),x77113)))+~P1(f319(f319(f321(f932(x77111,a923)),x77114),x77113))
% 28.25/28.12 [7738]~P90(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)))
% 28.25/28.12 [7739]~P91(x77391)+~P1(f319(f319(f226(x77391),x77393),x77394))+P1(f319(f319(f226(x77391),f319(f319(f74(x77391),x77392),x77393)),f319(f319(f74(x77391),x77392),x77394)))
% 28.25/28.12 [7740]~P90(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)))
% 28.25/28.12 [7741]~P91(x77411)+~P1(f319(f319(f226(x77411),x77412),x77414))+P1(f319(f319(f226(x77411),f319(f319(f74(x77411),x77412),x77413)),f319(f319(f74(x77411),x77414),x77413)))
% 28.25/28.12 [7742]~P89(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)))
% 28.25/28.12 [7743]~P90(x77431)+~P1(f319(f319(f227(x77431),x77433),x77434))+P1(f319(f319(f227(x77431),f319(f319(f74(x77431),x77432),x77433)),f319(f319(f74(x77431),x77432),x77434)))
% 28.25/28.12 [7744]~P89(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)))
% 28.25/28.12 [7745]~P90(x77451)+~P1(f319(f319(f227(x77451),x77452),x77454))+P1(f319(f319(f227(x77451),f319(f319(f74(x77451),x77452),x77453)),f319(f319(f74(x77451),x77454),x77453)))
% 28.25/28.12 [7746]~P117(x77461)+~P1(f319(f319(f279(x77461),x77463),x77464))+P1(f319(f319(f279(x77461),f319(f319(f75(x77461),x77462),x77463)),f319(f319(f75(x77461),x77462),x77464)))
% 28.25/28.12 [7747]~P117(x77471)+~P1(f319(f319(f279(x77471),x77472),x77474))+P1(f319(f319(f279(x77471),f319(f319(f75(x77471),x77472),x77473)),f319(f319(f75(x77471),x77474),x77473)))
% 28.25/28.12 [7754]~P116(x77541)+~P100(x77541)+E(f319(f319(f23(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(f23(x77541),x77542),x77544)),f319(f95(x77541),x77543)))
% 28.25/28.12 [7755]~P146(x77551)+~P100(x77551)+E(f319(f319(f74(x77551),f319(f319(f75(x77551),x77552),f319(f95(x77551),x77553))),f319(f319(f75(x77551),x77554),f319(f95(x77551),x77553))),f319(f319(f75(x77551),f319(f319(f74(x77551),x77552),x77554)),f319(f95(x77551),x77553)))
% 28.25/28.12 [7791]~P79(x77911)+E(f319(f319(f74(x77911),f319(x77912,x77913)),f319(f319(f6(a925,x77911),x77912),f295(a925,f319(a104,x77913),x77914))),f319(f319(f6(a925,x77911),x77912),f295(a925,x77913,x77914)))+~P1(f319(f319(f226(a925),x77913),x77914))
% 28.25/28.12 [7803]~P26(x78032,x78031,x78033,f319(f164(x78032),x78034))+~P1(f319(f129(x78032),x78034))+P1(f319(f129(x78031),f319(f319(f146(x78032,x78031),x78033),x78034)))
% 28.25/28.12 [7852]~P1(f319(f319(f226(a925),x78522),x78524))+~P1(f319(f319(f226(a925),x78521),x78523))+P1(f319(f319(f226(a925),f319(f319(f75(a925),x78521),x78522)),f319(f319(f75(a925),x78523),x78524)))
% 28.25/28.12 [7853]~P1(f319(f319(f226(a925),x78532),x78534))+~P1(f319(f319(f226(a925),x78531),x78533))+P1(f319(f319(f226(a925),f319(f319(f74(a925),x78531),x78532)),f319(f319(f74(a925),x78533),x78534)))
% 28.25/28.12 [7856]~P1(f319(f319(f227(a925),x78562),x78564))+~P1(f319(f319(f227(a925),x78561),x78563))+P1(f319(f319(f227(a925),f319(f319(f74(a925),x78561),x78562)),f319(f319(f74(a925),x78563),x78564)))
% 28.25/28.12 [7857]~P1(f319(f319(f226(a1),x78572),x78574))+~P1(f319(f319(f227(a1),x78571),x78573))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x78571),x78572)),f319(f319(f74(a1),x78573),x78574)))
% 28.25/28.12 [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))
% 28.25/28.12 [7905]P1(f319(f319(f321(x79051),x79052),x79053))+~P1(f319(f319(f321(x79051),x79052),f32(f932(x79051,a923),x79054)))+~P1(f319(f319(f321(f932(x79051,a923)),x79053),x79054))
% 28.25/28.12 [7921]~P1(f319(x79211,f679(x79211,x79213,x79212)))+P1(f319(x79211,f319(f319(f156(x79212),x79213),x79214)))+~P1(f319(f319(f227(a925),x79214),f319(f181(f926(x79212)),x79213)))
% 28.25/28.12 [7926]P1(f319(x79261,x79262))+~P1(f319(f319(f321(x79264),x79262),f319(f164(x79264),x79263)))+P1(f319(f319(f227(a925),f684(x79261,x79263,x79264)),f319(f181(f926(x79264)),x79263)))
% 28.25/28.12 [7973]~P3(x79731)+~P1(f319(f319(f227(f932(x79732,x79731)),x79734),x79733))+~P1(f319(f319(f226(f932(x79732,x79731)),x79733),x79734))
% 28.25/28.12 [8016]~P1(f319(x80164,x80162))+~P1(f319(f319(f321(x80161),x80162),x80163))+P1(f319(f319(f321(x80161),x80162),f319(f319(f93(f932(x80161,a923)),x80163),f319(f254(x80161),x80164))))
% 28.25/28.12 [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)))
% 28.25/28.12 [8030]P1(f319(f319(f321(x80301),x80302),x80303))+~P1(f319(f319(f226(f932(x80301,a923)),x80303),x80304))+P1(f319(f319(f226(f932(x80301,a923)),x80303),f319(f319(f301(x80301),x80302),x80304)))
% 28.25/28.12 [8164]~P1(f319(f319(f321(x81641),x81643),x81644))+~P1(f319(f319(f227(f932(x81641,a923)),x81642),x81644))+P1(f319(f319(f227(f932(x81641,a923)),x81642),f319(f319(f301(x81641),x81643),x81644)))
% 28.25/28.12 [8166]E(f319(f319(f93(f932(x81661,a923)),x81662),x81663),f180(f932(x81661,a923)))+~E(f319(f319(f93(f932(x81661,a923)),f31(f932(x81661,a923),x81664)),x81663),f180(f932(x81661,a923)))+~P1(f319(f319(f321(f932(x81661,a923)),x81662),x81664))
% 28.25/28.12 [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))
% 28.25/28.12 [8241]P1(f319(f319(f321(x82411),x82412),x82413))+~P1(f319(f319(f226(f932(x82411,a923)),x82413),f319(f319(f301(x82411),x82412),x82414)))+P1(f319(f319(f226(f932(x82411,a923)),x82413),x82414))
% 28.25/28.12 [8258]P1(f319(f319(f321(x82582),f679(x82581,x82583,x82582)),f319(f164(x82582),x82583)))+P1(f319(x82581,f319(f319(f156(x82582),x82583),x82584)))+~P1(f319(f319(f227(a925),x82584),f319(f181(f926(x82582)),x82583)))
% 28.25/28.12 [8266]~P1(f319(f319(f226(f932(x82661,a923)),x82662),x82664))+P1(f319(f319(f226(f932(x82661,a923)),x82662),x82663))+~P1(f319(f319(f226(f932(x82661,a923)),x82664),x82663))
% 28.25/28.12 [8267]~P1(f319(f319(f227(f932(x82671,a923)),x82672),x82674))+~P1(f319(f319(f226(f932(x82671,a923)),x82674),x82673))+P1(f319(f319(f227(f932(x82671,a923)),x82672),x82673))
% 28.25/28.12 [8268]~P1(f319(f319(f226(f932(x82681,a923)),x82682),x82684))+~P1(f319(f319(f227(f932(x82681,a923)),x82684),x82683))+P1(f319(f319(f227(f932(x82681,a923)),x82682),x82683))
% 28.25/28.12 [8269]~P1(f319(f319(f227(f932(x82691,a923)),x82692),x82694))+P1(f319(f319(f227(f932(x82691,a923)),x82692),x82693))+~P1(f319(f319(f227(f932(x82691,a923)),x82694),x82693))
% 28.25/28.12 [8313]~P1(f319(f319(f321(x83131),x83134),x83133))+~P1(f319(f319(f227(f932(x83131,a923)),x83132),f319(f319(f301(x83131),x83134),x83133)))+P1(f319(f319(f227(f932(x83131,a923)),x83132),x83133))
% 28.25/28.12 [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)))
% 28.25/28.12 [8324]~P90(x83241)+P1(f319(f319(f226(x83241),x83242),x83243))+~P1(f319(f319(f226(x83241),f319(f319(f74(x83241),x83244),x83242)),f319(f319(f74(x83241),x83244),x83243)))
% 28.25/28.12 [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)))
% 28.25/28.12 [8326]~P90(x83261)+P1(f319(f319(f226(x83261),x83262),x83263))+~P1(f319(f319(f226(x83261),f319(f319(f74(x83261),x83262),x83264)),f319(f319(f74(x83261),x83263),x83264)))
% 28.25/28.12 [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)))
% 28.25/28.12 [8328]~P90(x83281)+P1(f319(f319(f227(x83281),x83282),x83283))+~P1(f319(f319(f227(x83281),f319(f319(f74(x83281),x83284),x83282)),f319(f319(f74(x83281),x83284),x83283)))
% 28.25/28.12 [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)))
% 28.25/28.12 [8330]~P90(x83301)+P1(f319(f319(f227(x83301),x83302),x83303))+~P1(f319(f319(f227(x83301),f319(f319(f74(x83301),x83302),x83304)),f319(f319(f74(x83301),x83303),x83304)))
% 28.25/28.12 [8380]P1(f319(x83801,x83802))+~E(f319(f319(f130(x83803),f319(f181(f926(x83803)),f169(x83803,x83801,x83804))),x83804),f105(x83803))+~P1(f319(f319(f321(x83803),x83802),f319(f164(x83803),x83804)))
% 28.25/28.12 [8500]P1(f319(x85001,x85002))+~P1(f319(f319(f321(x85003),x85002),f319(f164(x85003),x85004)))+P1(f319(f319(f227(a925),f319(f181(f926(x85003)),f319(f128(x85003,x85001),x85004))),f319(f181(f926(x85003)),x85004)))
% 28.25/28.12 [8995]~P1(f319(x89951,f762(x89951,x89953,x89952,x89954)))+P1(f319(x89951,f319(f319(f156(x89952),x89953),x89954)))+~P1(f319(f319(f227(a925),x89954),f319(f181(f926(x89952)),x89953)))
% 28.25/28.12 [9020]~P26(x90204,x90203,x90201,f234(f932(x90204,a923)))+E(f319(x90201,f892(x90202,x90201,x90203,x90204)),x90202)+~P1(f319(f319(f321(x90203),x90202),f319(f302(x90204,x90203,x90201),f234(f932(x90204,a923)))))
% 28.25/28.12 [9088]E(f169(x90881,x90882,x90883),f319(f319(f167(x90881),x90884),x90883))+P1(f319(f319(f227(a925),f744(x90882,x90883,x90881,x90884)),x90884))+P1(f319(f319(f227(a925),x90884),f319(f181(f926(x90881)),x90883)))
% 28.25/28.12 [9091]E(f169(x90911,x90912,x90913),f319(f319(f167(x90911),x90914),x90913))+P1(f319(f319(f227(a925),f744(x90912,x90913,x90911,x90914)),x90914))+P1(f319(x90912,f319(f319(f156(x90911),x90913),x90914)))
% 28.25/28.12 [9127]P1(f319(x91271,x91272))+~P1(f319(f319(f321(x91274),x91272),f319(f164(x91274),x91273)))+P1(f319(f319(f227(a925),f719(x91272,x91271,x91273,x91274)),f319(f181(f926(x91274)),x91273)))
% 28.25/28.12 [9129]E(f169(x91291,x91292,x91293),f319(f319(f167(x91291),x91294),x91293))+P1(f319(f319(f227(a925),x91294),f319(f181(f926(x91291)),x91293)))+P1(f319(f319(f227(a925),f744(x91292,x91293,x91291,x91294)),f319(f181(f926(x91291)),x91293)))
% 28.25/28.12 [9136]E(f169(x91361,x91362,x91363),f319(f319(f167(x91361),x91364),x91363))+P1(f319(x91362,f319(f319(f156(x91361),x91363),x91364)))+P1(f319(f319(f227(a925),f744(x91362,x91363,x91361,x91364)),f319(f181(f926(x91361)),x91363)))
% 28.25/28.12 [9163]~P129(x91634)+P1(f319(f319(f321(x91631),f665(x91632,x91633,x91631,x91634)),x91633))+P1(f319(f319(f227(x91634),f2(x91634)),f319(f319(f9(x91631,x91634),x91632),x91633)))
% 28.25/28.12 [9164]~P129(x91644)+P1(f319(f319(f321(x91641),f669(x91642,x91643,x91641,x91644)),x91643))+P1(f319(f319(f226(x91644),f2(x91644)),f319(f319(f9(x91641,x91644),x91642),x91643)))
% 28.25/28.12 [9191]~P1(f319(f55(x91911),x91914))+P1(f319(f319(f321(x91911),f577(x91912,x91913,x91914,x91911)),x91914))+P1(f319(f55(f931(x91911,x91913)),f319(f319(f246(x91911,x91913),x91914),x91912)))
% 28.25/28.12 [9224]P1(f319(f319(f321(x92242),f762(x92241,x92243,x92242,x92244)),f319(f164(x92242),x92243)))+P1(f319(x92241,f319(f319(f156(x92242),x92243),x92244)))+~P1(f319(f319(f227(a925),x92244),f319(f181(f926(x92242)),x92243)))
% 28.25/28.12 [9355]P1(f319(f319(f226(a925),x93554),f319(f181(f926(x93552)),f169(x93552,x93553,x93551))))+P1(f319(f319(f227(a925),f745(x93551,x93552,x93553,x93554)),x93554))+~P1(f319(f319(f226(a925),x93554),f319(f181(f926(x93552)),x93551)))
% 28.25/28.12 [9509]E(f169(x95091,x95092,x95093),f319(f319(f167(x95091),x95094),x95093))+~P1(f319(x95092,f319(f319(f156(x95091),x95093),f744(x95092,x95093,x95091,x95094))))+P1(f319(f319(f227(a925),x95094),f319(f181(f926(x95091)),x95093)))
% 28.25/28.12 [9517]E(f169(x95171,x95172,x95173),f319(f319(f167(x95171),x95174),x95173))+~P1(f319(x95172,f319(f319(f156(x95171),x95173),f744(x95172,x95173,x95171,x95174))))+P1(f319(x95172,f319(f319(f156(x95171),x95173),x95174)))
% 28.25/28.12 [9521]~P1(f319(f55(x95211),x95213))+~P1(f319(f55(x95212),f319(x95214,f577(x95214,x95212,x95213,x95211))))+P1(f319(f55(f931(x95211,x95212)),f319(f319(f246(x95211,x95212),x95213),x95214)))
% 28.25/28.12 [9529]~P129(x95291)+~P1(f319(f319(f226(x95291),f2(x95291)),f319(x95293,f669(x95293,x95294,x95292,x95291))))+P1(f319(f319(f226(x95291),f2(x95291)),f319(f319(f9(x95292,x95291),x95293),x95294)))
% 28.25/28.12 [9530]~P129(x95301)+~P1(f319(f319(f227(x95301),f2(x95301)),f319(x95303,f665(x95303,x95304,x95302,x95301))))+P1(f319(f319(f227(x95301),f2(x95301)),f319(f319(f9(x95302,x95301),x95303),x95304)))
% 28.25/28.12 [9538]~E(f319(f181(f926(x95384)),x95382),f319(f181(f926(x95384)),x95383))+P1(f319(f319(f321(f931(f926(x95384),f926(x95384))),f319(f319(f244(f926(x95384),f926(x95384)),x95383),x95382)),f150(x95384,x95381)))+P1(f319(f319(f227(a925),f671(x95381,x95382,x95383,x95384)),f319(f181(f926(x95384)),x95383)))
% 28.25/28.12 [9591]~P1(f319(x95913,f319(f319(f156(x95912),x95914),f745(x95914,x95912,x95913,x95911))))+P1(f319(f319(f226(a925),x95911),f319(f181(f926(x95912)),f169(x95912,x95913,x95914))))+~P1(f319(f319(f226(a925),x95911),f319(f181(f926(x95912)),x95914)))
% 28.25/28.12 [9673]E(f319(f319(f167(x96731),f681(x96732,x96733,x96734,x96731)),x96733),f319(f319(f167(x96731),f681(x96732,x96733,x96734,x96731)),x96734))+~P1(f319(f319(f321(f931(f926(x96731),f926(x96731))),f319(f319(f244(f926(x96731),f926(x96731)),x96734),x96733)),f139(x96731,x96732)))+P1(f319(f319(f227(a925),f319(f181(f926(x96731)),x96734)),f319(f181(f926(x96731)),x96733)))
% 28.25/28.12 [9730]~P1(f319(f319(f227(a925),f2(a925)),x97303))+~P1(f319(f319(f227(a925),x97304),x97301))+P1(f319(f319(f227(a925),f319(f319(f74(a925),f319(f319(f75(a925),x97301),f39(a925,x97302,x97303))),x97304)),f319(f319(f75(a925),x97301),x97303)))
% 28.25/28.12 [9926]~P3(x99262)+~P1(f319(f319(f226(x99262),f319(x99263,f545(x99264,x99263,x99261,x99262))),f319(x99264,f545(x99264,x99263,x99261,x99262))))+P1(f319(f319(f226(f932(x99261,x99262)),x99263),x99264))
% 28.25/28.12 [9927]~P3(x99272)+~P1(f319(f319(f226(x99272),f319(x99273,f657(x99271,x99274,x99273,x99272))),f319(x99274,f657(x99271,x99274,x99273,x99272))))+P1(f319(f319(f226(f932(x99271,x99272)),x99273),x99274))
% 28.25/28.12 [10042]~P70(x100421)+E(f319(f319(f6(a925,x100421),f319(f319(f18(a925,x100421,x100421),f319(f319(f8(x100421,f932(x100421,x100421),a925),f23(x100421)),x100422)),f319(f319(f8(a925,x100421,a925),x100422),f319(f319(f7(a925,a925,a925),f74(a925)),f72(a925))))),f295(a925,x100423,x100424)),f319(f319(f23(x100421),f319(x100422,x100423)),f319(x100422,f319(f319(f74(a925),x100424),f72(a925)))))+~P1(f319(f319(f226(a925),x100423),x100424))
% 28.25/28.12 [10122]~P38(x101223,f319(f319(f281(x101223,x101223,x101223),x101222),f299(x101223,x101222)))+~P1(f319(f319(f321(f931(x101223,x101223)),f319(f319(f244(x101223,x101223),f319(x101221,f319(a104,f844(x101222,x101221,x101223)))),f319(x101221,f844(x101222,x101221,x101223)))),f299(x101223,x101222)))+E(f319(x101221,f319(f319(f74(a925),f843(x101222,x101221,x101223)),x101224)),f319(x101221,f843(x101222,x101221,x101223)))
% 28.25/28.12 [6965]~P65(x69651)+E(f319(f319(f30(x69651),f319(f319(f75(x69651),x69652),x69653)),x69654),f319(f319(f75(x69651),x69652),f319(f319(f30(x69651),x69653),x69654)))+~P1(f319(f319(f279(x69651),x69654),x69653))
% 28.25/28.12 [7050]E(f319(f319(f126(x70501),x70502),x70503),x70504)+~E(x70503,f319(f319(f130(x70501),f319(f181(f926(x70501)),x70502)),x70504))+~E(f319(f319(f167(x70501),f319(f181(f926(x70501)),x70502)),x70504),x70502)
% 28.25/28.12 [7108]~P73(x71082)+E(x71081,f2(x71082))+E(f319(f319(f283(x71082),f319(f319(f236(x71082),x71083),x71084)),f319(f319(f236(x71082),x71081),x71084)),f319(f319(f236(x71082),f319(f319(f283(x71082),x71083),x71081)),x71084))
% 28.25/28.12 [7249]~P65(x72491)+E(f319(f319(f30(x72491),f319(f319(f75(x72491),x72492),x72493)),x72494),f319(f319(f75(x72491),f319(f319(f30(x72491),x72492),x72494)),x72493))+~P1(f319(f319(f279(x72491),x72494),x72492))
% 28.25/28.12 [7257]~P108(x72571)+~P1(f319(f319(f226(x72571),x72573),x72574))+P1(f319(f319(f226(x72571),f319(f319(f93(x72571),x72572),x72573)),x72574))
% 28.25/28.12 [7258]~P108(x72581)+~P1(f319(f319(f226(x72581),x72582),x72584))+P1(f319(f319(f226(x72581),f319(f319(f93(x72581),x72582),x72583)),x72584))
% 28.25/28.12 [7259]~P4(x72591)+~P1(f319(f319(f226(x72591),x72593),x72594))+P1(f319(f319(f226(x72591),f319(f319(f224(x72591),x72592),x72593)),x72594))
% 28.25/28.12 [7260]~P4(x72601)+~P1(f319(f319(f226(x72601),x72603),x72604))+P1(f319(f319(f226(x72601),f319(f319(f224(x72601),x72602),x72603)),x72604))
% 28.25/28.12 [7261]~P4(x72611)+~P1(f319(f319(f226(x72611),x72612),x72614))+P1(f319(f319(f226(x72611),f319(f319(f224(x72611),x72612),x72613)),x72614))
% 28.25/28.12 [7262]~P4(x72621)+~P1(f319(f319(f226(x72621),x72622),x72624))+P1(f319(f319(f226(x72621),f319(f319(f224(x72621),x72622),x72623)),x72624))
% 28.25/28.12 [7263]~P108(x72631)+~P1(f319(f319(f227(x72631),x72633),x72634))+P1(f319(f319(f227(x72631),f319(f319(f93(x72631),x72632),x72633)),x72634))
% 28.25/28.12 [7264]~P108(x72641)+~P1(f319(f319(f227(x72641),x72642),x72644))+P1(f319(f319(f227(x72641),f319(f319(f93(x72641),x72642),x72643)),x72644))
% 28.25/28.12 [7265]~P4(x72651)+~P1(f319(f319(f227(x72651),x72653),x72654))+P1(f319(f319(f227(x72651),f319(f319(f224(x72651),x72652),x72653)),x72654))
% 28.25/28.12 [7266]~P4(x72661)+~P1(f319(f319(f227(x72661),x72663),x72664))+P1(f319(f319(f227(x72661),f319(f319(f224(x72661),x72662),x72663)),x72664))
% 28.25/28.12 [7267]~P4(x72671)+~P1(f319(f319(f227(x72671),x72672),x72674))+P1(f319(f319(f227(x72671),f319(f319(f224(x72671),x72672),x72673)),x72674))
% 28.25/28.12 [7268]~P4(x72681)+~P1(f319(f319(f227(x72681),x72682),x72684))+P1(f319(f319(f227(x72681),f319(f319(f224(x72681),x72682),x72683)),x72684))
% 28.25/28.12 [7291]~P1(f319(x72913,x72914))+~P1(f319(x72912,x72914))+P1(f319(f319(f319(f93(f932(x72911,a923)),x72912),x72913),x72914))
% 28.25/28.12 [7418]P15(x74181,x74182,x74183)+~P15(x74181,x74182,x74184)+~P1(f319(f319(f226(f932(f924(x74181),a923)),x74183),x74184))
% 28.25/28.12 [7781]~P79(x77811)+E(f319(f319(f74(x77811),f319(x77812,x77813)),f319(f319(f6(a925,x77811),x77812),f319(f294(a925,f319(a104,x77813)),x77814))),f319(f319(f6(a925,x77811),x77812),f319(f294(a925,x77813),x77814)))+~P1(f319(f319(f227(a925),x77813),x77814))
% 28.25/28.12 [7799]E(x77991,x77992)+P1(f319(f319(f164(x77993),x77994),x77992))+~P1(f319(f319(f164(x77993),f319(f319(f143(x77993),x77991),x77994)),x77992))
% 28.25/28.12 [7810]~P4(x78101)+P1(f319(f319(f226(x78101),x78102),x78103))+~P1(f319(f319(f226(x78101),f319(f319(f225(x78101),x78104),x78102)),x78103))
% 28.25/28.12 [7811]~P4(x78111)+P1(f319(f319(f226(x78111),x78112),x78113))+~P1(f319(f319(f226(x78111),f319(f319(f225(x78111),x78114),x78112)),x78113))
% 28.25/28.12 [7812]~P4(x78121)+P1(f319(f319(f226(x78121),x78122),x78123))+~P1(f319(f319(f226(x78121),f319(f319(f225(x78121),x78122),x78124)),x78123))
% 28.25/28.12 [7813]~P4(x78131)+P1(f319(f319(f226(x78131),x78132),x78133))+~P1(f319(f319(f226(x78131),f319(f319(f225(x78131),x78132),x78134)),x78133))
% 28.25/28.12 [7814]~P107(x78141)+P1(f319(f319(f226(x78141),x78142),x78143))+~P1(f319(f319(f226(x78141),f319(f319(f102(x78141),x78144),x78142)),x78143))
% 28.25/28.12 [7815]~P107(x78151)+P1(f319(f319(f226(x78151),x78152),x78153))+~P1(f319(f319(f226(x78151),f319(f319(f102(x78151),x78154),x78152)),x78153))
% 28.25/28.12 [7816]~P107(x78161)+P1(f319(f319(f226(x78161),x78162),x78163))+~P1(f319(f319(f226(x78161),f319(f319(f102(x78161),x78162),x78164)),x78163))
% 28.25/28.12 [7817]~P107(x78171)+P1(f319(f319(f226(x78171),x78172),x78173))+~P1(f319(f319(f226(x78171),f319(f319(f102(x78171),x78172),x78174)),x78173))
% 28.25/28.12 [7818]~P4(x78181)+P1(f319(f319(f227(x78181),x78182),x78183))+~P1(f319(f319(f227(x78181),f319(f319(f225(x78181),x78184),x78182)),x78183))
% 28.25/28.12 [7819]~P4(x78191)+P1(f319(f319(f227(x78191),x78192),x78193))+~P1(f319(f319(f227(x78191),f319(f319(f225(x78191),x78192),x78194)),x78193))
% 28.25/28.12 [7820]~P121(x78201)+P1(f319(f319(f279(x78201),x78202),x78203))+~P1(f319(f319(f279(x78201),f319(f319(f75(x78201),x78204),x78202)),x78203))
% 28.25/28.12 [7821]~P121(x78211)+P1(f319(f319(f279(x78211),x78212),x78213))+~P1(f319(f319(f279(x78211),f319(f319(f75(x78211),x78212),x78214)),x78213))
% 28.25/28.12 [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)))
% 28.25/28.12 [7896]~P1(f319(f319(f321(x78961),x78962),x78964))+P1(f319(f319(f321(x78961),x78962),x78963))+P1(f319(f319(f321(x78961),x78962),f319(f319(f23(f932(x78961,a923)),x78964),x78963)))
% 28.25/28.12 [7980]P1(f319(x79801,x79802))+P1(f319(x79803,x79802))+~P1(f319(f319(f319(f102(f932(x79804,a923)),x79803),x79801),x79802))
% 28.25/28.12 [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)))
% 28.25/28.12 [7991]~P1(f319(f319(f321(x79911),x79912),x79914))+~P1(f319(f319(f321(x79911),x79912),x79913))+P1(f319(f319(f321(x79911),x79912),f319(f319(f93(f932(x79911,a923)),x79913),x79914)))
% 28.25/28.12 [8039]~P107(x80391)+~P1(f319(f55(x80391),x80394))+E(f319(f319(f58(x80391,x80391,f102(x80391)),x80392),f319(f319(f301(x80391),x80393),x80394)),f319(f319(f102(x80391),x80393),f319(f319(f58(x80391,x80391,f102(x80391)),x80392),x80394)))
% 28.25/28.12 [8040]~P108(x80401)+~P1(f319(f55(x80401),x80404))+E(f319(f319(f58(x80401,x80401,f93(x80401)),x80402),f319(f319(f301(x80401),x80403),x80404)),f319(f319(f93(x80401),x80403),f319(f319(f58(x80401,x80401,f93(x80401)),x80402),x80404)))
% 28.25/28.12 [8041]~P4(x80411)+~P1(f319(f55(x80411),x80414))+E(f319(f319(f58(x80411,x80411,f224(x80411)),x80412),f319(f319(f301(x80411),x80413),x80414)),f319(f319(f224(x80411),x80413),f319(f319(f58(x80411,x80411,f224(x80411)),x80412),x80414)))
% 28.25/28.12 [8042]~P4(x80421)+~P1(f319(f55(x80421),x80424))+E(f319(f319(f58(x80421,x80421,f225(x80421)),x80422),f319(f319(f301(x80421),x80423),x80424)),f319(f319(f225(x80421),x80423),f319(f319(f58(x80421,x80421,f225(x80421)),x80422),x80424)))
% 28.25/28.12 [8044]~P116(x80441)+~P100(x80441)+E(f319(f319(f23(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(f23(x80441),x80443),x80444)))
% 28.25/28.12 [8045]~P146(x80451)+~P100(x80451)+E(f319(f319(f74(x80451),f319(f319(f75(x80451),f319(f95(x80451),x80452)),x80453)),f319(f319(f75(x80451),f319(f95(x80451),x80452)),x80454)),f319(f319(f75(x80451),f319(f95(x80451),x80452)),f319(f319(f74(x80451),x80453),x80454)))
% 28.25/28.12 [8161]E(x81611,x81612)+P1(f319(f319(f321(x81613),x81611),f319(f164(x81613),x81614)))+~P1(f319(f319(f321(x81613),x81611),f319(f164(x81613),f319(f319(f143(x81613),x81612),x81614))))
% 28.25/28.12 [8335]P59(x83351,x83352,x83353)+~P59(x83351,x83352,x83354)+~P1(f319(f319(f226(f932(f931(x83351,x83352),a923)),x83353),x83354))
% 28.25/28.12 [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)))
% 28.25/28.12 [8382]P1(f319(f319(f321(x83821),x83822),x83823))+P1(f319(f319(f321(x83821),x83822),x83824))+~P1(f319(f319(f321(x83821),x83822),f319(f319(f102(f932(x83821,a923)),x83824),x83823)))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [8393]~P57(x83931,x83934,x83933)+~P1(f319(f319(f321(x83931),x83932),x83934))+P1(f319(f319(f321(f931(x83931,x83931)),f319(f319(f244(x83931,x83931),x83932),x83932)),x83933))
% 28.25/28.12 [8405]~P1(f319(f55(x84052),x84054))+~P1(f319(f55(x84051),x84053))+P1(f319(f55(f931(x84051,x84052)),f319(f319(f246(x84051,x84052),x84053),f319(f16(f932(x84052,a923),x84051),x84054))))
% 28.25/28.12 [8406]~P1(f319(f319(f321(x84061),x84062),x84064))+~P1(f319(f319(f226(f932(x84061,a923)),x84063),x84064))+P1(f319(f319(f226(f932(x84061,a923)),f319(f319(f301(x84061),x84062),x84063)),x84064))
% 28.25/28.12 [8413]~P78(x84132)+~P149(x84132)+E(f319(f319(f9(x84131,x84132),f319(f319(f8(a925,x84132,x84131),f92(x84132)),x84133)),x84134),f319(f92(x84132),f319(f319(f9(x84131,a925),x84133),x84134)))
% 28.25/28.12 [8414]~P78(x84142)+~P145(x84142)+E(f319(f319(f9(x84141,x84142),f319(f319(f8(a1,x84142,x84141),f94(x84142)),x84143)),x84144),f319(f94(x84142),f319(f319(f9(x84141,a1),x84143),x84144)))
% 28.25/28.12 [8438]E(f319(f319(f23(f932(x84381,a923)),x84382),f319(f319(f23(f932(x84381,a923)),x84383),x84384)),x84384)+~P1(f319(f319(f226(f932(x84381,a923)),x84382),x84383))+~P1(f319(f319(f226(f932(x84381,a923)),x84384),x84382))
% 28.25/28.12 [8536]~P1(f319(f55(x85361),x85364))+E(f319(f319(f23(a925),f319(f319(f6(x85361,a925),x85362),x85363)),f319(f319(f6(x85361,a925),x85362),x85364)),f319(f319(f6(x85361,a925),x85362),f319(f319(f23(f932(x85361,a923)),x85363),x85364)))+~P1(f319(f319(f226(f932(x85361,a923)),x85364),x85363))
% 28.25/28.12 [8690]~P9(x86901,x86904,x86903)+~P1(f319(f319(f321(x86901),x86902),x86904))+P1(f319(f319(f321(x86901),x86902),f319(f277(x86901,x86901,x86903),f319(f319(f301(x86901),x86902),f180(f932(x86901,a923))))))
% 28.25/28.12 [8753]~P1(f319(f319(f226(f932(x87531,a923)),x87532),x87533))+~P1(f319(f319(f226(f932(x87531,a923)),x87532),x87534))+P1(f319(f319(f226(f932(x87531,a923)),x87532),f319(f319(f93(f932(x87531,a923)),x87533),x87534)))
% 28.25/28.12 [8856]E(x88561,f180(f932(x88562,a923)))+P1(f319(f55(x88563),x88564))+~P1(f319(f55(f931(x88563,x88562)),f319(f319(f246(x88563,x88562),x88564),f319(f16(f932(x88562,a923),x88563),x88561))))
% 28.25/28.12 [8857]E(x88571,f180(f932(x88572,a923)))+P1(f319(f55(x88573),x88574))+~P1(f319(f55(f931(x88572,x88573)),f319(f319(f246(x88572,x88573),x88571),f319(f16(f932(x88573,a923),x88572),x88574))))
% 28.25/28.12 [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))
% 28.25/28.12 [8930]P1(f319(f319(f321(x89301),x89302),f308(x89301,x89303)))+~P1(f319(f319(f321(x89301),x89304),f308(x89301,x89303)))+~P1(f319(f319(f321(f931(x89301,x89301)),f319(f319(f244(x89301,x89301),x89302),x89304)),x89303))
% 28.25/28.12 [8987]~P38(x89871,x89874)+P1(f319(f319(f321(f931(x89871,x89871)),f319(f319(f244(x89871,x89871),x89873),x89872)),f299(x89871,x89874)))+P38(x89871,f319(f319(f301(f931(x89871,x89871)),f319(f319(f244(x89871,x89871),x89872),x89873)),x89874))
% 28.25/28.12 [8988]~P62(x89881,x89884)+P1(f319(f319(f321(f931(x89881,x89881)),f319(f319(f244(x89881,x89881),x89883),x89882)),f299(x89881,x89884)))+P62(x89881,f319(f319(f301(f931(x89881,x89881)),f319(f319(f244(x89881,x89881),x89882),x89883)),x89884))
% 28.25/28.12 [9071]~E(x90712,x90713)+~P1(f319(f319(f321(x90711),x90712),f319(f164(x90711),x90714)))+P1(f319(f319(f321(f931(x90711,x90711)),f319(f319(f244(x90711,x90711),x90712),x90713)),f319(f164(f931(x90711,x90711)),f319(f319(f173(x90711,x90711),x90714),x90714))))
% 28.25/28.12 [9098]~P41(f932(x90981,a923),f932(x90981,a923),x90983)+~P1(f319(f319(f321(x90981),x90982),f88(f932(x90981,a923),x90983)))+P1(f319(f319(f321(x90981),x90982),f319(x90983,f319(f319(f102(f932(x90981,a923)),x90984),f88(f932(x90981,a923),x90983)))))
% 28.25/28.12 [9162]~E(x91623,x91624)+P1(f319(f319(f249(x91621,x91621,a923),a316),x91622))+~P1(f319(f319(f321(f931(x91621,x91621)),x91622),f319(f164(f931(x91621,x91621)),f319(f319(f173(x91621,x91621),x91623),x91624))))
% 28.25/28.12 [9208]P1(f319(f319(f321(f931(f926(x92081),f926(x92081))),f319(f319(f244(f926(x92081),f926(x92081)),x92082),x92083)),f139(x92081,x92084)))+~E(f319(f319(f167(x92081),f319(f181(f926(x92081)),x92082)),x92083),x92082)+~P1(f319(f319(f227(a925),f319(f181(f926(x92081)),x92082)),f319(f181(f926(x92081)),x92083)))
% 28.25/28.12 [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))
% 28.25/28.12 [9211]~P56(x92111,x92114)+~P1(f319(f319(f321(f931(x92111,x92111)),f319(f319(f244(x92111,x92111),x92113),x92112)),x92114))+P1(f319(f319(f321(f931(x92111,x92111)),f319(f319(f244(x92111,x92111),x92112),x92113)),x92114))
% 28.25/28.12 [9304]~P1(f319(f55(x93041),x93044))+P1(f319(f319(f321(x93041),f905(x93042,x93043,x93044,x93041)),x93044))+P1(f319(f55(x93043),f319(f319(f33(x93041,f932(x93043,a923)),x93044),x93042)))
% 28.25/28.12 [9305]~P1(f319(f55(x93051),x93054))+P1(f319(f319(f321(x93051),f341(x93052,x93053,x93054,x93051)),x93054))+P1(f319(f55(x93053),f319(f319(f33(x93051,f932(x93053,a923)),x93054),x93052)))
% 28.25/28.12 [9393]P1(f319(f319(f321(f931(x93931,x93931)),x93932),f319(f319(f281(x93931,x93931,x93931),x93933),f299(x93931,x93933))))+~P1(f319(f319(f227(a925),f2(a925)),x93934))+~P1(f319(f319(f321(f931(x93931,x93931)),x93932),f319(f319(f175(f931(x93931,x93931),a923),x93934),x93933)))
% 28.25/28.12 [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))
% 28.25/28.12 [9401]~P38(x94011,x94012)+~P1(f319(f319(f321(f931(x94011,x94011)),f319(f319(f244(x94011,x94011),x94014),x94013)),x94012))+~P1(f319(f319(f321(f931(x94011,x94011)),f319(f319(f244(x94011,x94011),x94013),x94014)),x94012))
% 28.25/28.12 [9528]~P1(f319(f55(x95281),x95284))+E(f319(f319(f6(x95281,a925),f319(f319(f8(f932(x95282,a923),a925,x95281),f29(x95282)),x95283)),x95284),f319(f29(f931(x95281,x95282)),f319(f319(f246(x95281,x95282),x95284),x95283)))+P1(f319(f319(f321(x95281),f578(x95283,x95282,x95284,x95281)),x95284))
% 28.25/28.12 [9532]~P1(f319(f129(x95321),x95322))+P1(f319(f129(x95321),f319(f319(f151(x95321,x95322),x95323),x95324)))+P1(f319(f319(f321(x95321),x95324),f319(f319(f23(f932(x95321,a923)),f319(f164(x95321),x95322)),f319(f319(f301(x95321),f319(f319(f156(x95321),x95322),x95323)),f180(f932(x95321,a923))))))
% 28.25/28.12 [9550]~P1(f319(f55(x95502),x95503))+~P1(f319(f55(x95501),f319(x95504,f905(x95504,x95501,x95503,x95502))))+P1(f319(f55(x95501),f319(f319(f33(x95502,f932(x95501,a923)),x95503),x95504)))
% 28.25/28.12 [9551]~P1(f319(f55(x95512),x95513))+~P1(f319(f55(x95511),f319(x95514,f341(x95514,x95511,x95513,x95512))))+P1(f319(f55(x95511),f319(f319(f33(x95512,f932(x95511,a923)),x95513),x95514)))
% 28.25/28.12 [9629]~P1(f319(f319(f321(f931(x96291,x96291)),x96292),f319(f319(f281(x96291,x96291,x96291),x96294),f299(x96291,x96294))))+P1(f319(f319(f321(f931(x96291,x96291)),x96292),f319(f319(f281(x96291,x96291,x96291),x96293),f299(x96291,x96293))))+~P1(f319(f319(f226(f932(f931(x96291,x96291),a923)),x96294),x96293))
% 28.25/28.12 [9639]E(f319(f319(f167(x96391),f681(x96394,x96393,x96392,x96391)),x96393),f319(f319(f167(x96391),f681(x96394,x96393,x96392,x96391)),x96392))+~P1(f319(f319(f321(f931(f926(x96391),f926(x96391))),f319(f319(f244(f926(x96391),f926(x96391)),x96392),x96393)),f139(x96391,x96394)))+E(f319(f319(f167(x96391),f319(f181(f926(x96391)),x96392)),x96393),x96392)
% 28.25/28.12 [9656]~P1(f319(f55(x96561),x96564))+E(f319(f319(f6(x96561,a925),f319(f319(f8(f932(x96562,a923),a925,x96561),f29(x96562)),x96563)),x96564),f319(f29(f931(x96561,x96562)),f319(f319(f246(x96561,x96562),x96564),x96563)))+~P1(f319(f55(x96562),f319(x96563,f578(x96563,x96562,x96564,x96561))))
% 28.25/28.12 [9660]~E(f319(f181(f926(x96601)),x96603),f319(f181(f926(x96601)),x96602))+P1(f319(f319(f321(f931(f926(x96601),f926(x96601))),f319(f319(f244(f926(x96601),f926(x96601)),x96602),x96603)),f150(x96601,x96604)))+P1(f319(f319(f321(f931(x96601,x96601)),f686(x96604,x96603,x96602,x96601)),f319(f164(f931(x96601,x96601)),f319(f319(f173(x96601,x96601),x96602),x96603))))
% 28.25/28.12 [9741]~P1(f319(f319(f321(f931(f926(x97411),f926(x97411))),f319(f319(f244(f926(x97411),f926(x97411)),x97412),x97413)),f139(x97411,x97414)))+E(f319(f319(f167(x97411),f319(f181(f926(x97411)),x97412)),x97413),x97412)+P1(f319(f319(f227(a925),f681(x97414,x97413,x97412,x97411)),f319(f319(f224(a925),f319(f181(f926(x97411)),x97412)),f319(f181(f926(x97411)),x97413))))
% 28.25/28.12 [9765]~P1(f319(f319(f321(f931(f926(x97651),f926(x97651))),f319(f319(f244(f926(x97651),f926(x97651)),x97652),x97653)),f139(x97651,x97654)))+P1(f319(f319(f227(a925),f319(f181(f926(x97651)),x97652)),f319(f181(f926(x97651)),x97653)))+P1(f319(f319(f227(a925),f681(x97654,x97653,x97652,x97651)),f319(f319(f224(a925),f319(f181(f926(x97651)),x97652)),f319(f181(f926(x97651)),x97653))))
% 28.25/28.12 [10189]~P1(f319(f319(f321(f931(f926(x101891),f926(x101891))),f319(f319(f244(f926(x101891),f926(x101891)),x101892),x101893)),f139(x101891,x101894)))+E(f319(f319(f167(x101891),f319(f181(f926(x101891)),x101892)),x101893),x101892)+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))
% 28.25/28.12 [10190]~P1(f319(f319(f321(f931(f926(x101901),f926(x101901))),f319(f319(f244(f926(x101901),f926(x101901)),x101902),x101903)),f139(x101901,x101904)))+P1(f319(f319(f227(a925),f319(f181(f926(x101901)),x101902)),f319(f181(f926(x101901)),x101903)))+P1(f319(f319(f321(f931(x101901,x101901)),f319(f319(f244(x101901,x101901),f319(f319(f156(x101901),x101902),f681(x101904,x101903,x101902,x101901))),f319(f319(f156(x101901),x101903),f681(x101904,x101903,x101902,x101901)))),x101904))
% 28.25/28.12 [10260]~E(f319(f181(f926(x102601)),x102602),f319(f181(f926(x102601)),x102603))+P1(f319(f319(f321(f931(f926(x102601),f926(x102601))),f319(f319(f244(f926(x102601),f926(x102601)),x102602),x102603)),f150(x102601,x102604)))+~P1(f319(f319(f321(f931(x102601,x102601)),f319(f319(f244(x102601,x102601),f319(f319(f156(x102601),x102602),f671(x102604,x102603,x102602,x102601))),f319(f319(f156(x102601),x102603),f671(x102604,x102603,x102602,x102601)))),x102604))
% 28.25/28.12 [10409]~P79(x104091)+~P1(f319(f55(x104092),x104094))+E(f319(f157(x104091),f319(f319(f146(x104092,x104091),x104093),f84(f926(x104092),f319(f319(f18(f926(x104092),a923,a923),f319(f319(f8(a923,f932(a923,a923),f926(x104092)),a317),f319(f319(f7(f926(x104092),f932(x104092,a923),a923),f319(f319(f8(f932(x104092,a923),f932(f932(x104092,a923),a923),f926(x104092)),a316),f164(x104092))),x104094))),f129(x104092))))),f223(x104092,x104091,x104093,x104094))
% 28.25/28.12 [7632]~P72(x76322)+E(x76321,f2(x76322))+E(f319(f319(f283(x76322),f319(f319(f74(x76322),x76323),f319(f319(f75(x76322),x76324),x76321))),x76321),f319(f319(f74(x76322),x76324),f319(f319(f283(x76322),x76323),x76321)))
% 28.25/28.12 [7633]~P65(x76332)+E(x76331,f2(x76332))+E(f319(f319(f30(x76332),f319(f319(f74(x76332),x76333),f319(f319(f75(x76332),x76334),x76331))),x76331),f319(f319(f74(x76332),x76334),f319(f319(f30(x76332),x76333),x76331)))
% 28.25/28.12 [7634]~P65(x76342)+E(x76341,f2(x76342))+E(f319(f319(f30(x76342),f319(f319(f74(x76342),x76343),f319(f319(f75(x76342),x76341),x76344))),x76341),f319(f319(f74(x76342),x76344),f319(f319(f30(x76342),x76343),x76341)))
% 28.25/28.12 [7860]~P73(x78602)+E(x78601,f2(x78602))+E(f319(f319(f283(x78602),f319(f319(f23(x78602),x78603),f319(f319(f75(x78602),x78601),x78604))),x78601),f319(f319(f23(x78602),f319(f319(f283(x78602),x78603),x78601)),x78604))
% 28.25/28.12 [7861]~P72(x78612)+E(x78611,f2(x78612))+E(f319(f319(f283(x78612),f319(f319(f74(x78612),x78613),f319(f319(f75(x78612),x78614),x78611))),x78611),f319(f319(f74(x78612),f319(f319(f283(x78612),x78613),x78611)),x78614))
% 28.25/28.12 [7862]~P73(x78622)+E(x78621,f2(x78622))+E(f319(f319(f283(x78622),f319(f319(f74(x78622),x78623),f319(f319(f75(x78622),x78621),x78624))),x78621),f319(f319(f74(x78622),f319(f319(f283(x78622),x78623),x78621)),x78624))
% 28.25/28.12 [8568]~P1(f319(f152(x85681,x85683),x85684))+~P1(f319(f152(x85681,x85682),x85684))+P1(f319(f152(x85681,f319(f319(f93(f932(x85681,a923)),x85682),x85683)),x85684))
% 28.25/28.12 [8945]~E(f319(f319(f281(x89451,x89451,x89451),x89452),x89454),f180(f932(f931(x89451,x89451),a923)))+~E(f319(f319(f281(x89451,x89451,x89451),x89452),x89453),f180(f932(f931(x89451,x89451),a923)))+E(f319(f319(f281(x89451,x89451,x89451),x89452),f319(f319(f102(f932(f931(x89451,x89451),a923)),x89453),x89454)),f180(f932(f931(x89451,x89451),a923)))
% 28.25/28.12 [9072]~P1(f319(f319(f226(f932(x90721,a923)),x90723),x90724))+~P1(f319(f319(f226(f932(x90721,a923)),x90722),x90724))+P1(f319(f319(f226(f932(x90721,a923)),f319(f319(f102(f932(x90721,a923)),x90722),x90723)),x90724))
% 28.25/28.12 [9456]~P1(f319(f55(x94561),x94564))+~P1(f319(f55(x94561),x94563))+E(f319(f319(f23(a925),f319(f319(f74(a925),f319(f319(f6(x94561,a925),x94562),x94563)),f319(f319(f6(x94561,a925),x94562),x94564))),f319(f319(f6(x94561,a925),x94562),f319(f319(f93(f932(x94561,a923)),x94563),x94564))),f319(f319(f6(x94561,a925),x94562),f319(f319(f102(f932(x94561,a923)),x94563),x94564)))
% 28.25/28.12 [9546]~P1(f319(f319(f321(x95461),x95463),x95462))+~P1(f319(f319(f226(f932(x95461,a923)),x95462),f319(f319(f301(x95461),x95463),x95464)))+P1(f319(f319(f226(f932(x95461,a923)),f319(f319(f23(f932(x95461,a923)),x95462),f319(f319(f301(x95461),x95463),f180(f932(x95461,a923))))),x95464))
% 28.25/28.12 [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))
% 28.25/28.12 [9717]~P1(f319(f319(f321(x97171),x97173),x97172))+P1(f319(f319(f226(f932(x97171,a923)),x97172),f319(f319(f301(x97171),x97173),x97174)))+~P1(f319(f319(f226(f932(x97171,a923)),f319(f319(f23(f932(x97171,a923)),x97172),f319(f319(f301(x97171),x97173),f180(f932(x97171,a923))))),x97174))
% 28.25/28.12 [9740]~P1(f319(f319(f226(f932(x97401,a923)),x97402),x97404))+P1(f319(f319(f226(f932(x97401,a923)),x97402),f319(f319(f301(x97401),x97403),x97404)))+~P1(f319(f319(f226(f932(x97401,a923)),f319(f319(f23(f932(x97401,a923)),x97402),f319(f319(f301(x97401),x97403),f180(f932(x97401,a923))))),x97404))
% 28.25/28.12 [9807]~P1(f319(f319(f226(a925),x98071),x98073))+~P1(f319(f319(f227(a925),x98072),x98074))+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))),a26))
% 28.25/28.12 [9808]~P1(f319(f319(f226(a925),x98082),x98084))+~P1(f319(f319(f226(a925),x98081),x98083))+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),x98081),x98082)),f319(f319(f244(a925,a925),x98083),x98084))),a64))
% 28.25/28.12 [10120]~P1(f319(f319(f321(f926(x101201)),x101204),f153(x101201,x101203)))+~P1(f319(f319(f321(f926(x101201)),x101204),f153(x101201,x101202)))+P1(f319(f152(x101201,f319(f319(f93(f932(x101201,a923)),f319(f319(f7(x101201,f932(x101201,a923),a923),f321(x101201)),x101202)),f319(f319(f7(x101201,f932(x101201,a923),a923),f321(x101201)),x101203))),x101204))
% 28.25/28.12 [10226]~P26(x102261,f932(f932(x102261,a923),a923),f319(f319(f7(x102261,f932(f931(x102261,x102261),a923),f932(f932(x102261,a923),a923)),f319(f319(f8(f932(x102261,a923),f932(f932(f931(x102261,x102261),a923),f932(f932(x102261,a923),a923)),x102261),f54(x102261)),f319(f319(f7(x102261,f932(x102261,a923),f932(x102261,a923)),f301(x102261)),f180(f932(x102261,a923))))),x102263),x102262)+~P1(f319(f319(f321(x102261),x102264),x102262))+E(f319(f319(f23(f932(f932(x102261,a923),a923)),f319(f319(f54(x102261),x102262),x102263)),f319(f319(f54(x102261),f319(f319(f301(x102261),x102264),f180(f932(x102261,a923)))),x102263)),f319(f319(f54(x102261),f319(f319(f23(f932(x102261,a923)),x102262),f319(f319(f301(x102261),x102264),f180(f932(x102261,a923))))),x102263))
% 28.25/28.12 [10364]~P57(x103641,x103642,x103644)+~P1(f319(f319(f321(f931(x103641,x103641)),x103643),x103644))+P1(f319(f319(f249(x103641,x103641,a923),f319(f319(f7(x103641,f932(x103641,a923),f932(x103641,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x103641,a923),f932(x103641,a923)),x103641),f8(a923,a923,x103641)),f319(f319(f8(a923,f932(a923,a923),x103641),a317),f319(f319(f7(x103641,f932(x103641,a923),a923),f321(x103641)),x103642)))),f319(f319(f7(x103641,f932(x103641,a923),a923),f321(x103641)),x103642))),x103643))
% 28.25/28.12 [10377]P1(f319(f55(x103771),x103772))+~P1(f319(f55(x103773),f319(f302(x103771,x103773,x103774),x103772)))+~P1(f319(f55(x103771),f319(f254(x103771),f319(f319(f18(x103771,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103771),a317),f319(f319(f7(x103771,f932(x103771,a923),a923),f321(x103771)),x103772))),f319(f319(f7(x103771,x103773,a923),f319(f319(f8(x103773,f932(x103773,a923),x103771),a316),x103774)),f319(x103774,f467(x103774,x103773,x103772,x103771)))))))
% 28.25/28.12 [8319]~P73(x83192)+E(x83191,f2(x83192))+E(f319(f319(f283(x83192),f319(f319(f23(x83192),f319(f319(f75(x83192),x83191),x83193)),x83194)),x83191),f319(f319(f23(x83192),x83193),f319(f319(f283(x83192),x83194),x83191)))
% 28.25/28.12 [8320]~P73(x83202)+E(x83201,f2(x83202))+E(f319(f319(f283(x83202),f319(f319(f74(x83202),f319(f319(f75(x83202),x83201),x83203)),x83204)),x83201),f319(f319(f74(x83202),x83203),f319(f319(f283(x83202),x83204),x83201)))
% 28.25/28.12 [9238]~E(f319(f319(f281(x92381,x92381,x92381),x92383),x92384),f180(f932(f931(x92381,x92381),a923)))+~E(f319(f319(f281(x92381,x92381,x92381),x92382),x92384),f180(f932(f931(x92381,x92381),a923)))+E(f319(f319(f281(x92381,x92381,x92381),f319(f319(f102(f932(f931(x92381,x92381),a923)),x92382),x92383)),x92384),f180(f932(f931(x92381,x92381),a923)))
% 28.25/28.12 [10031]~P1(f319(f152(x100311,x100313),x100314))+~P1(f319(f152(x100311,x100312),x100314))+P1(f319(f152(x100311,f319(f319(f18(x100311,a923,a923),f319(f319(f8(a923,f932(a923,a923),x100311),a317),x100312)),x100313)),x100314))
% 28.25/28.12 [10301]P1(f319(x103011,f463(x103012,x103013,x103011,x103014)))+~P1(f319(f55(x103014),f319(f254(x103014),x103011)))+P1(f319(f55(x103013),f319(f254(x103013),f319(f319(f8(f932(x103014,a923),a923,x103013),f81(x103014)),f319(f319(f8(f932(x103014,a923),f932(x103014,a923),x103013),f319(f18(x103014,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103014),a317),x103011))),x103012)))))
% 28.25/28.12 [10319]~P1(f319(f55(x103192),f319(f254(x103192),x103193)))+~P1(f319(f55(x103191),f319(f254(x103191),f319(f319(f7(x103191,x103192,a923),x103194),f463(x103194,x103191,x103193,x103192)))))+P1(f319(f55(x103191),f319(f254(x103191),f319(f319(f8(f932(x103192,a923),a923,x103191),f81(x103192)),f319(f319(f8(f932(x103192,a923),f932(x103192,a923),x103191),f319(f18(x103192,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103192),a317),x103193))),x103194)))))
% 28.25/28.12 [10388]~P1(f319(f55(x103881),x103884))+P1(f319(f319(f321(x103881),f815(x103882,x103883,x103884,x103881)),x103884))+P1(f319(f55(x103883),f319(f254(x103883),f319(f319(f8(f932(x103881,a923),a923,x103883),f81(x103881)),f319(f319(f8(f932(x103881,a923),f932(x103881,a923),x103883),f319(f18(x103881,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103881),a317),f319(f319(f7(x103881,f932(x103881,a923),a923),f321(x103881)),x103884)))),x103882)))))
% 28.25/28.12 [10394]~P1(f319(f55(x103942),x103943))+~P1(f319(f55(x103941),f319(f254(x103941),f319(f319(f7(x103941,x103942,a923),x103944),f815(x103944,x103941,x103943,x103942)))))+P1(f319(f55(x103941),f319(f254(x103941),f319(f319(f8(f932(x103942,a923),a923,x103941),f81(x103942)),f319(f319(f8(f932(x103942,a923),f932(x103942,a923),x103941),f319(f18(x103942,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103942),a317),f319(f319(f7(x103942,f932(x103942,a923),a923),f321(x103942)),x103943)))),x103944)))))
% 28.25/28.12 [5243]~E(x52432,x52434)+E(f161(x52431,x52432,x52433),f161(x52431,x52434,x52435))+~E(x52432,f2(a925))
% 28.25/28.12 [5496]E(x54961,x54962)+~E(f161(x54964,x54963,x54961),f161(x54964,x54965,x54962))+E(x54963,f2(a925))
% 28.25/28.12 [6760]E(x67601,x67602)+~E(f319(x67603,x67601),f319(x67603,x67602))+~P26(x67604,x67605,x67603,f234(f932(x67604,a923)))
% 28.25/28.12 [6761]E(x67611,x67612)+~E(f319(x67613,x67611),f319(x67613,x67612))+~P26(x67614,x67615,x67613,f234(f932(x67614,a923)))
% 28.25/28.12 [7664]E(x76641,x76642)+~P26(x76643,x76644,x76645,f234(f932(x76643,a923)))+~E(f319(f302(x76643,x76644,x76645),x76641),f319(f302(x76643,x76644,x76645),x76642))
% 28.25/28.12 [7914]P26(x79142,x79143,f888(x79144,x79143,x79142,x79141),x79141)+~E(f319(f302(x79143,x79142,x79145),x79144),x79141)+E(x79141,f180(f932(x79142,a923)))
% 28.25/28.12 [8449]~P1(f319(f319(x84493,x84492),x84495))+~P1(f319(f319(x84493,x84494),x84492))+P1(f319(f319(f321(x84491),x84492),f291(x84491,x84493,x84494,x84495)))
% 28.25/28.12 [8450]~P1(f319(f319(x84503,x84502),x84505))+~P1(f319(f319(x84503,x84504),x84502))+P1(f319(f319(f321(x84501),x84502),f282(x84501,x84503,x84504,x84505)))
% 28.25/28.12 [8761]~P26(x87611,x87612,x87613,x87614)+P27(x87611,x87612,x87613,x87614,x87615)+~E(f319(f302(x87611,x87612,x87613),x87614),x87615)
% 28.25/28.12 [8895]~P27(x88951,x88953,x88954,x88952,x88955)+~P1(f319(f55(x88953),x88955))+P1(f319(f55(x88951),x88952))
% 28.25/28.12 [8896]~P27(x88963,x88961,x88964,x88965,x88962)+~P1(f319(f55(x88963),x88965))+P1(f319(f55(x88961),x88962))
% 28.25/28.12 [9029]~P26(x90291,x90293,x90295,f234(f932(x90291,a923)))+~P26(x90293,x90292,x90294,f234(f932(x90293,a923)))+P26(x90291,x90292,f319(f66(x90293,x90292,x90291,x90294),x90295),f234(f932(x90291,a923)))
% 28.25/28.12 [9606]P1(f319(f319(f321(f931(x96061,x96061)),f319(f319(f244(x96061,x96061),x96062),x96063)),f299(x96061,x96064)))+~P1(f319(f319(f321(f931(x96061,x96061)),f319(f319(f244(x96061,x96061),x96062),x96065)),f299(x96061,x96064)))+~P1(f319(f319(f321(f931(x96061,x96061)),f319(f319(f244(x96061,x96061),x96065),x96063)),f299(x96061,x96064)))
% 28.25/28.12 [9646]~P4(x96462)+~P1(f319(f129(x96461),x96465))+P1(f319(f129(x96461),f141(x96461,x96462,x96463,x96464,x96465)))
% 28.25/28.12 [9778]~P27(x97783,x97782,x97784,f234(f932(x97783,a923)),f234(f932(x97782,a923)))+~P27(x97781,x97783,x97785,f234(f932(x97781,a923)),f234(f932(x97783,a923)))+P27(x97781,x97782,f319(f66(x97783,x97782,x97781,x97784),x97785),f234(f932(x97781,a923)),f234(f932(x97782,a923)))
% 28.25/28.12 [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))
% 28.25/28.12 [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)
% 28.25/28.12 [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)
% 28.25/28.12 [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)
% 28.25/28.12 [7202]~P4(x72021)+~P14(x72021,f319(f319(f146(x72022,x72021),x72023),x72025))+P14(x72021,f319(f319(f146(x72022,x72021),x72023),f319(f128(x72022,x72024),x72025)))
% 28.25/28.12 [7345]~P4(x73451)+P14(x73451,f319(f319(f146(x73452,x73451),x73453),f162(x73452,x73454,x73455)))+~P14(x73451,f319(f319(f146(x73452,x73451),x73453),x73455))
% 28.25/28.12 [7368]~P59(x73683,x73682,x73685)+~P59(x73681,x73683,x73684)+P59(x73681,x73682,f319(f319(f281(x73681,x73683,x73682),x73684),x73685))
% 28.25/28.12 [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))
% 28.25/28.12 [7465]E(x74651,x74652)+~P26(x74653,x74654,x74655,f234(f932(x74653,a923)))+~E(f319(f319(f146(x74653,x74654),x74655),x74651),f319(f319(f146(x74653,x74654),x74655),x74652))
% 28.25/28.12 [7619]~P1(f319(f319(f226(a925),x76191),f319(x76193,x76195)))+P1(f319(f319(f226(a925),x76191),f147(x76192,x76193,x76194)))+~P1(f319(f319(f321(x76192),x76195),f319(f164(x76192),x76194)))
% 28.25/28.12 [7620]~P1(f319(f319(f227(a925),x76201),f319(x76203,x76205)))+P1(f319(f319(f227(a925),x76201),f147(x76202,x76203,x76204)))+~P1(f319(f319(f321(x76202),x76205),f319(f164(x76202),x76204)))
% 28.25/28.12 [7974]~E(x79743,f2(a925))+P1(f319(x79741,x79742))+~P1(f319(f319(f321(x79744),x79742),f319(f164(x79744),f161(x79744,x79743,x79745))))
% 28.25/28.12 [7989]~E(x79891,f2(a925))+~P1(f319(x79892,x79893))+~P1(f319(f319(f321(x79894),x79893),f319(f164(x79894),f161(x79894,x79891,x79895))))
% 28.25/28.12 [8010]P1(f319(x80101,x80102))+~P1(f319(x80101,x80103))+~P1(f319(f319(f321(x80104),x80102),f319(f164(x80104),f161(x80104,x80105,x80103))))
% 28.25/28.12 [8011]P1(f319(x80111,x80112))+~P1(f319(x80111,x80113))+~P1(f319(f319(f321(x80114),x80113),f319(f164(x80114),f161(x80114,x80115,x80112))))
% 28.25/28.12 [8015]~P113(x80151)+P1(f319(f319(f226(f932(x80151,a923)),f295(x80151,x80152,x80153)),f295(x80151,x80154,x80155)))+P1(f319(f319(f226(x80151),x80152),x80153))
% 28.25/28.12 [8037]~P6(x80371)+P1(f319(f319(f226(x80371),f319(f319(f34(x80372,x80371),x80373),x80374)),f319(x80374,x80375)))+~P1(f319(f319(f321(x80372),x80375),x80373))
% 28.25/28.12 [8107]~P26(x81071,x81072,x81074,x81073)+E(f319(f71(x81071,x81072,x81073,x81074),f319(x81074,x81075)),x81075)+~P1(f319(f319(f321(x81071),x81075),x81073))
% 28.25/28.12 [8108]~P26(x81081,x81082,x81084,x81083)+E(f319(f85(x81081,x81082,x81083,x81084),f319(x81084,x81085)),x81085)+~P1(f319(f319(f321(x81081),x81085),x81083))
% 28.25/28.12 [8308]~P1(f319(x83081,x83085))+P1(f319(x83081,f615(x83081,x83082,x83083,x83084)))+~P1(f319(f319(f321(x83084),x83085),x83083))
% 28.25/28.12 [8309]~P1(f319(x83091,x83095))+P1(f319(x83091,f615(x83091,x83092,x83093,x83094)))+~P1(f319(f319(f321(x83094),x83095),x83092))
% 28.25/28.12 [8403]P1(f319(f55(x84031),x84032))+~P1(f319(f55(x84033),x84034))+~P1(f319(f319(f226(f932(x84031,a923)),x84032),f319(f302(x84033,x84031,x84035),x84034)))
% 28.25/28.12 [8412]~P26(x84124,x84121,x84122,f234(f932(x84124,a923)))+~P1(f319(f319(f321(x84124),x84123),x84125))+P1(f319(f319(f321(x84121),f319(x84122,x84123)),f319(f302(x84124,x84121,x84122),x84125)))
% 28.25/28.12 [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))
% 28.25/28.12 [8572]E(x85721,x85722)+~P26(x85723,x85724,x85725,f319(f319(f102(f932(x85723,a923)),f319(f164(x85723),x85721)),f319(f164(x85723),x85722)))+~E(f319(f319(f146(x85723,x85724),x85725),x85721),f319(f319(f146(x85723,x85724),x85725),x85722))
% 28.25/28.12 [8626]~P113(x86261)+~P1(f319(f319(f227(f932(x86261,a923)),f295(x86261,x86264,x86265)),f295(x86261,x86262,x86263)))+P1(f319(f319(f226(x86261),x86262),x86263))
% 28.25/28.12 [8689]~P26(x86891,x86894,x86895,f234(f932(x86891,a923)))+~P1(f319(f319(f321(x86894),f319(x86895,x86892)),f319(f302(x86891,x86894,x86895),x86893)))+P1(f319(f319(f321(x86891),x86892),x86893))
% 28.25/28.12 [8767]P1(f319(x87671,x87672))+~P1(f319(x87671,f567(x87671,x87673,x87674,x87675)))+~P1(f319(f319(f321(x87675),x87672),x87674))
% 28.25/28.12 [8768]P1(f319(x87681,x87682))+~P1(f319(x87681,f567(x87681,x87683,x87684,x87685)))+~P1(f319(f319(f321(x87685),x87682),x87683))
% 28.25/28.12 [9069]~P26(x90692,x90693,x90691,x90694)+E(f319(x90691,f319(f71(x90692,x90693,x90694,x90691),x90695)),x90695)+~P1(f319(f319(f321(x90693),x90695),f319(f302(x90692,x90693,x90691),x90694)))
% 28.25/28.12 [9177]E(x91771,f105(x91772))+E(f319(f319(f143(x91772),x91773),f700(x91774,x91773,x91775,x91771,x91772)),x91771)+~E(f319(f319(f126(x91772),x91771),x91775),f319(f319(f143(x91772),x91773),x91774))
% 28.25/28.12 [9178]E(x91781,f105(x91782))+E(f319(f319(f143(x91782),x91783),f701(x91784,x91781,x91785,x91783,x91782)),x91781)+~E(f319(f319(f126(x91782),x91781),x91784),f319(f319(f143(x91782),x91783),x91785))
% 28.25/28.12 [9196]E(f319(f319(f143(x91962),x91963),f700(x91964,x91963,x91961,x91965,x91962)),x91965)+~E(f319(f319(f126(x91962),x91965),x91961),f319(f319(f143(x91962),x91963),x91964))+E(x91961,f319(f319(f143(x91962),x91963),x91964))
% 28.25/28.12 [9197]E(f319(f319(f143(x91971),x91972),f701(x91974,x91975,x91973,x91972,x91971)),x91975)+~E(f319(f319(f126(x91971),x91975),x91974),f319(f319(f143(x91971),x91972),x91973))+E(f319(f319(f143(x91971),x91972),x91973),x91974)
% 28.25/28.12 [9275]~E(f319(f302(x92753,x92752,x92754),f234(f932(x92753,a923))),f234(f932(x92752,a923)))+~E(f319(f302(x92751,x92753,x92755),f234(f932(x92751,a923))),f234(f932(x92753,a923)))+E(f319(f302(x92751,x92752,f319(f66(x92753,x92752,x92751,x92754),x92755)),f234(f932(x92751,a923))),f234(f932(x92752,a923)))
% 28.25/28.12 [9653]E(x96531,f105(x96532))+~E(f319(f319(f126(x96532),x96531),x96533),f319(f319(f143(x96532),x96535),x96534))+E(f319(f319(f126(x96532),f701(x96533,x96531,x96534,x96535,x96532)),x96533),x96534)
% 28.25/28.12 [9654]E(x96541,f105(x96542))+~E(f319(f319(f126(x96542),x96541),x96545),f319(f319(f143(x96542),x96544),x96543))+E(f319(f319(f126(x96542),f700(x96543,x96544,x96545,x96541,x96542)),x96545),x96543)
% 28.25/28.12 [9661]E(f319(f319(f126(x96612),f700(x96614,x96613,x96611,x96615,x96612)),x96611),x96614)+~E(f319(f319(f126(x96612),x96615),x96611),f319(f319(f143(x96612),x96613),x96614))+E(x96611,f319(f319(f143(x96612),x96613),x96614))
% 28.25/28.12 [9662]~E(f319(f319(f126(x96621),x96625),x96624),f319(f319(f143(x96621),x96622),x96623))+E(f319(f319(f126(x96621),f701(x96624,x96625,x96623,x96622,x96621)),x96624),x96623)+E(f319(f319(f143(x96621),x96622),x96623),x96624)
% 28.25/28.12 [9663]E(f319(f319(f126(x96631),x96635),f703(x96633,x96632,x96634,x96635,x96631)),x96632)+E(f319(f319(f126(x96631),x96632),f702(x96633,x96632,x96634,x96635,x96631)),x96635)+~E(f319(f319(f126(x96631),x96635),x96634),f319(f319(f126(x96631),x96632),x96633))
% 28.25/28.12 [9700]~P4(x97001)+P14(x97001,f319(f319(f146(x97002,x97001),x97003),f141(x97002,x97001,x97003,x97004,x97005)))+~P14(x97001,f319(f319(f146(x97002,x97001),x97003),x97005))
% 28.25/28.12 [9714]~P63(x97145,x97141,x97144,x97143)+P1(f319(f319(x97141,x97142),f562(x97143,x97144,x97141,x97145,x97142)))+~P1(f319(f319(f321(x97145),x97142),x97144))
% 28.25/28.12 [9715]~P63(x97155,x97151,x97154,x97153)+P1(f319(f319(x97151,x97152),f819(x97153,x97154,x97151,x97155,x97152)))+~P1(f319(f319(f321(x97155),x97152),x97154))
% 28.25/28.12 [9819]~P1(f319(f319(f321(f931(x98191,x98191)),f319(f319(f244(x98191,x98191),x98195),x98193)),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),x98192),x98195)),f319(f319(f281(x98191,x98191,x98191),x98194),f299(x98191,x98194))))
% 28.25/28.12 [9820]~P1(f319(f319(f321(f931(x98201,x98201)),f319(f319(f244(x98201,x98201),x98202),x98205)),f299(x98201,x98204)))+P1(f319(f319(f321(f931(x98201,x98201)),f319(f319(f244(x98201,x98201),x98202),x98203)),f319(f319(f281(x98201,x98201,x98201),x98204),f299(x98201,x98204))))+~P1(f319(f319(f321(f931(x98201,x98201)),f319(f319(f244(x98201,x98201),x98205),x98203)),f319(f319(f281(x98201,x98201,x98201),x98204),f299(x98201,x98204))))
% 28.25/28.12 [9822]P1(f319(f319(f321(f931(f926(x98221),f926(x98221))),f319(f319(f244(f926(x98221),f926(x98221)),x98222),x98223)),f150(x98221,f299(x98221,x98224))))+~P1(f319(f319(f321(f931(f926(x98221),f926(x98221))),f319(f319(f244(f926(x98221),f926(x98221)),x98222),x98225)),f150(x98221,f299(x98221,x98224))))+~P1(f319(f319(f321(f931(f926(x98221),f926(x98221))),f319(f319(f244(f926(x98221),f926(x98221)),x98225),x98223)),f150(x98221,f299(x98221,x98224))))
% 28.25/28.12 [9826]E(f319(f319(f126(x98261),x98262),f702(x98263,x98262,x98264,x98265,x98261)),x98265)+E(f319(f319(f126(x98261),f703(x98263,x98262,x98264,x98265,x98261)),x98263),x98264)+~E(f319(f319(f126(x98261),x98262),x98263),f319(f319(f126(x98261),x98265),x98264))
% 28.25/28.12 [9827]E(f319(f319(f126(x98271),x98272),f703(x98273,x98274,x98275,x98272,x98271)),x98274)+E(f319(f319(f126(x98271),f702(x98273,x98274,x98275,x98272,x98271)),x98275),x98273)+~E(f319(f319(f126(x98271),x98272),x98275),f319(f319(f126(x98271),x98274),x98273))
% 28.25/28.12 [9882]P1(f319(f319(f321(f931(x98821,x98821)),f319(f319(f244(x98821,x98821),x98822),x98823)),f319(f319(f281(x98821,x98821,x98821),x98824),f299(x98821,x98824))))+~P1(f319(f319(f321(f931(x98821,x98821)),f319(f319(f244(x98821,x98821),x98822),x98825)),f319(f319(f281(x98821,x98821,x98821),x98824),f299(x98821,x98824))))+~P1(f319(f319(f321(f931(x98821,x98821)),f319(f319(f244(x98821,x98821),x98825),x98823)),f319(f319(f281(x98821,x98821,x98821),x98824),f299(x98821,x98824))))
% 28.25/28.12 [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),f720(x99115,x99114,x99113,x99112,x99111)))
% 28.25/28.12 [9912]P35(x99121,x99122,x99123,x99124,x99125)+~E(f319(f181(f926(x99121)),x99124),f319(f181(f926(x99122)),x99125))+~P1(f319(f319(f249(x99121,x99122,a923),x99123),f721(x99123,x99125,x99124,x99122,x99121)))
% 28.25/28.12 [9917]E(f319(f319(f126(x99171),f702(x99172,x99173,x99174,x99175,x99171)),x99174),x99172)+~E(f319(f319(f126(x99171),x99173),x99172),f319(f319(f126(x99171),x99175),x99174))+E(f319(f319(f126(x99171),f703(x99172,x99173,x99174,x99175,x99171)),x99172),x99174)
% 28.25/28.12 [9933]~P4(x99332)+E(f319(f319(f140(x99331,x99332,x99333),x99334),x99335),f319(f319(f143(x99331),x99334),x99335))+P1(f319(f319(f321(x99331),f766(x99334,x99333,x99335,x99331,x99332)),f319(f164(x99331),x99335)))
% 28.25/28.12 [9938]~P63(x99381,x99384,x99383,x99382)+~P1(f319(f319(f321(x99381),x99385),x99383))+P1(f319(f319(f321(x99381),f562(x99382,x99383,x99384,x99381,x99385)),x99382))
% 28.25/28.12 [9939]~P63(x99391,x99394,x99393,x99392)+~P1(f319(f319(f321(x99391),x99395),x99393))+P1(f319(f319(f321(x99391),f819(x99392,x99393,x99394,x99391,x99395)),x99392))
% 28.25/28.12 [10067]~P1(f319(f319(f321(f931(f932(x100671,a923),f932(x100671,a923))),f319(f319(f244(f932(x100671,a923),f932(x100671,a923)),x100674),x100673)),f311(x100671,x100672)))+~P1(f319(f319(f321(x100671),x100675),x100674))+P1(f319(f319(f321(x100671),f619(x100672,x100673,x100674,x100671,x100675)),x100673))
% 28.25/28.12 [10077]~P4(x100772)+E(f319(f319(f140(x100771,x100772,x100773),x100774),x100775),f319(f319(f143(x100771),x100774),x100775))+~P1(f319(f319(f226(x100772),f319(x100773,x100774)),f319(x100773,f766(x100774,x100773,x100775,x100771,x100772))))
% 28.25/28.12 [10129]~P26(x101293,x101294,x101295,f234(f932(x101293,a923)))+P1(f319(x101291,x101292))+~P1(f319(x101291,f319(f85(x101293,x101294,f234(f932(x101293,a923)),x101295),f793(x101292,x101291,x101295,x101294,x101293))))
% 28.25/28.12 [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),f722(x102775,x102774,x102773,x102772,x102771))),f319(f319(f156(x102772),x102775),f722(x102775,x102774,x102773,x102772,x102771))))
% 28.25/28.12 [10278]P35(x102781,x102782,x102783,x102784,x102785)+~E(f319(f181(f926(x102781)),x102784),f319(f181(f926(x102782)),x102785))+~P1(f319(f319(x102783,f319(f319(f156(x102781),x102784),f755(x102783,x102785,x102782,x102784,x102781))),f319(f319(f156(x102782),x102785),f755(x102783,x102785,x102782,x102784,x102781))))
% 28.25/28.12 [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))
% 28.25/28.12 [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)))))
% 28.25/28.12 [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)))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [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))
% 28.25/28.12 [7042]~E(x70424,f319(f319(f126(x70421),x70425),f319(f319(f143(x70421),x70422),x70423)))+P1(f319(f319(f321(x70421),x70422),f319(f164(x70421),x70423)))+P1(f319(f319(f321(x70421),x70422),f319(f164(x70421),x70424)))
% 28.25/28.12 [7043]~E(x70434,f319(f319(f126(x70431),x70433),f319(f319(f143(x70431),x70432),x70435)))+P1(f319(f319(f321(x70431),x70432),f319(f164(x70431),x70433)))+P1(f319(f319(f321(x70431),x70432),f319(f164(x70431),x70434)))
% 28.25/28.12 [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)))
% 28.25/28.12 [7355]~E(x73552,x73554)+~P148(x73551)+E(f319(f319(f74(x73551),f319(f319(f75(x73551),x73552),x73553)),f319(f319(f75(x73551),x73554),x73555)),f319(f319(f74(x73551),f319(f319(f75(x73551),x73552),x73555)),f319(f319(f75(x73551),x73554),x73553)))
% 28.25/28.12 [7417]~P6(x74171)+~P1(f319(f319(f321(x74174),x74173),x74175))+P1(f319(f319(f226(x74171),f319(x74172,x74173)),f319(f319(f33(x74174,x74171),x74175),x74172)))
% 28.25/28.12 [7468]~P3(x74681)+P1(f319(f319(f226(x74681),f319(x74682,x74683)),f319(x74684,x74683)))+~P1(f319(f319(f226(f932(x74685,x74681)),x74682),x74684))
% 28.25/28.12 [7469]~P3(x74691)+P1(f319(f319(f226(x74691),f319(x74692,x74693)),f319(x74694,x74693)))+~P1(f319(f319(f226(f932(x74695,x74691)),x74692),x74694))
% 28.25/28.12 [7470]~P3(x74701)+P1(f319(f319(f226(x74701),f319(x74702,x74703)),f319(x74704,x74703)))+~P1(f319(f319(f226(f932(x74705,x74701)),x74702),x74704))
% 28.25/28.12 [7589]E(x75891,x75892)+E(x75893,x75891)+~E(f319(f319(f301(x75894),x75891),f319(f319(f301(x75894),x75895),f180(f932(x75894,a923)))),f319(f319(f301(x75894),x75892),f319(f319(f301(x75894),x75893),f180(f932(x75894,a923)))))
% 28.25/28.12 [7590]E(x75901,x75902)+E(x75903,x75901)+~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)))))
% 28.25/28.12 [7591]E(x75911,x75912)+E(x75911,x75913)+~E(f319(f319(f301(x75914),x75913),f319(f319(f301(x75914),x75912),f180(f932(x75914,a923)))),f319(f319(f301(x75914),x75915),f319(f319(f301(x75914),x75911),f180(f932(x75914,a923)))))
% 28.25/28.12 [7592]E(x75921,x75922)+E(x75921,x75923)+~E(f319(f319(f301(x75924),x75921),f319(f319(f301(x75924),x75925),f180(f932(x75924,a923)))),f319(f319(f301(x75924),x75922),f319(f319(f301(x75924),x75923),f180(f932(x75924,a923)))))
% 28.25/28.12 [8117]P26(x81171,x81172,x81173,x81174)+~P26(x81171,x81172,x81173,x81175)+~P1(f319(f319(f226(f932(x81171,a923)),x81174),x81175))
% 28.25/28.12 [8147]~E(f319(x81473,x81475),x81474)+~P26(x81471,x81472,x81473,f234(f932(x81471,a923)))+E(f319(f85(x81471,x81472,f234(f932(x81471,a923)),x81473),x81474),x81475)
% 28.25/28.12 [8296]E(x82961,x82962)+~E(f319(f302(x82963,x82964,x82965),x82961),f319(f302(x82963,x82964,x82965),x82962))+~P26(x82963,x82964,x82965,f319(f319(f102(f932(x82963,a923)),x82961),x82962))
% 28.25/28.12 [8371]P1(f319(x83712,x83714))+E(f319(f319(f130(x83711),f319(f181(f926(x83711)),f169(x83711,x83712,x83713))),x83713),f319(f319(f143(x83711),x83714),x83715))+~E(f319(f319(f126(x83711),f169(x83711,x83712,x83713)),f319(f319(f143(x83711),x83714),x83715)),x83713)
% 28.25/28.12 [8401]~P26(x84011,x84012,x84013,x84015)+~P26(x84011,x84012,x84013,x84014)+P26(x84011,x84012,x84013,f319(f319(f93(f932(x84011,a923)),x84014),x84015))
% 28.25/28.12 [8510]~P79(x85101)+E(f319(f319(f74(x85101),f319(x85102,x85103)),f319(f157(x85101),f319(f319(f146(x85104,x85101),x85102),f162(x85104,x85103,x85105)))),f319(f157(x85101),f319(f319(f146(x85104,x85101),x85102),x85105)))+~P1(f319(f319(f321(x85104),x85103),f319(f164(x85104),x85105)))
% 28.25/28.12 [8598]~P4(x85981)+~P14(x85981,f319(f319(f146(x85982,x85981),x85983),x85985))+P14(x85981,f319(f319(f146(x85982,x85981),x85983),f319(f319(f140(x85982,x85981,x85983),x85984),x85985)))
% 28.25/28.12 [8685]~P6(x86851)+P1(f319(f319(f226(x86851),f319(f319(f33(x86852,x86851),x86853),x86854)),f319(f319(f33(x86852,x86851),x86855),x86854)))+~P1(f319(f319(f226(f932(x86852,a923)),x86853),x86855))
% 28.25/28.12 [8686]~P6(x86861)+P1(f319(f319(f226(x86861),f319(f319(f34(x86862,x86861),x86863),x86864)),f319(f319(f34(x86862,x86861),x86865),x86864)))+~P1(f319(f319(f226(f932(x86862,a923)),x86865),x86863))
% 28.25/28.12 [8722]~P4(x87223)+P1(f319(f129(x87221),x87222))+~P1(f319(f129(x87221),f319(f319(f140(x87221,x87223,x87224),x87225),x87222)))
% 28.25/28.12 [8867]~P4(x88671)+~P1(f319(f319(f321(x88672),x88673),f319(f164(x88672),x88674)))+~P1(f319(f129(x88672),f319(f319(f140(x88672,x88671,x88675),x88673),x88674)))
% 28.25/28.12 [8957]~P4(x89571)+P14(x89571,f319(f319(f146(x89572,x89571),x89573),x89574))+~P14(x89571,f319(f319(f146(x89572,x89571),x89573),f319(f319(f140(x89572,x89571,x89573),x89575),x89574)))
% 28.25/28.12 [9004]~P26(x90042,x90041,x90044,x90043)+E(f319(f302(x90041,x90042,f85(x90042,x90041,x90043,x90044)),f319(f302(x90042,x90041,x90044),x90045)),x90045)+~P1(f319(f319(f226(f932(x90042,a923)),x90045),x90043))
% 28.25/28.12 [9057]~P4(x90572)+E(f319(f319(f140(x90571,x90572,x90573),x90574),x90575),f141(x90571,x90572,x90573,x90574,x90575))+P1(f319(f319(f321(x90572),f319(x90573,x90574)),f319(f302(x90571,x90572,x90573),f319(f164(x90571),x90575))))
% 28.25/28.12 [9139]~P4(x91392)+E(f141(x91391,x91392,x91393,x91394,x91395),x91395)+~P1(f319(f319(f321(x91392),f319(x91393,x91394)),f319(f302(x91391,x91392,x91393),f319(f164(x91391),x91395))))
% 28.25/28.12 [9155]~P26(x91552,x91551,x91553,x91555)+P1(f319(f319(f227(f932(x91551,a923)),f319(f302(x91552,x91551,x91553),x91554)),f319(f302(x91552,x91551,x91553),x91555)))+~P1(f319(f319(f227(f932(x91552,a923)),x91554),x91555))
% 28.25/28.12 [9188]~P26(x91882,x91881,x91883,f234(f932(x91882,a923)))+P1(f319(f319(f226(f932(x91881,a923)),f319(f302(x91882,x91881,x91883),x91884)),f319(f302(x91882,x91881,x91883),x91885)))+~P1(f319(f319(f226(f932(x91882,a923)),x91884),x91885))
% 28.25/28.12 [9316]~P26(x93161,x93162,x93163,f234(f932(x93161,a923)))+~P1(f319(f319(f226(f932(x93162,a923)),x93164),f319(f302(x93161,x93162,x93163),x93165)))+P1(f319(f319(f226(f932(x93161,a923)),f319(f303(x93161,x93162,x93163),x93164)),x93165))
% 28.25/28.12 [9340]~E(f319(f302(x93403,x93401,x93404),f234(f932(x93403,a923))),f234(f932(x93401,a923)))+P1(f319(f319(f226(f932(x93401,a923)),x93402),f319(f302(x93403,x93401,x93404),x93405)))+~P1(f319(f319(f226(f932(x93403,a923)),f319(f303(x93403,x93401,x93404),x93402)),x93405))
% 28.25/28.12 [9449]~P26(x94491,x94494,x94495,f234(f932(x94491,a923)))+~P1(f319(f319(f226(f932(x94494,a923)),f319(f302(x94491,x94494,x94495),x94492)),f319(f302(x94491,x94494,x94495),x94493)))+P1(f319(f319(f226(f932(x94491,a923)),x94492),x94493))
% 28.25/28.12 [9574]~P88(x95741)+~E(f319(x95743,f741(x95743,x95744,x95745,x95742,x95741)),f2(x95741))+E(f319(f157(x95741),f319(f319(f146(x95742,x95741),x95743),f319(f128(x95742,x95744),x95745))),f319(f157(x95741),f319(f319(f146(x95742,x95741),x95743),x95745)))
% 28.25/28.12 [9601]~P27(x96011,x96012,x96013,f234(f932(x96011,a923)),f234(f932(x96012,a923)))+~P1(f319(f319(f226(f932(x96012,a923)),x96014),f319(f302(x96011,x96012,x96013),x96015)))+P1(f319(f319(f226(f932(x96011,a923)),f319(f303(x96011,x96012,x96013),x96014)),x96015))
% 28.25/28.12 [9630]~P27(x96303,x96301,x96304,f234(f932(x96303,a923)),f234(f932(x96301,a923)))+P1(f319(f319(f226(f932(x96301,a923)),x96302),f319(f302(x96303,x96301,x96304),x96305)))+~P1(f319(f319(f226(f932(x96303,a923)),f319(f303(x96303,x96301,x96304),x96302)),x96305))
% 28.25/28.12 [9758]~P18(x97581,x97582,x97583)+~P1(f319(f55(x97581),x97585))+P1(f319(f60(x97581,x97582,x97583,x97584,x97585),f319(f319(f58(x97581,x97582,x97583),x97584),x97585)))
% 28.25/28.12 [9839]~P27(x98392,x98391,x98394,f234(f932(x98392,a923)),f234(f932(x98391,a923)))+~P27(x98391,x98393,x98395,f234(f932(x98391,a923)),f234(f932(x98393,a923)))+E(f319(f66(x98391,x98392,x98393,f85(x98392,x98391,f234(f932(x98392,a923)),x98394)),f85(x98391,x98393,f234(f932(x98391,a923)),x98395)),f85(x98392,x98393,f234(f932(x98392,a923)),f319(f66(x98391,x98393,x98392,x98395),x98394)))
% 28.25/28.12 [9840]P1(f319(x98401,f664(x98402,x98401,x98403,x98404,x98405)))+~P1(f319(f319(f226(f932(x98405,a923)),x98404),x98403))+P1(f319(f319(f226(f932(x98405,a923)),f319(f319(f93(f932(x98405,a923)),x98404),f319(f254(x98405),x98401))),f319(f319(f93(f932(x98405,a923)),x98403),f319(f254(x98405),x98402))))
% 28.25/28.12 [9855]~P88(x98551)+~P1(f319(x98554,f741(x98553,x98554,x98555,x98552,x98551)))+E(f319(f157(x98551),f319(f319(f146(x98552,x98551),x98553),f319(f128(x98552,x98554),x98555))),f319(f157(x98551),f319(f319(f146(x98552,x98551),x98553),x98555)))
% 28.25/28.12 [9935]~P6(x99355)+P1(f319(f319(f321(x99351),f912(x99352,x99353,x99351,x99354,x99355)),x99353))+P1(f319(f319(f226(x99355),x99354),f319(f319(f34(x99351,x99355),x99353),x99352)))
% 28.25/28.12 [9936]~P6(x99365)+P1(f319(f319(f321(x99361),f557(x99362,x99363,x99364,x99361,x99365)),x99364))+P1(f319(f319(f226(x99365),x99363),f319(f319(f34(x99361,x99365),x99364),x99362)))
% 28.25/28.12 [9940]~P88(x99401)+E(f319(f157(x99401),f319(f319(f146(x99402,x99401),x99403),f319(f128(x99402,x99404),x99405))),f319(f157(x99401),f319(f319(f146(x99402,x99401),x99403),x99405)))+P1(f319(f319(f321(x99402),f741(x99403,x99404,x99405,x99402,x99401)),f319(f164(x99402),x99405)))
% 28.25/28.12 [9951]~P1(f319(x99515,f664(x99515,x99513,x99514,x99512,x99511)))+~P1(f319(f319(f226(f932(x99511,a923)),x99512),x99514))+P1(f319(f319(f226(f932(x99511,a923)),f319(f319(f93(f932(x99511,a923)),x99512),f319(f254(x99511),x99513))),f319(f319(f93(f932(x99511,a923)),x99514),f319(f254(x99511),x99515))))
% 28.25/28.12 [9971]~P26(x99715,x99713,x99714,f234(f932(x99715,a923)))+P1(f319(x99711,x99712))+P1(f319(f319(f321(x99713),f793(x99712,x99711,x99714,x99713,x99715)),f319(f302(x99715,x99713,x99714),f234(f932(x99715,a923)))))
% 28.25/28.12 [9998]P35(x99981,x99982,x99983,x99984,x99985)+~E(f319(f181(f926(x99982)),x99985),f319(f181(f926(x99981)),x99984))+P1(f319(f319(f227(a925),f722(x99985,x99984,x99983,x99982,x99981)),f319(f181(f926(x99981)),x99984)))
% 28.25/28.12 [9999]P35(x99991,x99992,x99993,x99994,x99995)+~E(f319(f181(f926(x99992)),x99995),f319(f181(f926(x99991)),x99994))+P1(f319(f319(f227(a925),f755(x99993,x99995,x99992,x99994,x99991)),f319(f181(f926(x99991)),x99994)))
% 28.25/28.12 [10033]P1(f319(f319(f321(x100331),f664(x100332,x100333,x100334,x100335,x100331)),x100335))+~P1(f319(f319(f226(f932(x100331,a923)),x100335),x100334))+P1(f319(f319(f226(f932(x100331,a923)),f319(f319(f93(f932(x100331,a923)),x100335),f319(f254(x100331),x100333))),f319(f319(f93(f932(x100331,a923)),x100334),f319(f254(x100331),x100332))))
% 28.25/28.12 [10078]~P6(x100781)+~P1(f319(f319(f226(x100781),x100782),f319(x100785,f912(x100785,x100784,x100783,x100782,x100781))))+P1(f319(f319(f226(x100781),x100782),f319(f319(f34(x100783,x100781),x100784),x100785)))
% 28.25/28.12 [10079]~P6(x100791)+~P1(f319(f319(f226(x100791),x100792),f319(x100795,f557(x100795,x100792,x100794,x100793,x100791))))+P1(f319(f319(f226(x100791),x100792),f319(f319(f34(x100793,x100791),x100794),x100795)))
% 28.25/28.12 [10118]~P78(x101181)+~P1(f319(f55(x101182),x101185))+E(f319(f319(f319(f59(x101181,x101182,f75(x101181)),f319(f319(f18(x101182,x101181,x101181),f319(f319(f8(x101181,f932(x101181,x101181),x101182),f75(x101181)),x101183)),x101184)),f72(x101181)),x101185),f319(f319(f75(x101181),f319(f319(f319(f59(x101181,x101182,f75(x101181)),x101183),f72(x101181)),x101185)),f319(f319(f319(f59(x101181,x101182,f75(x101181)),x101184),f72(x101181)),x101185)))
% 28.25/28.12 [10173]~P1(f319(f319(f321(f931(f932(x101731,a923),f932(x101731,a923))),f319(f319(f244(f932(x101731,a923),f932(x101731,a923)),x101735),x101734)),f311(x101731,x101733)))+~P1(f319(f319(f321(x101731),x101732),x101735))+P1(f319(f319(f321(f931(x101731,x101731)),f319(f319(f244(x101731,x101731),x101732),f619(x101733,x101734,x101735,x101731,x101732))),x101733))
% 28.25/28.12 [10316]~P1(f319(f319(f321(f931(f926(x103161),f926(x103161))),f319(f319(f244(f926(x103161),f926(x103161)),f319(f319(f126(x103161),x103165),x103162)),f319(f319(f126(x103161),x103165),x103163))),f139(x103161,x103164)))+P1(f319(f319(f321(f931(f926(x103161),f926(x103161))),f319(f319(f244(f926(x103161),f926(x103161)),x103162),x103163)),f139(x103161,x103164)))+P1(f319(f319(f321(f931(x103161,x103161)),f319(f319(f244(x103161,x103161),f709(x103164,x103163,x103162,x103165,x103161)),f709(x103164,x103163,x103162,x103165,x103161))),x103164))
% 28.25/28.12 [7473]~E(x74733,x74735)+E(f319(f319(f156(x74731),f319(f319(f151(x74731,x74732),x74733),x74734)),x74735),x74734)+~P1(f319(f319(f227(a925),x74733),f319(f181(f926(x74731)),x74732)))
% 28.25/28.12 [7586]~E(f319(f319(f126(x75861),x75862),x75864),f319(f319(f126(x75861),x75863),x75865))+E(f319(f319(f167(x75861),f319(f181(f926(x75861)),x75862)),x75863),x75862)+P1(f319(f319(f226(a925),f319(f181(f926(x75861)),x75863)),f319(f181(f926(x75861)),x75862)))
% 28.25/28.12 [7587]E(x75871,x75872)+E(f319(f319(f156(x75873),f319(f319(f151(x75873,x75874),x75871),x75875)),x75872),f319(f319(f156(x75873),x75874),x75872))+~P1(f319(f319(f227(a925),x75871),f319(f181(f926(x75873)),x75874)))
% 28.25/28.12 [8078]~E(f319(f319(f126(x80781),x80782),x80784),f319(f319(f126(x80781),x80783),x80785))+E(f319(f319(f167(x80781),f319(f181(f926(x80781)),x80782)),x80783),x80782)+~P1(f319(f319(f226(a925),f319(f181(f926(x80781)),x80782)),f319(f181(f926(x80781)),x80783)))
% 28.25/28.12 [8102]~P1(f319(f55(x81021),f319(x81024,x81025)))+~P1(f319(f319(f321(x81022),x81025),x81023))+P1(f319(f55(x81021),f319(f319(f34(x81022,f932(x81021,a923)),x81023),x81024)))
% 28.25/28.12 [8280]~P57(x82801,x82803,x82805)+~P57(x82801,x82802,x82804)+P57(x82801,f319(f319(f102(f932(x82801,a923)),x82802),x82803),f319(f319(f102(f932(f931(x82801,x82801),a923)),x82804),x82805))
% 28.25/28.12 [8281]~P57(x82811,x82813,x82815)+~P57(x82811,x82812,x82814)+P57(x82811,f319(f319(f93(f932(x82811,a923)),x82812),x82813),f319(f319(f93(f932(f931(x82811,x82811),a923)),x82814),x82815))
% 28.25/28.12 [8638]E(f319(f319(f244(x86381,x86382),f319(f319(f156(x86381),x86383),x86384)),f319(f319(f156(x86382),x86385),x86384)),f319(f319(f156(f931(x86381,x86382)),f319(f319(f173(x86381,x86382),x86383),x86385)),x86384))+~P1(f319(f319(f227(a925),x86384),f319(f181(f926(x86381)),x86383)))+~P1(f319(f319(f227(a925),x86384),f319(f181(f926(x86382)),x86385)))
% 28.25/28.12 [8795]~P57(x87951,x87953,x87954)+P1(f319(f319(f321(x87951),x87952),x87953))+~P1(f319(f319(f321(f931(x87951,x87951)),f319(f319(f244(x87951,x87951),x87955),x87952)),x87954))
% 28.25/28.12 [8796]~P57(x87961,x87963,x87964)+P1(f319(f319(f321(x87961),x87962),x87963))+~P1(f319(f319(f321(f931(x87961,x87961)),f319(f319(f244(x87961,x87961),x87962),x87965)),x87964))
% 28.25/28.12 [8797]~P9(x87971,x87973,x87974)+P1(f319(f319(f321(x87971),x87972),x87973))+~P1(f319(f319(f321(f931(x87971,x87971)),f319(f319(f244(x87971,x87971),x87975),x87972)),x87974))
% 28.25/28.12 [8798]~P9(x87981,x87983,x87984)+P1(f319(f319(f321(x87981),x87982),x87983))+~P1(f319(f319(f321(f931(x87981,x87981)),f319(f319(f244(x87981,x87981),x87982),x87985)),x87984))
% 28.25/28.12 [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))
% 28.25/28.12 [9081]~P9(x90811,x90815,x90812)+E(f319(f277(x90811,x90811,x90812),f319(f319(f301(x90811),x90813),f180(f932(x90811,a923)))),f319(f277(x90811,x90811,x90812),f319(f319(f301(x90811),x90814),f180(f932(x90811,a923)))))+~P1(f319(f319(f321(f931(x90811,x90811)),f319(f319(f244(x90811,x90811),x90813),x90814)),x90812))
% 28.25/28.13 [9272]P1(f319(x92721,x92722))+~P1(f319(f319(f321(x92723),x92722),x92725))+P1(f319(f319(f321(x92723),f567(x92721,x92724,x92725,x92723)),f319(f319(f102(f932(x92723,a923)),x92725),x92724)))
% 28.25/28.13 [9273]P1(f319(x92731,x92732))+~P1(f319(f319(f321(x92733),x92732),x92734))+P1(f319(f319(f321(x92733),f567(x92731,x92734,x92735,x92733)),f319(f319(f102(f932(x92733,a923)),x92735),x92734)))
% 28.25/28.13 [9281]~P1(f319(x92812,x92815))+~P1(f319(f319(f321(x92811),x92815),x92814))+P1(f319(f319(f321(x92811),f615(x92812,x92813,x92814,x92811)),f319(f319(f102(f932(x92811,a923)),x92814),x92813)))
% 28.25/28.13 [9282]~P1(f319(x92822,x92825))+~P1(f319(f319(f321(x92821),x92825),x92823))+P1(f319(f319(f321(x92821),f615(x92822,x92823,x92824,x92821)),f319(f319(f102(f932(x92821,a923)),x92824),x92823)))
% 28.25/28.13 [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(f102(f932(x92971,a923)),x92972),x92973)),f319(f319(f102(f932(x92971,a923)),x92974),x92975)))
% 28.25/28.13 [9298]~P1(f319(f319(f226(f932(x92981,a923)),x92983),x92985))+~P1(f319(f319(f226(f932(x92981,a923)),x92982),x92984))+P1(f319(f319(f226(f932(x92981,a923)),f319(f319(f93(f932(x92981,a923)),x92982),x92983)),f319(f319(f93(f932(x92981,a923)),x92984),x92985)))
% 28.25/28.13 [9299]~P1(f319(f319(f226(f932(x92991,a923)),x92995),x92993))+~P1(f319(f319(f226(f932(x92991,a923)),x92992),x92994))+P1(f319(f319(f226(f932(x92991,a923)),f319(f319(f23(f932(x92991,a923)),x92992),x92993)),f319(f319(f23(f932(x92991,a923)),x92994),x92995)))
% 28.25/28.13 [9396]P1(f319(f319(f321(f931(x93961,x93961)),f319(f319(f244(x93961,x93961),x93962),x93963)),f313(x93961,x93964,x93965)))+~P1(f319(f319(f226(a925),f319(x93964,x93962)),f319(x93964,x93963)))+~P1(f319(f319(f321(f931(x93961,x93961)),f319(f319(f244(x93961,x93961),x93962),x93963)),x93965))
% 28.25/28.13 [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),x95842),x95845)),f299(x95841,x95844)))+~P1(f319(f319(f321(f931(x95841,x95841)),f319(f319(f244(x95841,x95841),x95845),x95843)),x95844))
% 28.25/28.13 [9585]P1(f319(f319(f321(f931(x95851,x95851)),f319(f319(f244(x95851,x95851),x95852),x95853)),f299(x95851,x95854)))+~P1(f319(f319(f321(f931(x95851,x95851)),f319(f319(f244(x95851,x95851),x95855),x95853)),f299(x95851,x95854)))+~P1(f319(f319(f321(f931(x95851,x95851)),f319(f319(f244(x95851,x95851),x95852),x95855)),x95854))
% 28.25/28.13 [9686]E(x96861,x96862)+E(f319(a104,f635(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)))
% 28.25/28.13 [9687]E(x96871,x96872)+E(f319(a104,f637(x96873,x96874,x96871,x96872,x96875)),x96874)+~P1(f319(f319(f321(f931(x96875,x96875)),f319(f319(f244(x96875,x96875),x96872),x96871)),f319(f319(f175(f931(x96875,x96875),a923),x96874),x96873)))
% 28.25/28.13 [9688]E(x96881,f2(a925))+E(f319(a104,f635(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)))
% 28.25/28.13 [9689]E(x96891,f2(a925))+E(f319(a104,f637(x96892,x96891,x96893,x96894,x96895)),x96891)+~P1(f319(f319(f321(f931(x96895,x96895)),f319(f319(f244(x96895,x96895),x96894),x96893)),f319(f319(f175(f931(x96895,x96895),a923),x96891),x96892)))
% 28.25/28.13 [9711]P1(f319(f319(f321(f931(x97111,x97111)),f319(f319(f244(x97111,x97111),x97112),x97113)),f319(f319(f281(x97111,x97111,x97111),x97114),f299(x97111,x97114))))+~P1(f319(f319(f321(f931(x97111,x97111)),f319(f319(f244(x97111,x97111),x97112),x97115)),x97114))+~P1(f319(f319(f321(f931(x97111,x97111)),f319(f319(f244(x97111,x97111),x97115),x97113)),x97114))
% 28.25/28.13 [9718]~P1(f319(f319(f321(f931(x97181,x97181)),f319(f319(f244(x97181,x97181),x97182),x97185)),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),x97185),x97183)),x97184))
% 28.25/28.13 [9719]~P1(f319(f319(f321(f931(x97191,x97191)),f319(f319(f244(x97191,x97191),x97195),x97193)),f299(x97191,x97194)))+P1(f319(f319(f321(f931(x97191,x97191)),f319(f319(f244(x97191,x97191),x97192),x97193)),f319(f319(f281(x97191,x97191,x97191),x97194),f299(x97191,x97194))))+~P1(f319(f319(f321(f931(x97191,x97191)),f319(f319(f244(x97191,x97191),x97192),x97195)),x97194))
% 28.25/28.13 [9752]~P9(x97521,x97525,x97522)+~P1(f319(f319(f321(f931(x97521,x97521)),f319(f319(f244(x97521,x97521),x97523),x97524)),x97522))+P1(f319(f319(f226(f932(x97521,a923)),f319(f277(x97521,x97521,x97522),f319(f319(f301(x97521),x97523),f180(f932(x97521,a923))))),f319(f277(x97521,x97521,x97522),f319(f319(f301(x97521),x97524),f180(f932(x97521,a923))))))
% 28.25/28.13 [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),x98122),x98125)),f319(f319(f281(x98121,x98121,x98121),x98124),f299(x98121,x98124))))+~P1(f319(f319(f321(f931(x98121,x98121)),f319(f319(f244(x98121,x98121),x98125),x98123)),x98124))
% 28.25/28.13 [9813]P1(f319(f319(f321(f931(x98131,x98131)),f319(f319(f244(x98131,x98131),x98132),x98133)),f319(f319(f281(x98131,x98131,x98131),x98134),f299(x98131,x98134))))+~P1(f319(f319(f321(f931(x98131,x98131)),f319(f319(f244(x98131,x98131),x98135),x98133)),f319(f319(f281(x98131,x98131,x98131),x98134),f299(x98131,x98134))))+~P1(f319(f319(f321(f931(x98131,x98131)),f319(f319(f244(x98131,x98131),x98132),x98135)),x98134))
% 28.25/28.13 [9864]~P1(f319(f60(x98641,x98641,x98644,x98642,x98643),x98645))+P1(f319(f319(f321(x98641),x98642),x98643))+P1(f319(f56(x98641,x98644,f319(f319(f301(x98641),x98642),x98643)),x98645))
% 28.25/28.13 [9902]~E(f319(f302(x99023,x99022,x99025),x99024),x99021)+E(x99021,f180(f932(x99022,a923)))+P1(f319(f319(f226(f932(x99023,a923)),f319(f302(x99022,x99023,f888(x99024,x99023,x99022,x99021)),x99021)),x99024))
% 28.25/28.13 [9955]~P6(x99555)+P1(f319(f319(f321(x99551),f921(x99552,x99553,x99554,x99551,x99555)),x99554))+P1(f319(f319(f226(x99555),f319(f319(f33(x99551,x99555),x99554),x99553)),x99552))
% 28.25/28.13 [9956]~P6(x99565)+P1(f319(f319(f321(x99561),f638(x99562,x99563,x99564,x99561,x99565)),x99564))+P1(f319(f319(f226(x99565),f319(f319(f33(x99561,x99565),x99564),x99563)),x99562))
% 28.25/28.13 [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)),f720(x100195,x100194,x100193,x100192,x100191)),f319(f164(f931(x100191,x100192)),f319(f319(f173(x100191,x100192),x100194),x100195))))
% 28.25/28.13 [10020]P35(x100201,x100202,x100203,x100204,x100205)+~E(f319(f181(f926(x100201)),x100204),f319(f181(f926(x100202)),x100205))+P1(f319(f319(f321(f931(x100201,x100202)),f721(x100203,x100205,x100204,x100202,x100201)),f319(f164(f931(x100201,x100202)),f319(f319(f173(x100201,x100202),x100204),x100205))))
% 28.25/28.13 [10152]E(x101521,x101522)+P1(f319(f319(f321(f931(x101523,x101523)),f319(f319(f244(x101523,x101523),x101521),f639(x101524,x101525,x101522,x101521,x101523))),x101524))+~P1(f319(f319(f321(f931(x101523,x101523)),f319(f319(f244(x101523,x101523),x101521),x101522)),f319(f319(f175(f931(x101523,x101523),a923),x101525),x101524)))
% 28.25/28.13 [10153]E(x101531,f2(a925))+P1(f319(f319(f321(f931(x101532,x101532)),f319(f319(f244(x101532,x101532),x101533),f639(x101534,x101531,x101535,x101533,x101532))),x101534))+~P1(f319(f319(f321(f931(x101532,x101532)),f319(f319(f244(x101532,x101532),x101533),x101535)),f319(f319(f175(f931(x101532,x101532),a923),x101531),x101534)))
% 28.25/28.13 [10192]~P6(x101921)+~P1(f319(f319(f226(x101921),f319(x101924,f921(x101925,x101924,x101923,x101922,x101921))),x101925))+P1(f319(f319(f226(x101921),f319(f319(f33(x101922,x101921),x101923),x101924)),x101925))
% 28.25/28.13 [10193]~P6(x101931)+~P1(f319(f319(f226(x101931),f319(x101934,f638(x101935,x101934,x101933,x101932,x101931))),x101935))+P1(f319(f319(f226(x101931),f319(f319(f33(x101932,x101931),x101933),x101934)),x101935))
% 28.25/28.13 [10247]E(x102471,x102472)+P1(f319(f319(f321(f931(x102473,x102473)),f319(f319(f244(x102473,x102473),f636(x102474,x102475,x102471,x102472,x102473)),x102471)),x102474))+~P1(f319(f319(f321(f931(x102473,x102473)),f319(f319(f244(x102473,x102473),x102472),x102471)),f319(f319(f175(f931(x102473,x102473),a923),x102475),x102474)))
% 28.25/28.13 [10248]E(x102481,f2(a925))+P1(f319(f319(f321(f931(x102482,x102482)),f319(f319(f244(x102482,x102482),f636(x102483,x102481,x102484,x102485,x102482)),x102484)),x102483))+~P1(f319(f319(f321(f931(x102482,x102482)),f319(f319(f244(x102482,x102482),x102485),x102484)),f319(f319(f175(f931(x102482,x102482),a923),x102481),x102483)))
% 28.25/28.13 [10252]E(x102521,x102522)+P1(f319(f319(f321(f931(x102523,x102523)),f319(f319(f244(x102523,x102523),x102521),f636(x102524,x102525,x102522,x102521,x102523))),f319(f319(f175(f931(x102523,x102523),a923),f635(x102524,x102525,x102522,x102521,x102523)),x102524)))+~P1(f319(f319(f321(f931(x102523,x102523)),f319(f319(f244(x102523,x102523),x102521),x102522)),f319(f319(f175(f931(x102523,x102523),a923),x102525),x102524)))
% 28.25/28.13 [10253]E(x102531,f2(a925))+P1(f319(f319(f321(f931(x102532,x102532)),f319(f319(f244(x102532,x102532),x102533),f636(x102534,x102531,x102535,x102533,x102532))),f319(f319(f175(f931(x102532,x102532),a923),f635(x102534,x102531,x102535,x102533,x102532)),x102534)))+~P1(f319(f319(f321(f931(x102532,x102532)),f319(f319(f244(x102532,x102532),x102533),x102535)),f319(f319(f175(f931(x102532,x102532),a923),x102531),x102534)))
% 28.25/28.13 [10307]E(x103071,x103072)+P1(f319(f319(f321(f931(x103073,x103073)),f319(f319(f244(x103073,x103073),f639(x103074,x103075,x103071,x103072,x103073)),x103071)),f319(f319(f175(f931(x103073,x103073),a923),f637(x103074,x103075,x103071,x103072,x103073)),x103074)))+~P1(f319(f319(f321(f931(x103073,x103073)),f319(f319(f244(x103073,x103073),x103072),x103071)),f319(f319(f175(f931(x103073,x103073),a923),x103075),x103074)))
% 28.25/28.13 [10308]E(x103081,f2(a925))+P1(f319(f319(f321(f931(x103082,x103082)),f319(f319(f244(x103082,x103082),f639(x103083,x103081,x103084,x103085,x103082)),x103084)),f319(f319(f175(f931(x103082,x103082),a923),f637(x103083,x103081,x103084,x103085,x103082)),x103083)))+~P1(f319(f319(f321(f931(x103082,x103082)),f319(f319(f244(x103082,x103082),x103085),x103084)),f319(f319(f175(f931(x103082,x103082),a923),x103081),x103083)))
% 28.25/28.13 [10342]~P79(x103422)+~P1(f319(f55(x103421),x103425))+E(f319(f319(f6(x103421,x103422),f319(f319(f7(x103421,x103422,x103422),f319(f319(f18(x103421,x103422,f932(x103422,x103422)),f319(f319(f8(a923,f932(x103422,f932(x103422,x103422)),x103421),f86(x103422)),f319(f319(f7(x103421,f932(x103421,a923),a923),f321(x103421)),x103423))),x103424)),f2(x103422))),x103425),f319(f319(f6(x103421,x103422),x103424),f319(f319(f93(f932(x103421,a923)),x103425),x103423)))
% 28.25/28.13 [8864]~P79(x88641)+~P1(f319(f55(x88644),x88645))+E(f319(f319(f74(x88641),f319(x88642,x88643)),f319(f319(f6(x88644,x88641),x88642),f319(f319(f23(f932(x88644,a923)),x88645),f319(f319(f301(x88644),x88643),f180(f932(x88644,a923)))))),f319(f319(f6(x88644,x88641),x88642),f319(f319(f301(x88644),x88643),x88645)))
% 28.25/28.13 [8865]~P78(x88651)+~P1(f319(f55(x88654),x88655))+E(f319(f319(f75(x88651),f319(x88652,x88653)),f319(f319(f9(x88654,x88651),x88652),f319(f319(f23(f932(x88654,a923)),x88655),f319(f319(f301(x88654),x88653),f180(f932(x88654,a923)))))),f319(f319(f9(x88654,x88651),x88652),f319(f319(f301(x88654),x88653),x88655)))
% 28.25/28.13 [9203]~P4(x92032)+~P14(x92032,f319(f160(x92032),f319(f319(f146(x92031,x92032),x92034),x92035)))+E(f319(f128(x92031,f319(f319(f8(x92032,a923,x92031),f319(f227(x92032),x92033)),x92034)),x92035),f169(x92031,f319(f319(f8(x92032,a923,x92031),f319(f227(x92032),x92033)),x92034),x92035))
% 28.25/28.13 [9228]~P79(x92281)+E(f319(f319(f74(x92281),f319(f319(f6(a925,x92281),x92282),f295(a925,x92283,x92284))),f319(f319(f6(a925,x92281),x92282),f295(a925,f319(f319(f74(a925),x92284),f72(a925)),f319(f319(f74(a925),x92284),x92285)))),f319(f319(f6(a925,x92281),x92282),f295(a925,x92283,f319(f319(f74(a925),x92284),x92285))))+~P1(f319(f319(f226(a925),x92283),f319(f319(f74(a925),x92284),f72(a925))))
% 28.25/28.13 [9229]~P1(f319(f319(f321(x92291),x92294),x92295))+~P1(f319(f319(f226(f932(x92291,a923)),f319(f164(x92291),x92292)),x92295))+P1(f319(f319(f226(f932(x92291,a923)),f319(f164(x92291),f319(f319(f151(x92291,x92292),x92293),x92294))),x92295))
% 28.25/28.13 [9457]~P6(x94572)+~P1(f319(f55(x94571),x94575))+E(f319(f319(f58(x94571,x94572,f319(f319(f8(x94572,f932(x94572,x94572),x94571),f102(x94572)),x94573)),x94574),x94575),f319(f319(f102(x94572),x94574),f319(f319(f33(x94571,x94572),x94575),x94573)))
% 28.25/28.13 [9458]~P6(x94582)+~P1(f319(f55(x94581),x94585))+E(f319(f319(f58(x94581,x94582,f319(f319(f8(x94582,f932(x94582,x94582),x94581),f93(x94582)),x94583)),x94584),x94585),f319(f319(f93(x94582),x94584),f319(f319(f34(x94581,x94582),x94585),x94583)))
% 28.25/28.13 [9507]E(f319(x95071,x95072),f319(x95071,x95073))+P1(f319(f319(f227(a925),f319(x95071,x95072)),f319(x95071,x95073)))+~P1(f319(f319(f321(f931(x95074,x95074)),f319(f319(f244(x95074,x95074),x95072),x95073)),f145(x95074,f319(f319(f143(f932(x95074,a925)),x95071),x95075))))
% 28.25/28.13 [9541]~E(f319(x95414,x95412),f319(x95414,x95413))+~P1(f319(f319(f321(f931(x95411,x95411)),f319(f319(f244(x95411,x95411),x95412),x95413)),f145(x95411,x95415)))+P1(f319(f319(f321(f931(x95411,x95411)),f319(f319(f244(x95411,x95411),x95412),x95413)),f145(x95411,f319(f319(f143(f932(x95411,a925)),x95414),x95415))))
% 28.25/28.13 [9562]~P26(x95621,x95622,x95623,x95625)+P26(x95621,x95622,x95623,f319(f319(f301(x95621),x95624),x95625))+P1(f319(f319(f321(x95622),f319(x95623,x95624)),f319(f302(x95621,x95622,x95623),f319(f319(f23(f932(x95621,a923)),x95625),f319(f319(f301(x95621),x95624),f180(f932(x95621,a923)))))))
% 28.25/28.13 [9565]P1(f319(x95652,x95655))+~P1(f319(f319(f321(x95651),x95655),f319(f164(x95651),x95653)))+E(f319(f319(f130(x95651),f319(f181(f926(x95651)),f169(x95651,x95652,f319(f319(f126(x95651),x95653),x95654)))),f319(f319(f126(x95651),x95653),x95654)),f319(f319(f126(x95651),f319(f319(f130(x95651),f319(f181(f926(x95651)),f169(x95651,x95652,x95653))),x95653)),x95654))
% 28.25/28.13 [9570]~P1(f319(f319(f321(f931(x95701,x95701)),f319(f319(f244(x95701,x95701),x95702),x95703)),f145(x95701,x95705)))+~P1(f319(f319(f226(a925),f319(x95704,x95702)),f319(x95704,x95703)))+P1(f319(f319(f321(f931(x95701,x95701)),f319(f319(f244(x95701,x95701),x95702),x95703)),f145(x95701,f319(f319(f143(f932(x95701,a925)),x95704),x95705))))
% 28.25/28.13 [9637]P1(f319(f319(f321(f931(x96374,x96374)),f319(f319(f244(x96374,x96374),x96372),x96373)),f145(x96374,x96375)))+P1(f319(f319(f227(a925),f319(x96371,x96372)),f319(x96371,x96373)))+~P1(f319(f319(f321(f931(x96374,x96374)),f319(f319(f244(x96374,x96374),x96372),x96373)),f145(x96374,f319(f319(f143(f932(x96374,a925)),x96371),x96375))))
% 28.25/28.13 [9784]~P1(f319(f319(f321(f931(f926(x97841),f926(x97841))),f319(f319(f244(f926(x97841),f926(x97841)),x97842),x97844)),f150(x97841,x97845)))+~P1(f319(f319(f227(a925),x97843),f319(f181(f926(x97841)),x97842)))+P1(f319(f319(f321(f931(x97841,x97841)),f319(f319(f244(x97841,x97841),f319(f319(f156(x97841),x97842),x97843)),f319(f319(f156(x97841),x97844),x97843))),x97845))
% 28.25/28.13 [10043]E(x100431,f2(a1))+~P1(f319(f43(x100433,x100431),f319(f319(f244(a1,a1),x100434),x100435)))+P1(f319(f43(f319(f319(f75(a1),x100432),x100433),x100431),f319(f319(f244(a1,a1),f319(f319(f74(a1),f319(f319(f75(a1),x100432),x100434)),f319(f319(f30(a1),f319(f319(f75(a1),x100432),x100435)),x100431))),f39(a1,f319(f319(f75(a1),x100432),x100435),x100431))))
% 28.25/28.13 [10045]~P1(f319(f319(f227(a925),f2(a925)),x100453))+~P1(f319(f42(x100452,x100453),f319(f319(f244(a925,a925),x100454),x100455)))+P1(f319(f42(f319(f319(f75(a925),x100451),x100452),x100453),f319(f319(f244(a925,a925),f319(f319(f74(a925),f319(f319(f75(a925),x100451),x100454)),f319(f319(f30(a925),f319(f319(f75(a925),x100451),x100455)),x100453))),f39(a925,f319(f319(f75(a925),x100451),x100455),x100453))))
% 28.25/28.13 [10365]~P79(x103652)+~P1(f319(f55(x103651),x103654))+E(f319(f319(f6(x103651,x103652),x103653),f319(f254(x103651),f319(f319(f18(x103651,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103651),a317),f319(f319(f7(x103651,f932(x103651,a923),a923),f321(x103651)),x103654))),f319(f319(f7(x103651,f932(x103651,a923),a923),f321(x103651)),x103655)))),f319(f319(f6(x103651,x103652),f319(f319(f7(x103651,x103652,x103652),f319(f319(f18(x103651,x103652,f932(x103652,x103652)),f319(f319(f8(a923,f932(x103652,f932(x103652,x103652)),x103651),f86(x103652)),f319(f319(f7(x103651,f932(x103651,a923),a923),f321(x103651)),x103655))),x103653)),f2(x103652))),x103654))
% 28.25/28.13 [8488]~E(f319(f319(f126(x84881),x84882),x84885),f319(f319(f126(x84881),x84883),x84884))+E(f319(f319(f126(x84881),f319(f319(f130(x84881),f319(f181(f926(x84881)),x84882)),x84883)),x84884),x84885)+P1(f319(f319(f226(a925),f319(f181(f926(x84881)),x84883)),f319(f181(f926(x84881)),x84882)))
% 28.25/28.13 [8688]~E(f319(f319(f126(x86882),x86883),x86881),f319(f319(f126(x86882),x86884),x86885))+E(x86881,f319(f319(f126(x86882),f319(f319(f130(x86882),f319(f181(f926(x86882)),x86883)),x86884)),x86885))+~P1(f319(f319(f226(a925),f319(f181(f926(x86882)),x86883)),f319(f181(f926(x86882)),x86884)))
% 28.25/28.13 [8778]~E(f319(f319(f74(a925),f319(f319(f75(a925),x87783),x87784)),x87781),f319(f319(f74(a925),f319(f319(f75(a925),x87782),x87784)),x87785))+~P1(f319(f319(f226(a925),x87783),x87782))+E(x87781,f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x87782),x87783)),x87784)),x87785))
% 28.25/28.13 [8779]~E(f319(f319(f74(a925),f319(f319(f75(a925),x87791),x87793)),x87794),f319(f319(f74(a925),f319(f319(f75(a925),x87792),x87793)),x87795))+~P1(f319(f319(f226(a925),x87792),x87791))+E(f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x87791),x87792)),x87793)),x87794),x87795)
% 28.25/28.13 [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(x89485,f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x89481),x89484)),x89482)),x89483))
% 28.25/28.13 [8949]E(f319(f319(f74(a925),f319(f319(f75(a925),x89491),x89492)),x89493),f319(f319(f74(a925),f319(f319(f75(a925),x89494),x89492)),x89495))+~P1(f319(f319(f226(a925),x89494),x89491))+~E(f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x89491),x89494)),x89492)),x89493),x89495)
% 28.25/28.13 [9836]~P79(x98362)+~P1(f319(f55(x98361),x98365))+E(f319(f319(f6(x98361,x98362),f319(f319(f18(x98361,x98362,x98362),f319(f319(f8(x98362,f932(x98362,x98362),x98361),f74(x98362)),x98363)),x98364)),x98365),f319(f319(f74(x98362),f319(f319(f6(x98361,x98362),x98363),x98365)),f319(f319(f6(x98361,x98362),x98364),x98365)))
% 28.25/28.13 [9837]~P78(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),f75(x98372)),x98373)),x98374)),x98375),f319(f319(f75(x98372),f319(f319(f9(x98371,x98372),x98373),x98375)),f319(f319(f9(x98371,x98372),x98374),x98375)))
% 28.25/28.13 [9838]~P72(x98382)+~P1(f319(f55(x98381),x98385))+E(f319(f319(f9(x98381,x98382),f319(f319(f18(x98381,x98382,x98382),f319(f319(f8(x98382,f932(x98382,x98382),x98381),f283(x98382)),x98383)),x98384)),x98385),f319(f319(f283(x98382),f319(f319(f9(x98381,x98382),x98383),x98385)),f319(f319(f9(x98381,x98382),x98384),x98385)))
% 28.25/28.13 [9979]~E(f641(x99795,x99794,x99793,x99792,x99791),f642(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))))
% 28.25/28.13 [9980]~E(f643(x99805,x99804,x99803,x99802,x99801),f644(x99805,x99804,x99803,x99802,x99801))+P1(f319(f319(f321(f931(x99801,x99801)),f319(f319(f244(x99801,x99801),x99802),x99803)),f299(x99801,x99804)))+~P1(f319(f319(f321(f931(x99801,x99801)),f319(f319(f244(x99801,x99801),x99802),x99803)),f299(x99801,f319(f319(f102(f932(f931(x99801,x99801),a923)),x99804),x99805))))
% 28.25/28.13 [10182]P1(f319(f319(f321(f931(x101821,x101821)),f319(f319(f244(x101821,x101821),x101822),f644(x101825,x101824,x101823,x101822,x101821))),f299(x101821,x101824)))+P1(f319(f319(f321(f931(x101821,x101821)),f319(f319(f244(x101821,x101821),x101822),x101823)),f299(x101821,x101824)))+~P1(f319(f319(f321(f931(x101821,x101821)),f319(f319(f244(x101821,x101821),x101822),x101823)),f299(x101821,f319(f319(f102(f932(f931(x101821,x101821),a923)),x101824),x101825))))
% 28.25/28.13 [10274]P1(f319(f319(f321(f931(x102741,x102741)),f319(f319(f244(x102741,x102741),f642(x102745,x102744,x102743,x102742,x102741)),x102743)),f299(x102741,x102744)))+P1(f319(f319(f321(f931(x102741,x102741)),f319(f319(f244(x102741,x102741),x102742),x102743)),f299(x102741,x102744)))+~P1(f319(f319(f321(f931(x102741,x102741)),f319(f319(f244(x102741,x102741),x102742),x102743)),f299(x102741,f319(f319(f102(f932(f931(x102741,x102741),a923)),x102744),x102745))))
% 28.25/28.13 [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),f641(x103145,x103144,x103143,x103142,x103141)),f642(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))))
% 28.25/28.13 [10315]P1(f319(f319(f321(f931(x103151,x103151)),f319(f319(f244(x103151,x103151),x103152),x103153)),f299(x103151,x103154)))+P1(f319(f319(f321(f931(x103151,x103151)),f319(f319(f244(x103151,x103151),f644(x103155,x103154,x103153,x103152,x103151)),f643(x103155,x103154,x103153,x103152,x103151))),x103155))+~P1(f319(f319(f321(f931(x103151,x103151)),f319(f319(f244(x103151,x103151),x103152),x103153)),f299(x103151,f319(f319(f102(f932(f931(x103151,x103151),a923)),x103154),x103155))))
% 28.25/28.13 [10460]~P1(f319(f319(f321(f931(f926(x104601),f926(x104601))),f319(f319(f244(f926(x104601),f926(x104601)),x104604),x104605)),f150(x104601,x104602)))+~P1(f319(f319(f321(f931(x104601,x104601)),x104603),f319(f164(f931(x104601,x104601)),f319(f319(f173(x104601,x104601),x104604),x104605))))+P1(f319(f319(f249(x104601,x104601,a923),f319(f319(f7(x104601,f932(f931(x104601,x104601),a923),f932(x104601,a923)),f319(f319(f8(f932(x104601,f932(f932(f931(x104601,x104601),a923),a923)),f932(f932(f931(x104601,x104601),a923),f932(x104601,a923)),x104601),f7(x104601,f932(f931(x104601,x104601),a923),a923)),f319(f319(f8(f932(x104601,f931(x104601,x104601)),f932(x104601,f932(f932(f931(x104601,x104601),a923),a923)),x104601),f319(f8(f931(x104601,x104601),f932(f932(f931(x104601,x104601),a923),a923),x104601),f321(f931(x104601,x104601)))),f244(x104601,x104601)))),x104602)),x104603))
% 28.25/28.13 [9868]~P1(f319(f319(f226(a925),x98683),x98682))+~P1(f319(f319(f226(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(f226(a925),x98681),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x98682),x98683)),x98684)),x98685)))
% 28.25/28.13 [9869]~P1(f319(f319(f226(a925),x98693),x98692))+~P1(f319(f319(f227(a925),f319(f319(f74(a925),f319(f319(f75(a925),x98693),x98694)),x98691)),f319(f319(f74(a925),f319(f319(f75(a925),x98692),x98694)),x98695)))+P1(f319(f319(f227(a925),x98691),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x98692),x98693)),x98694)),x98695)))
% 28.25/28.13 [9886]~P1(f319(f319(f226(a925),x98861),x98864))+P1(f319(f319(f226(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(f226(a925),x98863),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x98864),x98861)),x98862)),x98865)))
% 28.25/28.13 [9887]~P1(f319(f319(f226(a925),x98871),x98874))+P1(f319(f319(f227(a925),f319(f319(f74(a925),f319(f319(f75(a925),x98871),x98872)),x98873)),f319(f319(f74(a925),f319(f319(f75(a925),x98874),x98872)),x98875)))+~P1(f319(f319(f227(a925),x98873),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x98874),x98871)),x98872)),x98875)))
% 28.25/28.13 [10017]~P1(f319(f319(f226(a925),x100172),x100171))+~P1(f319(f319(f226(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(f226(a925),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x100171),x100172)),x100173)),x100174)),x100175))
% 28.25/28.13 [10018]~P1(f319(f319(f226(a925),x100182),x100181))+~P1(f319(f319(f227(a925),f319(f319(f74(a925),f319(f319(f75(a925),x100181),x100183)),x100184)),f319(f319(f74(a925),f319(f319(f75(a925),x100182),x100183)),x100185)))+P1(f319(f319(f227(a925),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x100181),x100182)),x100183)),x100184)),x100185))
% 28.25/28.13 [10064]~P1(f319(f319(f226(a925),x100644),x100641))+P1(f319(f319(f226(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(f226(a925),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x100641),x100644)),x100642)),x100643)),x100645))
% 28.25/28.13 [10065]~P1(f319(f319(f226(a925),x100654),x100651))+P1(f319(f319(f227(a925),f319(f319(f74(a925),f319(f319(f75(a925),x100651),x100652)),x100653)),f319(f319(f74(a925),f319(f319(f75(a925),x100654),x100652)),x100655)))+~P1(f319(f319(f227(a925),f319(f319(f74(a925),f319(f319(f75(a925),f319(f319(f23(a925),x100651),x100654)),x100652)),x100653)),x100655))
% 28.25/28.13 [10302]~P12(x103021,x103022,x103025,x103023)+~P1(f319(f319(f321(f931(x103021,x103021)),x103024),x103025))+P1(f319(f319(f249(x103021,x103021,a923),f319(f319(f7(x103021,f932(x103021,x103022),f932(x103021,a923)),f319(f319(f8(f932(x103022,a923),f932(f932(x103021,x103022),f932(x103021,a923)),x103021),f8(x103022,a923,x103021)),f319(f319(f8(x103022,f932(x103022,a923),x103021),a316),x103023))),x103023)),x103024))
% 28.25/28.13 [10323]~P113(x103231)+~P41(x103231,f932(x103232,a923),x103233)+P41(x103231,f932(x103232,a923),f319(f319(f7(x103231,f932(x103232,a923),f932(x103232,a923)),f319(f319(f8(f932(x103232,a923),f932(f932(x103232,a923),f932(x103232,a923)),x103231),f102(f932(x103232,a923))),f319(f319(f7(x103231,f932(x103232,a923),f932(x103232,a923)),f319(f319(f8(f932(x103232,a923),f932(f932(x103232,a923),f932(x103232,a923)),x103231),f102(f932(x103232,a923))),x103233)),x103234))),x103235))
% 28.25/28.13 [8650]~P21(x86506,x86501,x86502,x86504)+E(f319(f66(x86501,x86501,x86501,f319(x86502,x86503)),f319(x86504,x86505)),f319(f66(x86501,x86501,x86501,f319(x86504,x86505)),f319(x86502,x86503)))+~P1(f319(f55(x86506),x86505))
% 28.25/28.13 [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)
% 28.25/28.13 [9093]~P26(x90931,x90933,x90935,x90936)+~P26(x90933,x90932,x90934,f319(f302(x90931,x90933,x90935),x90936))+P26(x90931,x90932,f319(f66(x90933,x90932,x90931,x90934),x90935),x90936)
% 28.25/28.13 [9277]~P26(x92774,x92771,x92775,x92776)+~P26(x92774,x92772,f319(f66(x92771,x92772,x92774,x92773),x92775),x92776)+P26(x92771,x92772,x92773,f319(f302(x92774,x92771,x92775),x92776))
% 28.25/28.13 [9670]~P1(f319(f319(x96703,x96702),x96706))+~P1(f319(f319(x96704,x96705),x96702))+P1(f319(f319(f321(x96701),x96702),f292(x96701,x96703,x96704,x96705,x96706)))
% 28.25/28.13 [9671]~P1(f319(f319(x96714,x96712),x96716))+~P1(f319(f319(x96713,x96715),x96712))+P1(f319(f319(f321(x96711),x96712),f289(x96711,x96713,x96714,x96715,x96716)))
% 28.25/28.13 [9785]E(x97851,x97852)+E(x97853,x97854)+~P1(f319(f319(f321(f931(f926(x97855),f926(x97855))),f319(f319(f244(f926(x97855),f926(x97855)),f319(f319(f143(x97855),x97853),x97851)),f319(f319(f143(x97855),x97854),x97852))),f149(x97855,x97856)))
% 28.25/28.13 [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))),f137(x97941,x97946)))+~P1(f319(f319(f321(f931(f926(x97941),f926(x97941))),f319(f319(f244(f926(x97941),f926(x97941)),x97943),x97945)),f137(x97941,x97946)))
% 28.25/28.13 [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))),f139(x97951,x97956)))+~P1(f319(f319(f321(f931(f926(x97951),f926(x97951))),f319(f319(f244(f926(x97951),f926(x97951)),x97953),x97955)),f139(x97951,x97956)))
% 28.25/28.13 [9796]~E(x97962,x97964)+P1(f319(f319(f321(f931(f926(x97961),f926(x97961))),f319(f319(f244(f926(x97961),f926(x97961)),f319(f319(f143(x97961),x97962),x97963)),f319(f319(f143(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)))
% 28.25/28.13 [9797]~E(x97972,x97974)+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)),x97973),x97975)),f149(x97971,x97976)))
% 28.25/28.13 [9798]~E(x97983,x97985)+P1(f319(f319(f321(f931(f926(x97981),f926(x97981))),f319(f319(f244(f926(x97981),f926(x97981)),f319(f319(f126(x97981),x97982),x97983)),f319(f319(f126(x97981),x97984),x97985))),f149(x97981,x97986)))+~P1(f319(f319(f321(f931(f926(x97981),f926(x97981))),f319(f319(f244(f926(x97981),f926(x97981)),x97982),x97984)),f149(x97981,x97986)))
% 28.25/28.13 [9856]E(x98561,x98562)+P1(f319(f319(f321(f931(f926(x98563),f926(x98563))),f319(f319(f244(f926(x98563),f926(x98563)),x98561),x98562)),f149(x98563,x98564)))+~P1(f319(f319(f321(f931(f926(x98563),f926(x98563))),f319(f319(f244(f926(x98563),f926(x98563)),f319(f319(f143(x98563),x98565),x98561)),f319(f319(f143(x98563),x98566),x98562))),f149(x98563,x98564)))
% 28.25/28.13 [10021]~E(x100213,x100215)+P1(f319(f319(f321(f931(f926(x100211),f926(x100211))),f319(f319(f244(f926(x100211),f926(x100211)),f319(f319(f126(x100211),x100212),f319(f319(f143(x100211),x100213),f105(x100211)))),f319(f319(f126(x100211),x100214),f319(f319(f143(x100211),x100215),f105(x100211))))),f149(x100211,x100216)))+~P1(f319(f319(f321(f931(f926(x100211),f926(x100211))),f319(f319(f244(f926(x100211),f926(x100211)),x100212),x100214)),f149(x100211,x100216)))
% 28.25/28.13 [10068]E(x100681,x100682)+E(x100683,x100684)+~P1(f319(f319(f321(f931(f926(x100685),f926(x100685))),f319(f319(f244(f926(x100685),f926(x100685)),f319(f319(f126(x100685),x100683),f319(f319(f143(x100685),x100681),f105(x100685)))),f319(f319(f126(x100685),x100684),f319(f319(f143(x100685),x100682),f105(x100685))))),f149(x100685,x100686)))
% 28.25/28.13 [10097]E(x100971,x100972)+~P1(f319(f319(f321(f931(f926(x100973),f926(x100973))),f319(f319(f244(f926(x100973),f926(x100973)),f319(f319(f126(x100973),x100971),f319(f319(f143(x100973),x100975),f105(x100973)))),f319(f319(f126(x100973),x100972),f319(f319(f143(x100973),x100976),f105(x100973))))),f149(x100973,x100974)))+P1(f319(f319(f321(f931(f926(x100973),f926(x100973))),f319(f319(f244(f926(x100973),f926(x100973)),x100971),x100972)),f149(x100973,x100974)))
% 28.25/28.13 [10135]~P1(f319(f319(f321(f931(f932(x101351,a923),f932(x101351,a923))),f319(f319(f244(f932(x101351,a923),f932(x101351,a923)),x101352),x101354)),f311(x101351,x101356)))+~P1(f319(f319(f321(f931(f932(x101351,a923),f932(x101351,a923))),f319(f319(f244(f932(x101351,a923),f932(x101351,a923)),x101353),x101355)),f311(x101351,x101356)))+P1(f319(f319(f321(f931(f932(x101351,a923),f932(x101351,a923))),f319(f319(f244(f932(x101351,a923),f932(x101351,a923)),f319(f319(f102(f932(x101351,a923)),x101352),x101353)),f319(f319(f102(f932(x101351,a923)),x101354),x101355))),f311(x101351,x101356)))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [7032]E(f319(x70321,x70322),f319(x70323,x70322))+~E(f319(f319(f146(x70324,x70325),x70321),x70326),f319(f319(f146(x70324,x70325),x70323),x70326))+~P1(f319(f319(f321(x70324),x70322),f319(f164(x70324),x70326)))
% 28.25/28.13 [7419]~P21(x74194,x74195,x74196,x74191)+E(f319(f319(x74191,x74192),x74193),f319(f319(f58(x74194,x74195,x74196),x74193),x74192))+~P1(f319(f55(x74194),x74192))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [7491]~E(x74912,f319(x74914,x74916))+~P1(f319(f319(f321(x74913),x74916),x74915))+P1(f319(f319(f321(x74911),x74912),f319(f302(x74913,x74911,x74914),x74915)))
% 28.25/28.13 [7492]~E(f319(x74924,x74922),x74926)+~P1(f319(f319(f321(x74923),x74926),x74925))+P1(f319(f319(f321(x74921),x74922),f319(f303(x74921,x74923,x74924),x74925)))
% 28.25/28.13 [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))
% 28.25/28.13 [7935]~P33(x79351,x79352,x79354,x79356)+P33(x79351,x79352,f319(f319(f143(x79351),x79353),x79354),f319(f319(f143(x79351),x79355),x79356))+~P1(f319(f319(x79352,x79353),x79355))
% 28.25/28.13 [8958]~P61(x89584,x89585,x89581,x89582,x89586)+E(f319(x89581,f319(x89582,x89583)),x89583)+~P1(f319(f319(f321(x89585),x89583),x89586))
% 28.25/28.13 [9466]~P27(x94662,x94661,x94665,x94664,x94663)+E(f319(f85(x94661,x94662,x94663,f85(x94662,x94661,x94664,x94665)),x94666),f319(x94665,x94666))+~P1(f319(f319(f321(x94662),x94666),x94664))
% 28.25/28.13 [9477]~P26(x94771,x94772,x94773,x94776)+P26(x94771,x94772,f68(x94771,x94772,x94773,x94774,x94775),x94776)+P1(f319(f319(f321(x94772),x94775),f319(f302(x94771,x94772,x94773),x94776)))
% 28.25/28.13 [9787]E(x97871,x97872)+E(f319(f181(f926(x97873)),x97874),f319(f181(f926(x97873)),x97875))+~P1(f319(f319(f321(f931(f926(x97873),f926(x97873))),f319(f319(f244(f926(x97873),f926(x97873)),f319(f319(f143(x97873),x97871),x97874)),f319(f319(f143(x97873),x97872),x97875))),f137(x97873,x97876)))
% 28.25/28.13 [9850]~P18(x98501,x98502,x98503)+E(f319(f319(f58(x98501,x98502,x98503),x98504),x98505),x98506)+~P1(f319(f60(x98501,x98502,x98503,x98504,x98505),x98506))
% 28.25/28.13 [9859]E(f319(f181(f926(x98591)),x98592),f319(f181(f926(x98591)),x98593))+P1(f319(f319(f321(f931(f926(x98591),f926(x98591))),f319(f319(f244(f926(x98591),f926(x98591)),x98592),x98593)),f137(x98591,x98594)))+~P1(f319(f319(f321(f931(f926(x98591),f926(x98591))),f319(f319(f244(f926(x98591),f926(x98591)),f319(f319(f143(x98591),x98595),x98592)),f319(f319(f143(x98591),x98596),x98593))),f137(x98591,x98594)))
% 28.25/28.13 [9880]~P1(f319(f319(f321(f931(x98801,x98801)),f319(f319(f244(x98801,x98801),x98802),x98804)),f299(x98801,x98806)))+P1(f319(f319(f321(f931(f926(x98801),f926(x98801))),f319(f319(f244(f926(x98801),f926(x98801)),f319(f319(f143(x98801),x98802),x98803)),f319(f319(f143(x98801),x98804),x98805))),f299(f926(x98801),f149(x98801,x98806))))+~P1(f319(f319(f321(f931(f926(x98801),f926(x98801))),f319(f319(f244(f926(x98801),f926(x98801)),x98803),x98805)),f299(f926(x98801),f149(x98801,x98806))))
% 28.25/28.13 [10074]~P1(f319(x100742,x100746))+~E(f319(f128(x100741,x100742),x100743),f319(f319(f143(x100741),x100744),x100745))+~P1(f319(f319(f321(x100741),x100746),f319(f164(x100741),f767(x100745,x100744,x100743,x100742,x100741))))
% 28.25/28.13 [10075]~P1(f319(x100754,x100756))+~E(f319(f319(f143(x100751),x100752),x100753),f319(f128(x100751,x100754),x100755))+~P1(f319(f319(f321(x100751),x100756),f319(f164(x100751),f765(x100755,x100754,x100753,x100752,x100751))))
% 28.25/28.13 [10399]~P79(x103992)+E(f319(f319(f6(x103991,x103992),f319(f319(f8(f932(x103993,a923),x103992,x103991),f319(f6(x103993,x103992),x103994)),f319(f319(f8(f932(x103993,a923),f932(x103993,a923),x103991),f254(x103993)),f319(f319(f8(f932(x103993,a923),f932(x103993,a923),x103991),f319(f18(x103993,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103993),a317),f319(f319(f7(x103993,f932(x103993,a923),a923),f321(x103993)),x103995)))),f319(f7(x103993,x103991,a923),f319(f319(f8(x103991,f932(x103991,a923),x103993),a316),x103996)))))),f319(f302(x103993,x103991,x103996),x103995)),f319(f319(f6(x103993,x103992),x103994),x103995))+~P1(f319(f55(x103993),x103995))
% 28.25/28.13 [7092]~P4(x70923)+P1(f319(x70922,x70925))+E(f319(f128(x70921,x70922),f319(f319(f140(x70921,x70923,x70924),x70925),x70926)),f319(f128(x70921,x70922),x70926))
% 28.25/28.13 [7094]P1(f319(x70941,x70942))+~E(f158(x70943,x70941,x70944),f319(f319(f244(f926(x70943),f926(x70943)),x70945),x70946))+~P1(f319(f319(f321(x70943),x70942),f319(f164(x70943),x70945)))
% 28.25/28.13 [7138]~P1(f319(x71382,x71386))+~E(f158(x71381,x71382,x71383),f319(f319(f244(f926(x71381),f926(x71381)),x71384),x71385))+~P1(f319(f319(f321(x71381),x71386),f319(f164(x71381),x71385)))
% 28.25/28.13 [7798]~P16(x77981,x77982,x77983)+~P1(f319(f55(x77981),x77986))+E(f319(f319(f58(x77981,x77982,x77983),x77984),f319(f319(f301(x77981),x77985),x77986)),f319(f319(f58(x77981,x77982,x77983),f319(f319(x77983,x77985),x77984)),x77986))
% 28.25/28.13 [7851]~P4(x78512)+~P1(f319(f319(f226(x78512),f319(x78513,x78514)),f319(x78513,x78515)))+E(f319(f319(f140(x78511,x78512,x78513),x78514),f319(f319(f143(x78511),x78515),x78516)),f319(f319(f143(x78511),x78514),f319(f319(f143(x78511),x78515),x78516)))
% 28.25/28.13 [7963]E(x79631,x79632)+~E(f319(f319(f246(x79633,x79634),x79631),f319(f16(f932(x79634,a923),x79633),x79635)),f319(f319(f246(x79633,x79634),x79632),f319(f16(f932(x79634,a923),x79633),x79635)))+~P1(f319(f319(f321(x79634),x79636),x79635))
% 28.25/28.13 [8028]~P16(x80281,x80282,x80283)+~P1(f319(f55(x80281),x80286))+E(f319(f319(f58(x80281,x80282,x80283),x80284),f319(f319(f301(x80281),x80285),x80286)),f319(f319(x80283,x80285),f319(f319(f58(x80281,x80282,x80283),x80284),x80286)))
% 28.25/28.13 [8148]~P18(x81481,x81482,x81483)+~P1(f319(f55(x81481),x81486))+E(f319(f319(f58(x81481,x81482,x81483),f319(f319(x81483,x81484),x81485)),x81486),f319(f319(x81483,x81484),f319(f319(f58(x81481,x81482,x81483),x81485),x81486)))
% 28.25/28.13 [8219]~P22(x82192,x82195,x82196,x82191)+~P1(f319(f55(x82192),x82194))+E(f319(x82191,f319(f319(f301(x82192),x82193),x82194)),f319(f66(x82195,x82195,x82195,f319(x82191,x82194)),f319(x82196,x82193)))
% 28.25/28.13 [8251]~P4(x82512)+P1(f319(f319(f226(x82512),f319(x82513,x82514)),f319(x82513,x82515)))+E(f319(f319(f140(x82511,x82512,x82513),x82514),f319(f319(f143(x82511),x82515),x82516)),f319(f319(f143(x82511),x82515),f319(f319(f140(x82511,x82512,x82513),x82514),x82516)))
% 28.25/28.13 [8394]~E(f319(f181(f926(x83941)),x83945),f319(f181(f926(x83942)),x83946))+~E(f319(f181(f926(x83941)),x83943),f319(f181(f926(x83942)),x83944))+E(f319(f319(f126(f931(x83941,x83942)),f319(f319(f173(x83941,x83942),x83943),x83944)),f319(f319(f173(x83941,x83942),x83945),x83946)),f319(f319(f173(x83941,x83942),f319(f319(f126(x83941),x83943),x83945)),f319(f319(f126(x83942),x83944),x83946)))
% 28.25/28.13 [8506]~E(x85062,f319(f302(x85063,x85061,x85064),x85066))+P1(f319(f319(f226(f932(x85061,a923)),x85062),f319(f302(x85063,x85061,x85064),x85065)))+~P1(f319(f319(f226(f932(x85063,a923)),x85066),x85065))
% 28.25/28.13 [8609]~P4(x86095)+E(f319(x86091,x86092),f319(x86091,x86093))+E(f319(f319(f140(x86094,x86095,x86091),x86092),f319(f319(f140(x86094,x86095,x86091),x86093),x86096)),f319(f319(f140(x86094,x86095,x86091),x86093),f319(f319(f140(x86094,x86095,x86091),x86092),x86096)))
% 28.25/28.13 [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)))
% 28.25/28.13 [8787]~P1(f319(f319(f321(x87872),x87874),f319(x87876,x87873)))+~P1(f319(f319(f321(x87871),x87873),x87875))+P1(f319(f319(f321(f931(x87871,x87872)),f319(f319(f244(x87871,x87872),x87873),x87874)),f319(f319(f246(x87871,x87872),x87875),x87876)))
% 28.25/28.13 [9270]~P79(x92702)+~P26(x92704,x92701,x92705,x92706)+E(f319(f319(f6(x92701,x92702),x92703),f319(f302(x92704,x92701,x92705),x92706)),f319(f319(f6(x92704,x92702),f319(f66(x92701,x92702,x92704,x92703),x92705)),x92706))
% 28.25/28.13 [9271]~P78(x92712)+~P26(x92714,x92711,x92715,x92716)+E(f319(f319(f9(x92711,x92712),x92713),f319(f302(x92714,x92711,x92715),x92716)),f319(f319(f9(x92714,x92712),f319(f66(x92711,x92712,x92714,x92713),x92715)),x92716))
% 28.25/28.13 [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(x93172)),x93173)))
% 28.25/28.13 [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(x93185)),x93186)))
% 28.25/28.13 [9319]~P35(x93192,x93195,x93191,x93193,x93196)+P1(f319(f319(x93191,f319(f319(f156(x93192),x93193),x93194)),f319(f319(f156(x93195),x93196),x93194)))+~P1(f319(f319(f227(a925),x93194),f319(f181(f926(x93192)),x93193)))
% 28.25/28.13 [9330]~E(f319(f302(x93301,x93302,x93303),x93304),x93306)+E(f319(f302(x93301,x93302,x93303),f319(f302(x93302,x93301,f85(x93301,x93302,x93304,x93303)),x93305)),x93305)+~P1(f319(f319(f226(f932(x93302,a923)),x93305),x93306))
% 28.25/28.13 [9536]~P21(x95363,x95361,x95366,x95362)+~P1(f319(f55(x95363),x95364))+E(f319(f66(x95361,x95361,x95361,f319(x95362,f319(f319(f23(f932(x95363,a923)),x95364),f319(f319(f301(x95363),x95365),f180(f932(x95363,a923)))))),f319(x95366,x95365)),f319(x95362,f319(f319(f301(x95363),x95365),x95364)))
% 28.25/28.13 [9549]~P1(f319(f319(f321(x95495),x95493),x95496))+P1(f319(f319(f321(x95491),f319(x95492,x95493)),f88(f932(x95491,a923),x95494)))+~P1(f319(f319(f226(f932(x95491,a923)),f319(f302(x95495,x95491,x95492),x95496)),f319(x95494,f319(f302(x95495,x95491,x95492),x95496))))
% 28.25/28.13 [10164]~E(f319(f302(x101642,x101644,x101646),f234(f932(x101642,a923))),f234(f932(x101644,a923)))+~E(f319(f302(x101641,x101643,x101645),f234(f932(x101641,a923))),f234(f932(x101643,a923)))+E(f319(f302(f931(x101641,x101642),f931(x101643,x101644),f250(x101641,x101643,x101642,x101644,x101645,x101646)),f234(f932(f931(x101641,x101642),a923))),f234(f932(f931(x101643,x101644),a923)))
% 28.25/28.13 [10218]~E(x102183,x102185)+~E(f319(x102186,f746(x102182,x102184,x102186,x102181,x102183,x102185)),f319(x102184,f746(x102182,x102184,x102186,x102181,x102183,x102185)))+E(f319(f319(f34(x102181,f932(x102182,a923)),x102183),x102184),f319(f319(f34(x102181,f932(x102182,a923)),x102185),x102186))
% 28.25/28.13 [10223]~P26(x102233,x102234,x102235,f319(x102236,f901(x102236,x102235,x102234,x102233,x102232,x102231)))+P26(x102233,x102234,x102235,f319(f319(f34(x102232,f932(x102233,a923)),x102231),x102236))+E(x102231,f180(f932(x102232,a923)))
% 28.25/28.13 [10279]~E(x102793,x102795)+E(f319(f319(f34(x102791,f932(x102792,a923)),x102793),x102794),f319(f319(f34(x102791,f932(x102792,a923)),x102795),x102796))+P1(f319(f319(f321(x102791),f746(x102792,x102794,x102796,x102791,x102793,x102795)),x102793))
% 28.25/28.13 [10282]P26(x102826,x102825,x102824,f319(f319(f34(x102822,f932(x102826,a923)),x102821),x102823))+E(x102821,f180(f932(x102822,a923)))+P1(f319(f319(f321(x102822),f901(x102823,x102824,x102825,x102826,x102822,x102821)),x102821))
% 28.25/28.13 [10288]P1(f319(f319(f321(x102881),f609(x102882,x102883,x102884,x102885,x102886,x102881)),x102886))+P1(f319(f319(f226(f932(f931(x102881,x102884),a923)),f319(f319(f246(x102881,x102884),x102886),x102883)),f319(f319(f246(x102881,x102884),x102885),x102882)))+~P1(f319(f319(f226(f932(x102881,a923)),x102886),x102885))
% 28.25/28.13 [10413]~P1(f319(f319(f226(f932(x104132,a923)),f319(x104134,f609(x104136,x104134,x104132,x104135,x104133,x104131))),f319(x104136,f609(x104136,x104134,x104132,x104135,x104133,x104131))))+~P1(f319(f319(f226(f932(x104131,a923)),x104133),x104135))+P1(f319(f319(f226(f932(f931(x104131,x104132),a923)),f319(f319(f246(x104131,x104132),x104133),x104134)),f319(f319(f246(x104131,x104132),x104135),x104136)))
% 28.25/28.13 [7985]~P1(f319(x79851,x79855))+~P1(f319(x79856,x79854))+P1(f319(x79851,f319(f248(x79852,x79853),f319(f319(f244(x79852,x79853),x79854),x79855))))
% 28.25/28.13 [7986]~P1(f319(x79861,x79864))+~P1(f319(x79866,x79865))+P1(f319(x79861,f319(f243(x79862,x79863),f319(f319(f244(x79862,x79863),x79864),x79865))))
% 28.25/28.13 [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))
% 28.25/28.13 [8034]~P1(f319(f319(x80344,x80346),x80345))+~P1(f319(f319(f321(x80341),x80346),x80343))+P1(f319(f319(f319(f33(x80341,f932(x80342,a923)),x80343),x80344),x80345))
% 28.25/28.13 [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)))
% 28.25/28.13 [8344]~P1(f319(f319(f321(x83441),x83442),f319(x83445,x83446)))+~P1(f319(f319(f321(x83443),x83446),x83444))+P1(f319(f319(f321(x83441),x83442),f319(f319(f33(x83443,f932(x83441,a923)),x83444),x83445)))
% 28.25/28.13 [8386]P1(f319(f319(x83861,x83862),x83863))+~P1(f319(f319(x83864,x83862),x83863))+~P1(f319(f319(f226(f932(x83865,f932(x83866,a923))),x83864),x83861))
% 28.25/28.13 [8387]P1(f319(f319(x83871,x83872),x83873))+~P1(f319(f319(x83874,x83872),x83873))+~P1(f319(f319(f226(f932(x83875,f932(x83876,a923))),x83874),x83871))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [8530]P1(f319(f319(x85301,x85302),x85303))+~P1(f319(f319(f321(x85304),x85302),x85305))+~P1(f319(f319(f319(f34(x85304,f932(x85306,a923)),x85305),x85301),x85303))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [8665]P1(f319(f319(f321(x86651),x86652),f319(x86653,x86654)))+~P1(f319(f319(f321(x86655),x86654),x86656))+~P1(f319(f319(f321(x86651),x86652),f319(f319(f34(x86655,f932(x86651,a923)),x86656),x86653)))
% 28.25/28.13 [8937]~P12(x89374,x89375,x89376,x89371)+E(f319(x89371,x89372),f319(x89371,x89373))+~P1(f319(f319(f321(f931(x89374,x89374)),f319(f319(f244(x89374,x89374),x89372),x89373)),x89376))
% 28.25/28.13 [8972]P1(f319(f319(f226(f932(x89721,a923)),x89722),f319(x89723,x89724)))+~P1(f319(f319(f321(x89725),x89724),x89726))+~P1(f319(f319(f226(f932(x89721,a923)),x89722),f319(f319(f34(x89725,f932(x89721,a923)),x89726),x89723)))
% 28.25/28.13 [9006]~P59(x90063,x90064,f319(f278(x90064,x90063),x90065))+E(x90061,f180(f932(x90062,a923)))+E(f319(f319(f34(x90062,f932(x90063,a923)),x90061),f319(f319(f8(f932(x90064,a923),f932(x90063,a923),x90062),f277(x90064,x90063,x90065)),x90066)),f319(f277(x90064,x90063,x90065),f319(f319(f34(x90062,f932(x90064,a923)),x90061),x90066)))
% 28.25/28.13 [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))
% 28.25/28.13 [9084]P1(f319(f319(f321(x90841),x90842),f319(f277(x90843,x90841,x90844),x90845)))+~P1(f319(f319(f321(x90843),x90846),x90845))+~P1(f319(f319(f321(f931(x90843,x90841)),f319(f319(f244(x90843,x90841),x90846),x90842)),x90844))
% 28.25/28.13 [9398]P1(f319(f319(f226(f932(x93981,a923)),f319(f277(x93982,x93981,x93983),x93984)),f319(f277(x93982,x93981,x93985),x93986)))+~P1(f319(f319(f226(f932(x93982,a923)),x93984),x93986))+~P1(f319(f319(f226(f932(f931(x93982,x93981),a923)),x93983),x93985))
% 28.25/28.13 [9586]~P1(f319(f319(f321(x95862),x95866),x95864))+~P1(f319(f319(f226(f932(x95861,a923)),x95863),x95865))+P1(f319(f319(f226(f932(f931(x95861,x95862),a923)),f319(f319(f246(x95861,x95862),x95863),f319(f16(f932(x95862,a923),x95861),x95864))),f319(f319(f246(x95861,x95862),x95865),f319(f16(f932(x95862,a923),x95861),x95864))))
% 28.25/28.13 [9598]~P35(x95981,x95982,x95983,x95985,x95986)+P1(f319(f319(f249(x95981,x95982,a923),x95983),x95984))+~P1(f319(f319(f321(f931(x95981,x95982)),x95984),f319(f164(f931(x95981,x95982)),f319(f319(f173(x95981,x95982),x95985),x95986))))
% 28.25/28.13 [9739]~E(x97393,x97395)+P1(f319(f319(f321(f931(f926(x97391),f926(x97391))),f319(f319(f244(f926(x97391),f926(x97391)),f319(f319(f143(x97391),x97392),x97393)),f319(f319(f143(x97391),x97394),x97395))),f149(x97391,x97396)))+~P1(f319(f319(f321(f931(x97391,x97391)),f319(f319(f244(x97391,x97391),x97392),x97394)),x97396))
% 28.25/28.13 [9745]~E(f319(f181(f926(x97451)),x97453),f319(f181(f926(x97451)),x97455))+P1(f319(f319(f321(f931(f926(x97451),f926(x97451))),f319(f319(f244(f926(x97451),f926(x97451)),f319(f319(f143(x97451),x97452),x97453)),f319(f319(f143(x97451),x97454),x97455))),f137(x97451,x97456)))+~P1(f319(f319(f321(f931(x97451,x97451)),f319(f319(f244(x97451,x97451),x97452),x97454)),x97456))
% 28.25/28.13 [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),x97796),x97793)),x97795))+~P1(f319(f319(f321(f931(x97791,x97791)),f319(f319(f244(x97791,x97791),x97792),x97796)),f319(f319(f175(f931(x97791,x97791),a923),x97794),x97795)))
% 28.25/28.13 [9780]P1(f319(f319(f321(f931(x97801,x97801)),f319(f319(f244(x97801,x97801),x97802),x97803)),f319(f319(f175(f931(x97801,x97801),a923),f319(a104,x97804)),x97805)))+~P1(f319(f319(f321(f931(x97801,x97801)),f319(f319(f244(x97801,x97801),x97802),x97806)),x97805))+~P1(f319(f319(f321(f931(x97801,x97801)),f319(f319(f244(x97801,x97801),x97806),x97803)),f319(f319(f175(f931(x97801,x97801),a923),x97804),x97805)))
% 28.25/28.13 [9783]~P1(f319(f319(f321(x97834),x97835),x97836))+P1(f319(f319(f226(f932(x97831,a923)),x97832),x97833))+~P1(f319(f319(f226(f932(f931(x97831,x97834),a923)),f319(f319(f246(x97831,x97834),x97832),f319(f16(f932(x97834,a923),x97831),x97836))),f319(f319(f246(x97831,x97834),x97833),f319(f16(f932(x97834,a923),x97831),x97836))))
% 28.25/28.13 [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))),f137(x98283,x98284)))+P1(f319(f319(f321(f931(x98283,x98283)),f319(f319(f244(x98283,x98283),x98281),x98282)),x98284))
% 28.25/28.13 [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))),f139(x98293,x98294)))+P1(f319(f319(f321(f931(x98293,x98293)),f319(f319(f244(x98293,x98293),x98291),x98292)),x98294))
% 28.25/28.13 [9830]E(x98301,x98302)+~P1(f319(f319(f321(f931(f926(x98303),f926(x98303))),f319(f319(f244(f926(x98303),f926(x98303)),f319(f319(f143(x98303),x98301),x98305)),f319(f319(f143(x98303),x98302),x98306))),f149(x98303,x98304)))+P1(f319(f319(f321(f931(x98303,x98303)),f319(f319(f244(x98303,x98303),x98301),x98302)),x98304))
% 28.25/28.13 [9867]P1(f319(f319(f321(f931(f926(x98671),f926(x98671))),f319(f319(f244(f926(x98671),f926(x98671)),f319(f319(f143(x98671),x98672),x98673)),f319(f319(f143(x98671),x98674),x98675))),f150(x98671,x98676)))+~P1(f319(f319(f321(f931(f926(x98671),f926(x98671))),f319(f319(f244(f926(x98671),f926(x98671)),x98673),x98675)),f150(x98671,x98676)))+~P1(f319(f319(f321(f931(x98671,x98671)),f319(f319(f244(x98671,x98671),x98672),x98674)),x98676))
% 28.25/28.13 [9884]P1(f319(x98841,x98842))+~P1(f319(x98841,f382(x98841,x98843,x98844,x98845,x98846)))+~P1(f319(f319(f321(x98846),x98842),f319(f319(f33(x98845,f932(x98846,a923)),x98844),x98843)))
% 28.25/28.13 [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))),f137(x98891,x98894)))+P1(f319(f319(f321(f931(f926(x98891),f926(x98891))),f319(f319(f244(f926(x98891),f926(x98891)),x98895),x98896)),f137(x98891,x98894)))+P1(f319(f319(f321(f931(x98891,x98891)),f319(f319(f244(x98891,x98891),x98892),x98893)),x98894))
% 28.25/28.13 [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))),f139(x98901,x98904)))+P1(f319(f319(f321(f931(f926(x98901),f926(x98901))),f319(f319(f244(f926(x98901),f926(x98901)),x98905),x98906)),f139(x98901,x98904)))+P1(f319(f319(f321(f931(x98901,x98901)),f319(f319(f244(x98901,x98901),x98902),x98903)),x98904))
% 28.25/28.13 [9891]~P1(f319(f319(f321(f931(f926(x98911),f926(x98911))),f319(f319(f244(f926(x98911),f926(x98911)),f319(f319(f143(x98911),x98912),x98915)),f319(f319(f143(x98911),x98913),x98916))),f149(x98911,x98914)))+P1(f319(f319(f321(f931(f926(x98911),f926(x98911))),f319(f319(f244(f926(x98911),f926(x98911)),x98915),x98916)),f149(x98911,x98914)))+P1(f319(f319(f321(f931(x98911,x98911)),f319(f319(f244(x98911,x98911),x98912),x98913)),x98914))
% 28.25/28.13 [9991]P1(f319(x99911,x99912))+P1(f319(f319(f321(x99913),f364(x99911,x99914,x99915,x99913,x99916)),x99915))+~P1(f319(f319(f321(x99916),x99912),f319(f319(f33(x99913,f932(x99916,a923)),x99915),x99914)))
% 28.25/28.13 [10003]~E(x100032,x100034)+P1(f319(f319(f321(f931(f926(x100031),f926(x100031))),f319(f319(f244(f926(x100031),f926(x100031)),f319(f319(f126(x100031),x100032),f319(f319(f143(x100031),x100033),f105(x100031)))),f319(f319(f126(x100031),x100034),f319(f319(f143(x100031),x100035),f105(x100031))))),f149(x100031,x100036)))+~P1(f319(f319(f321(f931(x100031,x100031)),f319(f319(f244(x100031,x100031),x100033),x100035)),x100036))
% 28.25/28.13 [10084]E(x100841,x100842)+~P1(f319(f319(f321(f931(f926(x100843),f926(x100843))),f319(f319(f244(f926(x100843),f926(x100843)),f319(f319(f126(x100843),x100845),f319(f319(f143(x100843),x100841),f105(x100843)))),f319(f319(f126(x100843),x100846),f319(f319(f143(x100843),x100842),f105(x100843))))),f149(x100843,x100844)))+P1(f319(f319(f321(f931(x100843,x100843)),f319(f319(f244(x100843,x100843),x100841),x100842)),x100844))
% 28.25/28.13 [10116]~P1(f319(f319(f321(f931(f926(x101161),f926(x101161))),f319(f319(f244(f926(x101161),f926(x101161)),f319(f319(f126(x101161),x101165),f319(f319(f143(x101161),x101162),f105(x101161)))),f319(f319(f126(x101161),x101166),f319(f319(f143(x101161),x101163),f105(x101161))))),f149(x101161,x101164)))+P1(f319(f319(f321(f931(f926(x101161),f926(x101161))),f319(f319(f244(f926(x101161),f926(x101161)),x101165),x101166)),f149(x101161,x101164)))+P1(f319(f319(f321(f931(x101161,x101161)),f319(f319(f244(x101161,x101161),x101162),x101163)),x101164))
% 28.25/28.13 [10136]P1(f319(x101361,x101362))+P1(f319(f319(f321(x101363),f382(x101361,x101364,x101365,x101366,x101363)),f319(x101364,f364(x101361,x101364,x101365,x101366,x101363))))+~P1(f319(f319(f321(x101363),x101362),f319(f319(f33(x101366,f932(x101363,a923)),x101365),x101364)))
% 28.25/28.13 [10292]P1(f319(f319(f321(x102921),f528(x102922,x102923,x102924,x102925,x102926,x102921)),x102925))+~P1(f319(f319(f226(f932(x102921,a923)),x102926),x102925))+P1(f319(f319(f226(f932(x102924,a923)),f319(f319(f34(x102921,f932(x102924,a923)),x102925),x102923)),f319(f319(f34(x102921,f932(x102924,a923)),x102925),x102922)))
% 28.25/28.13 [10293]P1(f319(f319(f321(x102931),f546(x102932,x102933,x102934,x102935,x102936,x102931)),x102936))+~P1(f319(f319(f226(f932(x102931,a923)),x102936),x102935))+P1(f319(f319(f226(f932(x102934,a923)),f319(f319(f33(x102931,f932(x102934,a923)),x102936),x102933)),f319(f319(f33(x102931,f932(x102934,a923)),x102935),x102932)))
% 28.25/28.13 [10414]~P1(f319(f319(f226(f932(x104141,a923)),f319(x104144,f546(x104146,x104144,x104141,x104145,x104143,x104142))),f319(x104146,f546(x104146,x104144,x104141,x104145,x104143,x104142))))+~P1(f319(f319(f226(f932(x104142,a923)),x104143),x104145))+P1(f319(f319(f226(f932(x104141,a923)),f319(f319(f33(x104142,f932(x104141,a923)),x104143),x104144)),f319(f319(f33(x104142,f932(x104141,a923)),x104145),x104146)))
% 28.25/28.13 [10415]~P1(f319(f319(f226(f932(x104151,a923)),f319(x104154,f528(x104155,x104154,x104151,x104153,x104156,x104152))),f319(x104155,f528(x104155,x104154,x104151,x104153,x104156,x104152))))+~P1(f319(f319(f226(f932(x104152,a923)),x104156),x104153))+P1(f319(f319(f226(f932(x104151,a923)),f319(f319(f34(x104152,f932(x104151,a923)),x104153),x104154)),f319(f319(f34(x104152,f932(x104151,a923)),x104153),x104155)))
% 28.25/28.13 [9105]~P18(x91053,x91054,x91051)+~P1(f319(f55(x91053),x91056))+E(f319(f319(x91051,x91052),f319(f319(f58(x91053,x91054,x91051),x91055),f319(f319(f23(f932(x91053,a923)),x91056),f319(f319(f301(x91053),x91052),f180(f932(x91053,a923)))))),f319(f319(f58(x91053,x91054,x91051),x91055),f319(f319(f301(x91053),x91052),x91056)))
% 28.25/28.13 [9407]~P1(f319(f319(f321(x94075),x94073),x94076))+P1(f319(f319(f226(f932(x94071,a923)),f319(x94072,x94073)),x94074))+~P1(f319(f319(f226(f932(x94071,a923)),f319(f319(f33(x94075,f932(x94071,a923)),x94076),x94072)),x94074))
% 28.25/28.13 [10057]~P9(x100571,x100575,x100574)+P1(f319(f319(f321(f931(x100571,x100571)),f319(f319(f244(x100571,x100571),x100572),x100573)),x100574))+~P1(f319(f319(f321(x100571),x100576),f319(f319(f93(f932(x100571,a923)),f319(f277(x100571,x100571,x100574),f319(f319(f301(x100571),x100572),f180(f932(x100571,a923))))),f319(f277(x100571,x100571,x100574),f319(f319(f301(x100571),x100573),f180(f932(x100571,a923)))))))
% 28.25/28.13 [8825]~P116(x88252)+~E(f319(f319(f74(x88252),f319(f319(f75(x88252),x88254),x88255)),x88251),f319(f319(f74(x88252),f319(f319(f75(x88252),x88253),x88255)),x88256))+E(x88251,f319(f319(f74(x88252),f319(f319(f75(x88252),f319(f319(f23(x88252),x88253),x88254)),x88255)),x88256))
% 28.25/28.13 [8826]~P116(x88261)+~E(f319(f319(f74(x88261),f319(f319(f75(x88261),x88262),x88264)),x88265),f319(f319(f74(x88261),f319(f319(f75(x88261),x88263),x88264)),x88266))+E(f319(f319(f74(x88261),f319(f319(f75(x88261),f319(f319(f23(x88261),x88262),x88263)),x88264)),x88265),x88266)
% 28.25/28.13 [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(x90096,f319(f319(f74(x90091),f319(f319(f75(x90091),f319(f319(f23(x90091),x90092),x90095)),x90093)),x90094))
% 28.25/28.13 [9010]~P116(x90101)+E(f319(f319(f74(x90101),f319(f319(f75(x90101),x90102),x90103)),x90104),f319(f319(f74(x90101),f319(f319(f75(x90101),x90105),x90103)),x90106))+~E(f319(f319(f74(x90101),f319(f319(f75(x90101),f319(f319(f23(x90101),x90102),x90105)),x90103)),x90104),x90106)
% 28.25/28.13 [9342]~P1(f319(f319(x93424,x93425),x93426))+~P1(f319(f319(x93423,x93425),x93426))+P1(f319(f319(f319(f319(f93(f932(x93421,f932(x93422,a923))),x93423),x93424),x93425),x93426))
% 28.25/28.13 [9607]P1(f319(f319(x96071,x96072),x96073))+P1(f319(f319(x96074,x96072),x96073))+~P1(f319(f319(f319(f319(f102(f932(x96075,f932(x96076,a923))),x96074),x96071),x96072),x96073))
% 28.25/28.13 [9904]~P132(x99041)+~P1(f319(f319(f226(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(f226(x99041),x99042),f319(f319(f74(x99041),f319(f319(f75(x99041),f319(f319(f23(x99041),x99043),x99044)),x99045)),x99046)))
% 28.25/28.13 [9905]~P132(x99051)+~P1(f319(f319(f227(x99051),f319(f319(f74(x99051),f319(f319(f75(x99051),x99054),x99055)),x99052)),f319(f319(f74(x99051),f319(f319(f75(x99051),x99053),x99055)),x99056)))+P1(f319(f319(f227(x99051),x99052),f319(f319(f74(x99051),f319(f319(f75(x99051),f319(f319(f23(x99051),x99053),x99054)),x99055)),x99056)))
% 28.25/28.13 [9931]~P132(x99311)+P1(f319(f319(f226(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(f226(x99311),x99314),f319(f319(f74(x99311),f319(f319(f75(x99311),f319(f319(f23(x99311),x99315),x99312)),x99313)),x99316)))
% 28.25/28.13 [9932]~P132(x99321)+P1(f319(f319(f227(x99321),f319(f319(f74(x99321),f319(f319(f75(x99321),x99322),x99323)),x99324)),f319(f319(f74(x99321),f319(f319(f75(x99321),x99325),x99323)),x99326)))+~P1(f319(f319(f227(x99321),x99324),f319(f319(f74(x99321),f319(f319(f75(x99321),f319(f319(f23(x99321),x99325),x99322)),x99323)),x99326)))
% 28.25/28.13 [10049]~P132(x100491)+~P1(f319(f319(f226(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(f226(x100491),f319(f319(f74(x100491),f319(f319(f75(x100491),f319(f319(f23(x100491),x100492),x100493)),x100494)),x100495)),x100496))
% 28.25/28.13 [10050]~P132(x100501)+~P1(f319(f319(f227(x100501),f319(f319(f74(x100501),f319(f319(f75(x100501),x100502),x100504)),x100505)),f319(f319(f74(x100501),f319(f319(f75(x100501),x100503),x100504)),x100506)))+P1(f319(f319(f227(x100501),f319(f319(f74(x100501),f319(f319(f75(x100501),f319(f319(f23(x100501),x100502),x100503)),x100504)),x100505)),x100506))
% 28.25/28.13 [10099]~P132(x100991)+P1(f319(f319(f226(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(f226(x100991),f319(f319(f74(x100991),f319(f319(f75(x100991),f319(f319(f23(x100991),x100992),x100995)),x100993)),x100994)),x100996))
% 28.25/28.13 [10100]~P132(x101001)+P1(f319(f319(f227(x101001),f319(f319(f74(x101001),f319(f319(f75(x101001),x101002),x101003)),x101004)),f319(f319(f74(x101001),f319(f319(f75(x101001),x101005),x101003)),x101006)))+~P1(f319(f319(f227(x101001),f319(f319(f74(x101001),f319(f319(f75(x101001),f319(f319(f23(x101001),x101002),x101005)),x101003)),x101004)),x101006))
% 28.25/28.13 [10275]~P79(x102752)+~P1(f319(f55(x102751),x102756))+E(f319(f319(f6(x102751,x102752),f319(f319(f18(x102751,x102752,x102752),f319(f319(f18(x102751,x102752,f932(x102752,x102752)),f319(f319(f8(a923,f932(x102752,f932(x102752,x102752)),x102751),f86(x102752)),x102753)),x102754)),x102755)),x102756),f319(f319(f74(x102752),f319(f319(f6(x102751,x102752),x102754),f319(f319(f93(f932(x102751,a923)),x102756),f319(f254(x102751),x102753)))),f319(f319(f6(x102751,x102752),x102755),f319(f319(f93(f932(x102751,a923)),x102756),f319(f73(f932(x102751,a923)),f319(f254(x102751),x102753))))))
% 28.25/28.13 [10338]P1(f319(f319(f321(x103382),x103384),x103386))+P1(f319(f319(f321(x103382),x103385),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),f180(f932(x103381,a923)))
% 28.25/28.13 [10339]P1(f319(f319(f321(x103392),x103395),x103396))+~P1(f319(f319(f321(x103392),x103394),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),x103393)
% 28.25/28.13 [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),f319(f73(f932(x103401,a923)),x103403))
% 28.25/28.13 [10341]~P1(f319(f319(f321(x103412),x103414),x103416))+~P1(f319(f319(f321(x103412),x103415),x103416))+E(f319(f303(x103411,x103412,f319(f319(f7(x103411,x103412,x103412),f319(f319(f7(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)),x103415)),x103416),f234(f932(x103411,a923)))
% 28.25/28.13 [8858]E(x88581,x88582)+~P61(x88584,x88585,x88583,x88586,x88587)+~E(f319(x88583,x88581),f319(x88583,x88582))
% 28.25/28.13 [8886]~P11(x88866,x88865,x88867,x88864,x88861)+E(f319(f319(x88861,x88862),x88863),x88864)+P1(f319(f55(x88865),x88863))
% 28.25/28.13 [8887]~P11(x88876,x88875,x88877,x88874,x88871)+E(f319(f319(x88871,x88872),x88873),x88874)+P1(f319(f55(x88875),x88873))
% 28.25/28.13 [9768]P44(x97681,x97682,x97683,x97684,x97685,f319(f319(x97683,x97686),x97687))+~E(f319(f319(x97683,x97686),x97687),x97684)+~E(x97685,f180(f932(x97681,a923)))
% 28.25/28.13 [9958]~P1(f319(x99586,x99583))+~P1(f319(f319(f321(f931(x99582,x99582)),f319(f319(f244(x99582,x99582),x99584),x99585)),f319(x99587,x99583)))+P1(f319(f319(f321(f931(f931(x99581,x99582),f931(x99581,x99582))),f319(f319(f244(f931(x99581,x99582),f931(x99581,x99582)),f319(f319(f244(x99581,x99582),x99583),x99584)),f319(f319(f244(x99581,x99582),x99583),x99585))),f272(x99581,x99582,x99586,x99587)))
% 28.25/28.13 [10402]~P44(x104022,x104027,x104023,x104026,x104021,f319(f319(x104023,x104025),x104024))+E(f319(f319(x104023,f897(x104024,x104025,x104021,x104026,x104023,x104027,x104022)),f898(x104024,x104025,x104021,x104026,x104023,x104027,x104022)),f319(f319(x104023,x104025),x104024))+E(x104021,f180(f932(x104022,a923)))
% 28.25/28.13 [10403]~P44(x104037,x104036,x104031,x104034,x104035,f319(f319(x104031,x104032),x104033))+E(f319(f319(x104031,f897(x104033,x104032,x104035,x104034,x104031,x104036,x104037)),f898(x104033,x104032,x104035,x104034,x104031,x104036,x104037)),f319(f319(x104031,x104032),x104033))+E(f319(f319(x104031,x104032),x104033),x104034)
% 28.25/28.13 [9441]~P35(x94411,x94412,x94413,x94415,x94417)+P35(x94411,x94412,x94413,f319(f319(f143(x94411),x94414),x94415),f319(f319(f143(x94412),x94416),x94417))+~P1(f319(f319(x94413,x94414),x94416))
% 28.25/28.13 [9459]P35(x94591,x94592,x94593,x94594,x94595)+~P35(x94591,x94592,x94593,f319(f319(f126(x94591),x94596),x94594),f319(f319(f126(x94592),x94597),x94595))+~E(f319(f181(f926(x94591)),x94596),f319(f181(f926(x94592)),x94597))
% 28.25/28.13 [9460]P35(x94601,x94602,x94603,x94604,x94605)+~P35(x94601,x94602,x94603,f319(f319(f126(x94601),x94604),x94606),f319(f319(f126(x94602),x94605),x94607))+~E(f319(f181(f926(x94601)),x94604),f319(f181(f926(x94602)),x94605))
% 28.25/28.13 [9674]~P35(x96741,x96742,x96743,x96745,x96747)+~P35(x96741,x96742,x96743,x96744,x96746)+P35(x96741,x96742,x96743,f319(f319(f126(x96741),x96744),x96745),f319(f319(f126(x96742),x96746),x96747))
% 28.25/28.13 [10040]~P1(f319(f60(x100401,x100404,x100405,x100406,x100403),x100407))+P1(f319(f60(x100401,x100404,x100405,x100406,f319(f319(f301(x100401),x100402),x100403)),f319(f319(x100405,x100402),x100407)))+P1(f319(f319(f321(x100401),x100402),x100403))
% 28.25/28.13 [10431]~P44(x104312,x104317,x104316,x104315,x104311,f319(f319(x104316,x104314),x104313))+E(x104311,f180(f932(x104312,a923)))+P1(f319(f319(f321(x104312),f897(x104313,x104314,x104311,x104315,x104316,x104317,x104312)),x104311))
% 28.25/28.13 [10432]~P44(x104325,x104327,x104321,x104324,x104326,f319(f319(x104321,x104322),x104323))+E(f319(f319(x104321,x104322),x104323),x104324)+P1(f319(f319(f321(x104325),f897(x104323,x104322,x104326,x104324,x104321,x104327,x104325)),x104326))
% 28.25/28.13 [10523]E(f319(f319(f244(x105231,x105232),x105233),x105234),f319(f319(f244(x105231,x105232),x105235),x105236))+P1(f319(f319(f321(f931(f931(x105231,x105232),f931(x105231,x105232))),f319(f319(f244(f931(x105231,x105232),f931(x105231,x105232)),f319(f319(f244(x105231,x105232),f850(x105237,x105234,x105233,x105236,x105235,x105232,x105231)),f851(x105237,x105234,x105233,x105236,x105235,x105232,x105231))),f319(f319(f244(x105231,x105232),x105233),x105234))),f299(f931(x105231,x105232),x105237)))+~P1(f319(f319(f321(f931(f931(x105231,x105232),f931(x105231,x105232))),f319(f319(f244(f931(x105231,x105232),f931(x105231,x105232)),f319(f319(f244(x105231,x105232),x105235),x105236)),f319(f319(f244(x105231,x105232),x105233),x105234))),f299(f931(x105231,x105232),x105237)))
% 28.25/28.13 [9130]~P23(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))
% 28.25/28.13 [9131]~P11(x91314,x91315,x91316,x91317,x91311)+~P1(f319(f55(x91315),x91313))+E(f319(f319(x91311,x91312),x91313),f319(f319(f319(f59(x91314,x91315,x91316),x91312),x91317),x91313))
% 28.25/28.13 [9925]~P25(x99253,x99254,x99255,x99257,x99256,x99251)+~P1(f319(f55(x99254),x99252))+E(f319(x99251,x99252),f319(f319(f319(f59(x99253,x99254,x99255),x99256),x99257),x99252))
% 28.25/28.13 [10094]P44(x100941,x100942,x100943,x100944,x100945,f319(f319(x100943,x100946),x100947))+~P44(x100941,x100942,x100943,x100944,f319(f319(f23(f932(x100941,a923)),x100945),f319(f319(f301(x100941),x100946),f180(f932(x100941,a923)))),x100947)+~P1(f319(f319(f321(x100941),x100946),x100945))
% 28.25/28.13 [10456]P1(f319(f319(x104567,f809(x104564,x104565,x104561,x104566,x104563,x104562,x104567)),f810(x104564,x104565,x104561,x104566,x104563,x104562,x104567)))+~P1(f319(f319(x104567,f319(f248(x104562,x104563),x104566)),f319(f243(x104562,x104563),x104566)))+P1(f319(x104561,f319(f319(f249(x104562,x104563,x104564),x104565),x104566)))
% 28.25/28.13 [10466]~P44(x104662,x104663,x104664,x104665,x104661,f319(f319(x104664,x104667),x104666))+P44(x104662,x104663,x104664,x104665,f319(f319(f23(f932(x104662,a923)),x104661),f319(f319(f301(x104662),f897(x104666,x104667,x104661,x104665,x104664,x104663,x104662)),f180(f932(x104662,a923)))),f898(x104666,x104667,x104661,x104665,x104664,x104663,x104662))+E(x104661,f180(f932(x104662,a923)))
% 28.25/28.13 [10467]~P44(x104675,x104676,x104671,x104674,x104677,f319(f319(x104671,x104672),x104673))+P44(x104675,x104676,x104671,x104674,f319(f319(f23(f932(x104675,a923)),x104677),f319(f319(f301(x104675),f897(x104673,x104672,x104677,x104674,x104671,x104676,x104675)),f180(f932(x104675,a923)))),f898(x104673,x104672,x104677,x104674,x104671,x104676,x104675))+E(f319(f319(x104671,x104672),x104673),x104674)
% 28.25/28.13 [10489]~P1(f319(x104891,f319(f319(x104895,f810(x104894,x104895,x104891,x104896,x104893,x104892,x104897)),f809(x104894,x104895,x104891,x104896,x104893,x104892,x104897))))+~P1(f319(f319(x104897,f319(f248(x104892,x104893),x104896)),f319(f243(x104892,x104893),x104896)))+P1(f319(x104891,f319(f319(f249(x104892,x104893,x104894),x104895),x104896)))
% 28.25/28.13 [9753]P1(f319(f319(f226(f932(f931(x97531,x97532),a923)),f319(f319(f281(x97531,x97533,x97532),x97534),x97535)),f319(f319(f281(x97531,x97533,x97532),x97536),x97537)))+~P1(f319(f319(f226(f932(f931(x97533,x97532),a923)),x97535),x97537))+~P1(f319(f319(f226(f932(f931(x97531,x97533),a923)),x97534),x97536))
% 28.25/28.13 [10517]E(f319(f319(f244(x105171,x105172),x105173),x105174),f319(f319(f244(x105171,x105172),x105175),x105176))+~P1(f319(f319(f321(f931(f931(x105171,x105172),f931(x105171,x105172))),f319(f319(f244(f931(x105171,x105172),f931(x105171,x105172)),f319(f319(f244(x105171,x105172),x105173),x105174)),f319(f319(f244(x105171,x105172),x105175),x105176))),f299(f931(x105171,x105172),x105177)))+P1(f319(f319(f321(f931(f931(x105171,x105172),f931(x105171,x105172))),f319(f319(f244(f931(x105171,x105172),f931(x105171,x105172)),f319(f319(f244(x105171,x105172),x105173),x105174)),f319(f319(f244(x105171,x105172),f850(x105177,x105176,x105175,x105174,x105173,x105172,x105171)),f851(x105177,x105176,x105175,x105174,x105173,x105172,x105171)))),x105177))
% 28.25/28.13 [10105]~P1(f319(f319(f321(x101051),x101056),x101055))+P1(f319(f60(x101051,x101052,x101053,x101054,x101055),f319(f319(x101053,x101056),x101057)))+~P1(f319(f60(x101051,x101052,x101053,x101054,f319(f319(f23(f932(x101051,a923)),x101055),f319(f319(f301(x101051),x101056),f180(f932(x101051,a923))))),x101057))
% 28.25/28.13 [10530]~P143(x105301)+~P26(f931(x105302,x105303),x105301,f319(f249(x105302,x105303,x105301),f319(f319(f7(x105302,f932(x105303,x105301),f932(x105303,x105301)),f319(f319(f8(f932(x105301,x105301),f932(f932(x105303,x105301),f932(x105303,x105301)),x105302),f8(x105301,x105301,x105303)),f319(f319(f8(x105301,f932(x105301,x105301),x105302),f75(x105301)),x105304))),x105305)),f319(f319(f246(x105302,x105303),x105306),f319(f16(f932(x105303,a923),x105302),x105307)))+E(f319(f319(f6(x105301,x105301),f25(x105301)),f319(f254(x105301),f319(f319(f8(f932(x105302,a923),a923,x105301),f81(x105302)),f319(f319(f8(f932(x105302,f932(x105303,a923)),f932(x105302,a923),x105301),f319(f8(f932(x105303,a923),a923,x105302),f81(x105303))),f319(f319(f7(x105301,f932(x105302,f932(x105303,a923)),f932(x105302,f932(x105303,a923))),f319(f319(f8(f932(x105302,f932(f932(x105303,a923),f932(x105303,a923))),f932(f932(x105302,f932(x105303,a923)),f932(x105302,f932(x105303,a923))),x105301),f18(x105302,f932(x105303,a923),f932(x105303,a923))),f319(f319(f8(f932(x105302,f932(x105303,f932(a923,a923))),f932(x105302,f932(f932(x105303,a923),f932(x105303,a923))),x105301),f319(f8(f932(x105303,f932(a923,a923)),f932(f932(x105303,a923),f932(x105303,a923)),x105302),f18(x105303,a923,a923))),f319(f319(f8(f932(x105302,f932(x105303,a923)),f932(x105302,f932(x105303,f932(a923,a923))),x105301),f319(f8(f932(x105303,a923),f932(x105303,f932(a923,a923)),x105302),f319(f8(a923,f932(a923,a923),x105303),a317))),f319(f319(f7(x105301,f932(x105302,f932(x105303,x105301)),f932(x105302,f932(x105303,a923))),f319(f319(f8(f932(f932(x105303,x105301),f932(x105303,a923)),f932(f932(x105302,f932(x105303,x105301)),f932(x105302,f932(x105303,a923))),x105301),f8(f932(x105303,x105301),f932(x105303,a923),x105302)),f319(f319(f8(f932(x105301,a923),f932(f932(x105303,x105301),f932(x105303,a923)),x105301),f8(x105301,a923,x105303)),a316))),f319(f319(f7(x105302,f932(x105303,x105301),f932(x105303,x105301)),f319(f319(f8(f932(x105301,x105301),f932(f932(x105303,x105301),f932(x105303,x105301)),x105302),f8(x105301,x105301,x105303)),f319(f319(f8(x105301,f932(x105301,x105301),x105302),f75(x105301)),x105304))),x105305)))))),f319(f319(f7(x105302,f932(x105303,a923),f932(x105303,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x105303,a923),f932(x105303,a923)),x105302),f8(a923,a923,x105303)),f319(f319(f8(a923,f932(a923,a923),x105302),a317),f319(f319(f7(x105302,f932(x105302,a923),a923),f321(x105302)),x105306)))),f319(f319(f7(x105303,f932(x105303,a923),a923),f321(x105303)),x105307))))))),f319(f319(f75(x105301),f319(f319(f6(x105302,x105301),x105304),x105306)),f319(f319(f6(x105303,x105301),x105305),x105307)))
% 28.25/28.13 [9756]~P27(x97563,x97562,x97564,x97568,x97567)+~P27(x97561,x97563,x97565,x97566,x97568)+P27(x97561,x97562,f319(f66(x97563,x97562,x97561,x97564),x97565),x97566,x97567)
% 28.25/28.13 [9757]~P27(x97571,x97573,x97575,x97576,x97578)+~P27(x97573,x97572,x97574,x97578,x97577)+P27(x97571,x97572,f319(f66(x97573,x97572,x97571,x97574),x97575),x97576,x97577)
% 28.25/28.13 [9788]P27(x97881,x97882,x97883,x97884,x97885)+~P27(x97886,x97881,x97887,x97888,x97884)+~P27(x97886,x97882,f319(f66(x97881,x97882,x97886,x97883),x97887),x97888,x97885)
% 28.25/28.13 [9922]~P1(f319(f319(x99224,x99226),x99228))+~P1(f319(f319(x99225,x99228),x99227))+P1(f319(f319(f245(x99221,x99222,x99223,x99224,x99225),x99226),x99227))
% 28.25/28.13 [9923]~P1(f319(f319(x99234,x99236),x99238))+~P1(f319(f319(x99235,x99238),x99237))+P1(f319(f319(f245(x99231,x99232,x99233,x99234,x99235),x99236),x99237))
% 28.25/28.13 [9512]~P21(x95128,x95121,x95123,x95125)+~P1(f319(f55(x95128),x95126))+E(f319(f66(x95121,x95121,x95122,f319(x95123,x95124)),f319(f66(x95121,x95121,x95122,f319(x95125,x95126)),x95127)),f319(f66(x95121,x95121,x95122,f319(x95125,x95126)),f319(f66(x95121,x95121,x95122,f319(x95123,x95124)),x95127)))
% 28.25/28.13 [9913]~P24(x99137,x99132,x99135,x99138,x99136,x99131)+~P1(f319(f55(x99132),x99134))+E(f319(x99131,f319(f319(f301(x99132),x99133),x99134)),f319(f319(x99135,f319(x99136,x99133)),f319(x99131,x99134)))
% 28.25/28.13 [10046]~P26(x100462,x100464,x100466,x100468)+~P26(x100461,x100463,x100465,x100467)+P26(f931(x100461,x100462),f931(x100463,x100464),f250(x100461,x100463,x100462,x100464,x100465,x100466),f319(f319(f246(x100461,x100462),x100467),f319(f16(f932(x100462,a923),x100461),x100468)))
% 28.25/28.13 [9701]P1(f319(f319(f321(f931(x97011,x97012)),f319(f319(f244(x97011,x97012),x97013),x97014)),f319(f319(f281(x97011,x97015,x97012),x97016),x97017)))+~P1(f319(f319(f321(f931(x97011,x97015)),f319(f319(f244(x97011,x97015),x97013),x97018)),x97016))+~P1(f319(f319(f321(f931(x97015,x97012)),f319(f319(f244(x97015,x97012),x97018),x97014)),x97017))
% 28.25/28.13 [9892]~P1(f319(f319(f226(f932(f931(x98923,x98922),a923)),x98925),f319(f319(f246(x98923,x98922),x98928),f319(f16(f932(x98922,a923),x98923),x98927))))+~P1(f319(f319(f226(f932(f931(x98921,x98923),a923)),x98924),f319(f319(f246(x98921,x98923),x98926),f319(f16(f932(x98923,a923),x98921),x98928))))+P1(f319(f319(f226(f932(f931(x98921,x98922),a923)),f319(f319(f281(x98921,x98923,x98922),x98924),x98925)),f319(f319(f246(x98921,x98922),x98926),f319(f16(f932(x98922,a923),x98921),x98927))))
% 28.25/28.13 [9950]~E(x99503,x99505)+P1(f319(f319(f321(f931(f931(x99501,x99502),f931(x99501,x99502))),f319(f319(f244(f931(x99501,x99502),f931(x99501,x99502)),f319(f319(f244(x99501,x99502),x99503),x99504)),f319(f319(f244(x99501,x99502),x99505),x99506))),f312(x99501,x99502,x99507,x99508)))+~P1(f319(f319(f321(f931(x99502,x99502)),f319(f319(f244(x99502,x99502),x99504),x99506)),x99508))
% 28.25/28.13 [10066]E(x100661,x100662)+~P1(f319(f319(f321(f931(f931(x100663,x100665),f931(x100663,x100665))),f319(f319(f244(f931(x100663,x100665),f931(x100663,x100665)),f319(f319(f244(x100663,x100665),x100661),x100666)),f319(f319(f244(x100663,x100665),x100662),x100667))),f312(x100663,x100665,x100664,x100668)))+P1(f319(f319(f321(f931(x100663,x100663)),f319(f319(f244(x100663,x100663),x100661),x100662)),x100664))
% 28.25/28.13 [10083]~P1(f319(f319(f321(f931(f931(x100831,x100835),f931(x100831,x100835))),f319(f319(f244(f931(x100831,x100835),f931(x100831,x100835)),f319(f319(f244(x100831,x100835),x100832),x100836)),f319(f319(f244(x100831,x100835),x100833),x100837))),f312(x100831,x100835,x100834,x100838)))+P1(f319(f319(f321(f931(x100831,x100831)),f319(f319(f244(x100831,x100831),x100832),x100833)),x100834))+P1(f319(f319(f321(f931(x100835,x100835)),f319(f319(f244(x100835,x100835),x100836),x100837)),x100838))
% 28.25/28.13 [9992]~P25(x99927,x99925,x99921,x99928,x99922,x99924)+~P1(f319(f55(x99925),x99926))+E(f319(f319(x99921,f319(x99922,x99923)),f319(x99924,f319(f319(f23(f932(x99925,a923)),x99926),f319(f319(f301(x99925),x99923),f180(f932(x99925,a923)))))),f319(x99924,f319(f319(f301(x99925),x99923),x99926)))
% 28.25/28.13 [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))
% 28.25/28.13 [9465]~P1(f319(f319(f319(x94655,x94658),x94656),x94657))+~P1(f319(f319(f321(x94651),x94658),x94654))+P1(f319(f319(f319(f319(f33(x94651,f932(x94652,f932(x94653,a923))),x94654),x94655),x94656),x94657))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [9685]P1(f319(f319(f319(x96851,x96852),x96853),x96854))+~P1(f319(f319(f321(x96855),x96852),x96856))+~P1(f319(f319(f319(f319(f34(x96855,f932(x96857,f932(x96858,a923))),x96856),x96851),x96853),x96854))
% 28.25/28.13 [9885]~P23(x98853,x98852,x98854,x98858,x98851)+~P1(f319(f55(x98852),x98857))+E(f319(f319(x98851,f319(f319(f18(x98852,x98853,x98853),f319(f319(f8(x98853,f932(x98853,x98853),x98852),x98854),x98855)),x98856)),x98857),f319(f319(x98854,f319(f319(x98851,x98855),x98857)),f319(f319(x98851,x98856),x98857)))
% 28.25/28.13 [10170]~E(f319(f302(x101702,x101704,x101706),x101708),x1017010)+~E(f319(f302(x101701,x101703,x101705),x101707),x101709)+E(f319(f302(f931(x101701,x101702),f931(x101703,x101704),f250(x101701,x101703,x101702,x101704,x101705,x101706)),f319(f319(f246(x101701,x101702),x101707),f319(f16(f932(x101702,a923),x101701),x101708))),f319(f319(f246(x101703,x101704),x101709),f319(f16(f932(x101704,a923),x101703),x1017010)))
% 28.25/28.13 [5087]~P50(x50871,x50872)+~P54(x50871,x50872)+~P55(x50871,x50872)+P8(x50871,x50872)
% 28.25/28.13 [5088]~P50(x50881,x50882)+~P54(x50881,x50882)+~P55(x50881,x50882)+P8(x50881,x50882)
% 28.25/28.13 [5044]~P4(x50442)+~P14(x50442,x50441)+P14(x50442,f106(x50442,x50441))+E(x50441,f105(x50442))
% 28.25/28.13 [5045]~P4(x50452)+~P14(x50452,x50451)+P14(x50452,f729(x50451,x50452))+E(x50451,f105(x50452))
% 28.25/28.13 [5287]~P6(x52872)+E(f10(x52872,x52871),f32(x52872,x52871))+E(x52871,f180(f932(x52872,a923)))+~P1(f319(f55(x52872),x52871))
% 28.25/28.13 [5288]~P6(x52882)+E(f13(x52882,x52881),f31(x52882,x52881))+E(x52881,f180(f932(x52882,a923)))+~P1(f319(f55(x52882),x52881))
% 28.25/28.13 [5451]~P4(x54512)+~P14(x54512,x54511)+E(x54511,f105(x54512))+E(f319(f319(f143(x54512),f748(x54511,x54512)),f729(x54511,x54512)),x54511)
% 28.25/28.13 [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))
% 28.25/28.13 [6270]~P42(x62702)+~P42(x62701)+E(x62701,x62702)+~E(f319(f302(a1,a925,a96),x62701),f319(f302(a1,a925,a96),x62702))
% 28.25/28.13 [9320]~P126(x93201)+~P1(f319(f319(f321(x93201),x93202),f101(x93201)))+P1(f319(f319(f227(x93201),f319(f319(f74(x93201),f319(f319(f74(x93201),f72(x93201)),x93202)),x93202)),f2(x93201)))+~P1(f319(f319(f227(x93201),x93202),f2(x93201)))
% 28.25/28.13 [9567]~P126(x95671)+~P1(f319(f319(f321(x95671),x95672),f101(x95671)))+~P1(f319(f319(f227(x95671),f319(f319(f74(x95671),f319(f319(f74(x95671),f72(x95671)),x95672)),x95672)),f2(x95671)))+P1(f319(f319(f227(x95671),x95672),f2(x95671)))
% 28.25/28.13 [5103]~P143(x51032)+~P119(x51032)+E(x51031,f2(a925))+E(f319(f319(f236(x51032),f2(x51032)),x51031),f2(x51032))
% 28.25/28.13 [5106]~P143(x51061)+~P119(x51061)+~E(x51062,f2(a925))+E(f319(f319(f236(x51061),f2(x51061)),x51062),f72(x51061))
% 28.25/28.13 [5273]~P144(x52732)+E(x52731,f72(x52732))+E(x52731,f319(f73(x52732),f72(x52732)))+~E(f319(f319(f75(x52732),x52731),x52731),f72(x52732))
% 28.25/28.13 [5525]~P94(x55252)+E(x55251,f2(x55252))+E(f76(x55252,x55251),f319(f73(x55252),f72(x55252)))+P1(f319(f319(f227(x55252),f2(x55252)),x55251))
% 28.25/28.13 [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))
% 28.25/28.13 [5764]~P94(x57642)+E(f76(x57642,x57641),f72(x57642))+E(x57641,f2(x57642))+~P1(f319(f319(f227(x57642),f2(x57642)),x57641))
% 28.25/28.13 [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)))
% 28.25/28.13 [5823]~P98(x58231)+~E(x58232,f2(x58231))+E(f319(f319(f74(x58231),x58232),x58232),f2(x58231))+~P1(f319(f319(f321(x58231),x58232),f101(x58231)))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [5962]~P98(x59622)+E(x59621,f2(x59622))+~E(f319(f319(f74(x59622),x59621),x59621),f2(x59622))+~P1(f319(f319(f321(x59622),x59621),f101(x59622)))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [6064]~P4(x60642)+E(x60641,f180(f932(x60642,a923)))+~P1(f319(f55(x60642),x60641))+P1(f319(f319(f321(x60642),f14(x60642,x60641)),x60641))
% 28.25/28.13 [6065]~P4(x60652)+E(x60651,f180(f932(x60652,a923)))+~P1(f319(f55(x60652),x60651))+P1(f319(f319(f321(x60652),f15(x60652,x60651)),x60651))
% 28.25/28.13 [6238]~P126(x62381)+~P99(x62381)+P1(f319(f319(f226(x62381),f2(x62381)),f319(f95(x62381),x62382)))+~P1(f319(f319(f226(a1),a77),x62382))
% 28.25/28.13 [6239]~P126(x62391)+~P99(x62391)+P1(f319(f319(f227(x62391),f2(x62391)),f319(f95(x62391),x62392)))+~P1(f319(f319(f227(a1),a77),x62392))
% 28.25/28.13 [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)))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [6487]~P99(x64872)+~P126(x64872)+~P1(f319(f319(f226(x64872),f2(x64872)),f319(f95(x64872),x64871)))+P1(f319(f319(f226(a1),a77),x64871))
% 28.25/28.13 [6488]~P99(x64882)+~P126(x64882)+~P1(f319(f319(f227(x64882),f2(x64882)),f319(f95(x64882),x64881)))+P1(f319(f319(f227(a1),a77),x64881))
% 28.25/28.13 [6493]~P126(x64931)+~P99(x64931)+P1(f319(f319(f226(x64931),f319(f95(x64931),x64932)),f2(x64931)))+~P1(f319(f319(f226(a1),x64932),a77))
% 28.25/28.13 [6494]~P126(x64941)+~P99(x64941)+P1(f319(f319(f227(x64941),f319(f95(x64941),x64942)),f2(x64941)))+~P1(f319(f319(f227(a1),x64942),a77))
% 28.25/28.13 [6816]~P99(x68162)+~P126(x68162)+~P1(f319(f319(f226(x68162),f319(f95(x68162),x68161)),f2(x68162)))+P1(f319(f319(f226(a1),x68161),a77))
% 28.25/28.13 [6817]~P99(x68172)+~P126(x68172)+~P1(f319(f319(f227(x68172),f319(f95(x68172),x68171)),f2(x68172)))+P1(f319(f319(f227(a1),x68171),a77))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [7100]E(x71001,x71002)+~E(f319(a3,x71001),f319(a3,x71002))+~P1(f319(f319(f321(a925),x71002),f234(f932(a925,a923))))+~P1(f319(f319(f321(a925),x71001),f234(f932(a925,a923))))
% 28.25/28.13 [7325]P1(f319(f319(f226(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(f226(a1),x73251),x73252))
% 28.25/28.13 [7326]P1(f319(f319(f227(a925),f319(a96,x73261)),f319(a96,x73262)))+~P1(f319(f319(f226(a1),f2(a1)),x73262))+~P1(f319(f319(f226(a1),f2(a1)),x73261))+~P1(f319(f319(f227(a1),x73261),x73262))
% 28.25/28.13 [7557]~P7(x75571)+~P42(x75572)+~P1(f319(f319(f321(a1),x75571),x75572))+P1(f319(f319(f321(a925),f319(a96,x75571)),f319(f302(a1,a925,a96),x75572)))
% 28.25/28.13 [7562]~P1(f319(f319(f226(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(f226(a1),x75621),x75622))
% 28.25/28.13 [7563]~P1(f319(f319(f227(a925),f319(a96,x75631)),f319(a96,x75632)))+~P1(f319(f319(f226(a1),f2(a1)),x75632))+~P1(f319(f319(f226(a1),f2(a1)),x75631))+P1(f319(f319(f227(a1),x75631),x75632))
% 28.25/28.13 [7805]~P4(x78052)+E(x78051,f180(f932(x78052,a923)))+~P1(f319(f55(x78052),x78051))+P1(f319(f319(f226(x78052),f11(x78052,f224(x78052),x78051)),f12(x78052,f225(x78052),x78051)))
% 28.25/28.13 [8124]~P7(x81241)+~P42(x81242)+P1(f319(f319(f321(a1),x81241),x81242))+~P1(f319(f319(f321(a925),f319(a96,x81241)),f319(f302(a1,a925,a96),x81242)))
% 28.25/28.13 [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)))
% 28.25/28.13 [6139]~P98(x61391)+~P99(x61391)+~P29(x61391,f319(f95(x61391),x61392))+P29(x61391,f319(f95(x61391),f319(f319(f74(a1),x61392),x61392)))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [6510]~P98(x65101)+~P99(x65101)+P29(x65101,f319(f95(x65101),x65102))+~P29(x65101,f319(f95(x65101),f319(f319(f74(a1),x65102),x65102)))
% 28.25/28.13 [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))
% 28.25/28.13 [7477]~P1(f319(f319(f226(a1),f2(a1)),x74771))+~P1(f319(f319(f227(a1),f2(a1)),x74772))+~P1(f319(f319(f226(a1),x74772),x74771))+P1(f319(f319(f227(a1),f2(a1)),f319(f319(f30(a1),x74771),x74772)))
% 28.25/28.13 [7880]~E(x78802,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)))
% 28.25/28.13 [7881]~E(x78811,f2(a1))+E(f207(x78811,x78812),f319(f319(f244(a1,a1),f2(a1)),f72(a1)))+P1(f319(f319(f227(a1),x78812),f2(a1)))+~P1(f319(f307(f931(a1,a1),a213),f319(f319(f244(a1,a1),x78811),x78812)))
% 28.25/28.13 [8914]~P42(x89142)+~P42(x89141)+P1(f319(f319(f226(f932(a925,a923)),f319(f302(a1,a925,a96),x89141)),f319(f302(a1,a925,a96),x89142)))+~P1(f319(f319(f226(f932(a1,a923)),x89141),x89142))
% 28.25/28.13 [8915]~P42(x89152)+~P42(x89151)+P1(f319(f319(f227(f932(a925,a923)),f319(f302(a1,a925,a96),x89151)),f319(f302(a1,a925,a96),x89152)))+~P1(f319(f319(f227(f932(a1,a923)),x89151),x89152))
% 28.25/28.13 [9150]~E(f750(x91502,x91501),f751(x91502,x91501))+~P1(f319(f129(x91501),f752(x91502,x91501)))+~P1(f319(f129(f926(x91501)),x91502))+P1(f319(f129(x91501),f319(f134(f926(x91501),f926(x91501),f126(x91501),f105(x91501)),x91502)))
% 28.25/28.13 [9239]~P42(x92392)+~P42(x92391)+~P1(f319(f319(f226(f932(a925,a923)),f319(f302(a1,a925,a96),x92391)),f319(f302(a1,a925,a96),x92392)))+P1(f319(f319(f226(f932(a1,a923)),x92391),x92392))
% 28.25/28.13 [9240]~P42(x92402)+~P42(x92401)+~P1(f319(f319(f227(f932(a925,a923)),f319(f302(a1,a925,a96),x92401)),f319(f302(a1,a925,a96),x92402)))+P1(f319(f319(f227(f932(a1,a923)),x92401),x92402))
% 28.25/28.13 [9246]~E(f750(x92462,x92461),f751(x92462,x92461))+~P1(f319(f129(f926(x92461)),x92462))+P1(f319(f129(x92461),f319(f134(f926(x92461),f926(x92461),f126(x92461),f105(x92461)),x92462)))+P1(f319(f319(f321(f926(x92461)),f752(x92462,x92461)),f319(f164(f926(x92461)),x92462)))
% 28.25/28.13 [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)),f751(x92882,x92881)),f319(f164(f926(x92881)),x92882)))
% 28.25/28.13 [9289]~P1(f319(f129(x92891),f752(x92892,x92891)))+~P1(f319(f129(f926(x92891)),x92892))+P1(f319(f129(x92891),f319(f134(f926(x92891),f926(x92891),f126(x92891),f105(x92891)),x92892)))+P1(f319(f319(f321(f926(x92891)),f750(x92892,x92891)),f319(f164(f926(x92891)),x92892)))
% 28.25/28.13 [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)),f751(x93672,x93671)),f319(f164(f926(x93671)),x93672)))+P1(f319(f319(f321(f926(x93671)),f752(x93672,x93671)),f319(f164(f926(x93671)),x93672)))
% 28.25/28.13 [9368]~P1(f319(f129(f926(x93681)),x93682))+P1(f319(f129(x93681),f319(f134(f926(x93681),f926(x93681),f126(x93681),f105(x93681)),x93682)))+P1(f319(f319(f321(f926(x93681)),f750(x93682,x93681)),f319(f164(f926(x93681)),x93682)))+P1(f319(f319(f321(f926(x93681)),f752(x93682,x93681)),f319(f164(f926(x93681)),x93682)))
% 28.25/28.13 [9382]~E(f319(f319(f93(f932(x93821,a923)),f319(f164(x93821),f751(x93822,x93821))),f319(f164(x93821),f750(x93822,x93821))),f180(f932(x93821,a923)))+~P1(f319(f129(x93821),f752(x93822,x93821)))+~P1(f319(f129(f926(x93821)),x93822))+P1(f319(f129(x93821),f319(f134(f926(x93821),f926(x93821),f126(x93821),f105(x93821)),x93822)))
% 28.25/28.13 [9447]~E(f319(f319(f93(f932(x94471,a923)),f319(f164(x94471),f751(x94472,x94471))),f319(f164(x94471),f750(x94472,x94471))),f180(f932(x94471,a923)))+~P1(f319(f129(f926(x94471)),x94472))+P1(f319(f129(x94471),f319(f134(f926(x94471),f926(x94471),f126(x94471),f105(x94471)),x94472)))+P1(f319(f319(f321(f926(x94471)),f752(x94472,x94471)),f319(f164(f926(x94471)),x94472)))
% 28.25/28.13 [9726]E(x97261,f2(a1))+E(x97262,f2(a1))+E(f319(f319(f80(a1,f931(a1,a1)),f319(f319(a209,x97262),x97261)),f319(f319(f18(a1,a1,f931(a1,a1)),f319(f319(f8(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f319(f30(a1),x97262))),f319(f30(a1),x97261))),f207(x97262,x97261))+P1(f319(f319(f227(a1),x97261),f2(a1)))
% 28.25/28.13 [8453]~P99(x84532)+~P126(x84532)+~P1(f319(f319(f226(x84532),f319(f95(x84532),x84531)),f72(x84532)))+P1(f319(f319(f226(a1),x84531),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))
% 28.25/28.13 [8454]~P99(x84542)+~P126(x84542)+~P1(f319(f319(f227(x84542),f319(f95(x84542),x84541)),f72(x84542)))+P1(f319(f319(f227(a1),x84541),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))
% 28.25/28.13 [8731]~P126(x87311)+~P99(x87311)+P1(f319(f319(f226(x87311),f319(f95(x87311),x87312)),f72(x87311)))+~P1(f319(f319(f226(a1),x87312),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))
% 28.25/28.13 [8732]~P126(x87321)+~P99(x87321)+P1(f319(f319(f227(x87321),f319(f95(x87321),x87322)),f72(x87321)))+~P1(f319(f319(f227(a1),x87322),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)))
% 28.25/28.13 [8943]~P99(x89432)+~P126(x89432)+~P1(f319(f319(f226(x89432),f72(x89432)),f319(f95(x89432),x89431)))+P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),x89431))
% 28.25/28.13 [8944]~P99(x89442)+~P126(x89442)+~P1(f319(f319(f227(x89442),f72(x89442)),f319(f95(x89442),x89441)))+P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),x89441))
% 28.25/28.13 [9326]~P126(x93261)+~P99(x93261)+P1(f319(f319(f226(x93261),f72(x93261)),f319(f95(x93261),x93262)))+~P1(f319(f319(f226(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),x93262))
% 28.25/28.13 [9327]~P126(x93271)+~P99(x93271)+P1(f319(f319(f227(x93271),f72(x93271)),f319(f95(x93271),x93272)))+~P1(f319(f319(f227(a1),f319(f319(f23(a1),f319(f319(f74(a1),a77),a77)),a89)),x93272))
% 28.25/28.13 [9858]~P144(x98582)+E(x98581,f72(x98582))+E(x98581,f319(f73(x98582),f72(x98582)))+~E(f319(f319(f236(x98582),x98581),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(x98582))
% 28.25/28.13 [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))))))
% 28.25/28.13 [10146]~P74(x101461)+~P99(x101461)+~P1(f319(f319(f227(x101461),f2(x101461)),x101462))+P1(f319(f319(f227(x101461),f2(x101461)),f319(f319(f283(x101461),x101462),f319(f95(x101461),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))))))
% 28.25/28.13 [10201]~P74(x102011)+~P99(x102011)+P1(f319(f319(f227(x102011),f2(x102011)),x102012))+~P1(f319(f319(f227(x102011),f2(x102011)),f319(f319(f283(x102011),x102012),f319(f95(x102011),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))))))
% 28.25/28.13 [10496]~P145(x104962)+E(x104961,f2(a1))+P1(f319(f319(f227(a1),x104961),f2(a1)))+E(f319(f319(f249(a1,a1,x104962),f319(f319(f7(a1,f932(a1,f932(x104962,x104962)),f932(a1,x104962)),f319(f319(f8(f932(f932(x104962,x104962),x104962),f932(f932(a1,f932(x104962,x104962)),f932(a1,x104962)),a1),f8(f932(x104962,x104962),x104962,a1)),f319(f319(f8(x104962,f932(f932(x104962,x104962),x104962),a1),f80(x104962,x104962)),f94(x104962)))),f319(f319(f7(a1,f932(x104962,x104962),f932(x104962,x104962)),f319(f319(f8(f932(x104962,f932(x104962,x104962)),f932(f932(x104962,x104962),f932(x104962,x104962)),a1),f18(x104962,x104962,x104962)),f319(f319(f7(a1,f932(x104962,x104962),f932(x104962,f932(x104962,x104962))),f319(f319(f8(f932(x104962,f932(x104962,x104962)),f932(f932(x104962,x104962),f932(x104962,f932(x104962,x104962))),a1),f8(x104962,f932(x104962,x104962),x104962)),f319(f319(f8(a923,f932(x104962,f932(x104962,x104962)),a1),f86(x104962)),f319(f319(f7(a1,a1,a923),a316),f2(a1))))),f319(f319(f18(x104962,x104962,x104962),f74(x104962)),f5(x104962))))),f319(f319(f7(x104962,x104962,x104962),f319(f319(f8(x104962,f932(x104962,x104962),x104962),f74(x104962)),f319(f319(f18(x104962,x104962,x104962),f74(x104962)),f5(x104962)))),f72(x104962))))),f40(x104961,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(x104962),x104961))
% 28.25/28.13 [10245]P1(f319(f319(f226(a1),x102451),f2(a1)))+P1(f319(f319(f227(a1),x102452),x102451))+~P1(f319(f307(f931(a1,a1),a52),f319(f319(f244(a1,a1),x102452),x102451)))+E(f319(f37(x102451),f41(x102452,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)))),x102451))),f41(x102452,x102451))
% 28.25/28.13 [10249]P1(f319(f319(f226(a1),x102491),f2(a1)))+~P1(f319(f307(f931(a1,a1),a46),f319(f319(f244(a1,a1),x102492),x102491)))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),x102492),x102491)))+E(f319(f37(x102491),f44(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)))),x102491))),f44(x102492,x102491))
% 28.25/28.13 [5406]~P113(x54061)+~P113(x54062)+~P51(x54061,x54062,x54063)+P41(x54061,x54062,x54063)
% 28.25/28.13 [5533]~P39(x55331,x55333)+~P56(x55331,x55333)+~P57(x55331,x55332,x55333)+P9(x55331,x55332,x55333)
% 28.25/28.13 [5534]~P39(x55341,x55343)+~P56(x55341,x55343)+~P57(x55341,x55342,x55343)+P9(x55341,x55342,x55343)
% 28.25/28.13 [5298]~P6(x52983)+~P41(x52983,x52983,x52981)+E(f319(x52981,x52982),x52982)+~E(x52982,f88(x52983,x52981))
% 28.25/28.13 [5299]~P6(x52993)+~P41(x52993,x52993,x52991)+E(f319(x52991,x52992),x52992)+~E(x52992,f87(x52993,x52991))
% 28.25/28.13 [5072]~P98(x50723)+~P99(x50723)+E(x50721,x50722)+~E(f319(f95(x50723),x50721),f319(f95(x50723),x50722))
% 28.25/28.13 [5543]~P54(x55431,x55432)+~P55(x55431,x55432)+P17(x55431,x55432)+~P1(f319(f319(x55432,x55433),x55433))
% 28.25/28.13 [5544]~P54(x55441,x55442)+~P55(x55441,x55442)+P17(x55441,x55442)+~P1(f319(f319(x55442,x55443),x55443))
% 28.25/28.13 [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))
% 28.25/28.13 [6072]~P113(x60721)+E(f230(x60721,x60722),x60723)+~P1(f319(x60722,x60723))+P1(f319(x60722,f334(x60723,x60722,x60721)))
% 28.25/28.13 [6248]~P1(f319(x62481,x62482))+~P1(f319(x62481,x62483))+~P1(f319(f319(f226(a925),x62483),f440(x62482,x62481)))+P1(f319(x62481,f2(a925)))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [6852]P152(x68522,x68521,x68523)+E(x68521,f2(a1))+~P1(f319(x68522,f869(x68523,x68521,x68522)))+P1(f319(f319(f227(a1),x68521),f2(a1)))
% 28.25/28.13 [6853]P151(x68532,x68531,x68533)+E(x68531,f2(a1))+~P1(f319(x68532,f874(x68533,x68531,x68532)))+P1(f319(f319(f227(a1),x68531),f2(a1)))
% 28.25/28.13 [6937]~P113(x69371)+E(f230(x69371,x69372),x69373)+~P1(f319(x69372,x69373))+~P1(f319(f319(f226(x69371),x69373),f334(x69373,x69372,x69371)))
% 28.25/28.13 [6956]~P4(x69561)+~P6(x69561)+~P1(f319(f319(f227(x69561),x69562),f31(x69561,x69563)))+P1(f319(f319(f227(x69561),x69562),f879(x69563,x69562,x69561)))
% 28.25/28.13 [6966]P151(x69661,x69662,x69663)+~P1(f319(x69661,x69663))+~P1(f319(x69661,f874(x69663,x69662,x69661)))+P1(f319(f319(f227(a1),x69662),f2(a1)))
% 28.25/28.13 [6996]P152(x69961,x69962,x69963)+~P1(f319(x69961,f869(x69963,x69962,x69961)))+~P1(f319(x69961,f2(a1)))+P1(f319(f319(f227(a1),x69962),f2(a1)))
% 28.25/28.13 [7245]P152(x72452,x72451,x72453)+E(x72451,f2(a1))+P1(f319(f319(f226(a1),f2(a1)),f868(x72453,x72451,x72452)))+P1(f319(f319(f227(a1),x72451),f867(x72453,x72451,x72452)))
% 28.25/28.13 [7246]P151(x72462,x72461,x72463)+E(x72461,f2(a1))+P1(f319(f319(f226(a1),f2(a1)),f874(x72463,x72461,x72462)))+P1(f319(f319(f227(a1),x72461),f878(x72463,x72461,x72462)))
% 28.25/28.13 [7367]P151(x73671,x73672,x73673)+~P1(f319(x73671,x73673))+P1(f319(f319(f226(a1),f2(a1)),f874(x73673,x73672,x73671)))+P1(f319(f319(f227(a1),x73672),f878(x73673,x73672,x73671)))
% 28.25/28.13 [7388]P152(x73881,x73882,x73883)+P1(f319(f319(f226(a1),f2(a1)),f868(x73883,x73882,x73881)))+P1(f319(f319(f227(a1),x73882),f867(x73883,x73882,x73881)))+~P1(f319(x73881,f2(a1)))
% 28.25/28.13 [7420]P152(x74202,x74201,x74203)+E(x74201,f2(a1))+~P1(f319(x74202,f869(x74203,x74201,x74202)))+P1(f319(f319(f227(a1),x74201),f867(x74203,x74201,x74202)))
% 28.25/28.13 [7421]P151(x74212,x74211,x74213)+E(x74211,f2(a1))+~P1(f319(x74212,f874(x74213,x74211,x74212)))+P1(f319(f319(f227(a1),x74211),f878(x74213,x74211,x74212)))
% 28.25/28.13 [7466]P152(x74662,x74661,x74663)+E(x74661,f2(a1))+P1(f319(f319(f226(a1),f2(a1)),f868(x74663,x74661,x74662)))+~P1(f319(x74662,f873(x74663,x74661,x74662)))
% 28.25/28.13 [7467]P151(x74672,x74671,x74673)+E(x74671,f2(a1))+P1(f319(f319(f226(a1),f2(a1)),f874(x74673,x74671,x74672)))+~P1(f319(x74672,f878(x74673,x74671,x74672)))
% 28.25/28.13 [7561]P151(x75611,x75612,x75613)+~P1(f319(x75611,x75613))+~P1(f319(x75611,f874(x75613,x75612,x75611)))+P1(f319(f319(f227(a1),x75612),f878(x75613,x75612,x75611)))
% 28.25/28.13 [7576]P152(x75761,x75762,x75763)+~P1(f319(x75761,f869(x75763,x75762,x75761)))+P1(f319(f319(f227(a1),x75762),f867(x75763,x75762,x75761)))+~P1(f319(x75761,f2(a1)))
% 28.25/28.13 [7579]P151(x75791,x75792,x75793)+~P1(f319(x75791,x75793))+P1(f319(f319(f226(a1),f2(a1)),f874(x75793,x75792,x75791)))+~P1(f319(x75791,f878(x75793,x75792,x75791)))
% 28.25/28.13 [7595]P152(x75951,x75952,x75953)+P1(f319(f319(f226(a1),f2(a1)),f868(x75953,x75952,x75951)))+~P1(f319(x75951,f873(x75953,x75952,x75951)))+~P1(f319(x75951,f2(a1)))
% 28.25/28.13 [7617]P152(x76172,x76171,x76173)+E(x76171,f2(a1))+~P1(f319(x76172,f869(x76173,x76171,x76172)))+~P1(f319(x76172,f873(x76173,x76171,x76172)))
% 28.25/28.13 [7618]P151(x76182,x76181,x76183)+E(x76181,f2(a1))+~P1(f319(x76182,f874(x76183,x76181,x76182)))+~P1(f319(x76182,f878(x76183,x76181,x76182)))
% 28.25/28.13 [7703]P151(x77031,x77032,x77033)+~P1(f319(x77031,x77033))+~P1(f319(x77031,f874(x77033,x77032,x77031)))+~P1(f319(x77031,f878(x77033,x77032,x77031)))
% 28.25/28.13 [7720]P152(x77201,x77202,x77203)+~P1(f319(x77201,f869(x77203,x77202,x77201)))+~P1(f319(x77201,f873(x77203,x77202,x77201)))+~P1(f319(x77201,f2(a1)))
% 28.25/28.13 [7764]P152(x77642,x77641,x77643)+E(x77641,f2(a1))+P1(f319(f319(f226(a1),f2(a1)),f868(x77643,x77641,x77642)))+P1(f319(f319(f226(a1),f867(x77643,x77641,x77642)),f2(a1)))
% 28.25/28.13 [7765]P151(x77652,x77651,x77653)+E(x77651,f2(a1))+P1(f319(f319(f226(a1),f2(a1)),f874(x77653,x77651,x77652)))+P1(f319(f319(f226(a1),f878(x77653,x77651,x77652)),f2(a1)))
% 28.25/28.13 [7766]~P93(x77661)+~P1(f319(f319(f226(x77661),x77663),f2(x77661)))+~P1(f319(f319(f226(x77661),x77662),f2(x77661)))+P1(f319(f319(f226(x77661),f319(f319(f74(x77661),x77662),x77663)),f2(x77661)))
% 28.25/28.13 [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(f23(x77671),x77672),x77673)),f101(x77671)))
% 28.25/28.13 [7768]~P145(x77681)+~P1(f319(f319(f321(x77681),x77683),f101(x77681)))+~P1(f319(f319(f321(x77681),x77682),f101(x77681)))+P1(f319(f319(f321(x77681),f319(f319(f75(x77681),x77682),x77683)),f101(x77681)))
% 28.25/28.13 [7769]~P149(x77691)+~P1(f319(f319(f321(x77691),x77693),f178(x77691)))+~P1(f319(f319(f321(x77691),x77692),f178(x77691)))+P1(f319(f319(f321(x77691),f319(f319(f75(x77691),x77692),x77693)),f178(x77691)))
% 28.25/28.13 [7770]~P145(x77701)+~P1(f319(f319(f321(x77701),x77703),f101(x77701)))+~P1(f319(f319(f321(x77701),x77702),f101(x77701)))+P1(f319(f319(f321(x77701),f319(f319(f74(x77701),x77702),x77703)),f101(x77701)))
% 28.25/28.13 [7771]~P149(x77711)+~P1(f319(f319(f321(x77711),x77713),f178(x77711)))+~P1(f319(f319(f321(x77711),x77712),f178(x77711)))+P1(f319(f319(f321(x77711),f319(f319(f74(x77711),x77712),x77713)),f178(x77711)))
% 28.25/28.13 [7772]~P93(x77721)+~P1(f319(f319(f226(x77721),x77723),f2(x77721)))+~P1(f319(f319(f227(x77721),x77722),f2(x77721)))+P1(f319(f319(f227(x77721),f319(f319(f74(x77721),x77722),x77723)),f2(x77721)))
% 28.25/28.13 [7773]~P93(x77731)+~P1(f319(f319(f226(x77731),x77732),f2(x77731)))+~P1(f319(f319(f227(x77731),x77733),f2(x77731)))+P1(f319(f319(f227(x77731),f319(f319(f74(x77731),x77732),x77733)),f2(x77731)))
% 28.25/28.13 [7774]~P93(x77741)+~P1(f319(f319(f227(x77741),x77743),f2(x77741)))+~P1(f319(f319(f227(x77741),x77742),f2(x77741)))+P1(f319(f319(f227(x77741),f319(f319(f74(x77741),x77742),x77743)),f2(x77741)))
% 28.25/28.13 [7801]P152(x78013,x78011,x78012)+E(x78011,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x78011),f869(x78012,x78011,x78013))),f868(x78012,x78011,x78013)),x78012)+P1(f319(f319(f227(a1),x78011),f2(a1)))
% 28.25/28.13 [7802]P151(x78023,x78021,x78022)+E(x78021,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x78021),f875(x78022,x78021,x78023))),f874(x78022,x78021,x78023)),x78022)+P1(f319(f319(f227(a1),x78021),f2(a1)))
% 28.25/28.13 [7885]P151(x78851,x78852,x78853)+~P1(f319(x78851,x78853))+P1(f319(f319(f226(a1),f2(a1)),f874(x78853,x78852,x78851)))+P1(f319(f319(f226(a1),f878(x78853,x78852,x78851)),f2(a1)))
% 28.25/28.13 [7915]P152(x79151,x79152,x79153)+P1(f319(f319(f226(a1),f2(a1)),f868(x79153,x79152,x79151)))+~P1(f319(x79151,f2(a1)))+P1(f319(f319(f226(a1),f867(x79153,x79152,x79151)),f2(a1)))
% 28.25/28.13 [7924]P151(x79243,x79241,x79242)+~P1(f319(x79243,x79242))+E(f319(f319(f74(a1),f319(f319(f75(a1),x79241),f875(x79242,x79241,x79243))),f874(x79242,x79241,x79243)),x79242)+P1(f319(f319(f227(a1),x79241),f2(a1)))
% 28.25/28.13 [7930]P152(x79302,x79301,x79303)+E(x79301,f2(a1))+~P1(f319(x79302,f869(x79303,x79301,x79302)))+P1(f319(f319(f226(a1),f867(x79303,x79301,x79302)),f2(a1)))
% 28.25/28.13 [7931]P151(x79312,x79311,x79313)+E(x79311,f2(a1))+~P1(f319(x79312,f874(x79313,x79311,x79312)))+P1(f319(f319(f226(a1),f878(x79313,x79311,x79312)),f2(a1)))
% 28.25/28.13 [7936]P152(x79363,x79361,x79362)+E(f319(f319(f74(a1),f319(f319(f75(a1),x79361),f869(x79362,x79361,x79363))),f868(x79362,x79361,x79363)),x79362)+~P1(f319(x79363,f2(a1)))+P1(f319(f319(f227(a1),x79361),f2(a1)))
% 28.25/28.13 [7992]P151(x79921,x79922,x79923)+~P1(f319(x79921,x79923))+~P1(f319(x79921,f874(x79923,x79922,x79921)))+P1(f319(f319(f226(a1),f878(x79923,x79922,x79921)),f2(a1)))
% 28.25/28.13 [7996]P152(x79961,x79962,x79963)+~P1(f319(x79961,f869(x79963,x79962,x79961)))+~P1(f319(x79961,f2(a1)))+P1(f319(f319(f226(a1),f867(x79963,x79962,x79961)),f2(a1)))
% 28.25/28.13 [8065]~P130(x80651)+~P1(f319(f319(f226(x80651),f319(f319(f75(x80651),x80653),x80652)),f2(x80651)))+P1(f319(f319(f226(x80651),x80652),f2(x80651)))+P1(f319(f319(f226(x80651),x80653),f2(x80651)))
% 28.25/28.13 [8066]~P74(x80661)+~P1(f319(f319(f226(x80661),f319(f319(f283(x80661),x80663),x80662)),f2(x80661)))+P1(f319(f319(f226(x80661),x80662),f2(x80661)))+P1(f319(f319(f226(x80661),x80663),f2(x80661)))
% 28.25/28.13 [8067]~P74(x80671)+~P1(f319(f319(f227(x80671),f319(f319(f283(x80671),x80673),x80672)),f2(x80671)))+P1(f319(f319(f227(x80671),x80672),f2(x80671)))+P1(f319(f319(f227(x80671),x80673),f2(x80671)))
% 28.25/28.13 [8181]P152(x81813,x81811,x81812)+E(x81811,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x81811),f869(x81812,x81811,x81813))),f868(x81812,x81811,x81813)),x81812)+P1(f319(f319(f227(a1),x81811),f867(x81812,x81811,x81813)))
% 28.25/28.13 [8182]P151(x81823,x81821,x81822)+E(x81821,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x81821),f875(x81822,x81821,x81823))),f874(x81822,x81821,x81823)),x81822)+P1(f319(f319(f227(a1),x81821),f878(x81822,x81821,x81823)))
% 28.25/28.13 [8195]P152(x81953,x81951,x81952)+E(x81951,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x81951),f873(x81952,x81951,x81953))),f867(x81952,x81951,x81953)),x81952)+P1(f319(f319(f226(a1),f2(a1)),f868(x81952,x81951,x81953)))
% 28.25/28.13 [8196]P151(x81963,x81961,x81962)+E(x81961,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x81961),f876(x81962,x81961,x81963))),f878(x81962,x81961,x81963)),x81962)+P1(f319(f319(f226(a1),f2(a1)),f874(x81962,x81961,x81963)))
% 28.25/28.13 [8239]P151(x82393,x82391,x82392)+~P1(f319(x82393,x82392))+E(f319(f319(f74(a1),f319(f319(f75(a1),x82391),f875(x82392,x82391,x82393))),f874(x82392,x82391,x82393)),x82392)+P1(f319(f319(f227(a1),x82391),f878(x82392,x82391,x82393)))
% 28.25/28.13 [8248]P152(x82483,x82481,x82482)+E(f319(f319(f74(a1),f319(f319(f75(a1),x82481),f869(x82482,x82481,x82483))),f868(x82482,x82481,x82483)),x82482)+P1(f319(f319(f227(a1),x82481),f867(x82482,x82481,x82483)))+~P1(f319(x82483,f2(a1)))
% 28.25/28.13 [8254]P151(x82543,x82541,x82542)+~P1(f319(x82543,x82542))+E(f319(f319(f74(a1),f319(f319(f75(a1),x82541),f876(x82542,x82541,x82543))),f878(x82542,x82541,x82543)),x82542)+P1(f319(f319(f226(a1),f2(a1)),f874(x82542,x82541,x82543)))
% 28.25/28.13 [8260]P152(x82603,x82601,x82602)+E(f319(f319(f74(a1),f319(f319(f75(a1),x82601),f873(x82602,x82601,x82603))),f867(x82602,x82601,x82603)),x82602)+P1(f319(f319(f226(a1),f2(a1)),f868(x82602,x82601,x82603)))+~P1(f319(x82603,f2(a1)))
% 28.25/28.13 [8271]P152(x82713,x82711,x82712)+E(x82711,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x82711),f869(x82712,x82711,x82713))),f868(x82712,x82711,x82713)),x82712)+~P1(f319(x82713,f873(x82712,x82711,x82713)))
% 28.25/28.13 [8272]P151(x82723,x82721,x82722)+E(x82721,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x82721),f875(x82722,x82721,x82723))),f874(x82722,x82721,x82723)),x82722)+~P1(f319(x82723,f878(x82722,x82721,x82723)))
% 28.25/28.13 [8273]P152(x82733,x82731,x82732)+E(x82731,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x82731),f873(x82732,x82731,x82733))),f867(x82732,x82731,x82733)),x82732)+~P1(f319(x82733,f869(x82732,x82731,x82733)))
% 28.25/28.13 [8274]P151(x82743,x82741,x82742)+E(x82741,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x82741),f876(x82742,x82741,x82743))),f878(x82742,x82741,x82743)),x82742)+~P1(f319(x82743,f874(x82742,x82741,x82743)))
% 28.25/28.13 [8333]P151(x83333,x83331,x83332)+~P1(f319(x83333,x83332))+E(f319(f319(f74(a1),f319(f319(f75(a1),x83331),f875(x83332,x83331,x83333))),f874(x83332,x83331,x83333)),x83332)+~P1(f319(x83333,f878(x83332,x83331,x83333)))
% 28.25/28.13 [8334]P151(x83343,x83341,x83342)+~P1(f319(x83343,x83342))+E(f319(f319(f74(a1),f319(f319(f75(a1),x83341),f876(x83342,x83341,x83343))),f878(x83342,x83341,x83343)),x83342)+~P1(f319(x83343,f874(x83342,x83341,x83343)))
% 28.25/28.13 [8347]P152(x83473,x83471,x83472)+E(f319(f319(f74(a1),f319(f319(f75(a1),x83471),f869(x83472,x83471,x83473))),f868(x83472,x83471,x83473)),x83472)+~P1(f319(x83473,f873(x83472,x83471,x83473)))+~P1(f319(x83473,f2(a1)))
% 28.25/28.13 [8348]P152(x83483,x83481,x83482)+E(f319(f319(f74(a1),f319(f319(f75(a1),x83481),f873(x83482,x83481,x83483))),f867(x83482,x83481,x83483)),x83482)+~P1(f319(x83483,f869(x83482,x83481,x83483)))+~P1(f319(x83483,f2(a1)))
% 28.25/28.13 [8446]P152(x84463,x84461,x84462)+E(x84461,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x84461),f869(x84462,x84461,x84463))),f868(x84462,x84461,x84463)),x84462)+P1(f319(f319(f226(a1),f867(x84462,x84461,x84463)),f2(a1)))
% 28.25/28.13 [8447]P151(x84473,x84471,x84472)+E(x84471,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x84471),f875(x84472,x84471,x84473))),f874(x84472,x84471,x84473)),x84472)+P1(f319(f319(f226(a1),f878(x84472,x84471,x84473)),f2(a1)))
% 28.25/28.13 [8487]P151(x84873,x84871,x84872)+~P1(f319(x84873,x84872))+E(f319(f319(f74(a1),f319(f319(f75(a1),x84871),f875(x84872,x84871,x84873))),f874(x84872,x84871,x84873)),x84872)+P1(f319(f319(f226(a1),f878(x84872,x84871,x84873)),f2(a1)))
% 28.25/28.13 [8492]P152(x84923,x84921,x84922)+E(f319(f319(f74(a1),f319(f319(f75(a1),x84921),f869(x84922,x84921,x84923))),f868(x84922,x84921,x84923)),x84922)+~P1(f319(x84923,f2(a1)))+P1(f319(f319(f226(a1),f867(x84922,x84921,x84923)),f2(a1)))
% 28.25/28.13 [8628]P152(x86283,x86281,x86282)+E(x86281,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x86281),f873(x86282,x86281,x86283))),f867(x86282,x86281,x86283)),x86282)+E(f319(f319(f74(a1),f319(f319(f75(a1),x86281),f869(x86282,x86281,x86283))),f868(x86282,x86281,x86283)),x86282)
% 28.25/28.13 [8629]P151(x86293,x86291,x86292)+E(x86291,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x86291),f876(x86292,x86291,x86293))),f878(x86292,x86291,x86293)),x86292)+E(f319(f319(f74(a1),f319(f319(f75(a1),x86291),f875(x86292,x86291,x86293))),f874(x86292,x86291,x86293)),x86292)
% 28.25/28.13 [8649]P151(x86493,x86491,x86492)+~P1(f319(x86493,x86492))+E(f319(f319(f74(a1),f319(f319(f75(a1),x86491),f876(x86492,x86491,x86493))),f878(x86492,x86491,x86493)),x86492)+E(f319(f319(f74(a1),f319(f319(f75(a1),x86491),f875(x86492,x86491,x86493))),f874(x86492,x86491,x86493)),x86492)
% 28.25/28.13 [8660]P152(x86603,x86601,x86602)+E(f319(f319(f74(a1),f319(f319(f75(a1),x86601),f873(x86602,x86601,x86603))),f867(x86602,x86601,x86603)),x86602)+E(f319(f319(f74(a1),f319(f319(f75(a1),x86601),f869(x86602,x86601,x86603))),f868(x86602,x86601,x86603)),x86602)+~P1(f319(x86603,f2(a1)))
% 28.25/28.13 [9335]~P130(x93351)+~E(x93353,f2(x93351))+~E(x93352,f2(x93351))+P1(f319(f319(f226(x93351),f319(f319(f74(x93351),f319(f319(f75(x93351),x93352),x93352)),f319(f319(f75(x93351),x93353),x93353))),f2(x93351)))
% 28.25/28.13 [10434]~P126(x104341)+~E(x104343,f2(x104341))+~E(x104342,f2(x104341))+P1(f319(f319(f226(x104341),f319(f319(f74(x104341),f319(f319(f236(x104341),x104342),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(x104341),x104343),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(x104341)))
% 28.25/28.13 [5020]~E(x50203,x50201)+~P124(x50202)+E(x50201,f2(x50202))+E(f319(f319(f283(x50202),x50203),x50201),f72(x50202))
% 28.25/28.13 [5073]~P104(x50731)+~E(x50733,f180(x50731))+~E(x50732,f180(x50731))+E(f319(f319(f102(x50731),x50732),x50733),f180(x50731))
% 28.25/28.13 [5074]~P103(x50741)+~E(x50743,f234(x50741))+~E(x50742,f234(x50741))+E(f319(f319(f93(x50741),x50742),x50743),f234(x50741))
% 28.25/28.13 [5168]~P124(x51683)+E(x51681,x51682)+E(x51682,f2(x51683))+~E(f319(f319(f283(x51683),x51681),x51682),f72(x51683))
% 28.25/28.13 [5185]~P147(x51852)+E(x51851,f2(x51852))+E(x51853,f2(x51852))+~E(f319(f319(f75(x51852),x51853),x51851),f2(x51852))
% 28.25/28.13 [5186]~P138(x51862)+E(x51861,f2(x51862))+E(x51863,f2(x51862))+~E(f319(f319(f75(x51862),x51863),x51861),f2(x51862))
% 28.25/28.13 [5187]~P138(x51872)+E(x51871,f2(x51872))+E(x51873,f2(x51872))+~E(f319(f319(f75(x51872),x51873),x51871),f2(x51872))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [5676]~P4(x56763)+E(x56761,x56762)+P1(f319(f319(f227(x56763),x56762),x56761))+P1(f319(f319(f227(x56763),x56761),x56762))
% 28.25/28.13 [5677]~P4(x56773)+E(x56771,x56772)+P1(f319(f319(f227(x56773),x56772),x56771))+P1(f319(f319(f227(x56773),x56771),x56772))
% 28.25/28.13 [5678]~P4(x56783)+E(x56781,x56782)+P1(f319(f319(f227(x56783),x56782),x56781))+P1(f319(f319(f227(x56783),x56781),x56782))
% 28.25/28.13 [5679]~P4(x56793)+E(x56791,x56792)+P1(f319(f319(f227(x56793),x56792),x56791))+P1(f319(f319(f227(x56793),x56791),x56792))
% 28.25/28.13 [5680]~P4(x56803)+E(x56801,x56802)+P1(f319(f319(f227(x56803),x56802),x56801))+P1(f319(f319(f227(x56803),x56801),x56802))
% 28.25/28.13 [5681]~P126(x56813)+E(x56811,x56812)+P1(f319(f319(f227(x56813),x56812),x56811))+P1(f319(f319(f227(x56813),x56811),x56812))
% 28.25/28.13 [5682]~P4(x56823)+E(x56821,x56822)+P1(f319(f319(f227(x56823),x56822),x56821))+P1(f319(f319(f227(x56823),x56821),x56822))
% 28.25/28.13 [5683]~E(x56832,x56833)+~P4(x56831)+P1(f319(f319(f227(x56831),x56832),x56833))+P1(f319(f319(f226(x56831),x56832),x56833))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [5881]E(x58811,x58812)+P1(f319(f319(x58813,x58811),x58812))+P1(f319(f319(f227(a925),x58812),x58811))+P1(f319(f319(f227(a925),x58811),x58812))
% 28.25/28.13 [5943]~P113(x59433)+E(x59431,x59432)+~P1(f319(f319(f226(x59433),x59432),x59431))+P1(f319(f319(f227(x59433),x59432),x59431))
% 28.25/28.13 [5944]~P4(x59443)+E(x59441,x59442)+~P1(f319(f319(f226(x59443),x59441),x59442))+P1(f319(f319(f227(x59443),x59441),x59442))
% 28.25/28.13 [5945]~P4(x59453)+E(x59451,x59452)+~P1(f319(f319(f226(x59453),x59451),x59452))+P1(f319(f319(f227(x59453),x59451),x59452))
% 28.25/28.13 [5946]~P113(x59463)+E(x59461,x59462)+~P1(f319(f319(f226(x59463),x59461),x59462))+P1(f319(f319(f227(x59463),x59461),x59462))
% 28.25/28.13 [5947]~P113(x59473)+E(x59471,x59472)+~P1(f319(f319(f226(x59473),x59471),x59472))+P1(f319(f319(f227(x59473),x59471),x59472))
% 28.25/28.13 [5948]~P113(x59483)+E(x59481,x59482)+~P1(f319(f319(f226(x59483),x59481),x59482))+P1(f319(f319(f227(x59483),x59481),x59482))
% 28.25/28.13 [5949]~P113(x59493)+E(x59491,x59492)+~P1(f319(f319(f226(x59493),x59491),x59492))+P1(f319(f319(f227(x59493),x59491),x59492))
% 28.25/28.13 [5950]~P113(x59503)+E(x59501,x59502)+~P1(f319(f319(f226(x59503),x59501),x59502))+P1(f319(f319(f227(x59503),x59501),x59502))
% 28.25/28.13 [5951]~P113(x59513)+E(x59511,x59512)+~P1(f319(f319(f226(x59513),x59511),x59512))+P1(f319(f319(f227(x59513),x59511),x59512))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [6195]E(x61951,x61952)+~P113(x61953)+~P1(f319(f319(f226(x61953),x61952),x61951))+~P1(f319(f319(f226(x61953),x61951),x61952))
% 28.25/28.13 [6196]E(x61961,x61962)+~P113(x61963)+~P1(f319(f319(f226(x61963),x61962),x61961))+~P1(f319(f319(f226(x61963),x61961),x61962))
% 28.25/28.13 [6197]E(x61971,x61972)+~P113(x61973)+~P1(f319(f319(f226(x61973),x61972),x61971))+~P1(f319(f319(f226(x61973),x61971),x61972))
% 28.25/28.13 [6198]E(x61981,x61982)+~P113(x61983)+~P1(f319(f319(f226(x61983),x61982),x61981))+~P1(f319(f319(f226(x61983),x61981),x61982))
% 28.25/28.13 [6200]~E(x62001,x62002)+~P4(x62003)+~P1(f319(f319(f226(x62003),x62001),x62002))+~P1(f319(f319(f227(x62003),x62001),x62002))
% 28.25/28.13 [6341]~P2(x63411)+P1(f319(f319(f227(x63411),x63413),x63412))+~P1(f319(f319(f226(x63411),x63413),x63412))+P1(f319(f319(f226(x63411),x63412),x63413))
% 28.25/28.13 [6367]~P4(x63671)+~P1(f319(f55(x63671),x63673))+P1(f319(f319(f226(x63671),x63672),f15(x63671,x63673)))+~P1(f319(f319(f321(x63671),x63672),x63673))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [6581]~P4(x65811)+~P1(f319(f55(x65811),x65812))+~P1(f319(f319(f321(x65811),x65813),x65812))+P1(f319(f319(f226(x65811),f14(x65811,x65812)),x65813))
% 28.25/28.13 [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)))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [6655]~P1(f319(x66551,x66552))+P1(f319(x66551,f523(x66552,x66551,x66553)))+P1(f319(x66551,f2(a925)))+~P1(f319(f319(f227(a925),x66552),x66553))
% 28.25/28.13 [6713]~P1(f319(x67131,x67132))+~P1(f319(f55(x67133),x67132))+P1(f319(x67131,f335(x67131,x67132,x67133)))+P1(f319(x67131,f180(f932(x67133,a923))))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [6893]P152(x68932,x68931,x68933)+E(x68931,f2(a1))+~P1(f319(x68932,f873(x68933,x68931,x68932)))+P1(f319(f319(f227(a1),f2(a1)),x68931))
% 28.25/28.13 [6894]P151(x68942,x68941,x68943)+E(x68941,f2(a1))+~P1(f319(x68942,f878(x68943,x68941,x68942)))+P1(f319(f319(f227(a1),f2(a1)),x68941))
% 28.25/28.13 [6898]P1(f319(x68981,x68982))+~P1(f319(f55(x68983),x68982))+P1(f319(x68981,f777(x68981,x68982,x68983)))+~P1(f319(x68981,f180(f932(x68983,a923))))
% 28.25/28.13 [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))))
% 28.25/28.13 [6985]P151(x69851,x69852,x69853)+~P1(f319(x69851,x69853))+~P1(f319(x69851,f878(x69853,x69852,x69851)))+P1(f319(f319(f227(a1),f2(a1)),x69852))
% 28.25/28.13 [7015]P152(x70151,x70152,x70153)+~P1(f319(x70151,f873(x70153,x70152,x70151)))+~P1(f319(x70151,f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x70152))
% 28.25/28.13 [7026]E(x70261,f2(a925))+~P1(f319(f42(x70263,x70261),x70262))+P1(f319(f319(f226(a925),f319(f248(a925,a925),x70262)),f2(a925)))+P1(f319(f319(f227(a925),f2(a925)),x70261))
% 28.25/28.13 [7124]~P99(x71243)+~P126(x71243)+~P1(f319(f319(f226(x71243),f319(f95(x71243),x71241)),f319(f95(x71243),x71242)))+P1(f319(f319(f226(a1),x71241),x71242))
% 28.25/28.13 [7125]~P99(x71253)+~P126(x71253)+~P1(f319(f319(f227(x71253),f319(f95(x71253),x71251)),f319(f95(x71253),x71252)))+P1(f319(f319(f227(a1),x71251),x71252))
% 28.25/28.13 [7153]~P4(x71531)+~P14(x71531,x71533)+P14(x71531,f319(f319(f143(x71531),x71532),x71533))+~P1(f319(f319(f226(x71531),x71532),f732(x71533,x71532,x71531)))
% 28.25/28.13 [7154]~P4(x71541)+~P14(x71541,x71543)+P14(x71541,f319(f319(f143(x71541),x71542),x71543))+~P1(f319(f319(f226(x71541),x71542),f734(x71543,x71542,x71541)))
% 28.25/28.13 [7155]~P4(x71551)+~P14(x71551,x71553)+P14(x71551,f319(f319(f143(x71551),x71552),x71553))+~P1(f319(f319(f226(x71551),x71552),f759(x71552,x71553,x71551)))
% 28.25/28.13 [7239]P152(x72392,x72391,x72393)+E(x72391,f2(a1))+P1(f319(f319(f227(a1),x72391),f2(a1)))+P1(f319(f319(f227(a1),f868(x72393,x72391,x72392)),x72391))
% 28.25/28.13 [7240]P151(x72402,x72401,x72403)+E(x72401,f2(a1))+P1(f319(f319(f227(a1),x72401),f2(a1)))+P1(f319(f319(f227(a1),f874(x72403,x72401,x72402)),x72401))
% 28.25/28.13 [7244]~P4(x72441)+~P100(x72441)+P1(f319(f319(f226(x72441),f319(f95(x72441),x72442)),f319(f95(x72441),x72443)))+P1(f319(f319(f227(x72441),f319(f95(x72441),x72443)),f319(f95(x72441),x72442)))
% 28.25/28.13 [7276]P152(x72762,x72761,x72763)+E(x72761,f2(a1))+P1(f319(f319(f226(a1),f867(x72763,x72761,x72762)),f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x72761))
% 28.25/28.13 [7277]P151(x72772,x72771,x72773)+E(x72771,f2(a1))+P1(f319(f319(f226(a1),f878(x72773,x72771,x72772)),f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x72771))
% 28.25/28.13 [7303]~P4(x73031)+~P14(x73031,x73033)+E(f319(f319(f140(x73031,x73031,f5(x73031)),x73032),f162(x73031,x73032,x73033)),x73033)+~P1(f319(f319(f321(x73031),x73032),f319(f164(x73031),x73033)))
% 28.25/28.13 [7350]P151(x73501,x73502,x73503)+~P1(f319(x73501,x73503))+P1(f319(f319(f227(a1),x73502),f2(a1)))+P1(f319(f319(f227(a1),f874(x73503,x73502,x73501)),x73502))
% 28.25/28.13 [7356]~P3(x73561)+~P100(x73561)+E(f319(f319(f224(x73561),f319(f95(x73561),x73562)),f319(f95(x73561),x73563)),f319(f95(x73561),x73562))+~P1(f319(f319(f226(x73561),f319(f95(x73561),x73562)),f319(f95(x73561),x73563)))
% 28.25/28.13 [7357]~P3(x73571)+~P100(x73571)+E(f319(f319(f225(x73571),f319(f95(x73571),x73572)),f319(f95(x73571),x73573)),f319(f95(x73571),x73573))+~P1(f319(f319(f226(x73571),f319(f95(x73571),x73572)),f319(f95(x73571),x73573)))
% 28.25/28.13 [7371]P152(x73711,x73712,x73713)+~P1(f319(x73711,f2(a1)))+P1(f319(f319(f227(a1),x73712),f2(a1)))+P1(f319(f319(f227(a1),f868(x73713,x73712,x73711)),x73712))
% 28.25/28.13 [7381]P151(x73811,x73812,x73813)+~P1(f319(x73811,x73813))+P1(f319(f319(f226(a1),f878(x73813,x73812,x73811)),f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x73812))
% 28.25/28.13 [7405]P152(x74051,x74052,x74053)+~P1(f319(x74051,f2(a1)))+P1(f319(f319(f226(a1),f867(x74053,x74052,x74051)),f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x74052))
% 28.25/28.13 [7433]~P1(f319(x74331,x74332))+P1(f319(x74331,f2(a925)))+~P1(f319(f319(f227(a925),x74332),x74333))+P1(f319(f319(f227(a925),f523(x74332,x74331,x74333)),x74333))
% 28.25/28.13 [7450]~P4(x74501)+~P14(x74501,x74503)+P14(x74501,f319(f319(f143(x74501),x74502),x74503))+P1(f319(f319(f321(x74501),f732(x74503,x74502,x74501)),f319(f164(x74501),x74503)))
% 28.25/28.13 [7451]~P4(x74511)+~P14(x74511,x74513)+P14(x74511,f319(f319(f143(x74511),x74512),x74513))+P1(f319(f319(f321(x74511),f734(x74513,x74512,x74511)),f319(f164(x74511),x74513)))
% 28.25/28.13 [7452]~P4(x74521)+~P14(x74521,x74523)+P14(x74521,f319(f319(f143(x74521),x74522),x74523))+P1(f319(f319(f321(x74521),f759(x74522,x74523,x74521)),f319(f164(x74521),x74523)))
% 28.25/28.13 [7565]~P4(x75651)+~P6(x75651)+~P1(f319(f319(f227(x75651),x75653),f31(x75651,x75652)))+P1(f319(f319(f321(x75651),f879(x75652,x75653,x75651)),x75652))
% 28.25/28.13 [7718]~P4(x77181)+~P6(x77181)+~P1(f319(f319(f227(x77181),f32(x77181,x77183)),x77182))+P1(f319(f319(f321(x77181),f885(x77182,x77183,x77181)),x77183))
% 28.25/28.13 [7719]~P4(x77191)+~P6(x77191)+~P1(f319(f319(f227(x77191),f32(x77191,x77193)),x77192))+P1(f319(f319(f227(x77191),f885(x77192,x77193,x77191)),x77192))
% 28.25/28.13 [7730]P152(x77302,x77301,x77303)+E(x77301,f2(a1))+P1(f319(f319(f227(a1),x77301),f867(x77303,x77301,x77302)))+P1(f319(f319(f227(a1),f868(x77303,x77301,x77302)),x77301))
% 28.25/28.13 [7731]P151(x77312,x77311,x77313)+E(x77311,f2(a1))+P1(f319(f319(f227(a1),x77311),f878(x77313,x77311,x77312)))+P1(f319(f319(f227(a1),f874(x77313,x77311,x77312)),x77311))
% 28.25/28.13 [7824]P152(x78243,x78241,x78242)+E(x78241,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x78241),f873(x78242,x78241,x78243))),f867(x78242,x78241,x78243)),x78242)+P1(f319(f319(f227(a1),f2(a1)),x78241))
% 28.25/28.13 [7825]P151(x78253,x78251,x78252)+E(x78251,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x78251),f876(x78252,x78251,x78253))),f878(x78252,x78251,x78253)),x78252)+P1(f319(f319(f227(a1),f2(a1)),x78251))
% 28.25/28.13 [7826]~P139(x78261)+~P1(f319(f319(f226(x78261),x78262),f2(x78261)))+P1(f319(f319(f226(x78261),f319(f319(f75(x78261),x78262),x78263)),f2(x78261)))+~P1(f319(f319(f226(x78261),f2(x78261)),x78263))
% 28.25/28.13 [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))
% 28.25/28.13 [7828]~P139(x78281)+~P1(f319(f319(f226(x78281),x78283),f2(x78281)))+P1(f319(f319(f226(x78281),f319(f319(f75(x78281),x78282),x78283)),f2(x78281)))+~P1(f319(f319(f226(x78281),f2(x78281)),x78282))
% 28.25/28.13 [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))
% 28.25/28.13 [7830]~P139(x78301)+~P1(f319(f319(f226(x78301),x78302),f2(x78301)))+P1(f319(f319(f226(x78301),f319(f319(f75(x78301),x78302),x78303)),f2(x78301)))+~P1(f319(f319(f226(x78301),f2(x78301)),x78303))
% 28.25/28.13 [7831]~P130(x78311)+~P1(f319(f319(f226(x78311),x78313),f2(x78311)))+P1(f319(f319(f226(x78311),f319(f319(f75(x78311),x78312),x78313)),f2(x78311)))+~P1(f319(f319(f226(x78311),f2(x78311)),x78312))
% 28.25/28.13 [7832]~P130(x78321)+~P1(f319(f319(f226(x78321),x78322),f2(x78321)))+P1(f319(f319(f226(x78321),f319(f319(f75(x78321),x78322),x78323)),f2(x78321)))+~P1(f319(f319(f226(x78321),f2(x78321)),x78323))
% 28.25/28.13 [7833]~P75(x78331)+~P1(f319(f319(f226(x78331),x78332),f2(x78331)))+P1(f319(f319(f226(x78331),f319(f319(f283(x78331),x78332),x78333)),f2(x78331)))+~P1(f319(f319(f227(x78331),f2(x78331)),x78333))
% 28.25/28.13 [7834]~P75(x78341)+~P1(f319(f319(f227(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))
% 28.25/28.13 [7835]~P74(x78351)+~P1(f319(f319(f226(x78351),x78353),f2(x78351)))+P1(f319(f319(f226(x78351),f319(f319(f283(x78351),x78352),x78353)),f2(x78351)))+~P1(f319(f319(f226(x78351),f2(x78351)),x78352))
% 28.25/28.13 [7836]~P74(x78361)+~P1(f319(f319(f226(x78361),x78362),f2(x78361)))+P1(f319(f319(f226(x78361),f319(f319(f283(x78361),x78362),x78363)),f2(x78361)))+~P1(f319(f319(f226(x78361),f2(x78361)),x78363))
% 28.25/28.13 [7837]~P134(x78371)+~P1(f319(f319(f227(x78371),x78372),f2(x78371)))+P1(f319(f319(f227(x78371),f319(f319(f75(x78371),x78372),x78373)),f2(x78371)))+~P1(f319(f319(f227(x78371),f2(x78371)),x78373))
% 28.25/28.13 [7838]~P134(x78381)+~P1(f319(f319(f227(x78381),x78383),f2(x78381)))+P1(f319(f319(f227(x78381),f319(f319(f75(x78381),x78382),x78383)),f2(x78381)))+~P1(f319(f319(f227(x78381),f2(x78381)),x78382))
% 28.25/28.13 [7839]~P134(x78391)+~P1(f319(f319(f227(x78391),x78392),f2(x78391)))+P1(f319(f319(f227(x78391),f319(f319(f75(x78391),x78392),x78393)),f2(x78391)))+~P1(f319(f319(f227(x78391),f2(x78391)),x78393))
% 28.25/28.13 [7840]~P75(x78401)+~P1(f319(f319(f227(x78401),x78403),f2(x78401)))+P1(f319(f319(f227(x78401),f319(f319(f283(x78401),x78402),x78403)),f2(x78401)))+~P1(f319(f319(f227(x78401),f2(x78401)),x78402))
% 28.25/28.13 [7841]~P75(x78411)+~P1(f319(f319(f227(x78411),x78412),f2(x78411)))+P1(f319(f319(f227(x78411),f319(f319(f283(x78411),x78412),x78413)),f2(x78411)))+~P1(f319(f319(f227(x78411),f2(x78411)),x78413))
% 28.25/28.13 [7842]~P74(x78421)+~P1(f319(f319(f227(x78421),x78423),f2(x78421)))+P1(f319(f319(f227(x78421),f319(f319(f283(x78421),x78422),x78423)),f2(x78421)))+~P1(f319(f319(f227(x78421),f2(x78421)),x78422))
% 28.25/28.13 [7843]~P74(x78431)+~P1(f319(f319(f227(x78431),x78432),f2(x78431)))+P1(f319(f319(f227(x78431),f319(f319(f283(x78431),x78432),x78433)),f2(x78431)))+~P1(f319(f319(f227(x78431),f2(x78431)),x78433))
% 28.25/28.13 [7858]P151(x78581,x78582,x78583)+~P1(f319(x78581,x78583))+P1(f319(f319(f227(a1),x78582),f878(x78583,x78582,x78581)))+P1(f319(f319(f227(a1),f874(x78583,x78582,x78581)),x78582))
% 28.25/28.13 [7871]P152(x78711,x78712,x78713)+P1(f319(f319(f227(a1),x78712),f867(x78713,x78712,x78711)))+~P1(f319(x78711,f2(a1)))+P1(f319(f319(f227(a1),f868(x78713,x78712,x78711)),x78712))
% 28.25/28.13 [7922]P152(x79222,x79221,x79223)+E(x79221,f2(a1))+~P1(f319(x79222,f873(x79223,x79221,x79222)))+P1(f319(f319(f227(a1),f868(x79223,x79221,x79222)),x79221))
% 28.25/28.13 [7923]P151(x79232,x79231,x79233)+E(x79231,f2(a1))+~P1(f319(x79232,f878(x79233,x79231,x79232)))+P1(f319(f319(f227(a1),f874(x79233,x79231,x79232)),x79231))
% 28.25/28.13 [7933]P151(x79333,x79331,x79332)+~P1(f319(x79333,x79332))+E(f319(f319(f74(a1),f319(f319(f75(a1),x79331),f876(x79332,x79331,x79333))),f878(x79332,x79331,x79333)),x79332)+P1(f319(f319(f227(a1),f2(a1)),x79331))
% 28.25/28.13 [7948]P152(x79483,x79481,x79482)+E(f319(f319(f74(a1),f319(f319(f75(a1),x79481),f873(x79482,x79481,x79483))),f867(x79482,x79481,x79483)),x79482)+~P1(f319(x79483,f2(a1)))+P1(f319(f319(f227(a1),f2(a1)),x79481))
% 28.25/28.13 [7976]~P1(f319(x79761,x79763))+~P1(f319(f55(x79762),x79763))+P1(f319(f319(f321(x79762),f336(x79761,x79763,x79762)),f335(x79761,x79763,x79762)))+P1(f319(x79761,f180(f932(x79762,a923))))
% 28.25/28.13 [7987]P151(x79871,x79872,x79873)+~P1(f319(x79871,x79873))+~P1(f319(x79871,f878(x79873,x79872,x79871)))+P1(f319(f319(f227(a1),f874(x79873,x79872,x79871)),x79872))
% 28.25/28.13 [7993]P152(x79931,x79932,x79933)+~P1(f319(x79931,f873(x79933,x79932,x79931)))+~P1(f319(x79931,f2(a1)))+P1(f319(f319(f227(a1),f868(x79933,x79932,x79931)),x79932))
% 28.25/28.13 [8060]~P100(x80601)+~P4(x80601)+~P1(f319(f319(f226(x80601),f319(f95(x80601),x80602)),f319(f95(x80601),x80603)))+~P1(f319(f319(f227(x80601),f319(f95(x80601),x80603)),f319(f95(x80601),x80602)))
% 28.25/28.13 [8096]~P130(x80961)+~P1(f319(f319(f226(x80961),f319(f319(f75(x80961),x80963),x80962)),f2(x80961)))+P1(f319(f319(f226(x80961),x80962),f2(x80961)))+P1(f319(f319(f226(x80961),f2(x80961)),x80962))
% 28.25/28.13 [8097]~P130(x80971)+~P1(f319(f319(f226(x80971),f319(f319(f75(x80971),x80972),x80973)),f2(x80971)))+P1(f319(f319(f226(x80971),x80972),f2(x80971)))+P1(f319(f319(f226(x80971),f2(x80971)),x80972))
% 28.25/28.13 [8098]~P74(x80981)+~P1(f319(f319(f226(x80981),f319(f319(f283(x80981),x80983),x80982)),f2(x80981)))+P1(f319(f319(f226(x80981),x80982),f2(x80981)))+P1(f319(f319(f226(x80981),f2(x80981)),x80982))
% 28.25/28.13 [8099]~P74(x80991)+~P1(f319(f319(f226(x80991),f319(f319(f283(x80991),x80992),x80993)),f2(x80991)))+P1(f319(f319(f226(x80991),x80992),f2(x80991)))+P1(f319(f319(f226(x80991),f2(x80991)),x80992))
% 28.25/28.13 [8100]~P74(x81001)+~P1(f319(f319(f227(x81001),f319(f319(f283(x81001),x81003),x81002)),f2(x81001)))+P1(f319(f319(f227(x81001),x81002),f2(x81001)))+P1(f319(f319(f227(x81001),f2(x81001)),x81002))
% 28.25/28.13 [8101]~P74(x81011)+~P1(f319(f319(f227(x81011),f319(f319(f283(x81011),x81012),x81013)),f2(x81011)))+P1(f319(f319(f227(x81011),x81012),f2(x81011)))+P1(f319(f319(f227(x81011),f2(x81011)),x81012))
% 28.25/28.13 [8125]~P130(x81251)+~P1(f319(f319(f226(x81251),f319(f319(f75(x81251),x81252),x81253)),f2(x81251)))+P1(f319(f319(f226(x81251),f2(x81251)),x81252))+P1(f319(f319(f226(x81251),f2(x81251)),x81253))
% 28.25/28.13 [8126]~P74(x81261)+~P1(f319(f319(f226(x81261),f319(f319(f283(x81261),x81262),x81263)),f2(x81261)))+P1(f319(f319(f226(x81261),f2(x81261)),x81262))+P1(f319(f319(f226(x81261),f2(x81261)),x81263))
% 28.25/28.13 [8127]~P74(x81271)+~P1(f319(f319(f227(x81271),f319(f319(f283(x81271),x81272),x81273)),f2(x81271)))+P1(f319(f319(f227(x81271),f2(x81271)),x81272))+P1(f319(f319(f227(x81271),f2(x81271)),x81273))
% 28.25/28.13 [8149]P152(x81492,x81491,x81493)+E(x81491,f2(a1))+P1(f319(f319(f226(a1),f867(x81493,x81491,x81492)),f2(a1)))+P1(f319(f319(f227(a1),f868(x81493,x81491,x81492)),x81491))
% 28.25/28.13 [8150]P151(x81502,x81501,x81503)+E(x81501,f2(a1))+P1(f319(f319(f226(a1),f878(x81503,x81501,x81502)),f2(a1)))+P1(f319(f319(f227(a1),f874(x81503,x81501,x81502)),x81501))
% 28.25/28.13 [8157]~P129(x81571)+~P1(f319(f319(f227(x81571),x81572),f72(x81571)))+P1(f319(f319(f227(x81571),f319(f319(f236(x81571),x81572),f319(a104,x81573))),f72(x81571)))+~P1(f319(f319(f227(x81571),f2(x81571)),x81572))
% 28.25/28.13 [8212]~P4(x82121)+~E(x82123,f105(x82121))+~P14(x82121,f319(f160(x82121),x82123))+E(f319(f134(x82121,x82121,f319(f7(x82121,x82121,x82121),f225(x82121)),x82122),f319(f160(x82121),x82123)),x82122)
% 28.25/28.13 [8216]P151(x82161,x82162,x82163)+~P1(f319(x82161,x82163))+P1(f319(f319(f226(a1),f878(x82163,x82162,x82161)),f2(a1)))+P1(f319(f319(f227(a1),f874(x82163,x82162,x82161)),x82162))
% 28.25/28.13 [8223]P152(x82231,x82232,x82233)+~P1(f319(x82231,f2(a1)))+P1(f319(f319(f226(a1),f867(x82233,x82232,x82231)),f2(a1)))+P1(f319(f319(f227(a1),f868(x82233,x82232,x82231)),x82232))
% 28.25/28.13 [8441]P152(x84413,x84411,x84412)+E(x84411,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x84411),f873(x84412,x84411,x84413))),f867(x84412,x84411,x84413)),x84412)+P1(f319(f319(f227(a1),f868(x84412,x84411,x84413)),x84411))
% 28.25/28.13 [8442]P151(x84423,x84421,x84422)+E(x84421,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x84421),f876(x84422,x84421,x84423))),f878(x84422,x84421,x84423)),x84422)+P1(f319(f319(f227(a1),f874(x84422,x84421,x84423)),x84421))
% 28.25/28.13 [8478]P151(x84783,x84781,x84782)+~P1(f319(x84783,x84782))+E(f319(f319(f74(a1),f319(f319(f75(a1),x84781),f876(x84782,x84781,x84783))),f878(x84782,x84781,x84783)),x84782)+P1(f319(f319(f227(a1),f874(x84782,x84781,x84783)),x84781))
% 28.25/28.13 [8479]~P78(x84791)+~P79(x84791)+~P42(x84793)+E(f319(f319(f6(a925,x84791),f319(f319(f8(a1,x84791,a925),x84792),f92(a1))),f319(f302(a1,a925,a96),x84793)),f319(f319(f6(a1,x84791),x84792),x84793))
% 28.25/28.13 [8480]~P78(x84801)+~P79(x84801)+~P42(x84803)+E(f319(f319(f9(a925,x84801),f319(f319(f8(a1,x84801,a925),x84802),f92(a1))),f319(f302(a1,a925,a96),x84803)),f319(f319(f9(a1,x84801),x84802),x84803))
% 28.25/28.13 [8489]P152(x84893,x84891,x84892)+E(f319(f319(f74(a1),f319(f319(f75(a1),x84891),f873(x84892,x84891,x84893))),f867(x84892,x84891,x84893)),x84892)+~P1(f319(x84893,f2(a1)))+P1(f319(f319(f227(a1),f868(x84892,x84891,x84893)),x84891))
% 28.25/28.13 [8512]~E(x85122,f2(a925))+~E(f319(f243(a925,a925),x85123),f2(a925))+~E(x85121,f319(f319(f74(a925),f319(f319(f75(a925),f319(f243(a925,a925),x85123)),x85122)),f319(f248(a925,a925),x85123)))+P1(f319(f42(x85121,x85122),x85123))
% 28.25/28.13 [8569]P1(f319(x85691,x85692))+~P1(f319(f319(f321(x85693),f784(x85691,x85692,x85693)),f777(x85691,x85692,x85693)))+~P1(f319(f55(x85693),x85692))+~P1(f319(x85691,f180(f932(x85693,a923))))
% 28.25/28.13 [9204]P1(f319(x92041,x92042))+~P1(f319(f55(x92043),x92042))+~P1(f319(x92041,f319(f319(f301(x92043),f784(x92041,x92042,x92043)),f777(x92041,x92042,x92043))))+~P1(f319(x92041,f180(f932(x92043,a923))))
% 28.25/28.13 [9440]P1(f319(f319(f226(a1),x94401),f2(a1)))+~P1(f319(f319(f227(a1),f319(f319(f74(a1),f319(f319(f75(a1),x94403),x94401)),x94402)),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x94402))+~P1(f319(f319(f227(a1),f2(a1)),x94403))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [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))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [6940]~P102(x69401)+~P1(f319(f55(x69401),x69403))+E(f319(f319(f58(x69401,x69401,f93(x69401)),x69402),x69403),f10(x69401,f319(f319(f301(x69401),x69402),x69403)))+P1(f319(f319(f321(x69401),x69402),x69403))
% 28.25/28.13 [6941]~P102(x69411)+~P1(f319(f55(x69411),x69413))+E(f319(f319(f58(x69411,x69411,f102(x69411)),x69412),x69413),f13(x69411,f319(f319(f301(x69411),x69412),x69413)))+P1(f319(f319(f321(x69411),x69412),x69413))
% 28.25/28.13 [6942]~P4(x69421)+~P1(f319(f55(x69421),x69423))+E(f319(f319(f58(x69421,x69421,f224(x69421)),x69422),x69423),f14(x69421,f319(f319(f301(x69421),x69422),x69423)))+P1(f319(f319(f321(x69421),x69422),x69423))
% 28.25/28.13 [6943]~P4(x69431)+~P1(f319(f55(x69431),x69433))+E(f319(f319(f58(x69431,x69431,f225(x69431)),x69432),x69433),f15(x69431,f319(f319(f301(x69431),x69432),x69433)))+P1(f319(f319(f321(x69431),x69432),x69433))
% 28.25/28.13 [7049]~P76(x70491)+~P1(f319(f55(x70491),x70493))+E(f319(f57(x70491,f75(x70491)),f319(f319(f301(x70491),x70492),x70493)),f319(f319(f58(x70491,x70491,f75(x70491)),x70492),x70493))+P1(f319(f319(f321(x70491),x70492),x70493))
% 28.25/28.13 [7066]~P4(x70661)+~P1(f319(f55(x70661),x70663))+E(f11(x70661,f224(x70661),f319(f319(f301(x70661),x70662),x70663)),f319(f319(f58(x70661,x70661,f224(x70661)),x70662),x70663))+P1(f319(f319(f321(x70661),x70662),x70663))
% 28.25/28.13 [7067]~P4(x70671)+~P1(f319(f55(x70671),x70673))+E(f12(x70671,f225(x70671),f319(f319(f301(x70671),x70672),x70673)),f319(f319(f58(x70671,x70671,f225(x70671)),x70672),x70673))+P1(f319(f319(f321(x70671),x70672),x70673))
% 28.25/28.13 [7131]~E(f319(f319(f74(a1),x71312),f319(f319(f75(a1),x71313),x71311)),x71313)+~P1(f319(f319(f227(a1),f2(a1)),x71313))+P1(f319(f319(f226(a1),f72(a1)),x71311))+~P1(f319(f319(f227(a1),x71312),x71313))
% 28.25/28.13 [7160]~E(f319(f319(f74(a1),x71602),f319(f319(f75(a1),x71603),x71601)),x71603)+P1(f319(f319(f226(a1),x71601),f72(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x71602))+~P1(f319(f319(f227(a1),f2(a1)),x71603))
% 28.25/28.13 [7176]E(x71761,f2(a925))+~P1(f319(f42(x71763,x71761),x71762))+~P1(f319(f319(f227(a925),f2(a925)),x71761))+P1(f319(f319(f227(a925),f319(f248(a925,a925),x71762)),x71761))
% 28.25/28.13 [7207]~P142(x72071)+~P1(f319(f319(f226(x72071),x72072),f2(x72071)))+~P1(f319(f319(f226(x72071),x72073),f2(x72071)))+E(f319(f319(f75(x72071),f319(f69(x72071),x72072)),f319(f69(x72071),x72073)),f319(f69(x72071),f319(f319(f75(x72071),x72072),x72073)))
% 28.25/28.13 [7253]~P142(x72531)+~P1(f319(f319(f226(x72531),x72532),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)),x72533))
% 28.25/28.13 [7254]~P142(x72541)+~P1(f319(f319(f226(x72541),x72543),f2(x72541)))+E(f319(f319(f75(x72541),f319(f69(x72541),x72542)),f319(f69(x72541),x72543)),f319(f69(x72541),f319(f319(f75(x72541),x72542),x72543)))+~P1(f319(f319(f226(x72541),f2(x72541)),x72542))
% 28.25/28.13 [7311]~P142(x73111)+E(f319(f319(f75(x73111),f319(f69(x73111),x73112)),f319(f69(x73111),x73113)),f319(f69(x73111),f319(f319(f75(x73111),x73112),x73113)))+~P1(f319(f319(f226(x73111),f2(x73111)),x73112))+~P1(f319(f319(f226(x73111),f2(x73111)),x73113))
% 28.25/28.13 [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)))
% 28.25/28.13 [7328]~P132(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)))
% 28.25/28.13 [7329]~P130(x73291)+~P1(f319(f319(f226(x73291),x73293),f2(x73291)))+~P1(f319(f319(f226(x73291),x73292),f2(x73291)))+P1(f319(f319(f226(x73291),f2(x73291)),f319(f319(f75(x73291),x73292),x73293)))
% 28.25/28.13 [7330]~P75(x73301)+~P1(f319(f319(f227(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)))
% 28.25/28.13 [7331]~P74(x73311)+~P1(f319(f319(f226(x73311),x73313),f2(x73311)))+~P1(f319(f319(f226(x73311),x73312),f2(x73311)))+P1(f319(f319(f226(x73311),f2(x73311)),f319(f319(f283(x73311),x73312),x73313)))
% 28.25/28.13 [7332]~P130(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(f75(x73321),x73322),x73323)))
% 28.25/28.13 [7333]~P75(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)))
% 28.25/28.13 [7334]~P74(x73341)+~P1(f319(f319(f227(x73341),x73343),f2(x73341)))+~P1(f319(f319(f227(x73341),x73342),f2(x73341)))+P1(f319(f319(f227(x73341),f2(x73341)),f319(f319(f283(x73341),x73342),x73343)))
% 28.25/28.13 [7335]~P129(x73351)+~P1(f319(f319(f227(a925),f2(a925)),x73353))+~P1(f319(f319(f227(x73351),f72(x73351)),x73352))+P1(f319(f319(f227(x73351),f72(x73351)),f319(f319(f236(x73351),x73352),x73353)))
% 28.25/28.13 [7434]~P132(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)))
% 28.25/28.13 [7435]~P139(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)))
% 28.25/28.13 [7436]~P130(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(f75(x74361),x74362),x74363)))
% 28.25/28.13 [7437]~P93(x74371)+~P1(f319(f319(f226(x74371),f2(x74371)),x74373))+~P1(f319(f319(f226(x74371),f2(x74371)),x74372))+P1(f319(f319(f226(x74371),f2(x74371)),f319(f319(f74(x74371),x74372),x74373)))
% 28.25/28.13 [7438]~P75(x74381)+~P1(f319(f319(f227(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)))
% 28.25/28.13 [7439]~P74(x74391)+~P1(f319(f319(f226(x74391),f2(x74391)),x74393))+~P1(f319(f319(f226(x74391),f2(x74391)),x74392))+P1(f319(f319(f226(x74391),f2(x74391)),f319(f319(f283(x74391),x74392),x74393)))
% 28.25/28.13 [7440]~P129(x74401)+~P1(f319(f319(f227(x74401),f72(x74401)),x74403))+~P1(f319(f319(f227(x74401),f72(x74401)),x74402))+P1(f319(f319(f227(x74401),f72(x74401)),f319(f319(f75(x74401),x74402),x74403)))
% 28.25/28.13 [7441]~P134(x74411)+~P1(f319(f319(f227(x74411),f2(x74411)),x74413))+~P1(f319(f319(f227(x74411),f2(x74411)),x74412))+P1(f319(f319(f227(x74411),f2(x74411)),f319(f319(f75(x74411),x74412),x74413)))
% 28.25/28.13 [7442]~P93(x74421)+~P1(f319(f319(f226(x74421),f2(x74421)),x74423))+~P1(f319(f319(f227(x74421),f2(x74421)),x74422))+P1(f319(f319(f227(x74421),f2(x74421)),f319(f319(f74(x74421),x74422),x74423)))
% 28.25/28.13 [7443]~P93(x74431)+~P1(f319(f319(f226(x74431),f2(x74431)),x74432))+~P1(f319(f319(f227(x74431),f2(x74431)),x74433))+P1(f319(f319(f227(x74431),f2(x74431)),f319(f319(f74(x74431),x74432),x74433)))
% 28.25/28.13 [7444]~P93(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(f74(x74441),x74442),x74443)))
% 28.25/28.13 [7445]~P75(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)))
% 28.25/28.13 [7446]~P74(x74461)+~P1(f319(f319(f227(x74461),f2(x74461)),x74463))+~P1(f319(f319(f227(x74461),f2(x74461)),x74462))+P1(f319(f319(f227(x74461),f2(x74461)),f319(f319(f283(x74461),x74462),x74463)))
% 28.25/28.13 [7525]~P102(x75251)+~P1(f319(f55(x75251),x75253))+E(f10(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)))
% 28.25/28.13 [7526]~P102(x75261)+~P1(f319(f55(x75261),x75263))+E(f13(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)))
% 28.25/28.13 [7527]~P4(x75271)+~P1(f319(f55(x75271),x75273))+E(f14(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)))
% 28.25/28.13 [7528]~P4(x75281)+~P1(f319(f55(x75281),x75283))+E(f15(x75281,f319(f319(f301(x75281),x75282),x75283)),x75282)+~E(f319(f319(f23(f932(x75281,a923)),x75283),f319(f319(f301(x75281),x75282),f180(f932(x75281,a923)))),f180(f932(x75281,a923)))
% 28.25/28.13 [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),x75303),x75302)))
% 28.25/28.13 [7531]~P130(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(f75(x75311),x75312),x75313)))
% 28.25/28.13 [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),x75323),x75322)))
% 28.25/28.13 [7533]~P74(x75331)+P1(f319(f319(f226(x75331),x75332),f2(x75331)))+P1(f319(f319(f226(x75331),f2(x75331)),x75333))+~P1(f319(f319(f226(x75331),f2(x75331)),f319(f319(f283(x75331),x75332),x75333)))
% 28.25/28.13 [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),x75343),x75342)))
% 28.25/28.13 [7535]~P130(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(f75(x75351),x75352),x75353)))
% 28.25/28.13 [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),x75363),x75362)))
% 28.25/28.13 [7537]~P74(x75371)+P1(f319(f319(f226(x75371),x75372),f2(x75371)))+P1(f319(f319(f226(x75371),f2(x75371)),x75372))+~P1(f319(f319(f226(x75371),f2(x75371)),f319(f319(f283(x75371),x75372),x75373)))
% 28.25/28.13 [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),x75383),x75382)))
% 28.25/28.13 [7539]~P74(x75391)+P1(f319(f319(f227(x75391),x75392),f2(x75391)))+P1(f319(f319(f227(x75391),f2(x75391)),x75393))+~P1(f319(f319(f227(x75391),f2(x75391)),f319(f319(f283(x75391),x75392),x75393)))
% 28.25/28.13 [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),x75403),x75402)))
% 28.25/28.13 [7541]~P74(x75411)+P1(f319(f319(f227(x75411),x75412),f2(x75411)))+P1(f319(f319(f227(x75411),f2(x75411)),x75412))+~P1(f319(f319(f227(x75411),f2(x75411)),f319(f319(f283(x75411),x75412),x75413)))
% 28.25/28.13 [7625]~E(f319(f319(f93(f932(x76251,a923)),f319(f164(x76251),x76252)),f319(f164(x76251),x76253)),f180(f932(x76251,a923)))+~P1(f319(f129(x76251),x76253))+~P1(f319(f129(x76251),x76252))+P1(f319(f129(x76251),f319(f319(f126(x76251),x76252),x76253)))
% 28.25/28.13 [7626]~P4(x76261)+~P1(f319(f55(x76261),x76263))+E(f11(x76261,f224(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)))
% 28.25/28.13 [7627]~P4(x76271)+~P1(f319(f55(x76271),x76273))+E(f12(x76271,f225(x76271),f319(f319(f301(x76271),x76272),x76273)),x76272)+~E(f319(f319(f23(f932(x76271,a923)),x76273),f319(f319(f301(x76271),x76272),f180(f932(x76271,a923)))),f180(f932(x76271,a923)))
% 28.25/28.13 [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))
% 28.25/28.13 [7640]~P92(x76401)+~P1(f319(f319(f226(x76401),x76402),x76403))+~P1(f319(f319(f226(x76401),f319(f73(x76401),x76402)),x76403))+P1(f319(f319(f226(x76401),f319(f69(x76401),x76402)),x76403))
% 28.25/28.13 [7641]~P126(x76411)+~P1(f319(f319(f227(x76411),x76412),x76413))+~P1(f319(f319(f227(x76411),f319(f73(x76411),x76412)),x76413))+P1(f319(f319(f227(x76411),f319(f69(x76411),x76412)),x76413))
% 28.25/28.13 [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),x77083),x77082)))
% 28.25/28.13 [7709]~P134(x77091)+P1(f319(f319(f227(x77091),f2(x77091)),x77092))+~P1(f319(f319(f227(x77091),f2(x77091)),x77093))+~P1(f319(f319(f227(x77091),f2(x77091)),f319(f319(f75(x77091),x77092),x77093)))
% 28.25/28.13 [8007]E(x80071,x80072)+~P1(f319(f55(x80073),x80071))+~P1(f319(f319(f226(a925),f319(f29(x80073),x80071)),f319(f29(x80073),x80072)))+~P1(f319(f319(f226(f932(x80073,a923)),x80072),x80071))
% 28.25/28.13 [8076]~P1(f319(f319(f226(a925),x80762),x80761))+~P1(f319(f319(f226(a925),x80762),x80763))+~P1(f319(f319(f226(a925),x80761),x80763))+P1(f319(f319(f226(a925),f319(f319(f23(a925),x80761),x80762)),f319(f319(f23(a925),x80763),x80762)))
% 28.25/28.13 [8077]~P1(f319(f319(f226(a925),x80772),x80771))+~P1(f319(f319(f226(a925),x80772),x80773))+~P1(f319(f319(f227(a925),x80771),x80773))+P1(f319(f319(f227(a925),f319(f319(f23(a925),x80771),x80772)),f319(f319(f23(a925),x80773),x80772)))
% 28.25/28.13 [8154]~P1(f319(f319(f227(a1),x81541),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x81542))+~P1(f319(f319(f226(a1),x81542),x81543))+P1(f319(f319(f226(a1),f319(f319(f30(a1),x81541),x81542)),f319(f319(f30(a1),x81541),x81543)))
% 28.25/28.13 [8165]~P1(f319(f319(f226(a1),f2(a1)),x81651))+~P1(f319(f319(f227(a1),f2(a1)),x81653))+~P1(f319(f319(f226(a1),x81653),x81652))+P1(f319(f319(f226(a1),f319(f319(f30(a1),x81651),x81652)),f319(f319(f30(a1),x81651),x81653)))
% 28.25/28.13 [8301]E(f319(x83011,f443(x83012,x83011,x83013)),x83012)+~P1(f319(f319(f226(a1),x83012),f319(x83011,x83013)))+P1(f319(f319(f227(a925),f444(x83012,x83011,x83013)),x83013))+~P1(f319(f319(f226(a1),f319(x83011,f2(a925))),x83012))
% 28.25/28.13 [8302]E(f319(x83021,f448(x83022,x83021,x83023)),x83022)+~P1(f319(f319(f226(a1),x83022),f319(x83021,x83023)))+P1(f319(f319(f227(a925),f449(x83022,x83021,x83023)),x83023))+~P1(f319(f319(f226(a1),f319(x83021,f2(a925))),x83022))
% 28.25/28.13 [8404]~P1(f319(f55(x84041),x84043))+~P1(f319(f319(f227(a925),f319(f29(x84041),x84042)),f319(f29(x84041),x84043)))+~P1(f319(f319(f226(f932(x84041,a923)),x84042),x84043))+P1(f319(f319(f227(f932(x84041,a923)),x84042),x84043))
% 28.25/28.13 [8431]E(f319(f319(f74(a1),f375(x84313,x84311,x84312)),f376(x84313,x84311,x84312)),x84311)+E(f319(f319(f23(a1),x84311),x84312),x84311)+~P1(f319(f319(f227(a1),f2(a1)),x84312))+~P1(f319(f319(f321(a1),f319(f319(f23(a1),x84311),f72(a1))),x84313))
% 28.25/28.13 [8432]E(f319(f319(f23(a1),f377(x84323,x84321,x84322)),f378(x84323,x84321,x84322)),x84321)+E(f319(f319(f74(a1),x84321),x84322),x84321)+~P1(f319(f319(f227(a1),f2(a1)),x84322))+~P1(f319(f319(f321(a1),f319(f319(f74(a1),x84321),f72(a1))),x84323))
% 28.25/28.13 [8484]~P1(f319(f319(f226(a925),x84843),x84841))+P1(f319(f319(f226(a925),x84841),x84842))+~P1(f319(f319(f226(a925),x84843),x84842))+~P1(f319(f319(f226(a925),f319(f319(f23(a925),x84841),x84843)),f319(f319(f23(a925),x84842),x84843)))
% 28.25/28.13 [8485]~P1(f319(f319(f226(a925),x84853),x84851))+P1(f319(f319(f227(a925),x84851),x84852))+~P1(f319(f319(f226(a925),x84853),x84852))+~P1(f319(f319(f227(a925),f319(f319(f23(a925),x84851),x84853)),f319(f319(f23(a925),x84852),x84853)))
% 28.25/28.13 [8504]~P4(x85042)+E(x85041,f105(x85042))+~P14(x85042,f319(f160(x85042),x85041))+E(f319(f134(x85042,x85042,f319(f7(x85042,x85042,x85042),f225(x85042)),x85043),f319(f160(x85042),x85041)),f319(f319(f225(x85042),f319(f319(f156(x85042),x85041),f2(a925))),x85043))
% 28.25/28.13 [8552]~P6(x85521)+~P41(x85521,x85521,x85523)+P1(f319(f319(f226(x85521),x85522),f88(x85521,x85523)))+~P1(f319(f319(f226(x85521),x85522),f319(x85523,f319(f319(f102(x85521),x85522),f88(x85521,x85523)))))
% 28.25/28.13 [8574]E(f319(f319(f23(a1),x85741),x85742),x85741)+~P1(f319(f319(f227(a1),f2(a1)),x85742))+P1(f319(f319(f321(a1),f375(x85743,x85741,x85742)),x85743))+~P1(f319(f319(f321(a1),f319(f319(f23(a1),x85741),f72(a1))),x85743))
% 28.25/28.13 [8575]E(f319(f319(f74(a1),x85751),x85752),x85751)+~P1(f319(f319(f227(a1),f2(a1)),x85752))+P1(f319(f319(f321(a1),f377(x85753,x85751,x85752)),x85753))+~P1(f319(f319(f321(a1),f319(f319(f74(a1),x85751),f72(a1))),x85753))
% 28.25/28.13 [8647]~P1(f319(f319(f226(a1),x86471),f319(x86472,x86473)))+P1(f319(f319(f227(a925),f444(x86471,x86472,x86473)),x86473))+P1(f319(f319(f226(a925),f443(x86471,x86472,x86473)),x86473))+~P1(f319(f319(f226(a1),f319(x86472,f2(a925))),x86471))
% 28.25/28.13 [8648]~P1(f319(f319(f226(a1),x86481),f319(x86482,x86483)))+P1(f319(f319(f227(a925),f449(x86481,x86482,x86483)),x86483))+P1(f319(f319(f226(a925),f448(x86481,x86482,x86483)),x86483))+~P1(f319(f319(f226(a1),f319(x86482,f2(a925))),x86481))
% 28.25/28.13 [8725]E(f319(f319(f23(a1),x87251),x87252),x87251)+~P1(f319(f319(f227(a1),f2(a1)),x87252))+P1(f319(f319(f321(a1),f376(x87253,x87251,x87252)),f295(a1,f72(a1),x87252)))+~P1(f319(f319(f321(a1),f319(f319(f23(a1),x87251),f72(a1))),x87253))
% 28.25/28.13 [8726]E(f319(f319(f74(a1),x87261),x87262),x87261)+~P1(f319(f319(f227(a1),f2(a1)),x87262))+P1(f319(f319(f321(a1),f378(x87263,x87261,x87262)),f295(a1,f72(a1),x87262)))+~P1(f319(f319(f321(a1),f319(f319(f74(a1),x87261),f72(a1))),x87263))
% 28.25/28.13 [8859]~P129(x88591)+~P1(f319(f319(f227(x88591),x88592),f72(x88591)))+~P1(f319(f319(f227(x88591),f2(x88591)),x88592))+P1(f319(f319(f227(x88591),f319(f319(f75(x88591),x88592),f319(f319(f236(x88591),x88592),x88593))),f319(f319(f236(x88591),x88592),x88593)))
% 28.25/28.13 [8952]~P1(f319(x89521,x89522))+P1(f319(x89521,f2(a925)))+~P1(f319(f319(f227(a925),x89522),x89523))+~P1(f319(x89521,f39(a925,f319(a104,f523(x89522,x89521,x89523)),x89523)))
% 28.25/28.13 [9106]E(f544(x91061,x91062,x91063),f2(a925))+P1(f319(f319(x91061,x91063),x91062))+P1(f319(f319(x91061,f544(x91061,x91062,x91063)),f39(a925,f543(x91061,x91062,x91063),f544(x91061,x91062,x91063))))+~P1(f319(f307(f931(a925,a925),a211),f319(f319(f244(a925,a925),x91063),x91062)))
% 28.25/28.13 [9144]~P26(x91441,x91441,x91442,x91443)+E(f319(f302(x91441,x91441,x91442),x91443),x91443)+~P1(f319(f55(x91441),x91443))+~P1(f319(f319(f226(f932(x91441,a923)),f319(f302(x91441,x91441,x91442),x91443)),x91443))
% 28.25/28.13 [9217]~P6(x92171)+~P41(x92171,x92171,x92173)+P1(f319(f319(f226(x92171),f319(f319(f102(x92171),x92172),f88(x92171,x92173))),f319(x92173,f319(f319(f102(x92171),x92172),f88(x92171,x92173)))))+~P1(f319(f319(f226(x92171),x92172),f319(x92173,f319(f319(f102(x92171),x92172),f88(x92171,x92173)))))
% 28.25/28.13 [9364]P1(f319(f319(x93641,x93642),x93643))+P1(f319(f319(f227(a1),f795(x93641,x93643,x93642)),f796(x93641,x93643,x93642)))+P1(f319(f319(x93641,f795(x93641,x93643,x93642)),f319(f319(f74(a1),f796(x93641,x93643,x93642)),f72(a1))))+~P1(f319(f307(f931(a1,a1),a125),f319(f319(f244(a1,a1),x93642),x93643)))
% 28.25/28.13 [9381]P1(f319(f319(x93811,x93812),x93813))+~P1(f319(f319(f227(a1),f542(x93811,x93813,x93812)),f2(a1)))+P1(f319(f319(x93811,f319(f73(a1),f541(x93811,x93813,x93812))),f319(f73(a1),f542(x93811,x93813,x93812))))+~P1(f319(f307(f931(a1,a1),a213),f319(f319(f244(a1,a1),x93812),x93813)))
% 28.25/28.13 [9573]P1(f319(f319(x95731,x95732),x95733))+P1(f319(f319(x95731,f319(f319(f74(a1),f698(x95731,x95733,x95732)),f72(a1))),f699(x95731,x95733,x95732)))+~P1(f319(f319(f226(a1),f698(x95731,x95733,x95732)),f699(x95731,x95733,x95732)))+~P1(f319(f307(f931(a1,a1),a174),f319(f319(f244(a1,a1),x95732),x95733)))
% 28.25/28.13 [10026]~P5(x100262)+~P5(x100261)+~P1(f319(f51(f931(x100261,x100262)),x100263))+P1(f319(f51(x100261),f319(f319(f8(f932(x100262,a923),a923,x100261),f51(x100262)),f319(f319(f8(f932(x100262,f931(x100261,x100262)),f932(x100262,a923),x100261),f319(f8(f931(x100261,x100262),a923,x100262),x100263)),f244(x100261,x100262)))))
% 28.25/28.13 [10027]~P5(x100272)+~P5(x100271)+~P1(f319(f50(f931(x100271,x100272)),x100273))+P1(f319(f50(x100271),f319(f319(f8(f932(x100272,a923),a923,x100271),f50(x100272)),f319(f319(f8(f932(x100272,f931(x100271,x100272)),f932(x100272,a923),x100271),f319(f8(f931(x100271,x100272),a923,x100272),x100273)),f244(x100271,x100272)))))
% 28.25/28.13 [10127]~P5(x101272)+~P5(x101271)+P1(f319(f51(f931(x101271,x101272)),x101273))+~P1(f319(f51(x101271),f319(f319(f8(f932(x101272,a923),a923,x101271),f51(x101272)),f319(f319(f8(f932(x101272,f931(x101271,x101272)),f932(x101272,a923),x101271),f319(f8(f931(x101271,x101272),a923,x101272),x101273)),f244(x101271,x101272)))))
% 28.25/28.13 [10128]~P5(x101282)+~P5(x101281)+P1(f319(f50(f931(x101281,x101282)),x101283))+~P1(f319(f50(x101281),f319(f319(f8(f932(x101282,a923),a923,x101281),f50(x101282)),f319(f319(f8(f932(x101282,f931(x101281,x101282)),f932(x101282,a923),x101281),f319(f8(f931(x101281,x101282),a923,x101282),x101283)),f244(x101281,x101282)))))
% 28.25/28.13 [10305]E(f319(x103051,f443(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),f444(x103052,x103051,x103053)),f72(a925)))),f319(x103051,f444(x103052,x103051,x103053))))),f72(a1)))+~P1(f319(f319(f226(a1),f319(x103051,f2(a925))),x103052))
% 28.25/28.13 [10306]E(f319(x103061,f448(x103062,x103061,x103063)),x103062)+~P1(f319(f319(f226(a1),x103062),f319(x103061,x103063)))+~P1(f319(f319(f226(a1),f319(f69(a1),f319(f319(f23(a1),f319(x103061,f319(f319(f74(a925),f449(x103062,x103061,x103063)),f72(a925)))),f319(x103061,f449(x103062,x103061,x103063))))),f72(a1)))+~P1(f319(f319(f226(a1),f319(x103061,f2(a925))),x103062))
% 28.25/28.13 [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),f444(x103091,x103092,x103093)),f72(a925)))),f319(x103092,f444(x103091,x103092,x103093))))),f72(a1)))+P1(f319(f319(f226(a925),f443(x103091,x103092,x103093)),x103093))+~P1(f319(f319(f226(a1),f319(x103092,f2(a925))),x103091))
% 28.25/28.13 [10310]~P1(f319(f319(f226(a1),x103101),f319(x103102,x103103)))+~P1(f319(f319(f226(a1),f319(f69(a1),f319(f319(f23(a1),f319(x103102,f319(f319(f74(a925),f449(x103101,x103102,x103103)),f72(a925)))),f319(x103102,f449(x103101,x103102,x103103))))),f72(a1)))+P1(f319(f319(f226(a925),f448(x103101,x103102,x103103)),x103103))+~P1(f319(f319(f226(a1),f319(x103102,f2(a925))),x103101))
% 28.25/28.13 [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)))),f724(x103682,x103681,x103683)))
% 28.25/28.13 [10369]E(x103691,x103692)+~E(f319(f134(f926(x103693),f926(x103693),f126(x103693),f105(x103693)),x103691),f319(f134(f926(x103693),f926(x103693),f126(x103693),f105(x103693)),x103692))+~E(f319(f181(f926(f926(x103693))),x103691),f319(f181(f926(f926(x103693))),x103692))+~P1(f319(f319(f249(f926(x103693),f926(x103693),a923),f319(f319(f7(f926(x103693),f932(f926(x103693),a925),f932(f926(x103693),a923)),f319(f319(f8(f932(a925,a923),f932(f932(f926(x103693),a925),f932(f926(x103693),a923)),f926(x103693)),f8(a925,a923,f926(x103693))),f319(f319(f8(a925,f932(a925,a923),f926(x103693)),a316),f181(f926(x103693))))),f181(f926(x103693)))),f725(x103691,x103692,x103693)))
% 28.25/28.13 [7037]~E(f72(a925),f2(a925))+~P1(f319(f55(x70371),x70373))+~P1(f319(f55(x70371),x70372))+E(f319(f319(f74(a925),f319(f29(x70371),x70372)),f319(f29(x70371),x70373)),f319(f29(x70371),f319(f319(f102(f932(x70371,a923)),x70372),x70373)))
% 28.25/28.13 [7453]~P108(x74531)+~P1(f319(f55(x74531),x74532))+~P1(f319(f319(f321(x74531),x74533),x74532))+P1(f319(f319(f226(x74531),f319(f57(x74531,f93(x74531)),x74532)),x74533))
% 28.25/28.13 [7454]~P4(x74541)+~P1(f319(f55(x74541),x74542))+~P1(f319(f319(f321(x74541),x74543),x74542))+P1(f319(f319(f226(x74541),f319(f57(x74541,f224(x74541)),x74542)),x74543))
% 28.25/28.13 [7702]~P1(f319(f55(x77021),x77023))+~P1(f319(f55(x77021),x77022))+~E(f319(f319(f93(f932(x77021,a923)),x77022),x77023),f180(f932(x77021,a923)))+E(f319(f319(f74(a925),f319(f29(x77021),x77022)),f319(f29(x77021),x77023)),f319(f29(x77021),f319(f319(f102(f932(x77021,a923)),x77022),x77023)))
% 28.25/28.13 [8490]~P38(x84901,x84903)+~P38(x84901,x84902)+~E(f319(f319(f93(f932(x84901,a923)),f319(f256(x84901,x84901),x84902)),f319(f276(x84901,x84901),x84903)),f180(f932(x84901,a923)))+P38(x84901,f319(f319(f102(f932(f931(x84901,x84901),a923)),x84902),x84903))
% 28.25/28.13 [8586]E(x85861,f319(f319(f30(a925),x85862),x85863))+~P1(f319(f319(f227(a925),f2(a925)),x85863))+~P1(f319(f319(f227(a925),x85862),f319(f319(f75(a925),x85863),f319(a104,x85861))))+~P1(f319(f319(f226(a925),f319(f319(f75(a925),x85863),x85861)),x85862))
% 28.25/28.13 [8723]~P1(f319(f55(x87231),x87232))+~P1(f319(f55(x87231),x87233))+E(f319(f319(f74(a925),f319(f29(x87231),x87232)),f319(f29(x87231),x87233)),f319(f29(x87231),f319(f319(f102(f932(x87231,a923)),x87232),x87233)))+P1(f319(f319(f321(x87231),f423(x87233,x87232,x87231)),f319(f319(f93(f932(x87231,a923)),x87232),x87233)))
% 28.25/28.13 [9118]~P130(x91182)+~E(x91181,f2(x91182))+~E(x91183,f2(x91182))+~P1(f319(f319(f227(x91182),f2(x91182)),f319(f319(f74(x91182),f319(f319(f75(x91182),x91183),x91183)),f319(f319(f75(x91182),x91181),x91181))))
% 28.25/28.13 [9655]~P38(x96551,x96553)+~P38(x96551,x96552)+P38(x96551,f319(f319(f102(f932(f931(x96551,x96551),a923)),x96552),x96553))+~P1(f319(f319(f226(f932(f931(x96551,x96551),a923)),f319(f319(f281(x96551,x96551,x96551),x96552),x96553)),x96552))
% 28.25/28.13 [9786]~P1(f319(x97861,x97863))+~P1(f319(f55(x97862),x97863))+P1(f319(x97861,f180(f932(x97862,a923))))+~P1(f319(x97861,f319(f319(f23(f932(x97862,a923)),f335(x97861,x97863,x97862)),f319(f319(f301(x97862),f336(x97861,x97863,x97862)),f180(f932(x97862,a923))))))
% 28.25/28.13 [8899]~P1(f319(f319(f227(a1),f2(a1)),x88993))+P1(f319(f319(f226(a1),f2(a1)),x88991))+~P1(f319(f319(f227(a1),x88992),x88993))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),f319(f319(f75(a1),x88993),x88991)),x88992)))
% 28.25/28.13 [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(f93(x89231),x89233),f10(x89231,f319(f319(f23(f932(x89231,a923)),x89232),f319(f319(f301(x89231),x89233),f180(f932(x89231,a923)))))),f10(x89231,f319(f319(f301(x89231),x89233),x89232)))
% 28.25/28.13 [8924]~P102(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(f102(x89241),x89243),f13(x89241,f319(f319(f23(f932(x89241,a923)),x89242),f319(f319(f301(x89241),x89243),f180(f932(x89241,a923)))))),f13(x89241,f319(f319(f301(x89241),x89243),x89242)))
% 28.25/28.13 [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(f224(x89251),x89253),f14(x89251,f319(f319(f23(f932(x89251,a923)),x89252),f319(f319(f301(x89251),x89253),f180(f932(x89251,a923)))))),f14(x89251,f319(f319(f301(x89251),x89253),x89252)))
% 28.25/28.13 [8926]~P4(x89261)+~P1(f319(f55(x89261),x89262))+E(f319(f319(f23(f932(x89261,a923)),x89262),f319(f319(f301(x89261),x89263),f180(f932(x89261,a923)))),f180(f932(x89261,a923)))+E(f319(f319(f225(x89261),x89263),f15(x89261,f319(f319(f23(f932(x89261,a923)),x89262),f319(f319(f301(x89261),x89263),f180(f932(x89261,a923)))))),f15(x89261,f319(f319(f301(x89261),x89263),x89262)))
% 28.25/28.13 [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(f224(x89991),x89993),f11(x89991,f224(x89991),f319(f319(f23(f932(x89991,a923)),x89992),f319(f319(f301(x89991),x89993),f180(f932(x89991,a923)))))),f11(x89991,f224(x89991),f319(f319(f301(x89991),x89993),x89992)))
% 28.25/28.13 [9000]~P4(x90001)+~P1(f319(f55(x90001),x90002))+E(f319(f319(f23(f932(x90001,a923)),x90002),f319(f319(f301(x90001),x90003),f180(f932(x90001,a923)))),f180(f932(x90001,a923)))+E(f319(f319(f225(x90001),x90003),f12(x90001,f225(x90001),f319(f319(f23(f932(x90001,a923)),x90002),f319(f319(f301(x90001),x90003),f180(f932(x90001,a923)))))),f12(x90001,f225(x90001),f319(f319(f301(x90001),x90003),x90002)))
% 28.25/28.13 [9386]~P6(x93861)+~P41(x93861,x93861,x93862)+P1(f319(f319(f226(x93861),f87(x93861,x93862)),x93863))+~P1(f319(f319(f226(x93861),f319(x93862,f319(f319(f93(x93861),f87(x93861,x93862)),x93863))),x93863))
% 28.25/28.13 [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))),f724(x95922,x95921,x95923)),f319(f164(f931(f926(x95923),f926(x95923))),f319(f319(f173(f926(x95923),f926(x95923)),x95921),x95922))))
% 28.25/28.13 [9593]E(x95931,x95932)+~E(f319(f134(f926(x95933),f926(x95933),f126(x95933),f105(x95933)),x95931),f319(f134(f926(x95933),f926(x95933),f126(x95933),f105(x95933)),x95932))+~E(f319(f181(f926(f926(x95933))),x95931),f319(f181(f926(f926(x95933))),x95932))+P1(f319(f319(f321(f931(f926(x95933),f926(x95933))),f725(x95931,x95932,x95933)),f319(f164(f931(f926(x95933),f926(x95933))),f319(f319(f173(f926(x95933),f926(x95933)),x95932),x95931))))
% 28.25/28.13 [10474]~P106(x104742)+E(x104741,f180(f932(x104742,a923)))+~P1(f319(f55(x104742),x104741))+E(f10(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(f102(x104742),x104743))))),f319(f319(f7(x104742,f932(x104742,a923),a923),f321(x104742)),x104741))))),f319(f319(f102(x104742),x104743),f10(x104742,x104741)))
% 28.25/28.13 [10475]~P106(x104752)+E(x104751,f180(f932(x104752,a923)))+~P1(f319(f55(x104752),x104751))+E(f13(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(f93(x104752),x104753))))),f319(f319(f7(x104752,f932(x104752,a923),a923),f321(x104752)),x104751))))),f319(f319(f93(x104752),x104753),f13(x104752,x104751)))
% 28.25/28.13 [10476]~P85(x104762)+E(x104761,f180(f932(x104762,a923)))+~P1(f319(f55(x104762),x104761))+E(f14(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),f14(x104762,x104761)))
% 28.25/28.13 [10477]~P85(x104772)+E(x104771,f180(f932(x104772,a923)))+~P1(f319(f55(x104772),x104771))+E(f15(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(f74(x104772),x104773))))),f319(f319(f7(x104772,f932(x104772,a923),a923),f321(x104772)),x104771))))),f319(f319(f74(x104772),x104773),f15(x104772,x104771)))
% 28.25/28.13 [10478]~P4(x104782)+E(x104781,f180(f932(x104782,a923)))+~P1(f319(f55(x104782),x104781))+E(f12(x104782,f225(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(f224(x104782),x104783))))),f319(f319(f7(x104782,f932(x104782,a923),a923),f321(x104782)),x104781))))),f319(f319(f224(x104782),x104783),f12(x104782,f225(x104782),x104781)))
% 28.25/28.13 [10479]~P4(x104792)+E(x104791,f180(f932(x104792,a923)))+~P1(f319(f55(x104792),x104791))+E(f11(x104792,f224(x104792),f319(f254(x104792),f319(f319(f8(f932(x104792,a923),a923,x104792),f81(x104792)),f319(f319(f7(x104792,f932(x104792,a923),f932(x104792,a923)),f319(f319(f8(f932(x104792,f932(a923,a923)),f932(f932(x104792,a923),f932(x104792,a923)),x104792),f18(x104792,a923,a923)),f319(f319(f8(f932(x104792,a923),f932(x104792,f932(a923,a923)),x104792),f319(f8(a923,f932(a923,a923),x104792),a317)),f319(f319(f7(x104792,f932(x104792,x104792),f932(x104792,a923)),f319(f319(f8(f932(x104792,a923),f932(f932(x104792,x104792),f932(x104792,a923)),x104792),f8(x104792,a923,x104792)),a316)),f319(f225(x104792),x104793))))),f319(f319(f7(x104792,f932(x104792,a923),a923),f321(x104792)),x104791))))),f319(f319(f225(x104792),x104793),f11(x104792,f224(x104792),x104791)))
% 28.25/28.13 [10191]~P126(x101911)+~E(x101913,f2(x101911))+~E(x101912,f2(x101911))+E(f319(f319(f74(x101911),f319(f319(f236(x101911),x101912),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(x101911),x101913),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(x101911))
% 28.25/28.13 [10349]~P129(x103491)+~P1(f319(f319(f226(x103491),f2(x103491)),x103493))+P1(f319(f319(f226(x103491),x103492),x103493))+~P1(f319(f319(f226(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))))))
% 28.25/28.13 [10350]~P129(x103501)+~P1(f319(f319(f226(x103501),f2(x103501)),x103503))+P1(f319(f319(f227(x103501),x103502),x103503))+~P1(f319(f319(f227(x103501),f319(f319(f236(x103501),x103502),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(x103501),x103503),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))))))
% 28.25/28.13 [10405]~P126(x104052)+~E(x104051,f2(x104052))+~E(x104053,f2(x104052))+~P1(f319(f319(f227(x104052),f2(x104052)),f319(f319(f74(x104052),f319(f319(f236(x104052),x104053),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(x104052),x104051),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)))))))
% 28.25/28.13 [6214]~P4(x62141)+~P113(x62142)+~P51(x62141,x62142,x62143)+P26(x62141,x62142,x62143,x62144)
% 28.25/28.13 [6919]~P8(x69193,x69192)+~P1(f319(x69191,x69194))+~P1(f319(f319(f321(x69193),x69194),f262(x69193,x69192)))+P1(f319(x69191,f840(x69191,x69192,x69193)))
% 28.25/28.13 [8834]P27(x88341,x88342,f415(x88343,x88342,x88344,x88341),x88344,x88343)+~E(f319(f29(x88341),x88344),f319(f29(x88342),x88343))+~P1(f319(f55(x88342),x88343))+~P1(f319(f55(x88341),x88344))
% 28.25/28.13 [9555]E(x95551,x95552)+~E(f680(x95551,x95552,x95554,x95553),f683(x95551,x95552,x95554,x95553))+P1(f319(f319(f321(f931(f926(x95553),f926(x95553))),f319(f319(f244(f926(x95553),f926(x95553)),x95552),x95551)),f139(x95553,x95554)))+P1(f319(f319(f321(f931(f926(x95553),f926(x95553))),f319(f319(f244(f926(x95553),f926(x95553)),x95551),x95552)),f139(x95553,x95554)))
% 28.25/28.13 [5058]~P72(x50582)+~E(x50584,f2(x50582))+~E(x50581,f2(x50582))+E(x50581,f319(f319(f283(x50582),x50583),x50584))
% 28.25/28.13 [5059]~P72(x50591)+~E(x50593,f2(x50591))+~E(x50594,f2(x50591))+E(f319(f319(f283(x50591),x50592),x50593),x50594)
% 28.25/28.13 [5176]~P72(x51762)+E(x51761,f2(x51762))+~E(x51763,f2(x51762))+~E(x51761,f319(f319(f283(x51762),x51764),x51763))
% 28.25/28.13 [5177]~P72(x51772)+E(x51771,f2(x51772))+~E(x51773,f2(x51772))+~E(f319(f319(f283(x51772),x51774),x51773),x51771)
% 28.25/28.13 [5364]~P124(x53642)+E(x53641,f2(x53642))+~E(f319(f319(f283(x53642),x53643),x53641),x53644)+E(x53643,f319(f319(f75(x53642),x53644),x53641))
% 28.25/28.13 [5365]~P124(x53652)+E(x53651,f2(x53652))+~E(f319(f319(f75(x53652),x53653),x53651),x53654)+E(x53653,f319(f319(f283(x53652),x53654),x53651))
% 28.25/28.13 [5366]~P124(x53662)+E(x53661,f2(x53662))+~E(f319(f319(f75(x53662),x53663),x53661),x53664)+E(x53663,f319(f319(f283(x53662),x53664),x53661))
% 28.25/28.13 [5367]~P72(x53672)+E(x53671,f2(x53672))+~E(f319(f319(f283(x53672),x53673),x53671),x53674)+E(x53673,f319(f319(f75(x53672),x53674),x53671))
% 28.25/28.13 [5368]~P72(x53682)+E(x53681,f2(x53682))+~E(f319(f319(f75(x53682),x53683),x53681),x53684)+E(x53683,f319(f319(f283(x53682),x53684),x53681))
% 28.25/28.13 [5369]~P124(x53692)+E(x53691,f2(x53692))+~E(x53693,f319(f319(f283(x53692),x53694),x53691))+E(f319(f319(f75(x53692),x53693),x53691),x53694)
% 28.25/28.13 [5370]~P124(x53702)+E(x53701,f2(x53702))+~E(x53703,f319(f319(f75(x53702),x53704),x53701))+E(f319(f319(f283(x53702),x53703),x53701),x53704)
% 28.25/28.13 [5371]~P124(x53712)+E(x53711,f2(x53712))+~E(x53713,f319(f319(f75(x53712),x53714),x53711))+E(f319(f319(f283(x53712),x53713),x53711),x53714)
% 28.25/28.13 [5372]~P72(x53722)+E(x53721,f2(x53722))+~E(x53723,f319(f319(f283(x53722),x53724),x53721))+E(f319(f319(f75(x53722),x53723),x53721),x53724)
% 28.25/28.13 [5373]~P72(x53732)+E(x53731,f2(x53732))+~E(x53733,f319(f319(f75(x53732),x53734),x53731))+E(f319(f319(f283(x53732),x53733),x53731),x53734)
% 28.25/28.13 [5397]~P72(x53972)+~E(x53971,f2(x53972))+~E(f319(f319(f75(x53972),x53971),x53974),x53973)+E(x53971,f319(f319(f283(x53972),x53973),x53974))
% 28.25/28.13 [5398]~P72(x53981)+~E(x53984,f2(x53981))+~E(x53982,f319(f319(f75(x53981),x53984),x53983))+E(f319(f319(f283(x53981),x53982),x53983),x53984)
% 28.25/28.13 [5472]~E(x54723,x54724)+~E(x54722,x54723)+~P113(x54721)+E(f295(x54721,x54722,x54723),f319(f319(f301(x54721),x54724),f180(f932(x54721,a923))))
% 28.25/28.13 [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)
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [6566]~P113(x65661)+~P1(f319(f319(f226(x65661),x65664),x65663))+P1(f319(f319(f226(x65661),x65662),x65663))+~P1(f319(f319(f226(x65661),x65662),x65664))
% 28.25/28.13 [6567]~P2(x65671)+~P1(f319(f319(f226(x65671),x65672),x65674))+P1(f319(f319(f226(x65671),x65672),x65673))+~P1(f319(f319(f226(x65671),x65674),x65673))
% 28.25/28.13 [6568]~P113(x65681)+~P1(f319(f319(f227(x65681),x65684),x65683))+P1(f319(f319(f227(x65681),x65682),x65683))+~P1(f319(f319(f226(x65681),x65682),x65684))
% 28.25/28.13 [6569]~P113(x65691)+~P1(f319(f319(f227(x65691),x65692),x65694))+P1(f319(f319(f227(x65691),x65692),x65693))+~P1(f319(f319(f226(x65691),x65694),x65693))
% 28.25/28.13 [6570]~P113(x65701)+~P1(f319(f319(f227(x65701),x65704),x65703))+P1(f319(f319(f227(x65701),x65702),x65703))+~P1(f319(f319(f227(x65701),x65702),x65704))
% 28.25/28.13 [6571]~P2(x65711)+~P1(f319(f319(f227(x65711),x65712),x65714))+P1(f319(f319(f227(x65711),x65712),x65713))+~P1(f319(f319(f226(x65711),x65714),x65713))
% 28.25/28.13 [6572]~P2(x65721)+~P1(f319(f319(f227(x65721),x65724),x65723))+P1(f319(f319(f227(x65721),x65722),x65723))+~P1(f319(f319(f226(x65721),x65722),x65724))
% 28.25/28.13 [6573]~P2(x65731)+~P1(f319(f319(f227(x65731),x65732),x65734))+P1(f319(f319(f227(x65731),x65732),x65733))+~P1(f319(f319(f227(x65731),x65734),x65733))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [6959]~P4(x69591)+~P14(x69591,f319(f319(f143(x69591),x69592),x69594))+~P1(f319(f319(f321(x69591),x69593),f319(f164(x69591),x69594)))+P1(f319(f319(f226(x69591),x69592),x69593))
% 28.25/28.13 [7047]~P6(x70471)+~P1(f319(f319(f226(x70471),f31(x70471,x70474)),x70473))+P1(f319(f319(f226(x70471),x70472),x70473))+~P1(f319(f319(f321(x70471),x70472),x70474))
% 28.25/28.13 [7456]~P4(x74561)+E(f319(f319(f102(f932(x74561,a923)),f319(f294(x74561,x74562),x74563)),f319(f294(x74561,x74563),x74564)),f319(f294(x74561,x74562),x74564))+~P1(f319(f319(f226(x74561),x74563),x74564))+~P1(f319(f319(f226(x74561),x74562),x74563))
% 28.25/28.13 [7500]P36(x75001,x75002,x75003)+~E(f789(x75003,x75002,x75001,x75004),x75004)+~P1(f319(x75002,x75004))+~P1(f319(f319(f321(x75001),x75004),f319(f164(x75001),x75003)))
% 28.25/28.13 [7501]P36(x75011,x75012,x75013)+~E(f799(x75013,x75012,x75011,x75014),x75014)+~P1(f319(x75012,x75014))+~P1(f319(f319(f321(x75011),x75014),f319(f164(x75011),x75013)))
% 28.25/28.13 [7575]~P4(x75751)+E(f319(f319(f102(f932(x75751,a923)),f319(f294(x75751,x75752),x75753)),f295(x75751,x75753,x75754)),f295(x75751,x75752,x75754))+~P1(f319(f319(f226(x75751),x75753),x75754))+~P1(f319(f319(f226(x75751),x75752),x75753))
% 28.25/28.13 [7635]~P4(x76351)+E(f319(f319(f102(f932(x76351,a923)),f298(x76351,x76352,x76353)),f319(f294(x76351,x76353),x76354)),f298(x76351,x76352,x76354))+~P1(f319(f319(f226(x76351),x76353),x76354))+~P1(f319(f319(f227(x76351),x76352),x76353))
% 28.25/28.13 [7652]~P4(x76521)+E(f319(f319(f102(f932(x76521,a923)),f295(x76521,x76522,x76523)),f298(x76521,x76523,x76524)),f319(f294(x76521,x76522),x76524))+~P1(f319(f319(f226(x76521),x76522),x76523))+~P1(f319(f319(f227(x76521),x76523),x76524))
% 28.25/28.13 [7683]~P4(x76831)+E(f319(f319(f102(f932(x76831,a923)),f295(x76831,x76832,x76833)),f297(x76831,x76833,x76834)),f295(x76831,x76832,x76834))+~P1(f319(f319(f226(x76831),x76833),x76834))+~P1(f319(f319(f226(x76831),x76832),x76833))
% 28.25/28.13 [7684]~P4(x76841)+E(f319(f319(f102(f932(x76841,a923)),f297(x76841,x76842,x76843)),f297(x76841,x76843,x76844)),f297(x76841,x76842,x76844))+~P1(f319(f319(f226(x76841),x76843),x76844))+~P1(f319(f319(f226(x76841),x76842),x76843))
% 28.25/28.13 [7685]~P4(x76851)+E(f319(f319(f102(f932(x76851,a923)),f297(x76851,x76852,x76853)),f298(x76851,x76853,x76854)),f298(x76851,x76852,x76854))+~P1(f319(f319(f226(x76851),x76852),x76853))+~P1(f319(f319(f227(x76851),x76853),x76854))
% 28.25/28.13 [7686]~P4(x76861)+E(f319(f319(f102(f932(x76861,a923)),f298(x76861,x76862,x76863)),f295(x76861,x76863,x76864)),f297(x76861,x76862,x76864))+~P1(f319(f319(f226(x76861),x76863),x76864))+~P1(f319(f319(f227(x76861),x76862),x76863))
% 28.25/28.13 [8474]P26(x84741,x84742,f422(x84743,x84742,x84744,x84741),x84744)+~P1(f319(f55(x84742),x84743))+~P1(f319(f55(x84741),x84744))+~P1(f319(f319(f226(a925),f319(f29(x84741),x84744)),f319(f29(x84742),x84743)))
% 28.25/28.13 [8495]P36(x84951,x84952,x84953)+~P1(f319(x84952,x84954))+P1(f319(x84952,f789(x84953,x84952,x84951,x84954)))+~P1(f319(f319(f321(x84951),x84954),f319(f164(x84951),x84953)))
% 28.25/28.13 [8496]P36(x84961,x84962,x84963)+~P1(f319(x84962,x84964))+P1(f319(x84962,f799(x84963,x84962,x84961,x84964)))+~P1(f319(f319(f321(x84961),x84964),f319(f164(x84961),x84963)))
% 28.25/28.13 [8551]~P78(x85511)+~E(f319(x85513,f521(x85513,x85514,x85512,x85511)),f72(x85511))+E(f319(f319(f319(f59(x85511,x85512,f75(x85511)),x85513),f72(x85511)),x85514),f72(x85511))+~P1(f319(f55(x85512),x85514))
% 28.25/28.13 [8823]~P129(x88231)+~P1(f319(f319(f226(x88231),f2(x88231)),x88233))+P1(f319(f319(f226(x88231),x88232),x88233))+~P1(f319(f319(f226(x88231),f319(f319(f236(x88231),x88232),f319(a104,x88234))),f319(f319(f236(x88231),x88233),f319(a104,x88234))))
% 28.25/28.13 [8998]~P41(f932(x89984,a923),f932(x89984,a923),x89983)+P1(f319(x89981,x89982))+~P1(f319(x89981,f460(x89981,x89983,x89982,x89984)))+~P1(f319(f319(f321(x89984),x89982),f87(f932(x89984,a923),x89983)))
% 28.25/28.13 [9145]P36(x91451,x91452,x91453)+~P1(f319(x91452,x91454))+~P1(f319(f319(f321(x91451),x91454),f319(f164(x91451),x91453)))+P1(f319(f319(f321(x91451),f789(x91453,x91452,x91451,x91454)),f319(f164(x91451),x91453)))
% 28.25/28.13 [9146]P36(x91461,x91462,x91463)+~P1(f319(x91462,x91464))+~P1(f319(f319(f321(x91461),x91464),f319(f164(x91461),x91463)))+P1(f319(f319(f321(x91461),f799(x91463,x91462,x91461,x91464)),f319(f164(x91461),x91463)))
% 28.25/28.13 [9225]~P78(x92251)+E(f319(f319(f319(f59(x92251,x92252,f75(x92251)),x92253),f72(x92251)),x92254),f72(x92251))+~P1(f319(f55(x92252),x92254))+P1(f319(f319(f321(x92252),f521(x92253,x92254,x92252,x92251)),x92254))
% 28.25/28.13 [9727]~P1(f319(f319(f226(a1),x97274),f2(a1)))+P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f75(a1),x97271),f39(a1,x97272,x97273))),x97274)),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x97273))+~P1(f319(f319(f227(a1),x97271),x97274))
% 28.25/28.13 [10184]~P1(f319(f55(x101841),x101842))+~P1(f319(f319(f321(x101841),x101844),x101842))+~P1(f319(f319(f321(x101841),x101843),x101842))+P1(f319(f319(f227(a925),f319(f29(x101841),f319(f319(f23(f932(x101841,a923)),f319(f319(f23(f932(x101841,a923)),x101842),f319(f319(f301(x101841),x101843),f180(f932(x101841,a923))))),f319(f319(f301(x101841),x101844),f180(f932(x101841,a923)))))),f319(f29(x101841),x101842)))
% 28.25/28.13 [7107]~P143(x71073)+~P123(x71073)+P1(f319(x71071,f871(x71072,x71071,x71073)))+~P1(f319(x71071,f319(f319(f75(x71073),x71072),x71074)))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [7164]~P108(x71641)+~P1(f319(f319(f226(x71641),x71642),x71644))+~P1(f319(f319(f226(x71641),x71642),x71643))+P1(f319(f319(f226(x71641),x71642),f319(f319(f93(x71641),x71643),x71644)))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [7167]~P4(x71671)+~P1(f319(f319(f226(x71671),x71672),x71674))+~P1(f319(f319(f226(x71671),x71672),x71673))+P1(f319(f319(f226(x71671),x71672),f319(f319(f224(x71671),x71673),x71674)))
% 28.25/28.13 [7168]~P4(x71681)+~P1(f319(f319(f227(x71681),x71682),x71684))+~P1(f319(f319(f227(x71681),x71682),x71683))+P1(f319(f319(f227(x71681),x71682),f319(f319(f224(x71681),x71683),x71684)))
% 28.25/28.13 [7188]~P73(x71882)+E(x71881,f2(x71882))+E(f319(f319(f283(x71882),f319(f319(f236(x71882),x71881),x71883)),f319(f319(f236(x71882),x71881),x71884)),f319(f319(f236(x71882),x71881),f319(f319(f23(a925),x71883),x71884)))+~P1(f319(f319(f226(a925),x71884),x71883))
% 28.25/28.13 [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))
% 28.25/28.13 [7233]~P4(x72331)+~P14(x72331,f319(f319(f143(x72331),x72333),x72334))+P14(x72331,f319(f319(f143(x72331),x72332),f319(f319(f143(x72331),x72333),x72334)))+~P1(f319(f319(f226(x72331),x72332),x72333))
% 28.25/28.13 [7269]~P93(x72691)+~P1(f319(f319(f226(x72691),f2(x72691)),x72694))+~P1(f319(f319(f226(x72691),x72692),x72693))+P1(f319(f319(f226(x72691),x72692),f319(f319(f74(x72691),x72693),x72694)))
% 28.25/28.13 [7270]~P93(x72701)+~P1(f319(f319(f226(x72701),f2(x72701)),x72703))+~P1(f319(f319(f226(x72701),x72702),x72704))+P1(f319(f319(f226(x72701),x72702),f319(f319(f74(x72701),x72703),x72704)))
% 28.25/28.13 [7271]~P129(x72711)+~P1(f319(f319(f227(x72711),f2(x72711)),x72713))+~P1(f319(f319(f227(x72711),x72712),x72714))+P1(f319(f319(f227(x72711),x72712),f319(f319(f74(x72711),x72713),x72714)))
% 28.25/28.13 [7272]~P93(x72721)+~P1(f319(f319(f226(x72721),x72722),x72724))+~P1(f319(f319(f227(x72721),f2(x72721)),x72723))+P1(f319(f319(f227(x72721),x72722),f319(f319(f74(x72721),x72723),x72724)))
% 28.25/28.13 [7273]~P93(x72731)+~P1(f319(f319(f226(x72731),f2(x72731)),x72733))+~P1(f319(f319(f227(x72731),x72732),x72734))+P1(f319(f319(f227(x72731),x72732),f319(f319(f74(x72731),x72733),x72734)))
% 28.25/28.13 [7315]~P4(x73151)+P1(f319(f319(f226(x73151),x73152),x73153))+P1(f319(f319(f226(x73151),x73152),x73154))+~P1(f319(f319(f226(x73151),x73152),f319(f319(f225(x73151),x73154),x73153)))
% 28.25/28.13 [7316]~P4(x73161)+P1(f319(f319(f227(x73161),x73162),x73163))+P1(f319(f319(f227(x73161),x73162),x73164))+~P1(f319(f319(f227(x73161),x73162),f319(f319(f225(x73161),x73164),x73163)))
% 28.25/28.13 [7608]~P113(x76082)+~P5(x76081)+~P1(f319(f319(f227(f932(x76081,x76082)),x76083),x76084))+P1(f319(f319(f226(f932(x76081,x76082)),x76083),x76084))
% 28.25/28.13 [7969]~P75(x79691)+~P1(f319(f319(f227(x79691),x79694),f2(x79691)))+~P1(f319(f319(f226(x79691),x79693),f319(f319(f283(x79691),x79692),x79694)))+P1(f319(f319(f226(x79691),x79692),f319(f319(f75(x79691),x79693),x79694)))
% 28.25/28.13 [7970]~P75(x79701)+~P1(f319(f319(f227(x79701),x79704),f2(x79701)))+~P1(f319(f319(f226(x79701),x79703),f319(f319(f75(x79701),x79702),x79704)))+P1(f319(f319(f226(x79701),x79702),f319(f319(f283(x79701),x79703),x79704)))
% 28.25/28.13 [7971]~P75(x79711)+~P1(f319(f319(f227(x79711),x79714),f2(x79711)))+~P1(f319(f319(f227(x79711),x79713),f319(f319(f283(x79711),x79712),x79714)))+P1(f319(f319(f227(x79711),x79712),f319(f319(f75(x79711),x79713),x79714)))
% 28.25/28.13 [7972]~P75(x79721)+~P1(f319(f319(f227(x79721),x79724),f2(x79721)))+~P1(f319(f319(f227(x79721),x79723),f319(f319(f75(x79721),x79722),x79724)))+P1(f319(f319(f227(x79721),x79722),f319(f319(f283(x79721),x79723),x79724)))
% 28.25/28.13 [8079]~P132(x80791)+~P1(f319(f319(f226(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)))
% 28.25/28.13 [8080]~P130(x80801)+~P1(f319(f319(f227(x80801),x80802),f2(x80801)))+~P1(f319(f319(f226(x80801),x80804),x80803))+P1(f319(f319(f226(x80801),f319(f319(f75(x80801),x80802),x80803)),f319(f319(f75(x80801),x80802),x80804)))
% 28.25/28.13 [8081]~P132(x80811)+~P1(f319(f319(f226(x80811),x80813),f2(x80811)))+~P1(f319(f319(f226(x80811),x80814),x80812))+P1(f319(f319(f226(x80811),f319(f319(f75(x80811),x80812),x80813)),f319(f319(f75(x80811),x80814),x80813)))
% 28.25/28.13 [8082]~P74(x80821)+~P1(f319(f319(f226(x80821),x80823),f2(x80821)))+~P1(f319(f319(f226(x80821),x80824),x80822))+P1(f319(f319(f226(x80821),f319(f319(f283(x80821),x80822),x80823)),f319(f319(f283(x80821),x80824),x80823)))
% 28.25/28.13 [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)))
% 28.25/28.13 [8084]~P130(x80841)+~P1(f319(f319(f227(x80841),x80842),f2(x80841)))+~P1(f319(f319(f227(x80841),x80844),x80843))+P1(f319(f319(f227(x80841),f319(f319(f75(x80841),x80842),x80843)),f319(f319(f75(x80841),x80842),x80844)))
% 28.25/28.13 [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)))
% 28.25/28.13 [8086]~P130(x80861)+~P1(f319(f319(f227(x80861),x80863),f2(x80861)))+~P1(f319(f319(f227(x80861),x80864),x80862))+P1(f319(f319(f227(x80861),f319(f319(f75(x80861),x80862),x80863)),f319(f319(f75(x80861),x80864),x80863)))
% 28.25/28.13 [8087]~P130(x80871)+~P1(f319(f319(f227(x80871),x80872),f2(x80871)))+~P1(f319(f319(f227(x80871),x80874),x80873))+P1(f319(f319(f227(x80871),f319(f319(f75(x80871),x80872),x80873)),f319(f319(f75(x80871),x80872),x80874)))
% 28.25/28.13 [8088]~P75(x80881)+~P1(f319(f319(f227(x80881),x80883),f2(x80881)))+~P1(f319(f319(f227(x80881),x80884),x80882))+P1(f319(f319(f227(x80881),f319(f319(f283(x80881),x80882),x80883)),f319(f319(f283(x80881),x80884),x80883)))
% 28.25/28.13 [8089]~P129(x80891)+~P1(f319(f319(f227(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)))
% 28.25/28.13 [8090]~P129(x80901)+~P1(f319(f319(f226(x80901),f72(x80901)),x80902))+~P1(f319(f319(f226(a925),x80903),x80904))+P1(f319(f319(f226(x80901),f319(f319(f236(x80901),x80902),x80903)),f319(f319(f236(x80901),x80902),x80904)))
% 28.25/28.13 [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)))
% 28.25/28.13 [8092]~P129(x80921)+~P1(f319(f319(f227(x80921),f72(x80921)),x80922))+~P1(f319(f319(f227(a925),x80923),x80924))+P1(f319(f319(f227(x80921),f319(f319(f236(x80921),x80922),x80923)),f319(f319(f236(x80921),x80922),x80924)))
% 28.25/28.13 [8119]P1(f319(f319(f227(a925),f2(a925)),f319(x81191,x81192)))+~P1(f319(f55(x81193),x81194))+~P1(f319(f319(f321(x81193),x81192),x81194))+~P1(f319(f319(f227(a925),f2(a925)),f319(f319(f9(x81193,a925),x81191),x81194)))
% 28.25/28.13 [8128]~P141(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)))
% 28.25/28.13 [8129]~P140(x81291)+~P1(f319(f319(f226(x81291),x81293),x81294))+~P1(f319(f319(f226(x81291),f2(x81291)),x81292))+P1(f319(f319(f226(x81291),f319(f319(f75(x81291),x81292),x81293)),f319(f319(f75(x81291),x81292),x81294)))
% 28.25/28.13 [8130]~P130(x81301)+~P1(f319(f319(f227(x81301),f2(x81301)),x81302))+~P1(f319(f319(f226(x81301),x81303),x81304))+P1(f319(f319(f226(x81301),f319(f319(f75(x81301),x81302),x81303)),f319(f319(f75(x81301),x81302),x81304)))
% 28.25/28.13 [8131]~P141(x81311)+~P1(f319(f319(f226(x81311),x81312),x81314))+~P1(f319(f319(f226(x81311),f2(x81311)),x81313))+P1(f319(f319(f226(x81311),f319(f319(f75(x81311),x81312),x81313)),f319(f319(f75(x81311),x81314),x81313)))
% 28.25/28.13 [8132]~P129(x81321)+~P1(f319(f319(f226(x81321),x81322),x81324))+~P1(f319(f319(f226(x81321),f2(x81321)),x81322))+P1(f319(f319(f226(x81321),f319(f319(f236(x81321),x81322),x81323)),f319(f319(f236(x81321),x81324),x81323)))
% 28.25/28.13 [8133]~P74(x81331)+~P1(f319(f319(f226(x81331),x81332),x81334))+~P1(f319(f319(f226(x81331),f2(x81331)),x81333))+P1(f319(f319(f226(x81331),f319(f319(f283(x81331),x81332),x81333)),f319(f319(f283(x81331),x81334),x81333)))
% 28.25/28.13 [8134]~P130(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)))
% 28.25/28.13 [8135]~P127(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)))
% 28.25/28.13 [8136]~P134(x81361)+~P1(f319(f319(f227(x81361),x81363),x81364))+~P1(f319(f319(f227(x81361),f2(x81361)),x81362))+P1(f319(f319(f227(x81361),f319(f319(f75(x81361),x81362),x81363)),f319(f319(f75(x81361),x81362),x81364)))
% 28.25/28.13 [8137]~P130(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)))
% 28.25/28.13 [8138]~P134(x81381)+~P1(f319(f319(f227(x81381),x81382),x81384))+~P1(f319(f319(f227(x81381),f2(x81381)),x81383))+P1(f319(f319(f227(x81381),f319(f319(f75(x81381),x81382),x81383)),f319(f319(f75(x81381),x81384),x81383)))
% 28.25/28.13 [8139]~P130(x81391)+~P1(f319(f319(f227(x81391),x81393),x81394))+~P1(f319(f319(f227(x81391),f2(x81391)),x81392))+P1(f319(f319(f227(x81391),f319(f319(f75(x81391),x81392),x81393)),f319(f319(f75(x81391),x81392),x81394)))
% 28.25/28.13 [8140]~P75(x81401)+~P1(f319(f319(f227(x81401),x81402),x81404))+~P1(f319(f319(f227(x81401),f2(x81401)),x81403))+P1(f319(f319(f227(x81401),f319(f319(f283(x81401),x81402),x81403)),f319(f319(f283(x81401),x81404),x81403)))
% 28.25/28.13 [8184]~P3(x81842)+P1(f319(f319(f227(f932(x81841,x81842)),x81844),x81843))+~P1(f319(f319(f226(f932(x81841,x81842)),x81844),x81843))+P1(f319(f319(f226(f932(x81841,x81842)),x81843),x81844))
% 28.25/28.13 [8225]P1(f319(f319(f321(x82251),x82252),x82253))+P1(f319(f319(f321(x82251),x82252),x82254))+~P1(f319(f319(f226(f932(x82251,a923)),x82254),x82253))+P1(f319(f319(f227(f932(x82251,a923)),x82254),f319(f319(f301(x82251),x82252),x82253)))
% 28.25/28.13 [8336]~P117(x83362)+E(x83361,f2(x83362))+P1(f319(f319(f279(x83362),x83363),x83364))+~P1(f319(f319(f279(x83362),f319(f319(f75(x83362),x83363),x83361)),f319(f319(f75(x83362),x83364),x83361)))
% 28.25/28.13 [8337]~P117(x83372)+E(x83371,f2(x83372))+P1(f319(f319(f279(x83372),x83373),x83374))+~P1(f319(f319(f279(x83372),f319(f319(f75(x83372),x83371),x83373)),f319(f319(f75(x83372),x83371),x83374)))
% 28.25/28.13 [8385]P1(f319(f319(f321(x83851),x83852),x83853))+P1(f319(f319(f321(x83851),x83852),x83854))+~P1(f319(f319(f227(f932(x83851,a923)),x83854),f319(f319(f301(x83851),x83852),x83853)))+P1(f319(f319(f226(f932(x83851,a923)),x83854),x83853))
% 28.25/28.13 [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),x84514),x84512)),f319(f319(f75(x84511),x84514),x84513)))
% 28.25/28.13 [8452]~P130(x84521)+P1(f319(f319(f227(x84521),x84523),x84522))+P1(f319(f319(f227(x84521),x84522),x84523))+~P1(f319(f319(f227(x84521),f319(f319(f75(x84521),x84522),x84524)),f319(f319(f75(x84521),x84523),x84524)))
% 28.25/28.13 [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),x84632),x84634)),f319(f319(f75(x84631),x84633),x84634)))
% 28.25/28.13 [8464]~P130(x84641)+P1(f319(f319(f227(x84641),x84644),f2(x84641)))+P1(f319(f319(f227(x84641),x84642),x84643))+~P1(f319(f319(f227(x84641),f319(f319(f75(x84641),x84644),x84642)),f319(f319(f75(x84641),x84644),x84643)))
% 28.25/28.13 [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),x84684),x84683)),f319(f319(f75(x84681),x84684),x84682)))
% 28.25/28.13 [8469]~P130(x84691)+P1(f319(f319(f227(x84691),x84692),x84693))+P1(f319(f319(f227(x84691),f2(x84691)),x84694))+~P1(f319(f319(f227(x84691),f319(f319(f75(x84691),x84693),x84694)),f319(f319(f75(x84691),x84692),x84694)))
% 28.25/28.13 [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),x84823),x84822)),f319(f319(f75(x84821),x84824),x84822)))
% 28.25/28.13 [8483]~P130(x84831)+P1(f319(f319(f227(x84831),x84832),f2(x84831)))+P1(f319(f319(f227(x84831),f2(x84831)),x84832))+~P1(f319(f319(f227(x84831),f319(f319(f75(x84831),x84832),x84833)),f319(f319(f75(x84831),x84832),x84834)))
% 28.25/28.13 [8513]~P130(x85131)+~P1(f319(f319(f227(x85131),x85134),f2(x85131)))+P1(f319(f319(f226(x85131),x85132),x85133))+~P1(f319(f319(f226(x85131),f319(f319(f75(x85131),x85134),x85133)),f319(f319(f75(x85131),x85134),x85132)))
% 28.25/28.13 [8514]~P130(x85141)+~P1(f319(f319(f227(x85141),x85144),f2(x85141)))+P1(f319(f319(f227(x85141),x85142),x85143))+~P1(f319(f319(f227(x85141),f319(f319(f75(x85141),x85144),x85143)),f319(f319(f75(x85141),x85144),x85142)))
% 28.25/28.13 [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)))
% 28.25/28.13 [8525]~P129(x85253)+~P1(f319(f319(f227(x85253),f72(x85253)),x85254))+P1(f319(f319(f226(a925),x85251),x85252))+~P1(f319(f319(f226(x85253),f319(f319(f236(x85253),x85254),x85251)),f319(f319(f236(x85253),x85254),x85252)))
% 28.25/28.13 [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)))
% 28.25/28.13 [8527]~P129(x85273)+~P1(f319(f319(f227(x85273),f72(x85273)),x85274))+P1(f319(f319(f227(a925),x85271),x85272))+~P1(f319(f319(f227(x85273),f319(f319(f236(x85273),x85274),x85271)),f319(f319(f236(x85273),x85274),x85272)))
% 28.25/28.13 [8537]~P130(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)))
% 28.25/28.13 [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),x85384),x85382)),f319(f319(f75(x85381),x85384),x85383)))
% 28.25/28.13 [8539]~P134(x85391)+P1(f319(f319(f226(x85391),x85392),x85393))+~P1(f319(f319(f227(x85391),f2(x85391)),x85394))+~P1(f319(f319(f226(x85391),f319(f319(f75(x85391),x85392),x85394)),f319(f319(f75(x85391),x85393),x85394)))
% 28.25/28.13 [8540]~P130(x85401)+P1(f319(f319(f227(x85401),x85402),x85403))+~P1(f319(f319(f227(x85401),f2(x85401)),x85404))+~P1(f319(f319(f227(x85401),f319(f319(f75(x85401),x85404),x85402)),f319(f319(f75(x85401),x85404),x85403)))
% 28.25/28.13 [8541]~P134(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)))
% 28.25/28.13 [8542]~P135(x85421)+P1(f319(f319(f227(x85421),x85422),x85423))+~P1(f319(f319(f226(x85421),f2(x85421)),x85424))+~P1(f319(f319(f227(x85421),f319(f319(f75(x85421),x85424),x85422)),f319(f319(f75(x85421),x85424),x85423)))
% 28.25/28.13 [8543]~P129(x85431)+~P1(f319(f319(f226(x85431),f2(x85431)),x85433))+P1(f319(f319(f227(x85431),x85432),x85433))+~P1(f319(f319(f227(x85431),f319(f319(f236(x85431),x85432),x85434)),f319(f319(f236(x85431),x85433),x85434)))
% 28.25/28.13 [8544]~P134(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)))
% 28.25/28.13 [8545]~P135(x85451)+P1(f319(f319(f227(x85451),x85452),x85453))+~P1(f319(f319(f226(x85451),f2(x85451)),x85454))+~P1(f319(f319(f227(x85451),f319(f319(f75(x85451),x85452),x85454)),f319(f319(f75(x85451),x85453),x85454)))
% 28.25/28.13 [8589]P1(f319(f319(f321(x85891),x85892),x85893))+~P1(f319(f319(f226(f932(x85891,a923)),x85893),x85894))+~P1(f319(f319(f227(f932(x85891,a923)),x85893),x85894))+P1(f319(f319(f227(f932(x85891,a923)),x85893),f319(f319(f301(x85891),x85892),x85894)))
% 28.25/28.13 [8622]~P143(x86221)+~P123(x86221)+P1(f319(f319(f279(x86221),x86222),f319(f319(f74(x86221),f871(x86222,x86223,x86221)),f2(x86221))))+~P1(f319(x86223,f319(f319(f75(x86221),x86222),x86224)))
% 28.25/28.13 [8973]E(f319(f319(f23(a1),f380(x89731,x89732,x89733,x89734)),f381(x89731,x89732,x89733,x89734)),x89734)+~P1(f319(f319(f227(a1),f2(a1)),x89733))+~P1(f319(f319(f226(a1),x89731),x89734))+P1(f319(f319(f226(a1),x89731),f319(f319(f74(a1),x89734),x89733)))
% 28.25/28.13 [8974]E(f319(f319(f23(a1),f403(x89741,x89742,x89743,x89744)),f404(x89741,x89742,x89743,x89744)),x89744)+~P1(f319(f319(f227(a1),f2(a1)),x89743))+~P1(f319(f319(f227(a1),x89741),x89744))+P1(f319(f319(f227(a1),x89741),f319(f319(f74(a1),x89744),x89743)))
% 28.25/28.13 [9126]~E(f319(f319(f156(x91261),x91263),f689(x91264,x91263,x91261,x91262)),f319(f319(f156(x91261),x91264),f689(x91264,x91263,x91261,x91262)))+E(f319(f319(f167(x91261),x91262),x91263),f319(f319(f167(x91261),x91262),x91264))+~P1(f319(f319(f226(a925),x91262),f319(f181(f926(x91261)),x91263)))+~P1(f319(f319(f226(a925),x91262),f319(f181(f926(x91261)),x91264)))
% 28.25/28.13 [9192]~P1(f319(f319(f227(a1),f2(a1)),x91923))+~P1(f319(f319(f226(a1),x91921),x91924))+P1(f319(f319(f321(a1),f380(x91921,x91922,x91923,x91924)),x91922))+P1(f319(f319(f226(a1),x91921),f319(f319(f74(a1),x91924),x91923)))
% 28.25/28.13 [9193]~P1(f319(f319(f227(a1),f2(a1)),x91933))+~P1(f319(f319(f227(a1),x91931),x91934))+P1(f319(f319(f321(a1),f403(x91931,x91932,x91933,x91934)),x91932))+P1(f319(f319(f227(a1),x91931),f319(f319(f74(a1),x91934),x91933)))
% 28.25/28.13 [9234]~P108(x92341)+~P1(f319(f55(x92341),x92343))+~P1(f319(f319(f321(x92341),x92344),x92343))+P1(f319(f319(f226(x92341),f319(f319(f58(x92341,x92341,f93(x92341)),x92342),x92343)),f319(f319(f93(x92341),x92344),x92342)))
% 28.25/28.13 [9235]~P4(x92351)+~P1(f319(f55(x92351),x92353))+~P1(f319(f319(f321(x92351),x92354),x92353))+P1(f319(f319(f226(x92351),f319(f319(f58(x92351,x92351,f224(x92351)),x92352),x92353)),f319(f319(f224(x92351),x92354),x92352)))
% 28.25/28.13 [9280]E(f319(f319(f167(x92801),x92802),x92803),f319(f319(f167(x92801),x92802),x92804))+P1(f319(f319(f227(a925),f689(x92803,x92804,x92801,x92802)),x92802))+~P1(f319(f319(f226(a925),x92802),f319(f181(f926(x92801)),x92803)))+~P1(f319(f319(f226(a925),x92802),f319(f181(f926(x92801)),x92804)))
% 28.25/28.13 [9285]~P1(f319(f319(f227(a1),f2(a1)),x92853))+~P1(f319(f319(f226(a1),x92851),x92852))+P1(f319(f319(f321(a1),f381(x92851,x92854,x92853,x92852)),f295(a1,f72(a1),x92853)))+P1(f319(f319(f226(a1),x92851),f319(f319(f74(a1),x92852),x92853)))
% 28.25/28.13 [9286]~P1(f319(f319(f227(a1),f2(a1)),x92863))+~P1(f319(f319(f227(a1),x92861),x92862))+P1(f319(f319(f321(a1),f404(x92861,x92864,x92863,x92862)),f295(a1,f72(a1),x92863)))+P1(f319(f319(f227(a1),x92861),f319(f319(f74(a1),x92862),x92863)))
% 28.25/28.13 [9613]~P4(x96131)+~P1(f319(f55(x96131),x96134))+P1(f319(f319(f321(x96131),f652(x96132,x96133,x96134,x96131)),x96134))+P1(f319(f319(f226(x96131),f319(f319(f58(x96131,x96131,f225(x96131)),x96132),x96134)),f319(f319(f225(x96131),x96133),x96132)))
% 28.25/28.13 [9614]~P107(x96141)+~P1(f319(f55(x96141),x96144))+P1(f319(f319(f321(x96141),f655(x96142,x96143,x96144,x96141)),x96144))+P1(f319(f319(f226(x96141),f319(f319(f58(x96141,x96141,f102(x96141)),x96142),x96144)),f319(f319(f102(x96141),x96143),x96142)))
% 28.25/28.13 [9743]~P107(x97431)+~P1(f319(f55(x97431),x97433))+~P1(f319(f319(f226(x97431),f655(x97432,x97434,x97433,x97431)),x97434))+P1(f319(f319(f226(x97431),f319(f319(f58(x97431,x97431,f102(x97431)),x97432),x97433)),f319(f319(f102(x97431),x97434),x97432)))
% 28.25/28.13 [9744]~P4(x97441)+~P1(f319(f55(x97441),x97443))+~P1(f319(f319(f226(x97441),f652(x97442,x97444,x97443,x97441)),x97444))+P1(f319(f319(f226(x97441),f319(f319(f58(x97441,x97441,f225(x97441)),x97442),x97443)),f319(f319(f225(x97441),x97444),x97442)))
% 28.25/28.13 [9746]~P1(f319(f319(f226(a1),f2(a1)),x97464))+~P1(f319(f319(f227(a1),f2(a1)),x97463))+~P1(f319(f319(f227(a1),x97464),x97461))+P1(f319(f319(f227(a1),f319(f319(f74(a1),f319(f319(f75(a1),x97461),f39(a1,x97462,x97463))),x97464)),f319(f319(f75(a1),x97461),x97463)))
% 28.25/28.13 [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),f680(x101561,x101562,x101564,x101563)),f683(x101561,x101562,x101564,x101563))),x101564))
% 28.25/28.13 [10157]E(x101571,x101572)+P1(f319(f319(f321(f931(f926(x101573),f926(x101573))),f319(f319(f244(f926(x101573),f926(x101573)),x101572),x101571)),f139(x101573,x101574)))+P1(f319(f319(f321(f931(f926(x101573),f926(x101573))),f319(f319(f244(f926(x101573),f926(x101573)),x101571),x101572)),f139(x101573,x101574)))+~P1(f319(f319(f321(f931(x101573,x101573)),f319(f319(f244(x101573,x101573),f683(x101571,x101572,x101574,x101573)),f680(x101571,x101572,x101574,x101573))),x101574))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [7674]~P107(x76741)+~P1(f319(f319(f226(x76741),x76743),x76744))+~P1(f319(f319(f226(x76741),x76742),x76744))+P1(f319(f319(f226(x76741),f319(f319(f102(x76741),x76742),x76743)),x76744))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [7677]~P4(x76771)+~P1(f319(f319(f226(x76771),x76773),x76774))+~P1(f319(f319(f226(x76771),x76772),x76774))+P1(f319(f319(f226(x76771),f319(f319(f225(x76771),x76772),x76773)),x76774))
% 28.25/28.13 [7678]~P4(x76781)+~P1(f319(f319(f227(x76781),x76783),x76784))+~P1(f319(f319(f227(x76781),x76782),x76784))+P1(f319(f319(f227(x76781),f319(f319(f225(x76781),x76782),x76783)),x76784))
% 28.25/28.13 [7994]~E(x79941,x79943)+E(f131(a925,f319(f294(a925,x79941),x79942)),f319(f319(f143(a925),x79943),x79944))+~E(f131(a925,f319(f294(a925,f319(f319(f74(a925),x79941),f72(a925))),x79942)),x79944)+~P1(f319(f319(f227(a925),x79941),x79942))
% 28.25/28.13 [8002]~P4(x80021)+P1(f319(f319(f226(x80021),x80022),x80023))+P1(f319(f319(f226(x80021),x80024),x80023))+~P1(f319(f319(f226(x80021),f319(f319(f224(x80021),x80024),x80022)),x80023))
% 28.25/28.13 [8003]~P4(x80031)+P1(f319(f319(f227(x80031),x80032),x80033))+P1(f319(f319(f227(x80031),x80034),x80033))+~P1(f319(f319(f227(x80031),f319(f319(f224(x80031),x80034),x80032)),x80033))
% 28.25/28.13 [8283]~P74(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))
% 28.25/28.13 [8284]~P75(x82841)+~P1(f319(f319(f227(x82841),f2(x82841)),x82843))+~P1(f319(f319(f226(x82841),x82842),f319(f319(f283(x82841),x82844),x82843)))+P1(f319(f319(f226(x82841),f319(f319(f75(x82841),x82842),x82843)),x82844))
% 28.25/28.13 [8285]~P75(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))
% 28.25/28.13 [8286]~P74(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))
% 28.25/28.13 [8287]~P75(x82871)+~P1(f319(f319(f227(x82871),f2(x82871)),x82873))+~P1(f319(f319(f226(x82871),x82872),f319(f319(f75(x82871),x82874),x82873)))+P1(f319(f319(f226(x82871),f319(f319(f283(x82871),x82872),x82873)),x82874))
% 28.25/28.13 [8288]~P74(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))
% 28.25/28.13 [8289]~P75(x82891)+~P1(f319(f319(f227(x82891),f2(x82891)),x82893))+~P1(f319(f319(f227(x82891),x82892),f319(f319(f283(x82891),x82894),x82893)))+P1(f319(f319(f227(x82891),f319(f319(f75(x82891),x82892),x82893)),x82894))
% 28.25/28.13 [8290]~P75(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))
% 28.25/28.13 [8291]~P74(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))
% 28.25/28.13 [8292]~P75(x82921)+~P1(f319(f319(f227(x82921),f2(x82921)),x82923))+~P1(f319(f319(f227(x82921),x82922),f319(f319(f75(x82921),x82924),x82923)))+P1(f319(f319(f227(x82921),f319(f319(f283(x82921),x82922),x82923)),x82924))
% 28.25/28.13 [8421]~P74(x84211)+~P1(f319(f319(f227(x84211),f2(x84211)),x84214))+P1(f319(f319(f226(x84211),x84212),f319(f319(f75(x84211),x84213),x84214)))+~P1(f319(f319(f226(x84211),f319(f319(f283(x84211),x84212),x84214)),x84213))
% 28.25/28.13 [8422]~P75(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))
% 28.25/28.13 [8423]~P74(x84231)+~P1(f319(f319(f227(x84231),f2(x84231)),x84234))+P1(f319(f319(f226(x84231),x84232),f319(f319(f283(x84231),x84233),x84234)))+~P1(f319(f319(f226(x84231),f319(f319(f75(x84231),x84232),x84234)),x84233))
% 28.25/28.13 [8424]~P75(x84241)+~P1(f319(f319(f227(x84241),f2(x84241)),x84244))+P1(f319(f319(f226(x84241),x84242),f319(f319(f75(x84241),x84243),x84244)))+~P1(f319(f319(f226(x84241),f319(f319(f283(x84241),x84242),x84244)),x84243))
% 28.25/28.13 [8425]~P75(x84251)+~P1(f319(f319(f227(x84251),f2(x84251)),x84254))+P1(f319(f319(f226(x84251),x84252),f319(f319(f283(x84251),x84253),x84254)))+~P1(f319(f319(f226(x84251),f319(f319(f75(x84251),x84252),x84254)),x84253))
% 28.25/28.13 [8426]~P74(x84261)+~P1(f319(f319(f227(x84261),f2(x84261)),x84264))+P1(f319(f319(f227(x84261),x84262),f319(f319(f75(x84261),x84263),x84264)))+~P1(f319(f319(f227(x84261),f319(f319(f283(x84261),x84262),x84264)),x84263))
% 28.25/28.13 [8427]~P75(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))
% 28.25/28.13 [8428]~P74(x84281)+~P1(f319(f319(f227(x84281),f2(x84281)),x84284))+P1(f319(f319(f227(x84281),x84282),f319(f319(f283(x84281),x84283),x84284)))+~P1(f319(f319(f227(x84281),f319(f319(f75(x84281),x84282),x84284)),x84283))
% 28.25/28.13 [8429]~P75(x84291)+~P1(f319(f319(f227(x84291),f2(x84291)),x84294))+P1(f319(f319(f227(x84291),x84292),f319(f319(f75(x84291),x84293),x84294)))+~P1(f319(f319(f227(x84291),f319(f319(f283(x84291),x84292),x84294)),x84293))
% 28.25/28.13 [8430]~P75(x84301)+~P1(f319(f319(f227(x84301),f2(x84301)),x84304))+P1(f319(f319(f227(x84301),x84302),f319(f319(f283(x84301),x84303),x84304)))+~P1(f319(f319(f227(x84301),f319(f319(f75(x84301),x84302),x84304)),x84303))
% 28.25/28.13 [8592]~P75(x85921)+~P1(f319(f319(f227(x85921),x85923),f2(x85921)))+~P1(f319(f319(f226(x85921),f319(f319(f283(x85921),x85924),x85923)),x85922))+P1(f319(f319(f226(x85921),f319(f319(f75(x85921),x85922),x85923)),x85924))
% 28.25/28.13 [8593]~P75(x85931)+~P1(f319(f319(f227(x85931),x85933),f2(x85931)))+~P1(f319(f319(f226(x85931),f319(f319(f75(x85931),x85934),x85933)),x85932))+P1(f319(f319(f226(x85931),f319(f319(f283(x85931),x85932),x85933)),x85934))
% 28.25/28.13 [8594]~P75(x85941)+~P1(f319(f319(f227(x85941),x85943),f2(x85941)))+~P1(f319(f319(f227(x85941),f319(f319(f283(x85941),x85944),x85943)),x85942))+P1(f319(f319(f227(x85941),f319(f319(f75(x85941),x85942),x85943)),x85944))
% 28.25/28.13 [8595]~P75(x85951)+~P1(f319(f319(f227(x85951),x85953),f2(x85951)))+~P1(f319(f319(f227(x85951),f319(f319(f75(x85951),x85954),x85953)),x85952))+P1(f319(f319(f227(x85951),f319(f319(f283(x85951),x85952),x85953)),x85954))
% 28.25/28.13 [8607]~P1(f319(x86071,x86074))+~P1(f319(f319(f227(a925),x86072),f319(f319(f75(a925),x86073),f319(a104,x86074))))+P1(f319(x86071,f319(f319(f30(a925),x86072),x86073)))+~P1(f319(f319(f226(a925),f319(f319(f75(a925),x86073),x86074)),x86072))
% 28.25/28.13 [8821]~P107(x88211)+~P1(f319(f55(x88211),x88214))+~P1(f319(f319(f321(x88211),x88212),x88214))+P1(f319(f319(f226(x88211),f319(f319(f102(x88211),x88212),x88213)),f319(f319(f58(x88211,x88211,f102(x88211)),x88213),x88214)))
% 28.25/28.13 [8822]~P4(x88221)+~P1(f319(f55(x88221),x88224))+~P1(f319(f319(f321(x88221),x88222),x88224))+P1(f319(f319(f226(x88221),f319(f319(f225(x88221),x88222),x88223)),f319(f319(f58(x88221,x88221,f225(x88221)),x88223),x88224)))
% 28.25/28.13 [8975]~P1(f319(f55(x89751),x89752))+E(f319(f29(x89751),f319(f319(f23(f932(x89751,a923)),x89752),f319(f319(f301(x89751),x89753),x89754))),f319(f319(f23(a925),f319(f29(x89751),f319(f319(f23(f932(x89751,a923)),x89752),x89754))),f72(a925)))+P1(f319(f319(f321(x89751),x89753),x89754))+~P1(f319(f319(f321(x89751),x89753),x89752))
% 28.25/28.13 [9053]E(f319(f319(f74(a1),f383(x90531,x90532,x90533,x90534)),f384(x90531,x90532,x90533,x90534)),x90534)+~P1(f319(f319(f227(a1),f2(a1)),x90533))+~P1(f319(f319(f226(a1),x90534),x90531))+P1(f319(f319(f226(a1),f319(f319(f23(a1),x90534),x90533)),x90531))
% 28.25/28.13 [9054]E(f319(f319(f74(a1),f405(x90541,x90542,x90543,x90544)),f406(x90541,x90542,x90543,x90544)),x90544)+~P1(f319(f319(f227(a1),f2(a1)),x90543))+~P1(f319(f319(f227(a1),x90544),x90541))+P1(f319(f319(f227(a1),f319(f319(f23(a1),x90544),x90543)),x90541))
% 28.25/28.13 [9265]~P1(f319(f319(f227(a1),f2(a1)),x92653))+~P1(f319(f319(f226(a1),x92654),x92651))+P1(f319(f319(f321(a1),f383(x92651,x92652,x92653,x92654)),x92652))+P1(f319(f319(f226(a1),f319(f319(f23(a1),x92654),x92653)),x92651))
% 28.25/28.13 [9266]~P1(f319(f319(f227(a1),f2(a1)),x92663))+~P1(f319(f319(f227(a1),x92664),x92661))+P1(f319(f319(f321(a1),f405(x92661,x92662,x92663,x92664)),x92662))+P1(f319(f319(f227(a1),f319(f319(f23(a1),x92664),x92663)),x92661))
% 28.25/28.13 [9353]~P1(f319(f319(f227(a1),f2(a1)),x93532))+~P1(f319(f319(f226(a1),x93531),x93533))+P1(f319(f319(f321(a1),f384(x93533,x93534,x93532,x93531)),f295(a1,f72(a1),x93532)))+P1(f319(f319(f226(a1),f319(f319(f23(a1),x93531),x93532)),x93533))
% 28.25/28.13 [9354]~P1(f319(f319(f227(a1),f2(a1)),x93542))+~P1(f319(f319(f227(a1),x93541),x93543))+P1(f319(f319(f321(a1),f406(x93543,x93544,x93542,x93541)),f295(a1,f72(a1),x93542)))+P1(f319(f319(f227(a1),f319(f319(f23(a1),x93541),x93542)),x93543))
% 28.25/28.13 [9372]~P1(f319(f319(f226(a1),f2(a1)),x93724))+~P1(f319(f319(f227(a1),f2(a1)),x93723))+~P1(f319(f319(f227(a1),x93724),x93721))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),f319(f319(f75(a1),x93721),f39(a1,x93722,x93723))),x93724)))
% 28.25/28.13 [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))
% 28.25/28.13 [9403]E(x94031,x94032)+~P40(x94033,x94034)+~P1(f319(f319(f321(f931(x94033,x94033)),f319(f319(f244(x94033,x94033),x94032),x94031)),x94034))+~P1(f319(f319(f321(f931(x94033,x94033)),f319(f319(f244(x94033,x94033),x94031),x94032)),x94034))
% 28.25/28.13 [9436]~P108(x94361)+~P1(f319(f55(x94361),x94364))+~P1(f319(f319(f226(x94361),x94362),f650(x94363,x94362,x94364,x94361)))+P1(f319(f319(f226(x94361),f319(f319(f93(x94361),x94362),x94363)),f319(f319(f58(x94361,x94361,f93(x94361)),x94363),x94364)))
% 28.25/28.13 [9437]~P4(x94371)+~P1(f319(f55(x94371),x94374))+~P1(f319(f319(f226(x94371),x94372),f651(x94373,x94372,x94374,x94371)))+P1(f319(f319(f226(x94371),f319(f319(f224(x94371),x94372),x94373)),f319(f319(f58(x94371,x94371,f224(x94371)),x94373),x94374)))
% 28.25/28.13 [9453]~P1(f319(f319(f226(a1),x94534),f2(a1)))+~P1(f319(f319(f227(a1),f2(a1)),x94532))+~P1(f319(f319(f227(a1),x94531),x94534))+P1(f319(f319(f227(a1),f319(f319(f75(a1),x94531),x94532)),f319(f319(f74(a1),f319(f319(f75(a1),x94531),f39(a1,x94533,x94532))),x94534)))
% 28.25/28.13 [9478]P1(f319(f55(x94781),x94782))+~P1(f319(f55(x94781),x94783))+~P1(f319(f319(f321(f932(x94781,a923)),x94782),f319(f319(f54(x94781),x94783),x94784)))+~P1(f319(f319(f226(f932(f931(x94781,x94781),a923)),x94784),f319(f319(f246(x94781,x94781),x94783),f319(f16(f932(x94781,a923),x94781),x94783))))
% 28.25/28.13 [9503]~P4(x95031)+~P1(f319(f55(x95031),x95034))+P1(f319(f319(f321(x95031),f651(x95032,x95033,x95034,x95031)),x95034))+P1(f319(f319(f226(x95031),f319(f319(f224(x95031),x95033),x95032)),f319(f319(f58(x95031,x95031,f224(x95031)),x95032),x95034)))
% 28.25/28.13 [9504]~P108(x95041)+~P1(f319(f55(x95041),x95044))+P1(f319(f319(f321(x95041),f650(x95042,x95043,x95044,x95041)),x95044))+P1(f319(f319(f226(x95041),f319(f319(f93(x95041),x95043),x95042)),f319(f319(f58(x95041,x95041,f93(x95041)),x95042),x95044)))
% 28.25/28.13 [9516]~P41(f932(x95161,a923),f932(x95161,a923),x95163)+~P1(f319(f319(f321(x95161),x95162),x95164))+P1(f319(f319(f321(x95161),x95162),f88(f932(x95161,a923),x95163)))+~P1(f319(f319(f226(f932(x95161,a923)),x95164),f319(x95163,f319(f319(f102(f932(x95161,a923)),x95164),f88(f932(x95161,a923),x95163)))))
% 28.25/28.13 [9699]~P41(f932(x96993,a923),f932(x96993,a923),x96994)+P1(f319(x96991,x96992))+~P1(f319(f319(f321(x96993),x96992),f87(f932(x96993,a923),x96994)))+P1(f319(f319(f321(x96993),f460(x96991,x96994,x96992,x96993)),f319(x96994,f319(f319(f93(f932(x96993,a923)),f87(f932(x96993,a923),x96994)),f319(f254(x96993),x96991)))))
% 28.25/28.13 [9915]~P1(f319(f55(x99152),x99154))+~P1(f319(f55(x99151),x99153))+~P1(f319(f319(f226(a925),f319(f29(x99152),x99154)),f319(f29(x99151),x99153)))+P1(f319(f319(f226(f932(x99151,a923)),f319(f302(x99152,x99151,f422(x99153,x99151,x99154,x99152)),x99154)),x99153))
% 28.25/28.13 [9554]~P1(f319(f319(f321(x95541),x95542),x95544))+P1(f319(f319(f321(x95541),x95542),x95543))+~P1(f319(f319(f227(f932(x95541,a923)),x95544),f319(f319(f301(x95541),x95542),x95543)))+P1(f319(f319(f227(f932(x95541,a923)),f319(f319(f23(f932(x95541,a923)),x95544),f319(f319(f301(x95541),x95542),f180(f932(x95541,a923))))),x95543))
% 28.25/28.13 [9724]~P1(f319(f319(f321(x97241),x97242),x97244))+P1(f319(f319(f321(x97241),x97242),x97243))+P1(f319(f319(f227(f932(x97241,a923)),x97244),f319(f319(f301(x97241),x97242),x97243)))+~P1(f319(f319(f227(f932(x97241,a923)),f319(f319(f23(f932(x97241,a923)),x97244),f319(f319(f301(x97241),x97242),f180(f932(x97241,a923))))),x97243))
% 28.25/28.13 [9749]P1(f319(f319(f321(x97491),x97492),x97493))+~P1(f319(f319(f226(f932(x97491,a923)),x97494),x97493))+P1(f319(f319(f227(f932(x97491,a923)),x97494),f319(f319(f301(x97491),x97492),x97493)))+~P1(f319(f319(f227(f932(x97491,a923)),f319(f319(f23(f932(x97491,a923)),x97494),f319(f319(f301(x97491),x97492),f180(f932(x97491,a923))))),x97493))
% 28.25/28.13 [9754]~P1(f319(f319(f321(x97541),x97543),x97542))+~P1(f319(f319(f227(f932(x97541,a923)),x97542),x97544))+P1(f319(f319(f227(f932(x97541,a923)),x97542),f319(f319(f301(x97541),x97543),x97544)))+~P1(f319(f319(f227(f932(x97541,a923)),f319(f319(f23(f932(x97541,a923)),x97542),f319(f319(f301(x97541),x97543),f180(f932(x97541,a923))))),x97544))
% 28.25/28.13 [9770]~P1(f319(f319(f226(f932(x97701,a923)),x97702),x97704))+~P1(f319(f319(f227(f932(x97701,a923)),x97702),x97704))+P1(f319(f319(f227(f932(x97701,a923)),x97702),f319(f319(f301(x97701),x97703),x97704)))+~P1(f319(f319(f227(f932(x97701,a923)),f319(f319(f23(f932(x97701,a923)),x97702),f319(f319(f301(x97701),x97703),f180(f932(x97701,a923))))),x97704))
% 28.25/28.13 [9817]~P113(x98172)+~P5(x98171)+~P1(f319(f319(f226(f932(x98171,x98172)),x98173),x98174))+P1(f319(f51(x98171),f319(f319(f18(x98171,x98172,a923),f319(f319(f8(x98172,f932(x98172,a923),x98171),f226(x98172)),x98173)),x98174)))
% 28.25/28.13 [9970]~P113(x99702)+~P5(x99701)+P1(f319(f319(f226(f932(x99701,x99702)),x99703),x99704))+~P1(f319(f51(x99701),f319(f319(f18(x99701,x99702,a923),f319(f319(f8(x99702,f932(x99702,a923),x99701),f226(x99702)),x99703)),x99704)))
% 28.25/28.13 [10488]~P41(f932(x104881,a923),f932(x104881,a923),x104883)+~P1(f319(f319(f321(x104881),x104882),x104884))+P1(f319(f319(f321(x104881),x104882),f88(f932(x104881,a923),x104883)))+~P1(f319(f319(f226(f932(x104881,a923)),x104884),f319(x104883,f87(f932(x104881,a923),f319(f319(f7(f932(x104881,a923),f932(x104881,a923),f932(x104881,a923)),f319(f319(f8(f932(x104881,a923),f932(f932(x104881,a923),f932(x104881,a923)),f932(x104881,a923)),f102(f932(x104881,a923))),f319(f319(f7(f932(x104881,a923),f932(x104881,a923),f932(x104881,a923)),f319(f319(f8(f932(x104881,a923),f932(f932(x104881,a923),f932(x104881,a923)),f932(x104881,a923)),f102(f932(x104881,a923))),x104883)),x104884))),f88(f932(x104881,a923),x104883))))))
% 28.25/28.13 [10147]E(f319(f319(f156(x101471),f319(f319(f156(f926(x101471)),f171(x101471,x101472)),x101473)),x101474),f319(f319(f156(x101471),f319(f319(f156(f926(x101471)),x101472),x101474)),x101473))+~P1(f319(f319(f227(a925),x101473),f319(f181(f926(f926(x101471))),f171(x101471,x101472))))+~P14(a925,f319(f160(a925),f319(f319(f146(f926(x101471),a925),f181(f926(x101471))),x101472)))+~P1(f319(f319(f227(a925),x101474),f319(f181(f926(f926(x101471))),f319(f128(f926(x101471),f319(f319(f8(a925,a923,f926(x101471)),f319(f227(a925),x101473)),f181(f926(x101471)))),x101472))))
% 28.25/28.13 [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)),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)),x101681),x101683)),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)),x101681),f319(f319(f301(f931(a925,a925)),x101682),x101683))),a27))
% 28.25/28.13 [10169]~P1(f319(f319(f321(f931(a925,a925)),x101694),x101691))+~P1(f319(f319(f321(f931(f931(a925,a925),f931(a925,a925))),f319(f319(f244(f931(a925,a925),f931(a925,a925)),x101694),x101692)),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)),x101691),x101693)),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)),x101691),f319(f319(f301(f931(a925,a925)),x101692),x101693))),a65))
% 28.25/28.13 [10056]~P113(x100562)+~P5(x100561)+~P1(f319(f319(f227(f932(x100561,x100562)),x100563),x100564))+P1(f319(f50(x100561),f319(f319(f8(a923,a923,x100561),a314),f319(f319(f18(x100561,x100562,a923),f319(f319(f8(x100562,f932(x100562,a923),x100561),a316),x100563)),x100564))))
% 28.25/28.13 [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)),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)),x101802),x101803)),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)),x101801),x101802)),x101803)),a28))
% 28.25/28.13 [10181]~P1(f319(f319(f321(f931(a925,a925)),x101814),x101813))+~P1(f319(f319(f321(f931(f931(a925,a925),f931(a925,a925))),f319(f319(f244(f931(a925,a925),f931(a925,a925)),x101811),x101814)),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)),x101812),x101813)),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)),x101811),x101812)),x101813)),a63))
% 28.25/28.13 [6257]~P8(x62574,x62571)+~P1(f319(f319(x62571,x62572),x62575))+P1(f319(f319(x62571,x62572),x62573))+~P1(f319(f319(x62571,x62575),x62573))
% 28.25/28.13 [6258]~P54(x62584,x62581)+~P1(f319(f319(x62581,x62582),x62585))+P1(f319(f319(x62581,x62582),x62583))+~P1(f319(f319(x62581,x62585),x62583))
% 28.25/28.13 [6259]~P17(x62594,x62591)+~P1(f319(f319(x62591,x62592),x62595))+P1(f319(f319(x62591,x62592),x62593))+~P1(f319(f319(x62591,x62595),x62593))
% 28.25/28.13 [8939]~P27(x89391,x89393,x89395,x89392,x89394)+E(f319(f29(x89391),x89392),f319(f29(x89393),x89394))+~P1(f319(f55(x89393),x89394))+~P1(f319(f55(x89391),x89392))
% 28.25/28.13 [8960]~P8(x89604,x89603)+~P1(f319(x89601,x89605))+P1(f319(x89602,f847(x89602,x89601,x89603,x89604)))+P1(f319(x89601,f846(x89602,x89601,x89603,x89604)))
% 28.25/28.13 [9200]~P8(x92004,x92003)+~P1(f319(x92002,x92005))+~P1(f319(x92001,f846(x92001,x92002,x92003,x92004)))+P1(f319(x92001,f847(x92001,x92002,x92003,x92004)))
% 28.25/28.13 [9385]~P8(x93854,x93853)+~P1(f319(x93851,x93855))+P1(f319(f319(f321(x93854),f847(x93852,x93851,x93853,x93854)),f262(x93854,x93853)))+P1(f319(x93851,f846(x93852,x93851,x93853,x93854)))
% 28.25/28.13 [9510]~P8(x95101,x95104)+~P1(f319(x95103,x95105))+~P1(f319(x95102,f846(x95102,x95103,x95104,x95101)))+P1(f319(f319(f321(x95101),f847(x95102,x95103,x95104,x95101)),f262(x95101,x95104)))
% 28.25/28.13 [9806]~P39(x98061,x98064)+P1(f319(f319(f321(f931(f926(x98061),f926(x98061))),f319(f319(f244(f926(x98061),f926(x98061)),x98062),x98063)),f139(x98061,x98064)))+~P1(f319(f319(f321(f931(f926(x98061),f926(x98061))),f319(f319(f244(f926(x98061),f926(x98061)),x98062),x98065)),f139(x98061,x98064)))+~P1(f319(f319(f321(f931(f926(x98061),f926(x98061))),f319(f319(f244(f926(x98061),f926(x98061)),x98065),x98063)),f139(x98061,x98064)))
% 28.25/28.13 [5494]~P70(x54945)+E(x54941,x54942)+~E(x54943,x54944)+~E(f319(f319(f23(x54945),x54943),x54944),f319(f319(f23(x54945),x54941),x54942))
% 28.25/28.13 [5495]~P70(x54955)+E(x54951,x54952)+~E(x54953,x54954)+~E(f319(f319(f23(x54955),x54953),x54954),f319(f319(f23(x54955),x54951),x54952))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [7543]~E(x75432,f319(f319(f143(x75431),x75434),x75435))+P1(f319(f319(f321(f926(x75431)),x75432),f153(x75431,x75433)))+~P1(f319(f319(f321(f926(x75431)),x75435),f153(x75431,x75433)))+~P1(f319(f319(f321(x75431),x75434),x75433))
% 28.25/28.13 [7943]~E(f319(f181(f926(x79431)),x79433),f319(f181(f926(x79432)),x79434))+~E(f319(f319(f146(f931(x79431,x79432),x79432),f248(x79431,x79432)),x79435),x79434)+~E(f319(f319(f146(f931(x79431,x79432),x79431),f243(x79431,x79432)),x79435),x79433)+E(f319(f319(f173(x79431,x79432),x79433),x79434),x79435)
% 28.25/28.13 [8279]~P113(x82791)+P1(f319(f319(f227(f932(x82791,a923)),f295(x82791,x82792,x82793)),f295(x82791,x82794,x82795)))+~P1(f319(f319(f226(x82791),x82794),x82795))+P1(f319(f319(f226(x82791),x82792),x82793))
% 28.25/28.13 [8378]~P113(x83781)+P1(f319(f319(f226(f932(x83781,a923)),f295(x83781,x83782,x83783)),f295(x83781,x83784,x83785)))+~P1(f319(f319(f226(x83781),x83783),x83785))+~P1(f319(f319(f226(x83781),x83784),x83782))
% 28.25/28.13 [8498]~P4(x84981)+P1(f319(f319(f226(x84981),x84982),x84983))+P1(f319(f319(f226(x84981),x84984),x84983))+~P1(f319(f319(f226(f932(x84981,a923)),f319(f294(x84981,x84983),x84982)),f319(f294(x84981,x84984),x84985)))
% 28.25/28.13 [8499]~P4(x84991)+P1(f319(f319(f226(x84991),x84992),x84993))+P1(f319(f319(f226(x84991),x84992),x84994))+~P1(f319(f319(f226(f932(x84991,a923)),f319(f294(x84991,x84993),x84992)),f319(f294(x84991,x84995),x84994)))
% 28.25/28.13 [8669]~P108(x86693)+~P108(x86691)+~P41(x86693,x86691,x86692)+P1(f319(f319(f226(x86691),f319(x86692,f319(f319(f93(x86693),x86694),x86695))),f319(f319(f93(x86691),f319(x86692,x86694)),f319(x86692,x86695))))
% 28.25/28.13 [8670]~P4(x86703)+~P108(x86701)+~P41(x86703,x86701,x86702)+P1(f319(f319(f226(x86701),f319(x86702,f319(f319(f224(x86703),x86704),x86705))),f319(f319(f93(x86701),f319(x86702,x86704)),f319(x86702,x86705))))
% 28.25/28.13 [8737]~P113(x87371)+~P1(f319(f319(f226(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))
% 28.25/28.13 [8738]~P113(x87381)+~P1(f319(f319(f227(f932(x87381,a923)),f295(x87381,x87384,x87382)),f295(x87381,x87385,x87383)))+P1(f319(f319(f226(x87381),x87382),x87383))+~P1(f319(f319(f226(x87381),x87384),x87382))
% 28.25/28.13 [8739]~P113(x87391)+~P1(f319(f319(f226(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))
% 28.25/28.13 [8740]~P113(x87401)+~P1(f319(f319(f227(f932(x87401,a923)),f295(x87401,x87403,x87404)),f295(x87401,x87402,x87405)))+P1(f319(f319(f226(x87401),x87402),x87403))+~P1(f319(f319(f226(x87401),x87403),x87404))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [7035]~E(x70351,x70352)+~E(f319(f319(f93(f932(x70353,a923)),x70354),x70355),f180(f932(x70353,a923)))+~P1(f319(f319(f321(x70353),x70352),x70355))+~P1(f319(f319(f321(x70353),x70351),x70354))
% 28.25/28.13 [7118]~P20(x71182,x71185,x71181)+~P1(f319(f55(x71182),x71184))+E(f319(x71181,f319(f319(f301(x71182),x71183),x71184)),f319(f319(f58(x71182,x71182,x71185),x71183),x71184))+P1(f319(f319(f321(x71182),x71183),x71184))
% 28.25/28.13 [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))
% 28.25/28.13 [7184]~P79(x71842)+~P1(f319(f55(x71841),x71845))+E(f319(f319(f6(x71841,x71842),x71843),f319(f319(f301(x71841),x71844),x71845)),f319(f319(f74(x71842),f319(x71843,x71844)),f319(f319(f6(x71841,x71842),x71843),x71845)))+P1(f319(f319(f321(x71841),x71844),x71845))
% 28.25/28.13 [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))
% 28.25/28.13 [7186]~P78(x71862)+~P1(f319(f55(x71861),x71865))+E(f319(f319(f9(x71861,x71862),x71863),f319(f319(f301(x71861),x71864),x71865)),f319(f319(f75(x71862),f319(x71863,x71864)),f319(f319(f9(x71861,x71862),x71863),x71865)))+P1(f319(f319(f321(x71861),x71864),x71865))
% 28.25/28.13 [7687]~P20(x76872,x76875,x76871)+~P1(f319(f55(x76872),x76874))+E(f319(x76871,f319(f319(f301(x76872),x76873),x76874)),x76873)+~E(f319(f319(f23(f932(x76872,a923)),x76874),f319(f319(f301(x76872),x76873),f180(f932(x76872,a923)))),f180(f932(x76872,a923)))
% 28.25/28.13 [8043]~P65(x80431)+E(f319(f319(f30(x80431),f319(f319(f75(x80431),x80432),x80433)),f319(f319(f75(x80431),x80434),x80435)),f319(f319(f75(x80431),f319(f319(f30(x80431),x80432),x80434)),f319(f319(f30(x80431),x80433),x80435)))+~P1(f319(f319(f279(x80431),x80435),x80433))+~P1(f319(f319(f279(x80431),x80434),x80432))
% 28.25/28.13 [8047]~P107(x80471)+~P1(f319(f319(f226(x80471),x80473),x80475))+~P1(f319(f319(f226(x80471),x80472),x80474))+P1(f319(f319(f226(x80471),f319(f319(f102(x80471),x80472),x80473)),f319(f319(f102(x80471),x80474),x80475)))
% 28.25/28.13 [8048]~P108(x80481)+~P1(f319(f319(f226(x80481),x80483),x80485))+~P1(f319(f319(f226(x80481),x80482),x80484))+P1(f319(f319(f226(x80481),f319(f319(f93(x80481),x80482),x80483)),f319(f319(f93(x80481),x80484),x80485)))
% 28.25/28.13 [8049]~P91(x80491)+~P1(f319(f319(f226(x80491),x80493),x80495))+~P1(f319(f319(f226(x80491),x80492),x80494))+P1(f319(f319(f226(x80491),f319(f319(f74(x80491),x80492),x80493)),f319(f319(f74(x80491),x80494),x80495)))
% 28.25/28.13 [8050]~P4(x80501)+~P1(f319(f319(f226(x80501),x80503),x80505))+~P1(f319(f319(f226(x80501),x80502),x80504))+P1(f319(f319(f226(x80501),f319(f319(f224(x80501),x80502),x80503)),f319(f319(f224(x80501),x80504),x80505)))
% 28.25/28.13 [8051]~P4(x80511)+~P1(f319(f319(f226(x80511),x80513),x80515))+~P1(f319(f319(f226(x80511),x80512),x80514))+P1(f319(f319(f226(x80511),f319(f319(f225(x80511),x80512),x80513)),f319(f319(f225(x80511),x80514),x80515)))
% 28.25/28.13 [8052]~P89(x80521)+~P1(f319(f319(f226(x80521),x80523),x80525))+~P1(f319(f319(f227(x80521),x80522),x80524))+P1(f319(f319(f227(x80521),f319(f319(f74(x80521),x80522),x80523)),f319(f319(f74(x80521),x80524),x80525)))
% 28.25/28.13 [8053]~P89(x80531)+~P1(f319(f319(f226(x80531),x80532),x80534))+~P1(f319(f319(f227(x80531),x80533),x80535))+P1(f319(f319(f227(x80531),f319(f319(f74(x80531),x80532),x80533)),f319(f319(f74(x80531),x80534),x80535)))
% 28.25/28.13 [8054]~P89(x80541)+~P1(f319(f319(f227(x80541),x80543),x80545))+~P1(f319(f319(f227(x80541),x80542),x80544))+P1(f319(f319(f227(x80541),f319(f319(f74(x80541),x80542),x80543)),f319(f319(f74(x80541),x80544),x80545)))
% 28.25/28.13 [8055]~P121(x80551)+~P1(f319(f319(f279(x80551),x80553),x80555))+~P1(f319(f319(f279(x80551),x80552),x80554))+P1(f319(f319(f279(x80551),f319(f319(f75(x80551),x80552),x80553)),f319(f319(f75(x80551),x80554),x80555)))
% 28.25/28.13 [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)))
% 28.25/28.13 [8194]~P148(x81945)+E(x81941,x81942)+E(x81943,x81944)+~E(f319(f319(f74(x81945),f319(f319(f75(x81945),x81943),x81941)),f319(f319(f75(x81945),x81944),x81942)),f319(f319(f74(x81945),f319(f319(f75(x81945),x81943),x81942)),f319(f319(f75(x81945),x81944),x81941)))
% 28.25/28.13 [8399]~P4(x83994)+~P1(f319(f129(x83991),x83993))+P1(f319(f319(f321(x83991),x83992),f319(f164(x83991),x83993)))+P1(f319(f129(x83991),f319(f319(f140(x83991,x83994,x83995),x83992),x83993)))
% 28.25/28.13 [8546]~P70(x85461)+E(f319(f319(f23(x85461),f319(f319(f6(a925,x85461),x85462),f319(f294(a925,x85463),x85464))),f319(f319(f6(a925,x85461),x85462),f319(f294(a925,x85463),x85465))),f319(f319(f6(a925,x85461),x85462),f319(f294(a925,x85465),x85464)))+~P1(f319(f319(f226(a925),x85465),x85464))+~P1(f319(f319(f226(a925),x85463),x85465))
% 28.25/28.13 [8547]~P79(x85471)+E(f319(f319(f74(x85471),f319(f319(f6(a925,x85471),x85472),f319(f294(a925,x85473),x85474))),f319(f319(f6(a925,x85471),x85472),f319(f294(a925,x85474),x85475))),f319(f319(f6(a925,x85471),x85472),f319(f294(a925,x85473),x85475)))+~P1(f319(f319(f226(a925),x85474),x85475))+~P1(f319(f319(f226(a925),x85473),x85474))
% 28.25/28.13 [8881]~P73(x88812)+E(x88811,f2(x88812))+E(x88813,f2(x88812))+E(f319(f319(f283(x88812),f319(f319(f23(x88812),f319(f319(f75(x88812),x88814),x88811)),f319(f319(f75(x88812),x88815),x88813))),f319(f319(f75(x88812),x88813),x88811)),f319(f319(f23(x88812),f319(f319(f283(x88812),x88814),x88813)),f319(f319(f283(x88812),x88815),x88811)))
% 28.25/28.13 [8882]~P73(x88822)+E(x88821,f2(x88822))+E(x88823,f2(x88822))+E(f319(f319(f283(x88822),f319(f319(f74(x88822),f319(f319(f75(x88822),x88824),x88821)),f319(f319(f75(x88822),x88825),x88823))),f319(f319(f75(x88822),x88823),x88821)),f319(f319(f74(x88822),f319(f319(f283(x88822),x88824),x88823)),f319(f319(f283(x88822),x88825),x88821)))
% 28.25/28.13 [8891]~E(x88912,f319(x88913,x88911))+E(x88911,f892(x88912,x88913,x88914,x88915))+~P26(x88915,x88914,x88913,f234(f932(x88915,a923)))+~P1(f319(f319(f321(x88914),x88912),f319(f302(x88915,x88914,x88913),f234(f932(x88915,a923)))))
% 28.25/28.13 [9110]~P126(x91101)+~P1(f319(f319(f227(x91101),f319(f69(x91101),x91102)),x91104))+P1(f319(f319(f227(x91101),f319(f319(f75(x91101),f319(f69(x91101),x91102)),f319(f69(x91101),x91103))),f319(f319(f75(x91101),x91104),x91105)))+~P1(f319(f319(f227(x91101),f319(f69(x91101),x91103)),x91105))
% 28.25/28.13 [9226]~P26(x92261,x92263,x92265,x92262)+~P1(f319(f55(x92263),x92264))+P1(f319(f319(f226(a925),f319(f29(x92261),x92262)),f319(f29(x92263),x92264)))+~P1(f319(f319(f226(f932(x92263,a923)),f319(f302(x92261,x92263,x92265),x92262)),x92264))
% 28.25/28.13 [9294]~P79(x92942)+~P26(x92941,x92941,x92944,x92945)+~P1(f319(f55(x92941),x92945))+E(f319(f319(f6(x92941,x92942),f319(f66(x92941,x92942,x92941,x92943),x92944)),x92945),f319(f319(f6(x92941,x92942),x92943),f319(f302(x92941,x92941,x92944),x92945)))
% 28.25/28.13 [9295]~P78(x92952)+~P26(x92951,x92951,x92954,x92955)+~P1(f319(f55(x92951),x92955))+E(f319(f319(f9(x92951,x92952),f319(f66(x92951,x92952,x92951,x92953),x92954)),x92955),f319(f319(f9(x92951,x92952),x92953),f319(f302(x92951,x92951,x92954),x92955)))
% 28.25/28.13 [9376]~E(f893(x93762,x93764,x93761,x93763,x93765),x93765)+~E(x93762,f319(x93764,x93765))+~P26(x93763,x93761,x93764,f234(f932(x93763,a923)))+P1(f319(f319(f321(x93761),x93762),f319(f302(x93763,x93761,x93764),f234(f932(x93763,a923)))))
% 28.25/28.13 [9415]~P38(x94151,x94152)+~P1(f319(f319(f321(x94151),x94153),x94154))+~P1(f319(f319(f321(x94151),x94155),x94154))+~P1(f319(f319(f321(f931(x94151,x94151)),f319(f319(f244(x94151,x94151),x94155),f630(x94152,x94151,x94154))),x94152))
% 28.25/28.13 [9452]~P26(x94522,x94523,x94525,x94521)+E(x94521,f180(f932(x94522,a923)))+E(f319(f302(x94523,x94522,f894(x94524,x94523,x94522,x94521)),x94524),x94521)+~P1(f319(f319(f226(f932(x94523,a923)),f319(f302(x94522,x94523,x94525),x94521)),x94524))
% 28.25/28.13 [9492]~E(x94922,f319(x94921,x94925))+~P26(x94924,x94923,x94921,f234(f932(x94924,a923)))+E(f319(x94921,f893(x94922,x94921,x94923,x94924,x94925)),x94922)+P1(f319(f319(f321(x94923),x94922),f319(f302(x94924,x94923,x94921),f234(f932(x94924,a923)))))
% 28.25/28.13 [9946]~P4(x99465)+~P6(x99465)+P1(f319(f319(f321(x99461),f886(x99462,x99463,x99461,x99464,x99465)),x99463))+~P1(f319(f319(f227(x99465),x99464),f319(f319(f33(x99461,x99465),x99463),x99462)))
% 28.25/28.13 [9952]~P4(x99521)+~P6(x99521)+P1(f319(f319(f227(x99521),x99522),f319(x99523,f886(x99523,x99524,x99525,x99522,x99521))))+~P1(f319(f319(f227(x99521),x99522),f319(f319(f33(x99525,x99521),x99524),x99523)))
% 28.25/28.13 [10041]~P76(x100411)+~P1(f319(f60(x100411,x100411,f75(x100411),x100412,x100413),x100415))+P1(f319(f319(f321(x100411),x100412),x100413))+P1(f319(f60(x100411,x100411,f75(x100411),x100414,f319(f319(f301(x100411),x100412),x100413)),f319(f319(f75(x100411),x100414),x100415)))
% 28.25/28.13 [10261]~P79(x102612)+~P1(f319(f55(x102611),x102615))+E(f319(f319(f6(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)),f2(x102612))),x102615),f2(x102612))+P1(f319(f319(f321(x102611),x102613),x102615))
% 28.25/28.13 [10262]~P78(x102622)+~P1(f319(f55(x102621),x102625))+E(f319(f319(f9(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)),f72(x102622))),x102625),f72(x102622))+P1(f319(f319(f321(x102621),x102623),x102625))
% 28.25/28.13 [10263]~P79(x102632)+~P1(f319(f55(x102631),x102635))+E(f319(f319(f6(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)),f2(x102632))),x102635),f319(x102634,x102633))+~P1(f319(f319(f321(x102631),x102633),x102635))
% 28.25/28.13 [10264]~P78(x102642)+~P1(f319(f55(x102641),x102645))+E(f319(f319(f9(x102641,x102642),f319(f319(f7(x102641,x102642,x102642),f319(f319(f18(x102641,x102642,f932(x102642,x102642)),f319(f319(f8(a923,f932(x102642,f932(x102642,x102642)),x102641),f86(x102642)),f319(a316,x102643))),x102644)),f72(x102642))),x102645),f319(x102644,x102643))+~P1(f319(f319(f321(x102641),x102643),x102645))
% 28.25/28.13 [10324]~P79(x103242)+~P1(f319(f55(x103241),x103245))+E(f319(f319(f6(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)),f2(x103242))),x103245),f2(x103242))+P1(f319(f319(f321(x103241),x103243),x103245))
% 28.25/28.13 [10325]~P78(x103252)+~P1(f319(f55(x103251),x103255))+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)),f72(x103252))),x103255),f72(x103252))+P1(f319(f319(f321(x103251),x103253),x103255))
% 28.25/28.13 [10327]~P79(x103272)+~P1(f319(f55(x103271),x103275))+E(f319(f319(f6(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)),f2(x103272))),x103275),f319(x103274,x103273))+~P1(f319(f319(f321(x103271),x103273),x103275))
% 28.25/28.13 [10328]~P78(x103282)+~P1(f319(f55(x103281),x103285))+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)),f72(x103282))),x103285),f319(x103284,x103283))+~P1(f319(f319(f321(x103281),x103283),x103285))
% 28.25/28.13 [8046]~P70(x80462)+~P1(f319(f55(x80461),x80464))+E(f319(f319(f6(x80461,x80462),x80463),f319(f319(f23(f932(x80461,a923)),x80464),f319(f319(f301(x80461),x80465),f180(f932(x80461,a923))))),f319(f319(f6(x80461,x80462),x80463),x80464))+P1(f319(f319(f321(x80461),x80465),x80464))
% 28.25/28.13 [8555]~P116(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))
% 28.25/28.13 [8556]~P70(x85562)+~P1(f319(f55(x85561),x85564))+E(f319(f319(f6(x85561,x85562),x85563),f319(f319(f23(f932(x85561,a923)),x85564),f319(f319(f301(x85561),x85565),f180(f932(x85561,a923))))),f319(f319(f23(x85562),f319(f319(f6(x85561,x85562),x85563),x85564)),f319(x85563,x85565)))+~P1(f319(f319(f321(x85561),x85565),x85564))
% 28.25/28.13 [8585]~P70(x85851)+~P1(f319(f55(x85852),x85854))+E(f319(f319(f23(x85851),f319(f319(f6(x85852,x85851),x85853),x85854)),f319(f319(f6(x85852,x85851),x85853),x85855)),f319(f319(f6(x85852,x85851),x85853),f319(f319(f23(f932(x85852,a923)),x85854),x85855)))+~P1(f319(f319(f226(f932(x85852,a923)),x85855),x85854))
% 28.25/28.13 [8604]P1(f319(f55(x86041),f319(x86042,x86043)))+~P1(f319(f55(x86044),x86045))+~P1(f319(f319(f321(x86044),x86043),x86045))+~P1(f319(f55(x86041),f319(f319(f33(x86044,f932(x86041,a923)),x86045),x86042)))
% 28.25/28.13 [8718]~P107(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(f102(x87185),x87183),x87184))))
% 28.25/28.13 [8719]~P4(x87195)+~P107(x87191)+~P41(x87195,x87191,x87192)+P1(f319(f319(f226(x87191),f319(f319(f102(x87191),f319(x87192,x87193)),f319(x87192,x87194))),f319(x87192,f319(f319(f225(x87195),x87193),x87194))))
% 28.25/28.13 [9065]~P9(x90651,x90655,x90654)+~E(f319(f277(x90651,x90651,x90654),f319(f319(f301(x90651),x90652),f180(f932(x90651,a923)))),f319(f277(x90651,x90651,x90654),f319(f319(f301(x90651),x90653),f180(f932(x90651,a923)))))+~P1(f319(f319(f321(x90651),x90653),x90655))+P1(f319(f319(f321(f931(x90651,x90651)),f319(f319(f244(x90651,x90651),x90652),x90653)),x90654))
% 28.25/28.13 [9370]~P1(f319(x93701,x93705))+P1(f319(x93701,f614(x93701,x93702,x93703,x93704)))+P1(f319(x93701,f602(x93701,x93702,x93703,x93704)))+~P1(f319(f319(f321(x93704),x93705),f319(f319(f102(f932(x93704,a923)),x93703),x93702)))
% 28.25/28.13 [9559]~P1(f319(x95591,x95595))+P1(f319(x95591,f602(x95591,x95592,x95593,x95594)))+P1(f319(f319(f321(x95594),f614(x95591,x95592,x95593,x95594)),x95592))+~P1(f319(f319(f321(x95594),x95595),f319(f319(f102(f932(x95594,a923)),x95593),x95592)))
% 28.25/28.13 [9560]~P1(f319(x95601,x95605))+P1(f319(x95601,f614(x95601,x95602,x95603,x95604)))+P1(f319(f319(f321(x95604),f602(x95601,x95602,x95603,x95604)),x95603))+~P1(f319(f319(f321(x95604),x95605),f319(f319(f102(f932(x95604,a923)),x95603),x95602)))
% 28.25/28.13 [9564]P1(f319(x95641,x95642))+~P1(f319(x95641,f592(x95641,x95643,x95644,x95645)))+~P1(f319(x95641,f579(x95641,x95643,x95644,x95645)))+~P1(f319(f319(f321(x95645),x95642),f319(f319(f102(f932(x95645,a923)),x95644),x95643)))
% 28.25/28.13 [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))
% 28.25/28.13 [9569]~P39(x95691,x95694)+~P1(f319(f319(f321(f931(x95691,x95691)),f319(f319(f244(x95691,x95691),x95692),x95695)),x95694))+P1(f319(f319(f321(f931(x95691,x95691)),f319(f319(f244(x95691,x95691),x95692),x95693)),x95694))+~P1(f319(f319(f321(f931(x95691,x95691)),f319(f319(f244(x95691,x95691),x95695),x95693)),x95694))
% 28.25/28.13 [9608]E(x96081,x96082)+~P1(f319(f319(f321(f931(x96083,x96083)),f319(f319(f244(x96083,x96083),x96081),x96082)),f299(x96083,x96085)))+P1(f319(f319(f321(x96083),x96081),x96084))+~P1(f319(f319(f226(f932(f931(x96083,x96083),a923)),x96085),f319(f319(f246(x96083,x96083),x96084),f319(f16(f932(x96083,a923),x96083),x96084))))
% 28.25/28.13 [9626]P1(f319(x96261,x96262))+~P1(f319(x96261,f579(x96261,x96264,x96265,x96263)))+P1(f319(f319(f321(x96263),f592(x96261,x96264,x96265,x96263)),x96264))+~P1(f319(f319(f321(x96263),x96262),f319(f319(f102(f932(x96263,a923)),x96265),x96264)))
% 28.25/28.13 [9627]P1(f319(x96271,x96272))+~P1(f319(x96271,f592(x96271,x96274,x96275,x96273)))+P1(f319(f319(f321(x96273),f579(x96271,x96274,x96275,x96273)),x96275))+~P1(f319(f319(f321(x96273),x96272),f319(f319(f102(f932(x96273,a923)),x96275),x96274)))
% 28.25/28.13 [9695]P1(f319(x96951,x96952))+P1(f319(f319(f321(x96953),f592(x96951,x96954,x96955,x96953)),x96954))+P1(f319(f319(f321(x96953),f579(x96951,x96954,x96955,x96953)),x96955))+~P1(f319(f319(f321(x96953),x96952),f319(f319(f102(f932(x96953,a923)),x96955),x96954)))
% 28.25/28.13 [9697]~P1(f319(x96972,x96975))+P1(f319(f319(f321(x96971),f614(x96972,x96973,x96974,x96971)),x96973))+P1(f319(f319(f321(x96971),f602(x96972,x96973,x96974,x96971)),x96974))+~P1(f319(f319(f321(x96971),x96975),f319(f319(f102(f932(x96971,a923)),x96974),x96973)))
% 28.25/28.13 [9848]~P9(x98481,x98485,x98484)+~P1(f319(f319(f321(x98481),x98483),x98485))+P1(f319(f319(f321(f931(x98481,x98481)),f319(f319(f244(x98481,x98481),x98482),x98483)),x98484))+~P1(f319(f319(f226(f932(x98481,a923)),f319(f277(x98481,x98481,x98484),f319(f319(f301(x98481),x98483),f180(f932(x98481,a923))))),f319(f277(x98481,x98481,x98484),f319(f319(f301(x98481),x98482),f180(f932(x98481,a923))))))
% 28.25/28.13 [9988]~P4(x99885)+~P6(x99885)+P1(f319(f319(f321(x99881),f887(x99882,x99883,x99884,x99881,x99885)),x99884))+~P1(f319(f319(f227(x99885),f319(f319(f34(x99881,x99885),x99884),x99883)),x99882))
% 28.25/28.13 [10023]~P91(x100235)+~P88(x100235)+P1(f319(f319(f321(x100231),f716(x100232,x100233,x100234,x100231,x100235)),f319(f164(x100231),x100234)))+P1(f319(f319(f226(x100235),f319(f157(x100235),f319(f319(f146(x100231,x100235),x100233),x100234))),f319(f157(x100235),f319(f319(f146(x100231,x100235),x100232),x100234))))
% 28.25/28.13 [10137]~P4(x101371)+~P6(x101371)+P1(f319(f319(f227(x101371),f319(x101372,f887(x101373,x101372,x101374,x101375,x101371))),x101373))+~P1(f319(f319(f227(x101371),f319(f319(f34(x101375,x101371),x101374),x101372)),x101373))
% 28.25/28.13 [10280]~P91(x102801)+~P88(x102801)+~P1(f319(f319(f226(x102801),f319(x102803,f716(x102805,x102803,x102804,x102802,x102801))),f319(x102805,f716(x102805,x102803,x102804,x102802,x102801))))+P1(f319(f319(f226(x102801),f319(f157(x102801),f319(f319(f146(x102802,x102801),x102803),x102804))),f319(f157(x102801),f319(f319(f146(x102802,x102801),x102805),x102804))))
% 28.25/28.13 [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))
% 28.25/28.13 [8904]~P79(x89041)+~P1(f319(f55(x89044),x89045))+~P1(f319(f319(f321(x89044),x89043),x89045))+E(f319(f319(f74(x89041),f319(x89042,x89043)),f319(f319(f6(x89044,x89041),x89042),f319(f319(f23(f932(x89044,a923)),x89045),f319(f319(f301(x89044),x89043),f180(f932(x89044,a923)))))),f319(f319(f6(x89044,x89041),x89042),x89045))
% 28.25/28.13 [8905]~P78(x89051)+~P1(f319(f55(x89054),x89055))+~P1(f319(f319(f321(x89054),x89053),x89055))+E(f319(f319(f75(x89051),f319(x89052,x89053)),f319(f319(f9(x89054,x89051),x89052),f319(f319(f23(f932(x89054,a923)),x89055),f319(f319(f301(x89054),x89053),f180(f932(x89054,a923)))))),f319(f319(f9(x89054,x89051),x89052),x89055))
% 28.25/28.13 [8965]~P20(x89651,x89654,x89655)+~P1(f319(f55(x89651),x89652))+E(f319(f319(f23(f932(x89651,a923)),x89652),f319(f319(f301(x89651),x89653),f180(f932(x89651,a923)))),f180(f932(x89651,a923)))+E(f319(f319(x89654,x89653),f319(x89655,f319(f319(f23(f932(x89651,a923)),x89652),f319(f319(f301(x89651),x89653),f180(f932(x89651,a923)))))),f319(x89655,f319(f319(f301(x89651),x89653),x89652)))
% 28.25/28.13 [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)))
% 28.25/28.13 [9349]~P78(x93491)+~P1(f319(f55(x93492),x93495))+~P1(f319(f55(x93492),x93494))+E(f319(f319(f75(x93491),f319(f319(f9(x93492,x93491),x93493),f319(f319(f102(f932(x93492,a923)),x93494),x93495))),f319(f319(f9(x93492,x93491),x93493),f319(f319(f93(f932(x93492,a923)),x93494),x93495))),f319(f319(f75(x93491),f319(f319(f9(x93492,x93491),x93493),x93494)),f319(f319(f9(x93492,x93491),x93493),x93495)))
% 28.25/28.13 [9350]~P79(x93501)+~P1(f319(f55(x93502),x93505))+~P1(f319(f55(x93502),x93504))+E(f319(f319(f74(x93501),f319(f319(f6(x93502,x93501),x93503),f319(f319(f102(f932(x93502,a923)),x93504),x93505))),f319(f319(f6(x93502,x93501),x93503),f319(f319(f93(f932(x93502,a923)),x93504),x93505))),f319(f319(f74(x93501),f319(f319(f6(x93502,x93501),x93503),x93504)),f319(f319(f6(x93502,x93501),x93503),x93505)))
% 28.25/28.13 [9491]~P70(x94911)+~P1(f319(f55(x94912),x94915))+~P1(f319(f55(x94912),x94914))+E(f319(f319(f23(x94911),f319(f319(f74(x94911),f319(f319(f6(x94912,x94911),x94913),x94914)),f319(f319(f6(x94912,x94911),x94913),x94915))),f319(f319(f6(x94912,x94911),x94913),f319(f319(f93(f932(x94912,a923)),x94914),x94915))),f319(f319(f6(x94912,x94911),x94913),f319(f319(f102(f932(x94912,a923)),x94914),x94915)))
% 28.25/28.13 [9708]~P26(x97081,x97082,x97083,x97085)+~P26(x97081,x97082,x97083,x97084)+P26(x97081,x97082,x97083,f319(f319(f102(f932(x97081,a923)),x97084),x97085))+~E(f319(f319(f93(f932(x97082,a923)),f319(f302(x97081,x97082,x97083),f319(f319(f23(f932(x97081,a923)),x97084),x97085))),f319(f302(x97081,x97082,x97083),f319(f319(f23(f932(x97081,a923)),x97085),x97084))),f180(f932(x97082,a923)))
% 28.25/28.13 [9823]E(x98231,f2(a1))+~P1(f319(f319(f227(a1),f2(a1)),x98233))+~P1(f319(f43(x98232,x98231),f319(f319(f244(a1,a1),x98234),x98235)))+P1(f319(f43(x98232,f319(f319(f75(a1),x98231),x98233)),f319(f319(f244(a1,a1),f319(f319(f30(a1),x98234),x98233)),f319(f319(f74(a1),f319(f319(f75(a1),x98231),f39(a1,x98234,x98233))),x98235))))
% 28.25/28.13 [9831]~P1(f319(f319(f227(a925),f2(a925)),x98313))+~P1(f319(f319(f227(a925),f2(a925)),x98312))+~P1(f319(f42(x98311,x98312),f319(f319(f244(a925,a925),x98314),x98315)))+P1(f319(f42(x98311,f319(f319(f75(a925),x98312),x98313)),f319(f319(f244(a925,a925),f319(f319(f30(a925),x98314),x98313)),f319(f319(f74(a925),f319(f319(f75(a925),x98312),f39(a925,x98314,x98313))),x98315))))
% 28.25/28.13 [9881]~P78(x98811)+~P1(f319(f55(x98812),x98815))+~P1(f319(f55(x98812),x98814))+E(f319(f319(f75(x98811),f319(f319(f319(f59(x98811,x98812,f75(x98811)),x98813),f72(x98811)),f319(f319(f102(f932(x98812,a923)),x98814),x98815))),f319(f319(f319(f59(x98811,x98812,f75(x98811)),x98813),f72(x98811)),f319(f319(f93(f932(x98812,a923)),x98814),x98815))),f319(f319(f75(x98811),f319(f319(f319(f59(x98811,x98812,f75(x98811)),x98813),f72(x98811)),x98814)),f319(f319(f319(f59(x98811,x98812,f75(x98811)),x98813),f72(x98811)),x98815)))
% 28.25/28.13 [9883]~E(f319(f319(f167(x98831),x98835),x98832),f319(f319(f167(x98831),x98835),x98833))+P1(f319(f319(f321(f931(f926(x98831),f926(x98831))),f319(f319(f244(f926(x98831),f926(x98831)),x98832),x98833)),f139(x98831,x98834)))+~P1(f319(f319(f227(a925),x98835),f319(f319(f224(a925),f319(f181(f926(x98831)),x98832)),f319(f181(f926(x98831)),x98833))))+~P1(f319(f319(f321(f931(x98831,x98831)),f319(f319(f244(x98831,x98831),f319(f319(f156(x98831),x98832),x98835)),f319(f319(f156(x98831),x98833),x98835))),x98834))
% 28.25/28.13 [10012]~P91(x100125)+~P149(x100125)+P1(f319(f319(f321(x100121),f424(x100122,x100123,x100124,x100121,x100125)),x100124))+P1(f319(f319(f226(x100125),f319(f319(f6(x100121,x100125),x100123),x100124)),f319(f319(f75(x100125),f319(f92(x100125),f319(f29(x100121),x100124))),x100122)))
% 28.25/28.13 [10196]~P91(x101961)+~P149(x101961)+~P1(f319(f319(f226(x101961),f319(x101963,f424(x101965,x101963,x101964,x101962,x101961))),x101965))+P1(f319(f319(f226(x101961),f319(f319(f6(x101962,x101961),x101963),x101964)),f319(f319(f75(x101961),f319(f92(x101961),f319(f29(x101962),x101964))),x101965)))
% 28.25/28.13 [8933]E(f319(f319(f126(x89331),x89332),x89333),f319(f319(f126(x89331),x89334),x89335))+~E(f319(f319(f167(x89331),f319(f181(f926(x89331)),x89332)),x89334),x89332)+~E(f319(f319(f126(x89331),f319(f319(f130(x89331),f319(f181(f926(x89331)),x89332)),x89334)),x89335),x89333)+P1(f319(f319(f226(a925),f319(f181(f926(x89331)),x89334)),f319(f181(f926(x89331)),x89332)))
% 28.25/28.13 [9064]E(f319(f319(f126(x90641),x90642),x90643),f319(f319(f126(x90641),x90644),x90645))+~E(f319(f319(f167(x90641),f319(f181(f926(x90641)),x90642)),x90644),x90642)+~E(x90643,f319(f319(f126(x90641),f319(f319(f130(x90641),f319(f181(f926(x90641)),x90642)),x90644)),x90645))+~P1(f319(f319(f226(a925),f319(f181(f926(x90641)),x90642)),f319(f181(f926(x90641)),x90644)))
% 28.25/28.13 [10345]~P1(f319(x103455,x103454))+~P1(f319(f55(x103452),f319(f254(x103452),x103455)))+P1(f319(f55(x103451),f319(f254(x103451),f319(f319(f7(x103451,x103452,a923),x103453),x103454))))+~P1(f319(f55(x103451),f319(f254(x103451),f319(f319(f8(f932(x103452,a923),a923,x103451),f81(x103452)),f319(f319(f8(f932(x103452,a923),f932(x103452,a923),x103451),f319(f18(x103452,a923,a923),f319(f319(f8(a923,f932(a923,a923),x103452),a317),x103455))),x103453)))))
% 28.25/28.13 [10417]~P1(f319(f55(x104172),x104175))+~P1(f319(f319(f321(x104172),x104174),x104175))+P1(f319(f55(x104171),f319(f254(x104171),f319(f319(f7(x104171,x104172,a923),x104173),x104174))))+~P1(f319(f55(x104171),f319(f254(x104171),f319(f319(f8(f932(x104172,a923),a923,x104171),f81(x104172)),f319(f319(f8(f932(x104172,a923),f932(x104172,a923),x104171),f319(f18(x104172,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104172),a317),f319(f319(f7(x104172,f932(x104172,a923),a923),f321(x104172)),x104175)))),x104173)))))
% 28.25/28.13 [8716]~P21(x87165,x87161,x87166,x87162)+E(f319(f66(x87161,x87161,x87161,f319(x87162,x87163)),f319(x87162,x87164)),f319(f66(x87161,x87161,x87161,f319(x87162,x87164)),f319(x87162,x87163)))+~P1(f319(f55(x87165),x87164))+~P1(f319(f55(x87165),x87163))
% 28.25/28.13 [8103]~P26(x81031,x81032,x81034,x81033)+~E(f319(x81034,x81036),x81035)+E(f319(f71(x81031,x81032,x81033,x81034),x81035),x81036)+~P1(f319(f319(f321(x81031),x81036),x81033))
% 28.25/28.13 [8104]~P26(x81041,x81042,x81044,x81043)+~E(f319(x81044,x81046),x81045)+E(f319(f85(x81041,x81042,x81043,x81044),x81045),x81046)+~P1(f319(f319(f321(x81041),x81046),x81043))
% 28.25/28.13 [8300]~P22(x83006,x83001,x83004,x83002)+E(f319(f66(x83001,x83001,x83001,f319(x83002,x83003)),f319(x83004,x83005)),f319(x83002,x83003))+~P1(f319(f55(x83006),x83003))+~P1(f319(f319(f321(x83006),x83005),x83003))
% 28.25/28.13 [9444]E(x94441,x94442)+~E(f319(f85(x94443,x94444,x94445,x94446),x94441),f319(f85(x94443,x94444,x94445,x94446),x94442))+~P1(f319(f319(f321(x94444),x94442),f319(f302(x94443,x94444,x94446),x94445)))+~P1(f319(f319(f321(x94444),x94441),f319(f302(x94443,x94444,x94446),x94445)))
% 28.25/28.13 [9542]~P21(x95423,x95421,x95426,x95422)+E(f319(f66(x95421,x95421,x95421,f319(x95422,f319(f319(f23(f932(x95423,a923)),x95424),f319(f319(f301(x95423),x95425),f180(f932(x95423,a923)))))),f319(x95426,x95425)),f319(x95422,x95424))+~P1(f319(f55(x95423),x95424))+~P1(f319(f319(f321(x95423),x95425),x95424))
% 28.25/28.13 [7189]~P66(x71891)+~E(f39(x71891,x71893,x71894),f39(x71891,x71896,x71894))+~E(f39(x71891,x71892,x71894),f39(x71891,x71895,x71894))+E(f39(x71891,f319(f319(f23(x71891),x71892),x71893),x71894),f39(x71891,f319(f319(f23(x71891),x71895),x71896),x71894))
% 28.25/28.13 [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(f75(x71901),x71902),x71903),x71904),f39(x71901,f319(f319(f75(x71901),x71905),x71906),x71904))
% 28.25/28.13 [7191]~P65(x71911)+~E(f39(x71911,x71913,x71914),f39(x71911,x71916,x71914))+~E(f39(x71911,x71912,x71914),f39(x71911,x71915,x71914))+E(f39(x71911,f319(f319(f74(x71911),x71912),x71913),x71914),f39(x71911,f319(f319(f74(x71911),x71915),x71916),x71914))
% 28.25/28.13 [7997]~P18(x79971,x79972,x79973)+~P1(f319(f55(x79971),x79976))+E(f319(f319(f58(x79971,x79972,x79973),x79974),f319(f319(f301(x79971),x79975),x79976)),f319(f319(f58(x79971,x79972,x79973),f319(f319(x79973,x79975),x79974)),x79976))+P1(f319(f319(f321(x79971),x79975),x79976))
% 28.25/28.13 [8062]~P6(x80621)+P1(f319(f319(f226(x80621),x80622),f319(x80623,x80624)))+~P1(f319(f319(f321(x80625),x80624),x80626))+~P1(f319(f319(f226(x80621),x80622),f319(f319(f34(x80625,x80621),x80626),x80623)))
% 28.25/28.13 [8222]~P18(x82221,x82222,x82223)+~P1(f319(f55(x82221),x82226))+E(f319(f319(f58(x82221,x82222,x82223),x82224),f319(f319(f301(x82221),x82225),x82226)),f319(f319(x82223,x82225),f319(f319(f58(x82221,x82222,x82223),x82224),x82226)))+P1(f319(f319(f321(x82221),x82225),x82226))
% 28.25/28.13 [8318]~P4(x83183)+~P1(f319(x83182,x83185))+~P14(x83183,f319(f319(f146(x83181,x83183),x83184),x83186))+E(f319(f128(x83181,x83182),f319(f319(f140(x83181,x83183,x83184),x83185),x83186)),f319(f319(f140(x83181,x83183,x83184),x83185),f319(f128(x83181,x83182),x83186)))
% 28.25/28.13 [8341]E(x83411,x83412)+E(x83413,f2(a1))+~P1(f319(f43(x83414,x83413),f319(f319(f244(a1,a1),x83415),x83412)))+~P1(f319(f43(x83414,x83413),f319(f319(f244(a1,a1),x83416),x83411)))
% 28.25/28.13 [8342]E(x83421,x83422)+E(x83423,f2(a1))+~P1(f319(f43(x83424,x83423),f319(f319(f244(a1,a1),x83422),x83425)))+~P1(f319(f43(x83424,x83423),f319(f319(f244(a1,a1),x83421),x83426)))
% 28.25/28.13 [8363]~P21(x83632,x83635,x83636,x83631)+~P1(f319(f55(x83632),x83634))+E(f319(x83631,f319(f319(f301(x83632),x83633),x83634)),f319(f66(x83635,x83635,x83635,f319(x83631,x83634)),f319(x83636,x83633)))+P1(f319(f319(f321(x83632),x83633),x83634))
% 28.25/28.13 [8588]~P22(x85885,x85881,x85886,x85882)+E(f319(f66(x85881,x85881,x85881,f319(x85882,x85883)),f319(x85882,x85884)),f319(x85882,x85883))+~P1(f319(f55(x85885),x85883))+~P1(f319(f319(f226(f932(x85885,a923)),x85884),x85883))
% 28.25/28.13 [9751]~P26(x97511,x97512,x97514,x97513)+~P1(f319(f319(f321(x97512),x97515),f319(f302(x97511,x97512,x97514),x97513)))+P1(f319(f319(f321(x97511),f319(f71(x97511,x97512,x97513,x97514),x97515)),x97516))+~P1(f319(f319(f226(f932(x97511,a923)),x97513),x97516))
% 28.25/28.13 [10148]~P79(x101482)+~E(f413(x101481,x101483,x101485,x101486,x101484,x101482),f414(x101481,x101483,x101485,x101486,x101484,x101482))+~P1(f319(f55(x101484),x101486))+E(f319(f319(f6(x101481,x101482),x101483),f319(f302(x101484,x101481,x101485),x101486)),f319(f319(f6(x101484,x101482),f319(f66(x101481,x101482,x101484,x101483),x101485)),x101486))
% 28.25/28.13 [10176]~P79(x101766)+E(f319(x101761,f413(x101762,x101763,x101761,x101764,x101765,x101766)),f319(x101761,f414(x101762,x101763,x101761,x101764,x101765,x101766)))+E(f319(f319(f6(x101762,x101766),x101763),f319(f302(x101765,x101762,x101761),x101764)),f319(f319(f6(x101765,x101766),f319(f66(x101762,x101766,x101765,x101763),x101761)),x101764))+~P1(f319(f55(x101765),x101764))
% 28.25/28.13 [10229]~P79(x102292)+~E(f319(x102293,f319(x102295,f414(x102291,x102293,x102295,x102296,x102294,x102292))),f2(x102292))+~P1(f319(f55(x102294),x102296))+E(f319(f319(f6(x102291,x102292),x102293),f319(f302(x102294,x102291,x102295),x102296)),f319(f319(f6(x102294,x102292),f319(f66(x102291,x102292,x102294,x102293),x102295)),x102296))
% 28.25/28.13 [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),f414(x102891,x102893,x102895,x102896,x102894,x102892)),x102896))
% 28.25/28.13 [10290]~P79(x102902)+~P1(f319(f55(x102904),x102906))+E(f319(f319(f6(x102901,x102902),x102903),f319(f302(x102904,x102901,x102905),x102906)),f319(f319(f6(x102904,x102902),f319(f66(x102901,x102902,x102904,x102903),x102905)),x102906))+P1(f319(f319(f321(x102904),f413(x102901,x102903,x102905,x102906,x102904,x102902)),x102906))
% 28.25/28.13 [10370]~P41(f932(f931(x103704,x103705),a923),f932(f931(x103704,x103705),a923),x103706)+~P1(f319(f319(x103701,f548(x103701,x103706,x103703,x103702,x103705,x103704)),f553(x103701,x103706,x103703,x103702,x103705,x103704)))+P1(f319(f319(x103701,x103702),x103703))+~P1(f319(f319(f321(f931(x103704,x103705)),f319(f319(f244(x103704,x103705),x103702),x103703)),f87(f932(f931(x103704,x103705),a923),x103706)))
% 28.25/28.13 [10416]~P78(x104161)+~P1(f319(f55(x104162),x104166))+E(f319(f319(f319(f59(x104161,x104162,f75(x104161)),f319(f319(f18(x104162,f932(x104163,a923),x104161),f319(f319(f7(x104162,x104161,f932(f932(x104163,a923),x104161)),f319(f319(f8(f932(x104163,x104161),f932(x104161,f932(f932(x104163,a923),x104161)),x104162),f59(x104161,x104163,f75(x104161))),x104164)),f72(x104161))),x104165)),f72(x104161)),x104166),f319(f319(f319(f59(x104161,f931(x104162,x104163),f75(x104161)),f319(f249(x104162,x104163,x104161),x104164)),f72(x104161)),f319(f319(f246(x104162,x104163),x104166),x104165)))+P1(f319(f319(f321(x104162),f580(x104164,x104165,x104163,x104166,x104162,x104161)),x104166))
% 28.25/28.13 [10438]~P78(x104381)+~P1(f319(f55(x104382),x104386))+E(f319(f319(f319(f59(x104381,x104382,f75(x104381)),f319(f319(f18(x104382,f932(x104383,a923),x104381),f319(f319(f7(x104382,x104381,f932(f932(x104383,a923),x104381)),f319(f319(f8(f932(x104383,x104381),f932(x104381,f932(f932(x104383,a923),x104381)),x104382),f59(x104381,x104383,f75(x104381))),x104384)),f72(x104381))),x104385)),f72(x104381)),x104386),f319(f319(f319(f59(x104381,f931(x104382,x104383),f75(x104381)),f319(f249(x104382,x104383,x104381),x104384)),f72(x104381)),f319(f319(f246(x104382,x104383),x104386),x104385)))+~P1(f319(f55(x104383),f319(x104385,f580(x104384,x104385,x104383,x104386,x104382,x104381))))
% 28.25/28.13 [8497]~P22(x84972,x84975,x84976,x84971)+~P1(f319(f55(x84972),x84974))+~P1(f319(f55(x84972),x84973))+E(f319(x84971,f319(f319(f102(f932(x84972,a923)),x84973),x84974)),f319(f66(x84975,x84975,x84975,f319(x84971,x84973)),f319(x84971,x84974)))
% 28.25/28.13 [8717]~P6(x87171)+P1(f319(f319(f226(x87171),f319(x87172,x87173)),x87174))+~P1(f319(f319(f321(x87175),x87173),x87176))+~P1(f319(f319(f226(x87171),f319(f319(f33(x87175,x87171),x87176),x87172)),x87174))
% 28.25/28.13 [9153]~P26(x91532,x91531,x91533,x91536)+E(f319(f319(f93(f932(x91531,a923)),f319(f302(x91532,x91531,x91533),x91534)),f319(f302(x91532,x91531,x91533),x91535)),f319(f302(x91532,x91531,x91533),f319(f319(f93(f932(x91532,a923)),x91534),x91535)))+~P1(f319(f319(f226(f932(x91532,a923)),x91535),x91536))+~P1(f319(f319(f226(f932(x91532,a923)),x91534),x91536))
% 28.25/28.13 [9154]~P26(x91542,x91541,x91543,x91546)+E(f319(f319(f23(f932(x91541,a923)),f319(f302(x91542,x91541,x91543),x91544)),f319(f302(x91542,x91541,x91543),x91545)),f319(f302(x91542,x91541,x91543),f319(f319(f23(f932(x91542,a923)),x91544),x91545)))+~P1(f319(f319(f226(f932(x91542,a923)),x91545),x91546))+~P1(f319(f319(f226(f932(x91542,a923)),x91544),x91546))
% 28.25/28.13 [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))
% 28.25/28.13 [9417]E(x94171,x94172)+~P59(x94173,x94174,x94175)+~P1(f319(f319(f321(f931(x94173,x94174)),f319(f319(f244(x94173,x94174),x94176),x94172)),x94175))+~P1(f319(f319(f321(f931(x94173,x94174)),f319(f319(f244(x94173,x94174),x94176),x94171)),x94175))
% 28.25/28.13 [10224]~P76(x102241)+~E(f319(x102243,f527(x102244,x102246,x102243,x102245,x102242,x102241)),f319(x102246,f527(x102244,x102246,x102243,x102245,x102242,x102241)))+~P1(f319(f55(x102242),x102245))+E(f319(f319(f319(f59(x102241,x102242,f75(x102241)),x102243),x102244),x102245),f319(f319(f319(f59(x102241,x102242,f75(x102241)),x102246),x102244),x102245))
% 28.25/28.13 [10286]~P76(x102861)+~P1(f319(f55(x102862),x102865))+E(f319(f319(f319(f59(x102861,x102862,f75(x102861)),x102863),x102864),x102865),f319(f319(f319(f59(x102861,x102862,f75(x102861)),x102866),x102864),x102865))+P1(f319(f319(f321(x102862),f527(x102864,x102863,x102866,x102865,x102862,x102861)),x102865))
% 28.25/28.13 [8947]~P76(x89471)+~P1(f319(f55(x89472),x89476))+P1(f319(f319(f321(x89472),x89475),x89476))+E(f319(f319(f319(f59(x89471,x89472,f75(x89471)),x89473),x89474),f319(f319(f301(x89472),x89475),x89476)),f319(f319(f75(x89471),f319(x89473,x89475)),f319(f319(f319(f59(x89471,x89472,f75(x89471)),x89473),x89474),x89476)))
% 28.25/28.13 [9001]~P9(x90011,x90016,x90013)+~P12(x90011,f932(x90012,a923),x90013,x90015)+~P1(f319(f319(f321(x90011),x90014),x90016))+E(f319(f319(f33(x90011,f932(x90012,a923)),f319(f277(x90011,x90011,x90013),f319(f319(f301(x90011),x90014),f180(f932(x90011,a923))))),x90015),f319(x90015,x90014))
% 28.25/28.13 [9128]~P18(x91283,x91284,x91281)+~P1(f319(f55(x91283),x91286))+~P1(f319(f319(f321(x91283),x91282),x91286))+E(f319(f319(x91281,x91282),f319(f319(f58(x91283,x91284,x91281),x91285),f319(f319(f23(f932(x91283,a923)),x91286),f319(f319(f301(x91283),x91282),f180(f932(x91283,a923)))))),f319(f319(f58(x91283,x91284,x91281),x91285),x91286))
% 28.25/28.13 [9428]~P21(x94283,x94281,x94286,x94282)+~P1(f319(f55(x94283),x94285))+~P1(f319(f55(x94283),x94284))+E(f319(f66(x94281,x94281,x94281,f319(x94282,f319(f319(f102(f932(x94283,a923)),x94284),x94285))),f319(x94282,f319(f319(f93(f932(x94283,a923)),x94284),x94285))),f319(f66(x94281,x94281,x94281,f319(x94282,x94284)),f319(x94282,x94285)))
% 28.25/28.13 [10448]~P41(f932(f931(x104484,x104485),a923),f932(f931(x104484,x104485),a923),x104486)+P1(f319(f319(x104481,x104482),x104483))+~P1(f319(f319(f321(f931(x104484,x104485)),f319(f319(f244(x104484,x104485),x104482),x104483)),f87(f932(f931(x104484,x104485),a923),x104486)))+P1(f319(f319(f321(f931(x104484,x104485)),f319(f319(f244(x104484,x104485),f548(x104481,x104486,x104483,x104482,x104485,x104484)),f553(x104481,x104486,x104483,x104482,x104485,x104484))),f319(x104486,f319(f319(f93(f932(f931(x104484,x104485),a923)),f87(f932(f931(x104484,x104485),a923),x104486)),f319(f254(f931(x104484,x104485)),f319(f249(x104484,x104485,a923),x104481))))))
% 28.25/28.13 [9776]~E(x97763,f319(f319(f151(x97761,x97762),x97765),x97766))+P1(f319(f319(f321(f931(f926(x97761),f926(x97761))),f319(f319(f244(f926(x97761),f926(x97761)),x97762),x97763)),f149(x97761,x97764)))+~P1(f319(f319(f227(a925),x97765),f319(f181(f926(x97761)),x97762)))+~P1(f319(f319(f321(f931(x97761,x97761)),f319(f319(f244(x97761,x97761),f319(f319(f156(x97761),x97762),x97765)),x97766)),x97764))
% 28.25/28.13 [10303]~P79(x103032)+~P1(f319(f55(x103031),x103036))+P1(f319(f319(f321(x103031),f581(x103034,x103035,x103033,x103036,x103031,x103032)),x103036))+E(f319(f319(f6(x103031,x103032),f319(f319(f18(x103031,f932(x103033,a923),x103032),f319(f319(f8(f932(x103033,x103032),f932(f932(x103033,a923),x103032),x103031),f6(x103033,x103032)),x103034)),x103035)),x103036),f319(f319(f6(f931(x103031,x103033),x103032),f319(f249(x103031,x103033,x103032),x103034)),f319(f319(f246(x103031,x103033),x103036),x103035)))
% 28.25/28.13 [10304]~P78(x103042)+~P1(f319(f55(x103041),x103046))+P1(f319(f319(f321(x103041),f582(x103044,x103045,x103043,x103046,x103041,x103042)),x103046))+E(f319(f319(f9(x103041,x103042),f319(f319(f18(x103041,f932(x103043,a923),x103042),f319(f319(f8(f932(x103043,x103042),f932(f932(x103043,a923),x103042),x103041),f9(x103043,x103042)),x103044)),x103045)),x103046),f319(f319(f9(f931(x103041,x103043),x103042),f319(f249(x103041,x103043,x103042),x103044)),f319(f319(f246(x103041,x103043),x103046),x103045)))
% 28.25/28.13 [10343]~P79(x103432)+~P1(f319(f55(x103431),x103436))+~P1(f319(f55(x103433),f319(x103435,f581(x103434,x103435,x103433,x103436,x103431,x103432))))+E(f319(f319(f6(x103431,x103432),f319(f319(f18(x103431,f932(x103433,a923),x103432),f319(f319(f8(f932(x103433,x103432),f932(f932(x103433,a923),x103432),x103431),f6(x103433,x103432)),x103434)),x103435)),x103436),f319(f319(f6(f931(x103431,x103433),x103432),f319(f249(x103431,x103433,x103432),x103434)),f319(f319(f246(x103431,x103433),x103436),x103435)))
% 28.25/28.13 [10344]~P78(x103442)+~P1(f319(f55(x103441),x103446))+~P1(f319(f55(x103443),f319(x103445,f582(x103444,x103445,x103443,x103446,x103441,x103442))))+E(f319(f319(f9(x103441,x103442),f319(f319(f18(x103441,f932(x103443,a923),x103442),f319(f319(f8(f932(x103443,x103442),f932(f932(x103443,a923),x103442),x103441),f9(x103443,x103442)),x103444)),x103445)),x103446),f319(f319(f9(f931(x103441,x103443),x103442),f319(f249(x103441,x103443,x103442),x103444)),f319(f319(f246(x103441,x103443),x103446),x103445)))
% 28.25/28.13 [10326]~P78(x103262)+~P1(f319(f55(x103261),x103266))+P1(f319(f319(f321(x103261),x103263),x103266))+E(f319(f319(f9(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)),x103265)),x103266),f319(f319(f236(x103262),x103265),f319(f29(x103261),x103266)))
% 28.25/28.13 [10329]~P78(x103292)+~P1(f319(f55(x103291),x103296))+~P1(f319(f319(f321(x103291),x103293),x103296))+E(f319(f319(f9(x103291,x103292),f319(f319(f7(x103291,x103292,x103292),f319(f319(f18(x103291,x103292,f932(x103292,x103292)),f319(f319(f8(a923,f932(x103292,f932(x103292,x103292)),x103291),f86(x103292)),f319(f319(f7(x103291,x103291,a923),a316),x103293))),x103294)),x103295)),x103296),f319(f319(f75(x103292),f319(x103294,x103293)),f319(f319(f236(x103292),x103295),f319(f319(f23(a925),f319(f29(x103291),x103296)),f72(a925)))))
% 28.25/28.13 [10406]~P1(f319(f55(x104061),x104065))+~P1(f319(f55(x104062),x104063))+P1(f319(f319(f321(x104062),f459(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(f75(a925),x104066),f319(f29(x104062),x104063)))
% 28.25/28.13 [10407]~P1(f319(f55(x104071),x104075))+~P1(f319(f55(x104072),x104073))+P1(f319(f319(f321(x104072),f464(x104076,x104074,x104073,x104072,x104075,x104071)),x104073))+E(f319(f319(f6(x104071,a925),f319(f319(f8(f932(x104072,a923),a925,x104071),f29(x104072)),f319(f319(f8(f932(x104072,a923),f932(x104072,a923),x104071),f254(x104072)),f319(f319(f8(f932(x104072,a923),f932(x104072,a923),x104071),f319(f18(x104072,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104072),a317),f319(f319(f7(x104072,f932(x104072,a923),a923),f321(x104072)),x104073)))),x104074)))),x104075),f319(f319(f6(x104072,a925),x104076),x104073))
% 28.25/28.13 [10452]~P1(f319(f55(x104522),x104523))+~P1(f319(f55(x104521),x104525))+~E(f319(f29(x104521),f319(f254(x104521),f319(f319(f18(x104521,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104521),a317),f319(f319(f7(x104521,f932(x104521,a923),a923),f321(x104521)),x104525))),f319(f319(f7(x104521,x104522,a923),x104524),f459(x104526,x104524,x104523,x104522,x104525,x104521))))),x104526)+E(f319(f319(f6(x104521,a925),f319(f319(f8(f932(x104522,a923),a925,x104521),f29(x104522)),f319(f319(f8(f932(x104522,a923),f932(x104522,a923),x104521),f254(x104522)),f319(f319(f8(f932(x104522,a923),f932(x104522,a923),x104521),f319(f18(x104522,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104522),a317),f319(f319(f7(x104522,f932(x104522,a923),a923),f321(x104522)),x104523)))),x104524)))),x104525),f319(f319(f75(a925),x104526),f319(f29(x104522),x104523)))
% 28.25/28.13 [10454]~P1(f319(f55(x104542),x104543))+~P1(f319(f55(x104541),x104545))+~E(f319(f29(x104541),f319(f254(x104541),f319(f319(f18(x104541,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104541),a317),f319(f319(f7(x104541,f932(x104541,a923),a923),f321(x104541)),x104545))),f319(f319(f7(x104541,x104542,a923),x104544),f464(x104546,x104544,x104543,x104542,x104545,x104541))))),f319(x104546,f464(x104546,x104544,x104543,x104542,x104545,x104541)))+E(f319(f319(f6(x104541,a925),f319(f319(f8(f932(x104542,a923),a925,x104541),f29(x104542)),f319(f319(f8(f932(x104542,a923),f932(x104542,a923),x104541),f254(x104542)),f319(f319(f8(f932(x104542,a923),f932(x104542,a923),x104541),f319(f18(x104542,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104542),a317),f319(f319(f7(x104542,f932(x104542,a923),a923),f321(x104542)),x104543)))),x104544)))),x104545),f319(f319(f6(x104542,a925),x104546),x104543))
% 28.25/28.13 [10071]E(x100711,x100712)+~P18(x100713,x100714,x100715)+~P1(f319(f60(x100713,x100714,x100715,x100716,x100717),x100712))+~P1(f319(f60(x100713,x100714,x100715,x100716,x100717),x100711))
% 28.25/28.13 [9698]~P35(x96981,x96982,x96983,x96985,x96987)+~P35(x96981,x96982,x96983,x96984,x96986)+P35(x96981,x96982,x96983,f319(f319(f126(x96981),x96984),x96985),f319(f319(f126(x96982),x96986),x96987))+~E(f319(f181(f926(x96981)),x96984),f319(f181(f926(x96982)),x96986))
% 28.25/28.13 [9853]P1(f319(x98531,x98532))+~P1(f319(f319(f321(x98537),x98532),f319(x98536,x98534)))+~P1(f319(x98531,f353(x98531,x98536,x98535,x98533,x98537)))+~P1(f319(f319(f321(x98533),x98534),x98535))
% 28.25/28.13 [10317]~P18(x103177,x103176,x103171)+E(f319(f319(x103171,x103172),f653(x103172,x103173,x103174,x103175,x103171,x103176,x103177)),x103173)+~P1(f319(f60(x103177,x103176,x103171,x103175,x103174),x103173))+~P1(f319(f319(f321(x103177),x103172),x103174))
% 28.25/28.13 [10384]~P18(x103841,x103842,x103843)+~P1(f319(f60(x103841,x103842,x103843,x103844,x103845),x103847))+P1(f319(f60(x103841,x103842,x103843,x103844,f319(f319(f23(f932(x103841,a923)),x103845),f319(f319(f301(x103841),x103846),f180(f932(x103841,a923))))),f653(x103846,x103847,x103845,x103844,x103843,x103842,x103841)))+~P1(f319(f319(f321(x103841),x103846),x103845))
% 28.25/28.13 [9499]P27(x94991,x94992,x94993,x94994,x94995)+~P27(x94991,x94992,x94993,x94996,x94997)+~E(f319(f302(x94991,x94992,x94993),x94994),x94995)+~P1(f319(f319(f226(f932(x94991,a923)),x94994),x94996))
% 28.25/28.13 [9742]~P27(x97421,x97422,x97423,x97425,x97427)+~P27(x97421,x97422,x97423,x97424,x97426)+P27(x97421,x97422,x97423,f319(f319(f102(f932(x97421,a923)),x97424),x97425),f319(f319(f102(f932(x97422,a923)),x97426),x97427))+~E(f319(f319(f93(f932(x97422,a923)),x97426),x97427),f180(f932(x97422,a923)))
% 28.25/28.13 [9747]~P76(x97471)+~P26(x97475,x97472,x97476,x97477)+~P1(f319(f55(x97475),x97477))+E(f319(f319(f319(f59(x97471,x97472,f75(x97471)),x97473),x97474),f319(f302(x97475,x97472,x97476),x97477)),f319(f319(f319(f59(x97471,x97475,f75(x97471)),f319(f66(x97472,x97471,x97475,x97473),x97476)),x97474),x97477))
% 28.25/28.13 [9876]~E(f319(f319(f301(x98761),x98765),x98766),f319(f319(f301(x98761),x98762),x98763))+~P1(f319(f60(x98761,x98761,x98764,x98762,x98763),x98767))+P1(f319(f319(f321(x98761),x98762),x98763))+P1(f319(f56(x98761,x98764,f319(f319(f301(x98761),x98765),x98766)),x98767))
% 28.25/28.13 [9969]P1(f319(x99691,x99692))+~P1(f319(f319(f321(x99693),x99692),f319(x99694,x99697)))+~P1(f319(f319(f321(x99696),x99697),x99695))+P1(f319(f319(f321(x99693),f353(x99691,x99694,x99695,x99696,x99693)),f319(f319(f33(x99696,f932(x99693,a923)),x99695),x99694)))
% 28.25/28.13 [9989]~P26(x99892,x99891,x99895,x99894)+~P26(x99891,x99893,x99896,f319(f302(x99892,x99891,x99895),x99894))+E(f319(f319(f66(x99891,x99892,x99893,f71(x99892,x99891,x99894,x99895)),f71(x99891,x99893,f319(f302(x99892,x99891,x99895),x99894),x99896)),x99897),f319(f71(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))))
% 28.25/28.13 [9990]~P26(x99902,x99901,x99905,x99904)+~P26(x99901,x99903,x99906,f319(f302(x99902,x99901,x99905),x99904))+E(f319(f319(f66(x99901,x99902,x99903,f85(x99902,x99901,x99904,x99905)),f85(x99901,x99903,f319(f302(x99902,x99901,x99905),x99904),x99906)),x99907),f319(f85(x99902,x99903,x99904,f319(f66(x99901,x99903,x99902,x99906),x99905)),x99907))+~P1(f319(f319(f321(x99903),x99907),f319(f302(x99901,x99903,x99906),f319(f302(x99902,x99901,x99905),x99904))))
% 28.25/28.13 [10318]~P18(x103187,x103186,x103181)+E(f319(f319(x103181,x103182),f654(x103183,x103184,x103182,x103185,x103181,x103186,x103187)),x103183)+P1(f319(f319(f321(x103187),x103182),x103184))+~P1(f319(f60(x103187,x103186,x103181,x103185,f319(f319(f301(x103187),x103182),x103184)),x103183))
% 28.25/28.13 [10383]~P18(x103831,x103834,x103835)+P1(f319(f60(x103831,x103834,x103835,x103836,x103833),f654(x103837,x103833,x103832,x103836,x103835,x103834,x103831)))+P1(f319(f319(f321(x103831),x103832),x103833))+~P1(f319(f60(x103831,x103834,x103835,x103836,f319(f319(f301(x103831),x103832),x103833)),x103837))
% 28.25/28.13 [10053]E(x100531,f2(a1))+~P1(f319(f43(x100533,x100531),f319(f319(f244(a1,a1),x100535),x100537)))+~P1(f319(f43(x100532,x100531),f319(f319(f244(a1,a1),x100534),x100536)))+P1(f319(f43(f319(f319(f74(a1),x100532),x100533),x100531),f319(f319(f244(a1,a1),f319(f319(f74(a1),f319(f319(f74(a1),x100534),x100535)),f319(f319(f30(a1),f319(f319(f74(a1),x100536),x100537)),x100531))),f39(a1,f319(f319(f74(a1),x100536),x100537),x100531))))
% 28.25/28.13 [10055]~P1(f319(f319(f227(a925),f2(a925)),x100553))+~P1(f319(f42(x100552,x100553),f319(f319(f244(a925,a925),x100555),x100557)))+~P1(f319(f42(x100551,x100553),f319(f319(f244(a925,a925),x100554),x100556)))+P1(f319(f42(f319(f319(f74(a925),x100551),x100552),x100553),f319(f319(f244(a925,a925),f319(f319(f74(a925),f319(f319(f74(a925),x100554),x100555)),f319(f319(f30(a925),f319(f319(f74(a925),x100556),x100557)),x100553))),f39(a925,f319(f319(f74(a925),x100556),x100557),x100553))))
% 28.25/28.13 [10451]~P79(x104512)+~P1(f319(f55(x104513),x104515))+~P1(f319(f55(x104511),x104517))+E(f319(f319(f6(x104511,x104512),f319(f319(f18(x104511,f932(x104513,a923),x104512),f319(f319(f8(f932(x104513,x104512),f932(f932(x104513,a923),x104512),x104511),f6(x104513,x104512)),x104514)),f319(f319(f8(f932(x104513,a923),f932(x104513,a923),x104511),f254(x104513)),f319(f319(f8(f932(x104513,a923),f932(x104513,a923),x104511),f319(f18(x104513,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104513),a317),f319(f319(f7(x104513,f932(x104513,a923),a923),f321(x104513)),x104515)))),x104516)))),x104517),f319(f319(f6(x104513,x104512),f319(f319(f18(x104513,f932(x104511,a923),x104512),f319(f319(f8(f932(x104511,x104512),f932(f932(x104511,a923),x104512),x104513),f6(x104511,x104512)),f319(f7(x104511,x104513,x104512),x104514))),f319(f319(f8(f932(x104511,a923),f932(x104511,a923),x104513),f254(x104511)),f319(f319(f8(f932(x104511,a923),f932(x104511,a923),x104513),f319(f18(x104511,a923,a923),f319(f319(f8(a923,f932(a923,a923),x104511),a317),f319(f319(f7(x104511,f932(x104511,a923),a923),f321(x104511)),x104517)))),f319(f7(x104511,x104513,a923),x104516))))),x104515))
% 28.25/28.13 [10404]~P23(x104048,x104047,x104046,x104045,x104041)+~E(f319(x104042,f866(x104044,x104042,x104043,x104041,x104045,x104046,x104047)),f319(x104044,f866(x104044,x104042,x104043,x104041,x104045,x104046,x104047)))+E(f319(f319(x104041,x104042),x104043),f319(f319(x104041,x104044),x104043))+~P1(f319(f55(x104047),x104043))
% 28.25/28.13 [9914]~P24(x99147,x99146,x99141,x99148,x99142,x99144)+E(f319(f319(x99141,f319(x99142,x99143)),f319(x99144,x99145)),f319(x99144,x99145))+~P1(f319(f55(x99146),x99145))+~P1(f319(f319(f321(x99146),x99143),x99145))
% 28.25/28.13 [9918]~P13(x99186,x99181,x99182,x99188,x99183,x99184)+~P9(x99186,x99187,x99188)+P12(x99181,x99182,x99183,f319(x99184,x99185))+~P1(f319(f319(f321(x99186),x99185),x99187))
% 28.25/28.13 [10423]~P23(x104238,x104235,x104237,x104236,x104231)+E(f319(f319(x104231,x104232),x104233),f319(f319(x104231,x104234),x104233))+~P1(f319(f55(x104235),x104233))+P1(f319(f319(f321(x104235),f866(x104232,x104234,x104233,x104231,x104236,x104237,x104235)),x104233))
% 28.25/28.13 [10503]~P1(f319(f319(x105031,x105036),x105035))+P1(f319(f319(x105031,f848(x105031,x105034,x105035,x105036,x105033,x105032,x105037,x105038)),f853(x105031,x105034,x105035,x105036,x105033,x105032,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),x105032),x105033)),f319(f319(f244(x105038,x105037),x105036),x105035))),f299(f931(x105038,x105037),x105034)))
% 28.25/28.13 [10504]~P1(f319(f319(x105041,x105046),x105045))+P1(f319(f319(x105041,f854(x105041,x105044,x105043,x105042,x105045,x105046,x105047,x105048)),f855(x105041,x105044,x105043,x105042,x105045,x105046,x105047,x105048)))+P1(f319(f319(x105041,x105042),x105043))+~P1(f319(f319(f321(f931(f931(x105048,x105047),f931(x105048,x105047))),f319(f319(f244(f931(x105048,x105047),f931(x105048,x105047)),f319(f319(f244(x105048,x105047),x105046),x105045)),f319(f319(f244(x105048,x105047),x105042),x105043))),f299(f931(x105048,x105047),x105044)))
% 28.25/28.13 [10515]~P1(f319(f319(x105151,f849(x105151,x105156,x105155,x105154,x105153,x105152,x105157,x105158)),f852(x105151,x105156,x105155,x105154,x105153,x105152,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),x105152),x105153)),f319(f319(f244(x105158,x105157),x105154),x105155))),f299(f931(x105158,x105157),x105156)))
% 28.25/28.13 [10516]~P1(f319(f319(x105161,f862(x105161,x105166,x105163,x105162,x105165,x105164,x105167,x105168)),f863(x105161,x105166,x105163,x105162,x105165,x105164,x105167,x105168)))+P1(f319(f319(x105161,x105162),x105163))+~P1(f319(f319(x105161,x105164),x105165))+~P1(f319(f319(f321(f931(f931(x105168,x105167),f931(x105168,x105167))),f319(f319(f244(f931(x105168,x105167),f931(x105168,x105167)),f319(f319(f244(x105168,x105167),x105164),x105165)),f319(f319(f244(x105168,x105167),x105162),x105163))),f299(f931(x105168,x105167),x105166)))
% 28.25/28.13 [10529]~P1(f319(f319(x105291,x105296),x105297))+P1(f319(f319(x105291,x105292),x105293))+P1(f319(f319(f321(f931(f931(x105294,x105295),f931(x105294,x105295))),f319(f319(f244(f931(x105294,x105295),f931(x105294,x105295)),f319(f319(f244(x105294,x105295),x105296),x105297)),f319(f319(f244(x105294,x105295),f854(x105291,x105298,x105293,x105292,x105297,x105296,x105295,x105294)),f855(x105291,x105298,x105293,x105292,x105297,x105296,x105295,x105294)))),f299(f931(x105294,x105295),x105298)))+~P1(f319(f319(f321(f931(f931(x105294,x105295),f931(x105294,x105295))),f319(f319(f244(f931(x105294,x105295),f931(x105294,x105295)),f319(f319(f244(x105294,x105295),x105296),x105297)),f319(f319(f244(x105294,x105295),x105292),x105293))),f299(f931(x105294,x105295),x105298)))
% 28.25/28.13 [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),f848(x105311,x105316,x105317,x105318,x105313,x105312,x105315,x105314)),f853(x105311,x105316,x105317,x105318,x105313,x105312,x105315,x105314))),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),x105312),x105313)),f319(f319(f244(x105314,x105315),x105318),x105317))),f299(f931(x105314,x105315),x105316)))
% 28.25/28.13 [9525]~P21(x95257,x95251,x95258,x95253)+~P1(f319(f55(x95257),x95255))+~P1(f319(f55(x95257),x95254))+E(f319(f66(x95251,x95251,x95252,f319(x95253,x95254)),f319(f66(x95251,x95251,x95252,f319(x95253,x95255)),x95256)),f319(f66(x95251,x95251,x95252,f319(x95253,x95255)),f319(f66(x95251,x95251,x95252,f319(x95253,x95254)),x95256)))
% 28.25/28.13 [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(x95341)),x95344)))
% 28.25/28.13 [9535]~P35(x95351,x95352,x95353,x95354,x95357)+P35(x95351,x95352,x95353,f319(f319(f151(x95351,x95354),x95355),x95356),f319(f319(f151(x95352,x95357),x95355),x95358))+~P1(f319(f319(x95353,x95356),x95358))+~P1(f319(f319(f227(a925),x95355),f319(f181(f926(x95352)),x95357)))
% 28.25/28.13 [9615]~P26(x96152,x96152,x96155,x96156)+~P23(x96153,x96152,x96157,x96158,x96151)+~P1(f319(f55(x96152),x96156))+E(f319(f319(x96151,f319(f66(x96152,x96153,x96152,x96154),x96155)),x96156),f319(f319(x96151,x96154),f319(f302(x96152,x96152,x96155),x96156)))
% 28.25/28.13 [9851]~P27(x98511,x98513,x98515,x98516,x98518)+~P27(x98513,x98512,x98514,x98518,x98517)+P27(x98511,x98512,f319(f66(x98513,x98512,x98511,x98514),x98515),x98516,x98517)+~P1(f319(f319(f226(f932(x98513,a923)),f319(f302(x98511,x98513,x98515),x98516)),x98518))
% 28.25/28.13 [9877]P27(x98771,x98772,x98773,x98774,x98775)+~P27(x98772,x98776,x98777,x98775,x98778)+~P27(x98771,x98776,f319(f66(x98772,x98776,x98771,x98777),x98773),x98774,x98778)+~P1(f319(f319(f226(f932(x98772,a923)),f319(f302(x98771,x98772,x98773),x98774)),x98775))
% 28.25/28.13 [9916]~P25(x99167,x99162,x99165,x99168,x99166,x99161)+~P1(f319(f55(x99162),x99164))+E(f319(x99161,f319(f319(f301(x99162),x99163),x99164)),f319(f319(x99165,f319(x99166,x99163)),f319(x99161,x99164)))+P1(f319(f319(f321(x99162),x99163),x99164))
% 28.25/28.13 [9928]~P24(x99286,x99285,x99281,x99287,x99288,x99282)+E(f319(f319(x99281,f319(x99282,x99283)),f319(x99282,x99284)),f319(x99282,x99284))+~P1(f319(f55(x99285),x99284))+~P1(f319(f319(f226(f932(x99285,a923)),x99283),x99284))
% 28.25/28.13 [9511]P1(f319(f319(f321(f931(f926(x95111),f926(x95111))),f319(f319(f244(f926(x95111),f926(x95111)),x95112),x95113)),f149(x95111,x95114)))+~E(x95113,f319(f319(f126(x95111),x95115),f319(f319(f143(x95111),x95116),x95117)))+~E(x95112,f319(f319(f126(x95111),x95115),f319(f319(f143(x95111),x95118),x95117)))+~P1(f319(f319(f321(f931(x95111,x95111)),f319(f319(f244(x95111,x95111),x95118),x95116)),x95114))
% 28.25/28.13 [9921]~P24(x99216,x99212,x99215,x99217,x99218,x99211)+~P1(f319(f55(x99212),x99214))+~P1(f319(f55(x99212),x99213))+E(f319(x99211,f319(f319(f102(f932(x99212,a923)),x99213),x99214)),f319(f319(x99215,f319(x99211,x99213)),f319(x99211,x99214)))
% 28.25/28.13 [10493]~P26(x104934,x104932,x104935,x104938)+E(f319(f319(f34(x104931,f932(x104932,a923)),x104933),f319(f319(f8(f932(x104934,a923),f932(x104932,a923),x104931),f302(x104934,x104932,x104935)),x104936)),f319(f302(x104934,x104932,x104935),f319(f319(f34(x104931,f932(x104934,a923)),x104933),x104936)))+~P1(f319(f319(f321(x104931),x104937),x104933))+P1(f319(f319(f321(x104931),f899(x104937,x104936,x104933,x104931,x104938,x104935,x104932,x104934)),x104933))
% 28.25/28.13 [10520]~P26(x105204,x105202,x105205,x105207)+E(f319(f319(f34(x105201,f932(x105202,a923)),x105203),f319(f319(f8(f932(x105204,a923),f932(x105202,a923),x105201),f302(x105204,x105202,x105205)),x105206)),f319(f302(x105204,x105202,x105205),f319(f319(f34(x105201,f932(x105204,a923)),x105203),x105206)))+~P1(f319(f319(f321(x105201),x105208),x105203))+~P1(f319(f319(f226(f932(x105204,a923)),f319(x105206,f899(x105208,x105206,x105203,x105201,x105207,x105205,x105202,x105204))),x105207))
% 28.25/28.13 [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),x105322),x105323)),f319(f319(f244(x105324,x105325),x105328),x105327))),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),f849(x105321,x105326,x105327,x105328,x105323,x105322,x105325,x105324)),f852(x105321,x105326,x105327,x105328,x105323,x105322,x105325,x105324))),f319(f319(f244(x105324,x105325),f848(x105321,x105326,x105327,x105328,x105323,x105322,x105325,x105324)),f853(x105321,x105326,x105327,x105328,x105323,x105322,x105325,x105324)))),x105326))
% 28.25/28.13 [10533]~P1(f319(f319(x105331,x105338),x105337))+P1(f319(f319(x105331,x105332),x105333))+~P1(f319(f319(f321(f931(f931(x105334,x105335),f931(x105334,x105335))),f319(f319(f244(f931(x105334,x105335),f931(x105334,x105335)),f319(f319(f244(x105334,x105335),x105338),x105337)),f319(f319(f244(x105334,x105335),x105332),x105333))),f299(f931(x105334,x105335),x105336)))+P1(f319(f319(f321(f931(f931(x105334,x105335),f931(x105334,x105335))),f319(f319(f244(f931(x105334,x105335),f931(x105334,x105335)),f319(f319(f244(x105334,x105335),f854(x105331,x105336,x105333,x105332,x105337,x105338,x105335,x105334)),f855(x105331,x105336,x105333,x105332,x105337,x105338,x105335,x105334))),f319(f319(f244(x105334,x105335),f862(x105331,x105336,x105333,x105332,x105337,x105338,x105335,x105334)),f863(x105331,x105336,x105333,x105332,x105337,x105338,x105335,x105334)))),x105336))
% 28.25/28.13 [10000]~P25(x100007,x100005,x100001,x100008,x100002,x100004)+~P1(f319(f55(x100005),x100006))+~P1(f319(f319(f321(x100005),x100003),x100006))+E(f319(f319(x100001,f319(x100002,x100003)),f319(x100004,f319(f319(f23(f932(x100005,a923)),x100006),f319(f319(f301(x100005),x100003),f180(f932(x100005,a923)))))),f319(x100004,x100006))
% 28.25/28.13 [10008]~P25(x100086,x100083,x100081,x100087,x100088,x100082)+~P1(f319(f55(x100083),x100085))+~P1(f319(f55(x100083),x100084))+E(f319(f319(x100081,f319(x100082,f319(f319(f102(f932(x100083,a923)),x100084),x100085))),f319(x100082,f319(f319(f93(f932(x100083,a923)),x100084),x100085))),f319(f319(x100081,f319(x100082,x100084)),f319(x100082,x100085)))
% 28.25/28.13 [10098]P44(x100981,x100982,x100983,x100984,x100985,f319(f319(x100983,x100986),x100987))+~P44(x100981,x100982,x100983,x100984,f319(f319(f23(f932(x100981,a923)),x100985),f319(f319(f301(x100981),x100988),f180(f932(x100981,a923)))),x100989)+~E(f319(f319(x100983,x100986),x100987),f319(f319(x100983,x100988),x100989))+~P1(f319(f319(f321(x100981),x100988),x100985))
% 28.25/28.13 [10035]~P13(x100356,x100357,x100358,x100359,x1003510,x100351)+E(f319(f319(x100351,x100352),x100353),f319(f319(x100351,x100354),x100355))+~P1(f319(f319(f321(f931(x100357,x100357)),f319(f319(f244(x100357,x100357),x100353),x100355)),x1003510))+~P1(f319(f319(f321(f931(x100356,x100356)),f319(f319(f244(x100356,x100356),x100352),x100354)),x100359))
% 28.25/28.13 [9775]E(x97751,f2(a1))+E(x97752,f2(a1))+E(f319(f319(f80(a1,f931(a1,a1)),f319(f319(a209,x97752),x97751)),f319(f319(f18(a1,a1,f931(a1,a1)),f319(f319(f8(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f319(f30(a1),x97752))),f319(f30(a1),x97751))),f207(x97752,x97751))+P1(f319(f319(f227(a1),x97751),f2(a1)))+~P1(f319(f307(f931(a1,a1),a213),f319(f319(f244(a1,a1),x97752),x97751)))
% 28.25/28.13 [9617]~P102(x96172)+E(x96171,f180(f932(x96172,a923)))+~P1(f319(f55(x96172),x96171))+P1(f319(f319(f321(x96172),f10(x96172,x96171)),x96171))+~P1(f319(f319(f321(x96172),f319(f319(f93(x96172),f911(x96171,x96172)),f913(x96171,x96172))),f319(f319(f301(x96172),f911(x96171,x96172)),f319(f319(f301(x96172),f913(x96171,x96172)),f180(f932(x96172,a923))))))
% 28.25/28.13 [9618]~P102(x96182)+E(x96181,f180(f932(x96182,a923)))+~P1(f319(f55(x96182),x96181))+P1(f319(f319(f321(x96182),f13(x96182,x96181)),x96181))+~P1(f319(f319(f321(x96182),f319(f319(f102(x96182),f915(x96181,x96182)),f918(x96181,x96182))),f319(f319(f301(x96182),f915(x96181,x96182)),f319(f319(f301(x96182),f918(x96181,x96182)),f180(f932(x96182,a923))))))
% 28.25/28.13 [9619]~P4(x96192)+E(x96191,f180(f932(x96192,a923)))+~P1(f319(f55(x96192),x96191))+P1(f319(f319(f321(x96192),f14(x96192,x96191)),x96191))+~P1(f319(f319(f321(x96192),f319(f319(f224(x96192),f489(x96191,x96192)),f491(x96191,x96192))),f319(f319(f301(x96192),f489(x96191,x96192)),f319(f319(f301(x96192),f491(x96191,x96192)),f180(f932(x96192,a923))))))
% 28.25/28.13 [9620]~P4(x96202)+E(x96201,f180(f932(x96202,a923)))+~P1(f319(f55(x96202),x96201))+P1(f319(f319(f321(x96202),f15(x96202,x96201)),x96201))+~P1(f319(f319(f321(x96202),f319(f319(f225(x96202),f480(x96201,x96202)),f490(x96201,x96202))),f319(f319(f301(x96202),f480(x96201,x96202)),f319(f319(f301(x96202),f490(x96201,x96202)),f180(f932(x96202,a923))))))
% 28.25/28.13 [9652]~P76(x96522)+E(x96521,f180(f932(x96522,a923)))+~P1(f319(f55(x96522),x96521))+P1(f319(f319(f321(x96522),f319(f57(x96522,f75(x96522)),x96521)),x96521))+~P1(f319(f319(f321(x96522),f319(f319(f75(x96522),f346(x96521,x96522)),f347(x96521,x96522))),f319(f319(f301(x96522),f346(x96521,x96522)),f319(f319(f301(x96522),f347(x96521,x96522)),f180(f932(x96522,a923))))))
% 28.25/28.13 [9657]~P4(x96572)+E(x96571,f180(f932(x96572,a923)))+~P1(f319(f55(x96572),x96571))+P1(f319(f319(f321(x96572),f11(x96572,f224(x96572),x96571)),x96571))+~P1(f319(f319(f321(x96572),f319(f319(f224(x96572),f481(x96571,x96572)),f482(x96571,x96572))),f319(f319(f301(x96572),f481(x96571,x96572)),f319(f319(f301(x96572),f482(x96571,x96572)),f180(f932(x96572,a923))))))
% 28.25/28.13 [9658]~P4(x96582)+E(x96581,f180(f932(x96582,a923)))+~P1(f319(f55(x96582),x96581))+P1(f319(f319(f321(x96582),f12(x96582,f225(x96582),x96581)),x96581))+~P1(f319(f319(f321(x96582),f319(f319(f225(x96582),f483(x96581,x96582)),f484(x96581,x96582))),f319(f319(f301(x96582),f483(x96581,x96582)),f319(f319(f301(x96582),f484(x96581,x96582)),f180(f932(x96582,a923))))))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [7289]~P4(x72892)+~P14(x72892,x72891)+E(x72891,f105(x72892))+~P1(f319(f319(f321(x72892),x72893),f319(f164(x72892),f729(x72891,x72892))))+P1(f319(f319(f226(x72892),f748(x72891,x72892)),x72893))
% 28.25/28.13 [7461]~P4(x74611)+E(f14(x74611,x74612),x74613)+~P1(f319(f55(x74611),x74612))+~P1(f319(f319(f226(x74611),x74613),f525(x74613,x74612,x74611)))+~P1(f319(f319(f321(x74611),x74613),x74612))
% 28.25/28.13 [7494]~P4(x74941)+~P14(x74941,x74942)+~P14(x74941,x74943)+P14(x74941,f319(f319(f126(x74941),x74942),x74943))+P1(f319(f319(f321(x74941),f735(x74943,x74942,x74941)),f319(f164(x74941),x74942)))
% 28.25/28.13 [7495]~P4(x74951)+~P14(x74951,x74952)+~P14(x74951,x74953)+P14(x74951,f319(f319(f126(x74951),x74952),x74953))+P1(f319(f319(f321(x74951),f736(x74953,x74952,x74951)),f319(f164(x74951),x74953)))
% 28.25/28.13 [7555]~P4(x75551)+E(f14(x75551,x75552),x75553)+~P1(f319(f55(x75551),x75552))+P1(f319(f319(f321(x75551),f525(x75553,x75552,x75551)),x75552))+~P1(f319(f319(f321(x75551),x75553),x75552))
% 28.25/28.13 [7556]~P4(x75561)+E(f15(x75561,x75562),x75563)+~P1(f319(f55(x75561),x75562))+P1(f319(f319(f321(x75561),f526(x75563,x75562,x75561)),x75562))+~P1(f319(f319(f321(x75561),x75563),x75562))
% 28.25/28.13 [8123]~P4(x81231)+E(f15(x81231,x81232),x81233)+~P1(f319(f55(x81231),x81232))+~P1(f319(f319(f321(x81231),x81233),x81232))+~P1(f319(f319(f226(x81231),f526(x81233,x81232,x81231)),x81233))
% 28.25/28.13 [8444]~P4(x84441)+~P14(x84441,x84442)+~P14(x84441,x84443)+P14(x84441,f319(f319(f126(x84441),x84442),x84443))+~P1(f319(f319(f226(x84441),f735(x84443,x84442,x84441)),f736(x84443,x84442,x84441)))
% 28.25/28.13 [9249]~P102(x92492)+E(x92491,f180(f932(x92492,a923)))+~E(f319(f319(f93(x92492),f319(x92493,f914(x92491,x92493,x92492))),f319(x92493,f919(x92491,x92493,x92492))),f319(x92493,f319(f319(f93(x92492),f914(x92491,x92493,x92492)),f919(x92491,x92493,x92492))))+E(f10(x92492,f319(f302(x92492,x92492,x92493),x92491)),f319(x92493,f10(x92492,x92491)))+~P1(f319(f55(x92492),x92491))
% 28.25/28.13 [9250]~P102(x92502)+E(x92501,f180(f932(x92502,a923)))+~E(f319(f319(f102(x92502),f319(x92503,f920(x92501,x92503,x92502))),f319(x92503,f337(x92501,x92503,x92502))),f319(x92503,f319(f319(f102(x92502),f920(x92501,x92503,x92502)),f337(x92501,x92503,x92502))))+E(f13(x92502,f319(f302(x92502,x92502,x92503),x92501)),f319(x92503,f13(x92502,x92501)))+~P1(f319(f55(x92502),x92501))
% 28.25/28.13 [9251]~P4(x92512)+E(x92511,f180(f932(x92512,a923)))+~E(f319(f319(f224(x92512),f319(x92513,f485(x92511,x92513,x92512))),f319(x92513,f499(x92511,x92513,x92512))),f319(x92513,f319(f319(f224(x92512),f485(x92511,x92513,x92512)),f499(x92511,x92513,x92512))))+E(f14(x92512,f319(f302(x92512,x92512,x92513),x92511)),f319(x92513,f14(x92512,x92511)))+~P1(f319(f55(x92512),x92511))
% 28.25/28.13 [9252]~P4(x92522)+E(x92521,f180(f932(x92522,a923)))+~E(f319(f319(f225(x92522),f319(x92523,f486(x92521,x92523,x92522))),f319(x92523,f498(x92521,x92523,x92522))),f319(x92523,f319(f319(f225(x92522),f486(x92521,x92523,x92522)),f498(x92521,x92523,x92522))))+E(f15(x92522,f319(f302(x92522,x92522,x92523),x92521)),f319(x92523,f15(x92522,x92521)))+~P1(f319(f55(x92522),x92521))
% 28.25/28.13 [9321]~P4(x93212)+E(x93211,f180(f932(x93212,a923)))+~E(f319(f319(f224(x93212),f319(x93213,f487(x93211,x93213,x93212))),f319(x93213,f496(x93211,x93213,x93212))),f319(x93213,f319(f319(f224(x93212),f487(x93211,x93213,x93212)),f496(x93211,x93213,x93212))))+E(f11(x93212,f224(x93212),f319(f302(x93212,x93212,x93213),x93211)),f319(x93213,f11(x93212,f224(x93212),x93211)))+~P1(f319(f55(x93212),x93211))
% 28.25/28.13 [9322]~P4(x93222)+E(x93221,f180(f932(x93222,a923)))+~E(f319(f319(f225(x93222),f319(x93223,f488(x93221,x93223,x93222))),f319(x93223,f494(x93221,x93223,x93222))),f319(x93223,f319(f319(f225(x93222),f488(x93221,x93223,x93222)),f494(x93221,x93223,x93222))))+E(f12(x93222,f225(x93222),f319(f302(x93222,x93222,x93223),x93221)),f319(x93223,f12(x93222,f225(x93222),x93221)))+~P1(f319(f55(x93222),x93221))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [7296]~P102(x72962)+E(f319(f319(f102(x72962),f13(x72962,x72961)),f13(x72962,x72963)),f13(x72962,x72963))+E(x72961,f180(f932(x72962,a923)))+~P1(f319(f55(x72962),x72963))+~P1(f319(f319(f226(f932(x72962,a923)),x72961),x72963))
% 28.25/28.13 [7297]~P102(x72972)+E(f319(f319(f93(x72972),f10(x72972,x72971)),f10(x72972,x72973)),f10(x72972,x72973))+E(x72971,f180(f932(x72972,a923)))+~P1(f319(f55(x72972),x72973))+~P1(f319(f319(f226(f932(x72972,a923)),x72971),x72973))
% 28.25/28.13 [7298]~P4(x72982)+E(f319(f319(f224(x72982),f14(x72982,x72981)),f14(x72982,x72983)),f14(x72982,x72983))+E(x72981,f180(f932(x72982,a923)))+~P1(f319(f55(x72982),x72983))+~P1(f319(f319(f226(f932(x72982,a923)),x72981),x72983))
% 28.25/28.13 [7299]~P4(x72992)+E(f319(f319(f225(x72992),f15(x72992,x72991)),f15(x72992,x72993)),f15(x72992,x72993))+E(x72991,f180(f932(x72992,a923)))+~P1(f319(f55(x72992),x72993))+~P1(f319(f319(f226(f932(x72992,a923)),x72991),x72993))
% 28.25/28.13 [7602]~P4(x76022)+E(x76021,f180(f932(x76022,a923)))+~P1(f319(f55(x76022),x76023))+P1(f319(f319(f226(x76022),f14(x76022,x76023)),f14(x76022,x76021)))+~P1(f319(f319(f226(f932(x76022,a923)),x76021),x76023))
% 28.25/28.13 [7603]~P4(x76032)+E(x76031,f180(f932(x76032,a923)))+~P1(f319(f55(x76032),x76033))+P1(f319(f319(f226(x76032),f15(x76032,x76031)),f15(x76032,x76033)))+~P1(f319(f319(f226(f932(x76032,a923)),x76031),x76033))
% 28.25/28.13 [7656]~P102(x76561)+E(f10(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))
% 28.25/28.13 [7657]~P102(x76571)+E(f13(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))
% 28.25/28.13 [7658]~P4(x76581)+E(f14(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))
% 28.25/28.13 [7659]~P4(x76591)+E(f15(x76591,x76592),x76593)+~P1(f319(f55(x76591),x76592))+~E(f319(f319(f23(f932(x76591,a923)),x76592),f319(f319(f301(x76591),x76593),f180(f932(x76591,a923)))),f180(f932(x76591,a923)))+~P1(f319(f319(f321(x76591),x76593),x76592))
% 28.25/28.13 [7752]~P4(x77521)+E(f11(x77521,f224(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))
% 28.25/28.13 [7753]~P4(x77531)+E(f12(x77531,f225(x77531),x77532),x77533)+~P1(f319(f55(x77531),x77532))+~E(f319(f319(f23(f932(x77531,a923)),x77532),f319(f319(f301(x77531),x77533),f180(f932(x77531,a923)))),f180(f932(x77531,a923)))+~P1(f319(f319(f321(x77531),x77533),x77532))
% 28.25/28.13 [7788]~P108(x77882)+E(x77881,f180(f932(x77882,a923)))+~P1(f319(f55(x77882),x77881))+~P1(f319(f319(f226(x77882),x77883),f338(x77883,x77881,x77882)))+P1(f319(f319(f226(x77882),x77883),f319(f57(x77882,f93(x77882)),x77881)))
% 28.25/28.13 [7789]~P4(x77892)+E(x77891,f180(f932(x77892,a923)))+~P1(f319(f55(x77892),x77891))+~P1(f319(f319(f226(x77892),x77893),f475(x77893,x77891,x77892)))+P1(f319(f319(f226(x77892),x77893),f319(f57(x77892,f224(x77892)),x77891)))
% 28.25/28.13 [7790]~P4(x77902)+E(x77901,f180(f932(x77902,a923)))+~P1(f319(f55(x77902),x77901))+~P1(f319(f319(f227(x77902),x77903),f477(x77903,x77901,x77902)))+P1(f319(f319(f227(x77902),x77903),f319(f57(x77902,f224(x77902)),x77901)))
% 28.25/28.13 [7877]~P108(x78772)+E(x78771,f180(f932(x78772,a923)))+~P1(f319(f55(x78772),x78771))+P1(f319(f319(f321(x78772),f338(x78773,x78771,x78772)),x78771))+P1(f319(f319(f226(x78772),x78773),f319(f57(x78772,f93(x78772)),x78771)))
% 28.25/28.13 [7878]~P4(x78782)+E(x78781,f180(f932(x78782,a923)))+~P1(f319(f55(x78782),x78781))+P1(f319(f319(f321(x78782),f475(x78783,x78781,x78782)),x78781))+P1(f319(f319(f226(x78782),x78783),f319(f57(x78782,f224(x78782)),x78781)))
% 28.25/28.13 [7879]~P4(x78792)+E(x78791,f180(f932(x78792,a923)))+~P1(f319(f55(x78792),x78791))+P1(f319(f319(f321(x78792),f477(x78793,x78791,x78792)),x78791))+P1(f319(f319(f227(x78792),x78793),f319(f57(x78792,f224(x78792)),x78791)))
% 28.25/28.13 [7999]~P4(x79992)+E(x79991,f180(f932(x79992,a923)))+E(f319(f319(f224(x79992),f11(x79992,f224(x79992),x79991)),f11(x79992,f224(x79992),x79993)),f11(x79992,f224(x79992),x79993))+~P1(f319(f55(x79992),x79993))+~P1(f319(f319(f226(f932(x79992,a923)),x79991),x79993))
% 28.25/28.13 [8000]~P4(x80002)+E(x80001,f180(f932(x80002,a923)))+E(f319(f319(f225(x80002),f12(x80002,f225(x80002),x80001)),f12(x80002,f225(x80002),x80003)),f12(x80002,f225(x80002),x80003))+~P1(f319(f55(x80002),x80003))+~P1(f319(f319(f226(f932(x80002,a923)),x80001),x80003))
% 28.25/28.13 [8202]~E(f502(x82021,x82023,x82022),f503(x82021,x82023,x82022))+~E(f319(f29(x82022),f504(x82021,x82023,x82022)),x82021)+E(f319(f319(f75(a925),x82021),f319(f29(f932(x82022,a923)),x82023)),f319(f29(x82022),f31(f932(x82022,a923),x82023)))+~P1(f319(f55(x82022),f31(f932(x82022,a923),x82023)))+~P1(f319(f55(f932(x82022,a923)),x82023))
% 28.25/28.13 [8383]~P4(x83832)+E(x83831,f180(f932(x83832,a923)))+~P1(f319(f55(x83832),x83833))+P1(f319(f319(f226(x83832),f319(f57(x83832,f224(x83832)),x83833)),f319(f57(x83832,f224(x83832)),x83831)))+~P1(f319(f319(f226(f932(x83832,a923)),x83831),x83833))
% 28.25/28.13 [8687]~E(f502(x86871,x86873,x86872),f503(x86871,x86873,x86872))+E(f319(f319(f75(a925),x86871),f319(f29(f932(x86872,a923)),x86873)),f319(f29(x86872),f31(f932(x86872,a923),x86873)))+P1(f319(f319(f321(f932(x86872,a923)),f504(x86871,x86873,x86872)),x86873))+~P1(f319(f55(x86872),f31(f932(x86872,a923),x86873)))+~P1(f319(f55(f932(x86872,a923)),x86873))
% 28.25/28.13 [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)),f503(x87131,x87133,x87132)),x87133))+~P1(f319(f55(x87132),f31(f932(x87132,a923),x87133)))+~P1(f319(f55(f932(x87132,a923)),x87133))
% 28.25/28.13 [8714]~E(f319(f29(x87142),f504(x87141,x87143,x87142)),x87141)+E(f319(f319(f75(a925),x87141),f319(f29(f932(x87142,a923)),x87143)),f319(f29(x87142),f31(f932(x87142,a923),x87143)))+P1(f319(f319(f321(f932(x87142,a923)),f502(x87141,x87143,x87142)),x87143))+~P1(f319(f55(x87142),f31(f932(x87142,a923),x87143)))+~P1(f319(f55(f932(x87142,a923)),x87143))
% 28.25/28.13 [8741]~E(f319(f29(x87412),f504(x87411,x87413,x87412)),x87411)+~E(f319(f319(f93(f932(x87412,a923)),f503(x87411,x87413,x87412)),f502(x87411,x87413,x87412)),f180(f932(x87412,a923)))+E(f319(f319(f75(a925),x87411),f319(f29(f932(x87412,a923)),x87413)),f319(f29(x87412),f31(f932(x87412,a923),x87413)))+~P1(f319(f55(f932(x87412,a923)),x87413))+~P1(f319(f55(x87412),f31(f932(x87412,a923),x87413)))
% 28.25/28.13 [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)),f503(x90071,x90073,x90072)),x90073))+~P1(f319(f55(f932(x90072,a923)),x90073))+~P1(f319(f55(x90072),f31(f932(x90072,a923),x90073)))
% 28.25/28.13 [9008]E(f319(f319(f75(a925),x90081),f319(f29(f932(x90082,a923)),x90083)),f319(f29(x90082),f31(f932(x90082,a923),x90083)))+P1(f319(f319(f321(f932(x90082,a923)),f504(x90081,x90083,x90082)),x90083))+P1(f319(f319(f321(f932(x90082,a923)),f502(x90081,x90083,x90082)),x90083))+~P1(f319(f55(f932(x90082,a923)),x90083))+~P1(f319(f55(x90082),f31(f932(x90082,a923),x90083)))
% 28.25/28.13 [9034]~E(f319(f319(f93(f932(x90342,a923)),f503(x90341,x90343,x90342)),f502(x90341,x90343,x90342)),f180(f932(x90342,a923)))+E(f319(f319(f75(a925),x90341),f319(f29(f932(x90342,a923)),x90343)),f319(f29(x90342),f31(f932(x90342,a923),x90343)))+~P1(f319(f55(f932(x90342,a923)),x90343))+P1(f319(f319(f321(f932(x90342,a923)),f504(x90341,x90343,x90342)),x90343))+~P1(f319(f55(x90342),f31(f932(x90342,a923),x90343)))
% 28.25/28.13 [9296]~P101(x92962)+E(x92961,f180(f932(x92962,a923)))+~E(f319(f319(f75(x92962),f319(x92963,f345(x92961,x92963,x92962))),f319(x92963,f348(x92961,x92963,x92962))),f319(x92963,f319(f319(f75(x92962),f345(x92961,x92963,x92962)),f348(x92961,x92963,x92962))))+~P1(f319(f55(x92962),x92961))+E(f319(f57(x92962,f75(x92962)),f319(f302(x92962,x92962,x92963),x92961)),f319(x92963,f319(f57(x92962,f75(x92962)),x92961)))
% 28.25/28.13 [10259]P1(f319(f319(x102591,x102592),x102593))+P1(f319(f319(f227(a1),f536(x102591,x102593,x102592)),f538(x102591,x102593,x102592)))+P1(f319(f319(f226(a1),f538(x102591,x102593,x102592)),f2(a1)))+P1(f319(f319(x102591,f536(x102591,x102593,x102592)),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(x102591,x102593,x102592))))+~P1(f319(f307(f931(a1,a1),a52),f319(f319(f244(a1,a1),x102592),x102593)))
% 28.25/28.13 [10265]P1(f319(f319(x102651,x102652),x102653))+P1(f319(f319(f226(a1),f535(x102651,x102653,x102652)),f2(a1)))+P1(f319(f319(x102651,f531(x102651,x102653,x102652)),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(x102651,x102653,x102652))))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),f531(x102651,x102653,x102652)),f535(x102651,x102653,x102652))))+~P1(f319(f307(f931(a1,a1),a46),f319(f319(f244(a1,a1),x102652),x102653)))
% 28.25/28.13 [8173]~P126(x81731)+~P1(f319(f319(f226(x81731),x81732),f72(x81731)))+~P1(f319(f319(f226(x81731),f2(x81731)),x81732))+~P1(f319(f319(f226(x81731),f2(x81731)),x81733))+P1(f319(f319(f226(x81731),f319(f319(f75(x81731),x81732),x81733)),x81733))
% 28.25/28.13 [8174]~P126(x81741)+~P1(f319(f319(f226(x81741),x81743),f72(x81741)))+~P1(f319(f319(f226(x81741),f2(x81741)),x81743))+~P1(f319(f319(f226(x81741),f2(x81741)),x81742))+P1(f319(f319(f226(x81741),f319(f319(f75(x81741),x81742),x81743)),x81742))
% 28.25/28.13 [8531]~P4(x85312)+E(x85311,f180(f932(x85312,a923)))+~P1(f319(f55(x85312),x85311))+P1(f319(f319(f226(x85312),f476(x85313,x85311,x85312)),x85313))+~P1(f319(f319(f226(x85312),f319(f57(x85312,f224(x85312)),x85311)),x85313))
% 28.25/28.13 [8532]~P4(x85322)+E(x85321,f180(f932(x85322,a923)))+~P1(f319(f55(x85322),x85321))+P1(f319(f319(f321(x85322),f476(x85323,x85321,x85322)),x85321))+~P1(f319(f319(f226(x85322),f319(f57(x85322,f224(x85322)),x85321)),x85323))
% 28.25/28.13 [8533]~P4(x85332)+E(x85331,f180(f932(x85332,a923)))+~P1(f319(f55(x85332),x85331))+P1(f319(f319(f321(x85332),f478(x85333,x85331,x85332)),x85331))+~P1(f319(f319(f227(x85332),f319(f57(x85332,f224(x85332)),x85331)),x85333))
% 28.25/28.13 [8534]~P4(x85342)+E(x85341,f180(f932(x85342,a923)))+~P1(f319(f55(x85342),x85341))+P1(f319(f319(f227(x85342),f478(x85343,x85341,x85342)),x85343))+~P1(f319(f319(f227(x85342),f319(f57(x85342,f224(x85342)),x85341)),x85343))
% 28.25/28.13 [8621]~P1(f319(x86211,x86213))+P1(f319(x86211,f390(x86211,x86212)))+P1(f319(x86211,f379(x86211,x86212)))+~P1(f319(f319(f227(a1),f2(a1)),x86212))+P1(f319(x86211,f319(f319(f23(a1),f379(x86211,x86212)),f319(f319(f75(a1),f391(x86211,x86212)),x86212))))
% 28.25/28.13 [8843]~P1(f319(x88431,x88433))+P1(f319(x88431,f379(x88431,x88432)))+~P1(f319(f319(f227(a1),f2(a1)),x88432))+P1(f319(f319(f321(a1),f390(x88431,x88432)),f295(a1,f72(a1),x88432)))+P1(f319(x88431,f319(f319(f23(a1),f379(x88431,x88432)),f319(f319(f75(a1),f391(x88431,x88432)),x88432))))
% 28.25/28.13 [9056]~P1(f319(x90561,x90563))+~P1(f319(x90561,f379(x90561,x90562)))+P1(f319(x90561,f390(x90561,x90562)))+~P1(f319(f319(f227(a1),f2(a1)),x90562))+~P1(f319(x90561,f319(f319(f23(a1),f379(x90561,x90562)),f319(f319(f75(a1),f391(x90561,x90562)),x90562))))
% 28.25/28.13 [9185]~P1(f319(x91851,x91853))+~P1(f319(x91851,f379(x91851,x91852)))+~P1(f319(f319(f227(a1),f2(a1)),x91852))+P1(f319(f319(f321(a1),f390(x91851,x91852)),f295(a1,f72(a1),x91852)))+~P1(f319(x91851,f319(f319(f23(a1),f379(x91851,x91852)),f319(f319(f75(a1),f391(x91851,x91852)),x91852))))
% 28.25/28.13 [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(f93(x89611),x89613),f10(x89611,f319(f319(f23(f932(x89611,a923)),x89612),f319(f319(f301(x89611),x89613),f180(f932(x89611,a923)))))),f10(x89611,x89612))
% 28.25/28.13 [8962]~P102(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(f102(x89621),x89623),f13(x89621,f319(f319(f23(f932(x89621,a923)),x89622),f319(f319(f301(x89621),x89623),f180(f932(x89621,a923)))))),f13(x89621,x89622))
% 28.25/28.13 [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(f224(x89631),x89633),f14(x89631,f319(f319(f23(f932(x89631,a923)),x89632),f319(f319(f301(x89631),x89633),f180(f932(x89631,a923)))))),f14(x89631,x89632))
% 28.25/28.13 [8964]~P4(x89641)+~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)))+~P1(f319(f319(f321(x89641),x89643),x89642))+E(f319(f319(f225(x89641),x89643),f15(x89641,f319(f319(f23(f932(x89641,a923)),x89642),f319(f319(f301(x89641),x89643),f180(f932(x89641,a923)))))),f15(x89641,x89642))
% 28.25/28.13 [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(f224(x90271),x90273),f11(x90271,f224(x90271),f319(f319(f23(f932(x90271,a923)),x90272),f319(f319(f301(x90271),x90273),f180(f932(x90271,a923)))))),f11(x90271,f224(x90271),x90272))
% 28.25/28.13 [9028]~P4(x90281)+~P1(f319(f55(x90281),x90282))+E(f319(f319(f23(f932(x90281,a923)),x90282),f319(f319(f301(x90281),x90283),f180(f932(x90281,a923)))),f180(f932(x90281,a923)))+~P1(f319(f319(f321(x90281),x90283),x90282))+E(f319(f319(f225(x90281),x90283),f12(x90281,f225(x90281),f319(f319(f23(f932(x90281,a923)),x90282),f319(f319(f301(x90281),x90283),f180(f932(x90281,a923)))))),f12(x90281,f225(x90281),x90282))
% 28.25/28.13 [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(f102(x90431),f13(x90431,f319(f319(f102(f932(x90431,a923)),x90432),x90433))),f13(x90431,f319(f319(f93(f932(x90431,a923)),x90432),x90433))),f319(f319(f102(x90431),f13(x90431,x90432)),f13(x90431,x90433)))
% 28.25/28.13 [9044]~P102(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(f93(x90441),f10(x90441,f319(f319(f102(f932(x90441,a923)),x90442),x90443))),f10(x90441,f319(f319(f93(f932(x90441,a923)),x90442),x90443))),f319(f319(f93(x90441),f10(x90441,x90442)),f10(x90441,x90443)))
% 28.25/28.13 [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(f224(x90451),f14(x90451,f319(f319(f102(f932(x90451,a923)),x90452),x90453))),f14(x90451,f319(f319(f93(f932(x90451,a923)),x90452),x90453))),f319(f319(f224(x90451),f14(x90451,x90452)),f14(x90451,x90453)))
% 28.25/28.13 [9046]~P4(x90461)+~P1(f319(f55(x90461),x90463))+~P1(f319(f55(x90461),x90462))+E(f319(f319(f93(f932(x90461,a923)),x90462),x90463),f180(f932(x90461,a923)))+E(f319(f319(f225(x90461),f15(x90461,f319(f319(f102(f932(x90461,a923)),x90462),x90463))),f15(x90461,f319(f319(f93(f932(x90461,a923)),x90462),x90463))),f319(f319(f225(x90461),f15(x90461,x90462)),f15(x90461,x90463)))
% 28.25/28.13 [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(f224(x92681),f11(x92681,f224(x92681),f319(f319(f102(f932(x92681,a923)),x92682),x92683))),f11(x92681,f224(x92681),f319(f319(f93(f932(x92681,a923)),x92682),x92683))),f319(f319(f224(x92681),f11(x92681,f224(x92681),x92682)),f11(x92681,f224(x92681),x92683)))
% 28.25/28.13 [9269]~P4(x92691)+~P1(f319(f55(x92691),x92693))+~P1(f319(f55(x92691),x92692))+E(f319(f319(f93(f932(x92691,a923)),x92692),x92693),f180(f932(x92691,a923)))+E(f319(f319(f225(x92691),f12(x92691,f225(x92691),f319(f319(f102(f932(x92691,a923)),x92692),x92693))),f12(x92691,f225(x92691),f319(f319(f93(f932(x92691,a923)),x92692),x92693))),f319(f319(f225(x92691),f12(x92691,f225(x92691),x92692)),f12(x92691,f225(x92691),x92693)))
% 28.25/28.13 [10095]~P129(x100953)+E(x100951,x100952)+~P1(f319(f319(f226(x100953),f2(x100953)),x100952))+~P1(f319(f319(f226(x100953),f2(x100953)),x100951))+~E(f319(f319(f236(x100953),x100951),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(x100953),x100952),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)))))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)
% 28.25/28.13 [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)
% 28.25/28.13 [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)
% 28.25/28.13 [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)))
% 28.25/28.13 [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)))
% 28.25/28.13 [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)
% 28.25/28.13 [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)
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [7175]~P129(x71753)+E(x71751,x71752)+~E(f319(f319(f236(x71753),x71751),f319(a104,x71754)),f319(f319(f236(x71753),x71752),f319(a104,x71754)))+~P1(f319(f319(f226(x71753),f2(x71753)),x71752))+~P1(f319(f319(f226(x71753),f2(x71753)),x71751))
% 28.25/28.13 [7387]~E(f359(x73872,x73873,x73871,x73874),x73874)+~E(f319(x73872,x73874),f72(a925))+E(f319(f319(f6(x73871,a925),x73872),x73873),f72(a925))+~P1(f319(f55(x73871),x73873))+~P1(f319(f319(f321(x73871),x73874),x73873))
% 28.25/28.13 [7394]~P121(x73944)+~P138(x73944)+E(f319(x73941,f455(x73941,x73942,x73943,x73944)),f2(x73944))+~E(f319(f319(f9(x73943,x73944),x73941),x73942),f2(x73944))+~P1(f319(f55(x73943),x73942))
% 28.25/28.13 [7484]~E(f421(x74842,x74843,x74841,x74844),x74844)+~E(f319(x74842,x74844),f319(a104,f2(a925)))+E(f319(f319(f6(x74841,a925),x74842),x74843),f319(a104,f2(a925)))+~P1(f319(f55(x74841),x74843))+~P1(f319(f319(f321(x74841),x74844),x74843))
% 28.25/28.13 [8215]~E(f319(x82152,x82154),f72(a925))+~E(f319(x82152,f359(x82152,x82153,x82151,x82154)),f2(a925))+E(f319(f319(f6(x82151,a925),x82152),x82153),f72(a925))+~P1(f319(f55(x82151),x82153))+~P1(f319(f319(f321(x82151),x82154),x82153))
% 28.25/28.13 [8253]~E(f319(x82532,x82534),f319(a104,f2(a925)))+~E(f319(x82532,f421(x82532,x82533,x82531,x82534)),f2(a925))+E(f319(f319(f6(x82531,a925),x82532),x82533),f319(a104,f2(a925)))+~P1(f319(f55(x82531),x82533))+~P1(f319(f319(f321(x82531),x82534),x82533))
% 28.25/28.13 [8339]~P143(x83392)+~P123(x83392)+~P1(f319(x83391,x83394))+~P1(f319(f319(f279(x83392),x83393),f319(f319(f74(x83392),x83394),f2(x83392))))+P1(f319(x83391,f319(f319(f75(x83392),x83393),f872(x83393,x83391,x83392))))
% 28.25/28.13 [8810]~P4(x88101)+~P14(x88101,x88104)+P14(x88101,x88102)+~E(x88102,f319(f319(f143(x88101),x88103),x88104))+~P1(f319(f319(f226(x88101),x88103),f749(x88102,x88101,x88104,x88103)))
% 28.25/28.13 [8847]E(x88471,x88472)+E(f319(f319(f23(a1),f393(x88473,x88472,x88474,x88471)),f394(x88473,x88472,x88474,x88471)),x88471)+~E(f319(f319(f74(a1),x88471),x88474),x88472)+~P1(f319(f319(f227(a1),f2(a1)),x88474))+~P1(f319(f319(f321(a1),x88472),x88473))
% 28.25/28.13 [8848]E(x88481,x88482)+E(f319(f319(f74(a1),f396(x88483,x88482,x88484,x88481)),f397(x88483,x88482,x88484,x88481)),x88481)+~E(f319(f319(f23(a1),x88481),x88484),x88482)+~P1(f319(f319(f227(a1),f2(a1)),x88484))+~P1(f319(f319(f321(a1),x88482),x88483))
% 28.25/28.13 [9041]E(f319(x90411,f616(x90412,x90411,x90413,x90414)),x90412)+P1(f319(f319(f226(a925),x90414),f617(x90412,x90411,x90413,x90414)))+~P1(f319(f319(f226(a1),x90412),f319(x90411,x90413)))+~P1(f319(f319(f227(a925),x90414),x90413))+~P1(f319(f319(f226(a1),f319(x90411,x90414)),x90412))
% 28.25/28.13 [9042]~P4(x90421)+~P14(x90421,x90423)+P14(x90421,x90422)+~E(x90422,f319(f319(f143(x90421),x90424),x90423))+P1(f319(f319(f321(x90421),f749(x90422,x90421,x90423,x90424)),f319(f164(x90421),x90423)))
% 28.25/28.13 [9060]~P121(x90604)+~P138(x90604)+~E(f319(f319(f9(x90601,x90604),x90602),x90603),f2(x90604))+~P1(f319(f55(x90601),x90603))+P1(f319(f319(f321(x90601),f455(x90602,x90603,x90601,x90604)),x90603))
% 28.25/28.13 [9099]~E(f319(x90992,x90994),f72(a925))+E(f319(f319(f6(x90991,a925),x90992),x90993),f72(a925))+~P1(f319(f55(x90991),x90993))+~P1(f319(f319(f321(x90991),x90994),x90993))+P1(f319(f319(f321(x90991),f359(x90992,x90993,x90991,x90994)),x90993))
% 28.25/28.13 [9111]E(x91111,x91112)+~E(f319(f319(f74(a1),x91112),x91114),x91111)+~P1(f319(f319(f227(a1),f2(a1)),x91114))+~P1(f319(f319(f321(a1),x91111),x91113))+P1(f319(f319(f321(a1),f393(x91113,x91111,x91114,x91112)),x91113))
% 28.25/28.13 [9112]E(x91121,x91122)+~E(f319(f319(f23(a1),x91122),x91124),x91121)+~P1(f319(f319(f227(a1),f2(a1)),x91124))+~P1(f319(f319(f321(a1),x91121),x91123))+P1(f319(f319(f321(a1),f396(x91123,x91121,x91124,x91122)),x91123))
% 28.25/28.13 [9114]~E(f319(x91142,x91144),f319(a104,f2(a925)))+E(f319(f319(f6(x91141,a925),x91142),x91143),f319(a104,f2(a925)))+~P1(f319(f55(x91141),x91143))+~P1(f319(f319(f321(x91141),x91144),x91143))+P1(f319(f319(f321(x91141),f421(x91142,x91143,x91141,x91144)),x91143))
% 28.25/28.13 [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),f817(x91193,x91191,x91194,x91192)),x91194))
% 28.25/28.13 [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),f561(x91201,x91204,x91203,x91202)),x91204))
% 28.25/28.13 [9121]P63(x91212,x91213,x91214,x91211)+E(x91211,f180(f932(x91212,a923)))+~P1(f319(f55(x91212),x91214))+~P1(f319(f55(x91212),x91211))+P1(f319(f319(f321(x91212),f818(x91211,x91214,x91213,x91212)),x91214))
% 28.25/28.13 [9198]E(x91981,x91982)+~E(f319(f319(f74(a1),x91982),x91984),x91981)+~P1(f319(f319(f227(a1),f2(a1)),x91984))+~P1(f319(f319(f321(a1),x91981),x91983))+P1(f319(f319(f321(a1),f394(x91983,x91981,x91984,x91982)),f295(a1,f72(a1),x91984)))
% 28.25/28.13 [9199]E(x91991,x91992)+~E(f319(f319(f23(a1),x91992),x91994),x91991)+~P1(f319(f319(f227(a1),f2(a1)),x91994))+~P1(f319(f319(f321(a1),x91991),x91993))+P1(f319(f319(f321(a1),f397(x91993,x91991,x91994,x91992)),f295(a1,f72(a1),x91994)))
% 28.25/28.13 [9274]P1(f319(f319(f226(a925),x92741),f616(x92742,x92743,x92744,x92741)))+~P1(f319(f319(f226(a1),x92742),f319(x92743,x92744)))+P1(f319(f319(f226(a925),x92741),f617(x92742,x92743,x92744,x92741)))+~P1(f319(f319(f227(a925),x92741),x92744))+~P1(f319(f319(f226(a1),f319(x92743,x92741)),x92742))
% 28.25/28.13 [9391]E(f319(x93911,f616(x93912,x93911,x93913,x93914)),x93912)+~P1(f319(f319(f226(a1),x93912),f319(x93911,x93913)))+P1(f319(f319(f227(a925),f617(x93912,x93911,x93913,x93914)),x93913))+~P1(f319(f319(f227(a925),x93914),x93913))+~P1(f319(f319(f226(a1),f319(x93911,x93914)),x93912))
% 28.25/28.13 [9522]~P1(f319(f319(f226(a1),x95222),f319(x95223,x95224)))+P1(f319(f319(f226(a925),x95221),f617(x95222,x95223,x95224,x95221)))+P1(f319(f319(f226(a925),f616(x95222,x95223,x95224,x95221)),x95224))+~P1(f319(f319(f227(a925),x95221),x95224))+~P1(f319(f319(f226(a1),f319(x95223,x95221)),x95222))
% 28.25/28.13 [9523]~P1(f319(f319(f226(a1),x95232),f319(x95233,x95234)))+P1(f319(f319(f226(a925),x95231),f616(x95232,x95233,x95234,x95231)))+P1(f319(f319(f227(a925),f617(x95232,x95233,x95234,x95231)),x95234))+~P1(f319(f319(f227(a925),x95231),x95234))+~P1(f319(f319(f226(a1),f319(x95233,x95231)),x95232))
% 28.25/28.13 [9632]~P1(f319(f319(f226(a1),x96321),f319(x96322,x96323)))+P1(f319(f319(f227(a925),f617(x96321,x96322,x96323,x96324)),x96323))+~P1(f319(f319(f227(a925),x96324),x96323))+~P1(f319(f319(f226(a1),f319(x96322,x96324)),x96321))+P1(f319(f319(f226(a925),f616(x96321,x96322,x96323,x96324)),x96323))
% 28.25/28.13 [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),f571(x97203,x97201,x97204,x97202)),x97204))
% 28.25/28.13 [9721]E(x97211,f180(f932(x97212,a923)))+~P1(f319(f55(x97212),x97214))+~P1(f319(f55(x97212),x97211))+P1(f319(f319(f321(f931(f932(x97212,a923),f932(x97212,a923))),f319(f319(f244(f932(x97212,a923),f932(x97212,a923)),x97214),x97211)),f311(x97212,x97213)))+P1(f319(f319(f321(x97212),f618(x97213,x97211,x97214,x97212)),x97214))
% 28.25/28.13 [10418]E(f319(x104181,f616(x104182,x104181,x104183,x104184)),x104182)+~P1(f319(f319(f226(a1),x104182),f319(x104181,x104183)))+~P1(f319(f319(f226(a1),f319(f69(a1),f319(f319(f23(a1),f319(x104181,f319(f319(f74(a925),f617(x104182,x104181,x104183,x104184)),f72(a925)))),f319(x104181,f617(x104182,x104181,x104183,x104184))))),f72(a1)))+~P1(f319(f319(f227(a925),x104184),x104183))+~P1(f319(f319(f226(a1),f319(x104181,x104184)),x104182))
% 28.25/28.13 [10419]~P1(f319(f319(f226(a1),x104192),f319(x104193,x104194)))+P1(f319(f319(f226(a925),x104191),f616(x104192,x104193,x104194,x104191)))+~P1(f319(f319(f226(a1),f319(f69(a1),f319(f319(f23(a1),f319(x104193,f319(f319(f74(a925),f617(x104192,x104193,x104194,x104191)),f72(a925)))),f319(x104193,f617(x104192,x104193,x104194,x104191))))),f72(a1)))+~P1(f319(f319(f227(a925),x104191),x104194))+~P1(f319(f319(f226(a1),f319(x104193,x104191)),x104192))
% 28.25/28.13 [10420]~P1(f319(f319(f226(a1),x104201),f319(x104202,x104203)))+~P1(f319(f319(f226(a1),f319(f69(a1),f319(f319(f23(a1),f319(x104202,f319(f319(f74(a925),f617(x104201,x104202,x104203,x104204)),f72(a925)))),f319(x104202,f617(x104201,x104202,x104203,x104204))))),f72(a1)))+~P1(f319(f319(f227(a925),x104204),x104203))+~P1(f319(f319(f226(a1),f319(x104202,x104204)),x104201))+P1(f319(f319(f226(a925),f616(x104201,x104202,x104203,x104204)),x104203))
% 28.25/28.13 [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))
% 28.25/28.13 [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)
% 28.25/28.13 [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)
% 28.25/28.13 [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))
% 28.25/28.13 [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)
% 28.25/28.13 [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))
% 28.25/28.13 [7447]~P74(x74471)+P1(f319(f319(f227(x74471),x74472),f2(x74471)))+~P1(f319(f319(f226(x74471),x74473),f2(x74471)))+P1(f319(f319(f227(x74471),f2(x74471)),x74472))+P1(f319(f319(f226(x74471),x74473),f319(f319(f283(x74471),x74474),x74472)))
% 28.25/28.13 [7448]~P74(x74481)+P1(f319(f319(f227(x74481),x74482),f2(x74481)))+~P1(f319(f319(f227(x74481),x74483),f2(x74481)))+P1(f319(f319(f227(x74481),f2(x74481)),x74482))+P1(f319(f319(f227(x74481),x74483),f319(f319(f283(x74481),x74484),x74482)))
% 28.25/28.13 [7693]~P74(x76931)+P1(f319(f319(f226(x76931),x76932),f2(x76931)))+P1(f319(f319(f227(x76931),x76933),f2(x76931)))+P1(f319(f319(f227(x76931),f2(x76931)),x76933))+~P1(f319(f319(f226(x76931),x76932),f319(f319(f283(x76931),x76934),x76933)))
% 28.25/28.13 [7694]~P74(x76941)+P1(f319(f319(f227(x76941),x76942),f2(x76941)))+P1(f319(f319(f227(x76941),x76943),f2(x76941)))+P1(f319(f319(f227(x76941),f2(x76941)),x76943))+~P1(f319(f319(f227(x76941),x76942),f319(f319(f283(x76941),x76944),x76943)))
% 28.25/28.13 [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)))
% 28.25/28.13 [7809]E(x78091,x78092)+~E(f319(f319(f156(x78093),x78094),x78091),f319(f319(f156(x78093),x78094),x78092))+~P1(f319(f129(x78093),x78094))+~P1(f319(f319(f227(a925),x78092),f319(f181(f926(x78093)),x78094)))+~P1(f319(f319(f227(a925),x78091),f319(f181(f926(x78093)),x78094)))
% 28.25/28.13 [8175]~P74(x81751)+~P1(f319(f319(f226(x81751),x81753),f2(x81751)))+P1(f319(f319(f227(x81751),f2(x81751)),x81752))+~P1(f319(f319(f226(x81751),x81754),f319(f319(f75(x81751),x81753),x81752)))+P1(f319(f319(f226(x81751),x81753),f319(f319(f283(x81751),x81754),x81752)))
% 28.25/28.13 [8176]~P74(x81761)+~P1(f319(f319(f227(x81761),x81763),f2(x81761)))+P1(f319(f319(f227(x81761),f2(x81761)),x81762))+~P1(f319(f319(f227(x81761),x81764),f319(f319(f75(x81761),x81763),x81762)))+P1(f319(f319(f227(x81761),x81763),f319(f319(f283(x81761),x81764),x81762)))
% 28.25/28.13 [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(f75(x81771),x81773),x81772)))+P1(f319(f319(f226(x81771),x81773),f319(f319(f283(x81771),x81774),x81772)))
% 28.25/28.13 [8178]~P74(x81781)+~P1(f319(f319(f227(x81781),x81782),f2(x81781)))+P1(f319(f319(f227(x81781),f2(x81781)),x81782))+~P1(f319(f319(f226(x81781),x81784),f319(f319(f283(x81781),x81783),x81782)))+P1(f319(f319(f226(x81781),x81783),f319(f319(f75(x81781),x81784),x81782)))
% 28.25/28.13 [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(f75(x81791),x81793),x81792)))+P1(f319(f319(f227(x81791),x81793),f319(f319(f283(x81791),x81794),x81792)))
% 28.25/28.13 [8180]~P74(x81801)+~P1(f319(f319(f227(x81801),x81802),f2(x81801)))+P1(f319(f319(f227(x81801),f2(x81801)),x81802))+~P1(f319(f319(f227(x81801),x81804),f319(f319(f283(x81801),x81803),x81802)))+P1(f319(f319(f227(x81801),x81803),f319(f319(f75(x81801),x81804),x81802)))
% 28.25/28.13 [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)))
% 28.25/28.13 [8322]~P4(x83221)+~P14(x83221,x83222)+~P1(f319(f319(f226(a925),x83223),x83224))+P1(f319(f319(f226(x83221),f319(f319(f156(x83221),x83222),x83223)),f319(f319(f156(x83221),x83222),x83224)))+~P1(f319(f319(f227(a925),x83224),f319(f181(f926(x83221)),x83222)))
% 28.25/28.13 [8374]~P129(x83741)+~P1(f319(f319(f226(x83741),x83742),f72(x83741)))+~P1(f319(f319(f226(x83741),f2(x83741)),x83742))+~P1(f319(f319(f226(a925),x83744),x83743))+P1(f319(f319(f226(x83741),f319(f319(f236(x83741),x83742),x83743)),f319(f319(f236(x83741),x83742),x83744)))
% 28.25/28.13 [8375]~P129(x83751)+~P1(f319(f319(f227(x83751),x83752),f72(x83751)))+~P1(f319(f319(f227(x83751),f2(x83751)),x83752))+~P1(f319(f319(f227(a925),x83754),x83753))+P1(f319(f319(f227(x83751),f319(f319(f236(x83751),x83752),x83753)),f319(f319(f236(x83751),x83752),x83754)))
% 28.25/28.13 [8376]~P129(x83761)+~P1(f319(f319(f226(x83761),f2(x83761)),x83762))+~P1(f319(f319(f227(a925),f2(a925)),x83763))+~P1(f319(f319(f227(x83761),x83762),x83764))+P1(f319(f319(f227(x83761),f319(f319(f236(x83761),x83762),x83763)),f319(f319(f236(x83761),x83764),x83763)))
% 28.25/28.13 [8395]~P4(x83951)+~P14(x83951,f319(f160(x83951),x83952))+~P1(f319(f319(f226(a925),x83954),x83953))+P1(f319(f319(f226(x83951),f319(f319(f156(x83951),x83952),x83953)),f319(f319(f156(x83951),x83952),x83954)))+~P1(f319(f319(f227(a925),x83953),f319(f181(f926(x83951)),x83952)))
% 28.25/28.13 [8642]~P74(x86421)+~P1(f319(f319(f226(x86421),x86422),f2(x86421)))+~P1(f319(f319(f226(x86421),x86423),x86424))+~P1(f319(f319(f227(x86421),f2(x86421)),f319(f319(f75(x86421),x86423),x86424)))+P1(f319(f319(f226(x86421),f319(f319(f283(x86421),x86422),x86423)),f319(f319(f283(x86421),x86422),x86424)))
% 28.25/28.13 [8643]~P75(x86431)+~P1(f319(f319(f227(x86431),x86432),f2(x86431)))+~P1(f319(f319(f227(x86431),x86433),x86434))+~P1(f319(f319(f227(x86431),f2(x86431)),f319(f319(f75(x86431),x86433),x86434)))+P1(f319(f319(f227(x86431),f319(f319(f283(x86431),x86432),x86433)),f319(f319(f283(x86431),x86432),x86434)))
% 28.25/28.13 [8652]~P75(x86521)+~P1(f319(f319(f226(x86521),x86524),x86523))+~P1(f319(f319(f226(x86521),f2(x86521)),x86522))+~P1(f319(f319(f227(x86521),f2(x86521)),f319(f319(f75(x86521),x86523),x86524)))+P1(f319(f319(f226(x86521),f319(f319(f283(x86521),x86522),x86523)),f319(f319(f283(x86521),x86522),x86524)))
% 28.25/28.13 [8653]~P75(x86531)+~P1(f319(f319(f227(x86531),x86534),x86533))+~P1(f319(f319(f227(x86531),f2(x86531)),x86532))+~P1(f319(f319(f227(x86531),f2(x86531)),f319(f319(f75(x86531),x86533),x86534)))+P1(f319(f319(f227(x86531),f319(f319(f283(x86531),x86532),x86533)),f319(f319(f283(x86531),x86532),x86534)))
% 28.25/28.13 [8757]P1(f319(x87571,x87572))+~P1(f319(f55(x87574),x87572))+P1(f319(x87571,f339(x87571,x87573,x87572,x87574)))+~P1(f319(x87571,f180(f932(x87574,a923))))+~P1(f319(f319(f226(f932(x87574,a923)),x87572),x87573))
% 28.25/28.13 [8766]P1(f319(x87661,x87662))+P1(f319(f55(x87663),f339(x87661,x87664,x87662,x87663)))+~P1(f319(f55(x87663),x87662))+~P1(f319(x87661,f180(f932(x87663,a923))))+~P1(f319(f319(f226(f932(x87663,a923)),x87662),x87664))
% 28.25/28.13 [9036]E(f319(f319(f74(a1),f398(x90361,x90362,x90363,x90364)),f399(x90361,x90362,x90363,x90364)),x90364)+~P1(f319(f319(f227(a1),f2(a1)),x90363))+~P1(f319(f319(f227(a1),x90362),x90364))+~P1(f319(f319(f321(a1),x90362),x90361))+P1(f319(f319(f227(a1),x90362),f319(f319(f23(a1),x90364),x90363)))
% 28.25/28.13 [9255]~P1(f319(f319(f227(a1),f2(a1)),x92553))+~P1(f319(f319(f227(a1),x92552),x92554))+~P1(f319(f319(f321(a1),x92552),x92551))+P1(f319(f319(f321(a1),f398(x92551,x92552,x92553,x92554)),x92551))+P1(f319(f319(f227(a1),x92552),f319(f319(f23(a1),x92554),x92553)))
% 28.25/28.13 [9267]P1(f319(x92671,x92672))+~P1(f319(f55(x92673),x92672))+P1(f319(f319(f321(x92673),f340(x92671,x92674,x92672,x92673)),x92674))+~P1(f319(x92671,f180(f932(x92673,a923))))+~P1(f319(f319(f226(f932(x92673,a923)),x92672),x92674))
% 28.25/28.13 [9284]E(f319(f319(f74(a1),f385(x92841,x92842,x92843,x92844)),f386(x92841,x92842,x92843,x92844)),x92844)+~P1(f319(f319(f227(a1),f2(a1)),x92843))+~P1(f319(f319(f226(a1),x92842),x92844))+P1(f319(f319(f226(a1),x92842),f319(f319(f23(a1),x92844),x92843)))+~P1(f319(f319(f321(a1),f319(f319(f23(a1),x92842),f72(a1))),x92841))
% 28.25/28.13 [9339]~P1(f319(f319(f227(a1),f2(a1)),x93393))+~P1(f319(f319(f227(a1),x93391),x93392))+~P1(f319(f319(f321(a1),x93391),x93394))+P1(f319(f319(f321(a1),f399(x93394,x93391,x93393,x93392)),f295(a1,f72(a1),x93393)))+P1(f319(f319(f227(a1),x93391),f319(f319(f23(a1),x93392),x93393)))
% 28.25/28.13 [9365]~P79(x93652)+~E(f803(x93653,x93654,x93651,x93652),f804(x93653,x93654,x93651,x93652))+~P1(f319(f55(x93651),f805(x93653,x93654,x93651,x93652)))+E(f319(f319(f6(f932(x93651,a923),x93652),f319(f6(x93651,x93652),x93653)),x93654),f319(f319(f6(x93651,x93652),x93653),f31(f932(x93651,a923),x93654)))+~P1(f319(f55(f932(x93651,a923)),x93654))
% 28.25/28.13 [9369]~P79(x93692)+~E(f319(x93693,f807(x93693,x93694,x93691,x93692)),f2(x93692))+~P1(f319(f55(x93691),f805(x93693,x93694,x93691,x93692)))+E(f319(f319(f6(f932(x93691,a923),x93692),f319(f6(x93691,x93692),x93693)),x93694),f319(f319(f6(x93691,x93692),x93693),f31(f932(x93691,a923),x93694)))+~P1(f319(f55(f932(x93691,a923)),x93694))
% 28.25/28.13 [9435]~P1(f319(f319(f227(a1),f2(a1)),x94353))+~P1(f319(f319(f226(a1),x94352),x94354))+P1(f319(f319(f321(a1),f385(x94351,x94352,x94353,x94354)),x94351))+P1(f319(f319(f226(a1),x94352),f319(f319(f23(a1),x94354),x94353)))+~P1(f319(f319(f321(a1),f319(f319(f23(a1),x94352),f72(a1))),x94351))
% 28.25/28.13 [9479]~P1(f319(f319(f227(a1),f2(a1)),x94793))+~P1(f319(f319(f226(a1),x94791),x94792))+P1(f319(f319(f321(a1),f386(x94794,x94791,x94793,x94792)),f295(a1,f72(a1),x94793)))+P1(f319(f319(f226(a1),x94791),f319(f319(f23(a1),x94792),x94793)))+~P1(f319(f319(f321(a1),f319(f319(f23(a1),x94791),f72(a1))),x94794))
% 28.25/28.13 [9501]~P79(x95012)+~E(f803(x95013,x95014,x95011,x95012),f804(x95013,x95014,x95011,x95012))+E(f319(f319(f6(f932(x95011,a923),x95012),f319(f6(x95011,x95012),x95013)),x95014),f319(f319(f6(x95011,x95012),x95013),f31(f932(x95011,a923),x95014)))+P1(f319(f319(f321(f932(x95011,a923)),f805(x95013,x95014,x95011,x95012)),x95014))+~P1(f319(f55(f932(x95011,a923)),x95014))
% 28.25/28.13 [9506]~P79(x95062)+~E(f319(x95063,f807(x95063,x95064,x95061,x95062)),f2(x95062))+E(f319(f319(f6(f932(x95061,a923),x95062),f319(f6(x95061,x95062),x95063)),x95064),f319(f319(f6(x95061,x95062),x95063),f31(f932(x95061,a923),x95064)))+P1(f319(f319(f321(f932(x95061,a923)),f805(x95063,x95064,x95061,x95062)),x95064))+~P1(f319(f55(f932(x95061,a923)),x95064))
% 28.25/28.13 [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)),f804(x96093,x96094,x96091,x96092)),x96094))+~P1(f319(f55(f932(x96091,a923)),x96094))
% 28.25/28.13 [9610]~P79(x96102)+~P1(f319(f55(x96101),f805(x96103,x96104,x96101,x96102)))+E(f319(f319(f6(f932(x96101,a923),x96102),f319(f6(x96101,x96102),x96103)),x96104),f319(f319(f6(x96101,x96102),x96103),f31(f932(x96101,a923),x96104)))+P1(f319(f319(f321(f932(x96101,a923)),f803(x96103,x96104,x96101,x96102)),x96104))+~P1(f319(f55(f932(x96101,a923)),x96104))
% 28.25/28.13 [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)),f804(x96903,x96904,x96901,x96902)),x96904))+~P1(f319(f55(f932(x96901,a923)),x96904))
% 28.25/28.13 [9691]~P79(x96912)+E(f319(f319(f6(f932(x96911,a923),x96912),f319(f6(x96911,x96912),x96913)),x96914),f319(f319(f6(x96911,x96912),x96913),f31(f932(x96911,a923),x96914)))+P1(f319(f319(f321(f932(x96911,a923)),f805(x96913,x96914,x96911,x96912)),x96914))+P1(f319(f319(f321(f932(x96911,a923)),f803(x96913,x96914,x96911,x96912)),x96914))+~P1(f319(f55(f932(x96911,a923)),x96914))
% 28.25/28.13 [9709]~P79(x97092)+P1(f319(f319(f321(x97091),f807(x97093,x97094,x97091,x97092)),f804(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))
% 28.25/28.13 [9710]~P79(x97102)+P1(f319(f319(f321(x97101),f807(x97103,x97104,x97101,x97102)),f803(x97103,x97104,x97101,x97102)))+~P1(f319(f55(x97101),f805(x97103,x97104,x97101,x97102)))+E(f319(f319(f6(f932(x97101,a923),x97102),f319(f6(x97101,x97102),x97103)),x97104),f319(f319(f6(x97101,x97102),x97103),f31(f932(x97101,a923),x97104)))+~P1(f319(f55(f932(x97101,a923)),x97104))
% 28.25/28.13 [9723]P1(f319(x97231,x97232))+~P1(f319(f319(f321(x97233),f340(x97231,x97234,x97232,x97233)),f339(x97231,x97234,x97232,x97233)))+~P1(f319(f55(x97233),x97232))+~P1(f319(x97231,f180(f932(x97233,a923))))+~P1(f319(f319(f226(f932(x97233,a923)),x97232),x97234))
% 28.25/28.13 [9760]~P79(x97602)+P1(f319(f319(f321(x97601),f807(x97603,x97604,x97601,x97602)),f804(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))
% 28.25/28.13 [9761]~P79(x97612)+P1(f319(f319(f321(x97611),f807(x97613,x97614,x97611,x97612)),f803(x97613,x97614,x97611,x97612)))+E(f319(f319(f6(f932(x97611,a923),x97612),f319(f6(x97611,x97612),x97613)),x97614),f319(f319(f6(x97611,x97612),x97613),f31(f932(x97611,a923),x97614)))+P1(f319(f319(f321(f932(x97611,a923)),f805(x97613,x97614,x97611,x97612)),x97614))+~P1(f319(f55(f932(x97611,a923)),x97614))
% 28.25/28.13 [9943]P1(f319(x99431,x99432))+~P1(f319(f55(x99433),x99432))+~P1(f319(x99431,f319(f319(f301(x99433),f340(x99431,x99434,x99432,x99433)),f339(x99431,x99434,x99432,x99433))))+~P1(f319(x99431,f180(f932(x99433,a923))))+~P1(f319(f319(f226(f932(x99433,a923)),x99432),x99434))
% 28.25/28.13 [7944]~P74(x79441)+P1(f319(f319(f227(x79441),x79442),f2(x79441)))+~P1(f319(f319(f226(x79441),f2(x79441)),x79444))+P1(f319(f319(f227(x79441),f2(x79441)),x79442))+P1(f319(f319(f226(x79441),f319(f319(f283(x79441),x79443),x79442)),x79444))
% 28.25/28.13 [7945]~P74(x79451)+P1(f319(f319(f227(x79451),x79452),f2(x79451)))+P1(f319(f319(f227(x79451),f2(x79451)),x79452))+~P1(f319(f319(f227(x79451),f2(x79451)),x79454))+P1(f319(f319(f227(x79451),f319(f319(f283(x79451),x79453),x79452)),x79454))
% 28.25/28.13 [8162]~P6(x81621)+~P41(x81621,x81621,x81624)+~E(x81623,f88(x81621,x81624))+P1(f319(f319(f226(x81621),x81622),x81623))+~P1(f319(f319(f226(x81621),x81622),f319(x81624,f319(f319(f102(x81621),x81622),x81623))))
% 28.25/28.13 [8228]~P1(f319(f319(f226(a1),x82284),f2(a1)))+~E(x82282,f319(f319(f74(a1),f319(f319(f75(a1),x82281),x82283)),x82284))+P1(f319(f319(f227(a1),f2(a1)),x82281))+~P1(f319(f319(f227(a1),x82281),x82284))+P1(f319(f43(x82282,x82281),f319(f319(f244(a1,a1),x82283),x82284)))
% 28.25/28.13 [8262]~P1(f319(x82621,x82624))+P1(f319(x82621,f435(x82622,x82621,x82623)))+~P1(f319(f319(f226(a1),f2(a1)),x82622))+~P1(f319(f319(f227(a1),f2(a1)),x82623))+P1(f319(x82621,f319(f319(f23(a1),x82624),f319(f319(f75(a1),x82622),x82623))))
% 28.25/28.13 [8263]~P1(f319(x82631,x82634))+P1(f319(x82631,f441(x82632,x82631,x82633)))+~P1(f319(f319(f226(a1),f2(a1)),x82632))+~P1(f319(f319(f227(a1),f2(a1)),x82633))+P1(f319(x82631,f319(f319(f74(a1),x82634),f319(f319(f75(a1),x82632),x82633))))
% 28.25/28.13 [8264]~P74(x82641)+P1(f319(f319(f227(x82641),x82642),f2(x82641)))+P1(f319(f319(f227(x82641),f2(x82641)),x82642))+P1(f319(f319(f226(x82641),f2(x82641)),x82643))+~P1(f319(f319(f226(x82641),f319(f319(f283(x82641),x82644),x82642)),x82643))
% 28.25/28.13 [8265]~P74(x82651)+P1(f319(f319(f227(x82651),x82652),f2(x82651)))+P1(f319(f319(f227(x82651),f2(x82651)),x82652))+P1(f319(f319(f227(x82651),f2(x82651)),x82653))+~P1(f319(f319(f227(x82651),f319(f319(f283(x82651),x82654),x82652)),x82653))
% 28.25/28.13 [8317]~E(x83171,f319(f319(f74(a1),f319(f319(f75(a1),x83172),x83173)),x83174))+~P1(f319(f319(f226(a1),f2(a1)),x83174))+~P1(f319(f319(f227(a1),f2(a1)),x83172))+~P1(f319(f319(f227(a1),x83174),x83172))+P1(f319(f43(x83171,x83172),f319(f319(f244(a1,a1),x83173),x83174)))
% 28.25/28.13 [8434]~P74(x84341)+P1(f319(f319(f227(x84341),x84342),f2(x84341)))+~P1(f319(f319(f226(x84341),f2(x84341)),x84344))+~P1(f319(f319(f226(x84341),x84343),f319(f319(f75(x84341),x84344),x84342)))+P1(f319(f319(f226(x84341),f319(f319(f283(x84341),x84343),x84342)),x84344))
% 28.25/28.13 [8435]~P74(x84351)+P1(f319(f319(f227(x84351),x84352),f2(x84351)))+~P1(f319(f319(f227(x84351),f2(x84351)),x84354))+~P1(f319(f319(f227(x84351),x84353),f319(f319(f75(x84351),x84354),x84352)))+P1(f319(f319(f227(x84351),f319(f319(f283(x84351),x84353),x84352)),x84354))
% 28.25/28.13 [8521]~P74(x85211)+P1(f319(f319(f227(x85211),x85212),f2(x85211)))+~P1(f319(f319(f226(x85211),x85213),f2(x85211)))+P1(f319(f319(f226(x85211),x85213),f319(f319(f283(x85211),x85214),x85212)))+~P1(f319(f319(f226(x85211),f319(f319(f75(x85211),x85213),x85212)),x85214))
% 28.25/28.13 [8522]~P74(x85221)+P1(f319(f319(f227(x85221),x85222),f2(x85221)))+~P1(f319(f319(f227(x85221),x85223),f2(x85221)))+P1(f319(f319(f227(x85221),x85223),f319(f319(f283(x85221),x85224),x85222)))+~P1(f319(f319(f227(x85221),f319(f319(f75(x85221),x85223),x85222)),x85224))
% 28.25/28.13 [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(f283(x86761),x86764),x86762)),x86763))+P1(f319(f319(f226(x86761),f319(f319(f75(x86761),x86763),x86762)),x86764))
% 28.25/28.13 [8677]~P74(x86771)+~P1(f319(f319(f227(x86771),x86772),f2(x86771)))+P1(f319(f319(f227(x86771),f2(x86771)),x86772))+~P1(f319(f319(f226(x86771),f319(f319(f75(x86771),x86774),x86772)),x86773))+P1(f319(f319(f226(x86771),f319(f319(f283(x86771),x86773),x86772)),x86774))
% 28.25/28.13 [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(f283(x86781),x86784),x86782)),x86783))+P1(f319(f319(f227(x86781),f319(f319(f75(x86781),x86783),x86782)),x86784))
% 28.25/28.13 [8679]~P74(x86791)+~P1(f319(f319(f227(x86791),x86792),f2(x86791)))+P1(f319(f319(f227(x86791),f2(x86791)),x86792))+~P1(f319(f319(f227(x86791),f319(f319(f75(x86791),x86794),x86792)),x86793))+P1(f319(f319(f227(x86791),f319(f319(f283(x86791),x86793),x86792)),x86794))
% 28.25/28.13 [8695]~P74(x86951)+~P1(f319(f319(f226(x86951),f2(x86951)),x86954))+P1(f319(f319(f227(x86951),f2(x86951)),x86952))+~P1(f319(f319(f226(x86951),f319(f319(f75(x86951),x86954),x86952)),x86953))+P1(f319(f319(f226(x86951),f319(f319(f283(x86951),x86953),x86952)),x86954))
% 28.25/28.13 [8696]~P74(x86961)+~P1(f319(f319(f227(x86961),f2(x86961)),x86964))+P1(f319(f319(f227(x86961),f2(x86961)),x86962))+~P1(f319(f319(f227(x86961),f319(f319(f75(x86961),x86964),x86962)),x86963))+P1(f319(f319(f227(x86961),f319(f319(f283(x86961),x86963),x86962)),x86964))
% 28.25/28.13 [8751]~P74(x87511)+~P100(x87511)+~P1(f319(f319(f227(x87511),f2(x87511)),x87514))+~P1(f319(f319(f226(x87511),f319(f319(f283(x87511),x87512),x87514)),f319(f95(x87511),x87513)))+P1(f319(f319(f226(x87511),x87512),f319(f319(f75(x87511),f319(f95(x87511),x87513)),x87514)))
% 28.25/28.13 [8752]~P74(x87521)+~P100(x87521)+~P1(f319(f319(f227(x87521),f2(x87521)),x87524))+~P1(f319(f319(f227(x87521),f319(f319(f283(x87521),x87522),x87524)),f319(f95(x87521),x87523)))+P1(f319(f319(f227(x87521),x87522),f319(f319(f75(x87521),f319(f95(x87521),x87523)),x87524)))
% 28.25/28.13 [8758]~P74(x87581)+~P100(x87581)+~P1(f319(f319(f227(x87581),f2(x87581)),x87583))+P1(f319(f319(f226(x87581),f319(f319(f283(x87581),x87582),x87583)),f319(f95(x87581),x87584)))+~P1(f319(f319(f226(x87581),x87582),f319(f319(f75(x87581),f319(f95(x87581),x87584)),x87583)))
% 28.25/28.13 [8759]~P74(x87591)+~P100(x87591)+~P1(f319(f319(f227(x87591),f2(x87591)),x87593))+P1(f319(f319(f227(x87591),f319(f319(f283(x87591),x87592),x87593)),f319(f95(x87591),x87594)))+~P1(f319(f319(f227(x87591),x87592),f319(f319(f75(x87591),f319(f95(x87591),x87594)),x87593)))
% 28.25/28.13 [8774]~P74(x87741)+~P1(f319(f319(f227(x87741),x87744),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))
% 28.25/28.13 [8775]~P74(x87751)+~P1(f319(f319(f226(x87751),x87752),f2(x87751)))+~P1(f319(f319(f226(x87751),x87753),f319(f319(f75(x87751),x87752),x87754)))+P1(f319(f319(f226(x87751),x87752),f319(f319(f283(x87751),x87753),x87754)))+~P1(f319(f319(f226(x87751),f319(f319(f75(x87751),x87752),x87754)),x87753))
% 28.25/28.13 [8776]~P74(x87761)+~P1(f319(f319(f227(x87761),x87764),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))
% 28.25/28.13 [8777]~P74(x87771)+~P1(f319(f319(f227(x87771),x87772),f2(x87771)))+~P1(f319(f319(f227(x87771),x87773),f319(f319(f75(x87771),x87772),x87774)))+P1(f319(f319(f227(x87771),x87772),f319(f319(f283(x87771),x87773),x87774)))+~P1(f319(f319(f227(x87771),f319(f319(f75(x87771),x87772),x87774)),x87773))
% 28.25/28.13 [8827]~P74(x88271)+~P100(x88271)+~P1(f319(f319(f227(x88271),f2(x88271)),f319(f95(x88271),x88273)))+~P1(f319(f319(f226(x88271),x88272),f319(f319(f283(x88271),x88274),f319(f95(x88271),x88273))))+P1(f319(f319(f226(x88271),f319(f319(f75(x88271),x88272),f319(f95(x88271),x88273))),x88274))
% 28.25/28.13 [8828]~P74(x88281)+~P100(x88281)+~P1(f319(f319(f227(x88281),f2(x88281)),f319(f95(x88281),x88283)))+~P1(f319(f319(f226(x88281),x88282),f319(f319(f75(x88281),x88284),f319(f95(x88281),x88283))))+P1(f319(f319(f226(x88281),f319(f319(f283(x88281),x88282),f319(f95(x88281),x88283))),x88284))
% 28.25/28.13 [8829]~P74(x88291)+~P100(x88291)+~P1(f319(f319(f227(x88291),f2(x88291)),f319(f95(x88291),x88293)))+~P1(f319(f319(f227(x88291),x88292),f319(f319(f283(x88291),x88294),f319(f95(x88291),x88293))))+P1(f319(f319(f227(x88291),f319(f319(f75(x88291),x88292),f319(f95(x88291),x88293))),x88294))
% 28.25/28.13 [8830]~P74(x88301)+~P100(x88301)+~P1(f319(f319(f227(x88301),f2(x88301)),f319(f95(x88301),x88303)))+~P1(f319(f319(f227(x88301),x88302),f319(f319(f75(x88301),x88304),f319(f95(x88301),x88303))))+P1(f319(f319(f227(x88301),f319(f319(f283(x88301),x88302),f319(f95(x88301),x88303))),x88304))
% 28.25/28.13 [8900]~P74(x89001)+~P1(f319(f319(f227(x89001),x89003),f2(x89001)))+~P1(f319(f319(f226(x89001),x89002),f319(f319(f75(x89001),x89004),x89003)))+~P1(f319(f319(f226(x89001),f319(f319(f75(x89001),x89004),x89003)),x89002))+P1(f319(f319(f226(x89001),f319(f319(f283(x89001),x89002),x89003)),x89004))
% 28.25/28.13 [8901]~P74(x89011)+~P1(f319(f319(f227(x89011),x89013),f2(x89011)))+~P1(f319(f319(f227(x89011),x89012),f319(f319(f75(x89011),x89014),x89013)))+~P1(f319(f319(f227(x89011),f319(f319(f75(x89011),x89014),x89013)),x89012))+P1(f319(f319(f227(x89011),f319(f319(f283(x89011),x89012),x89013)),x89014))
% 28.25/28.13 [8918]~P74(x89181)+~P1(f319(f319(f226(x89181),f2(x89181)),x89184))+~P1(f319(f319(f226(x89181),x89182),f319(f319(f75(x89181),x89184),x89183)))+~P1(f319(f319(f226(x89181),f319(f319(f75(x89181),x89184),x89183)),x89182))+P1(f319(f319(f226(x89181),f319(f319(f283(x89181),x89182),x89183)),x89184))
% 28.25/28.13 [8919]~P74(x89191)+~P1(f319(f319(f227(x89191),f2(x89191)),x89194))+~P1(f319(f319(f227(x89191),x89192),f319(f319(f75(x89191),x89194),x89193)))+~P1(f319(f319(f227(x89191),f319(f319(f75(x89191),x89194),x89193)),x89192))+P1(f319(f319(f227(x89191),f319(f319(f283(x89191),x89192),x89193)),x89194))
% 28.25/28.13 [8953]~P74(x89531)+~P100(x89531)+~P1(f319(f319(f227(x89531),f2(x89531)),f319(f95(x89531),x89534)))+P1(f319(f319(f226(x89531),x89532),f319(f319(f75(x89531),x89533),f319(f95(x89531),x89534))))+~P1(f319(f319(f226(x89531),f319(f319(f283(x89531),x89532),f319(f95(x89531),x89534))),x89533))
% 28.25/28.13 [8954]~P74(x89541)+~P100(x89541)+~P1(f319(f319(f227(x89541),f2(x89541)),f319(f95(x89541),x89544)))+P1(f319(f319(f226(x89541),x89542),f319(f319(f283(x89541),x89543),f319(f95(x89541),x89544))))+~P1(f319(f319(f226(x89541),f319(f319(f75(x89541),x89542),f319(f95(x89541),x89544))),x89543))
% 28.25/28.13 [8955]~P74(x89551)+~P100(x89551)+~P1(f319(f319(f227(x89551),f2(x89551)),f319(f95(x89551),x89554)))+P1(f319(f319(f227(x89551),x89552),f319(f319(f75(x89551),x89553),f319(f95(x89551),x89554))))+~P1(f319(f319(f227(x89551),f319(f319(f283(x89551),x89552),f319(f95(x89551),x89554))),x89553))
% 28.25/28.13 [8956]~P74(x89561)+~P100(x89561)+~P1(f319(f319(f227(x89561),f2(x89561)),f319(f95(x89561),x89564)))+P1(f319(f319(f227(x89561),x89562),f319(f319(f283(x89561),x89563),f319(f95(x89561),x89564))))+~P1(f319(f319(f227(x89561),f319(f319(f75(x89561),x89562),f319(f95(x89561),x89564))),x89563))
% 28.25/28.13 [9104]E(f319(f319(f23(a1),f400(x91041,x91042,x91043,x91044)),f401(x91041,x91042,x91043,x91044)),x91044)+~P1(f319(f319(f227(a1),f2(a1)),x91043))+~P1(f319(f319(f321(a1),x91042),x91041))+~P1(f319(f319(f227(a1),x91044),x91042))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x91044),x91043)),x91042))
% 28.25/28.13 [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(f23(a1),f435(x91793,x91791,x91794)),x91794)))+P1(f319(x91791,f319(f319(f23(a1),x91792),f319(f319(f75(a1),x91793),x91794))))
% 28.25/28.13 [9180]~P1(f319(x91801,x91802))+~P1(f319(f319(f226(a1),f2(a1)),x91803))+~P1(f319(f319(f227(a1),f2(a1)),x91804))+~P1(f319(x91801,f319(f319(f74(a1),f441(x91803,x91801,x91804)),x91804)))+P1(f319(x91801,f319(f319(f74(a1),x91802),f319(f319(f75(a1),x91803),x91804))))
% 28.25/28.13 [9332]~P1(f319(f319(f227(a1),f2(a1)),x93323))+~P1(f319(f319(f321(a1),x93322),x93321))+~P1(f319(f319(f227(a1),x93324),x93322))+P1(f319(f319(f321(a1),f400(x93321,x93322,x93323,x93324)),x93321))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x93324),x93323)),x93322))
% 28.25/28.13 [9352]E(f319(f319(f23(a1),f387(x93521,x93522,x93523,x93524)),f388(x93521,x93522,x93523,x93524)),x93524)+~P1(f319(f319(f227(a1),f2(a1)),x93523))+~P1(f319(f319(f226(a1),x93524),x93522))+~P1(f319(f319(f321(a1),f319(f319(f74(a1),x93522),f72(a1))),x93521))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x93524),x93523)),x93522))
% 28.25/28.13 [9380]~P1(f319(f319(f227(a1),f2(a1)),x93802))+~P1(f319(f319(f321(a1),x93803),x93804))+~P1(f319(f319(f227(a1),x93801),x93803))+P1(f319(f319(f321(a1),f401(x93804,x93803,x93802,x93801)),f295(a1,f72(a1),x93802)))+P1(f319(f319(f227(a1),f319(f319(f74(a1),x93801),x93802)),x93803))
% 28.25/28.13 [9471]~P1(f319(f319(f227(a1),f2(a1)),x94713))+~P1(f319(f319(f226(a1),x94714),x94712))+P1(f319(f319(f321(a1),f387(x94711,x94712,x94713,x94714)),x94711))+~P1(f319(f319(f321(a1),f319(f319(f74(a1),x94712),f72(a1))),x94711))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x94714),x94713)),x94712))
% 28.25/28.13 [9518]~P1(f319(f319(f227(a1),f2(a1)),x95182))+~P1(f319(f319(f226(a1),x95181),x95183))+P1(f319(f319(f321(a1),f388(x95184,x95183,x95182,x95181)),f295(a1,f72(a1),x95182)))+~P1(f319(f319(f321(a1),f319(f319(f74(a1),x95183),f72(a1))),x95184))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x95181),x95182)),x95183))
% 28.25/28.13 [9816]~P38(x98161,x98163)+~P28(x98161,x98164)+P38(x98161,f319(f319(f102(f932(f931(x98161,x98161),a923)),x98162),x98163))+~P1(f319(f319(f226(f932(f931(x98161,x98161),a923)),x98162),f319(f243(f932(f931(x98161,x98161),a923),f932(f931(x98161,x98161),a923)),x98164)))+~P1(f319(f319(f226(f932(f931(x98161,x98161),a923)),x98163),f319(f248(f932(f931(x98161,x98161),a923),f932(f931(x98161,x98161),a923)),x98164)))
% 28.25/28.13 [10228]~P20(x102282,x102284,x102283)+E(x102281,f180(f932(x102282,a923)))+~P1(f319(f55(x102282),x102281))+P1(f319(f319(f321(x102282),f319(x102283,x102281)),x102281))+~P1(f319(f319(f321(x102282),f319(f319(x102284,f916(x102281,x102283,x102284,x102282)),f917(x102281,x102283,x102284,x102282))),f319(f319(f301(x102282),f916(x102281,x102283,x102284,x102282)),f319(f319(f301(x102282),f917(x102281,x102283,x102284,x102282)),f180(f932(x102282,a923))))))
% 28.25/28.13 [8802]~P6(x88021)+~P41(x88021,x88021,x88024)+~E(x88022,f87(x88021,x88024))+P1(f319(f319(f226(x88021),x88022),x88023))+~P1(f319(f319(f226(x88021),f319(x88024,f319(f319(f93(x88021),x88022),x88023))),x88023))
% 28.25/28.13 [8941]~P74(x89411)+~P100(x89411)+~P1(f319(f319(f227(x89411),f2(x89411)),x89413))+~P1(f319(f319(f226(x89411),f319(f95(x89411),x89412)),f319(f319(f283(x89411),x89414),x89413)))+P1(f319(f319(f226(x89411),f319(f319(f75(x89411),f319(f95(x89411),x89412)),x89413)),x89414))
% 28.25/28.13 [8942]~P74(x89421)+~P100(x89421)+~P1(f319(f319(f227(x89421),f2(x89421)),x89423))+~P1(f319(f319(f227(x89421),f319(f95(x89421),x89422)),f319(f319(f283(x89421),x89424),x89423)))+P1(f319(f319(f227(x89421),f319(f319(f75(x89421),f319(f95(x89421),x89422)),x89423)),x89424))
% 28.25/28.13 [9107]~P74(x91071)+~P100(x91071)+~P1(f319(f319(f227(x91071),f2(x91071)),x91074))+P1(f319(f319(f226(x91071),f319(f95(x91071),x91072)),f319(f319(f283(x91071),x91073),x91074)))+~P1(f319(f319(f226(x91071),f319(f319(f75(x91071),f319(f95(x91071),x91072)),x91074)),x91073))
% 28.25/28.13 [9108]~P74(x91081)+~P100(x91081)+~P1(f319(f319(f227(x91081),f2(x91081)),x91084))+P1(f319(f319(f227(x91081),f319(f95(x91081),x91082)),f319(f319(f283(x91081),x91083),x91084)))+~P1(f319(f319(f227(x91081),f319(f319(f75(x91081),f319(f95(x91081),x91082)),x91084)),x91083))
% 28.25/28.13 [10150]~P113(x101502)+~P5(x101501)+~P1(f319(f319(f226(f932(x101501,x101502)),x101503),x101504))+P1(f319(f319(f227(f932(x101501,x101502)),x101503),x101504))+~P1(f319(f50(x101501),f319(f319(f8(a923,a923,x101501),a314),f319(f319(f18(x101501,x101502,a923),f319(f319(f8(x101502,f932(x101502,a923),x101501),a316),x101503)),x101504))))
% 28.25/28.13 [5348]~P51(x53484,x53485,x53483)+E(x53481,x53482)+~P4(x53484)+~P113(x53485)+~E(f319(x53483,x53481),f319(x53483,x53482))
% 28.25/28.13 [9729]~P59(x97291,x97291,x97294)+P1(f319(f319(f321(f931(x97291,x97291)),f319(f319(f244(x97291,x97291),x97292),x97293)),f299(x97291,x97294)))+P1(f319(f319(f321(f931(x97291,x97291)),f319(f319(f244(x97291,x97291),x97293),x97292)),f299(x97291,x97294)))+~P1(f319(f319(f321(f931(x97291,x97291)),f319(f319(f244(x97291,x97291),x97295),x97292)),f299(x97291,x97294)))+~P1(f319(f319(f321(f931(x97291,x97291)),f319(f319(f244(x97291,x97291),x97295),x97293)),f299(x97291,x97294)))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [7060]~P4(x70601)+~P51(x70601,x70604,x70605)+~P113(x70604)+~P1(f319(f319(f226(x70604),f319(x70605,x70602)),f319(x70605,x70603)))+P1(f319(f319(f226(x70601),x70602),x70603))
% 28.25/28.13 [7061]~P4(x70611)+~P51(x70611,x70614,x70615)+~P113(x70614)+~P1(f319(f319(f227(x70614),f319(x70615,x70612)),f319(x70615,x70613)))+P1(f319(f319(f227(x70611),x70612),x70613))
% 28.25/28.13 [7710]~P4(x77101)+~P14(x77101,f319(f319(f126(x77101),x77104),x77105))+~P1(f319(f319(f321(x77101),x77103),f319(f164(x77101),x77105)))+~P1(f319(f319(f321(x77101),x77102),f319(f164(x77101),x77104)))+P1(f319(f319(f226(x77101),x77102),x77103))
% 28.25/28.13 [8812]~P113(x88121)+~P1(f319(f319(f227(f932(x88121,a923)),f295(x88121,x88125,x88122)),f295(x88121,x88124,x88123)))+~P1(f319(f319(f226(x88121),x88125),x88122))+P1(f319(f319(f227(x88121),x88122),x88123))+P1(f319(f319(f227(x88121),x88124),x88125))
% 28.25/28.13 [9852]~P41(f932(x98524,a923),f932(x98524,a923),x98525)+P1(f319(x98521,x98522))+~E(x98523,f87(f932(x98524,a923),x98525))+~P1(f319(x98521,f461(x98521,x98522,x98525,x98524,x98523)))+~P1(f319(f319(f321(x98524),x98522),x98523))
% 28.25/28.13 [10271]~P19(x102712,x102715,x102713)+E(x102711,f180(f932(x102712,a923)))+~E(f319(f319(x102715,f319(x102714,f342(x102711,x102714,x102713,x102715,x102712))),f319(x102714,f343(x102711,x102714,x102713,x102715,x102712))),f319(x102714,f319(f319(x102715,f342(x102711,x102714,x102713,x102715,x102712)),f343(x102711,x102714,x102713,x102715,x102712))))+E(f319(x102713,f319(f302(x102712,x102712,x102714),x102711)),f319(x102714,f319(x102713,x102711)))+~P1(f319(f55(x102712),x102711))
% 28.25/28.13 [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))
% 28.25/28.13 [7475]~P19(x74752,x74753,x74754)+E(f319(f319(x74753,f319(x74754,x74751)),f319(x74754,x74755)),f319(x74754,x74755))+E(x74751,f180(f932(x74752,a923)))+~P1(f319(f55(x74752),x74755))+~P1(f319(f319(f226(f932(x74752,a923)),x74751),x74755))
% 28.25/28.13 [7844]~P20(x78444,x78445,x78441)+E(f319(x78441,x78442),x78443)+~P1(f319(f55(x78444),x78442))+~E(f319(f319(f23(f932(x78444,a923)),x78442),f319(f319(f301(x78444),x78443),f180(f932(x78444,a923)))),f180(f932(x78444,a923)))+~P1(f319(f319(f321(x78444),x78443),x78442))
% 28.25/28.13 [8781]E(x87811,x87812)+~P9(x87813,x87814,x87815)+E(f319(f319(f93(f932(x87813,a923)),x87811),x87812),f180(f932(x87813,a923)))+~P1(f319(f319(f321(f932(x87813,a923)),x87812),f319(f319(f54(x87813),x87814),x87815)))+~P1(f319(f319(f321(f932(x87813,a923)),x87811),f319(f319(f54(x87813),x87814),x87815)))
% 28.25/28.13 [9257]~P26(x92571,x92573,x92575,x92572)+~P1(f319(f55(x92573),x92574))+~P1(f319(f55(x92571),x92572))+P1(f319(f319(f226(a925),f319(f29(x92571),x92572)),f319(f29(x92573),x92574)))+~P1(f319(f319(f226(f932(x92573,a923)),f319(f302(x92571,x92573,x92575),x92572)),x92574))
% 28.25/28.13 [9602]~P79(x96022)+~E(f319(x96023,f445(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))
% 28.25/28.13 [9603]~P79(x96032)+~E(f319(x96033,f446(x96033,x96034,x96035,x96031,x96032)),f2(x96032))+E(f319(f319(f6(x96031,x96032),x96033),x96034),f319(f319(f6(x96031,x96032),x96033),x96035))+~P1(f319(f55(x96031),x96035))+~P1(f319(f319(f226(f932(x96031,a923)),x96034),x96035))
% 28.25/28.13 [9604]~P78(x96042)+~E(f319(x96043,f505(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))
% 28.25/28.13 [9605]~P78(x96052)+~E(f319(x96053,f506(x96053,x96054,x96055,x96051,x96052)),f72(x96052))+E(f319(f319(f9(x96051,x96052),x96053),x96054),f319(f319(f9(x96051,x96052),x96053),x96055))+~P1(f319(f55(x96051),x96055))+~P1(f319(f319(f226(f932(x96051,a923)),x96054),x96055))
% 28.25/28.13 [10044]~P41(f932(x100441,a923),f932(x100441,a923),f319(f319(f8(f932(x100441,a923),f932(x100441,a923),f932(x100441,a923)),f254(x100441)),x100444))+~P1(f319(f319(x100444,f319(f319(f102(f932(x100441,a923)),x100445),x100443)),f462(x100445,x100442,x100444,x100441,x100443)))+~E(x100443,f88(f932(x100441,a923),f319(f319(f8(f932(x100441,a923),f932(x100441,a923),f932(x100441,a923)),f254(x100441)),x100444)))+P1(f319(f319(f321(x100441),x100442),x100443))+~P1(f319(f319(f321(x100441),x100442),x100445))
% 28.25/28.13 [10048]~P41(f932(x100481,a923),f932(x100481,a923),f319(f319(f8(f932(x100481,a923),f932(x100481,a923),f932(x100481,a923)),f254(x100481)),x100485))+~E(x100483,f88(f932(x100481,a923),f319(f319(f8(f932(x100481,a923),f932(x100481,a923),f932(x100481,a923)),f254(x100481)),x100485)))+~P1(f319(f319(f321(x100481),x100482),x100484))+P1(f319(f319(f321(x100481),f462(x100484,x100482,x100485,x100481,x100483)),x100484))+P1(f319(f319(f321(x100481),x100482),x100483))
% 28.25/28.13 [10103]~P93(x101031)+~P1(f319(f55(x101032),x101035))+~P1(f319(f319(f226(x101031),f2(x101031)),f319(x101033,f389(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))
% 28.25/28.13 [7707]E(x77071,f2(a925))+P1(f319(x77072,x77073))+~E(x77074,f319(f319(f74(a925),f319(f319(f75(a925),x77071),x77073)),x77075))+~P1(f319(f319(f227(a925),x77075),x77071))+~P1(f319(x77072,f319(f319(f30(a925),x77074),x77071)))
% 28.25/28.13 [7782]E(x77821,f2(a925))+P1(f319(x77822,x77823))+~P1(f319(x77822,f39(a925,x77824,x77821)))+~E(x77824,f319(f319(f74(a925),f319(f319(f75(a925),x77821),x77825)),x77823))+~P1(f319(f319(f227(a925),x77823),x77821))
% 28.25/28.13 [8075]~P73(x80753)+E(f319(x80751,x80752),f2(x80753))+~P1(f319(f55(x80754),x80755))+E(f319(f319(f9(x80754,x80753),x80751),f319(f319(f23(f932(x80754,a923)),x80755),f319(f319(f301(x80754),x80752),f180(f932(x80754,a923))))),f319(f319(f9(x80754,x80753),x80751),x80755))+P1(f319(f319(f321(x80754),x80752),x80755))
% 28.25/28.13 [8475]~P79(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(f74(x84751),f319(f319(f6(x84752,x84751),x84753),x84754)),f319(f319(f6(x84752,x84751),x84753),x84755)),f319(f319(f6(x84752,x84751),x84753),f319(f319(f102(f932(x84752,a923)),x84754),x84755)))
% 28.25/28.13 [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)))
% 28.25/28.13 [8477]~P78(x84771)+~P1(f319(f55(x84772),x84775))+~P1(f319(f55(x84772),x84774))+~E(f319(f319(f93(f932(x84772,a923)),x84774),x84775),f180(f932(x84772,a923)))+E(f319(f319(f75(x84771),f319(f319(f9(x84772,x84771),x84773),x84774)),f319(f319(f9(x84772,x84771),x84773),x84775)),f319(f319(f9(x84772,x84771),x84773),f319(f319(f102(f932(x84772,a923)),x84774),x84775)))
% 28.25/28.13 [8577]~P73(x85773)+E(f319(x85771,x85772),f2(x85773))+~P1(f319(f55(x85774),x85775))+E(f319(f319(f9(x85774,x85773),x85771),f319(f319(f23(f932(x85774,a923)),x85775),f319(f319(f301(x85774),x85772),f180(f932(x85774,a923))))),f319(f319(f283(x85773),f319(f319(f9(x85774,x85773),x85771),x85775)),f319(x85771,x85772)))+~P1(f319(f319(f321(x85774),x85772),x85775))
% 28.25/28.13 [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))
% 28.25/28.13 [9123]~P9(x91231,x91235,x91234)+~E(f319(f277(x91231,x91231,x91234),f319(f319(f301(x91231),x91232),f180(f932(x91231,a923)))),f319(f277(x91231,x91231,x91234),f319(f319(f301(x91231),x91233),f180(f932(x91231,a923)))))+~P1(f319(f319(f321(x91231),x91233),x91235))+~P1(f319(f319(f321(x91231),x91232),x91235))+P1(f319(f319(f321(f931(x91231,x91231)),f319(f319(f244(x91231,x91231),x91232),x91233)),x91234))
% 28.25/28.13 [9220]~P9(x92201,x92205,x92202)+E(f319(f277(x92201,x92201,x92202),f319(f319(f301(x92201),x92203),f180(f932(x92201,a923)))),f319(f277(x92201,x92201,x92202),f319(f319(f301(x92201),x92204),f180(f932(x92201,a923)))))+~P1(f319(f319(f321(x92201),x92204),x92205))+~P1(f319(f319(f321(x92201),x92203),x92205))+~P1(f319(f319(f321(f931(x92201,x92201)),f319(f319(f244(x92201,x92201),x92203),x92204)),x92202))
% 28.25/28.13 [9309]~P9(x93091,x93095,x93094)+~E(f319(f319(f54(x93091),f319(f319(f301(x93091),x93092),f180(f932(x93091,a923)))),x93094),f319(f319(f54(x93091),f319(f319(f301(x93091),x93093),f180(f932(x93091,a923)))),x93094))+~P1(f319(f319(f321(x93091),x93093),x93095))+~P1(f319(f319(f321(x93091),x93092),x93095))+P1(f319(f319(f321(f931(x93091,x93091)),f319(f319(f244(x93091,x93091),x93092),x93093)),x93094))
% 28.25/28.13 [9331]~P9(x93311,x93315,x93313)+E(f319(f319(f54(x93311),f319(f319(f301(x93311),x93312),f180(f932(x93311,a923)))),x93313),f319(f319(f54(x93311),f319(f319(f301(x93311),x93314),f180(f932(x93311,a923)))),x93313))+~P1(f319(f319(f321(x93311),x93314),x93315))+~P1(f319(f319(f321(x93311),x93312),x93315))+~P1(f319(f319(f321(f931(x93311,x93311)),f319(f319(f244(x93311,x93311),x93312),x93314)),x93313))
% 28.25/28.13 [9631]~P78(x96311)+~P1(f319(f55(x96312),x96315))+~P1(f319(f55(x96312),x96314))+~E(f319(f319(f93(f932(x96312,a923)),x96314),x96315),f180(f932(x96312,a923)))+E(f319(f319(f75(x96311),f319(f319(f319(f59(x96311,x96312,f75(x96311)),x96313),f72(x96311)),x96314)),f319(f319(f319(f59(x96311,x96312,f75(x96311)),x96313),f72(x96311)),x96315)),f319(f319(f319(f59(x96311,x96312,f75(x96311)),x96313),f72(x96311)),f319(f319(f102(f932(x96312,a923)),x96314),x96315)))
% 28.25/28.13 [9642]~P79(x96421)+~E(f319(x96423,f407(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)))
% 28.25/28.13 [9643]~P79(x96431)+~E(f319(x96433,f408(x96433,x96435,x96434,x96432,x96431)),f2(x96431))+~P1(f319(f55(x96432),x96434))+~P1(f319(f55(x96432),x96435))+E(f319(f319(f74(x96431),f319(f319(f6(x96432,x96431),x96433),x96434)),f319(f319(f6(x96432,x96431),x96433),x96435)),f319(f319(f6(x96432,x96431),x96433),f319(f319(f102(f932(x96432,a923)),x96434),x96435)))
% 28.25/28.13 [9644]~P78(x96441)+~E(f319(x96443,f492(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)))
% 28.25/28.13 [9645]~P78(x96451)+~E(f319(x96453,f493(x96453,x96455,x96454,x96452,x96451)),f72(x96451))+~P1(f319(f55(x96452),x96454))+~P1(f319(f55(x96452),x96455))+E(f319(f319(f75(x96451),f319(f319(f9(x96452,x96451),x96453),x96454)),f319(f319(f9(x96452,x96451),x96453),x96455)),f319(f319(f9(x96452,x96451),x96453),f319(f319(f102(f932(x96452,a923)),x96454),x96455)))
% 28.25/28.13 [9860]~P78(x98601)+~E(f319(x98603,f349(x98603,x98605,x98604,x98602,x98601)),f72(x98601))+~P1(f319(f55(x98602),x98604))+~P1(f319(f55(x98602),x98605))+E(f319(f319(f75(x98601),f319(f319(f319(f59(x98601,x98602,f75(x98601)),x98603),f72(x98601)),x98604)),f319(f319(f319(f59(x98601,x98602,f75(x98601)),x98603),f72(x98601)),x98605)),f319(f319(f319(f59(x98601,x98602,f75(x98601)),x98603),f72(x98601)),f319(f319(f102(f932(x98602,a923)),x98604),x98605)))
% 28.25/28.13 [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),f445(x99813,x99814,x99815,x99811,x99812)),f319(f319(f23(f932(x99811,a923)),x99815),x99814)))
% 28.25/28.13 [9982]~P79(x99822)+E(f319(f319(f6(x99821,x99822),x99823),x99824),f319(f319(f6(x99821,x99822),x99823),x99825))+~P1(f319(f55(x99821),x99825))+~P1(f319(f319(f226(f932(x99821,a923)),x99824),x99825))+P1(f319(f319(f321(x99821),f446(x99823,x99824,x99825,x99821,x99822)),f319(f319(f23(f932(x99821,a923)),x99825),x99824)))
% 28.25/28.13 [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),f505(x99833,x99834,x99835,x99831,x99832)),f319(f319(f23(f932(x99831,a923)),x99835),x99834)))
% 28.25/28.13 [9984]~P78(x99842)+E(f319(f319(f9(x99841,x99842),x99843),x99844),f319(f319(f9(x99841,x99842),x99843),x99845))+~P1(f319(f55(x99841),x99845))+~P1(f319(f319(f226(f932(x99841,a923)),x99844),x99845))+P1(f319(f319(f321(x99841),f506(x99843,x99844,x99845,x99841,x99842)),f319(f319(f23(f932(x99841,a923)),x99845),x99844)))
% 28.25/28.13 [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),f407(x100043,x100045,x100044,x100042,x100041)),f319(f319(f93(f932(x100042,a923)),x100044),x100045)))
% 28.25/28.13 [10005]~P79(x100051)+~P1(f319(f55(x100052),x100054))+~P1(f319(f55(x100052),x100055))+E(f319(f319(f74(x100051),f319(f319(f6(x100052,x100051),x100053),x100054)),f319(f319(f6(x100052,x100051),x100053),x100055)),f319(f319(f6(x100052,x100051),x100053),f319(f319(f102(f932(x100052,a923)),x100054),x100055)))+P1(f319(f319(f321(x100052),f408(x100053,x100055,x100054,x100052,x100051)),f319(f319(f93(f932(x100052,a923)),x100054),x100055)))
% 28.25/28.13 [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),f492(x100063,x100065,x100064,x100062,x100061)),f319(f319(f93(f932(x100062,a923)),x100064),x100065)))
% 28.25/28.13 [10007]~P78(x100071)+~P1(f319(f55(x100072),x100074))+~P1(f319(f55(x100072),x100075))+E(f319(f319(f75(x100071),f319(f319(f9(x100072,x100071),x100073),x100074)),f319(f319(f9(x100072,x100071),x100073),x100075)),f319(f319(f9(x100072,x100071),x100073),f319(f319(f102(f932(x100072,a923)),x100074),x100075)))+P1(f319(f319(f321(x100072),f493(x100073,x100075,x100074,x100072,x100071)),f319(f319(f93(f932(x100072,a923)),x100074),x100075)))
% 28.25/28.13 [10011]~P41(f932(x100113,a923),f932(x100113,a923),x100114)+P1(f319(x100111,x100112))+~E(x100115,f87(f932(x100113,a923),x100114))+~P1(f319(f319(f321(x100113),x100112),x100115))+P1(f319(f319(f321(x100113),f461(x100111,x100112,x100114,x100113,x100115)),f319(x100114,f319(f319(f93(f932(x100113,a923)),x100115),f319(f254(x100113),x100111)))))
% 28.25/28.13 [10015]~P93(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),f389(x100152,x100153,x100154,x100151,x100155)),f319(f319(f23(f932(x100151,a923)),x100154),x100153)))
% 28.25/28.13 [10062]~P78(x100621)+~P1(f319(f55(x100622),x100624))+~P1(f319(f55(x100622),x100625))+E(f319(f319(f75(x100621),f319(f319(f319(f59(x100621,x100622,f75(x100621)),x100623),f72(x100621)),x100624)),f319(f319(f319(f59(x100621,x100622,f75(x100621)),x100623),f72(x100621)),x100625)),f319(f319(f319(f59(x100621,x100622,f75(x100621)),x100623),f72(x100621)),f319(f319(f102(f932(x100622,a923)),x100624),x100625)))+P1(f319(f319(f321(x100622),f349(x100623,x100625,x100624,x100622,x100621)),f319(f319(f93(f932(x100622,a923)),x100624),x100625)))
% 28.25/28.13 [8991]~P20(x89911,x89914,x89915)+~P1(f319(f55(x89911),x89912))+E(f319(f319(f23(f932(x89911,a923)),x89912),f319(f319(f301(x89911),x89913),f180(f932(x89911,a923)))),f180(f932(x89911,a923)))+~P1(f319(f319(f321(x89911),x89913),x89912))+E(f319(f319(x89914,x89913),f319(x89915,f319(f319(f23(f932(x89911,a923)),x89912),f319(f319(f301(x89911),x89913),f180(f932(x89911,a923)))))),f319(x89915,x89912))
% 28.25/28.13 [9070]~P20(x90701,x90704,x90705)+~P1(f319(f55(x90701),x90703))+~P1(f319(f55(x90701),x90702))+E(f319(f319(f93(f932(x90701,a923)),x90702),x90703),f180(f932(x90701,a923)))+E(f319(f319(x90704,f319(x90705,f319(f319(f102(f932(x90701,a923)),x90702),x90703))),f319(x90705,f319(f319(f93(f932(x90701,a923)),x90702),x90703))),f319(f319(x90704,f319(x90705,x90702)),f319(x90705,x90703)))
% 28.25/28.13 [9258]~P41(f932(x92581,a923),f932(x92581,a923),x92584)+~E(x92583,f88(f932(x92581,a923),x92584))+P1(f319(f319(f321(x92581),x92582),x92583))+~P1(f319(f319(f321(x92581),x92582),x92585))+~P1(f319(f319(f226(f932(x92581,a923)),x92585),f319(x92584,f319(f319(f102(f932(x92581,a923)),x92585),x92583))))
% 28.25/28.13 [9647]~P1(f319(f319(f226(a1),x96474),f2(a1)))+~P1(f319(f319(f227(a1),x96473),x96475))+P1(f319(f319(f226(a1),x96471),x96472))+~P1(f319(f319(f227(a1),x96473),x96474))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f75(a1),x96473),x96472)),x96475)),f319(f319(f74(a1),f319(f319(f75(a1),x96473),x96471)),x96474)))
% 28.25/28.13 [9649]~P1(f319(f319(f226(a1),f2(a1)),x96495))+P1(f319(f319(f226(a1),x96491),x96492))+~P1(f319(f319(f227(a1),x96493),x96494))+~P1(f319(f319(f227(a1),x96495),x96494))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f75(a1),x96494),x96491)),x96495)),f319(f319(f74(a1),f319(f319(f75(a1),x96494),x96492)),x96493)))
% 28.25/28.13 [9766]~P73(x97665)+E(f319(x97661,f495(x97661,x97662,x97663,x97664,x97665)),f2(x97665))+~P1(f319(f55(x97664),x97663))+~P1(f319(f55(x97664),x97662))+E(f319(f319(f283(x97665),f319(f319(f75(x97665),f319(f319(f9(x97664,x97665),x97661),x97663)),f319(f319(f9(x97664,x97665),x97661),x97662))),f319(f319(f9(x97664,x97665),x97661),f319(f319(f93(f932(x97664,a923)),x97663),x97662))),f319(f319(f9(x97664,x97665),x97661),f319(f319(f102(f932(x97664,a923)),x97663),x97662)))
% 28.25/28.13 [10054]~P73(x100541)+~P1(f319(f55(x100542),x100544))+~P1(f319(f55(x100542),x100545))+E(f319(f319(f283(x100541),f319(f319(f75(x100541),f319(f319(f9(x100542,x100541),x100543),x100544)),f319(f319(f9(x100542,x100541),x100543),x100545))),f319(f319(f9(x100542,x100541),x100543),f319(f319(f93(f932(x100542,a923)),x100544),x100545))),f319(f319(f9(x100542,x100541),x100543),f319(f319(f102(f932(x100542,a923)),x100544),x100545)))+P1(f319(f319(f321(x100542),f495(x100543,x100545,x100544,x100542,x100541)),f319(f319(f93(f932(x100542,a923)),x100544),x100545)))
% 28.25/28.13 [9351]E(f319(f319(f126(x93511),x93512),x93513),f319(f319(f126(x93511),x93514),x93515))+~E(f319(f319(f167(x93511),f319(f181(f926(x93511)),x93514)),x93512),x93514)+~E(f319(f319(f167(x93511),f319(f181(f926(x93511)),x93512)),x93514),x93512)+~E(x93515,f319(f319(f126(x93511),f319(f319(f130(x93511),f319(f181(f926(x93511)),x93514)),x93512)),x93513))+~E(f319(f319(f126(x93511),f319(f319(f130(x93511),f319(f181(f926(x93511)),x93512)),x93514)),x93515),x93513)
% 28.25/28.13 [9764]~P4(x97642)+E(f319(f319(f140(x97641,x97642,x97643),x97644),f162(x97641,x97644,x97645)),x97645)+~P14(x97642,f319(f319(f146(x97641,x97642),x97643),x97645))+~P1(f319(f319(f321(x97641),x97644),f319(f164(x97641),x97645)))+~E(f319(f133(x97641),f319(f128(x97641,f319(f319(f8(x97642,a923,x97641),f319(a316,f319(x97643,x97644))),x97643)),x97645)),x97644)
% 28.25/28.13 [10121]~P76(x101211)+~P1(f319(f60(x101211,x101211,f75(x101211),x101212,x101213),x101215))+~P1(f319(f319(f321(x101211),x101214),x101213))+P1(f319(f319(f321(x101211),x101212),x101213))+P1(f319(f60(x101211,x101211,f75(x101211),x101214,f319(f319(f301(x101211),x101212),f319(f319(f23(f932(x101211,a923)),x101213),f319(f319(f301(x101211),x101214),f180(f932(x101211,a923)))))),x101215))
% 28.25/28.13 [10487]~P41(f932(x104871,a923),f932(x104871,a923),x104874)+~E(x104873,f88(f932(x104871,a923),x104874))+P1(f319(f319(f321(x104871),x104872),x104873))+~P1(f319(f319(f321(x104871),x104872),x104875))+~P1(f319(f319(f226(f932(x104871,a923)),x104875),f319(x104874,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))),x104874)),x104875))),x104873)))))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [7483]E(x74831,x74832)+~P26(x74834,x74835,x74833,x74836)+~E(f319(x74833,x74831),f319(x74833,x74832))+~P1(f319(f319(f321(x74834),x74832),x74836))+~P1(f319(f319(f321(x74834),x74831),x74836))
% 28.25/28.13 [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)))
% 28.25/28.13 [7762]~P4(x77621)+~P6(x77621)+~P1(f319(f319(f227(x77621),x77622),f319(x77625,x77626)))+~P1(f319(f319(f321(x77623),x77626),x77624))+P1(f319(f319(f227(x77621),x77622),f319(f319(f33(x77623,x77621),x77624),x77625)))
% 28.25/28.13 [10117]~P26(x101172,x101171,x101173,x101174)+~P26(x101171,x101172,x101176,x101175)+P27(x101171,x101172,f468(x101173,x101174,x101175,x101176,x101172,x101171),x101175,x101174)+~P1(f319(f319(f226(f932(x101172,a923)),f319(f302(x101171,x101172,x101176),x101175)),x101174))+~P1(f319(f319(f226(f932(x101171,a923)),f319(f302(x101172,x101171,x101173),x101174)),x101175))
% 28.25/28.13 [8445]~P4(x84451)+~P6(x84451)+~P1(f319(f319(f227(x84451),f319(x84454,x84456)),x84455))+~P1(f319(f319(f321(x84452),x84456),x84453))+P1(f319(f319(f227(x84451),f319(f319(f34(x84452,x84451),x84453),x84454)),x84455))
% 28.25/28.13 [8702]~P21(x87022,x87025,x87026,x87021)+~P1(f319(f55(x87022),x87024))+~P1(f319(f55(x87022),x87023))+~E(f319(f319(f93(f932(x87022,a923)),x87023),x87024),f180(f932(x87022,a923)))+E(f319(x87021,f319(f319(f102(f932(x87022,a923)),x87023),x87024)),f319(f66(x87025,x87025,x87025,f319(x87021,x87023)),f319(x87021,x87024)))
% 28.25/28.13 [10333]~P78(x103331)+~E(f831(x103334,x103335,x103333,x103336,x103332,x103331),f832(x103334,x103335,x103333,x103336,x103332,x103331))+~P1(f319(f55(x103332),x103336))+E(f319(f319(f319(f59(x103331,x103332,f75(x103331)),f319(f319(f8(f932(x103333,a923),x103331,x103332),f319(f319(f59(x103331,x103333,f75(x103331)),x103334),f72(x103331))),x103335)),f72(x103331)),x103336),f319(f319(f319(f59(x103331,x103333,f75(x103331)),x103334),f72(x103331)),f319(f319(f33(x103332,f932(x103333,a923)),x103336),x103335)))+P1(f319(f319(f321(x103332),f829(x103334,x103335,x103333,x103336,x103332,x103331)),x103336))
% 28.25/28.13 [10363]~P78(x103631)+~E(f831(x103634,x103635,x103633,x103636,x103632,x103631),f832(x103634,x103635,x103633,x103636,x103632,x103631))+~P1(f319(f55(x103632),x103636))+E(f319(f319(f319(f59(x103631,x103632,f75(x103631)),f319(f319(f8(f932(x103633,a923),x103631,x103632),f319(f319(f59(x103631,x103633,f75(x103631)),x103634),f72(x103631))),x103635)),f72(x103631)),x103636),f319(f319(f319(f59(x103631,x103633,f75(x103631)),x103634),f72(x103631)),f319(f319(f33(x103632,f932(x103633,a923)),x103636),x103635)))+~P1(f319(f55(x103633),f319(x103635,f829(x103634,x103635,x103633,x103636,x103632,x103631))))
% 28.25/28.13 [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),f832(x103664,x103665,x103663,x103666,x103662,x103661)),x103666))
% 28.25/28.13 [10367]~P78(x103671)+~P1(f319(f55(x103672),x103676))+E(f319(f319(f319(f59(x103671,x103672,f75(x103671)),f319(f319(f8(f932(x103673,a923),x103671,x103672),f319(f319(f59(x103671,x103673,f75(x103671)),x103674),f72(x103671))),x103675)),f72(x103671)),x103676),f319(f319(f319(f59(x103671,x103673,f75(x103671)),x103674),f72(x103671)),f319(f319(f33(x103672,f932(x103673,a923)),x103676),x103675)))+P1(f319(f319(f321(x103672),f829(x103674,x103675,x103673,x103676,x103672,x103671)),x103676))+P1(f319(f319(f321(x103672),f831(x103674,x103675,x103673,x103676,x103672,x103671)),x103676))
% 28.25/28.13 [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),f832(x103854,x103855,x103853,x103856,x103852,x103851)),x103856))+~P1(f319(f55(x103853),f319(x103855,f829(x103854,x103855,x103853,x103856,x103852,x103851))))
% 28.25/28.13 [10386]~P78(x103861)+~P1(f319(f55(x103862),x103866))+E(f319(f319(f319(f59(x103861,x103862,f75(x103861)),f319(f319(f8(f932(x103863,a923),x103861,x103862),f319(f319(f59(x103861,x103863,f75(x103861)),x103864),f72(x103861))),x103865)),f72(x103861)),x103866),f319(f319(f319(f59(x103861,x103863,f75(x103861)),x103864),f72(x103861)),f319(f319(f33(x103862,f932(x103863,a923)),x103866),x103865)))+P1(f319(f319(f321(x103862),f831(x103864,x103865,x103863,x103866,x103862,x103861)),x103866))+~P1(f319(f55(x103863),f319(x103865,f829(x103864,x103865,x103863,x103866,x103862,x103861))))
% 28.25/28.13 [10397]~P78(x103971)+~E(f319(f319(f93(f932(x103973,a923)),f319(x103975,f832(x103974,x103975,x103973,x103976,x103972,x103971))),f319(x103975,f831(x103974,x103975,x103973,x103976,x103972,x103971))),f180(f932(x103973,a923)))+~P1(f319(f55(x103972),x103976))+E(f319(f319(f319(f59(x103971,x103972,f75(x103971)),f319(f319(f8(f932(x103973,a923),x103971,x103972),f319(f319(f59(x103971,x103973,f75(x103971)),x103974),f72(x103971))),x103975)),f72(x103971)),x103976),f319(f319(f319(f59(x103971,x103973,f75(x103971)),x103974),f72(x103971)),f319(f319(f33(x103972,f932(x103973,a923)),x103976),x103975)))+P1(f319(f319(f321(x103972),f829(x103974,x103975,x103973,x103976,x103972,x103971)),x103976))
% 28.25/28.13 [10408]~P78(x104081)+~E(f319(f319(f93(f932(x104083,a923)),f319(x104085,f832(x104084,x104085,x104083,x104086,x104082,x104081))),f319(x104085,f831(x104084,x104085,x104083,x104086,x104082,x104081))),f180(f932(x104083,a923)))+~P1(f319(f55(x104082),x104086))+E(f319(f319(f319(f59(x104081,x104082,f75(x104081)),f319(f319(f8(f932(x104083,a923),x104081,x104082),f319(f319(f59(x104081,x104083,f75(x104081)),x104084),f72(x104081))),x104085)),f72(x104081)),x104086),f319(f319(f319(f59(x104081,x104083,f75(x104081)),x104084),f72(x104081)),f319(f319(f33(x104082,f932(x104083,a923)),x104086),x104085)))+~P1(f319(f55(x104083),f319(x104085,f829(x104084,x104085,x104083,x104086,x104082,x104081))))
% 28.25/28.13 [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)))
% 28.25/28.13 [9443]~P123(x94431)+~P120(x94431)+~P1(f319(f319(f279(x94431),x94432),x94435))+~P1(f319(f319(f279(x94431),x94432),f319(f319(f74(x94431),x94433),x94436)))+P1(f319(f319(f279(x94431),x94432),f319(f319(f74(x94431),f319(f319(f23(x94431),x94433),f319(f319(f75(x94431),x94434),x94435))),x94436)))
% 28.25/28.13 [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)))
% 28.25/28.13 [9636]~P123(x96361)+~P120(x96361)+~P1(f319(f319(f279(x96361),x96362),x96365))+P1(f319(f319(f279(x96361),x96362),f319(f319(f74(x96361),x96363),x96364)))+~P1(f319(f319(f279(x96361),x96362),f319(f319(f74(x96361),f319(f319(f23(x96361),x96363),f319(f319(f75(x96361),x96366),x96365))),x96364)))
% 28.25/28.13 [9040]E(x90401,x90402)+~P61(x90404,x90405,x90406,x90403,x90407)+~E(f319(x90403,x90401),f319(x90403,x90402))+~P1(f319(f319(f321(x90405),x90402),x90407))+~P1(f319(f319(f321(x90405),x90401),x90407))
% 28.25/28.13 [9763]~P27(x97631,x97632,x97633,x97635,x97637)+~P27(x97631,x97632,x97633,x97634,x97636)+P27(x97631,x97632,x97633,f319(f319(f102(f932(x97631,a923)),x97634),x97635),f319(f319(f102(f932(x97632,a923)),x97636),x97637))+~E(f319(f319(f93(f932(x97632,a923)),x97636),x97637),f180(f932(x97632,a923)))+~E(f319(f319(f93(f932(x97631,a923)),x97634),x97635),f180(f932(x97631,a923)))
% 28.25/28.13 [10375]~P1(f319(x103752,x103754))+~E(x103755,f319(f128(x103751,x103752),x103757))+E(f319(f128(x103751,x103752),x103753),f319(f319(f143(x103751),x103754),x103755))+~E(x103753,f319(f319(f126(x103751),x103756),f319(f319(f143(x103751),x103754),x103757)))+P1(f319(x103752,f769(x103755,x103754,x103753,x103752,x103751,x103756,x103757)))
% 28.25/28.13 [10376]~P1(f319(x103764,x103762))+~E(x103763,f319(f128(x103761,x103764),x103767))+E(f319(f319(f143(x103761),x103762),x103763),f319(f128(x103761,x103764),x103765))+~E(x103765,f319(f319(f126(x103761),x103766),f319(f319(f143(x103761),x103762),x103767)))+P1(f319(x103764,f768(x103765,x103764,x103763,x103762,x103761,x103766,x103767)))
% 28.25/28.13 [10421]~P1(f319(x104212,x104214))+~E(x104215,f319(f128(x104211,x104212),x104217))+E(f319(f128(x104211,x104212),x104213),f319(f319(f143(x104211),x104214),x104215))+~E(x104213,f319(f319(f126(x104211),x104216),f319(f319(f143(x104211),x104214),x104217)))+P1(f319(f319(f321(x104211),f769(x104215,x104214,x104213,x104212,x104211,x104216,x104217)),f319(f164(x104211),x104216)))
% 28.25/28.13 [10422]~P1(f319(x104224,x104222))+~E(x104223,f319(f128(x104221,x104224),x104227))+E(f319(f319(f143(x104221),x104222),x104223),f319(f128(x104221,x104224),x104225))+~E(x104225,f319(f319(f126(x104221),x104226),f319(f319(f143(x104221),x104222),x104227)))+P1(f319(f319(f321(x104221),f768(x104225,x104224,x104223,x104222,x104221,x104226,x104227)),f319(f164(x104221),x104226)))
% 28.25/28.13 [10426]~P9(x104261,x104267,x104266)+~P12(x104261,f932(x104265,a923),x104266,x104264)+P1(f319(f319(f321(x104261),f550(x104262,x104263,x104264,x104265,x104266,x104267,x104261)),x104267))+~P1(f319(f319(f321(f932(x104261,a923)),x104263),f319(f319(f54(x104261),x104267),x104266)))+P1(f319(f319(f321(f932(x104265,a923)),f319(f319(f33(x104261,f932(x104265,a923)),x104263),x104264)),x104262))
% 28.25/28.13 [10482]~P9(x104822,x104826,x104827)+~P12(x104822,f932(x104821,a923),x104827,x104824)+~P1(f319(f319(f321(f932(x104822,a923)),x104823),f319(f319(f54(x104822),x104826),x104827)))+~P1(f319(f319(f321(f932(x104821,a923)),f319(x104824,f550(x104825,x104823,x104824,x104821,x104827,x104826,x104822))),x104825))+P1(f319(f319(f321(f932(x104821,a923)),f319(f319(f33(x104822,f932(x104821,a923)),x104823),x104824)),x104825))
% 28.25/28.13 [8620]~P78(x86202)+~P26(x86201,x86205,x86208,x86204)+~E(x86203,f319(f66(x86205,x86202,x86201,x86206),x86208))+~E(x86207,f319(f302(x86201,x86205,x86208),x86204))+E(f319(f319(f9(x86201,x86202),x86203),x86204),f319(f319(f9(x86205,x86202),x86206),x86207))
% 28.25/28.13 [10486]~P78(x104862)+~P26(x104865,x104861,x104868,x104867)+~E(f319(x104866,f500(x104863,x104866,x104864,x104867,x104868,x104861,x104865,x104862)),f319(f319(f66(x104861,x104862,x104865,x104863),x104868),f500(x104863,x104866,x104864,x104867,x104868,x104861,x104865,x104862)))+~E(x104864,f319(f302(x104865,x104861,x104868),x104867))+E(f319(f319(f9(x104861,x104862),x104863),x104864),f319(f319(f9(x104865,x104862),x104866),x104867))
% 28.25/28.13 [10491]~P79(x104912)+~P26(x104911,x104915,x104918,x104914)+~E(x104917,f319(f302(x104911,x104915,x104918),x104914))+E(f319(f319(f6(x104911,x104912),x104913),x104914),f319(f319(f6(x104915,x104912),x104916),x104917))+P1(f319(f319(f321(x104911),f622(x104916,x104913,x104917,x104914,x104918,x104915,x104911,x104912)),x104914))
% 28.25/28.13 [10492]~P78(x104922)+~P26(x104921,x104925,x104928,x104924)+~E(x104927,f319(f302(x104921,x104925,x104928),x104924))+E(f319(f319(f9(x104921,x104922),x104923),x104924),f319(f319(f9(x104925,x104922),x104926),x104927))+P1(f319(f319(f321(x104921),f500(x104926,x104923,x104927,x104924,x104928,x104925,x104921,x104922)),x104924))
% 28.25/28.13 [10497]~P79(x104972)+~P26(x104975,x104971,x104978,x104977)+~E(x104974,f319(f302(x104975,x104971,x104978),x104977))+~E(f319(x104976,f622(x104973,x104976,x104974,x104977,x104978,x104971,x104975,x104972)),f319(x104973,f319(x104978,f622(x104973,x104976,x104974,x104977,x104978,x104971,x104975,x104972))))+E(f319(f319(f6(x104971,x104972),x104973),x104974),f319(f319(f6(x104975,x104972),x104976),x104977))
% 28.25/28.13 [9937]~P25(x99376,x99372,x99375,x99377,x99378,x99371)+~P1(f319(f55(x99372),x99374))+~P1(f319(f55(x99372),x99373))+~E(f319(f319(f93(f932(x99372,a923)),x99373),x99374),f180(f932(x99372,a923)))+E(f319(x99371,f319(f319(f102(f932(x99372,a923)),x99373),x99374)),f319(f319(x99375,f319(x99371,x99373)),f319(x99371,x99374)))
% 28.25/28.13 [10360]~P25(x103608,x103602,x103605,x103607,x103606,x103601)+~E(f319(x103606,f344(x103604,x103603,x103601,x103606,x103607,x103605,x103602)),x103607)+~P1(f319(f55(x103602),x103603))+~P1(f319(f55(x103602),x103604))+E(f319(x103601,f319(f319(f102(f932(x103602,a923)),x103603),x103604)),f319(f319(x103605,f319(x103601,x103603)),f319(x103601,x103604)))
% 28.25/28.13 [10433]~P25(x104338,x104332,x104335,x104337,x104336,x104331)+~P1(f319(f55(x104332),x104333))+~P1(f319(f55(x104332),x104334))+E(f319(x104331,f319(f319(f102(f932(x104332,a923)),x104333),x104334)),f319(f319(x104335,f319(x104331,x104333)),f319(x104331,x104334)))+P1(f319(f319(f321(x104332),f344(x104334,x104333,x104331,x104336,x104337,x104335,x104332)),f319(f319(f93(f932(x104332,a923)),x104333),x104334)))
% 28.25/28.13 [10108]~P9(x101084,x101088,x101085)+~P9(x101081,x101089,x101083)+~P13(x101081,x101084,f932(x101082,a923),x101083,x101085,x101087)+P12(x101081,f932(x101082,a923),x101083,f319(f319(f8(f932(x101084,f932(x101082,a923)),f932(x101082,a923),x101081),f319(f33(x101084,f932(x101082,a923)),f319(f277(x101084,x101084,x101085),f319(f319(f301(x101084),x101086),f180(f932(x101084,a923)))))),x101087))+~P1(f319(f319(f321(x101084),x101086),x101088))
% 28.25/28.13 [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))
% 28.25/28.13 [7474]P17(x74741,x74742)+~E(f319(x74742,f827(x74742)),f319(x74742,f828(x74742)))+~P1(f319(f319(x74742,f827(x74742)),f827(x74742)))+~P1(f319(f319(x74742,f827(x74742)),f828(x74742)))+~P1(f319(f319(x74742,f828(x74742)),f828(x74742)))+~P1(f319(f319(x74742,x74743),x74743))
% 28.25/28.13 [5256]~P133(x52562)+~P138(x52562)+~P150(x52562)+~P119(x52562)+E(x52561,f2(x52562))+~E(f319(f319(f236(x52562),x52561),x52563),f2(x52562))
% 28.25/28.13 [5257]~P133(x52572)+~P138(x52572)+~P150(x52572)+~P119(x52572)+~E(x52571,f2(a925))+~E(f319(f319(f236(x52572),x52573),x52571),f2(x52572))
% 28.25/28.13 [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))
% 28.25/28.13 [9090]E(x90901,f2(a925))+~E(x90902,f319(f319(f74(a925),f319(f319(f75(a925),f319(f243(a925,a925),x90903)),x90901)),f319(f248(a925,a925),x90903)))+P1(f319(f42(x90902,x90901),x90903))+~P1(f319(f319(f226(a925),f319(f248(a925,a925),x90903)),f2(a925)))+P1(f319(f319(f227(a925),f2(a925)),x90901))+~P1(f319(f319(f227(a925),x90901),f319(f248(a925,a925),x90903)))
% 28.25/28.13 [9109]~E(f319(f243(a925,a925),x91093),f2(a925))+~E(x91091,f319(f319(f74(a925),f319(f319(f75(a925),f319(f243(a925,a925),x91093)),x91092)),f319(f248(a925,a925),x91093)))+P1(f319(f42(x91091,x91092),x91093))+~P1(f319(f319(f226(a925),f319(f248(a925,a925),x91093)),f2(a925)))+P1(f319(f319(f227(a925),f2(a925)),x91092))+~P1(f319(f319(f227(a925),x91092),f319(f248(a925,a925),x91093)))
% 28.25/28.13 [9117]E(x91171,f2(a925))+~E(x91172,f319(f319(f74(a925),f319(f319(f75(a925),f319(f243(a925,a925),x91173)),x91171)),f319(f248(a925,a925),x91173)))+P1(f319(f42(x91172,x91171),x91173))+~P1(f319(f319(f227(a925),f2(a925)),x91171))+~P1(f319(f319(f226(a925),f2(a925)),f319(f248(a925,a925),x91173)))+~P1(f319(f319(f227(a925),f319(f248(a925,a925),x91173)),x91171))
% 28.25/28.13 [9135]~E(f319(f243(a925,a925),x91353),f2(a925))+~E(x91351,f319(f319(f74(a925),f319(f319(f75(a925),f319(f243(a925,a925),x91353)),x91352)),f319(f248(a925,a925),x91353)))+P1(f319(f42(x91351,x91352),x91353))+~P1(f319(f319(f227(a925),f2(a925)),x91352))+~P1(f319(f319(f226(a925),f2(a925)),f319(f248(a925,a925),x91353)))+~P1(f319(f319(f227(a925),f319(f248(a925,a925),x91353)),x91352))
% 28.25/28.13 [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(f10(x71012,f319(f319(f102(f932(x71012,a923)),x71013),x71011)),f319(f319(f93(x71012),f10(x71012,x71013)),f10(x71012,x71011)))
% 28.25/28.13 [7102]~P102(x71022)+E(x71021,f180(f932(x71022,a923)))+E(x71023,f180(f932(x71022,a923)))+~P1(f319(f55(x71022),x71021))+~P1(f319(f55(x71022),x71023))+E(f13(x71022,f319(f319(f102(f932(x71022,a923)),x71023),x71021)),f319(f319(f102(x71022),f13(x71022,x71023)),f13(x71022,x71021)))
% 28.25/28.13 [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(f14(x71032,f319(f319(f102(f932(x71032,a923)),x71033),x71031)),f319(f319(f224(x71032),f14(x71032,x71033)),f14(x71032,x71031)))
% 28.25/28.13 [7104]~P4(x71042)+E(x71041,f180(f932(x71042,a923)))+E(x71043,f180(f932(x71042,a923)))+~P1(f319(f55(x71042),x71041))+~P1(f319(f55(x71042),x71043))+E(f15(x71042,f319(f319(f102(f932(x71042,a923)),x71043),x71041)),f319(f319(f225(x71042),f15(x71042,x71043)),f15(x71042,x71041)))
% 28.25/28.13 [7737]~P101(x77372)+E(x77371,f180(f932(x77372,a923)))+E(x77373,f180(f932(x77372,a923)))+~P1(f319(f55(x77372),x77371))+~P1(f319(f55(x77372),x77373))+E(f319(f319(f75(x77372),f319(f57(x77372,f75(x77372)),x77373)),f319(f57(x77372,f75(x77372)),x77371)),f319(f57(x77372,f75(x77372)),f319(f319(f102(f932(x77372,a923)),x77373),x77371)))
% 28.25/28.13 [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(f224(x78972),f11(x78972,f224(x78972),x78973)),f11(x78972,f224(x78972),x78971)),f11(x78972,f224(x78972),f319(f319(f102(f932(x78972,a923)),x78973),x78971)))
% 28.25/28.13 [7898]~P4(x78982)+E(x78981,f180(f932(x78982,a923)))+E(x78983,f180(f932(x78982,a923)))+~P1(f319(f55(x78982),x78981))+~P1(f319(f55(x78982),x78983))+E(f319(f319(f225(x78982),f12(x78982,f225(x78982),x78983)),f12(x78982,f225(x78982),x78981)),f12(x78982,f225(x78982),f319(f319(f102(f932(x78982,a923)),x78983),x78981)))
% 28.25/28.13 [8940]~P1(f319(x89401,x89403))+P1(f319(x89401,f395(x89401,x89402)))+P1(f319(x89401,f379(x89401,x89402)))+~P1(f319(f319(f227(a1),f2(a1)),x89402))+~P1(f319(f319(f321(a1),x89403),f295(a1,f72(a1),x89402)))+P1(f319(x89401,f319(f319(f23(a1),f379(x89401,x89402)),f319(f319(f75(a1),f391(x89401,x89402)),x89402))))
% 28.25/28.13 [9248]~P1(f319(x92481,x92483))+~P1(f319(x92481,f379(x92481,x92482)))+P1(f319(x92481,f395(x92481,x92482)))+~P1(f319(f319(f227(a1),f2(a1)),x92482))+~P1(f319(f319(f321(a1),x92483),f295(a1,f72(a1),x92482)))+~P1(f319(x92481,f319(f319(f23(a1),f379(x92481,x92482)),f319(f319(f75(a1),f391(x92481,x92482)),x92482))))
% 28.25/28.13 [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(f10(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))),f102(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(f102(x105252),f10(x105252,x105253)),f10(x105252,x105251)))
% 28.25/28.13 [10526]~P106(x105262)+E(x105261,f180(f932(x105262,a923)))+E(x105263,f180(f932(x105262,a923)))+~P1(f319(f55(x105262),x105261))+~P1(f319(f55(x105262),x105263))+E(f13(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))),f93(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(f93(x105262),f13(x105262,x105263)),f13(x105262,x105261)))
% 28.25/28.13 [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(f12(x105272,f225(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))),f224(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(f224(x105272),f12(x105272,f225(x105272),x105273)),f12(x105272,f225(x105272),x105271)))
% 28.25/28.13 [10528]~P4(x105282)+E(x105281,f180(f932(x105282,a923)))+E(x105283,f180(f932(x105282,a923)))+~P1(f319(f55(x105282),x105281))+~P1(f319(f55(x105282),x105283))+E(f11(x105282,f224(x105282),f319(f254(x105282),f319(f319(f8(f932(x105282,a923),a923,x105282),f81(x105282)),f319(f319(f8(f932(x105282,f932(x105282,a923)),f932(x105282,a923),x105282),f319(f8(f932(x105282,a923),a923,x105282),f81(x105282))),f319(f319(f7(x105282,f932(x105282,f932(x105282,a923)),f932(x105282,f932(x105282,a923))),f319(f319(f8(f932(x105282,f932(f932(x105282,a923),f932(x105282,a923))),f932(f932(x105282,f932(x105282,a923)),f932(x105282,f932(x105282,a923))),x105282),f18(x105282,f932(x105282,a923),f932(x105282,a923))),f319(f319(f8(f932(x105282,f932(x105282,f932(a923,a923))),f932(x105282,f932(f932(x105282,a923),f932(x105282,a923))),x105282),f319(f8(f932(x105282,f932(a923,a923)),f932(f932(x105282,a923),f932(x105282,a923)),x105282),f18(x105282,a923,a923))),f319(f319(f8(f932(x105282,f932(x105282,a923)),f932(x105282,f932(x105282,f932(a923,a923))),x105282),f319(f8(f932(x105282,a923),f932(x105282,f932(a923,a923)),x105282),f319(f8(a923,f932(a923,a923),x105282),a317))),f319(f319(f7(x105282,f932(x105282,f932(x105282,x105282)),f932(x105282,f932(x105282,a923))),f319(f319(f8(f932(f932(x105282,x105282),f932(x105282,a923)),f932(f932(x105282,f932(x105282,x105282)),f932(x105282,f932(x105282,a923))),x105282),f8(f932(x105282,x105282),f932(x105282,a923),x105282)),f319(f319(f8(f932(x105282,a923),f932(f932(x105282,x105282),f932(x105282,a923)),x105282),f8(x105282,a923,x105282)),a316))),f225(x105282)))))),f319(f319(f7(x105282,f932(x105282,a923),f932(x105282,a923)),f319(f319(f8(f932(a923,a923),f932(f932(x105282,a923),f932(x105282,a923)),x105282),f8(a923,a923,x105282)),f319(f319(f8(a923,f932(a923,a923),x105282),a317),f319(f319(f7(x105282,f932(x105282,a923),a923),f321(x105282)),x105283)))),f319(f319(f7(x105282,f932(x105282,a923),a923),f321(x105282)),x105281))))))),f319(f319(f225(x105282),f11(x105282,f224(x105282),x105283)),f11(x105282,f224(x105282),x105281)))
% 28.25/28.13 [7430]~P129(x74303)+E(x74301,x74302)+~E(f319(f319(f236(x74303),x74301),x74304),f319(f319(f236(x74303),x74302),x74304))+~P1(f319(f319(f226(x74303),f2(x74303)),x74302))+~P1(f319(f319(f226(x74303),f2(x74303)),x74301))+~P1(f319(f319(f227(a925),f2(a925)),x74304))
% 28.25/28.13 [8249]~P74(x82491)+~P100(x82491)+P1(f319(f319(f227(x82491),x82492),f2(x82491)))+P1(f319(f319(f227(x82491),f2(x82491)),x82492))+P1(f319(f319(f226(x82491),f319(f319(f283(x82491),x82493),x82492)),f319(f95(x82491),x82494)))+~P1(f319(f319(f226(x82491),f2(x82491)),f319(f95(x82491),x82494)))
% 28.25/28.13 [8250]~P74(x82501)+~P100(x82501)+P1(f319(f319(f227(x82501),x82502),f2(x82501)))+P1(f319(f319(f227(x82501),f2(x82501)),x82502))+P1(f319(f319(f227(x82501),f319(f319(f283(x82501),x82503),x82502)),f319(f95(x82501),x82504)))+~P1(f319(f319(f227(x82501),f2(x82501)),f319(f95(x82501),x82504)))
% 28.25/28.13 [8493]~P74(x84931)+~P100(x84931)+P1(f319(f319(f227(x84931),x84932),f2(x84931)))+P1(f319(f319(f227(x84931),f2(x84931)),x84932))+~P1(f319(f319(f226(x84931),f319(f319(f283(x84931),x84934),x84932)),f319(f95(x84931),x84933)))+P1(f319(f319(f226(x84931),f2(x84931)),f319(f95(x84931),x84933)))
% 28.25/28.13 [8494]~P74(x84941)+~P100(x84941)+P1(f319(f319(f227(x84941),x84942),f2(x84941)))+P1(f319(f319(f227(x84941),f2(x84941)),x84942))+~P1(f319(f319(f227(x84941),f319(f319(f283(x84941),x84944),x84942)),f319(f95(x84941),x84943)))+P1(f319(f319(f227(x84941),f2(x84941)),f319(f95(x84941),x84943)))
% 28.25/28.13 [9389]~P1(f319(x93892,x93893))+~P1(f319(x93891,x93894))+E(f230(a925,x93891),f319(a104,f230(a925,x93892)))+P1(f319(x93892,f841(x93893,x93892,x93894,x93891)))+P1(f319(x93891,f2(a925)))+P1(f319(x93891,f319(a104,f841(x93893,x93892,x93894,x93891))))
% 28.25/28.13 [9651]~P1(f319(x96512,x96513))+~P1(f319(x96511,x96514))+E(f230(a925,x96511),f319(a104,f230(a925,x96512)))+~P1(f319(x96512,f841(x96513,x96512,x96514,x96511)))+P1(f319(x96511,f2(a925)))+~P1(f319(x96511,f319(a104,f841(x96513,x96512,x96514,x96511))))
% 28.25/28.13 [7699]~P4(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,f224(x76992)),x76991)))
% 28.25/28.13 [7700]~P108(x77002)+E(x77001,f180(f932(x77002,a923)))+~P1(f319(f55(x77002),x77001))+~P1(f319(f319(f321(x77002),x77004),x77001))+P1(f319(f319(f226(x77002),x77003),x77004))+~P1(f319(f319(f226(x77002),x77003),f319(f57(x77002,f93(x77002)),x77001)))
% 28.25/28.13 [7701]~P4(x77012)+E(x77011,f180(f932(x77012,a923)))+~P1(f319(f55(x77012),x77011))+~P1(f319(f319(f321(x77012),x77014),x77011))+P1(f319(f319(f227(x77012),x77013),x77014))+~P1(f319(f319(f227(x77012),x77013),f319(f57(x77012,f224(x77012)),x77011)))
% 28.25/28.13 [8203]~P74(x82031)+~P100(x82031)+P1(f319(f319(f227(x82031),f319(f95(x82031),x82032)),f2(x82031)))+~P1(f319(f319(f226(x82031),x82033),f2(x82031)))+P1(f319(f319(f227(x82031),f2(x82031)),f319(f95(x82031),x82032)))+P1(f319(f319(f226(x82031),x82033),f319(f319(f283(x82031),x82034),f319(f95(x82031),x82032))))
% 28.25/28.13 [8204]~P74(x82041)+~P100(x82041)+P1(f319(f319(f227(x82041),f319(f95(x82041),x82042)),f2(x82041)))+~P1(f319(f319(f227(x82041),x82043),f2(x82041)))+P1(f319(f319(f227(x82041),f2(x82041)),f319(f95(x82041),x82042)))+P1(f319(f319(f227(x82041),x82043),f319(f319(f283(x82041),x82044),f319(f95(x82041),x82042))))
% 28.25/28.13 [8217]~P74(x82171)+~P100(x82171)+P1(f319(f319(f227(x82171),x82172),f2(x82171)))+~P1(f319(f319(f226(x82171),f319(f95(x82171),x82173)),f2(x82171)))+P1(f319(f319(f227(x82171),f2(x82171)),x82172))+P1(f319(f319(f226(x82171),f319(f95(x82171),x82173)),f319(f319(f283(x82171),x82174),x82172)))
% 28.25/28.13 [8218]~P74(x82181)+~P100(x82181)+P1(f319(f319(f227(x82181),x82182),f2(x82181)))+~P1(f319(f319(f227(x82181),f319(f95(x82181),x82183)),f2(x82181)))+P1(f319(f319(f227(x82181),f2(x82181)),x82182))+P1(f319(f319(f227(x82181),f319(f95(x82181),x82183)),f319(f319(f283(x82181),x82184),x82182)))
% 28.25/28.13 [8365]~P74(x83651)+~P100(x83651)+P1(f319(f319(f227(x83651),x83652),f2(x83651)))+P1(f319(f319(f226(x83651),f319(f95(x83651),x83653)),f2(x83651)))+P1(f319(f319(f227(x83651),f2(x83651)),x83652))+~P1(f319(f319(f226(x83651),f319(f95(x83651),x83653)),f319(f319(f283(x83651),x83654),x83652)))
% 28.25/28.13 [8366]~P74(x83661)+~P100(x83661)+P1(f319(f319(f227(x83661),x83662),f2(x83661)))+P1(f319(f319(f227(x83661),f319(f95(x83661),x83663)),f2(x83661)))+P1(f319(f319(f227(x83661),f2(x83661)),x83662))+~P1(f319(f319(f227(x83661),f319(f95(x83661),x83663)),f319(f319(f283(x83661),x83664),x83662)))
% 28.25/28.13 [8439]~P74(x84391)+~P100(x84391)+P1(f319(f319(f226(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(f226(x84391),x84392),f319(f319(f283(x84391),x84394),f319(f95(x84391),x84393))))
% 28.25/28.13 [8440]~P74(x84401)+~P100(x84401)+P1(f319(f319(f227(x84401),x84402),f2(x84401)))+P1(f319(f319(f227(x84401),f319(f95(x84401),x84403)),f2(x84401)))+P1(f319(f319(f227(x84401),f2(x84401)),f319(f95(x84401),x84403)))+~P1(f319(f319(f227(x84401),x84402),f319(f319(f283(x84401),x84404),f319(f95(x84401),x84403))))
% 28.25/28.13 [8634]~P74(x86341)+~P100(x86341)+~P1(f319(f319(f226(x86341),x86343),f2(x86341)))+P1(f319(f319(f227(x86341),f2(x86341)),f319(f95(x86341),x86342)))+~P1(f319(f319(f226(x86341),x86344),f319(f319(f75(x86341),x86343),f319(f95(x86341),x86342))))+P1(f319(f319(f226(x86341),x86343),f319(f319(f283(x86341),x86344),f319(f95(x86341),x86342))))
% 28.25/28.13 [8635]~P74(x86351)+~P100(x86351)+~P1(f319(f319(f227(x86351),x86353),f2(x86351)))+P1(f319(f319(f227(x86351),f2(x86351)),f319(f95(x86351),x86352)))+~P1(f319(f319(f227(x86351),x86354),f319(f319(f75(x86351),x86353),f319(f95(x86351),x86352))))+P1(f319(f319(f227(x86351),x86353),f319(f319(f283(x86351),x86354),f319(f95(x86351),x86352))))
% 28.25/28.13 [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(f75(x88051),x88053),f319(f95(x88051),x88052))))+P1(f319(f319(f226(x88051),x88053),f319(f319(f283(x88051),x88054),f319(f95(x88051),x88052))))
% 28.25/28.13 [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(f226(x88061),x88064),f319(f319(f283(x88061),x88063),f319(f95(x88061),x88062))))+P1(f319(f319(f226(x88061),x88063),f319(f319(f75(x88061),x88064),f319(f95(x88061),x88062))))
% 28.25/28.13 [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(f75(x88071),x88073),f319(f95(x88071),x88072))))+P1(f319(f319(f227(x88071),x88073),f319(f319(f283(x88071),x88074),f319(f95(x88071),x88072))))
% 28.25/28.13 [8808]~P74(x88081)+~P100(x88081)+~P1(f319(f319(f227(x88081),f319(f95(x88081),x88082)),f2(x88081)))+P1(f319(f319(f227(x88081),f2(x88081)),f319(f95(x88081),x88082)))+~P1(f319(f319(f227(x88081),x88084),f319(f319(f283(x88081),x88083),f319(f95(x88081),x88082))))+P1(f319(f319(f227(x88081),x88083),f319(f319(f75(x88081),x88084),f319(f95(x88081),x88082))))
% 28.25/28.13 [7606]E(x76061,f2(a1))+E(f319(f319(f30(a1),x76062),x76061),x76063)+~P1(f319(f319(f226(a1),x76064),f2(a1)))+~E(x76062,f319(f319(f74(a1),f319(f319(f75(a1),x76061),x76063)),x76064))+P1(f319(f319(f227(a1),f2(a1)),x76061))+~P1(f319(f319(f227(a1),x76061),x76064))
% 28.25/28.13 [7622]E(f39(a1,x76222,x76221),x76223)+E(x76221,f2(a1))+~P1(f319(f319(f226(a1),x76223),f2(a1)))+~E(x76222,f319(f319(f74(a1),f319(f319(f75(a1),x76221),x76224)),x76223))+P1(f319(f319(f227(a1),f2(a1)),x76221))+~P1(f319(f319(f227(a1),x76221),x76223))
% 28.25/28.13 [7736]E(x77361,f2(a1))+E(f319(f319(f30(a1),x77362),x77361),x77363)+~E(x77362,f319(f319(f74(a1),f319(f319(f75(a1),x77361),x77363)),x77364))+~P1(f319(f319(f226(a1),f2(a1)),x77364))+~P1(f319(f319(f227(a1),f2(a1)),x77361))+~P1(f319(f319(f227(a1),x77364),x77361))
% 28.25/28.13 [7758]E(f39(a1,x77582,x77581),x77583)+E(x77581,f2(a1))+~E(x77582,f319(f319(f74(a1),f319(f319(f75(a1),x77581),x77584)),x77583))+~P1(f319(f319(f226(a1),f2(a1)),x77583))+~P1(f319(f319(f227(a1),f2(a1)),x77581))+~P1(f319(f319(f227(a1),x77583),x77581))
% 28.25/28.13 [7901]~P4(x79012)+E(x79011,f180(f932(x79012,a923)))+~P1(f319(f55(x79012),x79011))+~P1(f319(f319(f321(x79012),x79014),x79011))+~P1(f319(f319(f226(x79012),x79014),x79013))+P1(f319(f319(f226(x79012),f319(f57(x79012,f224(x79012)),x79011)),x79013))
% 28.25/28.13 [7902]~P4(x79022)+E(x79021,f180(f932(x79022,a923)))+~P1(f319(f55(x79022),x79021))+~P1(f319(f319(f227(x79022),x79024),x79023))+~P1(f319(f319(f321(x79022),x79024),x79021))+P1(f319(f319(f227(x79022),f319(f57(x79022,f224(x79022)),x79021)),x79023))
% 28.25/28.13 [8470]~P1(f319(f319(f226(a1),x84704),f2(a1)))+~E(x84701,f319(f319(f74(a1),f319(f319(f75(a1),x84702),x84703)),x84704))+~P1(f319(f319(f226(a1),f2(a1)),x84704))+~P1(f319(f319(f227(a1),x84704),x84702))+~P1(f319(f319(f227(a1),x84702),x84704))+P1(f319(f43(x84701,x84702),f319(f319(f244(a1,a1),x84703),x84704)))
% 28.25/28.13 [8596]~P74(x85961)+~P100(x85961)+P1(f319(f319(f227(x85961),f319(f95(x85961),x85962)),f2(x85961)))+~P1(f319(f319(f226(x85961),f2(x85961)),x85964))+P1(f319(f319(f227(x85961),f2(x85961)),f319(f95(x85961),x85962)))+P1(f319(f319(f226(x85961),f319(f319(f283(x85961),x85963),f319(f95(x85961),x85962))),x85964))
% 28.25/28.13 [8597]~P74(x85971)+~P100(x85971)+P1(f319(f319(f227(x85971),f319(f95(x85971),x85972)),f2(x85971)))+~P1(f319(f319(f227(x85971),f2(x85971)),x85974))+P1(f319(f319(f227(x85971),f2(x85971)),f319(f95(x85971),x85972)))+P1(f319(f319(f227(x85971),f319(f319(f283(x85971),x85973),f319(f95(x85971),x85972))),x85974))
% 28.25/28.13 [8710]~P74(x87101)+~P100(x87101)+~P1(f319(f319(f227(x87101),x87102),f2(x87101)))+P1(f319(f319(f227(x87101),f2(x87101)),x87102))+~P1(f319(f319(f226(x87101),f319(f95(x87101),x87104)),f319(f319(f283(x87101),x87103),x87102)))+P1(f319(f319(f226(x87101),x87103),f319(f319(f75(x87101),f319(f95(x87101),x87104)),x87102)))
% 28.25/28.13 [8711]~P74(x87111)+~P100(x87111)+~P1(f319(f319(f227(x87111),x87112),f2(x87111)))+P1(f319(f319(f227(x87111),f2(x87111)),x87112))+~P1(f319(f319(f227(x87111),f319(f95(x87111),x87114)),f319(f319(f283(x87111),x87113),x87112)))+P1(f319(f319(f227(x87111),x87113),f319(f319(f75(x87111),f319(f95(x87111),x87114)),x87112)))
% 28.25/28.13 [8749]~P74(x87491)+~P100(x87491)+~P1(f319(f319(f227(x87491),x87492),f2(x87491)))+P1(f319(f319(f227(x87491),f2(x87491)),x87492))+P1(f319(f319(f226(x87491),f319(f95(x87491),x87493)),f319(f319(f283(x87491),x87494),x87492)))+~P1(f319(f319(f226(x87491),x87494),f319(f319(f75(x87491),f319(f95(x87491),x87493)),x87492)))
% 28.25/28.13 [8750]~P74(x87501)+~P100(x87501)+~P1(f319(f319(f227(x87501),x87502),f2(x87501)))+P1(f319(f319(f227(x87501),f2(x87501)),x87502))+P1(f319(f319(f227(x87501),f319(f95(x87501),x87503)),f319(f319(f283(x87501),x87504),x87502)))+~P1(f319(f319(f227(x87501),x87504),f319(f319(f75(x87501),f319(f95(x87501),x87503)),x87502)))
% 28.25/28.13 [8845]~P74(x88451)+~P100(x88451)+P1(f319(f319(f227(x88451),f319(f95(x88451),x88453)),f2(x88451)))+P1(f319(f319(f226(x88451),f2(x88451)),x88452))+P1(f319(f319(f227(x88451),f2(x88451)),f319(f95(x88451),x88453)))+~P1(f319(f319(f226(x88451),f319(f319(f283(x88451),x88454),f319(f95(x88451),x88453))),x88452))
% 28.25/28.13 [8846]~P74(x88461)+~P100(x88461)+P1(f319(f319(f227(x88461),f319(f95(x88461),x88463)),f2(x88461)))+P1(f319(f319(f227(x88461),f2(x88461)),x88462))+P1(f319(f319(f227(x88461),f2(x88461)),f319(f95(x88461),x88463)))+~P1(f319(f319(f227(x88461),f319(f319(f283(x88461),x88464),f319(f95(x88461),x88463))),x88462))
% 28.25/28.13 [8897]~P74(x88971)+~P100(x88971)+~P1(f319(f319(f226(x88971),f319(f95(x88971),x88973)),f2(x88971)))+P1(f319(f319(f227(x88971),f2(x88971)),x88972))+P1(f319(f319(f226(x88971),f319(f95(x88971),x88973)),f319(f319(f283(x88971),x88974),x88972)))+~P1(f319(f319(f226(x88971),x88974),f319(f319(f75(x88971),f319(f95(x88971),x88973)),x88972)))
% 28.25/28.13 [8898]~P74(x88981)+~P100(x88981)+~P1(f319(f319(f227(x88981),f319(f95(x88981),x88983)),f2(x88981)))+P1(f319(f319(f227(x88981),f2(x88981)),x88982))+P1(f319(f319(f227(x88981),f319(f95(x88981),x88983)),f319(f319(f283(x88981),x88984),x88982)))+~P1(f319(f319(f227(x88981),x88984),f319(f319(f75(x88981),f319(f95(x88981),x88983)),x88982)))
% 28.25/28.13 [8906]~P74(x89061)+~P100(x89061)+P1(f319(f319(f227(x89061),x89062),f2(x89061)))+P1(f319(f319(f226(x89061),f319(f319(f283(x89061),x89063),x89062)),f319(f95(x89061),x89064)))+~P1(f319(f319(f226(x89061),f2(x89061)),f319(f95(x89061),x89064)))+~P1(f319(f319(f226(x89061),x89063),f319(f319(f75(x89061),f319(f95(x89061),x89064)),x89062)))
% 28.25/28.13 [8907]~P74(x89071)+~P100(x89071)+P1(f319(f319(f227(x89071),x89072),f2(x89071)))+P1(f319(f319(f227(x89071),f319(f319(f283(x89071),x89073),x89072)),f319(f95(x89071),x89074)))+~P1(f319(f319(f227(x89071),f2(x89071)),f319(f95(x89071),x89074)))+~P1(f319(f319(f227(x89071),x89073),f319(f319(f75(x89071),f319(f95(x89071),x89074)),x89072)))
% 28.25/28.13 [8927]~P74(x89271)+~P100(x89271)+P1(f319(f319(f227(x89271),f319(f95(x89271),x89272)),f2(x89271)))+~P1(f319(f319(f226(x89271),f2(x89271)),x89274))+~P1(f319(f319(f226(x89271),x89273),f319(f319(f75(x89271),x89274),f319(f95(x89271),x89272))))+P1(f319(f319(f226(x89271),f319(f319(f283(x89271),x89273),f319(f95(x89271),x89272))),x89274))
% 28.25/28.13 [8928]~P74(x89281)+~P100(x89281)+P1(f319(f319(f227(x89281),f319(f95(x89281),x89282)),f2(x89281)))+~P1(f319(f319(f227(x89281),f2(x89281)),x89284))+~P1(f319(f319(f227(x89281),x89283),f319(f319(f75(x89281),x89284),f319(f95(x89281),x89282))))+P1(f319(f319(f227(x89281),f319(f319(f283(x89281),x89283),f319(f95(x89281),x89282))),x89284))
% 28.25/28.13 [9021]~P74(x90211)+~P100(x90211)+P1(f319(f319(f227(x90211),f319(f95(x90211),x90212)),f2(x90211)))+~P1(f319(f319(f226(x90211),x90213),f2(x90211)))+P1(f319(f319(f226(x90211),x90213),f319(f319(f283(x90211),x90214),f319(f95(x90211),x90212))))+~P1(f319(f319(f226(x90211),f319(f319(f75(x90211),x90213),f319(f95(x90211),x90212))),x90214))
% 28.25/28.13 [9022]~P74(x90221)+~P100(x90221)+P1(f319(f319(f227(x90221),f319(f95(x90221),x90222)),f2(x90221)))+~P1(f319(f319(f227(x90221),x90223),f2(x90221)))+P1(f319(f319(f227(x90221),x90223),f319(f319(f283(x90221),x90224),f319(f95(x90221),x90222))))+~P1(f319(f319(f227(x90221),f319(f319(f75(x90221),x90223),f319(f95(x90221),x90222))),x90224))
% 28.25/28.13 [9140]~P74(x91401)+~P100(x91401)+~P1(f319(f319(f226(x91401),f2(x91401)),x91404))+P1(f319(f319(f227(x91401),f2(x91401)),f319(f95(x91401),x91402)))+~P1(f319(f319(f226(x91401),f319(f319(f75(x91401),x91404),f319(f95(x91401),x91402))),x91403))+P1(f319(f319(f226(x91401),f319(f319(f283(x91401),x91403),f319(f95(x91401),x91402))),x91404))
% 28.25/28.13 [9141]~P74(x91411)+~P100(x91411)+~P1(f319(f319(f227(x91411),f2(x91411)),x91414))+P1(f319(f319(f227(x91411),f2(x91411)),f319(f95(x91411),x91412)))+~P1(f319(f319(f227(x91411),f319(f319(f75(x91411),x91414),f319(f95(x91411),x91412))),x91413))+P1(f319(f319(f227(x91411),f319(f319(f283(x91411),x91413),f319(f95(x91411),x91412))),x91414))
% 28.25/28.13 [9201]~P74(x92011)+~P100(x92011)+~P1(f319(f319(f226(x92011),x92012),f2(x92011)))+P1(f319(f319(f226(x92011),x92012),f319(f319(f283(x92011),x92013),f319(f95(x92011),x92014))))+~P1(f319(f319(f226(x92011),x92013),f319(f319(f75(x92011),x92012),f319(f95(x92011),x92014))))+~P1(f319(f319(f226(x92011),f319(f319(f75(x92011),x92012),f319(f95(x92011),x92014))),x92013))
% 28.25/28.13 [9202]~P74(x92021)+~P100(x92021)+~P1(f319(f319(f227(x92021),x92022),f2(x92021)))+P1(f319(f319(f227(x92021),x92022),f319(f319(f283(x92021),x92023),f319(f95(x92021),x92024))))+~P1(f319(f319(f227(x92021),x92023),f319(f319(f75(x92021),x92022),f319(f95(x92021),x92024))))+~P1(f319(f319(f227(x92021),f319(f319(f75(x92021),x92022),f319(f95(x92021),x92024))),x92023))
% 28.25/28.13 [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(f283(x92301),x92304),f319(f95(x92301),x92302))),x92303))+P1(f319(f319(f226(x92301),f319(f319(f75(x92301),x92303),f319(f95(x92301),x92302))),x92304))
% 28.25/28.13 [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(f226(x92311),f319(f319(f75(x92311),x92314),f319(f95(x92311),x92312))),x92313))+P1(f319(f319(f226(x92311),f319(f319(f283(x92311),x92313),f319(f95(x92311),x92312))),x92314))
% 28.25/28.13 [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(f283(x92321),x92324),f319(f95(x92321),x92322))),x92323))+P1(f319(f319(f227(x92321),f319(f319(f75(x92321),x92323),f319(f95(x92321),x92322))),x92324))
% 28.25/28.13 [9233]~P74(x92331)+~P100(x92331)+~P1(f319(f319(f227(x92331),f319(f95(x92331),x92332)),f2(x92331)))+P1(f319(f319(f227(x92331),f2(x92331)),f319(f95(x92331),x92332)))+~P1(f319(f319(f227(x92331),f319(f319(f75(x92331),x92334),f319(f95(x92331),x92332))),x92333))+P1(f319(f319(f227(x92331),f319(f319(f283(x92331),x92333),f319(f95(x92331),x92332))),x92334))
% 28.25/28.13 [9310]~P74(x93101)+~P100(x93101)+~P1(f319(f319(f227(x93101),f319(f95(x93101),x93104)),f2(x93101)))+P1(f319(f319(f226(x93101),x93102),f319(f319(f283(x93101),x93103),f319(f95(x93101),x93104))))+~P1(f319(f319(f226(x93101),x93103),f319(f319(f75(x93101),x93102),f319(f95(x93101),x93104))))+~P1(f319(f319(f226(x93101),f319(f319(f75(x93101),x93102),f319(f95(x93101),x93104))),x93103))
% 28.25/28.13 [9311]~P74(x93111)+~P100(x93111)+~P1(f319(f319(f227(x93111),f319(f95(x93111),x93114)),f2(x93111)))+P1(f319(f319(f227(x93111),x93112),f319(f319(f283(x93111),x93113),f319(f95(x93111),x93114))))+~P1(f319(f319(f227(x93111),x93113),f319(f319(f75(x93111),x93112),f319(f95(x93111),x93114))))+~P1(f319(f319(f227(x93111),f319(f319(f75(x93111),x93112),f319(f95(x93111),x93114))),x93113))
% 28.25/28.13 [9356]~P74(x93561)+~P100(x93561)+~P1(f319(f319(f226(x93561),f2(x93561)),x93564))+~P1(f319(f319(f226(x93561),x93562),f319(f319(f75(x93561),x93564),f319(f95(x93561),x93563))))+~P1(f319(f319(f226(x93561),f319(f319(f75(x93561),x93564),f319(f95(x93561),x93563))),x93562))+P1(f319(f319(f226(x93561),f319(f319(f283(x93561),x93562),f319(f95(x93561),x93563))),x93564))
% 28.25/28.13 [9357]~P74(x93571)+~P100(x93571)+~P1(f319(f319(f227(x93571),f2(x93571)),x93574))+~P1(f319(f319(f227(x93571),x93572),f319(f319(f75(x93571),x93574),f319(f95(x93571),x93573))))+~P1(f319(f319(f227(x93571),f319(f319(f75(x93571),x93574),f319(f95(x93571),x93573))),x93572))+P1(f319(f319(f227(x93571),f319(f319(f283(x93571),x93572),f319(f95(x93571),x93573))),x93574))
% 28.25/28.13 [9394]~P74(x93941)+~P100(x93941)+~P1(f319(f319(f227(x93941),f319(f95(x93941),x93943)),f2(x93941)))+~P1(f319(f319(f226(x93941),x93942),f319(f319(f75(x93941),x93944),f319(f95(x93941),x93943))))+~P1(f319(f319(f226(x93941),f319(f319(f75(x93941),x93944),f319(f95(x93941),x93943))),x93942))+P1(f319(f319(f226(x93941),f319(f319(f283(x93941),x93942),f319(f95(x93941),x93943))),x93944))
% 28.25/28.13 [9395]~P74(x93951)+~P100(x93951)+~P1(f319(f319(f227(x93951),f319(f95(x93951),x93953)),f2(x93951)))+~P1(f319(f319(f227(x93951),x93952),f319(f319(f75(x93951),x93954),f319(f95(x93951),x93953))))+~P1(f319(f319(f227(x93951),f319(f319(f75(x93951),x93954),f319(f95(x93951),x93953))),x93952))+P1(f319(f319(f227(x93951),f319(f319(f283(x93951),x93952),f319(f95(x93951),x93953))),x93954))
% 28.25/28.13 [9085]~P74(x90851)+~P100(x90851)+~P1(f319(f319(f227(x90851),x90852),f2(x90851)))+~P1(f319(f319(f226(x90851),f319(f319(f283(x90851),x90854),x90852)),f319(f95(x90851),x90853)))+P1(f319(f319(f227(x90851),f2(x90851)),x90852))+P1(f319(f319(f226(x90851),f319(f319(f75(x90851),f319(f95(x90851),x90853)),x90852)),x90854))
% 28.25/28.13 [9086]~P74(x90861)+~P100(x90861)+~P1(f319(f319(f227(x90861),x90862),f2(x90861)))+~P1(f319(f319(f227(x90861),f319(f319(f283(x90861),x90864),x90862)),f319(f95(x90861),x90863)))+P1(f319(f319(f227(x90861),f2(x90861)),x90862))+P1(f319(f319(f227(x90861),f319(f319(f75(x90861),f319(f95(x90861),x90863)),x90862)),x90864))
% 28.25/28.13 [9205]~P74(x92051)+~P100(x92051)+~P1(f319(f319(f227(x92051),x92052),f2(x92051)))+P1(f319(f319(f227(x92051),f2(x92051)),x92052))+P1(f319(f319(f226(x92051),f319(f319(f283(x92051),x92053),x92052)),f319(f95(x92051),x92054)))+~P1(f319(f319(f226(x92051),f319(f319(f75(x92051),f319(f95(x92051),x92054)),x92052)),x92053))
% 28.25/28.13 [9206]~P74(x92061)+~P100(x92061)+~P1(f319(f319(f227(x92061),x92062),f2(x92061)))+P1(f319(f319(f227(x92061),f2(x92061)),x92062))+P1(f319(f319(f227(x92061),f319(f319(f283(x92061),x92063),x92062)),f319(f95(x92061),x92064)))+~P1(f319(f319(f227(x92061),f319(f319(f75(x92061),f319(f95(x92061),x92064)),x92062)),x92063))
% 28.25/28.13 [9244]~P74(x92441)+~P100(x92441)+P1(f319(f319(f227(x92441),x92442),f2(x92441)))+~P1(f319(f319(f226(x92441),f319(f95(x92441),x92443)),f2(x92441)))+P1(f319(f319(f226(x92441),f319(f95(x92441),x92443)),f319(f319(f283(x92441),x92444),x92442)))+~P1(f319(f319(f226(x92441),f319(f319(f75(x92441),f319(f95(x92441),x92443)),x92442)),x92444))
% 28.25/28.13 [9245]~P74(x92451)+~P100(x92451)+P1(f319(f319(f227(x92451),x92452),f2(x92451)))+~P1(f319(f319(f227(x92451),f319(f95(x92451),x92453)),f2(x92451)))+P1(f319(f319(f227(x92451),f319(f95(x92451),x92453)),f319(f319(f283(x92451),x92454),x92452)))+~P1(f319(f319(f227(x92451),f319(f319(f75(x92451),f319(f95(x92451),x92453)),x92452)),x92454))
% 28.25/28.13 [9261]~P74(x92611)+~P100(x92611)+P1(f319(f319(f227(x92611),f2(x92611)),x92612))+P1(f319(f319(f226(x92611),f319(f319(f283(x92611),x92613),x92612)),f319(f95(x92611),x92614)))+~P1(f319(f319(f226(x92611),f2(x92611)),f319(f95(x92611),x92614)))+~P1(f319(f319(f226(x92611),f319(f319(f75(x92611),f319(f95(x92611),x92614)),x92612)),x92613))
% 28.25/28.13 [9262]~P74(x92621)+~P100(x92621)+P1(f319(f319(f227(x92621),f2(x92621)),x92622))+P1(f319(f319(f227(x92621),f319(f319(f283(x92621),x92623),x92622)),f319(f95(x92621),x92624)))+~P1(f319(f319(f227(x92621),f2(x92621)),f319(f95(x92621),x92624)))+~P1(f319(f319(f227(x92621),f319(f319(f75(x92621),f319(f95(x92621),x92624)),x92622)),x92623))
% 28.25/28.13 [9425]~P74(x94251)+~P100(x94251)+~P1(f319(f319(f227(x94251),x94254),f2(x94251)))+P1(f319(f319(f226(x94251),f319(f95(x94251),x94252)),f319(f319(f283(x94251),x94253),x94254)))+~P1(f319(f319(f226(x94251),x94253),f319(f319(f75(x94251),f319(f95(x94251),x94252)),x94254)))+~P1(f319(f319(f226(x94251),f319(f319(f75(x94251),f319(f95(x94251),x94252)),x94254)),x94253))
% 28.25/28.13 [9426]~P74(x94261)+~P100(x94261)+~P1(f319(f319(f227(x94261),x94264),f2(x94261)))+P1(f319(f319(f227(x94261),f319(f95(x94261),x94262)),f319(f319(f283(x94261),x94263),x94264)))+~P1(f319(f319(f227(x94261),x94263),f319(f319(f75(x94261),f319(f95(x94261),x94262)),x94264)))+~P1(f319(f319(f227(x94261),f319(f319(f75(x94261),f319(f95(x94261),x94262)),x94264)),x94263))
% 28.25/28.13 [9461]~P74(x94611)+~P100(x94611)+~P1(f319(f319(f227(x94611),x94613),f2(x94611)))+P1(f319(f319(f226(x94611),f319(f319(f283(x94611),x94612),x94613)),f319(f95(x94611),x94614)))+~P1(f319(f319(f226(x94611),x94612),f319(f319(f75(x94611),f319(f95(x94611),x94614)),x94613)))+~P1(f319(f319(f226(x94611),f319(f319(f75(x94611),f319(f95(x94611),x94614)),x94613)),x94612))
% 28.25/28.13 [9462]~P74(x94621)+~P100(x94621)+~P1(f319(f319(f227(x94621),x94623),f2(x94621)))+P1(f319(f319(f227(x94621),f319(f319(f283(x94621),x94622),x94623)),f319(f95(x94621),x94624)))+~P1(f319(f319(f227(x94621),x94622),f319(f319(f75(x94621),f319(f95(x94621),x94624)),x94623)))+~P1(f319(f319(f227(x94621),f319(f319(f75(x94621),f319(f95(x94621),x94624)),x94623)),x94622))
% 28.25/28.13 [9481]~P74(x94811)+~P100(x94811)+~P1(f319(f319(f226(x94811),f319(f95(x94811),x94812)),f2(x94811)))+P1(f319(f319(f226(x94811),f319(f95(x94811),x94812)),f319(f319(f283(x94811),x94813),x94814)))+~P1(f319(f319(f226(x94811),x94813),f319(f319(f75(x94811),f319(f95(x94811),x94812)),x94814)))+~P1(f319(f319(f226(x94811),f319(f319(f75(x94811),f319(f95(x94811),x94812)),x94814)),x94813))
% 28.25/28.13 [9482]~P74(x94821)+~P100(x94821)+~P1(f319(f319(f227(x94821),f319(f95(x94821),x94822)),f2(x94821)))+P1(f319(f319(f227(x94821),f319(f95(x94821),x94822)),f319(f319(f283(x94821),x94823),x94824)))+~P1(f319(f319(f227(x94821),x94823),f319(f319(f75(x94821),f319(f95(x94821),x94822)),x94824)))+~P1(f319(f319(f227(x94821),f319(f319(f75(x94821),f319(f95(x94821),x94822)),x94824)),x94823))
% 28.25/28.13 [9486]~P74(x94861)+~P100(x94861)+P1(f319(f319(f226(x94861),f319(f319(f283(x94861),x94862),x94863)),f319(f95(x94861),x94864)))+~P1(f319(f319(f226(x94861),f2(x94861)),f319(f95(x94861),x94864)))+~P1(f319(f319(f226(x94861),x94862),f319(f319(f75(x94861),f319(f95(x94861),x94864)),x94863)))+~P1(f319(f319(f226(x94861),f319(f319(f75(x94861),f319(f95(x94861),x94864)),x94863)),x94862))
% 28.25/28.13 [9487]~P74(x94871)+~P100(x94871)+P1(f319(f319(f227(x94871),f319(f319(f283(x94871),x94872),x94873)),f319(f95(x94871),x94874)))+~P1(f319(f319(f227(x94871),f2(x94871)),f319(f95(x94871),x94874)))+~P1(f319(f319(f227(x94871),x94872),f319(f319(f75(x94871),f319(f95(x94871),x94874)),x94873)))+~P1(f319(f319(f227(x94871),f319(f319(f75(x94871),f319(f95(x94871),x94874)),x94873)),x94872))
% 28.25/28.13 [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))
% 28.25/28.13 [8639]~P113(x86391)+P1(f319(f319(f227(f932(x86391,a923)),f295(x86391,x86392,x86393)),f295(x86391,x86394,x86395)))+~P1(f319(f319(f226(x86391),x86394),x86392))+~P1(f319(f319(f226(x86391),x86394),x86395))+~P1(f319(f319(f226(x86391),x86393),x86395))+~P1(f319(f319(f227(x86391),x86393),x86395))
% 28.25/28.13 [8640]~P113(x86401)+P1(f319(f319(f227(f932(x86401,a923)),f295(x86401,x86402,x86403)),f295(x86401,x86404,x86405)))+~P1(f319(f319(f226(x86401),x86403),x86405))+~P1(f319(f319(f226(x86401),x86404),x86405))+~P1(f319(f319(f226(x86401),x86404),x86402))+~P1(f319(f319(f227(x86401),x86404),x86402))
% 28.25/28.13 [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,f561(x95131,x95134,x95133,x95132)),x95135))+~P1(f319(f319(f321(x95132),x95135),x95131))
% 28.25/28.13 [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,f817(x95143,x95141,x95144,x95142)),x95145))+~P1(f319(f319(f321(x95142),x95145),x95141))
% 28.25/28.13 [9515]P63(x95152,x95153,x95154,x95151)+E(x95151,f180(f932(x95152,a923)))+~P1(f319(f55(x95152),x95154))+~P1(f319(f55(x95152),x95151))+~P1(f319(f319(x95153,f818(x95151,x95154,x95153,x95152)),x95155))+~P1(f319(f319(f321(x95152),x95155),x95151))
% 28.25/28.13 [9666]~E(x96663,x96665)+~P78(x96661)+~P79(x96661)+~P42(x96663)+E(f319(f319(f6(a1,x96661),x96662),x96663),f319(f319(f6(a1,x96661),x96664),x96665))+P1(f319(f319(f226(a1),f2(a1)),f447(x96662,x96664,x96663,x96665,x96661)))
% 28.25/28.13 [9667]~E(x96673,x96675)+~P78(x96671)+~P79(x96671)+~P42(x96673)+E(f319(f319(f9(a1,x96671),x96672),x96673),f319(f319(f9(a1,x96671),x96674),x96675))+P1(f319(f319(f226(a1),f2(a1)),f510(x96672,x96674,x96673,x96675,x96671)))
% 28.25/28.13 [9842]~E(x98425,x98423)+~P78(x98421)+~P79(x98421)+~P42(x98425)+~E(f319(x98422,f447(x98424,x98422,x98425,x98423,x98421)),f319(x98424,f447(x98424,x98422,x98425,x98423,x98421)))+E(f319(f319(f6(a1,x98421),x98422),x98423),f319(f319(f6(a1,x98421),x98424),x98425))
% 28.25/28.13 [9843]~E(x98435,x98433)+~P78(x98431)+~P79(x98431)+~P42(x98435)+~E(f319(x98432,f510(x98434,x98432,x98435,x98433,x98431)),f319(x98434,f510(x98434,x98432,x98435,x98433,x98431)))+E(f319(f319(f9(a1,x98431),x98432),x98433),f319(f319(f9(a1,x98431),x98434),x98435))
% 28.25/28.13 [9934]~P68(x99343)+E(f319(x99341,x99342),f2(x99343))+~E(f319(f319(f6(x99344,x99343),x99341),x99345),f2(x99343))+~P1(f319(f55(x99344),x99345))+P1(f319(f319(f321(x99344),f429(x99342,x99341,x99345,x99344,x99343)),x99345))+~P1(f319(f319(f321(x99344),x99342),x99345))
% 28.25/28.13 [10076]~P68(x100763)+E(f319(x100761,x100762),f2(x100763))+~E(f319(f319(f6(x100764,x100763),x100761),x100765),f2(x100763))+~P1(f319(f55(x100764),x100765))+~P1(f319(f319(f321(x100764),x100762),x100765))+~P1(f319(f319(f226(x100763),f2(x100763)),f319(x100761,f429(x100762,x100761,x100765,x100764,x100763))))
% 28.25/28.13 [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)),x85574))+P1(f319(f319(f226(x85571),f319(f319(f75(x85571),x85572),x85573)),f319(f319(f75(x85571),x85574),x85575)))
% 28.25/28.13 [8558]~P141(x85581)+~P1(f319(f319(f226(x85581),x85583),x85585))+~P1(f319(f319(f226(x85581),x85582),x85584))+~P1(f319(f319(f226(x85581),f2(x85581)),x85583))+~P1(f319(f319(f226(x85581),f2(x85581)),x85582))+P1(f319(f319(f226(x85581),f319(f319(f75(x85581),x85582),x85583)),f319(f319(f75(x85581),x85584),x85585)))
% 28.25/28.13 [8559]~P75(x85591)+~P1(f319(f319(f227(x85591),f2(x85591)),x85595))+~P1(f319(f319(f226(x85591),x85595),x85593))+~P1(f319(f319(f226(x85591),x85592),x85594))+~P1(f319(f319(f226(x85591),f2(x85591)),x85592))+P1(f319(f319(f226(x85591),f319(f319(f283(x85591),x85592),x85593)),f319(f319(f283(x85591),x85594),x85595)))
% 28.25/28.13 [8560]~P134(x85601)+~P1(f319(f319(f226(x85601),x85603),x85605))+~P1(f319(f319(f226(x85601),f2(x85601)),x85602))+~P1(f319(f319(f227(x85601),x85602),x85604))+~P1(f319(f319(f227(x85601),f2(x85601)),x85603))+P1(f319(f319(f227(x85601),f319(f319(f75(x85601),x85602),x85603)),f319(f319(f75(x85601),x85604),x85605)))
% 28.25/28.13 [8561]~P134(x85611)+~P1(f319(f319(f226(x85611),x85612),x85614))+~P1(f319(f319(f226(x85611),f2(x85611)),x85613))+~P1(f319(f319(f227(x85611),x85613),x85615))+~P1(f319(f319(f227(x85611),f2(x85611)),x85612))+P1(f319(f319(f227(x85611),f319(f319(f75(x85611),x85612),x85613)),f319(f319(f75(x85611),x85614),x85615)))
% 28.25/28.13 [8562]~P134(x85621)+~P1(f319(f319(f226(x85621),f2(x85621)),x85623))+~P1(f319(f319(f226(x85621),f2(x85621)),x85622))+~P1(f319(f319(f227(x85621),x85623),x85625))+~P1(f319(f319(f227(x85621),x85622),x85624))+P1(f319(f319(f227(x85621),f319(f319(f75(x85621),x85622),x85623)),f319(f319(f75(x85621),x85624),x85625)))
% 28.25/28.13 [8563]~P134(x85631)+~P1(f319(f319(f226(x85631),f2(x85631)),x85633))+~P1(f319(f319(f227(x85631),x85633),x85635))+~P1(f319(f319(f227(x85631),x85632),x85634))+~P1(f319(f319(f227(x85631),f2(x85631)),x85634))+P1(f319(f319(f227(x85631),f319(f319(f75(x85631),x85632),x85633)),f319(f319(f75(x85631),x85634),x85635)))
% 28.25/28.13 [8564]~P75(x85641)+~P1(f319(f319(f226(x85641),x85645),x85643))+~P1(f319(f319(f226(x85641),f2(x85641)),x85642))+~P1(f319(f319(f227(x85641),x85642),x85644))+~P1(f319(f319(f227(x85641),f2(x85641)),x85645))+P1(f319(f319(f227(x85641),f319(f319(f283(x85641),x85642),x85643)),f319(f319(f283(x85641),x85644),x85645)))
% 28.25/28.13 [8565]~P75(x85651)+~P1(f319(f319(f226(x85651),x85652),x85654))+~P1(f319(f319(f227(x85651),x85655),x85653))+~P1(f319(f319(f227(x85651),f2(x85651)),x85655))+~P1(f319(f319(f227(x85651),f2(x85651)),x85652))+P1(f319(f319(f227(x85651),f319(f319(f283(x85651),x85652),x85653)),f319(f319(f283(x85651),x85654),x85655)))
% 28.25/28.13 [9985]~P79(x99855)+~P89(x99855)+E(x99851,f180(f932(x99852,a923)))+~P1(f319(f55(x99852),x99851))+P1(f319(f319(f321(x99852),f350(x99853,x99854,x99851,x99852,x99855)),x99851))+P1(f319(f319(f227(x99855),f319(f319(f6(x99852,x99855),x99854),x99851)),f319(f319(f6(x99852,x99855),x99853),x99851)))
% 28.25/28.13 [10104]~P79(x101041)+~P91(x101041)+~P1(f319(f55(x101042),x101045))+~P1(f319(f319(f226(x101041),f2(x101041)),f319(x101043,f410(x101043,x101044,x101045,x101042,x101041))))+P1(f319(f319(f226(x101041),f319(f319(f6(x101042,x101041),x101043),x101044)),f319(f319(f6(x101042,x101041),x101043),x101045)))+~P1(f319(f319(f226(f932(x101042,a923)),x101044),x101045))
% 28.25/28.13 [10276]~P79(x102763)+~P89(x102763)+E(x102761,f180(f932(x102762,a923)))+~P1(f319(f55(x102762),x102761))+~P1(f319(f319(f227(x102763),f319(x102764,f350(x102765,x102764,x102761,x102762,x102763))),f319(x102765,f350(x102765,x102764,x102761,x102762,x102763))))+P1(f319(f319(f227(x102763),f319(f319(f6(x102762,x102763),x102764),x102761)),f319(f319(f6(x102762,x102763),x102765),x102761)))
% 28.25/28.13 [7283]~P19(x72832,x72835,x72834)+E(x72831,f180(f932(x72832,a923)))+E(x72833,f180(f932(x72832,a923)))+~P1(f319(f55(x72832),x72831))+~P1(f319(f55(x72832),x72833))+E(f319(x72834,f319(f319(f102(f932(x72832,a923)),x72833),x72831)),f319(f319(x72835,f319(x72834,x72833)),f319(x72834,x72831)))
% 28.25/28.13 [7868]~P152(x78681,x78684,x78683)+P1(f319(x78681,x78682))+~P1(f319(f319(f227(a1),x78684),f2(a1)))+~P1(f319(f319(f226(a1),x78685),f2(a1)))+~E(x78683,f319(f319(f74(a1),f319(f319(f75(a1),x78684),x78682)),x78685))+~P1(f319(f319(f227(a1),x78684),x78685))
% 28.25/28.13 [7869]~P151(x78691,x78694,x78693)+P1(f319(x78691,x78692))+~P1(f319(f319(f227(a1),x78694),f2(a1)))+~P1(f319(f319(f226(a1),x78692),f2(a1)))+~E(x78693,f319(f319(f74(a1),f319(f319(f75(a1),x78694),x78695)),x78692))+~P1(f319(f319(f227(a1),x78694),x78692))
% 28.25/28.13 [7911]~P152(x79111,x79114,x79113)+P1(f319(x79111,x79112))+~E(x79113,f319(f319(f74(a1),f319(f319(f75(a1),x79114),x79112)),x79115))+~P1(f319(f319(f226(a1),f2(a1)),x79115))+~P1(f319(f319(f227(a1),f2(a1)),x79114))+~P1(f319(f319(f227(a1),x79115),x79114))
% 28.25/28.13 [7912]~P151(x79121,x79124,x79123)+P1(f319(x79121,x79122))+~E(x79123,f319(f319(f74(a1),f319(f319(f75(a1),x79124),x79125)),x79122))+~P1(f319(f319(f226(a1),f2(a1)),x79122))+~P1(f319(f319(f227(a1),f2(a1)),x79124))+~P1(f319(f319(f227(a1),x79122),x79124))
% 28.25/28.13 [8853]P1(f319(f319(x88531,x88532),x88533))+~P1(f319(f319(x88531,f319(f319(f30(a1),x88534),x88535)),f39(a1,x88534,x88535)))+~P1(f319(f319(f227(a1),x88535),f2(a1)))+~P1(f319(f319(f226(a1),x88533),f2(a1)))+~E(x88534,f319(f319(f74(a1),f319(f319(f75(a1),x88535),x88532)),x88533))+~P1(f319(f319(f227(a1),x88535),x88533))
% 28.25/28.13 [8862]P1(f319(f319(x88621,x88622),x88623))+~P1(f319(f319(x88621,f319(f319(f30(a1),x88624),x88625)),f39(a1,x88624,x88625)))+~E(x88624,f319(f319(f74(a1),f319(f319(f75(a1),x88625),x88622)),x88623))+~P1(f319(f319(f226(a1),f2(a1)),x88623))+~P1(f319(f319(f227(a1),f2(a1)),x88625))+~P1(f319(f319(f227(a1),x88623),x88625))
% 28.25/28.13 [9125]E(x91251,x91252)+~P60(x91253,x91255,x91254)+~P1(f319(f319(f321(x91253),x91252),x91255))+~P1(f319(f319(f321(x91253),x91251),x91255))+P1(f319(f319(f321(f931(x91253,x91253)),f319(f319(f244(x91253,x91253),x91251),x91252)),x91254))+P1(f319(f319(f321(f931(x91253,x91253)),f319(f319(f244(x91253,x91253),x91252),x91251)),x91254))
% 28.25/28.13 [9957]~P113(x99571)+~P113(x99572)+~P41(x99572,x99571,x99573)+~P1(f319(f319(f226(x99572),x99575),f806(x99574,x99573,x99572,x99571,x99575)))+E(f230(x99571,f319(f319(f7(x99571,f932(x99571,a923),a923),f321(x99571)),f319(f302(x99572,x99571,x99573),x99574))),f319(x99573,f230(x99572,f319(f319(f7(x99572,f932(x99572,a923),a923),f321(x99572)),x99574))))+~P1(f319(f319(f321(x99572),x99575),x99574))
% 28.25/28.13 [10016]~P79(x100165)+~P91(x100165)+~P1(f319(f55(x100161),x100164))+P1(f319(f319(f226(x100165),f319(f319(f6(x100161,x100165),x100162),x100163)),f319(f319(f6(x100161,x100165),x100162),x100164)))+~P1(f319(f319(f226(f932(x100161,a923)),x100163),x100164))+P1(f319(f319(f321(x100161),f410(x100162,x100163,x100164,x100161,x100165)),f319(f319(f23(f932(x100161,a923)),x100164),x100163)))
% 28.25/28.13 [10032]~P113(x100321)+~P113(x100322)+~P41(x100322,x100321,x100323)+E(f230(x100321,f319(f319(f7(x100321,f932(x100321,a923),a923),f321(x100321)),f319(f302(x100322,x100321,x100323),x100324))),f319(x100323,f230(x100322,f319(f319(f7(x100322,f932(x100322,a923),a923),f321(x100322)),x100324))))+~P1(f319(f319(f321(x100322),x100325),x100324))+P1(f319(f319(f321(x100322),f806(x100324,x100323,x100322,x100321,x100325)),x100324))
% 28.25/28.13 [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),f571(x101124,x101121,x101123,x101122)),x101125)),x101124))
% 28.25/28.13 [10113]E(x101131,f180(f932(x101132,a923)))+~P1(f319(f55(x101132),x101133))+~P1(f319(f55(x101132),x101131))+P1(f319(f319(f321(f931(f932(x101132,a923),f932(x101132,a923))),f319(f319(f244(f932(x101132,a923),f932(x101132,a923)),x101133),x101131)),f311(x101132,x101134)))+~P1(f319(f319(f321(x101132),x101135),x101131))+~P1(f319(f319(f321(f931(x101132,x101132)),f319(f319(f244(x101132,x101132),f618(x101134,x101131,x101133,x101132)),x101135)),x101134))
% 28.25/28.13 [10281]~P68(x102811)+~E(f319(f319(f6(x102815,x102811),x102812),x102816),x102814)+~P1(f319(f55(x102815),x102816))+P1(f319(f319(f321(x102815),f437(x102813,x102814,x102812,x102816,x102815,x102811)),x102816))+P1(f319(f319(f226(x102811),f319(x102812,x102813)),x102814))+~P1(f319(f319(f321(x102815),x102813),x102816))
% 28.25/28.13 [10330]~P68(x103301)+~E(f319(f319(f6(x103305,x103301),x103302),x103306),x103304)+~P1(f319(f55(x103305),x103306))+~P1(f319(f319(f321(x103305),x103303),x103306))+~P1(f319(f319(f226(x103301),f2(x103301)),f319(x103302,f437(x103303,x103304,x103302,x103306,x103305,x103301))))+P1(f319(f319(f226(x103301),f319(x103302,x103303)),x103304))
% 28.25/28.13 [10469]~E(x104695,x104698)+~E(x104694,x104697)+~P3(x104691)+~P79(x104692)+E(f319(f319(f6(x104691,x104692),x104693),f319(f294(x104691,x104694),x104695)),f319(f319(f6(x104691,x104692),x104696),f319(f294(x104691,x104697),x104698)))+P1(f319(f319(f226(x104691),x104694),f621(x104693,x104696,x104695,x104698,x104694,x104697,x104691,x104692)))
% 28.25/28.13 [10485]~E(x104857,x104854)+~E(x104858,x104855)+~P3(x104851)+~P79(x104852)+~E(f319(x104853,f621(x104856,x104853,x104858,x104855,x104857,x104854,x104851,x104852)),f319(x104856,f621(x104856,x104853,x104858,x104855,x104857,x104854,x104851,x104852)))+E(f319(f319(f6(x104851,x104852),x104853),f319(f294(x104851,x104854),x104855)),f319(f319(f6(x104851,x104852),x104856),f319(f294(x104851,x104857),x104858)))
% 28.25/28.13 [10490]~E(x104904,x104907)+~E(x104905,x104908)+~P3(x104901)+~P79(x104902)+E(f319(f319(f6(x104901,x104902),x104903),f319(f294(x104901,x104904),x104905)),f319(f319(f6(x104901,x104902),x104906),f319(f294(x104901,x104907),x104908)))+P1(f319(f319(f227(x104901),f621(x104903,x104906,x104905,x104908,x104904,x104907,x104901,x104902)),x104905))
% 28.25/28.13 [10119]~P9(x101195,x101199,x101196)+~P9(x101191,x1011910,x101193)+~P13(x101191,x101195,f932(x101192,a923),x101193,x101196,x101198)+~P1(f319(f319(f321(x101195),x101197),x101199))+~P1(f319(f319(f321(x101191),x101194),x1011910))+E(f319(f319(f33(x101191,f932(x101192,a923)),f319(f277(x101191,x101191,x101193),f319(f319(f301(x101191),x101194),f180(f932(x101191,a923))))),f319(f319(f8(f932(x101195,f932(x101192,a923)),f932(x101192,a923),x101191),f319(f33(x101195,f932(x101192,a923)),f319(f277(x101195,x101195,x101196),f319(f319(f301(x101195),x101197),f180(f932(x101195,a923)))))),x101198)),f319(f319(x101198,x101194),x101197))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [9388]E(x93881,f2(a925))+~E(x93882,f319(f319(f74(a925),f319(f319(f75(a925),f319(f243(a925,a925),x93883)),x93881)),f319(f248(a925,a925),x93883)))+P1(f319(f42(x93882,x93881),x93883))+~P1(f319(f319(f226(a925),f319(f248(a925,a925),x93883)),f2(a925)))+~P1(f319(f319(f226(a925),f2(a925)),f319(f248(a925,a925),x93883)))+~P1(f319(f319(f227(a925),x93881),f319(f248(a925,a925),x93883)))+~P1(f319(f319(f227(a925),f319(f248(a925,a925),x93883)),x93881))
% 28.25/28.13 [9397]~E(f319(f243(a925,a925),x93973),f2(a925))+~E(x93971,f319(f319(f74(a925),f319(f319(f75(a925),f319(f243(a925,a925),x93973)),x93972)),f319(f248(a925,a925),x93973)))+P1(f319(f42(x93971,x93972),x93973))+~P1(f319(f319(f226(a925),f319(f248(a925,a925),x93973)),f2(a925)))+~P1(f319(f319(f226(a925),f2(a925)),f319(f248(a925,a925),x93973)))+~P1(f319(f319(f227(a925),x93972),f319(f248(a925,a925),x93973)))+~P1(f319(f319(f227(a925),f319(f248(a925,a925),x93973)),x93972))
% 28.25/28.13 [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(f10(x77482,f319(f319(f102(f932(x77482,a923)),x77483),x77481)),f319(f319(f93(x77482),f10(x77482,x77483)),f10(x77482,x77481)))
% 28.25/28.13 [7749]~P102(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(f13(x77492,f319(f319(f102(f932(x77492,a923)),x77493),x77491)),f319(f319(f102(x77492),f13(x77492,x77493)),f13(x77492,x77491)))
% 28.25/28.13 [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(f14(x77502,f319(f319(f102(f932(x77502,a923)),x77503),x77501)),f319(f319(f224(x77502),f14(x77502,x77503)),f14(x77502,x77501)))
% 28.25/28.13 [7751]~P4(x77512)+E(x77511,f180(f932(x77512,a923)))+E(x77513,f180(f932(x77512,a923)))+~P1(f319(f55(x77512),x77511))+~P1(f319(f55(x77512),x77513))+~E(f319(f319(f93(f932(x77512,a923)),x77513),x77511),f180(f932(x77512,a923)))+E(f15(x77512,f319(f319(f102(f932(x77512,a923)),x77513),x77511)),f319(f319(f225(x77512),f15(x77512,x77513)),f15(x77512,x77511)))
% 28.25/28.13 [8224]~P76(x82242)+E(x82241,f180(f932(x82242,a923)))+E(x82243,f180(f932(x82242,a923)))+~P1(f319(f55(x82242),x82241))+~P1(f319(f55(x82242),x82243))+~E(f319(f319(f93(f932(x82242,a923)),x82243),x82241),f180(f932(x82242,a923)))+E(f319(f319(f75(x82242),f319(f57(x82242,f75(x82242)),x82243)),f319(f57(x82242,f75(x82242)),x82241)),f319(f57(x82242,f75(x82242)),f319(f319(f102(f932(x82242,a923)),x82243),x82241)))
% 28.25/28.13 [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(f224(x82972),f11(x82972,f224(x82972),x82973)),f11(x82972,f224(x82972),x82971)),f11(x82972,f224(x82972),f319(f319(f102(f932(x82972,a923)),x82973),x82971)))
% 28.25/28.13 [8298]~P4(x82982)+E(x82981,f180(f932(x82982,a923)))+E(x82983,f180(f932(x82982,a923)))+~P1(f319(f55(x82982),x82981))+~P1(f319(f55(x82982),x82983))+~E(f319(f319(f93(f932(x82982,a923)),x82983),x82981),f180(f932(x82982,a923)))+E(f319(f319(f225(x82982),f12(x82982,f225(x82982),x82983)),f12(x82982,f225(x82982),x82981)),f12(x82982,f225(x82982),f319(f319(f102(f932(x82982,a923)),x82983),x82981)))
% 28.25/28.13 [8005]E(x80051,f2(a1))+E(f319(f319(f30(a1),x80052),x80051),x80053)+~P1(f319(f319(f226(a1),x80054),f2(a1)))+~E(x80052,f319(f319(f74(a1),f319(f319(f75(a1),x80051),x80053)),x80054))+~P1(f319(f319(f226(a1),f2(a1)),x80054))+~P1(f319(f319(f227(a1),x80054),x80051))+~P1(f319(f319(f227(a1),x80051),x80054))
% 28.25/28.13 [8013]E(f39(a1,x80132,x80131),x80133)+E(x80131,f2(a1))+~P1(f319(f319(f226(a1),x80133),f2(a1)))+~E(x80132,f319(f319(f74(a1),f319(f319(f75(a1),x80131),x80134)),x80133))+~P1(f319(f319(f226(a1),f2(a1)),x80133))+~P1(f319(f319(f227(a1),x80133),x80131))+~P1(f319(f319(f227(a1),x80131),x80133))
% 28.25/28.13 [7068]~P65(x70682)+E(x70681,f2(x70682))+E(x70683,f2(x70682))+~E(f319(f319(f30(x70682),x70684),x70683),f319(f319(f30(x70682),x70685),x70681))+E(f319(f319(f75(x70682),x70684),x70681),f319(f319(f75(x70682),x70683),x70685))+~P1(f319(f319(f279(x70682),x70681),x70685))+~P1(f319(f319(f279(x70682),x70683),x70684))
% 28.25/28.13 [7069]~P65(x70692)+E(x70691,f2(x70692))+E(x70693,f2(x70692))+~E(f319(f319(f75(x70692),x70694),x70693),f319(f319(f75(x70692),x70691),x70695))+E(f319(f319(f30(x70692),x70694),x70691),f319(f319(f30(x70692),x70695),x70693))+~P1(f319(f319(f279(x70692),x70691),x70694))+~P1(f319(f319(f279(x70692),x70693),x70695))
% 28.25/28.13 [7920]~P20(x79202,x79205,x79204)+E(x79201,f180(f932(x79202,a923)))+E(x79203,f180(f932(x79202,a923)))+~P1(f319(f55(x79202),x79201))+~P1(f319(f55(x79202),x79203))+~E(f319(f319(f93(f932(x79202,a923)),x79203),x79201),f180(f932(x79202,a923)))+E(f319(x79204,f319(f319(f102(f932(x79202,a923)),x79203),x79201)),f319(f319(x79205,f319(x79204,x79203)),f319(x79204,x79201)))
% 28.25/28.13 [9638]~P26(x96383,x96381,x96385,x96384)+~P26(x96381,x96383,x96386,x96382)+E(f319(f29(x96381),x96382),f319(f29(x96383),x96384))+~P1(f319(f55(x96383),x96384))+~P1(f319(f55(x96381),x96382))+~P1(f319(f319(f226(f932(x96383,a923)),f319(f302(x96381,x96383,x96386),x96382)),x96384))+~P1(f319(f319(f226(f932(x96381,a923)),f319(f302(x96383,x96381,x96385),x96384)),x96382))
% 28.25/28.13 [9580]~P1(f319(f319(f227(a1),f319(f319(f74(a1),f319(f319(f75(a1),x95805),x95801)),x95806)),f2(a1)))+~E(f319(f319(f74(a1),f319(f319(f75(a1),x95803),x95802)),x95804),f319(f319(f74(a1),f319(f319(f75(a1),x95805),x95801)),x95806))+~P1(f319(f319(f226(a1),f2(a1)),x95806))+~P1(f319(f319(f227(a1),f2(a1)),x95805))+~P1(f319(f319(f226(a1),x95805),x95803))+~P1(f319(f319(f227(a1),x95804),x95803))+P1(f319(f319(f226(a1),x95801),x95802))
% 28.25/28.13 [9338]~E(f319(f319(f74(a1),f319(f319(f75(a1),x93383),x93381)),x93384),f319(f319(f74(a1),f319(f319(f75(a1),x93385),x93382)),x93386))+~P1(f319(f319(f226(a1),f2(a1)),x93384))+~P1(f319(f319(f227(a1),f2(a1)),x93385))+~P1(f319(f319(f226(a1),x93385),x93383))+~P1(f319(f319(f227(a1),x93386),x93385))+P1(f319(f319(f226(a1),x93381),x93382))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),f319(f319(f75(a1),x93385),x93382)),x93386)))
% 28.25/28.13 [9519]~P136(x95191)+~E(f319(f319(f74(x95191),x95192),x95194),f72(x95191))+~P1(f319(f319(f226(x95191),x95195),x95196))+~P1(f319(f319(f226(x95191),x95193),x95196))+~P1(f319(f319(f226(x95191),f2(x95191)),x95194))+~P1(f319(f319(f226(x95191),f2(x95191)),x95192))+P1(f319(f319(f226(x95191),f319(f319(f74(x95191),f319(f319(f75(x95191),x95192),x95193)),f319(f319(f75(x95191),x95194),x95195))),x95196))
% 28.25/28.13 [9520]~P137(x95201)+~E(f319(f319(f74(x95201),x95202),x95204),f72(x95201))+~P1(f319(f319(f226(x95201),f2(x95201)),x95204))+~P1(f319(f319(f226(x95201),f2(x95201)),x95202))+~P1(f319(f319(f227(x95201),x95205),x95206))+~P1(f319(f319(f227(x95201),x95203),x95206))+P1(f319(f319(f227(x95201),f319(f319(f74(x95201),f319(f319(f75(x95201),x95202),x95203)),f319(f319(f75(x95201),x95204),x95205))),x95206))
% 28.25/28.13 [10378]~P9(x103787,x103786,x103785)+E(x103781,x103782)+~P12(x103787,f932(x103784,a923),x103785,x103783)+E(f319(x103783,f549(x103781,x103782,x103783,x103784,x103785,x103786,x103787)),f319(x103783,f547(x103781,x103782,x103783,x103784,x103785,x103786,x103787)))+~E(f319(f319(f33(x103787,f932(x103784,a923)),x103781),x103783),f319(f319(f33(x103787,f932(x103784,a923)),x103782),x103783))+~P1(f319(f319(f321(f932(x103787,a923)),x103782),f319(f319(f54(x103787),x103786),x103785)))+~P1(f319(f319(f321(f932(x103787,a923)),x103781),f319(f319(f54(x103787),x103786),x103785)))
% 28.25/28.13 [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),f547(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)))
% 28.25/28.13 [10425]~P9(x104253,x104257,x104256)+E(x104251,x104252)+~P12(x104253,f932(x104255,a923),x104256,x104254)+~E(f319(f319(f33(x104253,f932(x104255,a923)),x104251),x104254),f319(f319(f33(x104253,f932(x104255,a923)),x104252),x104254))+P1(f319(f319(f321(x104253),f549(x104251,x104252,x104254,x104255,x104256,x104257,x104253)),x104257))+~P1(f319(f319(f321(f932(x104253,a923)),x104252),f319(f319(f54(x104253),x104257),x104256)))+~P1(f319(f319(f321(f932(x104253,a923)),x104251),f319(f319(f54(x104253),x104257),x104256)))
% 28.25/28.13 [10506]E(x105061,x105062)+~P9(x105063,x105066,x105067)+~P12(x105063,f932(x105064,a923),x105067,x105065)+~E(f319(f319(f33(x105063,f932(x105064,a923)),x105061),x105065),f319(f319(f33(x105063,f932(x105064,a923)),x105062),x105065))+~P1(f319(f319(f321(f931(x105063,x105063)),f319(f319(f244(x105063,x105063),f547(x105061,x105062,x105065,x105064,x105067,x105066,x105063)),f549(x105061,x105062,x105065,x105064,x105067,x105066,x105063))),x105067))+~P1(f319(f319(f321(f932(x105063,a923)),x105062),f319(f319(f54(x105063),x105066),x105067)))+~P1(f319(f319(f321(f932(x105063,a923)),x105061),f319(f319(f54(x105063),x105066),x105067)))
% 28.25/28.13 [9337]~P9(x93371,x93377,x93374)+~E(x93375,x93376)+~P1(f319(f319(f321(x93371),x93373),x93376))+~P1(f319(f319(f321(x93371),x93372),x93375))+~P1(f319(f319(f321(f932(x93371,a923)),x93376),f319(f319(f54(x93371),x93377),x93374)))+~P1(f319(f319(f321(f932(x93371,a923)),x93375),f319(f319(f54(x93371),x93377),x93374)))+P1(f319(f319(f321(f931(x93371,x93371)),f319(f319(f244(x93371,x93371),x93372),x93373)),x93374))
% 28.25/28.13 [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))
% 28.25/28.13 [9476]E(x94761,x94762)+~P9(x94763,x94764,x94765)+~P1(f319(f319(f321(x94763),x94766),x94762))+~P1(f319(f319(f321(x94763),x94767),x94761))+~P1(f319(f319(f321(f932(x94763,a923)),x94762),f319(f319(f54(x94763),x94764),x94765)))+~P1(f319(f319(f321(f932(x94763,a923)),x94761),f319(f319(f54(x94763),x94764),x94765)))+~P1(f319(f319(f321(f931(x94763,x94763)),f319(f319(f244(x94763,x94763),x94767),x94766)),x94765))
% 28.25/28.13 [10534]~P9(x105349,x105348,x105347)+~P9(x105341,x1053411,x1053410)+~P13(x105341,x105349,f932(x105346,a923),x1053410,x105347,x105345)+P1(f319(f319(f321(x105341),f551(x105342,x105343,x105344,x105345,x105346,x105347,x105348,x105349,x1053410,x1053411,x105341)),x1053411))+~P1(f319(f319(f321(f932(x105349,a923)),x105343),f319(f319(f54(x105349),x105348),x105347)))+~P1(f319(f319(f321(f932(x105341,a923)),x105344),f319(f319(f54(x105341),x1053411),x1053410)))+P1(f319(f319(f321(f932(x105346,a923)),f319(f319(f33(x105341,f932(x105346,a923)),x105344),f319(f319(f8(f932(x105349,f932(x105346,a923)),f932(x105346,a923),x105341),f319(f33(x105349,f932(x105346,a923)),x105343)),x105345))),x105342))
% 28.25/28.13 [10535]~P9(x1053511,x1053510,x105359)+~P9(x105351,x105358,x105357)+~P13(x1053511,x105351,f932(x105356,a923),x105359,x105357,x105355)+P1(f319(f319(f321(x105351),f552(x105352,x105353,x105354,x105355,x105356,x105357,x105358,x105351,x105359,x1053510,x1053511)),x105358))+~P1(f319(f319(f321(f932(x1053511,a923)),x105354),f319(f319(f54(x1053511),x1053510),x105359)))+~P1(f319(f319(f321(f932(x105351,a923)),x105353),f319(f319(f54(x105351),x105358),x105357)))+P1(f319(f319(f321(f932(x105356,a923)),f319(f319(f33(x1053511,f932(x105356,a923)),x105354),f319(f319(f8(f932(x105351,f932(x105356,a923)),f932(x105356,a923),x1053511),f319(f33(x105351,f932(x105356,a923)),x105353)),x105355))),x105352))
% 28.25/28.13 [10536]~P9(x105362,x105368,x105369)+~P9(x105364,x1053610,x1053611)+~P13(x105362,x105364,f932(x105361,a923),x105369,x1053611,x105366)+~P1(f319(f319(f321(f932(x105362,a923)),x105363),f319(f319(f54(x105362),x105368),x105369)))+~P1(f319(f319(f321(f932(x105364,a923)),x105365),f319(f319(f54(x105364),x1053610),x1053611)))+~P1(f319(f319(f321(f932(x105361,a923)),f319(f319(x105366,f551(x105367,x105365,x105363,x105366,x105361,x1053611,x1053610,x105364,x105369,x105368,x105362)),f552(x105367,x105365,x105363,x105366,x105361,x1053611,x1053610,x105364,x105369,x105368,x105362))),x105367))+P1(f319(f319(f321(f932(x105361,a923)),f319(f319(f33(x105362,f932(x105361,a923)),x105363),f319(f319(f8(f932(x105364,f932(x105361,a923)),f932(x105361,a923),x105362),f319(f33(x105364,f932(x105361,a923)),x105365)),x105366))),x105367))
% 28.25/28.13 [9373]E(x93731,x93732)+~P4(x93734)+~P26(x93733,x93734,x93735,f319(f319(f102(f932(x93733,a923)),f319(f164(x93733),x93731)),f319(f164(x93733),x93732)))+~E(f319(f164(x93733),x93731),f319(f164(x93733),x93732))+~P14(x93734,f319(f319(f146(x93733,x93734),x93735),x93732))+~P14(x93734,f319(f319(f146(x93733,x93734),x93735),x93731))+~P1(f319(f129(x93734),f319(f319(f146(x93733,x93734),x93735),x93732)))+~P1(f319(f129(x93734),f319(f319(f146(x93733,x93734),x93735),x93731)))
% 28.25/28.13 %EqnAxiom
% 28.25/28.13 [1]E(x11,x11)
% 28.25/28.13 [2]E(x22,x21)+~E(x21,x22)
% 28.25/28.13 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 28.25/28.13 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 28.25/28.13 [5]~E(x51,x52)+E(f92(x51),f92(x52))
% 28.25/28.13 [6]~E(x61,x62)+E(f23(x61),f23(x62))
% 28.25/28.13 [7]~E(x71,x72)+E(f180(x71),f180(x72))
% 28.25/28.13 [8]~E(x81,x82)+E(f319(x81,x83),f319(x82,x83))
% 28.25/28.13 [9]~E(x91,x92)+E(f319(x93,x91),f319(x93,x92))
% 28.25/28.13 [10]~E(x101,x102)+E(f93(x101),f93(x102))
% 28.25/28.13 [11]~E(x111,x112)+E(f224(x111),f224(x112))
% 28.25/28.13 [12]~E(x121,x122)+E(f102(x121),f102(x122))
% 28.25/28.13 [13]~E(x131,x132)+E(f225(x131),f225(x132))
% 28.25/28.13 [14]~E(x141,x142)+E(f94(x141),f94(x142))
% 28.25/28.13 [15]~E(x151,x152)+E(f25(x151),f25(x152))
% 28.25/28.13 [16]~E(x161,x162)+E(f78(x161),f78(x162))
% 28.25/28.13 [17]~E(x171,x172)+E(f321(x171),f321(x172))
% 28.25/28.13 [18]~E(x181,x182)+E(f226(x181),f226(x182))
% 28.25/28.13 [19]~E(x191,x192)+E(f932(x191,x193),f932(x192,x193))
% 28.25/28.13 [20]~E(x201,x202)+E(f932(x203,x201),f932(x203,x202))
% 28.25/28.13 [21]~E(x211,x212)+E(f72(x211),f72(x212))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [33]~E(x331,x332)+E(f7(x331,x333,x334),f7(x332,x333,x334))
% 28.25/28.13 [34]~E(x341,x342)+E(f7(x343,x341,x344),f7(x343,x342,x344))
% 28.25/28.13 [35]~E(x351,x352)+E(f7(x353,x354,x351),f7(x353,x354,x352))
% 28.25/28.13 [36]~E(x361,x362)+E(f4(x361),f4(x362))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [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))
% 28.25/28.13 [48]~E(x481,x482)+E(f146(x481,x483),f146(x482,x483))
% 28.25/28.13 [49]~E(x491,x492)+E(f146(x493,x491),f146(x493,x492))
% 28.25/28.13 [50]~E(x501,x502)+E(f103(x501),f103(x502))
% 28.25/28.13 [51]~E(x511,x512)+E(f32(x511,x513),f32(x512,x513))
% 28.25/28.13 [52]~E(x521,x522)+E(f32(x523,x521),f32(x523,x522))
% 28.25/28.13 [53]~E(x531,x532)+E(f924(x531),f924(x532))
% 28.25/28.13 [54]~E(x541,x542)+E(f929(x541),f929(x542))
% 28.25/28.13 [55]~E(x551,x552)+E(f926(x551),f926(x552))
% 28.25/28.13 [56]~E(x561,x562)+E(f927(x561),f927(x562))
% 28.25/28.13 [57]~E(x571,x572)+E(f73(x571),f73(x572))
% 28.25/28.13 [58]~E(x581,x582)+E(f181(x581),f181(x582))
% 28.25/28.13 [59]~E(x591,x592)+E(f95(x591),f95(x592))
% 28.25/28.13 [60]~E(x601,x602)+E(f74(x601),f74(x602))
% 28.25/28.13 [61]~E(x611,x612)+E(f55(x611),f55(x612))
% 28.25/28.13 [62]~E(x621,x622)+E(f227(x621),f227(x622))
% 28.25/28.13 [63]~E(x631,x632)+E(f8(x631,x633,x634),f8(x632,x633,x634))
% 28.25/28.13 [64]~E(x641,x642)+E(f8(x643,x641,x644),f8(x643,x642,x644))
% 28.25/28.13 [65]~E(x651,x652)+E(f8(x653,x654,x651),f8(x653,x654,x652))
% 28.25/28.13 [66]~E(x661,x662)+E(f778(x661,x663,x664),f778(x662,x663,x664))
% 28.25/28.13 [67]~E(x671,x672)+E(f778(x673,x671,x674),f778(x673,x672,x674))
% 28.25/28.13 [68]~E(x681,x682)+E(f778(x683,x684,x681),f778(x683,x684,x682))
% 28.25/28.13 [69]~E(x691,x692)+E(f164(x691),f164(x692))
% 28.25/28.13 [70]~E(x701,x702)+E(f143(x701),f143(x702))
% 28.25/28.13 [71]~E(x711,x712)+E(f75(x711),f75(x712))
% 28.25/28.13 [72]~E(x721,x722)+E(f749(x721,x723,x724,x725),f749(x722,x723,x724,x725))
% 28.25/28.13 [73]~E(x731,x732)+E(f749(x733,x731,x734,x735),f749(x733,x732,x734,x735))
% 28.25/28.13 [74]~E(x741,x742)+E(f749(x743,x744,x741,x745),f749(x743,x744,x742,x745))
% 28.25/28.13 [75]~E(x751,x752)+E(f749(x753,x754,x755,x751),f749(x753,x754,x755,x752))
% 28.25/28.13 [76]~E(x761,x762)+E(f931(x761,x763),f931(x762,x763))
% 28.25/28.13 [77]~E(x771,x772)+E(f931(x773,x771),f931(x773,x772))
% 28.25/28.13 [78]~E(x781,x782)+E(f18(x781,x783,x784),f18(x782,x783,x784))
% 28.25/28.13 [79]~E(x791,x792)+E(f18(x793,x791,x794),f18(x793,x792,x794))
% 28.25/28.13 [80]~E(x801,x802)+E(f18(x803,x804,x801),f18(x803,x804,x802))
% 28.25/28.13 [81]~E(x811,x812)+E(f349(x811,x813,x814,x815,x816),f349(x812,x813,x814,x815,x816))
% 28.25/28.13 [82]~E(x821,x822)+E(f349(x823,x821,x824,x825,x826),f349(x823,x822,x824,x825,x826))
% 28.25/28.13 [83]~E(x831,x832)+E(f349(x833,x834,x831,x835,x836),f349(x833,x834,x832,x835,x836))
% 28.25/28.13 [84]~E(x841,x842)+E(f349(x843,x844,x845,x841,x846),f349(x843,x844,x845,x842,x846))
% 28.25/28.13 [85]~E(x851,x852)+E(f349(x853,x854,x855,x856,x851),f349(x853,x854,x855,x856,x852))
% 28.25/28.13 [86]~E(x861,x862)+E(f301(x861),f301(x862))
% 28.25/28.13 [87]~E(x871,x872)+E(f31(x871,x873),f31(x872,x873))
% 28.25/28.13 [88]~E(x881,x882)+E(f31(x883,x881),f31(x883,x882))
% 28.25/28.13 [89]~E(x891,x892)+E(f710(x891,x893,x894),f710(x892,x893,x894))
% 28.25/28.13 [90]~E(x901,x902)+E(f710(x903,x901,x904),f710(x903,x902,x904))
% 28.25/28.13 [91]~E(x911,x912)+E(f710(x913,x914,x911),f710(x913,x914,x912))
% 28.25/28.13 [92]~E(x921,x922)+E(f54(x921),f54(x922))
% 28.25/28.13 [93]~E(x931,x932)+E(f13(x931,x933),f13(x932,x933))
% 28.25/28.13 [94]~E(x941,x942)+E(f13(x943,x941),f13(x943,x942))
% 28.25/28.13 [95]~E(x951,x952)+E(f665(x951,x953,x954,x955),f665(x952,x953,x954,x955))
% 28.25/28.13 [96]~E(x961,x962)+E(f665(x963,x961,x964,x965),f665(x963,x962,x964,x965))
% 28.25/28.13 [97]~E(x971,x972)+E(f665(x973,x974,x971,x975),f665(x973,x974,x972,x975))
% 28.25/28.13 [98]~E(x981,x982)+E(f665(x983,x984,x985,x981),f665(x983,x984,x985,x982))
% 28.25/28.13 [99]~E(x991,x992)+E(f295(x991,x993,x994),f295(x992,x993,x994))
% 28.25/28.13 [100]~E(x1001,x1002)+E(f295(x1003,x1001,x1004),f295(x1003,x1002,x1004))
% 28.25/28.13 [101]~E(x1011,x1012)+E(f295(x1013,x1014,x1011),f295(x1013,x1014,x1012))
% 28.25/28.13 [102]~E(x1021,x1022)+E(f29(x1021),f29(x1022))
% 28.25/28.13 [103]~E(x1031,x1032)+E(f243(x1031,x1033),f243(x1032,x1033))
% 28.25/28.13 [104]~E(x1041,x1042)+E(f243(x1043,x1041),f243(x1043,x1042))
% 28.25/28.13 [105]~E(x1051,x1052)+E(f153(x1051,x1053),f153(x1052,x1053))
% 28.25/28.13 [106]~E(x1061,x1062)+E(f153(x1063,x1061),f153(x1063,x1062))
% 28.25/28.13 [107]~E(x1071,x1072)+E(f81(x1071),f81(x1072))
% 28.25/28.13 [108]~E(x1081,x1082)+E(f86(x1081),f86(x1082))
% 28.25/28.13 [109]~E(x1091,x1092)+E(f160(x1091),f160(x1092))
% 28.25/28.13 [110]~E(x1101,x1102)+E(f434(x1101,x1103,x1104),f434(x1102,x1103,x1104))
% 28.25/28.13 [111]~E(x1111,x1112)+E(f434(x1113,x1111,x1114),f434(x1113,x1112,x1114))
% 28.25/28.13 [112]~E(x1121,x1122)+E(f434(x1123,x1124,x1121),f434(x1123,x1124,x1122))
% 28.25/28.13 [113]~E(x1131,x1132)+E(f129(x1131),f129(x1132))
% 28.25/28.13 [114]~E(x1141,x1142)+E(f328(x1141,x1143,x1144),f328(x1142,x1143,x1144))
% 28.25/28.13 [115]~E(x1151,x1152)+E(f328(x1153,x1151,x1154),f328(x1153,x1152,x1154))
% 28.25/28.13 [116]~E(x1161,x1162)+E(f328(x1163,x1164,x1161),f328(x1163,x1164,x1162))
% 28.25/28.13 [117]~E(x1171,x1172)+E(f66(x1171,x1173,x1174,x1175),f66(x1172,x1173,x1174,x1175))
% 28.25/28.13 [118]~E(x1181,x1182)+E(f66(x1183,x1181,x1184,x1185),f66(x1183,x1182,x1184,x1185))
% 28.25/28.13 [119]~E(x1191,x1192)+E(f66(x1193,x1194,x1191,x1195),f66(x1193,x1194,x1192,x1195))
% 28.25/28.13 [120]~E(x1201,x1202)+E(f66(x1203,x1204,x1205,x1201),f66(x1203,x1204,x1205,x1202))
% 28.25/28.13 [121]~E(x1211,x1212)+E(f254(x1211),f254(x1212))
% 28.25/28.13 [122]~E(x1221,x1222)+E(f308(x1221,x1223),f308(x1222,x1223))
% 28.25/28.13 [123]~E(x1231,x1232)+E(f308(x1233,x1231),f308(x1233,x1232))
% 28.25/28.13 [124]~E(x1241,x1242)+E(f128(x1241,x1243),f128(x1242,x1243))
% 28.25/28.13 [125]~E(x1251,x1252)+E(f128(x1253,x1251),f128(x1253,x1252))
% 28.25/28.13 [126]~E(x1261,x1262)+E(f244(x1261,x1263),f244(x1262,x1263))
% 28.25/28.13 [127]~E(x1271,x1272)+E(f244(x1273,x1271),f244(x1273,x1272))
% 28.25/28.13 [128]~E(x1281,x1282)+E(f251(x1281,x1283,x1284,x1285),f251(x1282,x1283,x1284,x1285))
% 28.25/28.13 [129]~E(x1291,x1292)+E(f251(x1293,x1291,x1294,x1295),f251(x1293,x1292,x1294,x1295))
% 28.25/28.13 [130]~E(x1301,x1302)+E(f251(x1303,x1304,x1301,x1305),f251(x1303,x1304,x1302,x1305))
% 28.25/28.13 [131]~E(x1311,x1312)+E(f251(x1313,x1314,x1315,x1311),f251(x1313,x1314,x1315,x1312))
% 28.25/28.13 [132]~E(x1321,x1322)+E(f234(x1321),f234(x1322))
% 28.25/28.13 [133]~E(x1331,x1332)+E(f170(x1331,x1333),f170(x1332,x1333))
% 28.25/28.13 [134]~E(x1341,x1342)+E(f170(x1343,x1341),f170(x1343,x1342))
% 28.25/28.13 [135]~E(x1351,x1352)+E(f157(x1351),f157(x1352))
% 28.25/28.13 [136]~E(x1361,x1362)+E(f5(x1361),f5(x1362))
% 28.25/28.13 [137]~E(x1371,x1372)+E(f283(x1371),f283(x1372))
% 28.25/28.13 [138]~E(x1381,x1382)+E(f97(x1381),f97(x1382))
% 28.25/28.13 [139]~E(x1391,x1392)+E(f98(x1391),f98(x1392))
% 28.25/28.13 [140]~E(x1401,x1402)+E(f320(x1401),f320(x1402))
% 28.25/28.13 [141]~E(x1411,x1412)+E(f176(x1411,x1413,x1414),f176(x1412,x1413,x1414))
% 28.25/28.13 [142]~E(x1421,x1422)+E(f176(x1423,x1421,x1424),f176(x1423,x1422,x1424))
% 28.25/28.13 [143]~E(x1431,x1432)+E(f176(x1433,x1434,x1431),f176(x1433,x1434,x1432))
% 28.25/28.13 [144]~E(x1441,x1442)+E(f595(x1441),f595(x1442))
% 28.25/28.13 [145]~E(x1451,x1452)+E(f48(x1451,x1453),f48(x1452,x1453))
% 28.25/28.13 [146]~E(x1461,x1462)+E(f48(x1463,x1461),f48(x1463,x1462))
% 28.25/28.13 [147]~E(x1471,x1472)+E(f302(x1471,x1473,x1474),f302(x1472,x1473,x1474))
% 28.25/28.13 [148]~E(x1481,x1482)+E(f302(x1483,x1481,x1484),f302(x1483,x1482,x1484))
% 28.25/28.13 [149]~E(x1491,x1492)+E(f302(x1493,x1494,x1491),f302(x1493,x1494,x1492))
% 28.25/28.13 [150]~E(x1501,x1502)+E(f233(x1501,x1503),f233(x1502,x1503))
% 28.25/28.13 [151]~E(x1511,x1512)+E(f233(x1513,x1511),f233(x1513,x1512))
% 28.25/28.13 [152]~E(x1521,x1522)+E(f248(x1521,x1523),f248(x1522,x1523))
% 28.25/28.13 [153]~E(x1531,x1532)+E(f248(x1533,x1531),f248(x1533,x1532))
% 28.25/28.13 [154]~E(x1541,x1542)+E(f173(x1541,x1543),f173(x1542,x1543))
% 28.25/28.13 [155]~E(x1551,x1552)+E(f173(x1553,x1551),f173(x1553,x1552))
% 28.25/28.13 [156]~E(x1561,x1562)+E(f742(x1561,x1563),f742(x1562,x1563))
% 28.25/28.13 [157]~E(x1571,x1572)+E(f742(x1573,x1571),f742(x1573,x1572))
% 28.25/28.13 [158]~E(x1581,x1582)+E(f167(x1581),f167(x1582))
% 28.25/28.13 [159]~E(x1591,x1592)+E(f10(x1591,x1593),f10(x1592,x1593))
% 28.25/28.13 [160]~E(x1601,x1602)+E(f10(x1603,x1601),f10(x1603,x1602))
% 28.25/28.13 [161]~E(x1611,x1612)+E(f144(x1611,x1613),f144(x1612,x1613))
% 28.25/28.13 [162]~E(x1621,x1622)+E(f144(x1623,x1621),f144(x1623,x1622))
% 28.25/28.13 [163]~E(x1631,x1632)+E(f169(x1631,x1633,x1634),f169(x1632,x1633,x1634))
% 28.25/28.13 [164]~E(x1641,x1642)+E(f169(x1643,x1641,x1644),f169(x1643,x1642,x1644))
% 28.25/28.13 [165]~E(x1651,x1652)+E(f169(x1653,x1654,x1651),f169(x1653,x1654,x1652))
% 28.25/28.13 [166]~E(x1661,x1662)+E(f793(x1661,x1663,x1664,x1665,x1666),f793(x1662,x1663,x1664,x1665,x1666))
% 28.25/28.13 [167]~E(x1671,x1672)+E(f793(x1673,x1671,x1674,x1675,x1676),f793(x1673,x1672,x1674,x1675,x1676))
% 28.25/28.13 [168]~E(x1681,x1682)+E(f793(x1683,x1684,x1681,x1685,x1686),f793(x1683,x1684,x1682,x1685,x1686))
% 28.25/28.13 [169]~E(x1691,x1692)+E(f793(x1693,x1694,x1695,x1691,x1696),f793(x1693,x1694,x1695,x1692,x1696))
% 28.25/28.13 [170]~E(x1701,x1702)+E(f793(x1703,x1704,x1705,x1706,x1701),f793(x1703,x1704,x1705,x1706,x1702))
% 28.25/28.13 [171]~E(x1711,x1712)+E(f6(x1711,x1713),f6(x1712,x1713))
% 28.25/28.13 [172]~E(x1721,x1722)+E(f6(x1723,x1721),f6(x1723,x1722))
% 28.25/28.13 [173]~E(x1731,x1732)+E(f140(x1731,x1733,x1734),f140(x1732,x1733,x1734))
% 28.25/28.13 [174]~E(x1741,x1742)+E(f140(x1743,x1741,x1744),f140(x1743,x1742,x1744))
% 28.25/28.13 [175]~E(x1751,x1752)+E(f140(x1753,x1754,x1751),f140(x1753,x1754,x1752))
% 28.25/28.13 [176]~E(x1761,x1762)+E(f126(x1761),f126(x1762))
% 28.25/28.13 [177]~E(x1771,x1772)+E(f279(x1771),f279(x1772))
% 28.25/28.13 [178]~E(x1781,x1782)+E(f53(x1781,x1783,x1784,x1785),f53(x1782,x1783,x1784,x1785))
% 28.25/28.13 [179]~E(x1791,x1792)+E(f53(x1793,x1791,x1794,x1795),f53(x1793,x1792,x1794,x1795))
% 28.25/28.13 [180]~E(x1801,x1802)+E(f53(x1803,x1804,x1801,x1805),f53(x1803,x1804,x1802,x1805))
% 28.25/28.13 [181]~E(x1811,x1812)+E(f53(x1813,x1814,x1815,x1811),f53(x1813,x1814,x1815,x1812))
% 28.25/28.13 [182]~E(x1821,x1822)+E(f249(x1821,x1823,x1824),f249(x1822,x1823,x1824))
% 28.25/28.13 [183]~E(x1831,x1832)+E(f249(x1833,x1831,x1834),f249(x1833,x1832,x1834))
% 28.25/28.13 [184]~E(x1841,x1842)+E(f249(x1843,x1844,x1841),f249(x1843,x1844,x1842))
% 28.25/28.13 [185]~E(x1851,x1852)+E(f624(x1851,x1853,x1854,x1855,x1856),f624(x1852,x1853,x1854,x1855,x1856))
% 28.25/28.13 [186]~E(x1861,x1862)+E(f624(x1863,x1861,x1864,x1865,x1866),f624(x1863,x1862,x1864,x1865,x1866))
% 28.25/28.13 [187]~E(x1871,x1872)+E(f624(x1873,x1874,x1871,x1875,x1876),f624(x1873,x1874,x1872,x1875,x1876))
% 28.25/28.13 [188]~E(x1881,x1882)+E(f624(x1883,x1884,x1885,x1881,x1886),f624(x1883,x1884,x1885,x1882,x1886))
% 28.25/28.13 [189]~E(x1891,x1892)+E(f624(x1893,x1894,x1895,x1896,x1891),f624(x1893,x1894,x1895,x1896,x1892))
% 28.25/28.13 [190]~E(x1901,x1902)+E(f836(x1901,x1903),f836(x1902,x1903))
% 28.25/28.13 [191]~E(x1911,x1912)+E(f836(x1913,x1911),f836(x1913,x1912))
% 28.25/28.13 [192]~E(x1921,x1922)+E(f80(x1921,x1923),f80(x1922,x1923))
% 28.25/28.13 [193]~E(x1931,x1932)+E(f80(x1933,x1931),f80(x1933,x1932))
% 28.25/28.13 [194]~E(x1941,x1942)+E(f874(x1941,x1943,x1944),f874(x1942,x1943,x1944))
% 28.25/28.13 [195]~E(x1951,x1952)+E(f874(x1953,x1951,x1954),f874(x1953,x1952,x1954))
% 28.25/28.13 [196]~E(x1961,x1962)+E(f874(x1963,x1964,x1961),f874(x1963,x1964,x1962))
% 28.25/28.13 [197]~E(x1971,x1972)+E(f274(x1971),f274(x1972))
% 28.25/28.13 [198]~E(x1981,x1982)+E(f138(x1981,x1983),f138(x1982,x1983))
% 28.25/28.13 [199]~E(x1991,x1992)+E(f138(x1993,x1991),f138(x1993,x1992))
% 28.25/28.13 [200]~E(x2001,x2002)+E(f236(x2001),f236(x2002))
% 28.25/28.13 [201]~E(x2011,x2012)+E(f178(x2011),f178(x2012))
% 28.25/28.13 [202]~E(x2021,x2022)+E(f846(x2021,x2023,x2024,x2025),f846(x2022,x2023,x2024,x2025))
% 28.25/28.13 [203]~E(x2031,x2032)+E(f846(x2033,x2031,x2034,x2035),f846(x2033,x2032,x2034,x2035))
% 28.25/28.13 [204]~E(x2041,x2042)+E(f846(x2043,x2044,x2041,x2045),f846(x2043,x2044,x2042,x2045))
% 28.25/28.13 [205]~E(x2051,x2052)+E(f846(x2053,x2054,x2055,x2051),f846(x2053,x2054,x2055,x2052))
% 28.25/28.13 [206]~E(x2061,x2062)+E(f11(x2061,x2063,x2064),f11(x2062,x2063,x2064))
% 28.25/28.13 [207]~E(x2071,x2072)+E(f11(x2073,x2071,x2074),f11(x2073,x2072,x2074))
% 28.25/28.13 [208]~E(x2081,x2082)+E(f11(x2083,x2084,x2081),f11(x2083,x2084,x2082))
% 28.25/28.13 [209]~E(x2091,x2092)+E(f134(x2091,x2093,x2094,x2095),f134(x2092,x2093,x2094,x2095))
% 28.25/28.13 [210]~E(x2101,x2102)+E(f134(x2103,x2101,x2104,x2105),f134(x2103,x2102,x2104,x2105))
% 28.25/28.13 [211]~E(x2111,x2112)+E(f134(x2113,x2114,x2111,x2115),f134(x2113,x2114,x2112,x2115))
% 28.25/28.13 [212]~E(x2121,x2122)+E(f134(x2123,x2124,x2125,x2121),f134(x2123,x2124,x2125,x2122))
% 28.25/28.13 [213]~E(x2131,x2132)+E(f39(x2131,x2133,x2134),f39(x2132,x2133,x2134))
% 28.25/28.13 [214]~E(x2141,x2142)+E(f39(x2143,x2141,x2144),f39(x2143,x2142,x2144))
% 28.25/28.13 [215]~E(x2151,x2152)+E(f39(x2153,x2154,x2151),f39(x2153,x2154,x2152))
% 28.25/28.13 [216]~E(x2161,x2162)+E(f68(x2161,x2163,x2164,x2165,x2166),f68(x2162,x2163,x2164,x2165,x2166))
% 28.25/28.13 [217]~E(x2171,x2172)+E(f68(x2173,x2171,x2174,x2175,x2176),f68(x2173,x2172,x2174,x2175,x2176))
% 28.25/28.13 [218]~E(x2181,x2182)+E(f68(x2183,x2184,x2181,x2185,x2186),f68(x2183,x2184,x2182,x2185,x2186))
% 28.25/28.13 [219]~E(x2191,x2192)+E(f68(x2193,x2194,x2195,x2191,x2196),f68(x2193,x2194,x2195,x2192,x2196))
% 28.25/28.13 [220]~E(x2201,x2202)+E(f68(x2203,x2204,x2205,x2206,x2201),f68(x2203,x2204,x2205,x2206,x2202))
% 28.25/28.13 [221]~E(x2211,x2212)+E(f679(x2211,x2213,x2214),f679(x2212,x2213,x2214))
% 28.25/28.13 [222]~E(x2221,x2222)+E(f679(x2223,x2221,x2224),f679(x2223,x2222,x2224))
% 28.25/28.13 [223]~E(x2231,x2232)+E(f679(x2233,x2234,x2231),f679(x2233,x2234,x2232))
% 28.25/28.13 [224]~E(x2241,x2242)+E(f59(x2241,x2243,x2244),f59(x2242,x2243,x2244))
% 28.25/28.13 [225]~E(x2251,x2252)+E(f59(x2253,x2251,x2254),f59(x2253,x2252,x2254))
% 28.25/28.13 [226]~E(x2261,x2262)+E(f59(x2263,x2264,x2261),f59(x2263,x2264,x2262))
% 28.25/28.13 [227]~E(x2271,x2272)+E(f33(x2271,x2273),f33(x2272,x2273))
% 28.25/28.13 [228]~E(x2281,x2282)+E(f33(x2283,x2281),f33(x2283,x2282))
% 28.25/28.13 [229]~E(x2291,x2292)+E(f51(x2291),f51(x2292))
% 28.25/28.13 [230]~E(x2301,x2302)+E(f277(x2301,x2303,x2304),f277(x2302,x2303,x2304))
% 28.25/28.13 [231]~E(x2311,x2312)+E(f277(x2313,x2311,x2314),f277(x2313,x2312,x2314))
% 28.25/28.13 [232]~E(x2321,x2322)+E(f277(x2323,x2324,x2321),f277(x2323,x2324,x2322))
% 28.25/28.13 [233]~E(x2331,x2332)+E(f867(x2331,x2333,x2334),f867(x2332,x2333,x2334))
% 28.25/28.13 [234]~E(x2341,x2342)+E(f867(x2343,x2341,x2344),f867(x2343,x2342,x2344))
% 28.25/28.13 [235]~E(x2351,x2352)+E(f867(x2353,x2354,x2351),f867(x2353,x2354,x2352))
% 28.25/28.13 [236]~E(x2361,x2362)+E(f380(x2361,x2363,x2364,x2365),f380(x2362,x2363,x2364,x2365))
% 28.25/28.13 [237]~E(x2371,x2372)+E(f380(x2373,x2371,x2374,x2375),f380(x2373,x2372,x2374,x2375))
% 28.25/28.13 [238]~E(x2381,x2382)+E(f380(x2383,x2384,x2381,x2385),f380(x2383,x2384,x2382,x2385))
% 28.25/28.13 [239]~E(x2391,x2392)+E(f380(x2393,x2394,x2395,x2391),f380(x2393,x2394,x2395,x2392))
% 28.25/28.13 [240]~E(x2401,x2402)+E(f175(x2401,x2403),f175(x2402,x2403))
% 28.25/28.13 [241]~E(x2411,x2412)+E(f175(x2413,x2411),f175(x2413,x2412))
% 28.25/28.13 [242]~E(x2421,x2422)+E(f106(x2421,x2423),f106(x2422,x2423))
% 28.25/28.13 [243]~E(x2431,x2432)+E(f106(x2433,x2431),f106(x2433,x2432))
% 28.25/28.13 [244]~E(x2441,x2442)+E(f758(x2441,x2443),f758(x2442,x2443))
% 28.25/28.13 [245]~E(x2451,x2452)+E(f758(x2453,x2451),f758(x2453,x2452))
% 28.25/28.13 [246]~E(x2461,x2462)+E(f281(x2461,x2463,x2464),f281(x2462,x2463,x2464))
% 28.25/28.13 [247]~E(x2471,x2472)+E(f281(x2473,x2471,x2474),f281(x2473,x2472,x2474))
% 28.25/28.13 [248]~E(x2481,x2482)+E(f281(x2483,x2484,x2481),f281(x2483,x2484,x2482))
% 28.25/28.13 [249]~E(x2491,x2492)+E(f656(x2491,x2493,x2494),f656(x2492,x2493,x2494))
% 28.25/28.13 [250]~E(x2501,x2502)+E(f656(x2503,x2501,x2504),f656(x2503,x2502,x2504))
% 28.25/28.13 [251]~E(x2511,x2512)+E(f656(x2513,x2514,x2511),f656(x2513,x2514,x2512))
% 28.25/28.13 [252]~E(x2521,x2522)+E(f906(x2521,x2523,x2524,x2525,x2526),f906(x2522,x2523,x2524,x2525,x2526))
% 28.25/28.13 [253]~E(x2531,x2532)+E(f906(x2533,x2531,x2534,x2535,x2536),f906(x2533,x2532,x2534,x2535,x2536))
% 28.25/28.13 [254]~E(x2541,x2542)+E(f906(x2543,x2544,x2541,x2545,x2546),f906(x2543,x2544,x2542,x2545,x2546))
% 28.25/28.13 [255]~E(x2551,x2552)+E(f906(x2553,x2554,x2555,x2551,x2556),f906(x2553,x2554,x2555,x2552,x2556))
% 28.25/28.13 [256]~E(x2561,x2562)+E(f906(x2563,x2564,x2565,x2566,x2561),f906(x2563,x2564,x2565,x2566,x2562))
% 28.25/28.13 [257]~E(x2571,x2572)+E(f105(x2571),f105(x2572))
% 28.25/28.13 [258]~E(x2581,x2582)+E(f30(x2581),f30(x2582))
% 28.25/28.13 [259]~E(x2591,x2592)+E(f869(x2591,x2593,x2594),f869(x2592,x2593,x2594))
% 28.25/28.13 [260]~E(x2601,x2602)+E(f869(x2603,x2601,x2604),f869(x2603,x2602,x2604))
% 28.25/28.13 [261]~E(x2611,x2612)+E(f869(x2613,x2614,x2611),f869(x2613,x2614,x2612))
% 28.25/28.13 [262]~E(x2621,x2622)+E(f76(x2621,x2623),f76(x2622,x2623))
% 28.25/28.13 [263]~E(x2631,x2632)+E(f76(x2633,x2631),f76(x2633,x2632))
% 28.25/28.13 [264]~E(x2641,x2642)+E(f555(x2641,x2643,x2644),f555(x2642,x2643,x2644))
% 28.25/28.13 [265]~E(x2651,x2652)+E(f555(x2653,x2651,x2654),f555(x2653,x2652,x2654))
% 28.25/28.13 [266]~E(x2661,x2662)+E(f555(x2663,x2664,x2661),f555(x2663,x2664,x2662))
% 28.25/28.13 [267]~E(x2671,x2672)+E(f69(x2671),f69(x2672))
% 28.25/28.13 [268]~E(x2681,x2682)+E(f183(x2681),f183(x2682))
% 28.25/28.13 [269]~E(x2691,x2692)+E(f139(x2691,x2693),f139(x2692,x2693))
% 28.25/28.13 [270]~E(x2701,x2702)+E(f139(x2703,x2701),f139(x2703,x2702))
% 28.25/28.13 [271]~E(x2711,x2712)+E(f107(x2711),f107(x2712))
% 28.25/28.13 [272]~E(x2721,x2722)+E(f908(x2721,x2723,x2724,x2725,x2726),f908(x2722,x2723,x2724,x2725,x2726))
% 28.25/28.13 [273]~E(x2731,x2732)+E(f908(x2733,x2731,x2734,x2735,x2736),f908(x2733,x2732,x2734,x2735,x2736))
% 28.25/28.13 [274]~E(x2741,x2742)+E(f908(x2743,x2744,x2741,x2745,x2746),f908(x2743,x2744,x2742,x2745,x2746))
% 28.25/28.13 [275]~E(x2751,x2752)+E(f908(x2753,x2754,x2755,x2751,x2756),f908(x2753,x2754,x2755,x2752,x2756))
% 28.25/28.13 [276]~E(x2761,x2762)+E(f908(x2763,x2764,x2765,x2766,x2761),f908(x2763,x2764,x2765,x2766,x2762))
% 28.25/28.13 [277]~E(x2771,x2772)+E(f933(x2771,x2773),f933(x2772,x2773))
% 28.25/28.13 [278]~E(x2781,x2782)+E(f933(x2783,x2781),f933(x2783,x2782))
% 28.25/28.13 [279]~E(x2791,x2792)+E(f930(x2791,x2793),f930(x2792,x2793))
% 28.25/28.13 [280]~E(x2801,x2802)+E(f930(x2803,x2801),f930(x2803,x2802))
% 28.25/28.13 [281]~E(x2811,x2812)+E(f159(x2811),f159(x2812))
% 28.25/28.13 [282]~E(x2821,x2822)+E(f131(x2821,x2823),f131(x2822,x2823))
% 28.25/28.13 [283]~E(x2831,x2832)+E(f131(x2833,x2831),f131(x2833,x2832))
% 28.25/28.13 [284]~E(x2841,x2842)+E(f14(x2841,x2843),f14(x2842,x2843))
% 28.25/28.13 [285]~E(x2851,x2852)+E(f14(x2853,x2851),f14(x2853,x2852))
% 28.25/28.13 [286]~E(x2861,x2862)+E(f34(x2861,x2863),f34(x2862,x2863))
% 28.25/28.13 [287]~E(x2871,x2872)+E(f34(x2873,x2871),f34(x2873,x2872))
% 28.25/28.13 [288]~E(x2881,x2882)+E(f163(x2881),f163(x2882))
% 28.25/28.13 [289]~E(x2891,x2892)+E(f639(x2891,x2893,x2894,x2895,x2896),f639(x2892,x2893,x2894,x2895,x2896))
% 28.25/28.13 [290]~E(x2901,x2902)+E(f639(x2903,x2901,x2904,x2905,x2906),f639(x2903,x2902,x2904,x2905,x2906))
% 28.25/28.13 [291]~E(x2911,x2912)+E(f639(x2913,x2914,x2911,x2915,x2916),f639(x2913,x2914,x2912,x2915,x2916))
% 28.25/28.13 [292]~E(x2921,x2922)+E(f639(x2923,x2924,x2925,x2921,x2926),f639(x2923,x2924,x2925,x2922,x2926))
% 28.25/28.13 [293]~E(x2931,x2932)+E(f639(x2933,x2934,x2935,x2936,x2931),f639(x2933,x2934,x2935,x2936,x2932))
% 28.25/28.13 [294]~E(x2941,x2942)+E(f723(x2941,x2943,x2944),f723(x2942,x2943,x2944))
% 28.25/28.13 [295]~E(x2951,x2952)+E(f723(x2953,x2951,x2954),f723(x2953,x2952,x2954))
% 28.25/28.13 [296]~E(x2961,x2962)+E(f723(x2963,x2964,x2961),f723(x2963,x2964,x2962))
% 28.25/28.13 [297]~E(x2971,x2972)+E(f56(x2971,x2973,x2974),f56(x2972,x2973,x2974))
% 28.25/28.13 [298]~E(x2981,x2982)+E(f56(x2983,x2981,x2984),f56(x2983,x2982,x2984))
% 28.25/28.13 [299]~E(x2991,x2992)+E(f56(x2993,x2994,x2991),f56(x2993,x2994,x2992))
% 28.25/28.13 [300]~E(x3001,x3002)+E(f307(x3001,x3003),f307(x3002,x3003))
% 28.25/28.13 [301]~E(x3011,x3012)+E(f307(x3013,x3011),f307(x3013,x3012))
% 28.25/28.13 [302]~E(x3021,x3022)+E(f300(x3021),f300(x3022))
% 28.25/28.13 [303]~E(x3031,x3032)+E(f136(x3031,x3033),f136(x3032,x3033))
% 28.25/28.13 [304]~E(x3041,x3042)+E(f136(x3043,x3041),f136(x3043,x3042))
% 28.25/28.13 [305]~E(x3051,x3052)+E(f790(x3051,x3053,x3054,x3055),f790(x3052,x3053,x3054,x3055))
% 28.25/28.13 [306]~E(x3061,x3062)+E(f790(x3063,x3061,x3064,x3065),f790(x3063,x3062,x3064,x3065))
% 28.25/28.13 [307]~E(x3071,x3072)+E(f790(x3073,x3074,x3071,x3075),f790(x3073,x3074,x3072,x3075))
% 28.25/28.13 [308]~E(x3081,x3082)+E(f790(x3083,x3084,x3085,x3081),f790(x3083,x3084,x3085,x3082))
% 28.25/28.13 [309]~E(x3091,x3092)+E(f58(x3091,x3093,x3094),f58(x3092,x3093,x3094))
% 28.25/28.13 [310]~E(x3101,x3102)+E(f58(x3103,x3101,x3104),f58(x3103,x3102,x3104))
% 28.25/28.13 [311]~E(x3111,x3112)+E(f58(x3113,x3114,x3111),f58(x3113,x3114,x3112))
% 28.25/28.13 [312]~E(x3121,x3122)+E(f161(x3121,x3123,x3124),f161(x3122,x3123,x3124))
% 28.25/28.13 [313]~E(x3131,x3132)+E(f161(x3133,x3131,x3134),f161(x3133,x3132,x3134))
% 28.25/28.13 [314]~E(x3141,x3142)+E(f161(x3143,x3144,x3141),f161(x3143,x3144,x3142))
% 28.25/28.13 [315]~E(x3151,x3152)+E(f635(x3151,x3153,x3154,x3155,x3156),f635(x3152,x3153,x3154,x3155,x3156))
% 28.25/28.13 [316]~E(x3161,x3162)+E(f635(x3163,x3161,x3164,x3165,x3166),f635(x3163,x3162,x3164,x3165,x3166))
% 28.25/28.13 [317]~E(x3171,x3172)+E(f635(x3173,x3174,x3171,x3175,x3176),f635(x3173,x3174,x3172,x3175,x3176))
% 28.25/28.13 [318]~E(x3181,x3182)+E(f635(x3183,x3184,x3185,x3181,x3186),f635(x3183,x3184,x3185,x3182,x3186))
% 28.25/28.13 [319]~E(x3191,x3192)+E(f635(x3193,x3194,x3195,x3196,x3191),f635(x3193,x3194,x3195,x3196,x3192))
% 28.25/28.13 [320]~E(x3201,x3202)+E(f445(x3201,x3203,x3204,x3205,x3206),f445(x3202,x3203,x3204,x3205,x3206))
% 28.25/28.13 [321]~E(x3211,x3212)+E(f445(x3213,x3211,x3214,x3215,x3216),f445(x3213,x3212,x3214,x3215,x3216))
% 28.25/28.13 [322]~E(x3221,x3222)+E(f445(x3223,x3224,x3221,x3225,x3226),f445(x3223,x3224,x3222,x3225,x3226))
% 28.25/28.13 [323]~E(x3231,x3232)+E(f445(x3233,x3234,x3235,x3231,x3236),f445(x3233,x3234,x3235,x3232,x3236))
% 28.25/28.13 [324]~E(x3241,x3242)+E(f445(x3243,x3244,x3245,x3246,x3241),f445(x3243,x3244,x3245,x3246,x3242))
% 28.25/28.13 [325]~E(x3251,x3252)+E(f697(x3251,x3253),f697(x3252,x3253))
% 28.25/28.13 [326]~E(x3261,x3262)+E(f697(x3263,x3261),f697(x3263,x3262))
% 28.25/28.13 [327]~E(x3271,x3272)+E(f310(x3271,x3273),f310(x3272,x3273))
% 28.25/28.13 [328]~E(x3281,x3282)+E(f310(x3283,x3281),f310(x3283,x3282))
% 28.25/28.13 [329]~E(x3291,x3292)+E(f299(x3291,x3293),f299(x3292,x3293))
% 28.25/28.13 [330]~E(x3301,x3302)+E(f299(x3303,x3301),f299(x3303,x3302))
% 28.25/28.13 [331]~E(x3311,x3312)+E(f311(x3311,x3313),f311(x3312,x3313))
% 28.25/28.13 [332]~E(x3321,x3322)+E(f311(x3323,x3321),f311(x3323,x3322))
% 28.25/28.13 [333]~E(x3331,x3332)+E(f747(x3331,x3333),f747(x3332,x3333))
% 28.25/28.13 [334]~E(x3341,x3342)+E(f747(x3343,x3341),f747(x3343,x3342))
% 28.25/28.13 [335]~E(x3351,x3352)+E(f440(x3351,x3353),f440(x3352,x3353))
% 28.25/28.13 [336]~E(x3361,x3362)+E(f440(x3363,x3361),f440(x3363,x3362))
% 28.25/28.13 [337]~E(x3371,x3372)+E(f292(x3371,x3373,x3374,x3375,x3376),f292(x3372,x3373,x3374,x3375,x3376))
% 28.25/28.13 [338]~E(x3381,x3382)+E(f292(x3383,x3381,x3384,x3385,x3386),f292(x3383,x3382,x3384,x3385,x3386))
% 28.25/28.13 [339]~E(x3391,x3392)+E(f292(x3393,x3394,x3391,x3395,x3396),f292(x3393,x3394,x3392,x3395,x3396))
% 28.25/28.13 [340]~E(x3401,x3402)+E(f292(x3403,x3404,x3405,x3401,x3406),f292(x3403,x3404,x3405,x3402,x3406))
% 28.25/28.13 [341]~E(x3411,x3412)+E(f292(x3413,x3414,x3415,x3416,x3411),f292(x3413,x3414,x3415,x3416,x3412))
% 28.25/28.13 [342]~E(x3421,x3422)+E(f533(x3421,x3423,x3424),f533(x3422,x3423,x3424))
% 28.25/28.13 [343]~E(x3431,x3432)+E(f533(x3433,x3431,x3434),f533(x3433,x3432,x3434))
% 28.25/28.13 [344]~E(x3441,x3442)+E(f533(x3443,x3444,x3441),f533(x3443,x3444,x3442))
% 28.25/28.13 [345]~E(x3451,x3452)+E(f744(x3451,x3453,x3454,x3455),f744(x3452,x3453,x3454,x3455))
% 28.25/28.13 [346]~E(x3461,x3462)+E(f744(x3463,x3461,x3464,x3465),f744(x3463,x3462,x3464,x3465))
% 28.25/28.13 [347]~E(x3471,x3472)+E(f744(x3473,x3474,x3471,x3475),f744(x3473,x3474,x3472,x3475))
% 28.25/28.13 [348]~E(x3481,x3482)+E(f744(x3483,x3484,x3485,x3481),f744(x3483,x3484,x3485,x3482))
% 28.25/28.13 [349]~E(x3491,x3492)+E(f250(x3491,x3493,x3494,x3495,x3496,x3497),f250(x3492,x3493,x3494,x3495,x3496,x3497))
% 28.25/28.13 [350]~E(x3501,x3502)+E(f250(x3503,x3501,x3504,x3505,x3506,x3507),f250(x3503,x3502,x3504,x3505,x3506,x3507))
% 28.25/28.13 [351]~E(x3511,x3512)+E(f250(x3513,x3514,x3511,x3515,x3516,x3517),f250(x3513,x3514,x3512,x3515,x3516,x3517))
% 28.25/28.13 [352]~E(x3521,x3522)+E(f250(x3523,x3524,x3525,x3521,x3526,x3527),f250(x3523,x3524,x3525,x3522,x3526,x3527))
% 28.25/28.13 [353]~E(x3531,x3532)+E(f250(x3533,x3534,x3535,x3536,x3531,x3537),f250(x3533,x3534,x3535,x3536,x3532,x3537))
% 28.25/28.13 [354]~E(x3541,x3542)+E(f250(x3543,x3544,x3545,x3546,x3547,x3541),f250(x3543,x3544,x3545,x3546,x3547,x3542))
% 28.25/28.13 [355]~E(x3551,x3552)+E(f9(x3551,x3553),f9(x3552,x3553))
% 28.25/28.13 [356]~E(x3561,x3562)+E(f9(x3563,x3561),f9(x3563,x3562))
% 28.25/28.13 [357]~E(x3571,x3572)+E(f305(x3571,x3573,x3574,x3575),f305(x3572,x3573,x3574,x3575))
% 28.25/28.13 [358]~E(x3581,x3582)+E(f305(x3583,x3581,x3584,x3585),f305(x3583,x3582,x3584,x3585))
% 28.25/28.13 [359]~E(x3591,x3592)+E(f305(x3593,x3594,x3591,x3595),f305(x3593,x3594,x3592,x3595))
% 28.25/28.13 [360]~E(x3601,x3602)+E(f305(x3603,x3604,x3605,x3601),f305(x3603,x3604,x3605,x3602))
% 28.25/28.13 [361]~E(x3611,x3612)+E(f294(x3611,x3613),f294(x3612,x3613))
% 28.25/28.13 [362]~E(x3621,x3622)+E(f294(x3623,x3621),f294(x3623,x3622))
% 28.25/28.13 [363]~E(x3631,x3632)+E(f699(x3631,x3633,x3634),f699(x3632,x3633,x3634))
% 28.25/28.13 [364]~E(x3641,x3642)+E(f699(x3643,x3641,x3644),f699(x3643,x3642,x3644))
% 28.25/28.13 [365]~E(x3651,x3652)+E(f699(x3653,x3654,x3651),f699(x3653,x3654,x3652))
% 28.25/28.13 [366]~E(x3661,x3662)+E(f729(x3661,x3663),f729(x3662,x3663))
% 28.25/28.13 [367]~E(x3671,x3672)+E(f729(x3673,x3671),f729(x3673,x3672))
% 28.25/28.13 [368]~E(x3681,x3682)+E(f246(x3681,x3683),f246(x3682,x3683))
% 28.25/28.13 [369]~E(x3691,x3692)+E(f246(x3693,x3691),f246(x3693,x3692))
% 28.25/28.13 [370]~E(x3701,x3702)+E(f216(x3701,x3703,x3704,x3705,x3706),f216(x3702,x3703,x3704,x3705,x3706))
% 28.25/28.13 [371]~E(x3711,x3712)+E(f216(x3713,x3711,x3714,x3715,x3716),f216(x3713,x3712,x3714,x3715,x3716))
% 28.25/28.13 [372]~E(x3721,x3722)+E(f216(x3723,x3724,x3721,x3725,x3726),f216(x3723,x3724,x3722,x3725,x3726))
% 28.25/28.13 [373]~E(x3731,x3732)+E(f216(x3733,x3734,x3735,x3731,x3736),f216(x3733,x3734,x3735,x3732,x3736))
% 28.25/28.13 [374]~E(x3741,x3742)+E(f216(x3743,x3744,x3745,x3746,x3741),f216(x3743,x3744,x3745,x3746,x3742))
% 28.25/28.13 [375]~E(x3751,x3752)+E(f57(x3751,x3753),f57(x3752,x3753))
% 28.25/28.13 [376]~E(x3761,x3762)+E(f57(x3763,x3761),f57(x3763,x3762))
% 28.25/28.13 [377]~E(x3771,x3772)+E(f111(x3771),f111(x3772))
% 28.25/28.13 [378]~E(x3781,x3782)+E(f112(x3781,x3783),f112(x3782,x3783))
% 28.25/28.13 [379]~E(x3791,x3792)+E(f112(x3793,x3791),f112(x3793,x3792))
% 28.25/28.13 [380]~E(x3801,x3802)+E(f643(x3801,x3803,x3804,x3805,x3806),f643(x3802,x3803,x3804,x3805,x3806))
% 28.25/28.13 [381]~E(x3811,x3812)+E(f643(x3813,x3811,x3814,x3815,x3816),f643(x3813,x3812,x3814,x3815,x3816))
% 28.25/28.13 [382]~E(x3821,x3822)+E(f643(x3823,x3824,x3821,x3825,x3826),f643(x3823,x3824,x3822,x3825,x3826))
% 28.25/28.13 [383]~E(x3831,x3832)+E(f643(x3833,x3834,x3835,x3831,x3836),f643(x3833,x3834,x3835,x3832,x3836))
% 28.25/28.13 [384]~E(x3841,x3842)+E(f643(x3843,x3844,x3845,x3846,x3841),f643(x3843,x3844,x3845,x3846,x3842))
% 28.25/28.13 [385]~E(x3851,x3852)+E(f911(x3851,x3853),f911(x3852,x3853))
% 28.25/28.13 [386]~E(x3861,x3862)+E(f911(x3863,x3861),f911(x3863,x3862))
% 28.25/28.13 [387]~E(x3871,x3872)+E(f155(x3871,x3873,x3874,x3875),f155(x3872,x3873,x3874,x3875))
% 28.25/28.13 [388]~E(x3881,x3882)+E(f155(x3883,x3881,x3884,x3885),f155(x3883,x3882,x3884,x3885))
% 28.25/28.13 [389]~E(x3891,x3892)+E(f155(x3893,x3894,x3891,x3895),f155(x3893,x3894,x3892,x3895))
% 28.25/28.13 [390]~E(x3901,x3902)+E(f155(x3903,x3904,x3905,x3901),f155(x3903,x3904,x3905,x3902))
% 28.25/28.13 [391]~E(x3911,x3912)+E(f860(x3911,x3913,x3914,x3915,x3916,x3917),f860(x3912,x3913,x3914,x3915,x3916,x3917))
% 28.25/28.13 [392]~E(x3921,x3922)+E(f860(x3923,x3921,x3924,x3925,x3926,x3927),f860(x3923,x3922,x3924,x3925,x3926,x3927))
% 28.25/28.13 [393]~E(x3931,x3932)+E(f860(x3933,x3934,x3931,x3935,x3936,x3937),f860(x3933,x3934,x3932,x3935,x3936,x3937))
% 28.25/28.13 [394]~E(x3941,x3942)+E(f860(x3943,x3944,x3945,x3941,x3946,x3947),f860(x3943,x3944,x3945,x3942,x3946,x3947))
% 28.25/28.13 [395]~E(x3951,x3952)+E(f860(x3953,x3954,x3955,x3956,x3951,x3957),f860(x3953,x3954,x3955,x3956,x3952,x3957))
% 28.25/28.13 [396]~E(x3961,x3962)+E(f860(x3963,x3964,x3965,x3966,x3967,x3961),f860(x3963,x3964,x3965,x3966,x3967,x3962))
% 28.25/28.13 [397]~E(x3971,x3972)+E(f79(x3971,x3973),f79(x3972,x3973))
% 28.25/28.13 [398]~E(x3981,x3982)+E(f79(x3983,x3981),f79(x3983,x3982))
% 28.25/28.13 [399]~E(x3991,x3992)+E(f861(x3991,x3993,x3994,x3995,x3996,x3997),f861(x3992,x3993,x3994,x3995,x3996,x3997))
% 28.25/28.13 [400]~E(x4001,x4002)+E(f861(x4003,x4001,x4004,x4005,x4006,x4007),f861(x4003,x4002,x4004,x4005,x4006,x4007))
% 28.25/28.13 [401]~E(x4011,x4012)+E(f861(x4013,x4014,x4011,x4015,x4016,x4017),f861(x4013,x4014,x4012,x4015,x4016,x4017))
% 28.25/28.13 [402]~E(x4021,x4022)+E(f861(x4023,x4024,x4025,x4021,x4026,x4027),f861(x4023,x4024,x4025,x4022,x4026,x4027))
% 28.25/28.13 [403]~E(x4031,x4032)+E(f861(x4033,x4034,x4035,x4036,x4031,x4037),f861(x4033,x4034,x4035,x4036,x4032,x4037))
% 28.25/28.13 [404]~E(x4041,x4042)+E(f861(x4043,x4044,x4045,x4046,x4047,x4041),f861(x4043,x4044,x4045,x4046,x4047,x4042))
% 28.25/28.13 [405]~E(x4051,x4052)+E(f84(x4051,x4053),f84(x4052,x4053))
% 28.25/28.13 [406]~E(x4061,x4062)+E(f84(x4063,x4061),f84(x4063,x4062))
% 28.25/28.13 [407]~E(x4071,x4072)+E(f691(x4071,x4073,x4074,x4075,x4076),f691(x4072,x4073,x4074,x4075,x4076))
% 28.25/28.13 [408]~E(x4081,x4082)+E(f691(x4083,x4081,x4084,x4085,x4086),f691(x4083,x4082,x4084,x4085,x4086))
% 28.25/28.13 [409]~E(x4091,x4092)+E(f691(x4093,x4094,x4091,x4095,x4096),f691(x4093,x4094,x4092,x4095,x4096))
% 28.25/28.13 [410]~E(x4101,x4102)+E(f691(x4103,x4104,x4105,x4101,x4106),f691(x4103,x4104,x4105,x4102,x4106))
% 28.25/28.13 [411]~E(x4111,x4112)+E(f691(x4113,x4114,x4115,x4116,x4111),f691(x4113,x4114,x4115,x4116,x4112))
% 28.25/28.13 [412]~E(x4121,x4122)+E(f145(x4121,x4123),f145(x4122,x4123))
% 28.25/28.13 [413]~E(x4131,x4132)+E(f145(x4133,x4131),f145(x4133,x4132))
% 28.25/28.13 [414]~E(x4141,x4142)+E(f255(x4141,x4143),f255(x4142,x4143))
% 28.25/28.13 [415]~E(x4151,x4152)+E(f255(x4153,x4151),f255(x4153,x4152))
% 28.25/28.13 [416]~E(x4161,x4162)+E(f569(x4161,x4163,x4164),f569(x4162,x4163,x4164))
% 28.25/28.13 [417]~E(x4171,x4172)+E(f569(x4173,x4171,x4174),f569(x4173,x4172,x4174))
% 28.25/28.13 [418]~E(x4181,x4182)+E(f569(x4183,x4184,x4181),f569(x4183,x4184,x4182))
% 28.25/28.13 [419]~E(x4191,x4192)+E(f296(x4191),f296(x4192))
% 28.25/28.13 [420]~E(x4201,x4202)+E(f219(x4201,x4203),f219(x4202,x4203))
% 28.25/28.13 [421]~E(x4211,x4212)+E(f219(x4213,x4211),f219(x4213,x4212))
% 28.25/28.13 [422]~E(x4221,x4222)+E(f741(x4221,x4223,x4224,x4225,x4226),f741(x4222,x4223,x4224,x4225,x4226))
% 28.25/28.13 [423]~E(x4231,x4232)+E(f741(x4233,x4231,x4234,x4235,x4236),f741(x4233,x4232,x4234,x4235,x4236))
% 28.25/28.13 [424]~E(x4241,x4242)+E(f741(x4243,x4244,x4241,x4245,x4246),f741(x4243,x4244,x4242,x4245,x4246))
% 28.25/28.13 [425]~E(x4251,x4252)+E(f741(x4253,x4254,x4255,x4251,x4256),f741(x4253,x4254,x4255,x4252,x4256))
% 28.25/28.13 [426]~E(x4261,x4262)+E(f741(x4263,x4264,x4265,x4266,x4261),f741(x4263,x4264,x4265,x4266,x4262))
% 28.25/28.13 [427]~E(x4271,x4272)+E(f278(x4271,x4273),f278(x4272,x4273))
% 28.25/28.13 [428]~E(x4281,x4282)+E(f278(x4283,x4281),f278(x4283,x4282))
% 28.25/28.13 [429]~E(x4291,x4292)+E(f803(x4291,x4293,x4294,x4295),f803(x4292,x4293,x4294,x4295))
% 28.25/28.13 [430]~E(x4301,x4302)+E(f803(x4303,x4301,x4304,x4305),f803(x4303,x4302,x4304,x4305))
% 28.25/28.13 [431]~E(x4311,x4312)+E(f803(x4313,x4314,x4311,x4315),f803(x4313,x4314,x4312,x4315))
% 28.25/28.13 [432]~E(x4321,x4322)+E(f803(x4323,x4324,x4325,x4321),f803(x4323,x4324,x4325,x4322))
% 28.25/28.13 [433]~E(x4331,x4332)+E(f208(x4331,x4333),f208(x4332,x4333))
% 28.25/28.13 [434]~E(x4341,x4342)+E(f208(x4343,x4341),f208(x4343,x4342))
% 28.25/28.13 [435]~E(x4351,x4352)+E(f720(x4351,x4353,x4354,x4355,x4356),f720(x4352,x4353,x4354,x4355,x4356))
% 28.25/28.13 [436]~E(x4361,x4362)+E(f720(x4363,x4361,x4364,x4365,x4366),f720(x4363,x4362,x4364,x4365,x4366))
% 28.25/28.13 [437]~E(x4371,x4372)+E(f720(x4373,x4374,x4371,x4375,x4376),f720(x4373,x4374,x4372,x4375,x4376))
% 28.25/28.13 [438]~E(x4381,x4382)+E(f720(x4383,x4384,x4385,x4381,x4386),f720(x4383,x4384,x4385,x4382,x4386))
% 28.25/28.13 [439]~E(x4391,x4392)+E(f720(x4393,x4394,x4395,x4396,x4391),f720(x4393,x4394,x4395,x4396,x4392))
% 28.25/28.13 [440]~E(x4401,x4402)+E(f186(x4401,x4403),f186(x4402,x4403))
% 28.25/28.13 [441]~E(x4411,x4412)+E(f186(x4413,x4411),f186(x4413,x4412))
% 28.25/28.13 [442]~E(x4421,x4422)+E(f547(x4421,x4423,x4424,x4425,x4426,x4427,x4428),f547(x4422,x4423,x4424,x4425,x4426,x4427,x4428))
% 28.25/28.13 [443]~E(x4431,x4432)+E(f547(x4433,x4431,x4434,x4435,x4436,x4437,x4438),f547(x4433,x4432,x4434,x4435,x4436,x4437,x4438))
% 28.25/28.13 [444]~E(x4441,x4442)+E(f547(x4443,x4444,x4441,x4445,x4446,x4447,x4448),f547(x4443,x4444,x4442,x4445,x4446,x4447,x4448))
% 28.25/28.13 [445]~E(x4451,x4452)+E(f547(x4453,x4454,x4455,x4451,x4456,x4457,x4458),f547(x4453,x4454,x4455,x4452,x4456,x4457,x4458))
% 28.25/28.13 [446]~E(x4461,x4462)+E(f547(x4463,x4464,x4465,x4466,x4461,x4467,x4468),f547(x4463,x4464,x4465,x4466,x4462,x4467,x4468))
% 28.25/28.13 [447]~E(x4471,x4472)+E(f547(x4473,x4474,x4475,x4476,x4477,x4471,x4478),f547(x4473,x4474,x4475,x4476,x4477,x4472,x4478))
% 28.25/28.13 [448]~E(x4481,x4482)+E(f547(x4483,x4484,x4485,x4486,x4487,x4488,x4481),f547(x4483,x4484,x4485,x4486,x4487,x4488,x4482))
% 28.25/28.13 [449]~E(x4491,x4492)+E(f739(x4491,x4493,x4494),f739(x4492,x4493,x4494))
% 28.25/28.13 [450]~E(x4501,x4502)+E(f739(x4503,x4501,x4504),f739(x4503,x4502,x4504))
% 28.25/28.13 [451]~E(x4511,x4512)+E(f739(x4513,x4514,x4511),f739(x4513,x4514,x4512))
% 28.25/28.13 [452]~E(x4521,x4522)+E(f130(x4521),f130(x4522))
% 28.25/28.13 [453]~E(x4531,x4532)+E(f141(x4531,x4533,x4534,x4535,x4536),f141(x4532,x4533,x4534,x4535,x4536))
% 28.25/28.13 [454]~E(x4541,x4542)+E(f141(x4543,x4541,x4544,x4545,x4546),f141(x4543,x4542,x4544,x4545,x4546))
% 28.25/28.13 [455]~E(x4551,x4552)+E(f141(x4553,x4554,x4551,x4555,x4556),f141(x4553,x4554,x4552,x4555,x4556))
% 28.25/28.13 [456]~E(x4561,x4562)+E(f141(x4563,x4564,x4565,x4561,x4566),f141(x4563,x4564,x4565,x4562,x4566))
% 28.25/28.13 [457]~E(x4571,x4572)+E(f141(x4573,x4574,x4575,x4576,x4571),f141(x4573,x4574,x4575,x4576,x4572))
% 28.25/28.13 [458]~E(x4581,x4582)+E(f118(x4581,x4583,x4584),f118(x4582,x4583,x4584))
% 28.25/28.13 [459]~E(x4591,x4592)+E(f118(x4593,x4591,x4594),f118(x4593,x4592,x4594))
% 28.25/28.13 [460]~E(x4601,x4602)+E(f118(x4603,x4604,x4601),f118(x4603,x4604,x4602))
% 28.25/28.13 [461]~E(x4611,x4612)+E(f864(x4611,x4613,x4614,x4615,x4616,x4617),f864(x4612,x4613,x4614,x4615,x4616,x4617))
% 28.25/28.13 [462]~E(x4621,x4622)+E(f864(x4623,x4621,x4624,x4625,x4626,x4627),f864(x4623,x4622,x4624,x4625,x4626,x4627))
% 28.25/28.13 [463]~E(x4631,x4632)+E(f864(x4633,x4634,x4631,x4635,x4636,x4637),f864(x4633,x4634,x4632,x4635,x4636,x4637))
% 28.25/28.13 [464]~E(x4641,x4642)+E(f864(x4643,x4644,x4645,x4641,x4646,x4647),f864(x4643,x4644,x4645,x4642,x4646,x4647))
% 28.25/28.13 [465]~E(x4651,x4652)+E(f864(x4653,x4654,x4655,x4656,x4651,x4657),f864(x4653,x4654,x4655,x4656,x4652,x4657))
% 28.25/28.13 [466]~E(x4661,x4662)+E(f864(x4663,x4664,x4665,x4666,x4667,x4661),f864(x4663,x4664,x4665,x4666,x4667,x4662))
% 28.25/28.13 [467]~E(x4671,x4672)+E(f865(x4671,x4673,x4674,x4675,x4676,x4677),f865(x4672,x4673,x4674,x4675,x4676,x4677))
% 28.25/28.13 [468]~E(x4681,x4682)+E(f865(x4683,x4681,x4684,x4685,x4686,x4687),f865(x4683,x4682,x4684,x4685,x4686,x4687))
% 28.25/28.13 [469]~E(x4691,x4692)+E(f865(x4693,x4694,x4691,x4695,x4696,x4697),f865(x4693,x4694,x4692,x4695,x4696,x4697))
% 28.25/28.13 [470]~E(x4701,x4702)+E(f865(x4703,x4704,x4705,x4701,x4706,x4707),f865(x4703,x4704,x4705,x4702,x4706,x4707))
% 28.25/28.13 [471]~E(x4711,x4712)+E(f865(x4713,x4714,x4715,x4716,x4711,x4717),f865(x4713,x4714,x4715,x4716,x4712,x4717))
% 28.25/28.13 [472]~E(x4721,x4722)+E(f865(x4723,x4724,x4725,x4726,x4727,x4721),f865(x4723,x4724,x4725,x4726,x4727,x4722))
% 28.25/28.13 [473]~E(x4731,x4732)+E(f805(x4731,x4733,x4734,x4735),f805(x4732,x4733,x4734,x4735))
% 28.25/28.13 [474]~E(x4741,x4742)+E(f805(x4743,x4741,x4744,x4745),f805(x4743,x4742,x4744,x4745))
% 28.25/28.13 [475]~E(x4751,x4752)+E(f805(x4753,x4754,x4751,x4755),f805(x4753,x4754,x4752,x4755))
% 28.25/28.13 [476]~E(x4761,x4762)+E(f805(x4763,x4764,x4765,x4761),f805(x4763,x4764,x4765,x4762))
% 28.25/28.13 [477]~E(x4771,x4772)+E(f313(x4771,x4773,x4774),f313(x4772,x4773,x4774))
% 28.25/28.13 [478]~E(x4781,x4782)+E(f313(x4783,x4781,x4784),f313(x4783,x4782,x4784))
% 28.25/28.13 [479]~E(x4791,x4792)+E(f313(x4793,x4794,x4791),f313(x4793,x4794,x4792))
% 28.25/28.13 [480]~E(x4801,x4802)+E(f110(x4801,x4803,x4804),f110(x4802,x4803,x4804))
% 28.25/28.13 [481]~E(x4811,x4812)+E(f110(x4813,x4811,x4814),f110(x4813,x4812,x4814))
% 28.25/28.13 [482]~E(x4821,x4822)+E(f110(x4823,x4824,x4821),f110(x4823,x4824,x4822))
% 28.25/28.13 [483]~E(x4831,x4832)+E(f905(x4831,x4833,x4834,x4835),f905(x4832,x4833,x4834,x4835))
% 28.25/28.13 [484]~E(x4841,x4842)+E(f905(x4843,x4841,x4844,x4845),f905(x4843,x4842,x4844,x4845))
% 28.25/28.13 [485]~E(x4851,x4852)+E(f905(x4853,x4854,x4851,x4855),f905(x4853,x4854,x4852,x4855))
% 28.25/28.13 [486]~E(x4861,x4862)+E(f905(x4863,x4864,x4865,x4861),f905(x4863,x4864,x4865,x4862))
% 28.25/28.13 [487]~E(x4871,x4872)+E(f358(x4871,x4873,x4874),f358(x4872,x4873,x4874))
% 28.25/28.13 [488]~E(x4881,x4882)+E(f358(x4883,x4881,x4884),f358(x4883,x4882,x4884))
% 28.25/28.13 [489]~E(x4891,x4892)+E(f358(x4893,x4894,x4891),f358(x4893,x4894,x4892))
% 28.25/28.13 [490]~E(x4901,x4902)+E(f531(x4901,x4903,x4904),f531(x4902,x4903,x4904))
% 28.25/28.13 [491]~E(x4911,x4912)+E(f531(x4913,x4911,x4914),f531(x4913,x4912,x4914))
% 28.25/28.13 [492]~E(x4921,x4922)+E(f531(x4923,x4924,x4921),f531(x4923,x4924,x4922))
% 28.25/28.13 [493]~E(x4931,x4932)+E(f503(x4931,x4933,x4934),f503(x4932,x4933,x4934))
% 28.25/28.13 [494]~E(x4941,x4942)+E(f503(x4943,x4941,x4944),f503(x4943,x4942,x4944))
% 28.25/28.13 [495]~E(x4951,x4952)+E(f503(x4953,x4954,x4951),f503(x4953,x4954,x4952))
% 28.25/28.13 [496]~E(x4961,x4962)+E(f150(x4961,x4963),f150(x4962,x4963))
% 28.25/28.13 [497]~E(x4971,x4972)+E(f150(x4973,x4971),f150(x4973,x4972))
% 28.25/28.13 [498]~E(x4981,x4982)+E(f171(x4981,x4983),f171(x4982,x4983))
% 28.25/28.13 [499]~E(x4991,x4992)+E(f171(x4993,x4991),f171(x4993,x4992))
% 28.25/28.13 [500]~E(x5001,x5002)+E(f16(x5001,x5003),f16(x5002,x5003))
% 28.25/28.13 [501]~E(x5011,x5012)+E(f16(x5013,x5011),f16(x5013,x5012))
% 28.25/28.13 [502]~E(x5021,x5022)+E(f42(x5021,x5023),f42(x5022,x5023))
% 28.25/28.13 [503]~E(x5031,x5032)+E(f42(x5033,x5031),f42(x5033,x5032))
% 28.25/28.13 [504]~E(x5041,x5042)+E(f15(x5041,x5043),f15(x5042,x5043))
% 28.25/28.13 [505]~E(x5051,x5052)+E(f15(x5053,x5051),f15(x5053,x5052))
% 28.25/28.13 [506]~E(x5061,x5062)+E(f306(x5061),f306(x5062))
% 28.25/28.13 [507]~E(x5071,x5072)+E(f748(x5071,x5073),f748(x5072,x5073))
% 28.25/28.13 [508]~E(x5081,x5082)+E(f748(x5083,x5081),f748(x5083,x5082))
% 28.25/28.13 [509]~E(x5091,x5092)+E(f510(x5091,x5093,x5094,x5095,x5096),f510(x5092,x5093,x5094,x5095,x5096))
% 28.25/28.13 [510]~E(x5101,x5102)+E(f510(x5103,x5101,x5104,x5105,x5106),f510(x5103,x5102,x5104,x5105,x5106))
% 28.25/28.13 [511]~E(x5111,x5112)+E(f510(x5113,x5114,x5111,x5115,x5116),f510(x5113,x5114,x5112,x5115,x5116))
% 28.25/28.13 [512]~E(x5121,x5122)+E(f510(x5123,x5124,x5125,x5121,x5126),f510(x5123,x5124,x5125,x5122,x5126))
% 28.25/28.13 [513]~E(x5131,x5132)+E(f510(x5133,x5134,x5135,x5136,x5131),f510(x5133,x5134,x5135,x5136,x5132))
% 28.25/28.13 [514]~E(x5141,x5142)+E(f470(x5141,x5143,x5144),f470(x5142,x5143,x5144))
% 28.25/28.13 [515]~E(x5151,x5152)+E(f470(x5153,x5151,x5154),f470(x5153,x5152,x5154))
% 28.25/28.13 [516]~E(x5161,x5162)+E(f470(x5163,x5164,x5161),f470(x5163,x5164,x5162))
% 28.25/28.13 [517]~E(x5171,x5172)+E(f152(x5171,x5173),f152(x5172,x5173))
% 28.25/28.13 [518]~E(x5181,x5182)+E(f152(x5183,x5181),f152(x5183,x5182))
% 28.25/28.13 [519]~E(x5191,x5192)+E(f367(x5191,x5193),f367(x5192,x5193))
% 28.25/28.13 [520]~E(x5201,x5202)+E(f367(x5203,x5201),f367(x5203,x5202))
% 28.25/28.13 [521]~E(x5211,x5212)+E(f878(x5211,x5213,x5214),f878(x5212,x5213,x5214))
% 28.25/28.13 [522]~E(x5221,x5222)+E(f878(x5223,x5221,x5224),f878(x5223,x5222,x5224))
% 28.25/28.13 [523]~E(x5231,x5232)+E(f878(x5233,x5234,x5231),f878(x5233,x5234,x5232))
% 28.25/28.13 [524]~E(x5241,x5242)+E(f667(x5241,x5243,x5244,x5245,x5246,x5247),f667(x5242,x5243,x5244,x5245,x5246,x5247))
% 28.25/28.13 [525]~E(x5251,x5252)+E(f667(x5253,x5251,x5254,x5255,x5256,x5257),f667(x5253,x5252,x5254,x5255,x5256,x5257))
% 28.25/28.13 [526]~E(x5261,x5262)+E(f667(x5263,x5264,x5261,x5265,x5266,x5267),f667(x5263,x5264,x5262,x5265,x5266,x5267))
% 28.25/28.13 [527]~E(x5271,x5272)+E(f667(x5273,x5274,x5275,x5271,x5276,x5277),f667(x5273,x5274,x5275,x5272,x5276,x5277))
% 28.25/28.13 [528]~E(x5281,x5282)+E(f667(x5283,x5284,x5285,x5286,x5281,x5287),f667(x5283,x5284,x5285,x5286,x5282,x5287))
% 28.25/28.13 [529]~E(x5291,x5292)+E(f667(x5293,x5294,x5295,x5296,x5297,x5291),f667(x5293,x5294,x5295,x5296,x5297,x5292))
% 28.25/28.13 [530]~E(x5301,x5302)+E(f668(x5301,x5303,x5304,x5305,x5306,x5307),f668(x5302,x5303,x5304,x5305,x5306,x5307))
% 28.25/28.13 [531]~E(x5311,x5312)+E(f668(x5313,x5311,x5314,x5315,x5316,x5317),f668(x5313,x5312,x5314,x5315,x5316,x5317))
% 28.25/28.13 [532]~E(x5321,x5322)+E(f668(x5323,x5324,x5321,x5325,x5326,x5327),f668(x5323,x5324,x5322,x5325,x5326,x5327))
% 28.25/28.13 [533]~E(x5331,x5332)+E(f668(x5333,x5334,x5335,x5331,x5336,x5337),f668(x5333,x5334,x5335,x5332,x5336,x5337))
% 28.25/28.13 [534]~E(x5341,x5342)+E(f668(x5343,x5344,x5345,x5346,x5341,x5347),f668(x5343,x5344,x5345,x5346,x5342,x5347))
% 28.25/28.13 [535]~E(x5351,x5352)+E(f668(x5353,x5354,x5355,x5356,x5357,x5351),f668(x5353,x5354,x5355,x5356,x5357,x5352))
% 28.25/28.13 [536]~E(x5361,x5362)+E(f212(x5361,x5363,x5364,x5365),f212(x5362,x5363,x5364,x5365))
% 28.25/28.13 [537]~E(x5371,x5372)+E(f212(x5373,x5371,x5374,x5375),f212(x5373,x5372,x5374,x5375))
% 28.25/28.13 [538]~E(x5381,x5382)+E(f212(x5383,x5384,x5381,x5385),f212(x5383,x5384,x5382,x5385))
% 28.25/28.13 [539]~E(x5391,x5392)+E(f212(x5393,x5394,x5395,x5391),f212(x5393,x5394,x5395,x5392))
% 28.25/28.13 [540]~E(x5401,x5402)+E(f156(x5401),f156(x5402))
% 28.25/28.13 [541]~E(x5411,x5412)+E(f293(x5411),f293(x5412))
% 28.25/28.13 [542]~E(x5421,x5422)+E(f41(x5421,x5423),f41(x5422,x5423))
% 28.25/28.13 [543]~E(x5431,x5432)+E(f41(x5433,x5431),f41(x5433,x5432))
% 28.25/28.13 [544]~E(x5441,x5442)+E(f868(x5441,x5443,x5444),f868(x5442,x5443,x5444))
% 28.25/28.13 [545]~E(x5451,x5452)+E(f868(x5453,x5451,x5454),f868(x5453,x5452,x5454))
% 28.25/28.13 [546]~E(x5461,x5462)+E(f868(x5463,x5464,x5461),f868(x5463,x5464,x5462))
% 28.25/28.13 [547]~E(x5471,x5472)+E(f275(x5471),f275(x5472))
% 28.25/28.13 [548]~E(x5481,x5482)+E(f133(x5481),f133(x5482))
% 28.25/28.13 [549]~E(x5491,x5492)+E(f101(x5491),f101(x5492))
% 28.25/28.13 [550]~E(x5501,x5502)+E(f796(x5501,x5503,x5504),f796(x5502,x5503,x5504))
% 28.25/28.13 [551]~E(x5511,x5512)+E(f796(x5513,x5511,x5514),f796(x5513,x5512,x5514))
% 28.25/28.13 [552]~E(x5521,x5522)+E(f796(x5523,x5524,x5521),f796(x5523,x5524,x5522))
% 28.25/28.13 [553]~E(x5531,x5532)+E(f504(x5531,x5533,x5534),f504(x5532,x5533,x5534))
% 28.25/28.13 [554]~E(x5541,x5542)+E(f504(x5543,x5541,x5544),f504(x5543,x5542,x5544))
% 28.25/28.13 [555]~E(x5551,x5552)+E(f504(x5553,x5554,x5551),f504(x5553,x5554,x5552))
% 28.25/28.13 [556]~E(x5561,x5562)+E(f603(x5561,x5563,x5564),f603(x5562,x5563,x5564))
% 28.25/28.13 [557]~E(x5571,x5572)+E(f603(x5573,x5571,x5574),f603(x5573,x5572,x5574))
% 28.25/28.13 [558]~E(x5581,x5582)+E(f603(x5583,x5584,x5581),f603(x5583,x5584,x5582))
% 28.25/28.13 [559]~E(x5591,x5592)+E(f87(x5591,x5593),f87(x5592,x5593))
% 28.25/28.13 [560]~E(x5601,x5602)+E(f87(x5603,x5601),f87(x5603,x5602))
% 28.25/28.13 [561]~E(x5611,x5612)+E(f418(x5611,x5613,x5614),f418(x5612,x5613,x5614))
% 28.25/28.13 [562]~E(x5621,x5622)+E(f418(x5623,x5621,x5624),f418(x5623,x5622,x5624))
% 28.25/28.13 [563]~E(x5631,x5632)+E(f418(x5633,x5634,x5631),f418(x5633,x5634,x5632))
% 28.25/28.13 [564]~E(x5641,x5642)+E(f816(x5641,x5643,x5644),f816(x5642,x5643,x5644))
% 28.25/28.13 [565]~E(x5651,x5652)+E(f816(x5653,x5651,x5654),f816(x5653,x5652,x5654))
% 28.25/28.13 [566]~E(x5661,x5662)+E(f816(x5663,x5664,x5661),f816(x5663,x5664,x5662))
% 28.25/28.13 [567]~E(x5671,x5672)+E(f834(x5671,x5673),f834(x5672,x5673))
% 28.25/28.13 [568]~E(x5681,x5682)+E(f834(x5683,x5681),f834(x5683,x5682))
% 28.25/28.13 [569]~E(x5691,x5692)+E(f472(x5691,x5693,x5694),f472(x5692,x5693,x5694))
% 28.25/28.13 [570]~E(x5701,x5702)+E(f472(x5703,x5701,x5704),f472(x5703,x5702,x5704))
% 28.25/28.13 [571]~E(x5711,x5712)+E(f472(x5713,x5714,x5711),f472(x5713,x5714,x5712))
% 28.25/28.13 [572]~E(x5721,x5722)+E(f674(x5721,x5723,x5724,x5725,x5726),f674(x5722,x5723,x5724,x5725,x5726))
% 28.25/28.13 [573]~E(x5731,x5732)+E(f674(x5733,x5731,x5734,x5735,x5736),f674(x5733,x5732,x5734,x5735,x5736))
% 28.25/28.13 [574]~E(x5741,x5742)+E(f674(x5743,x5744,x5741,x5745,x5746),f674(x5743,x5744,x5742,x5745,x5746))
% 28.25/28.13 [575]~E(x5751,x5752)+E(f674(x5753,x5754,x5755,x5751,x5756),f674(x5753,x5754,x5755,x5752,x5756))
% 28.25/28.13 [576]~E(x5761,x5762)+E(f674(x5763,x5764,x5765,x5766,x5761),f674(x5763,x5764,x5765,x5766,x5762))
% 28.25/28.13 [577]~E(x5771,x5772)+E(f666(x5771,x5773,x5774,x5775,x5776,x5777),f666(x5772,x5773,x5774,x5775,x5776,x5777))
% 28.25/28.13 [578]~E(x5781,x5782)+E(f666(x5783,x5781,x5784,x5785,x5786,x5787),f666(x5783,x5782,x5784,x5785,x5786,x5787))
% 28.25/28.13 [579]~E(x5791,x5792)+E(f666(x5793,x5794,x5791,x5795,x5796,x5797),f666(x5793,x5794,x5792,x5795,x5796,x5797))
% 28.25/28.13 [580]~E(x5801,x5802)+E(f666(x5803,x5804,x5805,x5801,x5806,x5807),f666(x5803,x5804,x5805,x5802,x5806,x5807))
% 28.25/28.13 [581]~E(x5811,x5812)+E(f666(x5813,x5814,x5815,x5816,x5811,x5817),f666(x5813,x5814,x5815,x5816,x5812,x5817))
% 28.25/28.13 [582]~E(x5821,x5822)+E(f666(x5823,x5824,x5825,x5826,x5827,x5821),f666(x5823,x5824,x5825,x5826,x5827,x5822))
% 28.25/28.13 [583]~E(x5831,x5832)+E(f644(x5831,x5833,x5834,x5835,x5836),f644(x5832,x5833,x5834,x5835,x5836))
% 28.25/28.13 [584]~E(x5841,x5842)+E(f644(x5843,x5841,x5844,x5845,x5846),f644(x5843,x5842,x5844,x5845,x5846))
% 28.25/28.13 [585]~E(x5851,x5852)+E(f644(x5853,x5854,x5851,x5855,x5856),f644(x5853,x5854,x5852,x5855,x5856))
% 28.25/28.13 [586]~E(x5861,x5862)+E(f644(x5863,x5864,x5865,x5861,x5866),f644(x5863,x5864,x5865,x5862,x5866))
% 28.25/28.13 [587]~E(x5871,x5872)+E(f644(x5873,x5874,x5875,x5876,x5871),f644(x5873,x5874,x5875,x5876,x5872))
% 28.25/28.13 [588]~E(x5881,x5882)+E(f117(x5881,x5883),f117(x5882,x5883))
% 28.25/28.13 [589]~E(x5891,x5892)+E(f117(x5893,x5891),f117(x5893,x5892))
% 28.25/28.13 [590]~E(x5901,x5902)+E(f162(x5901,x5903,x5904),f162(x5902,x5903,x5904))
% 28.25/28.13 [591]~E(x5911,x5912)+E(f162(x5913,x5911,x5914),f162(x5913,x5912,x5914))
% 28.25/28.13 [592]~E(x5921,x5922)+E(f162(x5923,x5924,x5921),f162(x5923,x5924,x5922))
% 28.25/28.13 [593]~E(x5931,x5932)+E(f630(x5931,x5933,x5934),f630(x5932,x5933,x5934))
% 28.25/28.13 [594]~E(x5941,x5942)+E(f630(x5943,x5941,x5944),f630(x5943,x5942,x5944))
% 28.25/28.13 [595]~E(x5951,x5952)+E(f630(x5953,x5954,x5951),f630(x5953,x5954,x5952))
% 28.25/28.13 [596]~E(x5961,x5962)+E(f240(x5961,x5963),f240(x5962,x5963))
% 28.25/28.13 [597]~E(x5971,x5972)+E(f240(x5973,x5971),f240(x5973,x5972))
% 28.25/28.13 [598]~E(x5981,x5982)+E(f877(x5981,x5983,x5984,x5985),f877(x5982,x5983,x5984,x5985))
% 28.25/28.13 [599]~E(x5991,x5992)+E(f877(x5993,x5991,x5994,x5995),f877(x5993,x5992,x5994,x5995))
% 28.25/28.13 [600]~E(x6001,x6002)+E(f877(x6003,x6004,x6001,x6005),f877(x6003,x6004,x6002,x6005))
% 28.25/28.13 [601]~E(x6011,x6012)+E(f877(x6013,x6014,x6015,x6011),f877(x6013,x6014,x6015,x6012))
% 28.25/28.13 [602]~E(x6021,x6022)+E(f442(x6021,x6023),f442(x6022,x6023))
% 28.25/28.13 [603]~E(x6031,x6032)+E(f442(x6033,x6031),f442(x6033,x6032))
% 28.25/28.13 [604]~E(x6041,x6042)+E(f85(x6041,x6043,x6044,x6045),f85(x6042,x6043,x6044,x6045))
% 28.25/28.13 [605]~E(x6051,x6052)+E(f85(x6053,x6051,x6054,x6055),f85(x6053,x6052,x6054,x6055))
% 28.25/28.13 [606]~E(x6061,x6062)+E(f85(x6063,x6064,x6061,x6065),f85(x6063,x6064,x6062,x6065))
% 28.25/28.13 [607]~E(x6071,x6072)+E(f85(x6073,x6074,x6075,x6071),f85(x6073,x6074,x6075,x6072))
% 28.25/28.13 [608]~E(x6081,x6082)+E(f886(x6081,x6083,x6084,x6085,x6086),f886(x6082,x6083,x6084,x6085,x6086))
% 28.25/28.13 [609]~E(x6091,x6092)+E(f886(x6093,x6091,x6094,x6095,x6096),f886(x6093,x6092,x6094,x6095,x6096))
% 28.25/28.13 [610]~E(x6101,x6102)+E(f886(x6103,x6104,x6101,x6105,x6106),f886(x6103,x6104,x6102,x6105,x6106))
% 28.25/28.13 [611]~E(x6111,x6112)+E(f886(x6113,x6114,x6115,x6111,x6116),f886(x6113,x6114,x6115,x6112,x6116))
% 28.25/28.13 [612]~E(x6121,x6122)+E(f886(x6123,x6124,x6125,x6126,x6121),f886(x6123,x6124,x6125,x6126,x6122))
% 28.25/28.13 [613]~E(x6131,x6132)+E(f875(x6131,x6133,x6134),f875(x6132,x6133,x6134))
% 28.25/28.13 [614]~E(x6141,x6142)+E(f875(x6143,x6141,x6144),f875(x6143,x6142,x6144))
% 28.25/28.13 [615]~E(x6151,x6152)+E(f875(x6153,x6154,x6151),f875(x6153,x6154,x6152))
% 28.25/28.13 [616]~E(x6161,x6162)+E(f204(x6161),f204(x6162))
% 28.25/28.13 [617]~E(x6171,x6172)+E(f230(x6171,x6173),f230(x6172,x6173))
% 28.25/28.13 [618]~E(x6181,x6182)+E(f230(x6183,x6181),f230(x6183,x6182))
% 28.25/28.13 [619]~E(x6191,x6192)+E(f597(x6191,x6193),f597(x6192,x6193))
% 28.25/28.13 [620]~E(x6201,x6202)+E(f597(x6203,x6201),f597(x6203,x6202))
% 28.25/28.13 [621]~E(x6211,x6212)+E(f829(x6211,x6213,x6214,x6215,x6216,x6217),f829(x6212,x6213,x6214,x6215,x6216,x6217))
% 28.25/28.13 [622]~E(x6221,x6222)+E(f829(x6223,x6221,x6224,x6225,x6226,x6227),f829(x6223,x6222,x6224,x6225,x6226,x6227))
% 28.25/28.13 [623]~E(x6231,x6232)+E(f829(x6233,x6234,x6231,x6235,x6236,x6237),f829(x6233,x6234,x6232,x6235,x6236,x6237))
% 28.25/28.13 [624]~E(x6241,x6242)+E(f829(x6243,x6244,x6245,x6241,x6246,x6247),f829(x6243,x6244,x6245,x6242,x6246,x6247))
% 28.25/28.13 [625]~E(x6251,x6252)+E(f829(x6253,x6254,x6255,x6256,x6251,x6257),f829(x6253,x6254,x6255,x6256,x6252,x6257))
% 28.25/28.13 [626]~E(x6261,x6262)+E(f829(x6263,x6264,x6265,x6266,x6267,x6261),f829(x6263,x6264,x6265,x6266,x6267,x6262))
% 28.25/28.13 [627]~E(x6271,x6272)+E(f88(x6271,x6273),f88(x6272,x6273))
% 28.25/28.13 [628]~E(x6281,x6282)+E(f88(x6283,x6281),f88(x6283,x6282))
% 28.25/28.13 [629]~E(x6291,x6292)+E(f43(x6291,x6293),f43(x6292,x6293))
% 28.25/28.13 [630]~E(x6301,x6302)+E(f43(x6303,x6301),f43(x6303,x6302))
% 28.25/28.13 [631]~E(x6311,x6312)+E(f151(x6311,x6313),f151(x6312,x6313))
% 28.25/28.13 [632]~E(x6321,x6322)+E(f151(x6323,x6321),f151(x6323,x6322))
% 28.25/28.13 [633]~E(x6331,x6332)+E(f623(x6331,x6333),f623(x6332,x6333))
% 28.25/28.13 [634]~E(x6341,x6342)+E(f623(x6343,x6341),f623(x6343,x6342))
% 28.25/28.13 [635]~E(x6351,x6352)+E(f188(x6351,x6353,x6354,x6355),f188(x6352,x6353,x6354,x6355))
% 28.25/28.13 [636]~E(x6361,x6362)+E(f188(x6363,x6361,x6364,x6365),f188(x6363,x6362,x6364,x6365))
% 28.25/28.13 [637]~E(x6371,x6372)+E(f188(x6373,x6374,x6371,x6375),f188(x6373,x6374,x6372,x6375))
% 28.25/28.13 [638]~E(x6381,x6382)+E(f188(x6383,x6384,x6385,x6381),f188(x6383,x6384,x6385,x6382))
% 28.25/28.13 [639]~E(x6391,x6392)+E(f241(x6391,x6393,x6394),f241(x6392,x6393,x6394))
% 28.25/28.13 [640]~E(x6401,x6402)+E(f241(x6403,x6401,x6404),f241(x6403,x6402,x6404))
% 28.25/28.13 [641]~E(x6411,x6412)+E(f241(x6413,x6414,x6411),f241(x6413,x6414,x6412))
% 28.25/28.13 [642]~E(x6421,x6422)+E(f298(x6421,x6423,x6424),f298(x6422,x6423,x6424))
% 28.25/28.13 [643]~E(x6431,x6432)+E(f298(x6433,x6431,x6434),f298(x6433,x6432,x6434))
% 28.25/28.13 [644]~E(x6441,x6442)+E(f298(x6443,x6444,x6441),f298(x6443,x6444,x6442))
% 28.25/28.13 [645]~E(x6451,x6452)+E(f686(x6451,x6453,x6454,x6455),f686(x6452,x6453,x6454,x6455))
% 28.25/28.13 [646]~E(x6461,x6462)+E(f686(x6463,x6461,x6464,x6465),f686(x6463,x6462,x6464,x6465))
% 28.25/28.13 [647]~E(x6471,x6472)+E(f686(x6473,x6474,x6471,x6475),f686(x6473,x6474,x6472,x6475))
% 28.25/28.13 [648]~E(x6481,x6482)+E(f686(x6483,x6484,x6485,x6481),f686(x6483,x6484,x6485,x6482))
% 28.25/28.13 [649]~E(x6491,x6492)+E(f807(x6491,x6493,x6494,x6495),f807(x6492,x6493,x6494,x6495))
% 28.25/28.13 [650]~E(x6501,x6502)+E(f807(x6503,x6501,x6504,x6505),f807(x6503,x6502,x6504,x6505))
% 28.25/28.13 [651]~E(x6511,x6512)+E(f807(x6513,x6514,x6511,x6515),f807(x6513,x6514,x6512,x6515))
% 28.25/28.13 [652]~E(x6521,x6522)+E(f807(x6523,x6524,x6525,x6521),f807(x6523,x6524,x6525,x6522))
% 28.25/28.13 [653]~E(x6531,x6532)+E(f447(x6531,x6533,x6534,x6535,x6536),f447(x6532,x6533,x6534,x6535,x6536))
% 28.25/28.13 [654]~E(x6541,x6542)+E(f447(x6543,x6541,x6544,x6545,x6546),f447(x6543,x6542,x6544,x6545,x6546))
% 28.25/28.13 [655]~E(x6551,x6552)+E(f447(x6553,x6554,x6551,x6555,x6556),f447(x6553,x6554,x6552,x6555,x6556))
% 28.25/28.13 [656]~E(x6561,x6562)+E(f447(x6563,x6564,x6565,x6561,x6566),f447(x6563,x6564,x6565,x6562,x6566))
% 28.25/28.13 [657]~E(x6571,x6572)+E(f447(x6573,x6574,x6575,x6576,x6571),f447(x6573,x6574,x6575,x6576,x6572))
% 28.25/28.13 [658]~E(x6581,x6582)+E(f645(x6581,x6583,x6584,x6585,x6586),f645(x6582,x6583,x6584,x6585,x6586))
% 28.25/28.13 [659]~E(x6591,x6592)+E(f645(x6593,x6591,x6594,x6595,x6596),f645(x6593,x6592,x6594,x6595,x6596))
% 28.25/28.13 [660]~E(x6601,x6602)+E(f645(x6603,x6604,x6601,x6605,x6606),f645(x6603,x6604,x6602,x6605,x6606))
% 28.25/28.13 [661]~E(x6611,x6612)+E(f645(x6613,x6614,x6615,x6611,x6616),f645(x6613,x6614,x6615,x6612,x6616))
% 28.25/28.13 [662]~E(x6621,x6622)+E(f645(x6623,x6624,x6625,x6626,x6621),f645(x6623,x6624,x6625,x6626,x6622))
% 28.25/28.13 [663]~E(x6631,x6632)+E(f884(x6631,x6633,x6634),f884(x6632,x6633,x6634))
% 28.25/28.13 [664]~E(x6641,x6642)+E(f884(x6643,x6641,x6644),f884(x6643,x6642,x6644))
% 28.25/28.13 [665]~E(x6651,x6652)+E(f884(x6653,x6654,x6651),f884(x6653,x6654,x6652))
% 28.25/28.13 [666]~E(x6661,x6662)+E(f177(x6661,x6663,x6664,x6665),f177(x6662,x6663,x6664,x6665))
% 28.25/28.13 [667]~E(x6671,x6672)+E(f177(x6673,x6671,x6674,x6675),f177(x6673,x6672,x6674,x6675))
% 28.25/28.13 [668]~E(x6681,x6682)+E(f177(x6683,x6684,x6681,x6685),f177(x6683,x6684,x6682,x6685))
% 28.25/28.13 [669]~E(x6691,x6692)+E(f177(x6693,x6694,x6695,x6691),f177(x6693,x6694,x6695,x6692))
% 28.25/28.13 [670]~E(x6701,x6702)+E(f814(x6701,x6703,x6704),f814(x6702,x6703,x6704))
% 28.25/28.13 [671]~E(x6711,x6712)+E(f814(x6713,x6711,x6714),f814(x6713,x6712,x6714))
% 28.25/28.13 [672]~E(x6721,x6722)+E(f814(x6723,x6724,x6721),f814(x6723,x6724,x6722))
% 28.25/28.13 [673]~E(x6731,x6732)+E(f917(x6731,x6733,x6734,x6735),f917(x6732,x6733,x6734,x6735))
% 28.25/28.13 [674]~E(x6741,x6742)+E(f917(x6743,x6741,x6744,x6745),f917(x6743,x6742,x6744,x6745))
% 28.25/28.13 [675]~E(x6751,x6752)+E(f917(x6753,x6754,x6751,x6755),f917(x6753,x6754,x6752,x6755))
% 28.25/28.13 [676]~E(x6761,x6762)+E(f917(x6763,x6764,x6765,x6761),f917(x6763,x6764,x6765,x6762))
% 28.25/28.13 [677]~E(x6771,x6772)+E(f766(x6771,x6773,x6774,x6775,x6776),f766(x6772,x6773,x6774,x6775,x6776))
% 28.25/28.13 [678]~E(x6781,x6782)+E(f766(x6783,x6781,x6784,x6785,x6786),f766(x6783,x6782,x6784,x6785,x6786))
% 28.25/28.13 [679]~E(x6791,x6792)+E(f766(x6793,x6794,x6791,x6795,x6796),f766(x6793,x6794,x6792,x6795,x6796))
% 28.25/28.13 [680]~E(x6801,x6802)+E(f766(x6803,x6804,x6805,x6801,x6806),f766(x6803,x6804,x6805,x6802,x6806))
% 28.25/28.13 [681]~E(x6811,x6812)+E(f766(x6813,x6814,x6815,x6816,x6811),f766(x6813,x6814,x6815,x6816,x6812))
% 28.25/28.13 [682]~E(x6821,x6822)+E(f439(x6821),f439(x6822))
% 28.25/28.13 [683]~E(x6831,x6832)+E(f371(x6831),f371(x6832))
% 28.25/28.13 [684]~E(x6841,x6842)+E(f149(x6841,x6843),f149(x6842,x6843))
% 28.25/28.13 [685]~E(x6851,x6852)+E(f149(x6853,x6851),f149(x6853,x6852))
% 28.25/28.13 [686]~E(x6861,x6862)+E(f873(x6861,x6863,x6864),f873(x6862,x6863,x6864))
% 28.25/28.13 [687]~E(x6871,x6872)+E(f873(x6873,x6871,x6874),f873(x6873,x6872,x6874))
% 28.25/28.13 [688]~E(x6881,x6882)+E(f873(x6883,x6884,x6881),f873(x6883,x6884,x6882))
% 28.25/28.13 [689]~E(x6891,x6892)+E(f391(x6891,x6893),f391(x6892,x6893))
% 28.25/28.13 [690]~E(x6901,x6902)+E(f391(x6903,x6901),f391(x6903,x6902))
% 28.25/28.13 [691]~E(x6911,x6912)+E(f172(x6911),f172(x6912))
% 28.25/28.13 [692]~E(x6921,x6922)+E(f854(x6921,x6923,x6924,x6925,x6926,x6927,x6928,x6929),f854(x6922,x6923,x6924,x6925,x6926,x6927,x6928,x6929))
% 28.25/28.13 [693]~E(x6931,x6932)+E(f854(x6933,x6931,x6934,x6935,x6936,x6937,x6938,x6939),f854(x6933,x6932,x6934,x6935,x6936,x6937,x6938,x6939))
% 28.25/28.13 [694]~E(x6941,x6942)+E(f854(x6943,x6944,x6941,x6945,x6946,x6947,x6948,x6949),f854(x6943,x6944,x6942,x6945,x6946,x6947,x6948,x6949))
% 28.25/28.13 [695]~E(x6951,x6952)+E(f854(x6953,x6954,x6955,x6951,x6956,x6957,x6958,x6959),f854(x6953,x6954,x6955,x6952,x6956,x6957,x6958,x6959))
% 28.25/28.13 [696]~E(x6961,x6962)+E(f854(x6963,x6964,x6965,x6966,x6961,x6967,x6968,x6969),f854(x6963,x6964,x6965,x6966,x6962,x6967,x6968,x6969))
% 28.25/28.13 [697]~E(x6971,x6972)+E(f854(x6973,x6974,x6975,x6976,x6977,x6971,x6978,x6979),f854(x6973,x6974,x6975,x6976,x6977,x6972,x6978,x6979))
% 28.25/28.13 [698]~E(x6981,x6982)+E(f854(x6983,x6984,x6985,x6986,x6987,x6988,x6981,x6989),f854(x6983,x6984,x6985,x6986,x6987,x6988,x6982,x6989))
% 28.25/28.13 [699]~E(x6991,x6992)+E(f854(x6993,x6994,x6995,x6996,x6997,x6998,x6999,x6991),f854(x6993,x6994,x6995,x6996,x6997,x6998,x6999,x6992))
% 28.25/28.13 [700]~E(x7001,x7002)+E(f652(x7001,x7003,x7004,x7005),f652(x7002,x7003,x7004,x7005))
% 28.25/28.13 [701]~E(x7011,x7012)+E(f652(x7013,x7011,x7014,x7015),f652(x7013,x7012,x7014,x7015))
% 28.25/28.13 [702]~E(x7021,x7022)+E(f652(x7023,x7024,x7021,x7025),f652(x7023,x7024,x7022,x7025))
% 28.25/28.13 [703]~E(x7031,x7032)+E(f652(x7033,x7034,x7035,x7031),f652(x7033,x7034,x7035,x7032))
% 28.25/28.13 [704]~E(x7041,x7042)+E(f698(x7041,x7043,x7044),f698(x7042,x7043,x7044))
% 28.25/28.13 [705]~E(x7051,x7052)+E(f698(x7053,x7051,x7054),f698(x7053,x7052,x7054))
% 28.25/28.13 [706]~E(x7061,x7062)+E(f698(x7063,x7064,x7061),f698(x7063,x7064,x7062))
% 28.25/28.13 [707]~E(x7071,x7072)+E(f782(x7071,x7073,x7074),f782(x7072,x7073,x7074))
% 28.25/28.13 [708]~E(x7081,x7082)+E(f782(x7083,x7081,x7084),f782(x7083,x7082,x7084))
% 28.25/28.13 [709]~E(x7091,x7092)+E(f782(x7093,x7094,x7091),f782(x7093,x7094,x7092))
% 28.25/28.13 [710]~E(x7101,x7102)+E(f256(x7101,x7103),f256(x7102,x7103))
% 28.25/28.13 [711]~E(x7111,x7112)+E(f256(x7113,x7111),f256(x7113,x7112))
% 28.25/28.13 [712]~E(x7121,x7122)+E(f787(x7121,x7123,x7124),f787(x7122,x7123,x7124))
% 28.25/28.13 [713]~E(x7131,x7132)+E(f787(x7133,x7131,x7134),f787(x7133,x7132,x7134))
% 28.25/28.13 [714]~E(x7141,x7142)+E(f787(x7143,x7144,x7141),f787(x7143,x7144,x7142))
% 28.25/28.13 [715]~E(x7151,x7152)+E(f795(x7151,x7153,x7154),f795(x7152,x7153,x7154))
% 28.25/28.13 [716]~E(x7161,x7162)+E(f795(x7163,x7161,x7164),f795(x7163,x7162,x7164))
% 28.25/28.13 [717]~E(x7171,x7172)+E(f795(x7173,x7174,x7171),f795(x7173,x7174,x7172))
% 28.25/28.13 [718]~E(x7181,x7182)+E(f871(x7181,x7183,x7184),f871(x7182,x7183,x7184))
% 28.25/28.13 [719]~E(x7191,x7192)+E(f871(x7193,x7191,x7194),f871(x7193,x7192,x7194))
% 28.25/28.13 [720]~E(x7201,x7202)+E(f871(x7203,x7204,x7201),f871(x7203,x7204,x7202))
% 28.25/28.13 [721]~E(x7211,x7212)+E(f538(x7211,x7213,x7214),f538(x7212,x7213,x7214))
% 28.25/28.13 [722]~E(x7221,x7222)+E(f538(x7223,x7221,x7224),f538(x7223,x7222,x7224))
% 28.25/28.13 [723]~E(x7231,x7232)+E(f538(x7233,x7234,x7231),f538(x7233,x7234,x7232))
% 28.25/28.13 [724]~E(x7241,x7242)+E(f400(x7241,x7243,x7244,x7245),f400(x7242,x7243,x7244,x7245))
% 28.25/28.13 [725]~E(x7251,x7252)+E(f400(x7253,x7251,x7254,x7255),f400(x7253,x7252,x7254,x7255))
% 28.25/28.13 [726]~E(x7261,x7262)+E(f400(x7263,x7264,x7261,x7265),f400(x7263,x7264,x7262,x7265))
% 28.25/28.13 [727]~E(x7271,x7272)+E(f400(x7273,x7274,x7275,x7271),f400(x7273,x7274,x7275,x7272))
% 28.25/28.13 [728]~E(x7281,x7282)+E(f918(x7281,x7283),f918(x7282,x7283))
% 28.25/28.13 [729]~E(x7291,x7292)+E(f918(x7293,x7291),f918(x7293,x7292))
% 28.25/28.13 [730]~E(x7301,x7302)+E(f433(x7301,x7303),f433(x7302,x7303))
% 28.25/28.13 [731]~E(x7311,x7312)+E(f433(x7313,x7311),f433(x7313,x7312))
% 28.25/28.13 [732]~E(x7321,x7322)+E(f476(x7321,x7323,x7324),f476(x7322,x7323,x7324))
% 28.25/28.13 [733]~E(x7331,x7332)+E(f476(x7333,x7331,x7334),f476(x7333,x7332,x7334))
% 28.25/28.13 [734]~E(x7341,x7342)+E(f476(x7343,x7344,x7341),f476(x7343,x7344,x7342))
% 28.25/28.13 [735]~E(x7351,x7352)+E(f580(x7351,x7353,x7354,x7355,x7356,x7357),f580(x7352,x7353,x7354,x7355,x7356,x7357))
% 28.25/28.13 [736]~E(x7361,x7362)+E(f580(x7363,x7361,x7364,x7365,x7366,x7367),f580(x7363,x7362,x7364,x7365,x7366,x7367))
% 28.25/28.13 [737]~E(x7371,x7372)+E(f580(x7373,x7374,x7371,x7375,x7376,x7377),f580(x7373,x7374,x7372,x7375,x7376,x7377))
% 28.25/28.13 [738]~E(x7381,x7382)+E(f580(x7383,x7384,x7385,x7381,x7386,x7387),f580(x7383,x7384,x7385,x7382,x7386,x7387))
% 28.25/28.13 [739]~E(x7391,x7392)+E(f580(x7393,x7394,x7395,x7396,x7391,x7397),f580(x7393,x7394,x7395,x7396,x7392,x7397))
% 28.25/28.13 [740]~E(x7401,x7402)+E(f580(x7403,x7404,x7405,x7406,x7407,x7401),f580(x7403,x7404,x7405,x7406,x7407,x7402))
% 28.25/28.13 [741]~E(x7411,x7412)+E(f706(x7411,x7413,x7414,x7415),f706(x7412,x7413,x7414,x7415))
% 28.25/28.13 [742]~E(x7421,x7422)+E(f706(x7423,x7421,x7424,x7425),f706(x7423,x7422,x7424,x7425))
% 28.25/28.13 [743]~E(x7431,x7432)+E(f706(x7433,x7434,x7431,x7435),f706(x7433,x7434,x7432,x7435))
% 28.25/28.13 [744]~E(x7441,x7442)+E(f706(x7443,x7444,x7445,x7441),f706(x7443,x7444,x7445,x7442))
% 28.25/28.13 [745]~E(x7451,x7452)+E(f685(x7451,x7453,x7454),f685(x7452,x7453,x7454))
% 28.25/28.13 [746]~E(x7461,x7462)+E(f685(x7463,x7461,x7464),f685(x7463,x7462,x7464))
% 28.25/28.13 [747]~E(x7471,x7472)+E(f685(x7473,x7474,x7471),f685(x7473,x7474,x7472))
% 28.25/28.13 [748]~E(x7481,x7482)+E(f297(x7481,x7483,x7484),f297(x7482,x7483,x7484))
% 28.25/28.13 [749]~E(x7491,x7492)+E(f297(x7493,x7491,x7494),f297(x7493,x7492,x7494))
% 28.25/28.13 [750]~E(x7501,x7502)+E(f297(x7503,x7504,x7501),f297(x7503,x7504,x7502))
% 28.25/28.13 [751]~E(x7511,x7512)+E(f553(x7511,x7513,x7514,x7515,x7516,x7517),f553(x7512,x7513,x7514,x7515,x7516,x7517))
% 28.25/28.13 [752]~E(x7521,x7522)+E(f553(x7523,x7521,x7524,x7525,x7526,x7527),f553(x7523,x7522,x7524,x7525,x7526,x7527))
% 28.25/28.13 [753]~E(x7531,x7532)+E(f553(x7533,x7534,x7531,x7535,x7536,x7537),f553(x7533,x7534,x7532,x7535,x7536,x7537))
% 28.25/28.13 [754]~E(x7541,x7542)+E(f553(x7543,x7544,x7545,x7541,x7546,x7547),f553(x7543,x7544,x7545,x7542,x7546,x7547))
% 28.25/28.13 [755]~E(x7551,x7552)+E(f553(x7553,x7554,x7555,x7556,x7551,x7557),f553(x7553,x7554,x7555,x7556,x7552,x7557))
% 28.25/28.13 [756]~E(x7561,x7562)+E(f553(x7563,x7564,x7565,x7566,x7567,x7561),f553(x7563,x7564,x7565,x7566,x7567,x7562))
% 28.25/28.13 [757]~E(x7571,x7572)+E(f789(x7571,x7573,x7574,x7575),f789(x7572,x7573,x7574,x7575))
% 28.25/28.13 [758]~E(x7581,x7582)+E(f789(x7583,x7581,x7584,x7585),f789(x7583,x7582,x7584,x7585))
% 28.25/28.13 [759]~E(x7591,x7592)+E(f789(x7593,x7594,x7591,x7595),f789(x7593,x7594,x7592,x7595))
% 28.25/28.13 [760]~E(x7601,x7602)+E(f789(x7603,x7604,x7605,x7601),f789(x7603,x7604,x7605,x7602))
% 28.25/28.13 [761]~E(x7611,x7612)+E(f341(x7611,x7613,x7614,x7615),f341(x7612,x7613,x7614,x7615))
% 28.25/28.13 [762]~E(x7621,x7622)+E(f341(x7623,x7621,x7624,x7625),f341(x7623,x7622,x7624,x7625))
% 28.25/28.13 [763]~E(x7631,x7632)+E(f341(x7633,x7634,x7631,x7635),f341(x7633,x7634,x7632,x7635))
% 28.25/28.13 [764]~E(x7641,x7642)+E(f341(x7643,x7644,x7645,x7641),f341(x7643,x7644,x7645,x7642))
% 28.25/28.13 [765]~E(x7651,x7652)+E(f887(x7651,x7653,x7654,x7655,x7656),f887(x7652,x7653,x7654,x7655,x7656))
% 28.25/28.13 [766]~E(x7661,x7662)+E(f887(x7663,x7661,x7664,x7665,x7666),f887(x7663,x7662,x7664,x7665,x7666))
% 28.25/28.13 [767]~E(x7671,x7672)+E(f887(x7673,x7674,x7671,x7675,x7676),f887(x7673,x7674,x7672,x7675,x7676))
% 28.25/28.13 [768]~E(x7681,x7682)+E(f887(x7683,x7684,x7685,x7681,x7686),f887(x7683,x7684,x7685,x7682,x7686))
% 28.25/28.13 [769]~E(x7691,x7692)+E(f887(x7693,x7694,x7695,x7696,x7691),f887(x7693,x7694,x7695,x7696,x7692))
% 28.25/28.13 [770]~E(x7701,x7702)+E(f589(x7701),f589(x7702))
% 28.25/28.13 [771]~E(x7711,x7712)+E(f220(x7711,x7713,x7714),f220(x7712,x7713,x7714))
% 28.25/28.13 [772]~E(x7721,x7722)+E(f220(x7723,x7721,x7724),f220(x7723,x7722,x7724))
% 28.25/28.13 [773]~E(x7731,x7732)+E(f220(x7733,x7734,x7731),f220(x7733,x7734,x7732))
% 28.25/28.13 [774]~E(x7741,x7742)+E(f610(x7741,x7743,x7744),f610(x7742,x7743,x7744))
% 28.25/28.13 [775]~E(x7751,x7752)+E(f610(x7753,x7751,x7754),f610(x7753,x7752,x7754))
% 28.25/28.13 [776]~E(x7761,x7762)+E(f610(x7763,x7764,x7761),f610(x7763,x7764,x7762))
% 28.25/28.13 [777]~E(x7771,x7772)+E(f856(x7771,x7773,x7774),f856(x7772,x7773,x7774))
% 28.25/28.13 [778]~E(x7781,x7782)+E(f856(x7783,x7781,x7784),f856(x7783,x7782,x7784))
% 28.25/28.13 [779]~E(x7791,x7792)+E(f856(x7793,x7794,x7791),f856(x7793,x7794,x7792))
% 28.25/28.13 [780]~E(x7801,x7802)+E(f909(x7801,x7803,x7804,x7805,x7806),f909(x7802,x7803,x7804,x7805,x7806))
% 28.25/28.13 [781]~E(x7811,x7812)+E(f909(x7813,x7811,x7814,x7815,x7816),f909(x7813,x7812,x7814,x7815,x7816))
% 28.25/28.13 [782]~E(x7821,x7822)+E(f909(x7823,x7824,x7821,x7825,x7826),f909(x7823,x7824,x7822,x7825,x7826))
% 28.25/28.13 [783]~E(x7831,x7832)+E(f909(x7833,x7834,x7835,x7831,x7836),f909(x7833,x7834,x7835,x7832,x7836))
% 28.25/28.13 [784]~E(x7841,x7842)+E(f909(x7843,x7844,x7845,x7846,x7841),f909(x7843,x7844,x7845,x7846,x7842))
% 28.25/28.13 [785]~E(x7851,x7852)+E(f713(x7851,x7853,x7854),f713(x7852,x7853,x7854))
% 28.25/28.13 [786]~E(x7861,x7862)+E(f713(x7863,x7861,x7864),f713(x7863,x7862,x7864))
% 28.25/28.13 [787]~E(x7871,x7872)+E(f713(x7873,x7874,x7871),f713(x7873,x7874,x7872))
% 28.25/28.13 [788]~E(x7881,x7882)+E(f123(x7881,x7883,x7884,x7885),f123(x7882,x7883,x7884,x7885))
% 28.25/28.13 [789]~E(x7891,x7892)+E(f123(x7893,x7891,x7894,x7895),f123(x7893,x7892,x7894,x7895))
% 28.25/28.13 [790]~E(x7901,x7902)+E(f123(x7903,x7904,x7901,x7905),f123(x7903,x7904,x7902,x7905))
% 28.25/28.13 [791]~E(x7911,x7912)+E(f123(x7913,x7914,x7915,x7911),f123(x7913,x7914,x7915,x7912))
% 28.25/28.13 [792]~E(x7921,x7922)+E(f402(x7921,x7923,x7924,x7925,x7926),f402(x7922,x7923,x7924,x7925,x7926))
% 28.25/28.13 [793]~E(x7931,x7932)+E(f402(x7933,x7931,x7934,x7935,x7936),f402(x7933,x7932,x7934,x7935,x7936))
% 28.25/28.13 [794]~E(x7941,x7942)+E(f402(x7943,x7944,x7941,x7945,x7946),f402(x7943,x7944,x7942,x7945,x7946))
% 28.25/28.13 [795]~E(x7951,x7952)+E(f402(x7953,x7954,x7955,x7951,x7956),f402(x7953,x7954,x7955,x7952,x7956))
% 28.25/28.13 [796]~E(x7961,x7962)+E(f402(x7963,x7964,x7965,x7966,x7961),f402(x7963,x7964,x7965,x7966,x7962))
% 28.25/28.13 [797]~E(x7971,x7972)+E(f847(x7971,x7973,x7974,x7975),f847(x7972,x7973,x7974,x7975))
% 28.25/28.13 [798]~E(x7981,x7982)+E(f847(x7983,x7981,x7984,x7985),f847(x7983,x7982,x7984,x7985))
% 28.25/28.13 [799]~E(x7991,x7992)+E(f847(x7993,x7994,x7991,x7995),f847(x7993,x7994,x7992,x7995))
% 28.25/28.13 [800]~E(x8001,x8002)+E(f847(x8003,x8004,x8005,x8001),f847(x8003,x8004,x8005,x8002))
% 28.25/28.13 [801]~E(x8011,x8012)+E(f889(x8011,x8013,x8014,x8015),f889(x8012,x8013,x8014,x8015))
% 28.25/28.13 [802]~E(x8021,x8022)+E(f889(x8023,x8021,x8024,x8025),f889(x8023,x8022,x8024,x8025))
% 28.25/28.13 [803]~E(x8031,x8032)+E(f889(x8033,x8034,x8031,x8035),f889(x8033,x8034,x8032,x8035))
% 28.25/28.13 [804]~E(x8041,x8042)+E(f889(x8043,x8044,x8045,x8041),f889(x8043,x8044,x8045,x8042))
% 28.25/28.13 [805]~E(x8051,x8052)+E(f235(x8051,x8053,x8054),f235(x8052,x8053,x8054))
% 28.25/28.13 [806]~E(x8061,x8062)+E(f235(x8063,x8061,x8064),f235(x8063,x8062,x8064))
% 28.25/28.13 [807]~E(x8071,x8072)+E(f235(x8073,x8074,x8071),f235(x8073,x8074,x8072))
% 28.25/28.13 [808]~E(x8081,x8082)+E(f761(x8081,x8083,x8084,x8085),f761(x8082,x8083,x8084,x8085))
% 28.25/28.13 [809]~E(x8091,x8092)+E(f761(x8093,x8091,x8094,x8095),f761(x8093,x8092,x8094,x8095))
% 28.25/28.13 [810]~E(x8101,x8102)+E(f761(x8103,x8104,x8101,x8105),f761(x8103,x8104,x8102,x8105))
% 28.25/28.13 [811]~E(x8111,x8112)+E(f761(x8113,x8114,x8115,x8111),f761(x8113,x8114,x8115,x8112))
% 28.25/28.13 [812]~E(x8121,x8122)+E(f168(x8121,x8123,x8124),f168(x8122,x8123,x8124))
% 28.25/28.13 [813]~E(x8131,x8132)+E(f168(x8133,x8131,x8134),f168(x8133,x8132,x8134))
% 28.25/28.13 [814]~E(x8141,x8142)+E(f168(x8143,x8144,x8141),f168(x8143,x8144,x8142))
% 28.25/28.13 [815]~E(x8151,x8152)+E(f798(x8151,x8153,x8154,x8155),f798(x8152,x8153,x8154,x8155))
% 28.25/28.13 [816]~E(x8161,x8162)+E(f798(x8163,x8161,x8164,x8165),f798(x8163,x8162,x8164,x8165))
% 28.25/28.13 [817]~E(x8171,x8172)+E(f798(x8173,x8174,x8171,x8175),f798(x8173,x8174,x8172,x8175))
% 28.25/28.13 [818]~E(x8181,x8182)+E(f798(x8183,x8184,x8185,x8181),f798(x8183,x8184,x8185,x8182))
% 28.25/28.13 [819]~E(x8191,x8192)+E(f463(x8191,x8193,x8194,x8195),f463(x8192,x8193,x8194,x8195))
% 28.25/28.13 [820]~E(x8201,x8202)+E(f463(x8203,x8201,x8204,x8205),f463(x8203,x8202,x8204,x8205))
% 28.25/28.13 [821]~E(x8211,x8212)+E(f463(x8213,x8214,x8211,x8215),f463(x8213,x8214,x8212,x8215))
% 28.25/28.13 [822]~E(x8221,x8222)+E(f463(x8223,x8224,x8225,x8221),f463(x8223,x8224,x8225,x8222))
% 28.25/28.13 [823]~E(x8231,x8232)+E(f486(x8231,x8233,x8234),f486(x8232,x8233,x8234))
% 28.25/28.13 [824]~E(x8241,x8242)+E(f486(x8243,x8241,x8244),f486(x8243,x8242,x8244))
% 28.25/28.13 [825]~E(x8251,x8252)+E(f486(x8253,x8254,x8251),f486(x8253,x8254,x8252))
% 28.25/28.13 [826]~E(x8261,x8262)+E(f648(x8261,x8263),f648(x8262,x8263))
% 28.25/28.13 [827]~E(x8271,x8272)+E(f648(x8273,x8271),f648(x8273,x8272))
% 28.25/28.13 [828]~E(x8281,x8282)+E(f147(x8281,x8283,x8284),f147(x8282,x8283,x8284))
% 28.25/28.13 [829]~E(x8291,x8292)+E(f147(x8293,x8291,x8294),f147(x8293,x8292,x8294))
% 28.25/28.13 [830]~E(x8301,x8302)+E(f147(x8303,x8304,x8301),f147(x8303,x8304,x8302))
% 28.25/28.13 [831]~E(x8311,x8312)+E(f775(x8311,x8313,x8314),f775(x8312,x8313,x8314))
% 28.25/28.13 [832]~E(x8321,x8322)+E(f775(x8323,x8321,x8324),f775(x8323,x8322,x8324))
% 28.25/28.13 [833]~E(x8331,x8332)+E(f775(x8333,x8334,x8331),f775(x8333,x8334,x8332))
% 28.25/28.13 [834]~E(x8341,x8342)+E(f312(x8341,x8343,x8344,x8345),f312(x8342,x8343,x8344,x8345))
% 28.25/28.13 [835]~E(x8351,x8352)+E(f312(x8353,x8351,x8354,x8355),f312(x8353,x8352,x8354,x8355))
% 28.25/28.13 [836]~E(x8361,x8362)+E(f312(x8363,x8364,x8361,x8365),f312(x8363,x8364,x8362,x8365))
% 28.25/28.13 [837]~E(x8371,x8372)+E(f312(x8373,x8374,x8375,x8371),f312(x8373,x8374,x8375,x8372))
% 28.25/28.13 [838]~E(x8381,x8382)+E(f535(x8381,x8383,x8384),f535(x8382,x8383,x8384))
% 28.25/28.13 [839]~E(x8391,x8392)+E(f535(x8393,x8391,x8394),f535(x8393,x8392,x8394))
% 28.25/28.13 [840]~E(x8401,x8402)+E(f535(x8403,x8404,x8401),f535(x8403,x8404,x8402))
% 28.25/28.13 [841]~E(x8411,x8412)+E(f556(x8411,x8413,x8414,x8415,x8416),f556(x8412,x8413,x8414,x8415,x8416))
% 28.25/28.13 [842]~E(x8421,x8422)+E(f556(x8423,x8421,x8424,x8425,x8426),f556(x8423,x8422,x8424,x8425,x8426))
% 28.25/28.13 [843]~E(x8431,x8432)+E(f556(x8433,x8434,x8431,x8435,x8436),f556(x8433,x8434,x8432,x8435,x8436))
% 28.25/28.13 [844]~E(x8441,x8442)+E(f556(x8443,x8444,x8445,x8441,x8446),f556(x8443,x8444,x8445,x8442,x8446))
% 28.25/28.13 [845]~E(x8451,x8452)+E(f556(x8453,x8454,x8455,x8456,x8451),f556(x8453,x8454,x8455,x8456,x8452))
% 28.25/28.13 [846]~E(x8461,x8462)+E(f811(x8461,x8463),f811(x8462,x8463))
% 28.25/28.13 [847]~E(x8471,x8472)+E(f811(x8473,x8471),f811(x8473,x8472))
% 28.25/28.13 [848]~E(x8481,x8482)+E(f247(x8481,x8483,x8484,x8485),f247(x8482,x8483,x8484,x8485))
% 28.25/28.13 [849]~E(x8491,x8492)+E(f247(x8493,x8491,x8494,x8495),f247(x8493,x8492,x8494,x8495))
% 28.25/28.13 [850]~E(x8501,x8502)+E(f247(x8503,x8504,x8501,x8505),f247(x8503,x8504,x8502,x8505))
% 28.25/28.13 [851]~E(x8511,x8512)+E(f247(x8513,x8514,x8515,x8511),f247(x8513,x8514,x8515,x8512))
% 28.25/28.13 [852]~E(x8521,x8522)+E(f276(x8521,x8523),f276(x8522,x8523))
% 28.25/28.13 [853]~E(x8531,x8532)+E(f276(x8533,x8531),f276(x8533,x8532))
% 28.25/28.13 [854]~E(x8541,x8542)+E(f60(x8541,x8543,x8544,x8545,x8546),f60(x8542,x8543,x8544,x8545,x8546))
% 28.25/28.13 [855]~E(x8551,x8552)+E(f60(x8553,x8551,x8554,x8555,x8556),f60(x8553,x8552,x8554,x8555,x8556))
% 28.25/28.13 [856]~E(x8561,x8562)+E(f60(x8563,x8564,x8561,x8565,x8566),f60(x8563,x8564,x8562,x8565,x8566))
% 28.25/28.13 [857]~E(x8571,x8572)+E(f60(x8573,x8574,x8575,x8571,x8576),f60(x8573,x8574,x8575,x8572,x8576))
% 28.25/28.13 [858]~E(x8581,x8582)+E(f60(x8583,x8584,x8585,x8586,x8581),f60(x8583,x8584,x8585,x8586,x8582))
% 28.25/28.13 [859]~E(x8591,x8592)+E(f193(x8591),f193(x8592))
% 28.25/28.13 [860]~E(x8601,x8602)+E(f137(x8601,x8603),f137(x8602,x8603))
% 28.25/28.13 [861]~E(x8611,x8612)+E(f137(x8613,x8611),f137(x8613,x8612))
% 28.25/28.13 [862]~E(x8621,x8622)+E(f910(x8621,x8623,x8624,x8625,x8626),f910(x8622,x8623,x8624,x8625,x8626))
% 28.25/28.13 [863]~E(x8631,x8632)+E(f910(x8633,x8631,x8634,x8635,x8636),f910(x8633,x8632,x8634,x8635,x8636))
% 28.25/28.13 [864]~E(x8641,x8642)+E(f910(x8643,x8644,x8641,x8645,x8646),f910(x8643,x8644,x8642,x8645,x8646))
% 28.25/28.13 [865]~E(x8651,x8652)+E(f910(x8653,x8654,x8655,x8651,x8656),f910(x8653,x8654,x8655,x8652,x8656))
% 28.25/28.13 [866]~E(x8661,x8662)+E(f910(x8663,x8664,x8665,x8666,x8661),f910(x8663,x8664,x8665,x8666,x8662))
% 28.25/28.13 [867]~E(x8671,x8672)+E(f736(x8671,x8673,x8674),f736(x8672,x8673,x8674))
% 28.25/28.13 [868]~E(x8681,x8682)+E(f736(x8683,x8681,x8684),f736(x8683,x8682,x8684))
% 28.25/28.13 [869]~E(x8691,x8692)+E(f736(x8693,x8694,x8691),f736(x8693,x8694,x8692))
% 28.25/28.13 [870]~E(x8701,x8702)+E(f771(x8701,x8703,x8704),f771(x8702,x8703,x8704))
% 28.25/28.13 [871]~E(x8711,x8712)+E(f771(x8713,x8711,x8714),f771(x8713,x8712,x8714))
% 28.25/28.13 [872]~E(x8721,x8722)+E(f771(x8723,x8724,x8721),f771(x8723,x8724,x8722))
% 28.25/28.13 [873]~E(x8731,x8732)+E(f332(x8731,x8733),f332(x8732,x8733))
% 28.25/28.13 [874]~E(x8741,x8742)+E(f332(x8743,x8741),f332(x8743,x8742))
% 28.25/28.13 [875]~E(x8751,x8752)+E(f394(x8751,x8753,x8754,x8755),f394(x8752,x8753,x8754,x8755))
% 28.25/28.13 [876]~E(x8761,x8762)+E(f394(x8763,x8761,x8764,x8765),f394(x8763,x8762,x8764,x8765))
% 28.25/28.13 [877]~E(x8771,x8772)+E(f394(x8773,x8774,x8771,x8775),f394(x8773,x8774,x8772,x8775))
% 28.25/28.13 [878]~E(x8781,x8782)+E(f394(x8783,x8784,x8785,x8781),f394(x8783,x8784,x8785,x8782))
% 28.25/28.13 [879]~E(x8791,x8792)+E(f471(x8791,x8793,x8794),f471(x8792,x8793,x8794))
% 28.25/28.13 [880]~E(x8801,x8802)+E(f471(x8803,x8801,x8804),f471(x8803,x8802,x8804))
% 28.25/28.13 [881]~E(x8811,x8812)+E(f471(x8813,x8814,x8811),f471(x8813,x8814,x8812))
% 28.25/28.13 [882]~E(x8821,x8822)+E(f690(x8821,x8823,x8824,x8825),f690(x8822,x8823,x8824,x8825))
% 28.25/28.13 [883]~E(x8831,x8832)+E(f690(x8833,x8831,x8834,x8835),f690(x8833,x8832,x8834,x8835))
% 28.25/28.13 [884]~E(x8841,x8842)+E(f690(x8843,x8844,x8841,x8845),f690(x8843,x8844,x8842,x8845))
% 28.25/28.13 [885]~E(x8851,x8852)+E(f690(x8853,x8854,x8855,x8851),f690(x8853,x8854,x8855,x8852))
% 28.25/28.13 [886]~E(x8861,x8862)+E(f12(x8861,x8863,x8864),f12(x8862,x8863,x8864))
% 28.25/28.13 [887]~E(x8871,x8872)+E(f12(x8873,x8871,x8874),f12(x8873,x8872,x8874))
% 28.25/28.13 [888]~E(x8881,x8882)+E(f12(x8883,x8884,x8881),f12(x8883,x8884,x8882))
% 28.25/28.13 [889]~E(x8891,x8892)+E(f664(x8891,x8893,x8894,x8895,x8896),f664(x8892,x8893,x8894,x8895,x8896))
% 28.25/28.13 [890]~E(x8901,x8902)+E(f664(x8903,x8901,x8904,x8905,x8906),f664(x8903,x8902,x8904,x8905,x8906))
% 28.25/28.13 [891]~E(x8911,x8912)+E(f664(x8913,x8914,x8911,x8915,x8916),f664(x8913,x8914,x8912,x8915,x8916))
% 28.25/28.13 [892]~E(x8921,x8922)+E(f664(x8923,x8924,x8925,x8921,x8926),f664(x8923,x8924,x8925,x8922,x8926))
% 28.25/28.13 [893]~E(x8931,x8932)+E(f664(x8933,x8934,x8935,x8936,x8931),f664(x8933,x8934,x8935,x8936,x8932))
% 28.25/28.13 [894]~E(x8941,x8942)+E(f82(x8941),f82(x8942))
% 28.25/28.13 [895]~E(x8951,x8952)+E(f325(x8951),f325(x8952))
% 28.25/28.13 [896]~E(x8961,x8962)+E(f273(x8961),f273(x8962))
% 28.25/28.13 [897]~E(x8971,x8972)+E(f462(x8971,x8973,x8974,x8975,x8976),f462(x8972,x8973,x8974,x8975,x8976))
% 28.25/28.13 [898]~E(x8981,x8982)+E(f462(x8983,x8981,x8984,x8985,x8986),f462(x8983,x8982,x8984,x8985,x8986))
% 28.25/28.13 [899]~E(x8991,x8992)+E(f462(x8993,x8994,x8991,x8995,x8996),f462(x8993,x8994,x8992,x8995,x8996))
% 28.25/28.13 [900]~E(x9001,x9002)+E(f462(x9003,x9004,x9005,x9001,x9006),f462(x9003,x9004,x9005,x9002,x9006))
% 28.25/28.13 [901]~E(x9011,x9012)+E(f462(x9013,x9014,x9015,x9016,x9011),f462(x9013,x9014,x9015,x9016,x9012))
% 28.25/28.13 [902]~E(x9021,x9022)+E(f702(x9021,x9023,x9024,x9025,x9026),f702(x9022,x9023,x9024,x9025,x9026))
% 28.25/28.13 [903]~E(x9031,x9032)+E(f702(x9033,x9031,x9034,x9035,x9036),f702(x9033,x9032,x9034,x9035,x9036))
% 28.25/28.13 [904]~E(x9041,x9042)+E(f702(x9043,x9044,x9041,x9045,x9046),f702(x9043,x9044,x9042,x9045,x9046))
% 28.25/28.13 [905]~E(x9051,x9052)+E(f702(x9053,x9054,x9055,x9051,x9056),f702(x9053,x9054,x9055,x9052,x9056))
% 28.25/28.13 [906]~E(x9061,x9062)+E(f702(x9063,x9064,x9065,x9066,x9061),f702(x9063,x9064,x9065,x9066,x9062))
% 28.25/28.13 [907]~E(x9071,x9072)+E(f184(x9071,x9073),f184(x9072,x9073))
% 28.25/28.13 [908]~E(x9081,x9082)+E(f184(x9083,x9081),f184(x9083,x9082))
% 28.25/28.13 [909]~E(x9091,x9092)+E(f773(x9091,x9093,x9094),f773(x9092,x9093,x9094))
% 28.25/28.13 [910]~E(x9101,x9102)+E(f773(x9103,x9101,x9104),f773(x9103,x9102,x9104))
% 28.25/28.13 [911]~E(x9111,x9112)+E(f773(x9113,x9114,x9111),f773(x9113,x9114,x9112))
% 28.25/28.13 [912]~E(x9121,x9122)+E(f113(x9121,x9123),f113(x9122,x9123))
% 28.25/28.13 [913]~E(x9131,x9132)+E(f113(x9133,x9131),f113(x9133,x9132))
% 28.25/28.13 [914]~E(x9141,x9142)+E(f257(x9141,x9143,x9144),f257(x9142,x9143,x9144))
% 28.25/28.13 [915]~E(x9151,x9152)+E(f257(x9153,x9151,x9154),f257(x9153,x9152,x9154))
% 28.25/28.13 [916]~E(x9161,x9162)+E(f257(x9163,x9164,x9161),f257(x9163,x9164,x9162))
% 28.25/28.13 [917]~E(x9171,x9172)+E(f727(x9171,x9173),f727(x9172,x9173))
% 28.25/28.13 [918]~E(x9181,x9182)+E(f727(x9183,x9181),f727(x9183,x9182))
% 28.25/28.13 [919]~E(x9191,x9192)+E(f44(x9191,x9193),f44(x9192,x9193))
% 28.25/28.13 [920]~E(x9201,x9202)+E(f44(x9203,x9201),f44(x9203,x9202))
% 28.25/28.13 [921]~E(x9211,x9212)+E(f616(x9211,x9213,x9214,x9215),f616(x9212,x9213,x9214,x9215))
% 28.25/28.13 [922]~E(x9221,x9222)+E(f616(x9223,x9221,x9224,x9225),f616(x9223,x9222,x9224,x9225))
% 28.25/28.13 [923]~E(x9231,x9232)+E(f616(x9233,x9234,x9231,x9235),f616(x9233,x9234,x9232,x9235))
% 28.25/28.13 [924]~E(x9241,x9242)+E(f616(x9243,x9244,x9245,x9241),f616(x9243,x9244,x9245,x9242))
% 28.25/28.13 [925]~E(x9251,x9252)+E(f120(x9251,x9253),f120(x9252,x9253))
% 28.25/28.13 [926]~E(x9261,x9262)+E(f120(x9263,x9261),f120(x9263,x9262))
% 28.25/28.13 [927]~E(x9271,x9272)+E(f591(x9271,x9273,x9274),f591(x9272,x9273,x9274))
% 28.25/28.13 [928]~E(x9281,x9282)+E(f591(x9283,x9281,x9284),f591(x9283,x9282,x9284))
% 28.25/28.13 [929]~E(x9291,x9292)+E(f591(x9293,x9294,x9291),f591(x9293,x9294,x9292))
% 28.25/28.13 [930]~E(x9301,x9302)+E(f124(x9301,x9303),f124(x9302,x9303))
% 28.25/28.13 [931]~E(x9311,x9312)+E(f124(x9313,x9311),f124(x9313,x9312))
% 28.25/28.13 [932]~E(x9321,x9322)+E(f303(x9321,x9323,x9324),f303(x9322,x9323,x9324))
% 28.25/28.13 [933]~E(x9331,x9332)+E(f303(x9333,x9331,x9334),f303(x9333,x9332,x9334))
% 28.25/28.13 [934]~E(x9341,x9342)+E(f303(x9343,x9344,x9341),f303(x9343,x9344,x9342))
% 28.25/28.13 [935]~E(x9351,x9352)+E(f751(x9351,x9353),f751(x9352,x9353))
% 28.25/28.13 [936]~E(x9361,x9362)+E(f751(x9363,x9361),f751(x9363,x9362))
% 28.25/28.13 [937]~E(x9371,x9372)+E(f502(x9371,x9373,x9374),f502(x9372,x9373,x9374))
% 28.25/28.13 [938]~E(x9381,x9382)+E(f502(x9383,x9381,x9384),f502(x9383,x9382,x9384))
% 28.25/28.13 [939]~E(x9391,x9392)+E(f502(x9393,x9394,x9391),f502(x9393,x9394,x9392))
% 28.25/28.13 [940]~E(x9401,x9402)+E(f474(x9401,x9403,x9404),f474(x9402,x9403,x9404))
% 28.25/28.13 [941]~E(x9411,x9412)+E(f474(x9413,x9411,x9414),f474(x9413,x9412,x9414))
% 28.25/28.13 [942]~E(x9421,x9422)+E(f474(x9423,x9424,x9421),f474(x9423,x9424,x9422))
% 28.25/28.13 [943]~E(x9431,x9432)+E(f119(x9431,x9433,x9434,x9435,x9436),f119(x9432,x9433,x9434,x9435,x9436))
% 28.25/28.13 [944]~E(x9441,x9442)+E(f119(x9443,x9441,x9444,x9445,x9446),f119(x9443,x9442,x9444,x9445,x9446))
% 28.25/28.13 [945]~E(x9451,x9452)+E(f119(x9453,x9454,x9451,x9455,x9456),f119(x9453,x9454,x9452,x9455,x9456))
% 28.25/28.13 [946]~E(x9461,x9462)+E(f119(x9463,x9464,x9465,x9461,x9466),f119(x9463,x9464,x9465,x9462,x9466))
% 28.25/28.13 [947]~E(x9471,x9472)+E(f119(x9473,x9474,x9475,x9476,x9471),f119(x9473,x9474,x9475,x9476,x9472))
% 28.25/28.13 [948]~E(x9481,x9482)+E(f501(x9481,x9483,x9484),f501(x9482,x9483,x9484))
% 28.25/28.13 [949]~E(x9491,x9492)+E(f501(x9493,x9491,x9494),f501(x9493,x9492,x9494))
% 28.25/28.13 [950]~E(x9501,x9502)+E(f501(x9503,x9504,x9501),f501(x9503,x9504,x9502))
% 28.25/28.13 [951]~E(x9511,x9512)+E(f166(x9511,x9513,x9514),f166(x9512,x9513,x9514))
% 28.25/28.13 [952]~E(x9521,x9522)+E(f166(x9523,x9521,x9524),f166(x9523,x9522,x9524))
% 28.25/28.13 [953]~E(x9531,x9532)+E(f166(x9533,x9534,x9531),f166(x9533,x9534,x9532))
% 28.25/28.13 [954]~E(x9541,x9542)+E(f50(x9541),f50(x9542))
% 28.25/28.13 [955]~E(x9551,x9552)+E(f489(x9551,x9553),f489(x9552,x9553))
% 28.25/28.13 [956]~E(x9561,x9562)+E(f489(x9563,x9561),f489(x9563,x9562))
% 28.25/28.13 [957]~E(x9571,x9572)+E(f449(x9571,x9573,x9574),f449(x9572,x9573,x9574))
% 28.25/28.13 [958]~E(x9581,x9582)+E(f449(x9583,x9581,x9584),f449(x9583,x9582,x9584))
% 28.25/28.13 [959]~E(x9591,x9592)+E(f449(x9593,x9594,x9591),f449(x9593,x9594,x9592))
% 28.25/28.13 [960]~E(x9601,x9602)+E(f406(x9601,x9603,x9604,x9605),f406(x9602,x9603,x9604,x9605))
% 28.25/28.13 [961]~E(x9611,x9612)+E(f406(x9613,x9611,x9614,x9615),f406(x9613,x9612,x9614,x9615))
% 28.25/28.13 [962]~E(x9621,x9622)+E(f406(x9623,x9624,x9621,x9625),f406(x9623,x9624,x9622,x9625))
% 28.25/28.13 [963]~E(x9631,x9632)+E(f406(x9633,x9634,x9635,x9631),f406(x9633,x9634,x9635,x9632))
% 28.25/28.13 [964]~E(x9641,x9642)+E(f121(x9641),f121(x9642))
% 28.25/28.13 [965]~E(x9651,x9652)+E(f210(x9651,x9653),f210(x9652,x9653))
% 28.25/28.13 [966]~E(x9661,x9662)+E(f210(x9663,x9661),f210(x9663,x9662))
% 28.25/28.13 [967]~E(x9671,x9672)+E(f703(x9671,x9673,x9674,x9675,x9676),f703(x9672,x9673,x9674,x9675,x9676))
% 28.25/28.13 [968]~E(x9681,x9682)+E(f703(x9683,x9681,x9684,x9685,x9686),f703(x9683,x9682,x9684,x9685,x9686))
% 28.25/28.13 [969]~E(x9691,x9692)+E(f703(x9693,x9694,x9691,x9695,x9696),f703(x9693,x9694,x9692,x9695,x9696))
% 28.25/28.13 [970]~E(x9701,x9702)+E(f703(x9703,x9704,x9705,x9701,x9706),f703(x9703,x9704,x9705,x9702,x9706))
% 28.25/28.13 [971]~E(x9711,x9712)+E(f703(x9713,x9714,x9715,x9716,x9711),f703(x9713,x9714,x9715,x9716,x9712))
% 28.25/28.13 [972]~E(x9721,x9722)+E(f291(x9721,x9723,x9724,x9725),f291(x9722,x9723,x9724,x9725))
% 28.25/28.13 [973]~E(x9731,x9732)+E(f291(x9733,x9731,x9734,x9735),f291(x9733,x9732,x9734,x9735))
% 28.25/28.13 [974]~E(x9741,x9742)+E(f291(x9743,x9744,x9741,x9745),f291(x9743,x9744,x9742,x9745))
% 28.25/28.13 [975]~E(x9751,x9752)+E(f291(x9753,x9754,x9755,x9751),f291(x9753,x9754,x9755,x9752))
% 28.25/28.13 [976]~E(x9761,x9762)+E(f426(x9761),f426(x9762))
% 28.25/28.13 [977]~E(x9771,x9772)+E(f596(x9771),f596(x9772))
% 28.25/28.13 [978]~E(x9781,x9782)+E(f190(x9781,x9783,x9784,x9785),f190(x9782,x9783,x9784,x9785))
% 28.25/28.13 [979]~E(x9791,x9792)+E(f190(x9793,x9791,x9794,x9795),f190(x9793,x9792,x9794,x9795))
% 28.25/28.13 [980]~E(x9801,x9802)+E(f190(x9803,x9804,x9801,x9805),f190(x9803,x9804,x9802,x9805))
% 28.25/28.13 [981]~E(x9811,x9812)+E(f190(x9813,x9814,x9815,x9811),f190(x9813,x9814,x9815,x9812))
% 28.25/28.13 [982]~E(x9821,x9822)+E(f640(x9821,x9823,x9824,x9825),f640(x9822,x9823,x9824,x9825))
% 28.25/28.13 [983]~E(x9831,x9832)+E(f640(x9833,x9831,x9834,x9835),f640(x9833,x9832,x9834,x9835))
% 28.25/28.13 [984]~E(x9841,x9842)+E(f640(x9843,x9844,x9841,x9845),f640(x9843,x9844,x9842,x9845))
% 28.25/28.13 [985]~E(x9851,x9852)+E(f640(x9853,x9854,x9855,x9851),f640(x9853,x9854,x9855,x9852))
% 28.25/28.13 [986]~E(x9861,x9862)+E(f127(x9861),f127(x9862))
% 28.25/28.13 [987]~E(x9871,x9872)+E(f797(x9871,x9873,x9874,x9875,x9876),f797(x9872,x9873,x9874,x9875,x9876))
% 28.25/28.13 [988]~E(x9881,x9882)+E(f797(x9883,x9881,x9884,x9885,x9886),f797(x9883,x9882,x9884,x9885,x9886))
% 28.25/28.13 [989]~E(x9891,x9892)+E(f797(x9893,x9894,x9891,x9895,x9896),f797(x9893,x9894,x9892,x9895,x9896))
% 28.25/28.13 [990]~E(x9901,x9902)+E(f797(x9903,x9904,x9905,x9901,x9906),f797(x9903,x9904,x9905,x9902,x9906))
% 28.25/28.13 [991]~E(x9911,x9912)+E(f797(x9913,x9914,x9915,x9916,x9911),f797(x9913,x9914,x9915,x9916,x9912))
% 28.25/28.13 [992]~E(x9921,x9922)+E(f916(x9921,x9923,x9924,x9925),f916(x9922,x9923,x9924,x9925))
% 28.25/28.13 [993]~E(x9931,x9932)+E(f916(x9933,x9931,x9934,x9935),f916(x9933,x9932,x9934,x9935))
% 28.25/28.14 [994]~E(x9941,x9942)+E(f916(x9943,x9944,x9941,x9945),f916(x9943,x9944,x9942,x9945))
% 28.25/28.14 [995]~E(x9951,x9952)+E(f916(x9953,x9954,x9955,x9951),f916(x9953,x9954,x9955,x9952))
% 28.25/28.14 [996]~E(x9961,x9962)+E(f567(x9961,x9963,x9964,x9965),f567(x9962,x9963,x9964,x9965))
% 28.25/28.14 [997]~E(x9971,x9972)+E(f567(x9973,x9971,x9974,x9975),f567(x9973,x9972,x9974,x9975))
% 28.25/28.14 [998]~E(x9981,x9982)+E(f567(x9983,x9984,x9981,x9985),f567(x9983,x9984,x9982,x9985))
% 28.25/28.14 [999]~E(x9991,x9992)+E(f567(x9993,x9994,x9995,x9991),f567(x9993,x9994,x9995,x9992))
% 28.25/28.14 [1000]~E(x10001,x10002)+E(f203(x10001,x10003,x10004,x10005,x10006,x10007,x10008),f203(x10002,x10003,x10004,x10005,x10006,x10007,x10008))
% 28.25/28.14 [1001]~E(x10011,x10012)+E(f203(x10013,x10011,x10014,x10015,x10016,x10017,x10018),f203(x10013,x10012,x10014,x10015,x10016,x10017,x10018))
% 28.25/28.14 [1002]~E(x10021,x10022)+E(f203(x10023,x10024,x10021,x10025,x10026,x10027,x10028),f203(x10023,x10024,x10022,x10025,x10026,x10027,x10028))
% 28.25/28.14 [1003]~E(x10031,x10032)+E(f203(x10033,x10034,x10035,x10031,x10036,x10037,x10038),f203(x10033,x10034,x10035,x10032,x10036,x10037,x10038))
% 28.25/28.14 [1004]~E(x10041,x10042)+E(f203(x10043,x10044,x10045,x10046,x10041,x10047,x10048),f203(x10043,x10044,x10045,x10046,x10042,x10047,x10048))
% 28.25/28.14 [1005]~E(x10051,x10052)+E(f203(x10053,x10054,x10055,x10056,x10057,x10051,x10058),f203(x10053,x10054,x10055,x10056,x10057,x10052,x10058))
% 28.25/28.14 [1006]~E(x10061,x10062)+E(f203(x10063,x10064,x10065,x10066,x10067,x10068,x10061),f203(x10063,x10064,x10065,x10066,x10067,x10068,x10062))
% 28.25/28.14 [1007]~E(x10071,x10072)+E(f649(x10071,x10073,x10074,x10075),f649(x10072,x10073,x10074,x10075))
% 28.25/28.14 [1008]~E(x10081,x10082)+E(f649(x10083,x10081,x10084,x10085),f649(x10083,x10082,x10084,x10085))
% 28.25/28.14 [1009]~E(x10091,x10092)+E(f649(x10093,x10094,x10091,x10095),f649(x10093,x10094,x10092,x10095))
% 28.25/28.14 [1010]~E(x10101,x10102)+E(f649(x10103,x10104,x10105,x10101),f649(x10103,x10104,x10105,x10102))
% 28.25/28.14 [1011]~E(x10111,x10112)+E(f880(x10111,x10113,x10114),f880(x10112,x10113,x10114))
% 28.25/28.14 [1012]~E(x10121,x10122)+E(f880(x10123,x10121,x10124),f880(x10123,x10122,x10124))
% 28.25/28.14 [1013]~E(x10131,x10132)+E(f880(x10133,x10134,x10131),f880(x10133,x10134,x10132))
% 28.25/28.14 [1014]~E(x10141,x10142)+E(f762(x10141,x10143,x10144,x10145),f762(x10142,x10143,x10144,x10145))
% 28.25/28.14 [1015]~E(x10151,x10152)+E(f762(x10153,x10151,x10154,x10155),f762(x10153,x10152,x10154,x10155))
% 28.25/28.14 [1016]~E(x10161,x10162)+E(f762(x10163,x10164,x10161,x10165),f762(x10163,x10164,x10162,x10165))
% 28.25/28.14 [1017]~E(x10171,x10172)+E(f762(x10173,x10174,x10175,x10171),f762(x10173,x10174,x10175,x10172))
% 28.25/28.14 [1018]~E(x10181,x10182)+E(f386(x10181,x10183,x10184,x10185),f386(x10182,x10183,x10184,x10185))
% 28.25/28.14 [1019]~E(x10191,x10192)+E(f386(x10193,x10191,x10194,x10195),f386(x10193,x10192,x10194,x10195))
% 28.25/28.14 [1020]~E(x10201,x10202)+E(f386(x10203,x10204,x10201,x10205),f386(x10203,x10204,x10202,x10205))
% 28.25/28.14 [1021]~E(x10211,x10212)+E(f386(x10213,x10214,x10215,x10211),f386(x10213,x10214,x10215,x10212))
% 28.25/28.14 [1022]~E(x10221,x10222)+E(f37(x10221),f37(x10222))
% 28.25/28.14 [1023]~E(x10231,x10232)+E(f634(x10231,x10233,x10234),f634(x10232,x10233,x10234))
% 28.25/28.14 [1024]~E(x10241,x10242)+E(f634(x10243,x10241,x10244),f634(x10243,x10242,x10244))
% 28.25/28.14 [1025]~E(x10251,x10252)+E(f634(x10253,x10254,x10251),f634(x10253,x10254,x10252))
% 28.25/28.14 [1026]~E(x10261,x10262)+E(f663(x10261,x10263),f663(x10262,x10263))
% 28.25/28.14 [1027]~E(x10271,x10272)+E(f663(x10273,x10271),f663(x10273,x10272))
% 28.25/28.14 [1028]~E(x10281,x10282)+E(f444(x10281,x10283,x10284),f444(x10282,x10283,x10284))
% 28.25/28.14 [1029]~E(x10291,x10292)+E(f444(x10293,x10291,x10294),f444(x10293,x10292,x10294))
% 28.25/28.14 [1030]~E(x10301,x10302)+E(f444(x10303,x10304,x10301),f444(x10303,x10304,x10302))
% 28.25/28.14 [1031]~E(x10311,x10312)+E(f651(x10311,x10313,x10314,x10315),f651(x10312,x10313,x10314,x10315))
% 28.25/28.14 [1032]~E(x10321,x10322)+E(f651(x10323,x10321,x10324,x10325),f651(x10323,x10322,x10324,x10325))
% 28.25/28.14 [1033]~E(x10331,x10332)+E(f651(x10333,x10334,x10331,x10335),f651(x10333,x10334,x10332,x10335))
% 28.25/28.14 [1034]~E(x10341,x10342)+E(f651(x10343,x10344,x10345,x10341),f651(x10343,x10344,x10345,x10342))
% 28.25/28.14 [1035]~E(x10351,x10352)+E(f642(x10351,x10353,x10354,x10355,x10356),f642(x10352,x10353,x10354,x10355,x10356))
% 28.25/28.14 [1036]~E(x10361,x10362)+E(f642(x10363,x10361,x10364,x10365,x10366),f642(x10363,x10362,x10364,x10365,x10366))
% 28.25/28.14 [1037]~E(x10371,x10372)+E(f642(x10373,x10374,x10371,x10375,x10376),f642(x10373,x10374,x10372,x10375,x10376))
% 28.25/28.14 [1038]~E(x10381,x10382)+E(f642(x10383,x10384,x10385,x10381,x10386),f642(x10383,x10384,x10385,x10382,x10386))
% 28.25/28.14 [1039]~E(x10391,x10392)+E(f642(x10393,x10394,x10395,x10396,x10391),f642(x10393,x10394,x10395,x10396,x10392))
% 28.25/28.14 [1040]~E(x10401,x10402)+E(f852(x10401,x10403,x10404,x10405,x10406,x10407,x10408,x10409),f852(x10402,x10403,x10404,x10405,x10406,x10407,x10408,x10409))
% 28.25/28.14 [1041]~E(x10411,x10412)+E(f852(x10413,x10411,x10414,x10415,x10416,x10417,x10418,x10419),f852(x10413,x10412,x10414,x10415,x10416,x10417,x10418,x10419))
% 28.25/28.14 [1042]~E(x10421,x10422)+E(f852(x10423,x10424,x10421,x10425,x10426,x10427,x10428,x10429),f852(x10423,x10424,x10422,x10425,x10426,x10427,x10428,x10429))
% 28.25/28.14 [1043]~E(x10431,x10432)+E(f852(x10433,x10434,x10435,x10431,x10436,x10437,x10438,x10439),f852(x10433,x10434,x10435,x10432,x10436,x10437,x10438,x10439))
% 28.25/28.14 [1044]~E(x10441,x10442)+E(f852(x10443,x10444,x10445,x10446,x10441,x10447,x10448,x10449),f852(x10443,x10444,x10445,x10446,x10442,x10447,x10448,x10449))
% 28.25/28.14 [1045]~E(x10451,x10452)+E(f852(x10453,x10454,x10455,x10456,x10457,x10451,x10458,x10459),f852(x10453,x10454,x10455,x10456,x10457,x10452,x10458,x10459))
% 28.25/28.14 [1046]~E(x10461,x10462)+E(f852(x10463,x10464,x10465,x10466,x10467,x10468,x10461,x10469),f852(x10463,x10464,x10465,x10466,x10467,x10468,x10462,x10469))
% 28.25/28.14 [1047]~E(x10471,x10472)+E(f852(x10473,x10474,x10475,x10476,x10477,x10478,x10479,x10471),f852(x10473,x10474,x10475,x10476,x10477,x10478,x10479,x10472))
% 28.25/28.14 [1048]~E(x10481,x10482)+E(f683(x10481,x10483,x10484,x10485),f683(x10482,x10483,x10484,x10485))
% 28.25/28.14 [1049]~E(x10491,x10492)+E(f683(x10493,x10491,x10494,x10495),f683(x10493,x10492,x10494,x10495))
% 28.25/28.14 [1050]~E(x10501,x10502)+E(f683(x10503,x10504,x10501,x10505),f683(x10503,x10504,x10502,x10505))
% 28.25/28.14 [1051]~E(x10511,x10512)+E(f683(x10513,x10514,x10515,x10511),f683(x10513,x10514,x10515,x10512))
% 28.25/28.14 [1052]~E(x10521,x10522)+E(f799(x10521,x10523,x10524,x10525),f799(x10522,x10523,x10524,x10525))
% 28.25/28.14 [1053]~E(x10531,x10532)+E(f799(x10533,x10531,x10534,x10535),f799(x10533,x10532,x10534,x10535))
% 28.25/28.14 [1054]~E(x10541,x10542)+E(f799(x10543,x10544,x10541,x10545),f799(x10543,x10544,x10542,x10545))
% 28.25/28.14 [1055]~E(x10551,x10552)+E(f799(x10553,x10554,x10555,x10551),f799(x10553,x10554,x10555,x10552))
% 28.25/28.14 [1056]~E(x10561,x10562)+E(f631(x10561,x10563,x10564),f631(x10562,x10563,x10564))
% 28.25/28.14 [1057]~E(x10571,x10572)+E(f631(x10573,x10571,x10574),f631(x10573,x10572,x10574))
% 28.25/28.14 [1058]~E(x10581,x10582)+E(f631(x10583,x10584,x10581),f631(x10583,x10584,x10582))
% 28.25/28.14 [1059]~E(x10591,x10592)+E(f364(x10591,x10593,x10594,x10595,x10596),f364(x10592,x10593,x10594,x10595,x10596))
% 28.25/28.14 [1060]~E(x10601,x10602)+E(f364(x10603,x10601,x10604,x10605,x10606),f364(x10603,x10602,x10604,x10605,x10606))
% 28.25/28.14 [1061]~E(x10611,x10612)+E(f364(x10613,x10614,x10611,x10615,x10616),f364(x10613,x10614,x10612,x10615,x10616))
% 28.25/28.14 [1062]~E(x10621,x10622)+E(f364(x10623,x10624,x10625,x10621,x10626),f364(x10623,x10624,x10625,x10622,x10626))
% 28.25/28.14 [1063]~E(x10631,x10632)+E(f364(x10633,x10634,x10635,x10636,x10631),f364(x10633,x10634,x10635,x10636,x10632))
% 28.25/28.14 [1064]~E(x10641,x10642)+E(f809(x10641,x10643,x10644,x10645,x10646,x10647,x10648),f809(x10642,x10643,x10644,x10645,x10646,x10647,x10648))
% 28.25/28.14 [1065]~E(x10651,x10652)+E(f809(x10653,x10651,x10654,x10655,x10656,x10657,x10658),f809(x10653,x10652,x10654,x10655,x10656,x10657,x10658))
% 28.25/28.14 [1066]~E(x10661,x10662)+E(f809(x10663,x10664,x10661,x10665,x10666,x10667,x10668),f809(x10663,x10664,x10662,x10665,x10666,x10667,x10668))
% 28.25/28.14 [1067]~E(x10671,x10672)+E(f809(x10673,x10674,x10675,x10671,x10676,x10677,x10678),f809(x10673,x10674,x10675,x10672,x10676,x10677,x10678))
% 28.25/28.14 [1068]~E(x10681,x10682)+E(f809(x10683,x10684,x10685,x10686,x10681,x10687,x10688),f809(x10683,x10684,x10685,x10686,x10682,x10687,x10688))
% 28.25/28.14 [1069]~E(x10691,x10692)+E(f809(x10693,x10694,x10695,x10696,x10697,x10691,x10698),f809(x10693,x10694,x10695,x10696,x10697,x10692,x10698))
% 28.25/28.14 [1070]~E(x10701,x10702)+E(f809(x10703,x10704,x10705,x10706,x10707,x10708,x10701),f809(x10703,x10704,x10705,x10706,x10707,x10708,x10702))
% 28.25/28.14 [1071]~E(x10711,x10712)+E(f359(x10711,x10713,x10714,x10715),f359(x10712,x10713,x10714,x10715))
% 28.25/28.14 [1072]~E(x10721,x10722)+E(f359(x10723,x10721,x10724,x10725),f359(x10723,x10722,x10724,x10725))
% 28.25/28.14 [1073]~E(x10731,x10732)+E(f359(x10733,x10734,x10731,x10735),f359(x10733,x10734,x10732,x10735))
% 28.25/28.14 [1074]~E(x10741,x10742)+E(f359(x10743,x10744,x10745,x10741),f359(x10743,x10744,x10745,x10742))
% 28.25/28.14 [1075]~E(x10751,x10752)+E(f280(x10751,x10753),f280(x10752,x10753))
% 28.25/28.14 [1076]~E(x10761,x10762)+E(f280(x10763,x10761),f280(x10763,x10762))
% 28.25/28.14 [1077]~E(x10771,x10772)+E(f379(x10771,x10773),f379(x10772,x10773))
% 28.25/28.14 [1078]~E(x10781,x10782)+E(f379(x10783,x10781),f379(x10783,x10782))
% 28.25/28.14 [1079]~E(x10791,x10792)+E(f267(x10791,x10793),f267(x10792,x10793))
% 28.25/28.14 [1080]~E(x10801,x10802)+E(f267(x10803,x10801),f267(x10803,x10802))
% 28.25/28.14 [1081]~E(x10811,x10812)+E(f461(x10811,x10813,x10814,x10815,x10816),f461(x10812,x10813,x10814,x10815,x10816))
% 28.25/28.14 [1082]~E(x10821,x10822)+E(f461(x10823,x10821,x10824,x10825,x10826),f461(x10823,x10822,x10824,x10825,x10826))
% 28.25/28.14 [1083]~E(x10831,x10832)+E(f461(x10833,x10834,x10831,x10835,x10836),f461(x10833,x10834,x10832,x10835,x10836))
% 28.25/28.14 [1084]~E(x10841,x10842)+E(f461(x10843,x10844,x10845,x10841,x10846),f461(x10843,x10844,x10845,x10842,x10846))
% 28.25/28.14 [1085]~E(x10851,x10852)+E(f461(x10853,x10854,x10855,x10856,x10851),f461(x10853,x10854,x10855,x10856,x10852))
% 28.25/28.14 [1086]~E(x10861,x10862)+E(f304(x10861,x10863),f304(x10862,x10863))
% 28.25/28.14 [1087]~E(x10871,x10872)+E(f304(x10873,x10871),f304(x10873,x10872))
% 28.25/28.14 [1088]~E(x10881,x10882)+E(f815(x10881,x10883,x10884,x10885),f815(x10882,x10883,x10884,x10885))
% 28.25/28.14 [1089]~E(x10891,x10892)+E(f815(x10893,x10891,x10894,x10895),f815(x10893,x10892,x10894,x10895))
% 28.25/28.14 [1090]~E(x10901,x10902)+E(f815(x10903,x10904,x10901,x10905),f815(x10903,x10904,x10902,x10905))
% 28.25/28.14 [1091]~E(x10911,x10912)+E(f815(x10913,x10914,x10915,x10911),f815(x10913,x10914,x10915,x10912))
% 28.25/28.14 [1092]~E(x10921,x10922)+E(f804(x10921,x10923,x10924,x10925),f804(x10922,x10923,x10924,x10925))
% 28.25/28.14 [1093]~E(x10931,x10932)+E(f804(x10933,x10931,x10934,x10935),f804(x10933,x10932,x10934,x10935))
% 28.25/28.14 [1094]~E(x10941,x10942)+E(f804(x10943,x10944,x10941,x10945),f804(x10943,x10944,x10942,x10945))
% 28.25/28.14 [1095]~E(x10951,x10952)+E(f804(x10953,x10954,x10955,x10951),f804(x10953,x10954,x10955,x10952))
% 28.25/28.14 [1096]~E(x10961,x10962)+E(f393(x10961,x10963,x10964,x10965),f393(x10962,x10963,x10964,x10965))
% 28.25/28.14 [1097]~E(x10971,x10972)+E(f393(x10973,x10971,x10974,x10975),f393(x10973,x10972,x10974,x10975))
% 28.25/28.14 [1098]~E(x10981,x10982)+E(f393(x10983,x10984,x10981,x10985),f393(x10983,x10984,x10982,x10985))
% 28.25/28.14 [1099]~E(x10991,x10992)+E(f393(x10993,x10994,x10995,x10991),f393(x10993,x10994,x10995,x10992))
% 28.25/28.14 [1100]~E(x11001,x11002)+E(f806(x11001,x11003,x11004,x11005,x11006),f806(x11002,x11003,x11004,x11005,x11006))
% 28.25/28.14 [1101]~E(x11011,x11012)+E(f806(x11013,x11011,x11014,x11015,x11016),f806(x11013,x11012,x11014,x11015,x11016))
% 28.25/28.14 [1102]~E(x11021,x11022)+E(f806(x11023,x11024,x11021,x11025,x11026),f806(x11023,x11024,x11022,x11025,x11026))
% 28.25/28.14 [1103]~E(x11031,x11032)+E(f806(x11033,x11034,x11035,x11031,x11036),f806(x11033,x11034,x11035,x11032,x11036))
% 28.25/28.14 [1104]~E(x11041,x11042)+E(f806(x11043,x11044,x11045,x11046,x11041),f806(x11043,x11044,x11045,x11046,x11042))
% 28.25/28.14 [1105]~E(x11051,x11052)+E(f327(x11051),f327(x11052))
% 28.25/28.14 [1106]~E(x11061,x11062)+E(f109(x11061,x11063,x11064),f109(x11062,x11063,x11064))
% 28.25/28.14 [1107]~E(x11071,x11072)+E(f109(x11073,x11071,x11074),f109(x11073,x11072,x11074))
% 28.25/28.14 [1108]~E(x11081,x11082)+E(f109(x11083,x11084,x11081),f109(x11083,x11084,x11082))
% 28.25/28.14 [1109]~E(x11091,x11092)+E(f714(x11091,x11093,x11094),f714(x11092,x11093,x11094))
% 28.25/28.14 [1110]~E(x11101,x11102)+E(f714(x11103,x11101,x11104),f714(x11103,x11102,x11104))
% 28.25/28.14 [1111]~E(x11111,x11112)+E(f714(x11113,x11114,x11111),f714(x11113,x11114,x11112))
% 28.25/28.14 [1112]~E(x11121,x11122)+E(f260(x11121,x11123),f260(x11122,x11123))
% 28.25/28.14 [1113]~E(x11131,x11132)+E(f260(x11133,x11131),f260(x11133,x11132))
% 28.25/28.14 [1114]~E(x11141,x11142)+E(f335(x11141,x11143,x11144),f335(x11142,x11143,x11144))
% 28.25/28.14 [1115]~E(x11151,x11152)+E(f335(x11153,x11151,x11154),f335(x11153,x11152,x11154))
% 28.25/28.14 [1116]~E(x11161,x11162)+E(f335(x11163,x11164,x11161),f335(x11163,x11164,x11162))
% 28.25/28.14 [1117]~E(x11171,x11172)+E(f272(x11171,x11173,x11174,x11175),f272(x11172,x11173,x11174,x11175))
% 28.25/28.14 [1118]~E(x11181,x11182)+E(f272(x11183,x11181,x11184,x11185),f272(x11183,x11182,x11184,x11185))
% 28.25/28.14 [1119]~E(x11191,x11192)+E(f272(x11193,x11194,x11191,x11195),f272(x11193,x11194,x11192,x11195))
% 28.25/28.14 [1120]~E(x11201,x11202)+E(f272(x11203,x11204,x11205,x11201),f272(x11203,x11204,x11205,x11202))
% 28.25/28.14 [1121]~E(x11211,x11212)+E(f495(x11211,x11213,x11214,x11215,x11216),f495(x11212,x11213,x11214,x11215,x11216))
% 28.25/28.14 [1122]~E(x11221,x11222)+E(f495(x11223,x11221,x11224,x11225,x11226),f495(x11223,x11222,x11224,x11225,x11226))
% 28.25/28.14 [1123]~E(x11231,x11232)+E(f495(x11233,x11234,x11231,x11235,x11236),f495(x11233,x11234,x11232,x11235,x11236))
% 28.25/28.14 [1124]~E(x11241,x11242)+E(f495(x11243,x11244,x11245,x11241,x11246),f495(x11243,x11244,x11245,x11242,x11246))
% 28.25/28.14 [1125]~E(x11251,x11252)+E(f495(x11253,x11254,x11255,x11256,x11251),f495(x11253,x11254,x11255,x11256,x11252))
% 28.25/28.14 [1126]~E(x11261,x11262)+E(f763(x11261,x11263,x11264,x11265,x11266),f763(x11262,x11263,x11264,x11265,x11266))
% 28.25/28.14 [1127]~E(x11271,x11272)+E(f763(x11273,x11271,x11274,x11275,x11276),f763(x11273,x11272,x11274,x11275,x11276))
% 28.25/28.14 [1128]~E(x11281,x11282)+E(f763(x11283,x11284,x11281,x11285,x11286),f763(x11283,x11284,x11282,x11285,x11286))
% 28.25/28.14 [1129]~E(x11291,x11292)+E(f763(x11293,x11294,x11295,x11291,x11296),f763(x11293,x11294,x11295,x11292,x11296))
% 28.25/28.14 [1130]~E(x11301,x11302)+E(f763(x11303,x11304,x11305,x11306,x11301),f763(x11303,x11304,x11305,x11306,x11302))
% 28.25/28.14 [1131]~E(x11311,x11312)+E(f845(x11311,x11313,x11314),f845(x11312,x11313,x11314))
% 28.25/28.14 [1132]~E(x11321,x11322)+E(f845(x11323,x11321,x11324),f845(x11323,x11322,x11324))
% 28.25/28.14 [1133]~E(x11331,x11332)+E(f845(x11333,x11334,x11331),f845(x11333,x11334,x11332))
% 28.25/28.14 [1134]~E(x11341,x11342)+E(f539(x11341,x11343,x11344),f539(x11342,x11343,x11344))
% 28.25/28.14 [1135]~E(x11351,x11352)+E(f539(x11353,x11351,x11354),f539(x11353,x11352,x11354))
% 28.25/28.14 [1136]~E(x11361,x11362)+E(f539(x11363,x11364,x11361),f539(x11363,x11364,x11362))
% 28.25/28.14 [1137]~E(x11371,x11372)+E(f215(x11371,x11373,x11374,x11375,x11376),f215(x11372,x11373,x11374,x11375,x11376))
% 28.25/28.14 [1138]~E(x11381,x11382)+E(f215(x11383,x11381,x11384,x11385,x11386),f215(x11383,x11382,x11384,x11385,x11386))
% 28.25/28.14 [1139]~E(x11391,x11392)+E(f215(x11393,x11394,x11391,x11395,x11396),f215(x11393,x11394,x11392,x11395,x11396))
% 28.25/28.14 [1140]~E(x11401,x11402)+E(f215(x11403,x11404,x11405,x11401,x11406),f215(x11403,x11404,x11405,x11402,x11406))
% 28.25/28.14 [1141]~E(x11411,x11412)+E(f215(x11413,x11414,x11415,x11416,x11411),f215(x11413,x11414,x11415,x11416,x11412))
% 28.25/28.14 [1142]~E(x11421,x11422)+E(f392(x11421,x11423,x11424,x11425,x11426),f392(x11422,x11423,x11424,x11425,x11426))
% 28.25/28.14 [1143]~E(x11431,x11432)+E(f392(x11433,x11431,x11434,x11435,x11436),f392(x11433,x11432,x11434,x11435,x11436))
% 28.25/28.14 [1144]~E(x11441,x11442)+E(f392(x11443,x11444,x11441,x11445,x11446),f392(x11443,x11444,x11442,x11445,x11446))
% 28.25/28.14 [1145]~E(x11451,x11452)+E(f392(x11453,x11454,x11455,x11451,x11456),f392(x11453,x11454,x11455,x11452,x11456))
% 28.25/28.14 [1146]~E(x11461,x11462)+E(f392(x11463,x11464,x11465,x11466,x11461),f392(x11463,x11464,x11465,x11466,x11462))
% 28.25/28.14 [1147]~E(x11471,x11472)+E(f473(x11471,x11473,x11474),f473(x11472,x11473,x11474))
% 28.25/28.14 [1148]~E(x11481,x11482)+E(f473(x11483,x11481,x11484),f473(x11483,x11482,x11484))
% 28.25/28.14 [1149]~E(x11491,x11492)+E(f473(x11493,x11494,x11491),f473(x11493,x11494,x11492))
% 28.25/28.14 [1150]~E(x11501,x11502)+E(f618(x11501,x11503,x11504,x11505),f618(x11502,x11503,x11504,x11505))
% 28.25/28.14 [1151]~E(x11511,x11512)+E(f618(x11513,x11511,x11514,x11515),f618(x11513,x11512,x11514,x11515))
% 28.25/28.14 [1152]~E(x11521,x11522)+E(f618(x11523,x11524,x11521,x11525),f618(x11523,x11524,x11522,x11525))
% 28.25/28.14 [1153]~E(x11531,x11532)+E(f618(x11533,x11534,x11535,x11531),f618(x11533,x11534,x11535,x11532))
% 28.25/28.14 [1154]~E(x11541,x11542)+E(f730(x11541,x11543),f730(x11542,x11543))
% 28.25/28.14 [1155]~E(x11551,x11552)+E(f730(x11553,x11551),f730(x11553,x11552))
% 28.25/28.14 [1156]~E(x11561,x11562)+E(f808(x11561,x11563),f808(x11562,x11563))
% 28.25/28.14 [1157]~E(x11571,x11572)+E(f808(x11573,x11571),f808(x11573,x11572))
% 28.25/28.14 [1158]~E(x11581,x11582)+E(f361(x11581,x11583),f361(x11582,x11583))
% 28.25/28.14 [1159]~E(x11591,x11592)+E(f361(x11593,x11591),f361(x11593,x11592))
% 28.25/28.14 [1160]~E(x11601,x11602)+E(f833(x11601),f833(x11602))
% 28.25/28.14 [1161]~E(x11611,x11612)+E(f142(x11611,x11613,x11614,x11615),f142(x11612,x11613,x11614,x11615))
% 28.25/28.14 [1162]~E(x11621,x11622)+E(f142(x11623,x11621,x11624,x11625),f142(x11623,x11622,x11624,x11625))
% 28.25/28.14 [1163]~E(x11631,x11632)+E(f142(x11633,x11634,x11631,x11635),f142(x11633,x11634,x11632,x11635))
% 28.25/28.14 [1164]~E(x11641,x11642)+E(f142(x11643,x11644,x11645,x11641),f142(x11643,x11644,x11645,x11642))
% 28.25/28.14 [1165]~E(x11651,x11652)+E(f512(x11651,x11653,x11654),f512(x11652,x11653,x11654))
% 28.25/28.14 [1166]~E(x11661,x11662)+E(f512(x11663,x11661,x11664),f512(x11663,x11662,x11664))
% 28.25/28.14 [1167]~E(x11671,x11672)+E(f512(x11673,x11674,x11671),f512(x11673,x11674,x11672))
% 28.25/28.14 [1168]~E(x11681,x11682)+E(f191(x11681,x11683),f191(x11682,x11683))
% 28.25/28.14 [1169]~E(x11691,x11692)+E(f191(x11693,x11691),f191(x11693,x11692))
% 28.25/28.14 [1170]~E(x11701,x11702)+E(f602(x11701,x11703,x11704,x11705),f602(x11702,x11703,x11704,x11705))
% 28.25/28.14 [1171]~E(x11711,x11712)+E(f602(x11713,x11711,x11714,x11715),f602(x11713,x11712,x11714,x11715))
% 28.25/28.14 [1172]~E(x11721,x11722)+E(f602(x11723,x11724,x11721,x11725),f602(x11723,x11724,x11722,x11725))
% 28.25/28.14 [1173]~E(x11731,x11732)+E(f602(x11733,x11734,x11735,x11731),f602(x11733,x11734,x11735,x11732))
% 28.25/28.14 [1174]~E(x11741,x11742)+E(f282(x11741,x11743,x11744,x11745),f282(x11742,x11743,x11744,x11745))
% 28.25/28.14 [1175]~E(x11751,x11752)+E(f282(x11753,x11751,x11754,x11755),f282(x11753,x11752,x11754,x11755))
% 28.25/28.14 [1176]~E(x11761,x11762)+E(f282(x11763,x11764,x11761,x11765),f282(x11763,x11764,x11762,x11765))
% 28.25/28.14 [1177]~E(x11771,x11772)+E(f282(x11773,x11774,x11775,x11771),f282(x11773,x11774,x11775,x11772))
% 28.25/28.14 [1178]~E(x11781,x11782)+E(f565(x11781,x11783),f565(x11782,x11783))
% 28.25/28.14 [1179]~E(x11791,x11792)+E(f565(x11793,x11791),f565(x11793,x11792))
% 28.25/28.14 [1180]~E(x11801,x11802)+E(f485(x11801,x11803,x11804),f485(x11802,x11803,x11804))
% 28.25/28.14 [1181]~E(x11811,x11812)+E(f485(x11813,x11811,x11814),f485(x11813,x11812,x11814))
% 28.25/28.14 [1182]~E(x11821,x11822)+E(f485(x11823,x11824,x11821),f485(x11823,x11824,x11822))
% 28.25/28.14 [1183]~E(x11831,x11832)+E(f36(x11831),f36(x11832))
% 28.25/28.14 [1184]~E(x11841,x11842)+E(f431(x11841),f431(x11842))
% 28.25/28.14 [1185]~E(x11851,x11852)+E(f752(x11851,x11853),f752(x11852,x11853))
% 28.25/28.14 [1186]~E(x11861,x11862)+E(f752(x11863,x11861),f752(x11863,x11862))
% 28.25/28.14 [1187]~E(x11871,x11872)+E(f207(x11871,x11873),f207(x11872,x11873))
% 28.25/28.14 [1188]~E(x11881,x11882)+E(f207(x11883,x11881),f207(x11883,x11882))
% 28.25/28.14 [1189]~E(x11891,x11892)+E(f879(x11891,x11893,x11894),f879(x11892,x11893,x11894))
% 28.25/28.14 [1190]~E(x11901,x11902)+E(f879(x11903,x11901,x11904),f879(x11903,x11902,x11904))
% 28.25/28.14 [1191]~E(x11911,x11912)+E(f879(x11913,x11914,x11911),f879(x11913,x11914,x11912))
% 28.25/28.14 [1192]~E(x11921,x11922)+E(f853(x11921,x11923,x11924,x11925,x11926,x11927,x11928,x11929),f853(x11922,x11923,x11924,x11925,x11926,x11927,x11928,x11929))
% 28.25/28.14 [1193]~E(x11931,x11932)+E(f853(x11933,x11931,x11934,x11935,x11936,x11937,x11938,x11939),f853(x11933,x11932,x11934,x11935,x11936,x11937,x11938,x11939))
% 28.25/28.14 [1194]~E(x11941,x11942)+E(f853(x11943,x11944,x11941,x11945,x11946,x11947,x11948,x11949),f853(x11943,x11944,x11942,x11945,x11946,x11947,x11948,x11949))
% 28.25/28.14 [1195]~E(x11951,x11952)+E(f853(x11953,x11954,x11955,x11951,x11956,x11957,x11958,x11959),f853(x11953,x11954,x11955,x11952,x11956,x11957,x11958,x11959))
% 28.25/28.14 [1196]~E(x11961,x11962)+E(f853(x11963,x11964,x11965,x11966,x11961,x11967,x11968,x11969),f853(x11963,x11964,x11965,x11966,x11962,x11967,x11968,x11969))
% 28.25/28.14 [1197]~E(x11971,x11972)+E(f853(x11973,x11974,x11975,x11976,x11977,x11971,x11978,x11979),f853(x11973,x11974,x11975,x11976,x11977,x11972,x11978,x11979))
% 28.25/28.14 [1198]~E(x11981,x11982)+E(f853(x11983,x11984,x11985,x11986,x11987,x11988,x11981,x11989),f853(x11983,x11984,x11985,x11986,x11987,x11988,x11982,x11989))
% 28.25/28.14 [1199]~E(x11991,x11992)+E(f853(x11993,x11994,x11995,x11996,x11997,x11998,x11999,x11991),f853(x11993,x11994,x11995,x11996,x11997,x11998,x11999,x11992))
% 28.25/28.14 [1200]~E(x12001,x12002)+E(f70(x12001,x12003,x12004,x12005,x12006),f70(x12002,x12003,x12004,x12005,x12006))
% 28.25/28.14 [1201]~E(x12011,x12012)+E(f70(x12013,x12011,x12014,x12015,x12016),f70(x12013,x12012,x12014,x12015,x12016))
% 28.25/28.14 [1202]~E(x12021,x12022)+E(f70(x12023,x12024,x12021,x12025,x12026),f70(x12023,x12024,x12022,x12025,x12026))
% 28.25/28.14 [1203]~E(x12031,x12032)+E(f70(x12033,x12034,x12035,x12031,x12036),f70(x12033,x12034,x12035,x12032,x12036))
% 28.25/28.14 [1204]~E(x12041,x12042)+E(f70(x12043,x12044,x12045,x12046,x12041),f70(x12043,x12044,x12045,x12046,x12042))
% 28.25/28.14 [1205]~E(x12051,x12052)+E(f357(x12051,x12053,x12054),f357(x12052,x12053,x12054))
% 28.25/28.14 [1206]~E(x12061,x12062)+E(f357(x12063,x12061,x12064),f357(x12063,x12062,x12064))
% 28.25/28.14 [1207]~E(x12071,x12072)+E(f357(x12073,x12074,x12071),f357(x12073,x12074,x12072))
% 28.25/28.14 [1208]~E(x12081,x12082)+E(f731(x12081,x12083),f731(x12082,x12083))
% 28.25/28.14 [1209]~E(x12091,x12092)+E(f731(x12093,x12091),f731(x12093,x12092))
% 28.25/28.14 [1210]~E(x12101,x12102)+E(f492(x12101,x12103,x12104,x12105,x12106),f492(x12102,x12103,x12104,x12105,x12106))
% 28.25/28.14 [1211]~E(x12111,x12112)+E(f492(x12113,x12111,x12114,x12115,x12116),f492(x12113,x12112,x12114,x12115,x12116))
% 28.25/28.14 [1212]~E(x12121,x12122)+E(f492(x12123,x12124,x12121,x12125,x12126),f492(x12123,x12124,x12122,x12125,x12126))
% 28.25/28.14 [1213]~E(x12131,x12132)+E(f492(x12133,x12134,x12135,x12131,x12136),f492(x12133,x12134,x12135,x12132,x12136))
% 28.25/28.14 [1214]~E(x12141,x12142)+E(f492(x12143,x12144,x12145,x12146,x12141),f492(x12143,x12144,x12145,x12146,x12142))
% 28.25/28.14 [1215]~E(x12151,x12152)+E(f269(x12151,x12153,x12154,x12155),f269(x12152,x12153,x12154,x12155))
% 28.25/28.14 [1216]~E(x12161,x12162)+E(f269(x12163,x12161,x12164,x12165),f269(x12163,x12162,x12164,x12165))
% 28.25/28.14 [1217]~E(x12171,x12172)+E(f269(x12173,x12174,x12171,x12175),f269(x12173,x12174,x12172,x12175))
% 28.25/28.14 [1218]~E(x12181,x12182)+E(f269(x12183,x12184,x12185,x12181),f269(x12183,x12184,x12185,x12182))
% 28.25/28.14 [1219]~E(x12191,x12192)+E(f165(x12191,x12193,x12194),f165(x12192,x12193,x12194))
% 28.25/28.14 [1220]~E(x12201,x12202)+E(f165(x12203,x12201,x12204),f165(x12203,x12202,x12204))
% 28.25/28.14 [1221]~E(x12211,x12212)+E(f165(x12213,x12214,x12211),f165(x12213,x12214,x12212))
% 28.25/28.14 [1222]~E(x12221,x12222)+E(f154(x12221,x12223),f154(x12222,x12223))
% 28.25/28.14 [1223]~E(x12231,x12232)+E(f154(x12233,x12231),f154(x12233,x12232))
% 28.25/28.14 [1224]~E(x12241,x12242)+E(f382(x12241,x12243,x12244,x12245,x12246),f382(x12242,x12243,x12244,x12245,x12246))
% 28.25/28.14 [1225]~E(x12251,x12252)+E(f382(x12253,x12251,x12254,x12255,x12256),f382(x12253,x12252,x12254,x12255,x12256))
% 28.25/28.14 [1226]~E(x12261,x12262)+E(f382(x12263,x12264,x12261,x12265,x12266),f382(x12263,x12264,x12262,x12265,x12266))
% 28.25/28.14 [1227]~E(x12271,x12272)+E(f382(x12273,x12274,x12275,x12271,x12276),f382(x12273,x12274,x12275,x12272,x12276))
% 28.25/28.14 [1228]~E(x12281,x12282)+E(f382(x12283,x12284,x12285,x12286,x12281),f382(x12283,x12284,x12285,x12286,x12282))
% 28.25/28.14 [1229]~E(x12291,x12292)+E(f148(x12291,x12293,x12294,x12295),f148(x12292,x12293,x12294,x12295))
% 28.25/28.14 [1230]~E(x12301,x12302)+E(f148(x12303,x12301,x12304,x12305),f148(x12303,x12302,x12304,x12305))
% 28.25/28.14 [1231]~E(x12311,x12312)+E(f148(x12313,x12314,x12311,x12315),f148(x12313,x12314,x12312,x12315))
% 28.25/28.14 [1232]~E(x12321,x12322)+E(f148(x12323,x12324,x12325,x12321),f148(x12323,x12324,x12325,x12322))
% 28.25/28.14 [1233]~E(x12331,x12332)+E(f108(x12331,x12333,x12334),f108(x12332,x12333,x12334))
% 28.25/28.14 [1234]~E(x12341,x12342)+E(f108(x12343,x12341,x12344),f108(x12343,x12342,x12344))
% 28.25/28.14 [1235]~E(x12351,x12352)+E(f108(x12353,x12354,x12351),f108(x12353,x12354,x12352))
% 28.25/28.14 [1236]~E(x12361,x12362)+E(f660(x12361,x12363,x12364),f660(x12362,x12363,x12364))
% 28.25/28.14 [1237]~E(x12371,x12372)+E(f660(x12373,x12371,x12374),f660(x12373,x12372,x12374))
% 28.25/28.14 [1238]~E(x12381,x12382)+E(f660(x12383,x12384,x12381),f660(x12383,x12384,x12382))
% 28.25/28.14 [1239]~E(x12391,x12392)+E(f764(x12391,x12393,x12394,x12395,x12396),f764(x12392,x12393,x12394,x12395,x12396))
% 28.25/28.14 [1240]~E(x12401,x12402)+E(f764(x12403,x12401,x12404,x12405,x12406),f764(x12403,x12402,x12404,x12405,x12406))
% 28.25/28.14 [1241]~E(x12411,x12412)+E(f764(x12413,x12414,x12411,x12415,x12416),f764(x12413,x12414,x12412,x12415,x12416))
% 28.25/28.14 [1242]~E(x12421,x12422)+E(f764(x12423,x12424,x12425,x12421,x12426),f764(x12423,x12424,x12425,x12422,x12426))
% 28.25/28.14 [1243]~E(x12431,x12432)+E(f764(x12433,x12434,x12435,x12436,x12431),f764(x12433,x12434,x12435,x12436,x12432))
% 28.25/28.14 [1244]~E(x12441,x12442)+E(f872(x12441,x12443,x12444),f872(x12442,x12443,x12444))
% 28.25/28.14 [1245]~E(x12451,x12452)+E(f872(x12453,x12451,x12454),f872(x12453,x12452,x12454))
% 28.25/28.14 [1246]~E(x12461,x12462)+E(f872(x12463,x12464,x12461),f872(x12463,x12464,x12462))
% 28.25/28.14 [1247]~E(x12471,x12472)+E(f696(x12471,x12473,x12474),f696(x12472,x12473,x12474))
% 28.25/28.14 [1248]~E(x12481,x12482)+E(f696(x12483,x12481,x12484),f696(x12483,x12482,x12484))
% 28.25/28.14 [1249]~E(x12491,x12492)+E(f696(x12493,x12494,x12491),f696(x12493,x12494,x12492))
% 28.25/28.14 [1250]~E(x12501,x12502)+E(f339(x12501,x12503,x12504,x12505),f339(x12502,x12503,x12504,x12505))
% 28.25/28.14 [1251]~E(x12511,x12512)+E(f339(x12513,x12511,x12514,x12515),f339(x12513,x12512,x12514,x12515))
% 28.25/28.14 [1252]~E(x12521,x12522)+E(f339(x12523,x12524,x12521,x12525),f339(x12523,x12524,x12522,x12525))
% 28.25/28.14 [1253]~E(x12531,x12532)+E(f339(x12533,x12534,x12535,x12531),f339(x12533,x12534,x12535,x12532))
% 28.25/28.14 [1254]~E(x12541,x12542)+E(f363(x12541,x12543),f363(x12542,x12543))
% 28.25/28.14 [1255]~E(x12551,x12552)+E(f363(x12553,x12551),f363(x12553,x12552))
% 28.25/28.14 [1256]~E(x12561,x12562)+E(f519(x12561,x12563,x12564),f519(x12562,x12563,x12564))
% 28.25/28.14 [1257]~E(x12571,x12572)+E(f519(x12573,x12571,x12574),f519(x12573,x12572,x12574))
% 28.25/28.14 [1258]~E(x12581,x12582)+E(f519(x12583,x12584,x12581),f519(x12583,x12584,x12582))
% 28.25/28.14 [1259]~E(x12591,x12592)+E(f554(x12591),f554(x12592))
% 28.25/28.14 [1260]~E(x12601,x12602)+E(f832(x12601,x12603,x12604,x12605,x12606,x12607),f832(x12602,x12603,x12604,x12605,x12606,x12607))
% 28.25/28.14 [1261]~E(x12611,x12612)+E(f832(x12613,x12611,x12614,x12615,x12616,x12617),f832(x12613,x12612,x12614,x12615,x12616,x12617))
% 28.25/28.14 [1262]~E(x12621,x12622)+E(f832(x12623,x12624,x12621,x12625,x12626,x12627),f832(x12623,x12624,x12622,x12625,x12626,x12627))
% 28.25/28.14 [1263]~E(x12631,x12632)+E(f832(x12633,x12634,x12635,x12631,x12636,x12637),f832(x12633,x12634,x12635,x12632,x12636,x12637))
% 28.25/28.14 [1264]~E(x12641,x12642)+E(f832(x12643,x12644,x12645,x12646,x12641,x12647),f832(x12643,x12644,x12645,x12646,x12642,x12647))
% 28.25/28.14 [1265]~E(x12651,x12652)+E(f832(x12653,x12654,x12655,x12656,x12657,x12651),f832(x12653,x12654,x12655,x12656,x12657,x12652))
% 28.25/28.14 [1266]~E(x12661,x12662)+E(f657(x12661,x12663,x12664,x12665),f657(x12662,x12663,x12664,x12665))
% 28.25/28.14 [1267]~E(x12671,x12672)+E(f657(x12673,x12671,x12674,x12675),f657(x12673,x12672,x12674,x12675))
% 28.25/28.14 [1268]~E(x12681,x12682)+E(f657(x12683,x12684,x12681,x12685),f657(x12683,x12684,x12682,x12685))
% 28.25/28.14 [1269]~E(x12691,x12692)+E(f657(x12693,x12694,x12695,x12691),f657(x12693,x12694,x12695,x12692))
% 28.25/28.14 [1270]~E(x12701,x12702)+E(f469(x12701,x12703,x12704),f469(x12702,x12703,x12704))
% 28.25/28.14 [1271]~E(x12711,x12712)+E(f469(x12713,x12711,x12714),f469(x12713,x12712,x12714))
% 28.25/28.14 [1272]~E(x12721,x12722)+E(f469(x12723,x12724,x12721),f469(x12723,x12724,x12722))
% 28.25/28.14 [1273]~E(x12731,x12732)+E(f285(x12731,x12733),f285(x12732,x12733))
% 28.25/28.14 [1274]~E(x12741,x12742)+E(f285(x12743,x12741),f285(x12743,x12742))
% 28.25/28.14 [1275]~E(x12751,x12752)+E(f475(x12751,x12753,x12754),f475(x12752,x12753,x12754))
% 28.25/28.14 [1276]~E(x12761,x12762)+E(f475(x12763,x12761,x12764),f475(x12763,x12762,x12764))
% 28.25/28.14 [1277]~E(x12771,x12772)+E(f475(x12773,x12774,x12771),f475(x12773,x12774,x12772))
% 28.25/28.14 [1278]~E(x12781,x12782)+E(f47(x12781,x12783),f47(x12782,x12783))
% 28.25/28.14 [1279]~E(x12791,x12792)+E(f47(x12793,x12791),f47(x12793,x12792))
% 28.25/28.14 [1280]~E(x12801,x12802)+E(f612(x12801,x12803,x12804),f612(x12802,x12803,x12804))
% 28.25/28.14 [1281]~E(x12811,x12812)+E(f612(x12813,x12811,x12814),f612(x12813,x12812,x12814))
% 28.25/28.14 [1282]~E(x12821,x12822)+E(f612(x12823,x12824,x12821),f612(x12823,x12824,x12822))
% 28.25/28.14 [1283]~E(x12831,x12832)+E(f687(x12831,x12833),f687(x12832,x12833))
% 28.25/28.14 [1284]~E(x12841,x12842)+E(f687(x12843,x12841),f687(x12843,x12842))
% 28.25/28.14 [1285]~E(x12851,x12852)+E(f448(x12851,x12853,x12854),f448(x12852,x12853,x12854))
% 28.25/28.14 [1286]~E(x12861,x12862)+E(f448(x12863,x12861,x12864),f448(x12863,x12862,x12864))
% 28.25/28.14 [1287]~E(x12871,x12872)+E(f448(x12873,x12874,x12871),f448(x12873,x12874,x12872))
% 28.25/28.14 [1288]~E(x12881,x12882)+E(f777(x12881,x12883,x12884),f777(x12882,x12883,x12884))
% 28.25/28.14 [1289]~E(x12891,x12892)+E(f777(x12893,x12891,x12894),f777(x12893,x12892,x12894))
% 28.25/28.14 [1290]~E(x12901,x12902)+E(f777(x12903,x12904,x12901),f777(x12903,x12904,x12902))
% 28.25/28.14 [1291]~E(x12911,x12912)+E(f611(x12911,x12913,x12914),f611(x12912,x12913,x12914))
% 28.25/28.14 [1292]~E(x12921,x12922)+E(f611(x12923,x12921,x12924),f611(x12923,x12922,x12924))
% 28.25/28.14 [1293]~E(x12931,x12932)+E(f611(x12933,x12934,x12931),f611(x12933,x12934,x12932))
% 28.25/28.14 [1294]~E(x12941,x12942)+E(f893(x12941,x12943,x12944,x12945,x12946),f893(x12942,x12943,x12944,x12945,x12946))
% 28.25/28.14 [1295]~E(x12951,x12952)+E(f893(x12953,x12951,x12954,x12955,x12956),f893(x12953,x12952,x12954,x12955,x12956))
% 28.25/28.14 [1296]~E(x12961,x12962)+E(f893(x12963,x12964,x12961,x12965,x12966),f893(x12963,x12964,x12962,x12965,x12966))
% 28.25/28.14 [1297]~E(x12971,x12972)+E(f893(x12973,x12974,x12975,x12971,x12976),f893(x12973,x12974,x12975,x12972,x12976))
% 28.25/28.14 [1298]~E(x12981,x12982)+E(f893(x12983,x12984,x12985,x12986,x12981),f893(x12983,x12984,x12985,x12986,x12982))
% 28.25/28.14 [1299]~E(x12991,x12992)+E(f399(x12991,x12993,x12994,x12995),f399(x12992,x12993,x12994,x12995))
% 28.25/28.14 [1300]~E(x13001,x13002)+E(f399(x13003,x13001,x13004,x13005),f399(x13003,x13002,x13004,x13005))
% 28.25/28.14 [1301]~E(x13011,x13012)+E(f399(x13013,x13014,x13011,x13015),f399(x13013,x13014,x13012,x13015))
% 28.25/28.14 [1302]~E(x13021,x13022)+E(f399(x13023,x13024,x13025,x13021),f399(x13023,x13024,x13025,x13022))
% 28.25/28.14 [1303]~E(x13031,x13032)+E(f262(x13031,x13033),f262(x13032,x13033))
% 28.25/28.14 [1304]~E(x13041,x13042)+E(f262(x13043,x13041),f262(x13043,x13042))
% 28.25/28.14 [1305]~E(x13051,x13052)+E(f695(x13051,x13053,x13054),f695(x13052,x13053,x13054))
% 28.25/28.14 [1306]~E(x13061,x13062)+E(f695(x13063,x13061,x13064),f695(x13063,x13062,x13064))
% 28.25/28.14 [1307]~E(x13071,x13072)+E(f695(x13073,x13074,x13071),f695(x13073,x13074,x13072))
% 28.25/28.14 [1308]~E(x13081,x13082)+E(f779(x13081,x13083,x13084),f779(x13082,x13083,x13084))
% 28.25/28.14 [1309]~E(x13091,x13092)+E(f779(x13093,x13091,x13094),f779(x13093,x13092,x13094))
% 28.25/28.14 [1310]~E(x13101,x13102)+E(f779(x13103,x13104,x13101),f779(x13103,x13104,x13102))
% 28.25/28.14 [1311]~E(x13111,x13112)+E(f810(x13111,x13113,x13114,x13115,x13116,x13117,x13118),f810(x13112,x13113,x13114,x13115,x13116,x13117,x13118))
% 28.25/28.14 [1312]~E(x13121,x13122)+E(f810(x13123,x13121,x13124,x13125,x13126,x13127,x13128),f810(x13123,x13122,x13124,x13125,x13126,x13127,x13128))
% 28.25/28.14 [1313]~E(x13131,x13132)+E(f810(x13133,x13134,x13131,x13135,x13136,x13137,x13138),f810(x13133,x13134,x13132,x13135,x13136,x13137,x13138))
% 28.25/28.14 [1314]~E(x13141,x13142)+E(f810(x13143,x13144,x13145,x13141,x13146,x13147,x13148),f810(x13143,x13144,x13145,x13142,x13146,x13147,x13148))
% 28.25/28.14 [1315]~E(x13151,x13152)+E(f810(x13153,x13154,x13155,x13156,x13151,x13157,x13158),f810(x13153,x13154,x13155,x13156,x13152,x13157,x13158))
% 28.25/28.14 [1316]~E(x13161,x13162)+E(f810(x13163,x13164,x13165,x13166,x13167,x13161,x13168),f810(x13163,x13164,x13165,x13166,x13167,x13162,x13168))
% 28.25/28.14 [1317]~E(x13171,x13172)+E(f810(x13173,x13174,x13175,x13176,x13177,x13178,x13171),f810(x13173,x13174,x13175,x13176,x13177,x13178,x13172))
% 28.25/28.14 [1318]~E(x13181,x13182)+E(f414(x13181,x13183,x13184,x13185,x13186,x13187),f414(x13182,x13183,x13184,x13185,x13186,x13187))
% 28.25/28.14 [1319]~E(x13191,x13192)+E(f414(x13193,x13191,x13194,x13195,x13196,x13197),f414(x13193,x13192,x13194,x13195,x13196,x13197))
% 28.25/28.14 [1320]~E(x13201,x13202)+E(f414(x13203,x13204,x13201,x13205,x13206,x13207),f414(x13203,x13204,x13202,x13205,x13206,x13207))
% 28.25/28.14 [1321]~E(x13211,x13212)+E(f414(x13213,x13214,x13215,x13211,x13216,x13217),f414(x13213,x13214,x13215,x13212,x13216,x13217))
% 28.25/28.14 [1322]~E(x13221,x13222)+E(f414(x13223,x13224,x13225,x13226,x13221,x13227),f414(x13223,x13224,x13225,x13226,x13222,x13227))
% 28.25/28.14 [1323]~E(x13231,x13232)+E(f414(x13233,x13234,x13235,x13236,x13237,x13231),f414(x13233,x13234,x13235,x13236,x13237,x13232))
% 28.25/28.14 [1324]~E(x13241,x13242)+E(f542(x13241,x13243,x13244),f542(x13242,x13243,x13244))
% 28.25/28.14 [1325]~E(x13251,x13252)+E(f542(x13253,x13251,x13254),f542(x13253,x13252,x13254))
% 28.25/28.14 [1326]~E(x13261,x13262)+E(f542(x13263,x13264,x13261),f542(x13263,x13264,x13262))
% 28.25/28.14 [1327]~E(x13271,x13272)+E(f719(x13271,x13273,x13274,x13275),f719(x13272,x13273,x13274,x13275))
% 28.25/28.14 [1328]~E(x13281,x13282)+E(f719(x13283,x13281,x13284,x13285),f719(x13283,x13282,x13284,x13285))
% 28.25/28.14 [1329]~E(x13291,x13292)+E(f719(x13293,x13294,x13291,x13295),f719(x13293,x13294,x13292,x13295))
% 28.25/28.14 [1330]~E(x13301,x13302)+E(f719(x13303,x13304,x13305,x13301),f719(x13303,x13304,x13305,x13302))
% 28.25/28.14 [1331]~E(x13311,x13312)+E(f289(x13311,x13313,x13314,x13315,x13316),f289(x13312,x13313,x13314,x13315,x13316))
% 28.25/28.14 [1332]~E(x13321,x13322)+E(f289(x13323,x13321,x13324,x13325,x13326),f289(x13323,x13322,x13324,x13325,x13326))
% 28.25/28.14 [1333]~E(x13331,x13332)+E(f289(x13333,x13334,x13331,x13335,x13336),f289(x13333,x13334,x13332,x13335,x13336))
% 28.25/28.14 [1334]~E(x13341,x13342)+E(f289(x13343,x13344,x13345,x13341,x13346),f289(x13343,x13344,x13345,x13342,x13346))
% 28.25/28.14 [1335]~E(x13351,x13352)+E(f289(x13353,x13354,x13355,x13356,x13351),f289(x13353,x13354,x13355,x13356,x13352))
% 28.25/28.14 [1336]~E(x13361,x13362)+E(f385(x13361,x13363,x13364,x13365),f385(x13362,x13363,x13364,x13365))
% 28.25/28.14 [1337]~E(x13371,x13372)+E(f385(x13373,x13371,x13374,x13375),f385(x13373,x13372,x13374,x13375))
% 28.25/28.14 [1338]~E(x13381,x13382)+E(f385(x13383,x13384,x13381,x13385),f385(x13383,x13384,x13382,x13385))
% 28.25/28.14 [1339]~E(x13391,x13392)+E(f385(x13393,x13394,x13395,x13391),f385(x13393,x13394,x13395,x13392))
% 28.25/28.14 [1340]~E(x13401,x13402)+E(f265(x13401,x13403,x13404,x13405),f265(x13402,x13403,x13404,x13405))
% 28.25/28.14 [1341]~E(x13411,x13412)+E(f265(x13413,x13411,x13414,x13415),f265(x13413,x13412,x13414,x13415))
% 28.25/28.14 [1342]~E(x13421,x13422)+E(f265(x13423,x13424,x13421,x13425),f265(x13423,x13424,x13422,x13425))
% 28.25/28.14 [1343]~E(x13431,x13432)+E(f265(x13433,x13434,x13435,x13431),f265(x13433,x13434,x13435,x13432))
% 28.25/28.14 [1344]~E(x13441,x13442)+E(f405(x13441,x13443,x13444,x13445),f405(x13442,x13443,x13444,x13445))
% 28.25/28.14 [1345]~E(x13451,x13452)+E(f405(x13453,x13451,x13454,x13455),f405(x13453,x13452,x13454,x13455))
% 28.25/28.14 [1346]~E(x13461,x13462)+E(f405(x13463,x13464,x13461,x13465),f405(x13463,x13464,x13462,x13465))
% 28.25/28.14 [1347]~E(x13471,x13472)+E(f405(x13473,x13474,x13475,x13471),f405(x13473,x13474,x13475,x13472))
% 28.25/28.14 [1348]~E(x13481,x13482)+E(f158(x13481,x13483,x13484),f158(x13482,x13483,x13484))
% 28.25/28.14 [1349]~E(x13491,x13492)+E(f158(x13493,x13491,x13494),f158(x13493,x13492,x13494))
% 28.25/28.14 [1350]~E(x13501,x13502)+E(f158(x13503,x13504,x13501),f158(x13503,x13504,x13502))
% 28.25/28.14 [1351]~E(x13511,x13512)+E(f715(x13511,x13513,x13514,x13515,x13516),f715(x13512,x13513,x13514,x13515,x13516))
% 28.25/28.14 [1352]~E(x13521,x13522)+E(f715(x13523,x13521,x13524,x13525,x13526),f715(x13523,x13522,x13524,x13525,x13526))
% 28.25/28.14 [1353]~E(x13531,x13532)+E(f715(x13533,x13534,x13531,x13535,x13536),f715(x13533,x13534,x13532,x13535,x13536))
% 28.25/28.14 [1354]~E(x13541,x13542)+E(f715(x13543,x13544,x13545,x13541,x13546),f715(x13543,x13544,x13545,x13542,x13546))
% 28.25/28.14 [1355]~E(x13551,x13552)+E(f715(x13553,x13554,x13555,x13556,x13551),f715(x13553,x13554,x13555,x13556,x13552))
% 28.25/28.14 [1356]~E(x13561,x13562)+E(f617(x13561,x13563,x13564,x13565),f617(x13562,x13563,x13564,x13565))
% 28.25/28.14 [1357]~E(x13571,x13572)+E(f617(x13573,x13571,x13574,x13575),f617(x13573,x13572,x13574,x13575))
% 28.25/28.14 [1358]~E(x13581,x13582)+E(f617(x13583,x13584,x13581,x13585),f617(x13583,x13584,x13582,x13585))
% 28.25/28.14 [1359]~E(x13591,x13592)+E(f617(x13593,x13594,x13595,x13591),f617(x13593,x13594,x13595,x13592))
% 28.25/28.14 [1360]~E(x13601,x13602)+E(f828(x13601),f828(x13602))
% 28.25/28.14 [1361]~E(x13611,x13612)+E(f570(x13611,x13613,x13614,x13615),f570(x13612,x13613,x13614,x13615))
% 28.25/28.14 [1362]~E(x13621,x13622)+E(f570(x13623,x13621,x13624,x13625),f570(x13623,x13622,x13624,x13625))
% 28.25/28.14 [1363]~E(x13631,x13632)+E(f570(x13633,x13634,x13631,x13635),f570(x13633,x13634,x13632,x13635))
% 28.25/28.14 [1364]~E(x13641,x13642)+E(f570(x13643,x13644,x13645,x13641),f570(x13643,x13644,x13645,x13642))
% 28.25/28.14 [1365]~E(x13651,x13652)+E(f403(x13651,x13653,x13654,x13655),f403(x13652,x13653,x13654,x13655))
% 28.25/28.14 [1366]~E(x13661,x13662)+E(f403(x13663,x13661,x13664,x13665),f403(x13663,x13662,x13664,x13665))
% 28.25/28.14 [1367]~E(x13671,x13672)+E(f403(x13673,x13674,x13671,x13675),f403(x13673,x13674,x13672,x13675))
% 28.25/28.14 [1368]~E(x13681,x13682)+E(f403(x13683,x13684,x13685,x13681),f403(x13683,x13684,x13685,x13682))
% 28.25/28.14 [1369]~E(x13691,x13692)+E(f201(x13691,x13693,x13694,x13695),f201(x13692,x13693,x13694,x13695))
% 28.25/28.14 [1370]~E(x13701,x13702)+E(f201(x13703,x13701,x13704,x13705),f201(x13703,x13702,x13704,x13705))
% 28.25/28.14 [1371]~E(x13711,x13712)+E(f201(x13713,x13714,x13711,x13715),f201(x13713,x13714,x13712,x13715))
% 28.25/28.14 [1372]~E(x13721,x13722)+E(f201(x13723,x13724,x13725,x13721),f201(x13723,x13724,x13725,x13722))
% 28.25/28.14 [1373]~E(x13731,x13732)+E(f883(x13731,x13733,x13734),f883(x13732,x13733,x13734))
% 28.25/28.14 [1374]~E(x13741,x13742)+E(f883(x13743,x13741,x13744),f883(x13743,x13742,x13744))
% 28.25/28.14 [1375]~E(x13751,x13752)+E(f883(x13753,x13754,x13751),f883(x13753,x13754,x13752))
% 28.25/28.14 [1376]~E(x13761,x13762)+E(f390(x13761,x13763),f390(x13762,x13763))
% 28.25/28.14 [1377]~E(x13771,x13772)+E(f390(x13773,x13771),f390(x13773,x13772))
% 28.25/28.14 [1378]~E(x13781,x13782)+E(f441(x13781,x13783,x13784),f441(x13782,x13783,x13784))
% 28.25/28.14 [1379]~E(x13791,x13792)+E(f441(x13793,x13791,x13794),f441(x13793,x13792,x13794))
% 28.25/28.14 [1380]~E(x13801,x13802)+E(f441(x13803,x13804,x13801),f441(x13803,x13804,x13802))
% 28.25/28.14 [1381]~E(x13811,x13812)+E(f780(x13811,x13813,x13814),f780(x13812,x13813,x13814))
% 28.25/28.14 [1382]~E(x13821,x13822)+E(f780(x13823,x13821,x13824),f780(x13823,x13822,x13824))
% 28.25/28.14 [1383]~E(x13831,x13832)+E(f780(x13833,x13834,x13831),f780(x13833,x13834,x13832))
% 28.25/28.14 [1384]~E(x13841,x13842)+E(f650(x13841,x13843,x13844,x13845),f650(x13842,x13843,x13844,x13845))
% 28.25/28.14 [1385]~E(x13851,x13852)+E(f650(x13853,x13851,x13854,x13855),f650(x13853,x13852,x13854,x13855))
% 28.25/28.14 [1386]~E(x13861,x13862)+E(f650(x13863,x13864,x13861,x13865),f650(x13863,x13864,x13862,x13865))
% 28.25/28.14 [1387]~E(x13871,x13872)+E(f650(x13873,x13874,x13875,x13871),f650(x13873,x13874,x13875,x13872))
% 28.25/28.14 [1388]~E(x13881,x13882)+E(f593(x13881,x13883,x13884),f593(x13882,x13883,x13884))
% 28.25/28.14 [1389]~E(x13891,x13892)+E(f593(x13893,x13891,x13894),f593(x13893,x13892,x13894))
% 28.25/28.14 [1390]~E(x13901,x13902)+E(f593(x13903,x13904,x13901),f593(x13903,x13904,x13902))
% 28.25/28.14 [1391]~E(x13911,x13912)+E(f682(x13911,x13913,x13914,x13915,x13916),f682(x13912,x13913,x13914,x13915,x13916))
% 28.25/28.14 [1392]~E(x13921,x13922)+E(f682(x13923,x13921,x13924,x13925,x13926),f682(x13923,x13922,x13924,x13925,x13926))
% 28.25/28.14 [1393]~E(x13931,x13932)+E(f682(x13933,x13934,x13931,x13935,x13936),f682(x13933,x13934,x13932,x13935,x13936))
% 28.25/28.14 [1394]~E(x13941,x13942)+E(f682(x13943,x13944,x13945,x13941,x13946),f682(x13943,x13944,x13945,x13942,x13946))
% 28.25/28.14 [1395]~E(x13951,x13952)+E(f682(x13953,x13954,x13955,x13956,x13951),f682(x13953,x13954,x13955,x13956,x13952))
% 28.25/28.14 [1396]~E(x13961,x13962)+E(f40(x13961,x13963),f40(x13962,x13963))
% 28.25/28.14 [1397]~E(x13971,x13972)+E(f40(x13973,x13971),f40(x13973,x13972))
% 28.25/28.14 [1398]~E(x13981,x13982)+E(f500(x13981,x13983,x13984,x13985,x13986,x13987,x13988,x13989),f500(x13982,x13983,x13984,x13985,x13986,x13987,x13988,x13989))
% 28.25/28.14 [1399]~E(x13991,x13992)+E(f500(x13993,x13991,x13994,x13995,x13996,x13997,x13998,x13999),f500(x13993,x13992,x13994,x13995,x13996,x13997,x13998,x13999))
% 28.25/28.14 [1400]~E(x14001,x14002)+E(f500(x14003,x14004,x14001,x14005,x14006,x14007,x14008,x14009),f500(x14003,x14004,x14002,x14005,x14006,x14007,x14008,x14009))
% 28.25/28.14 [1401]~E(x14011,x14012)+E(f500(x14013,x14014,x14015,x14011,x14016,x14017,x14018,x14019),f500(x14013,x14014,x14015,x14012,x14016,x14017,x14018,x14019))
% 28.25/28.14 [1402]~E(x14021,x14022)+E(f500(x14023,x14024,x14025,x14026,x14021,x14027,x14028,x14029),f500(x14023,x14024,x14025,x14026,x14022,x14027,x14028,x14029))
% 28.25/28.14 [1403]~E(x14031,x14032)+E(f500(x14033,x14034,x14035,x14036,x14037,x14031,x14038,x14039),f500(x14033,x14034,x14035,x14036,x14037,x14032,x14038,x14039))
% 28.25/28.14 [1404]~E(x14041,x14042)+E(f500(x14043,x14044,x14045,x14046,x14047,x14048,x14041,x14049),f500(x14043,x14044,x14045,x14046,x14047,x14048,x14042,x14049))
% 28.25/28.14 [1405]~E(x14051,x14052)+E(f500(x14053,x14054,x14055,x14056,x14057,x14058,x14059,x14051),f500(x14053,x14054,x14055,x14056,x14057,x14058,x14059,x14052))
% 28.25/28.14 [1406]~E(x14061,x14062)+E(f899(x14061,x14063,x14064,x14065,x14066,x14067,x14068,x14069),f899(x14062,x14063,x14064,x14065,x14066,x14067,x14068,x14069))
% 28.25/28.14 [1407]~E(x14071,x14072)+E(f899(x14073,x14071,x14074,x14075,x14076,x14077,x14078,x14079),f899(x14073,x14072,x14074,x14075,x14076,x14077,x14078,x14079))
% 28.25/28.14 [1408]~E(x14081,x14082)+E(f899(x14083,x14084,x14081,x14085,x14086,x14087,x14088,x14089),f899(x14083,x14084,x14082,x14085,x14086,x14087,x14088,x14089))
% 28.25/28.14 [1409]~E(x14091,x14092)+E(f899(x14093,x14094,x14095,x14091,x14096,x14097,x14098,x14099),f899(x14093,x14094,x14095,x14092,x14096,x14097,x14098,x14099))
% 28.25/28.14 [1410]~E(x14101,x14102)+E(f899(x14103,x14104,x14105,x14106,x14101,x14107,x14108,x14109),f899(x14103,x14104,x14105,x14106,x14102,x14107,x14108,x14109))
% 28.25/28.14 [1411]~E(x14111,x14112)+E(f899(x14113,x14114,x14115,x14116,x14117,x14111,x14118,x14119),f899(x14113,x14114,x14115,x14116,x14117,x14112,x14118,x14119))
% 28.25/28.14 [1412]~E(x14121,x14122)+E(f899(x14123,x14124,x14125,x14126,x14127,x14128,x14121,x14129),f899(x14123,x14124,x14125,x14126,x14127,x14128,x14122,x14129))
% 28.25/28.14 [1413]~E(x14131,x14132)+E(f899(x14133,x14134,x14135,x14136,x14137,x14138,x14139,x14131),f899(x14133,x14134,x14135,x14136,x14137,x14138,x14139,x14132))
% 28.25/28.14 [1414]~E(x14141,x14142)+E(f740(x14141,x14143,x14144),f740(x14142,x14143,x14144))
% 28.25/28.14 [1415]~E(x14151,x14152)+E(f740(x14153,x14151,x14154),f740(x14153,x14152,x14154))
% 28.25/28.14 [1416]~E(x14161,x14162)+E(f740(x14163,x14164,x14161),f740(x14163,x14164,x14162))
% 28.25/28.14 [1417]~E(x14171,x14172)+E(f368(x14171,x14173),f368(x14172,x14173))
% 28.25/28.14 [1418]~E(x14181,x14182)+E(f368(x14183,x14181),f368(x14183,x14182))
% 28.25/28.14 [1419]~E(x14191,x14192)+E(f350(x14191,x14193,x14194,x14195,x14196),f350(x14192,x14193,x14194,x14195,x14196))
% 28.25/28.14 [1420]~E(x14201,x14202)+E(f350(x14203,x14201,x14204,x14205,x14206),f350(x14203,x14202,x14204,x14205,x14206))
% 28.25/28.14 [1421]~E(x14211,x14212)+E(f350(x14213,x14214,x14211,x14215,x14216),f350(x14213,x14214,x14212,x14215,x14216))
% 28.25/28.14 [1422]~E(x14221,x14222)+E(f350(x14223,x14224,x14225,x14221,x14226),f350(x14223,x14224,x14225,x14222,x14226))
% 28.25/28.14 [1423]~E(x14231,x14232)+E(f350(x14233,x14234,x14235,x14236,x14231),f350(x14233,x14234,x14235,x14236,x14232))
% 28.25/28.14 [1424]~E(x14241,x14242)+E(f629(x14241,x14243),f629(x14242,x14243))
% 28.25/28.14 [1425]~E(x14251,x14252)+E(f629(x14253,x14251),f629(x14253,x14252))
% 28.25/28.14 [1426]~E(x14261,x14262)+E(f443(x14261,x14263,x14264),f443(x14262,x14263,x14264))
% 28.25/28.14 [1427]~E(x14271,x14272)+E(f443(x14273,x14271,x14274),f443(x14273,x14272,x14274))
% 28.25/28.14 [1428]~E(x14281,x14282)+E(f443(x14283,x14284,x14281),f443(x14283,x14284,x14282))
% 28.25/28.14 [1429]~E(x14291,x14292)+E(f420(x14291,x14293,x14294),f420(x14292,x14293,x14294))
% 28.25/28.14 [1430]~E(x14301,x14302)+E(f420(x14303,x14301,x14304),f420(x14303,x14302,x14304))
% 28.25/28.14 [1431]~E(x14311,x14312)+E(f420(x14313,x14314,x14311),f420(x14313,x14314,x14312))
% 28.25/28.14 [1432]~E(x14321,x14322)+E(f754(x14321,x14323,x14324,x14325,x14326,x14327,x14328,x14329),f754(x14322,x14323,x14324,x14325,x14326,x14327,x14328,x14329))
% 28.25/28.14 [1433]~E(x14331,x14332)+E(f754(x14333,x14331,x14334,x14335,x14336,x14337,x14338,x14339),f754(x14333,x14332,x14334,x14335,x14336,x14337,x14338,x14339))
% 28.25/28.14 [1434]~E(x14341,x14342)+E(f754(x14343,x14344,x14341,x14345,x14346,x14347,x14348,x14349),f754(x14343,x14344,x14342,x14345,x14346,x14347,x14348,x14349))
% 28.25/28.14 [1435]~E(x14351,x14352)+E(f754(x14353,x14354,x14355,x14351,x14356,x14357,x14358,x14359),f754(x14353,x14354,x14355,x14352,x14356,x14357,x14358,x14359))
% 28.25/28.14 [1436]~E(x14361,x14362)+E(f754(x14363,x14364,x14365,x14366,x14361,x14367,x14368,x14369),f754(x14363,x14364,x14365,x14366,x14362,x14367,x14368,x14369))
% 28.25/28.14 [1437]~E(x14371,x14372)+E(f754(x14373,x14374,x14375,x14376,x14377,x14371,x14378,x14379),f754(x14373,x14374,x14375,x14376,x14377,x14372,x14378,x14379))
% 28.25/28.14 [1438]~E(x14381,x14382)+E(f754(x14383,x14384,x14385,x14386,x14387,x14388,x14381,x14389),f754(x14383,x14384,x14385,x14386,x14387,x14388,x14382,x14389))
% 28.25/28.14 [1439]~E(x14391,x14392)+E(f754(x14393,x14394,x14395,x14396,x14397,x14398,x14399,x14391),f754(x14393,x14394,x14395,x14396,x14397,x14398,x14399,x14392))
% 28.25/28.14 [1440]~E(x14401,x14402)+E(f49(x14401,x14403,x14404),f49(x14402,x14403,x14404))
% 28.25/28.14 [1441]~E(x14411,x14412)+E(f49(x14413,x14411,x14414),f49(x14413,x14412,x14414))
% 28.25/28.14 [1442]~E(x14421,x14422)+E(f49(x14423,x14424,x14421),f49(x14423,x14424,x14422))
% 28.25/28.14 [1443]~E(x14431,x14432)+E(f384(x14431,x14433,x14434,x14435),f384(x14432,x14433,x14434,x14435))
% 28.25/28.14 [1444]~E(x14441,x14442)+E(f384(x14443,x14441,x14444,x14445),f384(x14443,x14442,x14444,x14445))
% 28.25/28.14 [1445]~E(x14451,x14452)+E(f384(x14453,x14454,x14451,x14455),f384(x14453,x14454,x14452,x14455))
% 28.25/28.14 [1446]~E(x14461,x14462)+E(f384(x14463,x14464,x14465,x14461),f384(x14463,x14464,x14465,x14462))
% 28.25/28.14 [1447]~E(x14471,x14472)+E(f620(x14471,x14473,x14474),f620(x14472,x14473,x14474))
% 28.25/28.14 [1448]~E(x14481,x14482)+E(f620(x14483,x14481,x14484),f620(x14483,x14482,x14484))
% 28.25/28.14 [1449]~E(x14491,x14492)+E(f620(x14493,x14494,x14491),f620(x14493,x14494,x14492))
% 28.25/28.14 [1450]~E(x14501,x14502)+E(f903(x14501,x14503),f903(x14502,x14503))
% 28.25/28.14 [1451]~E(x14511,x14512)+E(f903(x14513,x14511),f903(x14513,x14512))
% 28.25/28.14 [1452]~E(x14521,x14522)+E(f583(x14521,x14523,x14524),f583(x14522,x14523,x14524))
% 28.25/28.14 [1453]~E(x14531,x14532)+E(f583(x14533,x14531,x14534),f583(x14533,x14532,x14534))
% 28.25/28.14 [1454]~E(x14541,x14542)+E(f583(x14543,x14544,x14541),f583(x14543,x14544,x14542))
% 28.25/28.14 [1455]~E(x14551,x14552)+E(f892(x14551,x14553,x14554,x14555),f892(x14552,x14553,x14554,x14555))
% 28.25/28.14 [1456]~E(x14561,x14562)+E(f892(x14563,x14561,x14564,x14565),f892(x14563,x14562,x14564,x14565))
% 28.25/28.14 [1457]~E(x14571,x14572)+E(f892(x14573,x14574,x14571,x14575),f892(x14573,x14574,x14572,x14575))
% 28.25/28.14 [1458]~E(x14581,x14582)+E(f892(x14583,x14584,x14585,x14581),f892(x14583,x14584,x14585,x14582))
% 28.25/28.14 [1459]~E(x14591,x14592)+E(f541(x14591,x14593,x14594),f541(x14592,x14593,x14594))
% 28.25/28.14 [1460]~E(x14601,x14602)+E(f541(x14603,x14601,x14604),f541(x14603,x14602,x14604))
% 28.25/28.14 [1461]~E(x14611,x14612)+E(f541(x14613,x14614,x14611),f541(x14613,x14614,x14612))
% 28.25/28.14 [1462]~E(x14621,x14622)+E(f429(x14621,x14623,x14624,x14625,x14626),f429(x14622,x14623,x14624,x14625,x14626))
% 28.25/28.14 [1463]~E(x14631,x14632)+E(f429(x14633,x14631,x14634,x14635,x14636),f429(x14633,x14632,x14634,x14635,x14636))
% 28.25/28.14 [1464]~E(x14641,x14642)+E(f429(x14643,x14644,x14641,x14645,x14646),f429(x14643,x14644,x14642,x14645,x14646))
% 28.25/28.14 [1465]~E(x14651,x14652)+E(f429(x14653,x14654,x14655,x14651,x14656),f429(x14653,x14654,x14655,x14652,x14656))
% 28.25/28.14 [1466]~E(x14661,x14662)+E(f429(x14663,x14664,x14665,x14666,x14661),f429(x14663,x14664,x14665,x14666,x14662))
% 28.25/28.14 [1467]~E(x14671,x14672)+E(f430(x14671,x14673),f430(x14672,x14673))
% 28.25/28.14 [1468]~E(x14681,x14682)+E(f430(x14683,x14681),f430(x14683,x14682))
% 28.25/28.14 [1469]~E(x14691,x14692)+E(f536(x14691,x14693,x14694),f536(x14692,x14693,x14694))
% 28.25/28.14 [1470]~E(x14701,x14702)+E(f536(x14703,x14701,x14704),f536(x14703,x14702,x14704))
% 28.25/28.14 [1471]~E(x14711,x14712)+E(f536(x14713,x14714,x14711),f536(x14713,x14714,x14712))
% 28.25/28.14 [1472]~E(x14721,x14722)+E(f585(x14721,x14723,x14724,x14725,x14726),f585(x14722,x14723,x14724,x14725,x14726))
% 28.25/28.14 [1473]~E(x14731,x14732)+E(f585(x14733,x14731,x14734,x14735,x14736),f585(x14733,x14732,x14734,x14735,x14736))
% 28.25/28.14 [1474]~E(x14741,x14742)+E(f585(x14743,x14744,x14741,x14745,x14746),f585(x14743,x14744,x14742,x14745,x14746))
% 28.25/28.14 [1475]~E(x14751,x14752)+E(f585(x14753,x14754,x14755,x14751,x14756),f585(x14753,x14754,x14755,x14752,x14756))
% 28.25/28.14 [1476]~E(x14761,x14762)+E(f585(x14763,x14764,x14765,x14766,x14761),f585(x14763,x14764,x14765,x14766,x14762))
% 28.25/28.14 [1477]~E(x14771,x14772)+E(f370(x14771),f370(x14772))
% 28.25/28.14 [1478]~E(x14781,x14782)+E(f514(x14781,x14783,x14784,x14785,x14786),f514(x14782,x14783,x14784,x14785,x14786))
% 28.25/28.14 [1479]~E(x14791,x14792)+E(f514(x14793,x14791,x14794,x14795,x14796),f514(x14793,x14792,x14794,x14795,x14796))
% 28.25/28.14 [1480]~E(x14801,x14802)+E(f514(x14803,x14804,x14801,x14805,x14806),f514(x14803,x14804,x14802,x14805,x14806))
% 28.25/28.14 [1481]~E(x14811,x14812)+E(f514(x14813,x14814,x14815,x14811,x14816),f514(x14813,x14814,x14815,x14812,x14816))
% 28.25/28.14 [1482]~E(x14821,x14822)+E(f514(x14823,x14824,x14825,x14826,x14821),f514(x14823,x14824,x14825,x14826,x14822))
% 28.25/28.14 [1483]~E(x14831,x14832)+E(f206(x14831,x14833),f206(x14832,x14833))
% 28.25/28.14 [1484]~E(x14841,x14842)+E(f206(x14843,x14841),f206(x14843,x14842))
% 28.25/28.14 [1485]~E(x14851,x14852)+E(f425(x14851),f425(x14852))
% 28.25/28.14 [1486]~E(x14861,x14862)+E(f546(x14861,x14863,x14864,x14865,x14866,x14867),f546(x14862,x14863,x14864,x14865,x14866,x14867))
% 28.25/28.14 [1487]~E(x14871,x14872)+E(f546(x14873,x14871,x14874,x14875,x14876,x14877),f546(x14873,x14872,x14874,x14875,x14876,x14877))
% 28.25/28.14 [1488]~E(x14881,x14882)+E(f546(x14883,x14884,x14881,x14885,x14886,x14887),f546(x14883,x14884,x14882,x14885,x14886,x14887))
% 28.25/28.14 [1489]~E(x14891,x14892)+E(f546(x14893,x14894,x14895,x14891,x14896,x14897),f546(x14893,x14894,x14895,x14892,x14896,x14897))
% 28.25/28.14 [1490]~E(x14901,x14902)+E(f546(x14903,x14904,x14905,x14906,x14901,x14907),f546(x14903,x14904,x14905,x14906,x14902,x14907))
% 28.25/28.14 [1491]~E(x14911,x14912)+E(f546(x14913,x14914,x14915,x14916,x14917,x14911),f546(x14913,x14914,x14915,x14916,x14917,x14912))
% 28.25/28.14 [1492]~E(x14921,x14922)+E(f242(x14921,x14923,x14924),f242(x14922,x14923,x14924))
% 28.25/28.14 [1493]~E(x14931,x14932)+E(f242(x14933,x14931,x14934),f242(x14933,x14932,x14934))
% 28.25/28.14 [1494]~E(x14941,x14942)+E(f242(x14943,x14944,x14941),f242(x14943,x14944,x14942))
% 28.25/28.14 [1495]~E(x14951,x14952)+E(f460(x14951,x14953,x14954,x14955),f460(x14952,x14953,x14954,x14955))
% 28.25/28.14 [1496]~E(x14961,x14962)+E(f460(x14963,x14961,x14964,x14965),f460(x14963,x14962,x14964,x14965))
% 28.25/28.14 [1497]~E(x14971,x14972)+E(f460(x14973,x14974,x14971,x14975),f460(x14973,x14974,x14972,x14975))
% 28.25/28.14 [1498]~E(x14981,x14982)+E(f460(x14983,x14984,x14985,x14981),f460(x14983,x14984,x14985,x14982))
% 28.25/28.14 [1499]~E(x14991,x14992)+E(f676(x14991,x14993,x14994,x14995,x14996),f676(x14992,x14993,x14994,x14995,x14996))
% 28.25/28.14 [1500]~E(x15001,x15002)+E(f676(x15003,x15001,x15004,x15005,x15006),f676(x15003,x15002,x15004,x15005,x15006))
% 28.25/28.14 [1501]~E(x15011,x15012)+E(f676(x15013,x15014,x15011,x15015,x15016),f676(x15013,x15014,x15012,x15015,x15016))
% 28.25/28.14 [1502]~E(x15021,x15022)+E(f676(x15023,x15024,x15025,x15021,x15026),f676(x15023,x15024,x15025,x15022,x15026))
% 28.25/28.14 [1503]~E(x15031,x15032)+E(f676(x15033,x15034,x15035,x15036,x15031),f676(x15033,x15034,x15035,x15036,x15032))
% 28.25/28.14 [1504]~E(x15041,x15042)+E(f572(x15041,x15043,x15044,x15045),f572(x15042,x15043,x15044,x15045))
% 28.25/28.14 [1505]~E(x15051,x15052)+E(f572(x15053,x15051,x15054,x15055),f572(x15053,x15052,x15054,x15055))
% 28.25/28.14 [1506]~E(x15061,x15062)+E(f572(x15063,x15064,x15061,x15065),f572(x15063,x15064,x15062,x15065))
% 28.25/28.14 [1507]~E(x15071,x15072)+E(f572(x15073,x15074,x15075,x15071),f572(x15073,x15074,x15075,x15072))
% 28.25/28.14 [1508]~E(x15081,x15082)+E(f62(x15081,x15083,x15084),f62(x15082,x15083,x15084))
% 28.25/28.14 [1509]~E(x15091,x15092)+E(f62(x15093,x15091,x15094),f62(x15093,x15092,x15094))
% 28.25/28.14 [1510]~E(x15101,x15102)+E(f62(x15103,x15104,x15101),f62(x15103,x15104,x15102))
% 28.25/28.14 [1511]~E(x15111,x15112)+E(f725(x15111,x15113,x15114),f725(x15112,x15113,x15114))
% 28.25/28.14 [1512]~E(x15121,x15122)+E(f725(x15123,x15121,x15124),f725(x15123,x15122,x15124))
% 28.25/28.14 [1513]~E(x15131,x15132)+E(f725(x15133,x15134,x15131),f725(x15133,x15134,x15132))
% 28.25/28.14 [1514]~E(x15141,x15142)+E(f647(x15141,x15143,x15144,x15145,x15146),f647(x15142,x15143,x15144,x15145,x15146))
% 28.25/28.14 [1515]~E(x15151,x15152)+E(f647(x15153,x15151,x15154,x15155,x15156),f647(x15153,x15152,x15154,x15155,x15156))
% 28.25/28.14 [1516]~E(x15161,x15162)+E(f647(x15163,x15164,x15161,x15165,x15166),f647(x15163,x15164,x15162,x15165,x15166))
% 28.25/28.14 [1517]~E(x15171,x15172)+E(f647(x15173,x15174,x15175,x15171,x15176),f647(x15173,x15174,x15175,x15172,x15176))
% 28.25/28.14 [1518]~E(x15181,x15182)+E(f647(x15183,x15184,x15185,x15186,x15181),f647(x15183,x15184,x15185,x15186,x15182))
% 28.25/28.14 [1519]~E(x15191,x15192)+E(f689(x15191,x15193,x15194,x15195),f689(x15192,x15193,x15194,x15195))
% 28.25/28.14 [1520]~E(x15201,x15202)+E(f689(x15203,x15201,x15204,x15205),f689(x15203,x15202,x15204,x15205))
% 28.25/28.14 [1521]~E(x15211,x15212)+E(f689(x15213,x15214,x15211,x15215),f689(x15213,x15214,x15212,x15215))
% 28.25/28.14 [1522]~E(x15221,x15222)+E(f689(x15223,x15224,x15225,x15221),f689(x15223,x15224,x15225,x15222))
% 28.25/28.14 [1523]~E(x15231,x15232)+E(f876(x15231,x15233,x15234),f876(x15232,x15233,x15234))
% 28.25/28.14 [1524]~E(x15241,x15242)+E(f876(x15243,x15241,x15244),f876(x15243,x15242,x15244))
% 28.25/28.14 [1525]~E(x15251,x15252)+E(f876(x15253,x15254,x15251),f876(x15253,x15254,x15252))
% 28.25/28.14 [1526]~E(x15261,x15262)+E(f882(x15261,x15263,x15264),f882(x15262,x15263,x15264))
% 28.25/28.14 [1527]~E(x15271,x15272)+E(f882(x15273,x15271,x15274),f882(x15273,x15272,x15274))
% 28.25/28.14 [1528]~E(x15281,x15282)+E(f882(x15283,x15284,x15281),f882(x15283,x15284,x15282))
% 28.25/28.14 [1529]~E(x15291,x15292)+E(f838(x15291,x15293),f838(x15292,x15293))
% 28.25/28.14 [1530]~E(x15301,x15302)+E(f838(x15303,x15301),f838(x15303,x15302))
% 28.25/28.14 [1531]~E(x15311,x15312)+E(f422(x15311,x15313,x15314,x15315),f422(x15312,x15313,x15314,x15315))
% 28.25/28.14 [1532]~E(x15321,x15322)+E(f422(x15323,x15321,x15324,x15325),f422(x15323,x15322,x15324,x15325))
% 28.25/28.14 [1533]~E(x15331,x15332)+E(f422(x15333,x15334,x15331,x15335),f422(x15333,x15334,x15332,x15335))
% 28.25/28.14 [1534]~E(x15341,x15342)+E(f422(x15343,x15344,x15345,x15341),f422(x15343,x15344,x15345,x15342))
% 28.25/28.14 [1535]~E(x15351,x15352)+E(f654(x15351,x15353,x15354,x15355,x15356,x15357,x15358),f654(x15352,x15353,x15354,x15355,x15356,x15357,x15358))
% 28.25/28.14 [1536]~E(x15361,x15362)+E(f654(x15363,x15361,x15364,x15365,x15366,x15367,x15368),f654(x15363,x15362,x15364,x15365,x15366,x15367,x15368))
% 28.25/28.14 [1537]~E(x15371,x15372)+E(f654(x15373,x15374,x15371,x15375,x15376,x15377,x15378),f654(x15373,x15374,x15372,x15375,x15376,x15377,x15378))
% 28.25/28.14 [1538]~E(x15381,x15382)+E(f654(x15383,x15384,x15385,x15381,x15386,x15387,x15388),f654(x15383,x15384,x15385,x15382,x15386,x15387,x15388))
% 28.25/28.14 [1539]~E(x15391,x15392)+E(f654(x15393,x15394,x15395,x15396,x15391,x15397,x15398),f654(x15393,x15394,x15395,x15396,x15392,x15397,x15398))
% 28.25/28.14 [1540]~E(x15401,x15402)+E(f654(x15403,x15404,x15405,x15406,x15407,x15401,x15408),f654(x15403,x15404,x15405,x15406,x15407,x15402,x15408))
% 28.25/28.14 [1541]~E(x15411,x15412)+E(f654(x15413,x15414,x15415,x15416,x15417,x15418,x15411),f654(x15413,x15414,x15415,x15416,x15417,x15418,x15412))
% 28.25/28.14 [1542]~E(x15421,x15422)+E(f258(x15421,x15423),f258(x15422,x15423))
% 28.25/28.14 [1543]~E(x15431,x15432)+E(f258(x15433,x15431),f258(x15433,x15432))
% 28.25/28.14 [1544]~E(x15441,x15442)+E(f543(x15441,x15443,x15444),f543(x15442,x15443,x15444))
% 28.25/28.14 [1545]~E(x15451,x15452)+E(f543(x15453,x15451,x15454),f543(x15453,x15452,x15454))
% 28.25/28.14 [1546]~E(x15461,x15462)+E(f543(x15463,x15464,x15461),f543(x15463,x15464,x15462))
% 28.25/28.14 [1547]~E(x15471,x15472)+E(f375(x15471,x15473,x15474),f375(x15472,x15473,x15474))
% 28.25/28.14 [1548]~E(x15481,x15482)+E(f375(x15483,x15481,x15484),f375(x15483,x15482,x15484))
% 28.25/28.14 [1549]~E(x15491,x15492)+E(f375(x15493,x15494,x15491),f375(x15493,x15494,x15492))
% 28.25/28.14 [1550]~E(x15501,x15502)+E(f693(x15501,x15503,x15504,x15505),f693(x15502,x15503,x15504,x15505))
% 28.25/28.14 [1551]~E(x15511,x15512)+E(f693(x15513,x15511,x15514,x15515),f693(x15513,x15512,x15514,x15515))
% 28.25/28.14 [1552]~E(x15521,x15522)+E(f693(x15523,x15524,x15521,x15525),f693(x15523,x15524,x15522,x15525))
% 28.25/28.14 [1553]~E(x15531,x15532)+E(f693(x15533,x15534,x15535,x15531),f693(x15533,x15534,x15535,x15532))
% 28.25/28.14 [1554]~E(x15541,x15542)+E(f347(x15541,x15543),f347(x15542,x15543))
% 28.25/28.14 [1555]~E(x15551,x15552)+E(f347(x15553,x15551),f347(x15553,x15552))
% 28.25/28.14 [1556]~E(x15561,x15562)+E(f841(x15561,x15563,x15564,x15565),f841(x15562,x15563,x15564,x15565))
% 28.25/28.14 [1557]~E(x15571,x15572)+E(f841(x15573,x15571,x15574,x15575),f841(x15573,x15572,x15574,x15575))
% 28.25/28.14 [1558]~E(x15581,x15582)+E(f841(x15583,x15584,x15581,x15585),f841(x15583,x15584,x15582,x15585))
% 28.25/28.14 [1559]~E(x15591,x15592)+E(f841(x15593,x15594,x15595,x15591),f841(x15593,x15594,x15595,x15592))
% 28.25/28.14 [1560]~E(x15601,x15602)+E(f655(x15601,x15603,x15604,x15605),f655(x15602,x15603,x15604,x15605))
% 28.25/28.14 [1561]~E(x15611,x15612)+E(f655(x15613,x15611,x15614,x15615),f655(x15613,x15612,x15614,x15615))
% 28.25/28.14 [1562]~E(x15621,x15622)+E(f655(x15623,x15624,x15621,x15625),f655(x15623,x15624,x15622,x15625))
% 28.25/28.14 [1563]~E(x15631,x15632)+E(f655(x15633,x15634,x15635,x15631),f655(x15633,x15634,x15635,x15632))
% 28.25/28.14 [1564]~E(x15641,x15642)+E(f527(x15641,x15643,x15644,x15645,x15646,x15647),f527(x15642,x15643,x15644,x15645,x15646,x15647))
% 28.25/28.14 [1565]~E(x15651,x15652)+E(f527(x15653,x15651,x15654,x15655,x15656,x15657),f527(x15653,x15652,x15654,x15655,x15656,x15657))
% 28.25/28.14 [1566]~E(x15661,x15662)+E(f527(x15663,x15664,x15661,x15665,x15666,x15667),f527(x15663,x15664,x15662,x15665,x15666,x15667))
% 28.25/28.14 [1567]~E(x15671,x15672)+E(f527(x15673,x15674,x15675,x15671,x15676,x15677),f527(x15673,x15674,x15675,x15672,x15676,x15677))
% 28.25/28.14 [1568]~E(x15681,x15682)+E(f527(x15683,x15684,x15685,x15686,x15681,x15687),f527(x15683,x15684,x15685,x15686,x15682,x15687))
% 28.25/28.14 [1569]~E(x15691,x15692)+E(f527(x15693,x15694,x15695,x15696,x15697,x15691),f527(x15693,x15694,x15695,x15696,x15697,x15692))
% 28.25/28.14 [1570]~E(x15701,x15702)+E(f458(x15701,x15703),f458(x15702,x15703))
% 28.25/28.14 [1571]~E(x15711,x15712)+E(f458(x15713,x15711),f458(x15713,x15712))
% 28.25/28.14 [1572]~E(x15721,x15722)+E(f71(x15721,x15723,x15724,x15725),f71(x15722,x15723,x15724,x15725))
% 28.25/28.14 [1573]~E(x15731,x15732)+E(f71(x15733,x15731,x15734,x15735),f71(x15733,x15732,x15734,x15735))
% 28.25/28.14 [1574]~E(x15741,x15742)+E(f71(x15743,x15744,x15741,x15745),f71(x15743,x15744,x15742,x15745))
% 28.25/28.14 [1575]~E(x15751,x15752)+E(f71(x15753,x15754,x15755,x15751),f71(x15753,x15754,x15755,x15752))
% 28.25/28.14 [1576]~E(x15761,x15762)+E(f228(x15761,x15763),f228(x15762,x15763))
% 28.25/28.14 [1577]~E(x15771,x15772)+E(f228(x15773,x15771),f228(x15773,x15772))
% 28.25/28.14 [1578]~E(x15781,x15782)+E(f218(x15781,x15783,x15784,x15785,x15786),f218(x15782,x15783,x15784,x15785,x15786))
% 28.25/28.14 [1579]~E(x15791,x15792)+E(f218(x15793,x15791,x15794,x15795,x15796),f218(x15793,x15792,x15794,x15795,x15796))
% 28.25/28.14 [1580]~E(x15801,x15802)+E(f218(x15803,x15804,x15801,x15805,x15806),f218(x15803,x15804,x15802,x15805,x15806))
% 28.25/28.14 [1581]~E(x15811,x15812)+E(f218(x15813,x15814,x15815,x15811,x15816),f218(x15813,x15814,x15815,x15812,x15816))
% 28.25/28.14 [1582]~E(x15821,x15822)+E(f218(x15823,x15824,x15825,x15826,x15821),f218(x15823,x15824,x15825,x15826,x15822))
% 28.25/28.14 [1583]~E(x15831,x15832)+E(f366(x15831,x15833),f366(x15832,x15833))
% 28.25/28.14 [1584]~E(x15841,x15842)+E(f366(x15843,x15841),f366(x15843,x15842))
% 28.25/28.14 [1585]~E(x15851,x15852)+E(f413(x15851,x15853,x15854,x15855,x15856,x15857),f413(x15852,x15853,x15854,x15855,x15856,x15857))
% 28.25/28.14 [1586]~E(x15861,x15862)+E(f413(x15863,x15861,x15864,x15865,x15866,x15867),f413(x15863,x15862,x15864,x15865,x15866,x15867))
% 28.25/28.14 [1587]~E(x15871,x15872)+E(f413(x15873,x15874,x15871,x15875,x15876,x15877),f413(x15873,x15874,x15872,x15875,x15876,x15877))
% 28.25/28.14 [1588]~E(x15881,x15882)+E(f413(x15883,x15884,x15885,x15881,x15886,x15887),f413(x15883,x15884,x15885,x15882,x15886,x15887))
% 28.25/28.14 [1589]~E(x15891,x15892)+E(f413(x15893,x15894,x15895,x15896,x15891,x15897),f413(x15893,x15894,x15895,x15896,x15892,x15897))
% 28.25/28.14 [1590]~E(x15901,x15902)+E(f413(x15903,x15904,x15905,x15906,x15907,x15901),f413(x15903,x15904,x15905,x15906,x15907,x15902))
% 28.25/28.14 [1591]~E(x15911,x15912)+E(f619(x15911,x15913,x15914,x15915,x15916),f619(x15912,x15913,x15914,x15915,x15916))
% 28.25/28.14 [1592]~E(x15921,x15922)+E(f619(x15923,x15921,x15924,x15925,x15926),f619(x15923,x15922,x15924,x15925,x15926))
% 28.25/28.14 [1593]~E(x15931,x15932)+E(f619(x15933,x15934,x15931,x15935,x15936),f619(x15933,x15934,x15932,x15935,x15936))
% 28.25/28.14 [1594]~E(x15941,x15942)+E(f619(x15943,x15944,x15945,x15941,x15946),f619(x15943,x15944,x15945,x15942,x15946))
% 28.25/28.14 [1595]~E(x15951,x15952)+E(f619(x15953,x15954,x15955,x15956,x15951),f619(x15953,x15954,x15955,x15956,x15952))
% 28.25/28.14 [1596]~E(x15961,x15962)+E(f785(x15961,x15963,x15964),f785(x15962,x15963,x15964))
% 28.25/28.14 [1597]~E(x15971,x15972)+E(f785(x15973,x15971,x15974),f785(x15973,x15972,x15974))
% 28.25/28.14 [1598]~E(x15981,x15982)+E(f785(x15983,x15984,x15981),f785(x15983,x15984,x15982))
% 28.25/28.14 [1599]~E(x15991,x15992)+E(f377(x15991,x15993,x15994),f377(x15992,x15993,x15994))
% 28.25/28.14 [1600]~E(x16001,x16002)+E(f377(x16003,x16001,x16004),f377(x16003,x16002,x16004))
% 28.25/28.14 [1601]~E(x16011,x16012)+E(f377(x16013,x16014,x16011),f377(x16013,x16014,x16012))
% 28.25/28.14 [1602]~E(x16021,x16022)+E(f614(x16021,x16023,x16024,x16025),f614(x16022,x16023,x16024,x16025))
% 28.25/28.14 [1603]~E(x16031,x16032)+E(f614(x16033,x16031,x16034,x16035),f614(x16033,x16032,x16034,x16035))
% 28.25/28.14 [1604]~E(x16041,x16042)+E(f614(x16043,x16044,x16041,x16045),f614(x16043,x16044,x16042,x16045))
% 28.25/28.14 [1605]~E(x16051,x16052)+E(f614(x16053,x16054,x16055,x16051),f614(x16053,x16054,x16055,x16052))
% 28.25/28.14 [1606]~E(x16061,x16062)+E(f237(x16061,x16063,x16064),f237(x16062,x16063,x16064))
% 28.25/28.14 [1607]~E(x16071,x16072)+E(f237(x16073,x16071,x16074),f237(x16073,x16072,x16074))
% 28.25/28.14 [1608]~E(x16081,x16082)+E(f237(x16083,x16084,x16081),f237(x16083,x16084,x16082))
% 28.25/28.14 [1609]~E(x16091,x16092)+E(f344(x16091,x16093,x16094,x16095,x16096,x16097,x16098),f344(x16092,x16093,x16094,x16095,x16096,x16097,x16098))
% 28.25/28.14 [1610]~E(x16101,x16102)+E(f344(x16103,x16101,x16104,x16105,x16106,x16107,x16108),f344(x16103,x16102,x16104,x16105,x16106,x16107,x16108))
% 28.25/28.14 [1611]~E(x16111,x16112)+E(f344(x16113,x16114,x16111,x16115,x16116,x16117,x16118),f344(x16113,x16114,x16112,x16115,x16116,x16117,x16118))
% 28.25/28.14 [1612]~E(x16121,x16122)+E(f344(x16123,x16124,x16125,x16121,x16126,x16127,x16128),f344(x16123,x16124,x16125,x16122,x16126,x16127,x16128))
% 28.25/28.14 [1613]~E(x16131,x16132)+E(f344(x16133,x16134,x16135,x16136,x16131,x16137,x16138),f344(x16133,x16134,x16135,x16136,x16132,x16137,x16138))
% 28.25/28.14 [1614]~E(x16141,x16142)+E(f344(x16143,x16144,x16145,x16146,x16147,x16141,x16148),f344(x16143,x16144,x16145,x16146,x16147,x16142,x16148))
% 28.25/28.14 [1615]~E(x16151,x16152)+E(f344(x16153,x16154,x16155,x16156,x16157,x16158,x16151),f344(x16153,x16154,x16155,x16156,x16157,x16158,x16152))
% 28.25/28.14 [1616]~E(x16161,x16162)+E(f662(x16161,x16163,x16164,x16165),f662(x16162,x16163,x16164,x16165))
% 28.25/28.14 [1617]~E(x16171,x16172)+E(f662(x16173,x16171,x16174,x16175),f662(x16173,x16172,x16174,x16175))
% 28.25/28.14 [1618]~E(x16181,x16182)+E(f662(x16183,x16184,x16181,x16185),f662(x16183,x16184,x16182,x16185))
% 28.25/28.14 [1619]~E(x16191,x16192)+E(f662(x16193,x16194,x16195,x16191),f662(x16193,x16194,x16195,x16192))
% 28.25/28.14 [1620]~E(x16201,x16202)+E(f767(x16201,x16203,x16204,x16205,x16206),f767(x16202,x16203,x16204,x16205,x16206))
% 28.25/28.14 [1621]~E(x16211,x16212)+E(f767(x16213,x16211,x16214,x16215,x16216),f767(x16213,x16212,x16214,x16215,x16216))
% 28.25/28.14 [1622]~E(x16221,x16222)+E(f767(x16223,x16224,x16221,x16225,x16226),f767(x16223,x16224,x16222,x16225,x16226))
% 28.25/28.14 [1623]~E(x16231,x16232)+E(f767(x16233,x16234,x16235,x16231,x16236),f767(x16233,x16234,x16235,x16232,x16236))
% 28.25/28.14 [1624]~E(x16241,x16242)+E(f767(x16243,x16244,x16245,x16246,x16241),f767(x16243,x16244,x16245,x16246,x16242))
% 28.25/28.14 [1625]~E(x16251,x16252)+E(f197(x16251,x16253,x16254,x16255),f197(x16252,x16253,x16254,x16255))
% 28.25/28.14 [1626]~E(x16261,x16262)+E(f197(x16263,x16261,x16264,x16265),f197(x16263,x16262,x16264,x16265))
% 28.25/28.14 [1627]~E(x16271,x16272)+E(f197(x16273,x16274,x16271,x16275),f197(x16273,x16274,x16272,x16275))
% 28.25/28.14 [1628]~E(x16281,x16282)+E(f197(x16283,x16284,x16285,x16281),f197(x16283,x16284,x16285,x16282))
% 28.25/28.14 [1629]~E(x16291,x16292)+E(f436(x16291,x16293,x16294),f436(x16292,x16293,x16294))
% 28.25/28.14 [1630]~E(x16301,x16302)+E(f436(x16303,x16301,x16304),f436(x16303,x16302,x16304))
% 28.25/28.14 [1631]~E(x16311,x16312)+E(f436(x16313,x16314,x16311),f436(x16313,x16314,x16312))
% 28.25/28.14 [1632]~E(x16321,x16322)+E(f526(x16321,x16323,x16324),f526(x16322,x16323,x16324))
% 28.25/28.14 [1633]~E(x16331,x16332)+E(f526(x16333,x16331,x16334),f526(x16333,x16332,x16334))
% 28.25/28.14 [1634]~E(x16341,x16342)+E(f526(x16343,x16344,x16341),f526(x16343,x16344,x16342))
% 28.25/28.14 [1635]~E(x16351,x16352)+E(f412(x16351,x16353,x16354,x16355),f412(x16352,x16353,x16354,x16355))
% 28.25/28.14 [1636]~E(x16361,x16362)+E(f412(x16363,x16361,x16364,x16365),f412(x16363,x16362,x16364,x16365))
% 28.25/28.14 [1637]~E(x16371,x16372)+E(f412(x16373,x16374,x16371,x16375),f412(x16373,x16374,x16372,x16375))
% 28.25/28.14 [1638]~E(x16381,x16382)+E(f412(x16383,x16384,x16385,x16381),f412(x16383,x16384,x16385,x16382))
% 28.25/28.14 [1639]~E(x16391,x16392)+E(f850(x16391,x16393,x16394,x16395,x16396,x16397,x16398),f850(x16392,x16393,x16394,x16395,x16396,x16397,x16398))
% 28.25/28.14 [1640]~E(x16401,x16402)+E(f850(x16403,x16401,x16404,x16405,x16406,x16407,x16408),f850(x16403,x16402,x16404,x16405,x16406,x16407,x16408))
% 28.25/28.14 [1641]~E(x16411,x16412)+E(f850(x16413,x16414,x16411,x16415,x16416,x16417,x16418),f850(x16413,x16414,x16412,x16415,x16416,x16417,x16418))
% 28.25/28.14 [1642]~E(x16421,x16422)+E(f850(x16423,x16424,x16425,x16421,x16426,x16427,x16428),f850(x16423,x16424,x16425,x16422,x16426,x16427,x16428))
% 28.25/28.14 [1643]~E(x16431,x16432)+E(f850(x16433,x16434,x16435,x16436,x16431,x16437,x16438),f850(x16433,x16434,x16435,x16436,x16432,x16437,x16438))
% 28.25/28.14 [1644]~E(x16441,x16442)+E(f850(x16443,x16444,x16445,x16446,x16447,x16441,x16448),f850(x16443,x16444,x16445,x16446,x16447,x16442,x16448))
% 28.25/28.14 [1645]~E(x16451,x16452)+E(f850(x16453,x16454,x16455,x16456,x16457,x16458,x16451),f850(x16453,x16454,x16455,x16456,x16457,x16458,x16452))
% 28.25/28.14 [1646]~E(x16461,x16462)+E(f637(x16461,x16463,x16464,x16465,x16466),f637(x16462,x16463,x16464,x16465,x16466))
% 28.25/28.14 [1647]~E(x16471,x16472)+E(f637(x16473,x16471,x16474,x16475,x16476),f637(x16473,x16472,x16474,x16475,x16476))
% 28.25/28.14 [1648]~E(x16481,x16482)+E(f637(x16483,x16484,x16481,x16485,x16486),f637(x16483,x16484,x16482,x16485,x16486))
% 28.25/28.14 [1649]~E(x16491,x16492)+E(f637(x16493,x16494,x16495,x16491,x16496),f637(x16493,x16494,x16495,x16492,x16496))
% 28.25/28.14 [1650]~E(x16501,x16502)+E(f637(x16503,x16504,x16505,x16506,x16501),f637(x16503,x16504,x16505,x16506,x16502))
% 28.25/28.14 [1651]~E(x16511,x16512)+E(f897(x16511,x16513,x16514,x16515,x16516,x16517,x16518),f897(x16512,x16513,x16514,x16515,x16516,x16517,x16518))
% 28.25/28.14 [1652]~E(x16521,x16522)+E(f897(x16523,x16521,x16524,x16525,x16526,x16527,x16528),f897(x16523,x16522,x16524,x16525,x16526,x16527,x16528))
% 28.25/28.14 [1653]~E(x16531,x16532)+E(f897(x16533,x16534,x16531,x16535,x16536,x16537,x16538),f897(x16533,x16534,x16532,x16535,x16536,x16537,x16538))
% 28.25/28.14 [1654]~E(x16541,x16542)+E(f897(x16543,x16544,x16545,x16541,x16546,x16547,x16548),f897(x16543,x16544,x16545,x16542,x16546,x16547,x16548))
% 28.25/28.14 [1655]~E(x16551,x16552)+E(f897(x16553,x16554,x16555,x16556,x16551,x16557,x16558),f897(x16553,x16554,x16555,x16556,x16552,x16557,x16558))
% 28.25/28.14 [1656]~E(x16561,x16562)+E(f897(x16563,x16564,x16565,x16566,x16567,x16561,x16568),f897(x16563,x16564,x16565,x16566,x16567,x16562,x16568))
% 28.25/28.14 [1657]~E(x16571,x16572)+E(f897(x16573,x16574,x16575,x16576,x16577,x16578,x16571),f897(x16573,x16574,x16575,x16576,x16577,x16578,x16572))
% 28.25/28.14 [1658]~E(x16581,x16582)+E(f351(x16581,x16583),f351(x16582,x16583))
% 28.25/28.14 [1659]~E(x16591,x16592)+E(f351(x16593,x16591),f351(x16593,x16592))
% 28.25/28.14 [1660]~E(x16601,x16602)+E(f323(x16601,x16603,x16604,x16605),f323(x16602,x16603,x16604,x16605))
% 28.25/28.14 [1661]~E(x16611,x16612)+E(f323(x16613,x16611,x16614,x16615),f323(x16613,x16612,x16614,x16615))
% 28.25/28.14 [1662]~E(x16621,x16622)+E(f323(x16623,x16624,x16621,x16625),f323(x16623,x16624,x16622,x16625))
% 28.25/28.14 [1663]~E(x16631,x16632)+E(f323(x16633,x16634,x16635,x16631),f323(x16633,x16634,x16635,x16632))
% 28.25/28.14 [1664]~E(x16641,x16642)+E(f863(x16641,x16643,x16644,x16645,x16646,x16647,x16648,x16649),f863(x16642,x16643,x16644,x16645,x16646,x16647,x16648,x16649))
% 28.25/28.14 [1665]~E(x16651,x16652)+E(f863(x16653,x16651,x16654,x16655,x16656,x16657,x16658,x16659),f863(x16653,x16652,x16654,x16655,x16656,x16657,x16658,x16659))
% 28.25/28.14 [1666]~E(x16661,x16662)+E(f863(x16663,x16664,x16661,x16665,x16666,x16667,x16668,x16669),f863(x16663,x16664,x16662,x16665,x16666,x16667,x16668,x16669))
% 28.25/28.14 [1667]~E(x16671,x16672)+E(f863(x16673,x16674,x16675,x16671,x16676,x16677,x16678,x16679),f863(x16673,x16674,x16675,x16672,x16676,x16677,x16678,x16679))
% 28.25/28.14 [1668]~E(x16681,x16682)+E(f863(x16683,x16684,x16685,x16686,x16681,x16687,x16688,x16689),f863(x16683,x16684,x16685,x16686,x16682,x16687,x16688,x16689))
% 28.25/28.14 [1669]~E(x16691,x16692)+E(f863(x16693,x16694,x16695,x16696,x16697,x16691,x16698,x16699),f863(x16693,x16694,x16695,x16696,x16697,x16692,x16698,x16699))
% 28.25/28.14 [1670]~E(x16701,x16702)+E(f863(x16703,x16704,x16705,x16706,x16707,x16708,x16701,x16709),f863(x16703,x16704,x16705,x16706,x16707,x16708,x16702,x16709))
% 28.25/28.14 [1671]~E(x16711,x16712)+E(f863(x16713,x16714,x16715,x16716,x16717,x16718,x16719,x16711),f863(x16713,x16714,x16715,x16716,x16717,x16718,x16719,x16712))
% 28.25/28.14 [1672]~E(x16721,x16722)+E(f716(x16721,x16723,x16724,x16725,x16726),f716(x16722,x16723,x16724,x16725,x16726))
% 28.25/28.14 [1673]~E(x16731,x16732)+E(f716(x16733,x16731,x16734,x16735,x16736),f716(x16733,x16732,x16734,x16735,x16736))
% 28.25/28.14 [1674]~E(x16741,x16742)+E(f716(x16743,x16744,x16741,x16745,x16746),f716(x16743,x16744,x16742,x16745,x16746))
% 28.25/28.14 [1675]~E(x16751,x16752)+E(f716(x16753,x16754,x16755,x16751,x16756),f716(x16753,x16754,x16755,x16752,x16756))
% 28.25/28.14 [1676]~E(x16761,x16762)+E(f716(x16763,x16764,x16765,x16766,x16761),f716(x16763,x16764,x16765,x16766,x16762))
% 28.25/28.14 [1677]~E(x16771,x16772)+E(f898(x16771,x16773,x16774,x16775,x16776,x16777,x16778),f898(x16772,x16773,x16774,x16775,x16776,x16777,x16778))
% 28.25/28.14 [1678]~E(x16781,x16782)+E(f898(x16783,x16781,x16784,x16785,x16786,x16787,x16788),f898(x16783,x16782,x16784,x16785,x16786,x16787,x16788))
% 28.25/28.14 [1679]~E(x16791,x16792)+E(f898(x16793,x16794,x16791,x16795,x16796,x16797,x16798),f898(x16793,x16794,x16792,x16795,x16796,x16797,x16798))
% 28.25/28.14 [1680]~E(x16801,x16802)+E(f898(x16803,x16804,x16805,x16801,x16806,x16807,x16808),f898(x16803,x16804,x16805,x16802,x16806,x16807,x16808))
% 28.25/28.14 [1681]~E(x16811,x16812)+E(f898(x16813,x16814,x16815,x16816,x16811,x16817,x16818),f898(x16813,x16814,x16815,x16816,x16812,x16817,x16818))
% 28.25/28.14 [1682]~E(x16821,x16822)+E(f898(x16823,x16824,x16825,x16826,x16827,x16821,x16828),f898(x16823,x16824,x16825,x16826,x16827,x16822,x16828))
% 28.25/28.14 [1683]~E(x16831,x16832)+E(f898(x16833,x16834,x16835,x16836,x16837,x16838,x16831),f898(x16833,x16834,x16835,x16836,x16837,x16838,x16832))
% 28.25/28.14 [1684]~E(x16841,x16842)+E(f509(x16841,x16843,x16844),f509(x16842,x16843,x16844))
% 28.25/28.14 [1685]~E(x16851,x16852)+E(f509(x16853,x16851,x16854),f509(x16853,x16852,x16854))
% 28.25/28.14 [1686]~E(x16861,x16862)+E(f509(x16863,x16864,x16861),f509(x16863,x16864,x16862))
% 28.25/28.14 [1687]~E(x16871,x16872)+E(f343(x16871,x16873,x16874,x16875,x16876),f343(x16872,x16873,x16874,x16875,x16876))
% 28.25/28.14 [1688]~E(x16881,x16882)+E(f343(x16883,x16881,x16884,x16885,x16886),f343(x16883,x16882,x16884,x16885,x16886))
% 28.25/28.14 [1689]~E(x16891,x16892)+E(f343(x16893,x16894,x16891,x16895,x16896),f343(x16893,x16894,x16892,x16895,x16896))
% 28.25/28.14 [1690]~E(x16901,x16902)+E(f343(x16903,x16904,x16905,x16901,x16906),f343(x16903,x16904,x16905,x16902,x16906))
% 28.25/28.14 [1691]~E(x16911,x16912)+E(f343(x16913,x16914,x16915,x16916,x16911),f343(x16913,x16914,x16915,x16916,x16912))
% 28.25/28.14 [1692]~E(x16921,x16922)+E(f734(x16921,x16923,x16924),f734(x16922,x16923,x16924))
% 28.25/28.14 [1693]~E(x16931,x16932)+E(f734(x16933,x16931,x16934),f734(x16933,x16932,x16934))
% 28.25/28.14 [1694]~E(x16941,x16942)+E(f734(x16943,x16944,x16941),f734(x16943,x16944,x16942))
% 28.25/28.14 [1695]~E(x16951,x16952)+E(f896(x16951,x16953,x16954,x16955),f896(x16952,x16953,x16954,x16955))
% 28.25/28.14 [1696]~E(x16961,x16962)+E(f896(x16963,x16961,x16964,x16965),f896(x16963,x16962,x16964,x16965))
% 28.25/28.14 [1697]~E(x16971,x16972)+E(f896(x16973,x16974,x16971,x16975),f896(x16973,x16974,x16972,x16975))
% 28.25/28.14 [1698]~E(x16981,x16982)+E(f896(x16983,x16984,x16985,x16981),f896(x16983,x16984,x16985,x16982))
% 28.25/28.14 [1699]~E(x16991,x16992)+E(f661(x16991,x16993,x16994,x16995),f661(x16992,x16993,x16994,x16995))
% 28.25/28.14 [1700]~E(x17001,x17002)+E(f661(x17003,x17001,x17004,x17005),f661(x17003,x17002,x17004,x17005))
% 28.25/28.14 [1701]~E(x17011,x17012)+E(f661(x17013,x17014,x17011,x17015),f661(x17013,x17014,x17012,x17015))
% 28.25/28.14 [1702]~E(x17021,x17022)+E(f661(x17023,x17024,x17025,x17021),f661(x17023,x17024,x17025,x17022))
% 28.25/28.14 [1703]~E(x17031,x17032)+E(f345(x17031,x17033,x17034),f345(x17032,x17033,x17034))
% 28.25/28.14 [1704]~E(x17041,x17042)+E(f345(x17043,x17041,x17044),f345(x17043,x17042,x17044))
% 28.25/28.14 [1705]~E(x17051,x17052)+E(f345(x17053,x17054,x17051),f345(x17053,x17054,x17052))
% 28.25/28.14 [1706]~E(x17061,x17062)+E(f586(x17061,x17063,x17064,x17065,x17066,x17067,x17068,x17069),f586(x17062,x17063,x17064,x17065,x17066,x17067,x17068,x17069))
% 28.25/28.14 [1707]~E(x17071,x17072)+E(f586(x17073,x17071,x17074,x17075,x17076,x17077,x17078,x17079),f586(x17073,x17072,x17074,x17075,x17076,x17077,x17078,x17079))
% 28.25/28.14 [1708]~E(x17081,x17082)+E(f586(x17083,x17084,x17081,x17085,x17086,x17087,x17088,x17089),f586(x17083,x17084,x17082,x17085,x17086,x17087,x17088,x17089))
% 28.25/28.14 [1709]~E(x17091,x17092)+E(f586(x17093,x17094,x17095,x17091,x17096,x17097,x17098,x17099),f586(x17093,x17094,x17095,x17092,x17096,x17097,x17098,x17099))
% 28.25/28.14 [1710]~E(x17101,x17102)+E(f586(x17103,x17104,x17105,x17106,x17101,x17107,x17108,x17109),f586(x17103,x17104,x17105,x17106,x17102,x17107,x17108,x17109))
% 28.25/28.14 [1711]~E(x17111,x17112)+E(f586(x17113,x17114,x17115,x17116,x17117,x17111,x17118,x17119),f586(x17113,x17114,x17115,x17116,x17117,x17112,x17118,x17119))
% 28.25/28.14 [1712]~E(x17121,x17122)+E(f586(x17123,x17124,x17125,x17126,x17127,x17128,x17121,x17129),f586(x17123,x17124,x17125,x17126,x17127,x17128,x17122,x17129))
% 28.25/28.14 [1713]~E(x17131,x17132)+E(f586(x17133,x17134,x17135,x17136,x17137,x17138,x17139,x17131),f586(x17133,x17134,x17135,x17136,x17137,x17138,x17139,x17132))
% 28.25/28.14 [1714]~E(x17141,x17142)+E(f346(x17141,x17143),f346(x17142,x17143))
% 28.25/28.14 [1715]~E(x17151,x17152)+E(f346(x17153,x17151),f346(x17153,x17152))
% 28.25/28.14 [1716]~E(x17161,x17162)+E(f901(x17161,x17163,x17164,x17165,x17166,x17167),f901(x17162,x17163,x17164,x17165,x17166,x17167))
% 28.25/28.14 [1717]~E(x17171,x17172)+E(f901(x17173,x17171,x17174,x17175,x17176,x17177),f901(x17173,x17172,x17174,x17175,x17176,x17177))
% 28.25/28.14 [1718]~E(x17181,x17182)+E(f901(x17183,x17184,x17181,x17185,x17186,x17187),f901(x17183,x17184,x17182,x17185,x17186,x17187))
% 28.25/28.14 [1719]~E(x17191,x17192)+E(f901(x17193,x17194,x17195,x17191,x17196,x17197),f901(x17193,x17194,x17195,x17192,x17196,x17197))
% 28.25/28.14 [1720]~E(x17201,x17202)+E(f901(x17203,x17204,x17205,x17206,x17201,x17207),f901(x17203,x17204,x17205,x17206,x17202,x17207))
% 28.25/28.14 [1721]~E(x17211,x17212)+E(f901(x17213,x17214,x17215,x17216,x17217,x17211),f901(x17213,x17214,x17215,x17216,x17217,x17212))
% 28.25/28.14 [1722]~E(x17221,x17222)+E(f592(x17221,x17223,x17224,x17225),f592(x17222,x17223,x17224,x17225))
% 28.25/28.14 [1723]~E(x17231,x17232)+E(f592(x17233,x17231,x17234,x17235),f592(x17233,x17232,x17234,x17235))
% 28.25/28.14 [1724]~E(x17241,x17242)+E(f592(x17243,x17244,x17241,x17245),f592(x17243,x17244,x17242,x17245))
% 28.25/28.14 [1725]~E(x17251,x17252)+E(f592(x17253,x17254,x17255,x17251),f592(x17253,x17254,x17255,x17252))
% 28.25/28.14 [1726]~E(x17261,x17262)+E(f497(x17261,x17263,x17264,x17265,x17266,x17267,x17268),f497(x17262,x17263,x17264,x17265,x17266,x17267,x17268))
% 28.25/28.14 [1727]~E(x17271,x17272)+E(f497(x17273,x17271,x17274,x17275,x17276,x17277,x17278),f497(x17273,x17272,x17274,x17275,x17276,x17277,x17278))
% 28.25/28.14 [1728]~E(x17281,x17282)+E(f497(x17283,x17284,x17281,x17285,x17286,x17287,x17288),f497(x17283,x17284,x17282,x17285,x17286,x17287,x17288))
% 28.25/28.14 [1729]~E(x17291,x17292)+E(f497(x17293,x17294,x17295,x17291,x17296,x17297,x17298),f497(x17293,x17294,x17295,x17292,x17296,x17297,x17298))
% 28.25/28.14 [1730]~E(x17301,x17302)+E(f497(x17303,x17304,x17305,x17306,x17301,x17307,x17308),f497(x17303,x17304,x17305,x17306,x17302,x17307,x17308))
% 28.25/28.14 [1731]~E(x17311,x17312)+E(f497(x17313,x17314,x17315,x17316,x17317,x17311,x17318),f497(x17313,x17314,x17315,x17316,x17317,x17312,x17318))
% 28.25/28.14 [1732]~E(x17321,x17322)+E(f497(x17323,x17324,x17325,x17326,x17327,x17328,x17321),f497(x17323,x17324,x17325,x17326,x17327,x17328,x17322))
% 28.25/28.14 [1733]~E(x17331,x17332)+E(f770(x17331,x17333,x17334,x17335,x17336),f770(x17332,x17333,x17334,x17335,x17336))
% 28.25/28.14 [1734]~E(x17341,x17342)+E(f770(x17343,x17341,x17344,x17345,x17346),f770(x17343,x17342,x17344,x17345,x17346))
% 28.25/28.14 [1735]~E(x17351,x17352)+E(f770(x17353,x17354,x17351,x17355,x17356),f770(x17353,x17354,x17352,x17355,x17356))
% 28.25/28.14 [1736]~E(x17361,x17362)+E(f770(x17363,x17364,x17365,x17361,x17366),f770(x17363,x17364,x17365,x17362,x17366))
% 28.25/28.14 [1737]~E(x17371,x17372)+E(f770(x17373,x17374,x17375,x17376,x17371),f770(x17373,x17374,x17375,x17376,x17372))
% 28.25/28.14 [1738]~E(x17381,x17382)+E(f452(x17381,x17383),f452(x17382,x17383))
% 28.25/28.14 [1739]~E(x17391,x17392)+E(f452(x17393,x17391),f452(x17393,x17392))
% 28.25/28.14 [1740]~E(x17401,x17402)+E(f840(x17401,x17403,x17404),f840(x17402,x17403,x17404))
% 28.25/28.14 [1741]~E(x17411,x17412)+E(f840(x17413,x17411,x17414),f840(x17413,x17412,x17414))
% 28.25/28.14 [1742]~E(x17421,x17422)+E(f840(x17423,x17424,x17421),f840(x17423,x17424,x17422))
% 28.25/28.14 [1743]~E(x17431,x17432)+E(f759(x17431,x17433,x17434),f759(x17432,x17433,x17434))
% 28.25/28.14 [1744]~E(x17441,x17442)+E(f759(x17443,x17441,x17444),f759(x17443,x17442,x17444))
% 28.25/28.14 [1745]~E(x17451,x17452)+E(f759(x17453,x17454,x17451),f759(x17453,x17454,x17452))
% 28.25/28.14 [1746]~E(x17461,x17462)+E(f355(x17461,x17463,x17464),f355(x17462,x17463,x17464))
% 28.25/28.14 [1747]~E(x17471,x17472)+E(f355(x17473,x17471,x17474),f355(x17473,x17472,x17474))
% 28.25/28.14 [1748]~E(x17481,x17482)+E(f355(x17483,x17484,x17481),f355(x17483,x17484,x17482))
% 28.25/28.14 [1749]~E(x17491,x17492)+E(f581(x17491,x17493,x17494,x17495,x17496,x17497),f581(x17492,x17493,x17494,x17495,x17496,x17497))
% 28.25/28.14 [1750]~E(x17501,x17502)+E(f581(x17503,x17501,x17504,x17505,x17506,x17507),f581(x17503,x17502,x17504,x17505,x17506,x17507))
% 28.25/28.14 [1751]~E(x17511,x17512)+E(f581(x17513,x17514,x17511,x17515,x17516,x17517),f581(x17513,x17514,x17512,x17515,x17516,x17517))
% 28.25/28.14 [1752]~E(x17521,x17522)+E(f581(x17523,x17524,x17525,x17521,x17526,x17527),f581(x17523,x17524,x17525,x17522,x17526,x17527))
% 28.25/28.14 [1753]~E(x17531,x17532)+E(f581(x17533,x17534,x17535,x17536,x17531,x17537),f581(x17533,x17534,x17535,x17536,x17532,x17537))
% 28.25/28.14 [1754]~E(x17541,x17542)+E(f581(x17543,x17544,x17545,x17546,x17547,x17541),f581(x17543,x17544,x17545,x17546,x17547,x17542))
% 28.25/28.14 [1755]~E(x17551,x17552)+E(f483(x17551,x17553),f483(x17552,x17553))
% 28.25/28.14 [1756]~E(x17561,x17562)+E(f483(x17563,x17561),f483(x17563,x17562))
% 28.25/28.14 [1757]~E(x17571,x17572)+E(f560(x17571,x17573,x17574),f560(x17572,x17573,x17574))
% 28.25/28.14 [1758]~E(x17581,x17582)+E(f560(x17583,x17581,x17584),f560(x17583,x17582,x17584))
% 28.25/28.14 [1759]~E(x17591,x17592)+E(f560(x17593,x17594,x17591),f560(x17593,x17594,x17592))
% 28.25/28.14 [1760]~E(x17601,x17602)+E(f415(x17601,x17603,x17604,x17605),f415(x17602,x17603,x17604,x17605))
% 28.25/28.14 [1761]~E(x17611,x17612)+E(f415(x17613,x17611,x17614,x17615),f415(x17613,x17612,x17614,x17615))
% 28.25/28.14 [1762]~E(x17621,x17622)+E(f415(x17623,x17624,x17621,x17625),f415(x17623,x17624,x17622,x17625))
% 28.25/28.14 [1763]~E(x17631,x17632)+E(f415(x17633,x17634,x17635,x17631),f415(x17633,x17634,x17635,x17632))
% 28.25/28.14 [1764]~E(x17641,x17642)+E(f338(x17641,x17643,x17644),f338(x17642,x17643,x17644))
% 28.25/28.14 [1765]~E(x17651,x17652)+E(f338(x17653,x17651,x17654),f338(x17653,x17652,x17654))
% 28.25/28.14 [1766]~E(x17661,x17662)+E(f338(x17663,x17664,x17661),f338(x17663,x17664,x17662))
% 28.25/28.14 [1767]~E(x17671,x17672)+E(f915(x17671,x17673),f915(x17672,x17673))
% 28.25/28.14 [1768]~E(x17681,x17682)+E(f915(x17683,x17681),f915(x17683,x17682))
% 28.25/28.14 [1769]~E(x17691,x17692)+E(f450(x17691,x17693,x17694,x17695,x17696,x17697,x17698),f450(x17692,x17693,x17694,x17695,x17696,x17697,x17698))
% 28.25/28.14 [1770]~E(x17701,x17702)+E(f450(x17703,x17701,x17704,x17705,x17706,x17707,x17708),f450(x17703,x17702,x17704,x17705,x17706,x17707,x17708))
% 28.25/28.14 [1771]~E(x17711,x17712)+E(f450(x17713,x17714,x17711,x17715,x17716,x17717,x17718),f450(x17713,x17714,x17712,x17715,x17716,x17717,x17718))
% 28.25/28.14 [1772]~E(x17721,x17722)+E(f450(x17723,x17724,x17725,x17721,x17726,x17727,x17728),f450(x17723,x17724,x17725,x17722,x17726,x17727,x17728))
% 28.25/28.14 [1773]~E(x17731,x17732)+E(f450(x17733,x17734,x17735,x17736,x17731,x17737,x17738),f450(x17733,x17734,x17735,x17736,x17732,x17737,x17738))
% 28.25/28.14 [1774]~E(x17741,x17742)+E(f450(x17743,x17744,x17745,x17746,x17747,x17741,x17748),f450(x17743,x17744,x17745,x17746,x17747,x17742,x17748))
% 28.25/28.14 [1775]~E(x17751,x17752)+E(f450(x17753,x17754,x17755,x17756,x17757,x17758,x17751),f450(x17753,x17754,x17755,x17756,x17757,x17758,x17752))
% 28.25/28.14 [1776]~E(x17761,x17762)+E(f858(x17761,x17763,x17764,x17765),f858(x17762,x17763,x17764,x17765))
% 28.25/28.14 [1777]~E(x17771,x17772)+E(f858(x17773,x17771,x17774,x17775),f858(x17773,x17772,x17774,x17775))
% 28.25/28.14 [1778]~E(x17781,x17782)+E(f858(x17783,x17784,x17781,x17785),f858(x17783,x17784,x17782,x17785))
% 28.25/28.14 [1779]~E(x17791,x17792)+E(f858(x17793,x17794,x17795,x17791),f858(x17793,x17794,x17795,x17792))
% 28.25/28.14 [1780]~E(x17801,x17802)+E(f544(x17801,x17803,x17804),f544(x17802,x17803,x17804))
% 28.25/28.14 [1781]~E(x17811,x17812)+E(f544(x17813,x17811,x17814),f544(x17813,x17812,x17814))
% 28.25/28.14 [1782]~E(x17821,x17822)+E(f544(x17823,x17824,x17821),f544(x17823,x17824,x17822))
% 28.25/28.14 [1783]~E(x17831,x17832)+E(f606(x17831,x17833,x17834,x17835,x17836,x17837),f606(x17832,x17833,x17834,x17835,x17836,x17837))
% 28.25/28.14 [1784]~E(x17841,x17842)+E(f606(x17843,x17841,x17844,x17845,x17846,x17847),f606(x17843,x17842,x17844,x17845,x17846,x17847))
% 28.25/28.14 [1785]~E(x17851,x17852)+E(f606(x17853,x17854,x17851,x17855,x17856,x17857),f606(x17853,x17854,x17852,x17855,x17856,x17857))
% 28.25/28.14 [1786]~E(x17861,x17862)+E(f606(x17863,x17864,x17865,x17861,x17866,x17867),f606(x17863,x17864,x17865,x17862,x17866,x17867))
% 28.25/28.14 [1787]~E(x17871,x17872)+E(f606(x17873,x17874,x17875,x17876,x17871,x17877),f606(x17873,x17874,x17875,x17876,x17872,x17877))
% 28.25/28.14 [1788]~E(x17881,x17882)+E(f606(x17883,x17884,x17885,x17886,x17887,x17881),f606(x17883,x17884,x17885,x17886,x17887,x17882))
% 28.25/28.14 [1789]~E(x17891,x17892)+E(f692(x17891,x17893,x17894,x17895),f692(x17892,x17893,x17894,x17895))
% 28.25/28.14 [1790]~E(x17901,x17902)+E(f692(x17903,x17901,x17904,x17905),f692(x17903,x17902,x17904,x17905))
% 28.25/28.14 [1791]~E(x17911,x17912)+E(f692(x17913,x17914,x17911,x17915),f692(x17913,x17914,x17912,x17915))
% 28.25/28.14 [1792]~E(x17921,x17922)+E(f692(x17923,x17924,x17925,x17921),f692(x17923,x17924,x17925,x17922))
% 28.25/28.14 [1793]~E(x17931,x17932)+E(f835(x17931,x17933),f835(x17932,x17933))
% 28.25/28.14 [1794]~E(x17941,x17942)+E(f835(x17943,x17941),f835(x17943,x17942))
% 28.25/28.14 [1795]~E(x17951,x17952)+E(f524(x17951,x17953,x17954),f524(x17952,x17953,x17954))
% 28.25/28.14 [1796]~E(x17961,x17962)+E(f524(x17963,x17961,x17964),f524(x17963,x17962,x17964))
% 28.25/28.14 [1797]~E(x17971,x17972)+E(f524(x17973,x17974,x17971),f524(x17973,x17974,x17972))
% 28.25/28.14 [1798]~E(x17981,x17982)+E(f671(x17981,x17983,x17984,x17985),f671(x17982,x17983,x17984,x17985))
% 28.25/28.14 [1799]~E(x17991,x17992)+E(f671(x17993,x17991,x17994,x17995),f671(x17993,x17992,x17994,x17995))
% 28.25/28.14 [1800]~E(x18001,x18002)+E(f671(x18003,x18004,x18001,x18005),f671(x18003,x18004,x18002,x18005))
% 28.25/28.14 [1801]~E(x18011,x18012)+E(f671(x18013,x18014,x18015,x18011),f671(x18013,x18014,x18015,x18012))
% 28.25/28.14 [1802]~E(x18021,x18022)+E(f819(x18021,x18023,x18024,x18025,x18026),f819(x18022,x18023,x18024,x18025,x18026))
% 28.25/28.14 [1803]~E(x18031,x18032)+E(f819(x18033,x18031,x18034,x18035,x18036),f819(x18033,x18032,x18034,x18035,x18036))
% 28.25/28.14 [1804]~E(x18041,x18042)+E(f819(x18043,x18044,x18041,x18045,x18046),f819(x18043,x18044,x18042,x18045,x18046))
% 28.25/28.14 [1805]~E(x18051,x18052)+E(f819(x18053,x18054,x18055,x18051,x18056),f819(x18053,x18054,x18055,x18052,x18056))
% 28.25/28.14 [1806]~E(x18061,x18062)+E(f819(x18063,x18064,x18065,x18066,x18061),f819(x18063,x18064,x18065,x18066,x18062))
% 28.25/28.14 [1807]~E(x18071,x18072)+E(f507(x18071,x18073,x18074,x18075,x18076,x18077,x18078),f507(x18072,x18073,x18074,x18075,x18076,x18077,x18078))
% 28.25/28.14 [1808]~E(x18081,x18082)+E(f507(x18083,x18081,x18084,x18085,x18086,x18087,x18088),f507(x18083,x18082,x18084,x18085,x18086,x18087,x18088))
% 28.25/28.14 [1809]~E(x18091,x18092)+E(f507(x18093,x18094,x18091,x18095,x18096,x18097,x18098),f507(x18093,x18094,x18092,x18095,x18096,x18097,x18098))
% 28.25/28.14 [1810]~E(x18101,x18102)+E(f507(x18103,x18104,x18105,x18101,x18106,x18107,x18108),f507(x18103,x18104,x18105,x18102,x18106,x18107,x18108))
% 28.25/28.14 [1811]~E(x18111,x18112)+E(f507(x18113,x18114,x18115,x18116,x18111,x18117,x18118),f507(x18113,x18114,x18115,x18116,x18112,x18117,x18118))
% 28.25/28.14 [1812]~E(x18121,x18122)+E(f507(x18123,x18124,x18125,x18126,x18127,x18121,x18128),f507(x18123,x18124,x18125,x18126,x18127,x18122,x18128))
% 28.25/28.14 [1813]~E(x18131,x18132)+E(f507(x18133,x18134,x18135,x18136,x18137,x18138,x18131),f507(x18133,x18134,x18135,x18136,x18137,x18138,x18132))
% 28.25/28.14 [1814]~E(x18141,x18142)+E(f404(x18141,x18143,x18144,x18145),f404(x18142,x18143,x18144,x18145))
% 28.25/28.14 [1815]~E(x18151,x18152)+E(f404(x18153,x18151,x18154,x18155),f404(x18153,x18152,x18154,x18155))
% 28.25/28.14 [1816]~E(x18161,x18162)+E(f404(x18163,x18164,x18161,x18165),f404(x18163,x18164,x18162,x18165))
% 28.25/28.14 [1817]~E(x18171,x18172)+E(f404(x18173,x18174,x18175,x18171),f404(x18173,x18174,x18175,x18172))
% 28.25/28.14 [1818]~E(x18181,x18182)+E(f561(x18181,x18183,x18184,x18185),f561(x18182,x18183,x18184,x18185))
% 28.25/28.14 [1819]~E(x18191,x18192)+E(f561(x18193,x18191,x18194,x18195),f561(x18193,x18192,x18194,x18195))
% 28.25/28.14 [1820]~E(x18201,x18202)+E(f561(x18203,x18204,x18201,x18205),f561(x18203,x18204,x18202,x18205))
% 28.25/28.14 [1821]~E(x18211,x18212)+E(f561(x18213,x18214,x18215,x18211),f561(x18213,x18214,x18215,x18212))
% 28.25/28.14 [1822]~E(x18221,x18222)+E(f407(x18221,x18223,x18224,x18225,x18226),f407(x18222,x18223,x18224,x18225,x18226))
% 28.25/28.14 [1823]~E(x18231,x18232)+E(f407(x18233,x18231,x18234,x18235,x18236),f407(x18233,x18232,x18234,x18235,x18236))
% 28.25/28.14 [1824]~E(x18241,x18242)+E(f407(x18243,x18244,x18241,x18245,x18246),f407(x18243,x18244,x18242,x18245,x18246))
% 28.25/28.14 [1825]~E(x18251,x18252)+E(f407(x18253,x18254,x18255,x18251,x18256),f407(x18253,x18254,x18255,x18252,x18256))
% 28.25/28.14 [1826]~E(x18261,x18262)+E(f407(x18263,x18264,x18265,x18266,x18261),f407(x18263,x18264,x18265,x18266,x18262))
% 28.25/28.14 [1827]~E(x18271,x18272)+E(f329(x18271),f329(x18272))
% 28.25/28.14 [1828]~E(x18281,x18282)+E(f783(x18281,x18283,x18284,x18285),f783(x18282,x18283,x18284,x18285))
% 28.25/28.14 [1829]~E(x18291,x18292)+E(f783(x18293,x18291,x18294,x18295),f783(x18293,x18292,x18294,x18295))
% 28.25/28.14 [1830]~E(x18301,x18302)+E(f783(x18303,x18304,x18301,x18305),f783(x18303,x18304,x18302,x18305))
% 28.25/28.14 [1831]~E(x18311,x18312)+E(f783(x18313,x18314,x18315,x18311),f783(x18313,x18314,x18315,x18312))
% 28.25/28.14 [1832]~E(x18321,x18322)+E(f842(x18321,x18323,x18324,x18325,x18326),f842(x18322,x18323,x18324,x18325,x18326))
% 28.25/28.14 [1833]~E(x18331,x18332)+E(f842(x18333,x18331,x18334,x18335,x18336),f842(x18333,x18332,x18334,x18335,x18336))
% 28.25/28.14 [1834]~E(x18341,x18342)+E(f842(x18343,x18344,x18341,x18345,x18346),f842(x18343,x18344,x18342,x18345,x18346))
% 28.25/28.14 [1835]~E(x18351,x18352)+E(f842(x18353,x18354,x18355,x18351,x18356),f842(x18353,x18354,x18355,x18352,x18356))
% 28.25/28.14 [1836]~E(x18361,x18362)+E(f842(x18363,x18364,x18365,x18366,x18361),f842(x18363,x18364,x18365,x18366,x18362))
% 28.25/28.14 [1837]~E(x18371,x18372)+E(f722(x18371,x18373,x18374,x18375,x18376),f722(x18372,x18373,x18374,x18375,x18376))
% 28.25/28.14 [1838]~E(x18381,x18382)+E(f722(x18383,x18381,x18384,x18385,x18386),f722(x18383,x18382,x18384,x18385,x18386))
% 28.25/28.14 [1839]~E(x18391,x18392)+E(f722(x18393,x18394,x18391,x18395,x18396),f722(x18393,x18394,x18392,x18395,x18396))
% 28.25/28.14 [1840]~E(x18401,x18402)+E(f722(x18403,x18404,x18405,x18401,x18406),f722(x18403,x18404,x18405,x18402,x18406))
% 28.25/28.14 [1841]~E(x18411,x18412)+E(f722(x18413,x18414,x18415,x18416,x18411),f722(x18413,x18414,x18415,x18416,x18412))
% 28.25/28.14 [1842]~E(x18421,x18422)+E(f786(x18421,x18423,x18424),f786(x18422,x18423,x18424))
% 28.25/28.14 [1843]~E(x18431,x18432)+E(f786(x18433,x18431,x18434),f786(x18433,x18432,x18434))
% 28.25/28.14 [1844]~E(x18441,x18442)+E(f786(x18443,x18444,x18441),f786(x18443,x18444,x18442))
% 28.25/28.14 [1845]~E(x18451,x18452)+E(f365(x18451,x18453),f365(x18452,x18453))
% 28.25/28.14 [1846]~E(x18461,x18462)+E(f365(x18463,x18461),f365(x18463,x18462))
% 28.25/28.14 [1847]~E(x18471,x18472)+E(f465(x18471,x18473,x18474,x18475,x18476,x18477,x18478),f465(x18472,x18473,x18474,x18475,x18476,x18477,x18478))
% 28.25/28.14 [1848]~E(x18481,x18482)+E(f465(x18483,x18481,x18484,x18485,x18486,x18487,x18488),f465(x18483,x18482,x18484,x18485,x18486,x18487,x18488))
% 28.25/28.14 [1849]~E(x18491,x18492)+E(f465(x18493,x18494,x18491,x18495,x18496,x18497,x18498),f465(x18493,x18494,x18492,x18495,x18496,x18497,x18498))
% 28.25/28.14 [1850]~E(x18501,x18502)+E(f465(x18503,x18504,x18505,x18501,x18506,x18507,x18508),f465(x18503,x18504,x18505,x18502,x18506,x18507,x18508))
% 28.25/28.14 [1851]~E(x18511,x18512)+E(f465(x18513,x18514,x18515,x18516,x18511,x18517,x18518),f465(x18513,x18514,x18515,x18516,x18512,x18517,x18518))
% 28.25/28.14 [1852]~E(x18521,x18522)+E(f465(x18523,x18524,x18525,x18526,x18527,x18521,x18528),f465(x18523,x18524,x18525,x18526,x18527,x18522,x18528))
% 28.25/28.14 [1853]~E(x18531,x18532)+E(f465(x18533,x18534,x18535,x18536,x18537,x18538,x18531),f465(x18533,x18534,x18535,x18536,x18537,x18538,x18532))
% 28.25/28.14 [1854]~E(x18541,x18542)+E(f776(x18541,x18543,x18544),f776(x18542,x18543,x18544))
% 28.25/28.14 [1855]~E(x18551,x18552)+E(f776(x18553,x18551,x18554),f776(x18553,x18552,x18554))
% 28.25/28.14 [1856]~E(x18561,x18562)+E(f776(x18563,x18564,x18561),f776(x18563,x18564,x18562))
% 28.25/28.14 [1857]~E(x18571,x18572)+E(f885(x18571,x18573,x18574),f885(x18572,x18573,x18574))
% 28.25/28.14 [1858]~E(x18581,x18582)+E(f885(x18583,x18581,x18584),f885(x18583,x18582,x18584))
% 28.25/28.14 [1859]~E(x18591,x18592)+E(f885(x18593,x18594,x18591),f885(x18593,x18594,x18592))
% 28.25/28.14 [1860]~E(x18601,x18602)+E(f496(x18601,x18603,x18604),f496(x18602,x18603,x18604))
% 28.25/28.14 [1861]~E(x18611,x18612)+E(f496(x18613,x18611,x18614),f496(x18613,x18612,x18614))
% 28.25/28.14 [1862]~E(x18621,x18622)+E(f496(x18623,x18624,x18621),f496(x18623,x18624,x18622))
% 28.25/28.14 [1863]~E(x18631,x18632)+E(f195(x18631,x18633,x18634),f195(x18632,x18633,x18634))
% 28.25/28.14 [1864]~E(x18641,x18642)+E(f195(x18643,x18641,x18644),f195(x18643,x18642,x18644))
% 28.25/28.14 [1865]~E(x18651,x18652)+E(f195(x18653,x18654,x18651),f195(x18653,x18654,x18652))
% 28.25/28.14 [1866]~E(x18661,x18662)+E(f577(x18661,x18663,x18664,x18665),f577(x18662,x18663,x18664,x18665))
% 28.25/28.14 [1867]~E(x18671,x18672)+E(f577(x18673,x18671,x18674,x18675),f577(x18673,x18672,x18674,x18675))
% 28.25/28.14 [1868]~E(x18681,x18682)+E(f577(x18683,x18684,x18681,x18685),f577(x18683,x18684,x18682,x18685))
% 28.25/28.14 [1869]~E(x18691,x18692)+E(f577(x18693,x18694,x18695,x18691),f577(x18693,x18694,x18695,x18692))
% 28.25/28.14 [1870]~E(x18701,x18702)+E(f189(x18701,x18703,x18704,x18705),f189(x18702,x18703,x18704,x18705))
% 28.25/28.14 [1871]~E(x18711,x18712)+E(f189(x18713,x18711,x18714,x18715),f189(x18713,x18712,x18714,x18715))
% 28.25/28.14 [1872]~E(x18721,x18722)+E(f189(x18723,x18724,x18721,x18725),f189(x18723,x18724,x18722,x18725))
% 28.25/28.14 [1873]~E(x18731,x18732)+E(f189(x18733,x18734,x18735,x18731),f189(x18733,x18734,x18735,x18732))
% 28.25/28.14 [1874]~E(x18741,x18742)+E(f446(x18741,x18743,x18744,x18745,x18746),f446(x18742,x18743,x18744,x18745,x18746))
% 28.25/28.14 [1875]~E(x18751,x18752)+E(f446(x18753,x18751,x18754,x18755,x18756),f446(x18753,x18752,x18754,x18755,x18756))
% 28.25/28.14 [1876]~E(x18761,x18762)+E(f446(x18763,x18764,x18761,x18765,x18766),f446(x18763,x18764,x18762,x18765,x18766))
% 28.25/28.14 [1877]~E(x18771,x18772)+E(f446(x18773,x18774,x18775,x18771,x18776),f446(x18773,x18774,x18775,x18772,x18776))
% 28.25/28.14 [1878]~E(x18781,x18782)+E(f446(x18783,x18784,x18785,x18786,x18781),f446(x18783,x18784,x18785,x18786,x18782))
% 28.25/28.14 [1879]~E(x18791,x18792)+E(f286(x18791,x18793,x18794),f286(x18792,x18793,x18794))
% 28.25/28.14 [1880]~E(x18801,x18802)+E(f286(x18803,x18801,x18804),f286(x18803,x18802,x18804))
% 28.25/28.14 [1881]~E(x18811,x18812)+E(f286(x18813,x18814,x18811),f286(x18813,x18814,x18812))
% 28.25/28.14 [1882]~E(x18821,x18822)+E(f608(x18821,x18823),f608(x18822,x18823))
% 28.25/28.14 [1883]~E(x18831,x18832)+E(f608(x18833,x18831),f608(x18833,x18832))
% 28.25/28.14 [1884]~E(x18841,x18842)+E(f198(x18841,x18843,x18844,x18845),f198(x18842,x18843,x18844,x18845))
% 28.25/28.14 [1885]~E(x18851,x18852)+E(f198(x18853,x18851,x18854,x18855),f198(x18853,x18852,x18854,x18855))
% 28.25/28.14 [1886]~E(x18861,x18862)+E(f198(x18863,x18864,x18861,x18865),f198(x18863,x18864,x18862,x18865))
% 28.25/28.14 [1887]~E(x18871,x18872)+E(f198(x18873,x18874,x18875,x18871),f198(x18873,x18874,x18875,x18872))
% 28.25/28.14 [1888]~E(x18881,x18882)+E(f848(x18881,x18883,x18884,x18885,x18886,x18887,x18888,x18889),f848(x18882,x18883,x18884,x18885,x18886,x18887,x18888,x18889))
% 28.25/28.14 [1889]~E(x18891,x18892)+E(f848(x18893,x18891,x18894,x18895,x18896,x18897,x18898,x18899),f848(x18893,x18892,x18894,x18895,x18896,x18897,x18898,x18899))
% 28.25/28.14 [1890]~E(x18901,x18902)+E(f848(x18903,x18904,x18901,x18905,x18906,x18907,x18908,x18909),f848(x18903,x18904,x18902,x18905,x18906,x18907,x18908,x18909))
% 28.25/28.14 [1891]~E(x18911,x18912)+E(f848(x18913,x18914,x18915,x18911,x18916,x18917,x18918,x18919),f848(x18913,x18914,x18915,x18912,x18916,x18917,x18918,x18919))
% 28.25/28.14 [1892]~E(x18921,x18922)+E(f848(x18923,x18924,x18925,x18926,x18921,x18927,x18928,x18929),f848(x18923,x18924,x18925,x18926,x18922,x18927,x18928,x18929))
% 28.25/28.14 [1893]~E(x18931,x18932)+E(f848(x18933,x18934,x18935,x18936,x18937,x18931,x18938,x18939),f848(x18933,x18934,x18935,x18936,x18937,x18932,x18938,x18939))
% 28.25/28.14 [1894]~E(x18941,x18942)+E(f848(x18943,x18944,x18945,x18946,x18947,x18948,x18941,x18949),f848(x18943,x18944,x18945,x18946,x18947,x18948,x18942,x18949))
% 28.25/28.14 [1895]~E(x18951,x18952)+E(f848(x18953,x18954,x18955,x18956,x18957,x18958,x18959,x18951),f848(x18953,x18954,x18955,x18956,x18957,x18958,x18959,x18952))
% 28.25/28.14 [1896]~E(x18961,x18962)+E(f395(x18961,x18963),f395(x18962,x18963))
% 28.25/28.14 [1897]~E(x18971,x18972)+E(f395(x18973,x18971),f395(x18973,x18972))
% 28.25/28.14 [1898]~E(x18981,x18982)+E(f353(x18981,x18983,x18984,x18985,x18986),f353(x18982,x18983,x18984,x18985,x18986))
% 28.25/28.14 [1899]~E(x18991,x18992)+E(f353(x18993,x18991,x18994,x18995,x18996),f353(x18993,x18992,x18994,x18995,x18996))
% 28.25/28.14 [1900]~E(x19001,x19002)+E(f353(x19003,x19004,x19001,x19005,x19006),f353(x19003,x19004,x19002,x19005,x19006))
% 28.25/28.14 [1901]~E(x19011,x19012)+E(f353(x19013,x19014,x19015,x19011,x19016),f353(x19013,x19014,x19015,x19012,x19016))
% 28.25/28.14 [1902]~E(x19021,x19022)+E(f353(x19023,x19024,x19025,x19026,x19021),f353(x19023,x19024,x19025,x19026,x19022))
% 28.25/28.14 [1903]~E(x19031,x19032)+E(f540(x19031,x19033),f540(x19032,x19033))
% 28.25/28.14 [1904]~E(x19041,x19042)+E(f540(x19043,x19041),f540(x19043,x19042))
% 28.25/28.14 [1905]~E(x19051,x19052)+E(f61(x19051,x19053,x19054),f61(x19052,x19053,x19054))
% 28.25/28.14 [1906]~E(x19061,x19062)+E(f61(x19063,x19061,x19064),f61(x19063,x19062,x19064))
% 28.25/28.14 [1907]~E(x19071,x19072)+E(f61(x19073,x19074,x19071),f61(x19073,x19074,x19072))
% 28.25/28.14 [1908]~E(x19081,x19082)+E(f513(x19081,x19083,x19084),f513(x19082,x19083,x19084))
% 28.25/28.14 [1909]~E(x19091,x19092)+E(f513(x19093,x19091,x19094),f513(x19093,x19092,x19094))
% 28.25/28.14 [1910]~E(x19101,x19102)+E(f513(x19103,x19104,x19101),f513(x19103,x19104,x19102))
% 28.25/28.14 [1911]~E(x19111,x19112)+E(f694(x19111,x19113),f694(x19112,x19113))
% 28.25/28.14 [1912]~E(x19121,x19122)+E(f694(x19123,x19121),f694(x19123,x19122))
% 28.25/28.14 [1913]~E(x19131,x19132)+E(f374(x19131,x19133),f374(x19132,x19133))
% 28.25/28.14 [1914]~E(x19141,x19142)+E(f374(x19143,x19141),f374(x19143,x19142))
% 28.25/28.14 [1915]~E(x19151,x19152)+E(f738(x19151,x19153),f738(x19152,x19153))
% 28.25/28.14 [1916]~E(x19161,x19162)+E(f738(x19163,x19161),f738(x19163,x19162))
% 28.25/28.14 [1917]~E(x19171,x19172)+E(f487(x19171,x19173,x19174),f487(x19172,x19173,x19174))
% 28.25/28.14 [1918]~E(x19181,x19182)+E(f487(x19183,x19181,x19184),f487(x19183,x19182,x19184))
% 28.25/28.14 [1919]~E(x19191,x19192)+E(f487(x19193,x19194,x19191),f487(x19193,x19194,x19192))
% 28.25/28.14 [1920]~E(x19201,x19202)+E(f550(x19201,x19203,x19204,x19205,x19206,x19207,x19208),f550(x19202,x19203,x19204,x19205,x19206,x19207,x19208))
% 28.25/28.14 [1921]~E(x19211,x19212)+E(f550(x19213,x19211,x19214,x19215,x19216,x19217,x19218),f550(x19213,x19212,x19214,x19215,x19216,x19217,x19218))
% 28.25/28.14 [1922]~E(x19221,x19222)+E(f550(x19223,x19224,x19221,x19225,x19226,x19227,x19228),f550(x19223,x19224,x19222,x19225,x19226,x19227,x19228))
% 28.25/28.14 [1923]~E(x19231,x19232)+E(f550(x19233,x19234,x19235,x19231,x19236,x19237,x19238),f550(x19233,x19234,x19235,x19232,x19236,x19237,x19238))
% 28.25/28.14 [1924]~E(x19241,x19242)+E(f550(x19243,x19244,x19245,x19246,x19241,x19247,x19248),f550(x19243,x19244,x19245,x19246,x19242,x19247,x19248))
% 28.25/28.14 [1925]~E(x19251,x19252)+E(f550(x19253,x19254,x19255,x19256,x19257,x19251,x19258),f550(x19253,x19254,x19255,x19256,x19257,x19252,x19258))
% 28.25/28.14 [1926]~E(x19261,x19262)+E(f550(x19263,x19264,x19265,x19266,x19267,x19268,x19261),f550(x19263,x19264,x19265,x19266,x19267,x19268,x19262))
% 28.25/28.14 [1927]~E(x19271,x19272)+E(f114(x19271,x19273,x19274,x19275),f114(x19272,x19273,x19274,x19275))
% 28.25/28.14 [1928]~E(x19281,x19282)+E(f114(x19283,x19281,x19284,x19285),f114(x19283,x19282,x19284,x19285))
% 28.25/28.14 [1929]~E(x19291,x19292)+E(f114(x19293,x19294,x19291,x19295),f114(x19293,x19294,x19292,x19295))
% 28.25/28.14 [1930]~E(x19301,x19302)+E(f114(x19303,x19304,x19305,x19301),f114(x19303,x19304,x19305,x19302))
% 28.25/28.14 [1931]~E(x19311,x19312)+E(f259(x19311),f259(x19312))
% 28.25/28.14 [1932]~E(x19321,x19322)+E(f530(x19321,x19323,x19324,x19325,x19326),f530(x19322,x19323,x19324,x19325,x19326))
% 28.25/28.14 [1933]~E(x19331,x19332)+E(f530(x19333,x19331,x19334,x19335,x19336),f530(x19333,x19332,x19334,x19335,x19336))
% 28.25/28.14 [1934]~E(x19341,x19342)+E(f530(x19343,x19344,x19341,x19345,x19346),f530(x19343,x19344,x19342,x19345,x19346))
% 28.25/28.14 [1935]~E(x19351,x19352)+E(f530(x19353,x19354,x19355,x19351,x19356),f530(x19353,x19354,x19355,x19352,x19356))
% 28.25/28.14 [1936]~E(x19361,x19362)+E(f530(x19363,x19364,x19365,x19366,x19361),f530(x19363,x19364,x19365,x19366,x19362))
% 28.25/28.14 [1937]~E(x19371,x19372)+E(f477(x19371,x19373,x19374),f477(x19372,x19373,x19374))
% 28.25/28.14 [1938]~E(x19381,x19382)+E(f477(x19383,x19381,x19384),f477(x19383,x19382,x19384))
% 28.25/28.14 [1939]~E(x19391,x19392)+E(f477(x19393,x19394,x19391),f477(x19393,x19394,x19392))
% 28.25/28.14 [1940]~E(x19401,x19402)+E(f194(x19401,x19403),f194(x19402,x19403))
% 28.25/28.14 [1941]~E(x19411,x19412)+E(f194(x19413,x19411),f194(x19413,x19412))
% 28.25/28.14 [1942]~E(x19421,x19422)+E(f238(x19421,x19423,x19424,x19425,x19426,x19427),f238(x19422,x19423,x19424,x19425,x19426,x19427))
% 28.25/28.14 [1943]~E(x19431,x19432)+E(f238(x19433,x19431,x19434,x19435,x19436,x19437),f238(x19433,x19432,x19434,x19435,x19436,x19437))
% 28.25/28.14 [1944]~E(x19441,x19442)+E(f238(x19443,x19444,x19441,x19445,x19446,x19447),f238(x19443,x19444,x19442,x19445,x19446,x19447))
% 28.25/28.14 [1945]~E(x19451,x19452)+E(f238(x19453,x19454,x19455,x19451,x19456,x19457),f238(x19453,x19454,x19455,x19452,x19456,x19457))
% 28.25/28.14 [1946]~E(x19461,x19462)+E(f238(x19463,x19464,x19465,x19466,x19461,x19467),f238(x19463,x19464,x19465,x19466,x19462,x19467))
% 28.25/28.14 [1947]~E(x19471,x19472)+E(f238(x19473,x19474,x19475,x19476,x19477,x19471),f238(x19473,x19474,x19475,x19476,x19477,x19472))
% 28.25/28.14 [1948]~E(x19481,x19482)+E(f784(x19481,x19483,x19484),f784(x19482,x19483,x19484))
% 28.25/28.14 [1949]~E(x19491,x19492)+E(f784(x19493,x19491,x19494),f784(x19493,x19492,x19494))
% 28.25/28.14 [1950]~E(x19501,x19502)+E(f784(x19503,x19504,x19501),f784(x19503,x19504,x19502))
% 28.25/28.14 [1951]~E(x19511,x19512)+E(f559(x19511,x19513),f559(x19512,x19513))
% 28.25/28.14 [1952]~E(x19521,x19522)+E(f559(x19523,x19521),f559(x19523,x19522))
% 28.25/28.14 [1953]~E(x19531,x19532)+E(f455(x19531,x19533,x19534,x19535),f455(x19532,x19533,x19534,x19535))
% 28.25/28.14 [1954]~E(x19541,x19542)+E(f455(x19543,x19541,x19544,x19545),f455(x19543,x19542,x19544,x19545))
% 28.25/28.14 [1955]~E(x19551,x19552)+E(f455(x19553,x19554,x19551,x19555),f455(x19553,x19554,x19552,x19555))
% 28.25/28.14 [1956]~E(x19561,x19562)+E(f455(x19563,x19564,x19565,x19561),f455(x19563,x19564,x19565,x19562))
% 28.25/28.14 [1957]~E(x19571,x19572)+E(f890(x19571,x19573,x19574,x19575),f890(x19572,x19573,x19574,x19575))
% 28.25/28.14 [1958]~E(x19581,x19582)+E(f890(x19583,x19581,x19584,x19585),f890(x19583,x19582,x19584,x19585))
% 28.25/28.14 [1959]~E(x19591,x19592)+E(f890(x19593,x19594,x19591,x19595),f890(x19593,x19594,x19592,x19595))
% 28.25/28.14 [1960]~E(x19601,x19602)+E(f890(x19603,x19604,x19605,x19601),f890(x19603,x19604,x19605,x19602))
% 28.25/28.14 [1961]~E(x19611,x19612)+E(f772(x19611,x19613,x19614),f772(x19612,x19613,x19614))
% 28.25/28.14 [1962]~E(x19621,x19622)+E(f772(x19623,x19621,x19624),f772(x19623,x19622,x19624))
% 28.25/28.14 [1963]~E(x19631,x19632)+E(f772(x19633,x19634,x19631),f772(x19633,x19634,x19632))
% 28.25/28.14 [1964]~E(x19641,x19642)+E(f827(x19641),f827(x19642))
% 28.25/28.14 [1965]~E(x19651,x19652)+E(f681(x19651,x19653,x19654,x19655),f681(x19652,x19653,x19654,x19655))
% 28.25/28.14 [1966]~E(x19661,x19662)+E(f681(x19663,x19661,x19664,x19665),f681(x19663,x19662,x19664,x19665))
% 28.25/28.14 [1967]~E(x19671,x19672)+E(f681(x19673,x19674,x19671,x19675),f681(x19673,x19674,x19672,x19675))
% 28.25/28.14 [1968]~E(x19681,x19682)+E(f681(x19683,x19684,x19685,x19681),f681(x19683,x19684,x19685,x19682))
% 28.25/28.14 [1969]~E(x19691,x19692)+E(f627(x19691,x19693,x19694),f627(x19692,x19693,x19694))
% 28.25/28.14 [1970]~E(x19701,x19702)+E(f627(x19703,x19701,x19704),f627(x19703,x19702,x19704))
% 28.25/28.14 [1971]~E(x19711,x19712)+E(f627(x19713,x19714,x19711),f627(x19713,x19714,x19712))
% 28.25/28.14 [1972]~E(x19721,x19722)+E(f678(x19721,x19723,x19724),f678(x19722,x19723,x19724))
% 28.25/28.14 [1973]~E(x19731,x19732)+E(f678(x19733,x19731,x19734),f678(x19733,x19732,x19734))
% 28.25/28.14 [1974]~E(x19741,x19742)+E(f678(x19743,x19744,x19741),f678(x19743,x19744,x19742))
% 28.25/28.14 [1975]~E(x19751,x19752)+E(f528(x19751,x19753,x19754,x19755,x19756,x19757),f528(x19752,x19753,x19754,x19755,x19756,x19757))
% 28.25/28.14 [1976]~E(x19761,x19762)+E(f528(x19763,x19761,x19764,x19765,x19766,x19767),f528(x19763,x19762,x19764,x19765,x19766,x19767))
% 28.25/28.14 [1977]~E(x19771,x19772)+E(f528(x19773,x19774,x19771,x19775,x19776,x19777),f528(x19773,x19774,x19772,x19775,x19776,x19777))
% 28.25/28.14 [1978]~E(x19781,x19782)+E(f528(x19783,x19784,x19785,x19781,x19786,x19787),f528(x19783,x19784,x19785,x19782,x19786,x19787))
% 28.25/28.14 [1979]~E(x19791,x19792)+E(f528(x19793,x19794,x19795,x19796,x19791,x19797),f528(x19793,x19794,x19795,x19796,x19792,x19797))
% 28.25/28.14 [1980]~E(x19801,x19802)+E(f528(x19803,x19804,x19805,x19806,x19807,x19801),f528(x19803,x19804,x19805,x19806,x19807,x19802))
% 28.25/28.14 [1981]~E(x19811,x19812)+E(f423(x19811,x19813,x19814),f423(x19812,x19813,x19814))
% 28.25/28.14 [1982]~E(x19821,x19822)+E(f423(x19823,x19821,x19824),f423(x19823,x19822,x19824))
% 28.25/28.14 [1983]~E(x19831,x19832)+E(f423(x19833,x19834,x19831),f423(x19833,x19834,x19832))
% 28.25/28.14 [1984]~E(x19841,x19842)+E(f563(x19841,x19843,x19844,x19845),f563(x19842,x19843,x19844,x19845))
% 28.25/28.14 [1985]~E(x19851,x19852)+E(f563(x19853,x19851,x19854,x19855),f563(x19853,x19852,x19854,x19855))
% 28.25/28.14 [1986]~E(x19861,x19862)+E(f563(x19863,x19864,x19861,x19865),f563(x19863,x19864,x19862,x19865))
% 28.25/28.14 [1987]~E(x19871,x19872)+E(f563(x19873,x19874,x19875,x19871),f563(x19873,x19874,x19875,x19872))
% 28.25/28.14 [1988]~E(x19881,x19882)+E(f397(x19881,x19883,x19884,x19885),f397(x19882,x19883,x19884,x19885))
% 28.25/28.14 [1989]~E(x19891,x19892)+E(f397(x19893,x19891,x19894,x19895),f397(x19893,x19892,x19894,x19895))
% 28.25/28.14 [1990]~E(x19901,x19902)+E(f397(x19903,x19904,x19901,x19905),f397(x19903,x19904,x19902,x19905))
% 28.25/28.14 [1991]~E(x19911,x19912)+E(f397(x19913,x19914,x19915,x19911),f397(x19913,x19914,x19915,x19912))
% 28.25/28.14 [1992]~E(x19921,x19922)+E(f360(x19921,x19923),f360(x19922,x19923))
% 28.25/28.14 [1993]~E(x19931,x19932)+E(f360(x19933,x19931),f360(x19933,x19932))
% 28.25/28.14 [1994]~E(x19941,x19942)+E(f757(x19941,x19943,x19944),f757(x19942,x19943,x19944))
% 28.25/28.14 [1995]~E(x19951,x19952)+E(f757(x19953,x19951,x19954),f757(x19953,x19952,x19954))
% 28.25/28.14 [1996]~E(x19961,x19962)+E(f757(x19963,x19964,x19961),f757(x19963,x19964,x19962))
% 28.25/28.14 [1997]~E(x19971,x19972)+E(f549(x19971,x19973,x19974,x19975,x19976,x19977,x19978),f549(x19972,x19973,x19974,x19975,x19976,x19977,x19978))
% 28.25/28.14 [1998]~E(x19981,x19982)+E(f549(x19983,x19981,x19984,x19985,x19986,x19987,x19988),f549(x19983,x19982,x19984,x19985,x19986,x19987,x19988))
% 28.25/28.14 [1999]~E(x19991,x19992)+E(f549(x19993,x19994,x19991,x19995,x19996,x19997,x19998),f549(x19993,x19994,x19992,x19995,x19996,x19997,x19998))
% 28.25/28.14 [2000]~E(x20001,x20002)+E(f549(x20003,x20004,x20005,x20001,x20006,x20007,x20008),f549(x20003,x20004,x20005,x20002,x20006,x20007,x20008))
% 28.25/28.14 [2001]~E(x20011,x20012)+E(f549(x20013,x20014,x20015,x20016,x20011,x20017,x20018),f549(x20013,x20014,x20015,x20016,x20012,x20017,x20018))
% 28.25/28.14 [2002]~E(x20021,x20022)+E(f549(x20023,x20024,x20025,x20026,x20027,x20021,x20028),f549(x20023,x20024,x20025,x20026,x20027,x20022,x20028))
% 28.25/28.14 [2003]~E(x20031,x20032)+E(f549(x20033,x20034,x20035,x20036,x20037,x20038,x20031),f549(x20033,x20034,x20035,x20036,x20037,x20038,x20032))
% 28.25/28.14 [2004]~E(x20041,x20042)+E(f523(x20041,x20043,x20044),f523(x20042,x20043,x20044))
% 28.25/28.14 [2005]~E(x20051,x20052)+E(f523(x20053,x20051,x20054),f523(x20053,x20052,x20054))
% 28.25/28.14 [2006]~E(x20061,x20062)+E(f523(x20063,x20064,x20061),f523(x20063,x20064,x20062))
% 28.25/28.14 [2007]~E(x20071,x20072)+E(f718(x20071,x20073),f718(x20072,x20073))
% 28.25/28.14 [2008]~E(x20081,x20082)+E(f718(x20083,x20081),f718(x20083,x20082))
% 28.25/28.14 [2009]~E(x20091,x20092)+E(f675(x20091,x20093,x20094,x20095,x20096),f675(x20092,x20093,x20094,x20095,x20096))
% 28.25/28.14 [2010]~E(x20101,x20102)+E(f675(x20103,x20101,x20104,x20105,x20106),f675(x20103,x20102,x20104,x20105,x20106))
% 28.25/28.14 [2011]~E(x20111,x20112)+E(f675(x20113,x20114,x20111,x20115,x20116),f675(x20113,x20114,x20112,x20115,x20116))
% 28.25/28.14 [2012]~E(x20121,x20122)+E(f675(x20123,x20124,x20125,x20121,x20126),f675(x20123,x20124,x20125,x20122,x20126))
% 28.25/28.14 [2013]~E(x20131,x20132)+E(f675(x20133,x20134,x20135,x20136,x20131),f675(x20133,x20134,x20135,x20136,x20132))
% 28.25/28.14 [2014]~E(x20141,x20142)+E(f287(x20141,x20143,x20144),f287(x20142,x20143,x20144))
% 28.25/28.14 [2015]~E(x20151,x20152)+E(f287(x20153,x20151,x20154),f287(x20153,x20152,x20154))
% 28.25/28.14 [2016]~E(x20161,x20162)+E(f287(x20163,x20164,x20161),f287(x20163,x20164,x20162))
% 28.25/28.14 [2017]~E(x20171,x20172)+E(f545(x20171,x20173,x20174,x20175),f545(x20172,x20173,x20174,x20175))
% 28.25/28.14 [2018]~E(x20181,x20182)+E(f545(x20183,x20181,x20184,x20185),f545(x20183,x20182,x20184,x20185))
% 28.25/28.14 [2019]~E(x20191,x20192)+E(f545(x20193,x20194,x20191,x20195),f545(x20193,x20194,x20192,x20195))
% 28.25/28.14 [2020]~E(x20201,x20202)+E(f545(x20203,x20204,x20205,x20201),f545(x20203,x20204,x20205,x20202))
% 28.25/28.14 [2021]~E(x20211,x20212)+E(f571(x20211,x20213,x20214,x20215),f571(x20212,x20213,x20214,x20215))
% 28.25/28.14 [2022]~E(x20221,x20222)+E(f571(x20223,x20221,x20224,x20225),f571(x20223,x20222,x20224,x20225))
% 28.25/28.14 [2023]~E(x20231,x20232)+E(f571(x20233,x20234,x20231,x20235),f571(x20233,x20234,x20232,x20235))
% 28.25/28.14 [2024]~E(x20241,x20242)+E(f571(x20243,x20244,x20245,x20241),f571(x20243,x20244,x20245,x20242))
% 28.25/28.14 [2025]~E(x20251,x20252)+E(f708(x20251,x20253,x20254,x20255),f708(x20252,x20253,x20254,x20255))
% 28.25/28.14 [2026]~E(x20261,x20262)+E(f708(x20263,x20261,x20264,x20265),f708(x20263,x20262,x20264,x20265))
% 28.25/28.14 [2027]~E(x20271,x20272)+E(f708(x20273,x20274,x20271,x20275),f708(x20273,x20274,x20272,x20275))
% 28.25/28.14 [2028]~E(x20281,x20282)+E(f708(x20283,x20284,x20285,x20281),f708(x20283,x20284,x20285,x20282))
% 28.25/28.14 [2029]~E(x20291,x20292)+E(f800(x20291),f800(x20292))
% 28.25/28.14 [2030]~E(x20301,x20302)+E(f704(x20301,x20303,x20304,x20305,x20306),f704(x20302,x20303,x20304,x20305,x20306))
% 28.25/28.14 [2031]~E(x20311,x20312)+E(f704(x20313,x20311,x20314,x20315,x20316),f704(x20313,x20312,x20314,x20315,x20316))
% 28.25/28.14 [2032]~E(x20321,x20322)+E(f704(x20323,x20324,x20321,x20325,x20326),f704(x20323,x20324,x20322,x20325,x20326))
% 28.25/28.14 [2033]~E(x20331,x20332)+E(f704(x20333,x20334,x20335,x20331,x20336),f704(x20333,x20334,x20335,x20332,x20336))
% 28.25/28.14 [2034]~E(x20341,x20342)+E(f704(x20343,x20344,x20345,x20346,x20341),f704(x20343,x20344,x20345,x20346,x20342))
% 28.25/28.14 [2035]~E(x20351,x20352)+E(f646(x20351,x20353,x20354,x20355,x20356),f646(x20352,x20353,x20354,x20355,x20356))
% 28.25/28.14 [2036]~E(x20361,x20362)+E(f646(x20363,x20361,x20364,x20365,x20366),f646(x20363,x20362,x20364,x20365,x20366))
% 28.25/28.14 [2037]~E(x20371,x20372)+E(f646(x20373,x20374,x20371,x20375,x20376),f646(x20373,x20374,x20372,x20375,x20376))
% 28.25/28.14 [2038]~E(x20381,x20382)+E(f646(x20383,x20384,x20385,x20381,x20386),f646(x20383,x20384,x20385,x20382,x20386))
% 28.25/28.14 [2039]~E(x20391,x20392)+E(f646(x20393,x20394,x20395,x20396,x20391),f646(x20393,x20394,x20395,x20396,x20392))
% 28.25/28.14 [2040]~E(x20401,x20402)+E(f820(x20401),f820(x20402))
% 28.25/28.14 [2041]~E(x20411,x20412)+E(f245(x20411,x20413,x20414,x20415,x20416),f245(x20412,x20413,x20414,x20415,x20416))
% 28.25/28.14 [2042]~E(x20421,x20422)+E(f245(x20423,x20421,x20424,x20425,x20426),f245(x20423,x20422,x20424,x20425,x20426))
% 28.25/28.14 [2043]~E(x20431,x20432)+E(f245(x20433,x20434,x20431,x20435,x20436),f245(x20433,x20434,x20432,x20435,x20436))
% 28.25/28.14 [2044]~E(x20441,x20442)+E(f245(x20443,x20444,x20445,x20441,x20446),f245(x20443,x20444,x20445,x20442,x20446))
% 28.25/28.14 [2045]~E(x20451,x20452)+E(f245(x20453,x20454,x20455,x20456,x20451),f245(x20453,x20454,x20455,x20456,x20452))
% 28.25/28.14 [2046]~E(x20461,x20462)+E(f750(x20461,x20463),f750(x20462,x20463))
% 28.25/28.14 [2047]~E(x20471,x20472)+E(f750(x20473,x20471),f750(x20473,x20472))
% 28.25/28.14 [2048]~E(x20481,x20482)+E(f389(x20481,x20483,x20484,x20485,x20486),f389(x20482,x20483,x20484,x20485,x20486))
% 28.25/28.14 [2049]~E(x20491,x20492)+E(f389(x20493,x20491,x20494,x20495,x20496),f389(x20493,x20492,x20494,x20495,x20496))
% 28.25/28.14 [2050]~E(x20501,x20502)+E(f389(x20503,x20504,x20501,x20505,x20506),f389(x20503,x20504,x20502,x20505,x20506))
% 28.25/28.14 [2051]~E(x20511,x20512)+E(f389(x20513,x20514,x20515,x20511,x20516),f389(x20513,x20514,x20515,x20512,x20516))
% 28.25/28.14 [2052]~E(x20521,x20522)+E(f389(x20523,x20524,x20525,x20526,x20521),f389(x20523,x20524,x20525,x20526,x20522))
% 28.25/28.14 [2053]~E(x20531,x20532)+E(f330(x20531),f330(x20532))
% 28.25/28.14 [2054]~E(x20541,x20542)+E(f781(x20541,x20543,x20544),f781(x20542,x20543,x20544))
% 28.25/28.14 [2055]~E(x20551,x20552)+E(f781(x20553,x20551,x20554),f781(x20553,x20552,x20554))
% 28.25/28.14 [2056]~E(x20561,x20562)+E(f781(x20563,x20564,x20561),f781(x20563,x20564,x20562))
% 28.25/28.14 [2057]~E(x20571,x20572)+E(f821(x20571,x20573),f821(x20572,x20573))
% 28.25/28.14 [2058]~E(x20581,x20582)+E(f821(x20583,x20581),f821(x20583,x20582))
% 28.25/28.14 [2059]~E(x20591,x20592)+E(f437(x20591,x20593,x20594,x20595,x20596,x20597),f437(x20592,x20593,x20594,x20595,x20596,x20597))
% 28.25/28.14 [2060]~E(x20601,x20602)+E(f437(x20603,x20601,x20604,x20605,x20606,x20607),f437(x20603,x20602,x20604,x20605,x20606,x20607))
% 28.25/28.14 [2061]~E(x20611,x20612)+E(f437(x20613,x20614,x20611,x20615,x20616,x20617),f437(x20613,x20614,x20612,x20615,x20616,x20617))
% 28.25/28.14 [2062]~E(x20621,x20622)+E(f437(x20623,x20624,x20625,x20621,x20626,x20627),f437(x20623,x20624,x20625,x20622,x20626,x20627))
% 28.25/28.14 [2063]~E(x20631,x20632)+E(f437(x20633,x20634,x20635,x20636,x20631,x20637),f437(x20633,x20634,x20635,x20636,x20632,x20637))
% 28.25/28.14 [2064]~E(x20641,x20642)+E(f437(x20643,x20644,x20645,x20646,x20647,x20641),f437(x20643,x20644,x20645,x20646,x20647,x20642))
% 28.25/28.14 [2065]~E(x20651,x20652)+E(f849(x20651,x20653,x20654,x20655,x20656,x20657,x20658,x20659),f849(x20652,x20653,x20654,x20655,x20656,x20657,x20658,x20659))
% 28.25/28.14 [2066]~E(x20661,x20662)+E(f849(x20663,x20661,x20664,x20665,x20666,x20667,x20668,x20669),f849(x20663,x20662,x20664,x20665,x20666,x20667,x20668,x20669))
% 28.25/28.14 [2067]~E(x20671,x20672)+E(f849(x20673,x20674,x20671,x20675,x20676,x20677,x20678,x20679),f849(x20673,x20674,x20672,x20675,x20676,x20677,x20678,x20679))
% 28.25/28.14 [2068]~E(x20681,x20682)+E(f849(x20683,x20684,x20685,x20681,x20686,x20687,x20688,x20689),f849(x20683,x20684,x20685,x20682,x20686,x20687,x20688,x20689))
% 28.25/28.14 [2069]~E(x20691,x20692)+E(f849(x20693,x20694,x20695,x20696,x20691,x20697,x20698,x20699),f849(x20693,x20694,x20695,x20696,x20692,x20697,x20698,x20699))
% 28.25/28.14 [2070]~E(x20701,x20702)+E(f849(x20703,x20704,x20705,x20706,x20707,x20701,x20708,x20709),f849(x20703,x20704,x20705,x20706,x20707,x20702,x20708,x20709))
% 28.25/28.14 [2071]~E(x20711,x20712)+E(f849(x20713,x20714,x20715,x20716,x20717,x20718,x20711,x20719),f849(x20713,x20714,x20715,x20716,x20717,x20718,x20712,x20719))
% 28.25/28.14 [2072]~E(x20721,x20722)+E(f849(x20723,x20724,x20725,x20726,x20727,x20728,x20729,x20721),f849(x20723,x20724,x20725,x20726,x20727,x20728,x20729,x20722))
% 28.25/28.14 [2073]~E(x20731,x20732)+E(f135(x20731,x20733),f135(x20732,x20733))
% 28.25/28.14 [2074]~E(x20741,x20742)+E(f135(x20743,x20741),f135(x20743,x20742))
% 28.25/28.14 [2075]~E(x20751,x20752)+E(f658(x20751,x20753,x20754),f658(x20752,x20753,x20754))
% 28.25/28.14 [2076]~E(x20761,x20762)+E(f658(x20763,x20761,x20764),f658(x20763,x20762,x20764))
% 28.25/28.14 [2077]~E(x20771,x20772)+E(f658(x20773,x20774,x20771),f658(x20773,x20774,x20772))
% 28.25/28.14 [2078]~E(x20781,x20782)+E(f765(x20781,x20783,x20784,x20785,x20786),f765(x20782,x20783,x20784,x20785,x20786))
% 28.25/28.14 [2079]~E(x20791,x20792)+E(f765(x20793,x20791,x20794,x20795,x20796),f765(x20793,x20792,x20794,x20795,x20796))
% 28.25/28.14 [2080]~E(x20801,x20802)+E(f765(x20803,x20804,x20801,x20805,x20806),f765(x20803,x20804,x20802,x20805,x20806))
% 28.25/28.14 [2081]~E(x20811,x20812)+E(f765(x20813,x20814,x20815,x20811,x20816),f765(x20813,x20814,x20815,x20812,x20816))
% 28.25/28.14 [2082]~E(x20821,x20822)+E(f765(x20823,x20824,x20825,x20826,x20821),f765(x20823,x20824,x20825,x20826,x20822))
% 28.25/28.14 [2083]~E(x20831,x20832)+E(f340(x20831,x20833,x20834,x20835),f340(x20832,x20833,x20834,x20835))
% 28.25/28.14 [2084]~E(x20841,x20842)+E(f340(x20843,x20841,x20844,x20845),f340(x20843,x20842,x20844,x20845))
% 28.25/28.14 [2085]~E(x20851,x20852)+E(f340(x20853,x20854,x20851,x20855),f340(x20853,x20854,x20852,x20855))
% 28.25/28.14 [2086]~E(x20861,x20862)+E(f340(x20863,x20864,x20865,x20861),f340(x20863,x20864,x20865,x20862))
% 28.25/28.14 [2087]~E(x20871,x20872)+E(f518(x20871,x20873,x20874),f518(x20872,x20873,x20874))
% 28.25/28.14 [2088]~E(x20881,x20882)+E(f518(x20883,x20881,x20884),f518(x20883,x20882,x20884))
% 28.25/28.14 [2089]~E(x20891,x20892)+E(f518(x20893,x20894,x20891),f518(x20893,x20894,x20892))
% 28.25/28.14 [2090]~E(x20901,x20902)+E(f35(x20901),f35(x20902))
% 28.25/28.14 [2091]~E(x20911,x20912)+E(f529(x20911,x20913,x20914),f529(x20912,x20913,x20914))
% 28.25/28.14 [2092]~E(x20921,x20922)+E(f529(x20923,x20921,x20924),f529(x20923,x20922,x20924))
% 28.25/28.14 [2093]~E(x20931,x20932)+E(f529(x20933,x20934,x20931),f529(x20933,x20934,x20932))
% 28.25/28.14 [2094]~E(x20941,x20942)+E(f253(x20941,x20943,x20944,x20945,x20946),f253(x20942,x20943,x20944,x20945,x20946))
% 28.25/28.14 [2095]~E(x20951,x20952)+E(f253(x20953,x20951,x20954,x20955,x20956),f253(x20953,x20952,x20954,x20955,x20956))
% 28.25/28.14 [2096]~E(x20961,x20962)+E(f253(x20963,x20964,x20961,x20965,x20966),f253(x20963,x20964,x20962,x20965,x20966))
% 28.25/28.14 [2097]~E(x20971,x20972)+E(f253(x20973,x20974,x20975,x20971,x20976),f253(x20973,x20974,x20975,x20972,x20976))
% 28.25/28.14 [2098]~E(x20981,x20982)+E(f253(x20983,x20984,x20985,x20986,x20981),f253(x20983,x20984,x20985,x20986,x20982))
% 28.25/28.14 [2099]~E(x20991,x20992)+E(f182(x20991,x20993,x20994,x20995),f182(x20992,x20993,x20994,x20995))
% 28.25/28.14 [2100]~E(x21001,x21002)+E(f182(x21003,x21001,x21004,x21005),f182(x21003,x21002,x21004,x21005))
% 28.25/28.14 [2101]~E(x21011,x21012)+E(f182(x21013,x21014,x21011,x21015),f182(x21013,x21014,x21012,x21015))
% 28.25/28.14 [2102]~E(x21021,x21022)+E(f182(x21023,x21024,x21025,x21021),f182(x21023,x21024,x21025,x21022))
% 28.25/28.14 [2103]~E(x21031,x21032)+E(f454(x21031,x21033,x21034),f454(x21032,x21033,x21034))
% 28.25/28.14 [2104]~E(x21041,x21042)+E(f454(x21043,x21041,x21044),f454(x21043,x21042,x21044))
% 28.25/28.14 [2105]~E(x21051,x21052)+E(f454(x21053,x21054,x21051),f454(x21053,x21054,x21052))
% 28.25/28.14 [2106]~E(x21061,x21062)+E(f913(x21061,x21063),f913(x21062,x21063))
% 28.25/28.14 [2107]~E(x21071,x21072)+E(f913(x21073,x21071),f913(x21073,x21072))
% 28.25/28.14 [2108]~E(x21081,x21082)+E(f484(x21081,x21083),f484(x21082,x21083))
% 28.25/28.14 [2109]~E(x21091,x21092)+E(f484(x21093,x21091),f484(x21093,x21092))
% 28.25/28.14 [2110]~E(x21101,x21102)+E(f506(x21101,x21103,x21104,x21105,x21106),f506(x21102,x21103,x21104,x21105,x21106))
% 28.25/28.14 [2111]~E(x21111,x21112)+E(f506(x21113,x21111,x21114,x21115,x21116),f506(x21113,x21112,x21114,x21115,x21116))
% 28.25/28.14 [2112]~E(x21121,x21122)+E(f506(x21123,x21124,x21121,x21125,x21126),f506(x21123,x21124,x21122,x21125,x21126))
% 28.25/28.14 [2113]~E(x21131,x21132)+E(f506(x21133,x21134,x21135,x21131,x21136),f506(x21133,x21134,x21135,x21132,x21136))
% 28.25/28.14 [2114]~E(x21141,x21142)+E(f506(x21143,x21144,x21145,x21146,x21141),f506(x21143,x21144,x21145,x21146,x21142))
% 28.25/28.14 [2115]~E(x21151,x21152)+E(f633(x21151,x21153),f633(x21152,x21153))
% 28.25/28.14 [2116]~E(x21161,x21162)+E(f633(x21163,x21161),f633(x21163,x21162))
% 28.25/28.14 [2117]~E(x21171,x21172)+E(f866(x21171,x21173,x21174,x21175,x21176,x21177,x21178),f866(x21172,x21173,x21174,x21175,x21176,x21177,x21178))
% 28.25/28.14 [2118]~E(x21181,x21182)+E(f866(x21183,x21181,x21184,x21185,x21186,x21187,x21188),f866(x21183,x21182,x21184,x21185,x21186,x21187,x21188))
% 28.25/28.14 [2119]~E(x21191,x21192)+E(f866(x21193,x21194,x21191,x21195,x21196,x21197,x21198),f866(x21193,x21194,x21192,x21195,x21196,x21197,x21198))
% 28.25/28.14 [2120]~E(x21201,x21202)+E(f866(x21203,x21204,x21205,x21201,x21206,x21207,x21208),f866(x21203,x21204,x21205,x21202,x21206,x21207,x21208))
% 28.25/28.14 [2121]~E(x21211,x21212)+E(f866(x21213,x21214,x21215,x21216,x21211,x21217,x21218),f866(x21213,x21214,x21215,x21216,x21212,x21217,x21218))
% 28.25/28.14 [2122]~E(x21221,x21222)+E(f866(x21223,x21224,x21225,x21226,x21227,x21221,x21228),f866(x21223,x21224,x21225,x21226,x21227,x21222,x21228))
% 28.25/28.14 [2123]~E(x21231,x21232)+E(f866(x21233,x21234,x21235,x21236,x21237,x21238,x21231),f866(x21233,x21234,x21235,x21236,x21237,x21238,x21232))
% 28.25/28.14 [2124]~E(x21241,x21242)+E(f516(x21241),f516(x21242))
% 28.25/28.14 [2125]~E(x21251,x21252)+E(f222(x21251,x21253,x21254),f222(x21252,x21253,x21254))
% 28.25/28.14 [2126]~E(x21261,x21262)+E(f222(x21263,x21261,x21264),f222(x21263,x21262,x21264))
% 28.25/28.14 [2127]~E(x21271,x21272)+E(f222(x21273,x21274,x21271),f222(x21273,x21274,x21272))
% 28.25/28.14 [2128]~E(x21281,x21282)+E(f680(x21281,x21283,x21284,x21285),f680(x21282,x21283,x21284,x21285))
% 28.25/28.14 [2129]~E(x21291,x21292)+E(f680(x21293,x21291,x21294,x21295),f680(x21293,x21292,x21294,x21295))
% 28.25/28.14 [2130]~E(x21301,x21302)+E(f680(x21303,x21304,x21301,x21305),f680(x21303,x21304,x21302,x21305))
% 28.25/28.14 [2131]~E(x21311,x21312)+E(f680(x21313,x21314,x21315,x21311),f680(x21313,x21314,x21315,x21312))
% 28.25/28.14 [2132]~E(x21321,x21322)+E(f217(x21321,x21323,x21324,x21325,x21326),f217(x21322,x21323,x21324,x21325,x21326))
% 28.25/28.14 [2133]~E(x21331,x21332)+E(f217(x21333,x21331,x21334,x21335,x21336),f217(x21333,x21332,x21334,x21335,x21336))
% 28.25/28.14 [2134]~E(x21341,x21342)+E(f217(x21343,x21344,x21341,x21345,x21346),f217(x21343,x21344,x21342,x21345,x21346))
% 28.25/28.14 [2135]~E(x21351,x21352)+E(f217(x21353,x21354,x21355,x21351,x21356),f217(x21353,x21354,x21355,x21352,x21356))
% 28.25/28.14 [2136]~E(x21361,x21362)+E(f217(x21363,x21364,x21365,x21366,x21361),f217(x21363,x21364,x21365,x21366,x21362))
% 28.25/28.14 [2137]~E(x21371,x21372)+E(f557(x21371,x21373,x21374,x21375,x21376),f557(x21372,x21373,x21374,x21375,x21376))
% 28.25/28.14 [2138]~E(x21381,x21382)+E(f557(x21383,x21381,x21384,x21385,x21386),f557(x21383,x21382,x21384,x21385,x21386))
% 28.25/28.14 [2139]~E(x21391,x21392)+E(f557(x21393,x21394,x21391,x21395,x21396),f557(x21393,x21394,x21392,x21395,x21396))
% 28.25/28.14 [2140]~E(x21401,x21402)+E(f557(x21403,x21404,x21405,x21401,x21406),f557(x21403,x21404,x21405,x21402,x21406))
% 28.25/28.14 [2141]~E(x21411,x21412)+E(f557(x21413,x21414,x21415,x21416,x21411),f557(x21413,x21414,x21415,x21416,x21412))
% 28.25/28.14 [2142]~E(x21421,x21422)+E(f67(x21421,x21423),f67(x21422,x21423))
% 28.25/28.14 [2143]~E(x21431,x21432)+E(f67(x21433,x21431),f67(x21433,x21432))
% 28.25/28.14 [2144]~E(x21441,x21442)+E(f534(x21441,x21443,x21444),f534(x21442,x21443,x21444))
% 28.25/28.14 [2145]~E(x21451,x21452)+E(f534(x21453,x21451,x21454),f534(x21453,x21452,x21454))
% 28.25/28.14 [2146]~E(x21461,x21462)+E(f534(x21463,x21464,x21461),f534(x21463,x21464,x21462))
% 28.25/28.14 [2147]~E(x21471,x21472)+E(f802(x21471,x21473),f802(x21472,x21473))
% 28.25/28.14 [2148]~E(x21481,x21482)+E(f802(x21483,x21481),f802(x21483,x21482))
% 28.25/28.14 [2149]~E(x21491,x21492)+E(f187(x21491,x21493,x21494,x21495),f187(x21492,x21493,x21494,x21495))
% 28.25/28.14 [2150]~E(x21501,x21502)+E(f187(x21503,x21501,x21504,x21505),f187(x21503,x21502,x21504,x21505))
% 28.25/28.14 [2151]~E(x21511,x21512)+E(f187(x21513,x21514,x21511,x21515),f187(x21513,x21514,x21512,x21515))
% 28.25/28.14 [2152]~E(x21521,x21522)+E(f187(x21523,x21524,x21525,x21521),f187(x21523,x21524,x21525,x21522))
% 28.25/28.14 [2153]~E(x21531,x21532)+E(f636(x21531,x21533,x21534,x21535,x21536),f636(x21532,x21533,x21534,x21535,x21536))
% 28.25/28.14 [2154]~E(x21541,x21542)+E(f636(x21543,x21541,x21544,x21545,x21546),f636(x21543,x21542,x21544,x21545,x21546))
% 28.25/28.14 [2155]~E(x21551,x21552)+E(f636(x21553,x21554,x21551,x21555,x21556),f636(x21553,x21554,x21552,x21555,x21556))
% 28.25/28.14 [2156]~E(x21561,x21562)+E(f636(x21563,x21564,x21565,x21561,x21566),f636(x21563,x21564,x21565,x21562,x21566))
% 28.25/28.14 [2157]~E(x21571,x21572)+E(f636(x21573,x21574,x21575,x21576,x21571),f636(x21573,x21574,x21575,x21576,x21572))
% 28.25/28.14 [2158]~E(x21581,x21582)+E(f768(x21581,x21583,x21584,x21585,x21586,x21587,x21588),f768(x21582,x21583,x21584,x21585,x21586,x21587,x21588))
% 28.25/28.14 [2159]~E(x21591,x21592)+E(f768(x21593,x21591,x21594,x21595,x21596,x21597,x21598),f768(x21593,x21592,x21594,x21595,x21596,x21597,x21598))
% 28.25/28.14 [2160]~E(x21601,x21602)+E(f768(x21603,x21604,x21601,x21605,x21606,x21607,x21608),f768(x21603,x21604,x21602,x21605,x21606,x21607,x21608))
% 28.25/28.14 [2161]~E(x21611,x21612)+E(f768(x21613,x21614,x21615,x21611,x21616,x21617,x21618),f768(x21613,x21614,x21615,x21612,x21616,x21617,x21618))
% 28.25/28.14 [2162]~E(x21621,x21622)+E(f768(x21623,x21624,x21625,x21626,x21621,x21627,x21628),f768(x21623,x21624,x21625,x21626,x21622,x21627,x21628))
% 28.25/28.14 [2163]~E(x21631,x21632)+E(f768(x21633,x21634,x21635,x21636,x21637,x21631,x21638),f768(x21633,x21634,x21635,x21636,x21637,x21632,x21638))
% 28.25/28.14 [2164]~E(x21641,x21642)+E(f768(x21643,x21644,x21645,x21646,x21647,x21648,x21641),f768(x21643,x21644,x21645,x21646,x21647,x21648,x21642))
% 28.25/28.14 [2165]~E(x21651,x21652)+E(f270(x21651),f270(x21652))
% 28.25/28.14 [2166]~E(x21661,x21662)+E(f590(x21661,x21663),f590(x21662,x21663))
% 28.25/28.14 [2167]~E(x21671,x21672)+E(f590(x21673,x21671),f590(x21673,x21672))
% 28.25/28.14 [2168]~E(x21681,x21682)+E(f895(x21681,x21683,x21684),f895(x21682,x21683,x21684))
% 28.25/28.14 [2169]~E(x21691,x21692)+E(f895(x21693,x21691,x21694),f895(x21693,x21692,x21694))
% 28.25/28.14 [2170]~E(x21701,x21702)+E(f895(x21703,x21704,x21701),f895(x21703,x21704,x21702))
% 28.25/28.14 [2171]~E(x21711,x21712)+E(f376(x21711,x21713,x21714),f376(x21712,x21713,x21714))
% 28.25/28.14 [2172]~E(x21721,x21722)+E(f376(x21723,x21721,x21724),f376(x21723,x21722,x21724))
% 28.25/28.14 [2173]~E(x21731,x21732)+E(f376(x21733,x21734,x21731),f376(x21733,x21734,x21732))
% 28.25/28.14 [2174]~E(x21741,x21742)+E(f831(x21741,x21743,x21744,x21745,x21746,x21747),f831(x21742,x21743,x21744,x21745,x21746,x21747))
% 28.25/28.14 [2175]~E(x21751,x21752)+E(f831(x21753,x21751,x21754,x21755,x21756,x21757),f831(x21753,x21752,x21754,x21755,x21756,x21757))
% 28.25/28.14 [2176]~E(x21761,x21762)+E(f831(x21763,x21764,x21761,x21765,x21766,x21767),f831(x21763,x21764,x21762,x21765,x21766,x21767))
% 28.25/28.14 [2177]~E(x21771,x21772)+E(f831(x21773,x21774,x21775,x21771,x21776,x21777),f831(x21773,x21774,x21775,x21772,x21776,x21777))
% 28.25/28.14 [2178]~E(x21781,x21782)+E(f831(x21783,x21784,x21785,x21786,x21781,x21787),f831(x21783,x21784,x21785,x21786,x21782,x21787))
% 28.25/28.14 [2179]~E(x21791,x21792)+E(f831(x21793,x21794,x21795,x21796,x21797,x21791),f831(x21793,x21794,x21795,x21796,x21797,x21792))
% 28.25/28.14 [2180]~E(x21801,x21802)+E(f587(x21801,x21803,x21804,x21805,x21806,x21807,x21808,x21809),f587(x21802,x21803,x21804,x21805,x21806,x21807,x21808,x21809))
% 28.25/28.14 [2181]~E(x21811,x21812)+E(f587(x21813,x21811,x21814,x21815,x21816,x21817,x21818,x21819),f587(x21813,x21812,x21814,x21815,x21816,x21817,x21818,x21819))
% 28.25/28.14 [2182]~E(x21821,x21822)+E(f587(x21823,x21824,x21821,x21825,x21826,x21827,x21828,x21829),f587(x21823,x21824,x21822,x21825,x21826,x21827,x21828,x21829))
% 28.25/28.14 [2183]~E(x21831,x21832)+E(f587(x21833,x21834,x21835,x21831,x21836,x21837,x21838,x21839),f587(x21833,x21834,x21835,x21832,x21836,x21837,x21838,x21839))
% 28.25/28.14 [2184]~E(x21841,x21842)+E(f587(x21843,x21844,x21845,x21846,x21841,x21847,x21848,x21849),f587(x21843,x21844,x21845,x21846,x21842,x21847,x21848,x21849))
% 28.25/28.14 [2185]~E(x21851,x21852)+E(f587(x21853,x21854,x21855,x21856,x21857,x21851,x21858,x21859),f587(x21853,x21854,x21855,x21856,x21857,x21852,x21858,x21859))
% 28.25/28.14 [2186]~E(x21861,x21862)+E(f587(x21863,x21864,x21865,x21866,x21867,x21868,x21861,x21869),f587(x21863,x21864,x21865,x21866,x21867,x21868,x21862,x21869))
% 28.25/28.14 [2187]~E(x21871,x21872)+E(f587(x21873,x21874,x21875,x21876,x21877,x21878,x21879,x21871),f587(x21873,x21874,x21875,x21876,x21877,x21878,x21879,x21872))
% 28.25/28.14 [2188]~E(x21881,x21882)+E(f515(x21881,x21883),f515(x21882,x21883))
% 28.25/28.14 [2189]~E(x21891,x21892)+E(f515(x21893,x21891),f515(x21893,x21892))
% 28.25/28.14 [2190]~E(x21901,x21902)+E(f688(x21901,x21903),f688(x21902,x21903))
% 28.25/28.14 [2191]~E(x21911,x21912)+E(f688(x21913,x21911),f688(x21913,x21912))
% 28.25/28.14 [2192]~E(x21921,x21922)+E(f548(x21921,x21923,x21924,x21925,x21926,x21927),f548(x21922,x21923,x21924,x21925,x21926,x21927))
% 28.25/28.14 [2193]~E(x21931,x21932)+E(f548(x21933,x21931,x21934,x21935,x21936,x21937),f548(x21933,x21932,x21934,x21935,x21936,x21937))
% 28.25/28.14 [2194]~E(x21941,x21942)+E(f548(x21943,x21944,x21941,x21945,x21946,x21947),f548(x21943,x21944,x21942,x21945,x21946,x21947))
% 28.25/28.14 [2195]~E(x21951,x21952)+E(f548(x21953,x21954,x21955,x21951,x21956,x21957),f548(x21953,x21954,x21955,x21952,x21956,x21957))
% 28.25/28.14 [2196]~E(x21961,x21962)+E(f548(x21963,x21964,x21965,x21966,x21961,x21967),f548(x21963,x21964,x21965,x21966,x21962,x21967))
% 28.25/28.14 [2197]~E(x21971,x21972)+E(f548(x21973,x21974,x21975,x21976,x21977,x21971),f548(x21973,x21974,x21975,x21976,x21977,x21972))
% 28.25/28.14 [2198]~E(x21981,x21982)+E(f532(x21981,x21983),f532(x21982,x21983))
% 28.25/28.14 [2199]~E(x21991,x21992)+E(f532(x21993,x21991),f532(x21993,x21992))
% 28.25/28.14 [2200]~E(x22001,x22002)+E(f705(x22001,x22003,x22004,x22005),f705(x22002,x22003,x22004,x22005))
% 28.25/28.14 [2201]~E(x22011,x22012)+E(f705(x22013,x22011,x22014,x22015),f705(x22013,x22012,x22014,x22015))
% 28.25/28.14 [2202]~E(x22021,x22022)+E(f705(x22023,x22024,x22021,x22025),f705(x22023,x22024,x22022,x22025))
% 28.25/28.14 [2203]~E(x22031,x22032)+E(f705(x22033,x22034,x22035,x22031),f705(x22033,x22034,x22035,x22032))
% 28.25/28.14 [2204]~E(x22041,x22042)+E(f466(x22041,x22043,x22044,x22045),f466(x22042,x22043,x22044,x22045))
% 28.25/28.14 [2205]~E(x22051,x22052)+E(f466(x22053,x22051,x22054,x22055),f466(x22053,x22052,x22054,x22055))
% 28.25/28.14 [2206]~E(x22061,x22062)+E(f466(x22063,x22064,x22061,x22065),f466(x22063,x22064,x22062,x22065))
% 28.25/28.14 [2207]~E(x22071,x22072)+E(f466(x22073,x22074,x22075,x22071),f466(x22073,x22074,x22075,x22072))
% 28.25/28.14 [2208]~E(x22081,x22082)+E(f132(x22081,x22083,x22084),f132(x22082,x22083,x22084))
% 28.25/28.14 [2209]~E(x22091,x22092)+E(f132(x22093,x22091,x22094),f132(x22093,x22092,x22094))
% 28.25/28.14 [2210]~E(x22101,x22102)+E(f132(x22103,x22104,x22101),f132(x22103,x22104,x22102))
% 28.25/28.14 [2211]~E(x22111,x22112)+E(f508(x22111,x22113,x22114),f508(x22112,x22113,x22114))
% 28.25/28.14 [2212]~E(x22121,x22122)+E(f508(x22123,x22121,x22124),f508(x22123,x22122,x22124))
% 28.25/28.14 [2213]~E(x22131,x22132)+E(f508(x22133,x22134,x22131),f508(x22133,x22134,x22132))
% 28.25/28.14 [2214]~E(x22141,x22142)+E(f672(x22141,x22143,x22144,x22145,x22146),f672(x22142,x22143,x22144,x22145,x22146))
% 28.25/28.14 [2215]~E(x22151,x22152)+E(f672(x22153,x22151,x22154,x22155,x22156),f672(x22153,x22152,x22154,x22155,x22156))
% 28.25/28.14 [2216]~E(x22161,x22162)+E(f672(x22163,x22164,x22161,x22165,x22166),f672(x22163,x22164,x22162,x22165,x22166))
% 28.25/28.14 [2217]~E(x22171,x22172)+E(f672(x22173,x22174,x22175,x22171,x22176),f672(x22173,x22174,x22175,x22172,x22176))
% 28.25/28.14 [2218]~E(x22181,x22182)+E(f672(x22183,x22184,x22185,x22186,x22181),f672(x22183,x22184,x22185,x22186,x22182))
% 28.25/28.14 [2219]~E(x22191,x22192)+E(f769(x22191,x22193,x22194,x22195,x22196,x22197,x22198),f769(x22192,x22193,x22194,x22195,x22196,x22197,x22198))
% 28.25/28.14 [2220]~E(x22201,x22202)+E(f769(x22203,x22201,x22204,x22205,x22206,x22207,x22208),f769(x22203,x22202,x22204,x22205,x22206,x22207,x22208))
% 28.25/28.14 [2221]~E(x22211,x22212)+E(f769(x22213,x22214,x22211,x22215,x22216,x22217,x22218),f769(x22213,x22214,x22212,x22215,x22216,x22217,x22218))
% 28.25/28.14 [2222]~E(x22221,x22222)+E(f769(x22223,x22224,x22225,x22221,x22226,x22227,x22228),f769(x22223,x22224,x22225,x22222,x22226,x22227,x22228))
% 28.25/28.14 [2223]~E(x22231,x22232)+E(f769(x22233,x22234,x22235,x22236,x22231,x22237,x22238),f769(x22233,x22234,x22235,x22236,x22232,x22237,x22238))
% 28.25/28.14 [2224]~E(x22241,x22242)+E(f769(x22243,x22244,x22245,x22246,x22247,x22241,x22248),f769(x22243,x22244,x22245,x22246,x22247,x22242,x22248))
% 28.25/28.14 [2225]~E(x22251,x22252)+E(f769(x22253,x22254,x22255,x22256,x22257,x22258,x22251),f769(x22253,x22254,x22255,x22256,x22257,x22258,x22252))
% 28.25/28.14 [2226]~E(x22261,x22262)+E(f348(x22261,x22263,x22264),f348(x22262,x22263,x22264))
% 28.25/28.14 [2227]~E(x22271,x22272)+E(f348(x22273,x22271,x22274),f348(x22273,x22272,x22274))
% 28.25/28.14 [2228]~E(x22281,x22282)+E(f348(x22283,x22284,x22281),f348(x22283,x22284,x22282))
% 28.25/28.14 [2229]~E(x22291,x22292)+E(f817(x22291,x22293,x22294,x22295),f817(x22292,x22293,x22294,x22295))
% 28.25/28.14 [2230]~E(x22301,x22302)+E(f817(x22303,x22301,x22304,x22305),f817(x22303,x22302,x22304,x22305))
% 28.25/28.14 [2231]~E(x22311,x22312)+E(f817(x22313,x22314,x22311,x22315),f817(x22313,x22314,x22312,x22315))
% 28.25/28.14 [2232]~E(x22321,x22322)+E(f817(x22323,x22324,x22325,x22321),f817(x22323,x22324,x22325,x22322))
% 28.25/28.14 [2233]~E(x22331,x22332)+E(f417(x22331,x22333,x22334,x22335,x22336),f417(x22332,x22333,x22334,x22335,x22336))
% 28.25/28.14 [2234]~E(x22341,x22342)+E(f417(x22343,x22341,x22344,x22345,x22346),f417(x22343,x22342,x22344,x22345,x22346))
% 28.25/28.14 [2235]~E(x22351,x22352)+E(f417(x22353,x22354,x22351,x22355,x22356),f417(x22353,x22354,x22352,x22355,x22356))
% 28.25/28.14 [2236]~E(x22361,x22362)+E(f417(x22363,x22364,x22365,x22361,x22366),f417(x22363,x22364,x22365,x22362,x22366))
% 28.25/28.14 [2237]~E(x22371,x22372)+E(f417(x22373,x22374,x22375,x22376,x22371),f417(x22373,x22374,x22375,x22376,x22372))
% 28.25/28.14 [2238]~E(x22381,x22382)+E(f383(x22381,x22383,x22384,x22385),f383(x22382,x22383,x22384,x22385))
% 28.25/28.14 [2239]~E(x22391,x22392)+E(f383(x22393,x22391,x22394,x22395),f383(x22393,x22392,x22394,x22395))
% 28.25/28.14 [2240]~E(x22401,x22402)+E(f383(x22403,x22404,x22401,x22405),f383(x22403,x22404,x22402,x22405))
% 28.25/28.14 [2241]~E(x22411,x22412)+E(f383(x22413,x22414,x22415,x22411),f383(x22413,x22414,x22415,x22412))
% 28.25/28.14 [2242]~E(x22421,x22422)+E(f626(x22421,x22423,x22424),f626(x22422,x22423,x22424))
% 28.25/28.14 [2243]~E(x22431,x22432)+E(f626(x22433,x22431,x22434),f626(x22433,x22432,x22434))
% 28.25/28.14 [2244]~E(x22441,x22442)+E(f626(x22443,x22444,x22441),f626(x22443,x22444,x22442))
% 28.25/28.14 [2245]~E(x22451,x22452)+E(f823(x22451,x22453),f823(x22452,x22453))
% 28.25/28.14 [2246]~E(x22461,x22462)+E(f823(x22463,x22461),f823(x22463,x22462))
% 28.25/28.14 [2247]~E(x22471,x22472)+E(f517(x22471,x22473),f517(x22472,x22473))
% 28.25/28.14 [2248]~E(x22481,x22482)+E(f517(x22483,x22481),f517(x22483,x22482))
% 28.25/28.14 [2249]~E(x22491,x22492)+E(f812(x22491,x22493),f812(x22492,x22493))
% 28.25/28.14 [2250]~E(x22501,x22502)+E(f812(x22503,x22501),f812(x22503,x22502))
% 28.25/28.14 [2251]~E(x22511,x22512)+E(f579(x22511,x22513,x22514,x22515),f579(x22512,x22513,x22514,x22515))
% 28.25/28.14 [2252]~E(x22521,x22522)+E(f579(x22523,x22521,x22524,x22525),f579(x22523,x22522,x22524,x22525))
% 28.25/28.14 [2253]~E(x22531,x22532)+E(f579(x22533,x22534,x22531,x22535),f579(x22533,x22534,x22532,x22535))
% 28.25/28.14 [2254]~E(x22541,x22542)+E(f579(x22543,x22544,x22545,x22541),f579(x22543,x22544,x22545,x22542))
% 28.25/28.14 [2255]~E(x22551,x22552)+E(f830(x22551,x22553),f830(x22552,x22553))
% 28.25/28.14 [2256]~E(x22561,x22562)+E(f830(x22563,x22561),f830(x22563,x22562))
% 28.25/28.14 [2257]~E(x22571,x22572)+E(f122(x22571,x22573,x22574,x22575),f122(x22572,x22573,x22574,x22575))
% 28.25/28.14 [2258]~E(x22581,x22582)+E(f122(x22583,x22581,x22584,x22585),f122(x22583,x22582,x22584,x22585))
% 28.25/28.14 [2259]~E(x22591,x22592)+E(f122(x22593,x22594,x22591,x22595),f122(x22593,x22594,x22592,x22595))
% 28.25/28.14 [2260]~E(x22601,x22602)+E(f122(x22603,x22604,x22605,x22601),f122(x22603,x22604,x22605,x22602))
% 28.25/28.14 [2261]~E(x22611,x22612)+E(f342(x22611,x22613,x22614,x22615,x22616),f342(x22612,x22613,x22614,x22615,x22616))
% 28.25/28.14 [2262]~E(x22621,x22622)+E(f342(x22623,x22621,x22624,x22625,x22626),f342(x22623,x22622,x22624,x22625,x22626))
% 28.25/28.14 [2263]~E(x22631,x22632)+E(f342(x22633,x22634,x22631,x22635,x22636),f342(x22633,x22634,x22632,x22635,x22636))
% 28.25/28.14 [2264]~E(x22641,x22642)+E(f342(x22643,x22644,x22645,x22641,x22646),f342(x22643,x22644,x22645,x22642,x22646))
% 28.25/28.14 [2265]~E(x22651,x22652)+E(f342(x22653,x22654,x22655,x22656,x22651),f342(x22653,x22654,x22655,x22656,x22652))
% 28.25/28.14 [2266]~E(x22661,x22662)+E(f912(x22661,x22663,x22664,x22665,x22666),f912(x22662,x22663,x22664,x22665,x22666))
% 28.25/28.14 [2267]~E(x22671,x22672)+E(f912(x22673,x22671,x22674,x22675,x22676),f912(x22673,x22672,x22674,x22675,x22676))
% 28.25/28.14 [2268]~E(x22681,x22682)+E(f912(x22683,x22684,x22681,x22685,x22686),f912(x22683,x22684,x22682,x22685,x22686))
% 28.25/28.14 [2269]~E(x22691,x22692)+E(f912(x22693,x22694,x22695,x22691,x22696),f912(x22693,x22694,x22695,x22692,x22696))
% 28.25/28.14 [2270]~E(x22701,x22702)+E(f912(x22703,x22704,x22705,x22706,x22701),f912(x22703,x22704,x22705,x22706,x22702))
% 28.25/28.14 [2271]~E(x22711,x22712)+E(f568(x22711,x22713),f568(x22712,x22713))
% 28.25/28.14 [2272]~E(x22721,x22722)+E(f568(x22723,x22721),f568(x22723,x22722))
% 28.25/28.14 [2273]~E(x22731,x22732)+E(f438(x22731),f438(x22732))
% 28.25/28.14 [2274]~E(x22741,x22742)+E(f625(x22741,x22743,x22744),f625(x22742,x22743,x22744))
% 28.25/28.14 [2275]~E(x22751,x22752)+E(f625(x22753,x22751,x22754),f625(x22753,x22752,x22754))
% 28.25/28.14 [2276]~E(x22761,x22762)+E(f625(x22763,x22764,x22761),f625(x22763,x22764,x22762))
% 28.25/28.14 [2277]~E(x22771,x22772)+E(f794(x22771,x22773,x22774,x22775),f794(x22772,x22773,x22774,x22775))
% 28.25/28.14 [2278]~E(x22781,x22782)+E(f794(x22783,x22781,x22784,x22785),f794(x22783,x22782,x22784,x22785))
% 28.25/28.14 [2279]~E(x22791,x22792)+E(f794(x22793,x22794,x22791,x22795),f794(x22793,x22794,x22792,x22795))
% 28.25/28.14 [2280]~E(x22801,x22802)+E(f794(x22803,x22804,x22805,x22801),f794(x22803,x22804,x22805,x22802))
% 28.25/28.14 [2281]~E(x22811,x22812)+E(f813(x22811,x22813,x22814,x22815),f813(x22812,x22813,x22814,x22815))
% 28.25/28.14 [2282]~E(x22821,x22822)+E(f813(x22823,x22821,x22824,x22825),f813(x22823,x22822,x22824,x22825))
% 28.25/28.14 [2283]~E(x22831,x22832)+E(f813(x22833,x22834,x22831,x22835),f813(x22833,x22834,x22832,x22835))
% 28.25/28.14 [2284]~E(x22841,x22842)+E(f813(x22843,x22844,x22845,x22841),f813(x22843,x22844,x22845,x22842))
% 28.25/28.14 [2285]~E(x22851,x22852)+E(f522(x22851,x22853,x22854,x22855),f522(x22852,x22853,x22854,x22855))
% 28.25/28.14 [2286]~E(x22861,x22862)+E(f522(x22863,x22861,x22864,x22865),f522(x22863,x22862,x22864,x22865))
% 28.25/28.14 [2287]~E(x22871,x22872)+E(f522(x22873,x22874,x22871,x22875),f522(x22873,x22874,x22872,x22875))
% 28.25/28.14 [2288]~E(x22881,x22882)+E(f522(x22883,x22884,x22885,x22881),f522(x22883,x22884,x22885,x22882))
% 28.25/28.14 [2289]~E(x22891,x22892)+E(f288(x22891,x22893,x22894),f288(x22892,x22893,x22894))
% 28.25/28.14 [2290]~E(x22901,x22902)+E(f288(x22903,x22901,x22904),f288(x22903,x22902,x22904))
% 28.25/28.14 [2291]~E(x22911,x22912)+E(f288(x22913,x22914,x22911),f288(x22913,x22914,x22912))
% 28.25/28.14 [2292]~E(x22921,x22922)+E(f362(x22921,x22923),f362(x22922,x22923))
% 28.25/28.14 [2293]~E(x22931,x22932)+E(f362(x22933,x22931),f362(x22933,x22932))
% 28.25/28.14 [2294]~E(x22941,x22942)+E(f408(x22941,x22943,x22944,x22945,x22946),f408(x22942,x22943,x22944,x22945,x22946))
% 28.25/28.14 [2295]~E(x22951,x22952)+E(f408(x22953,x22951,x22954,x22955,x22956),f408(x22953,x22952,x22954,x22955,x22956))
% 28.25/28.14 [2296]~E(x22961,x22962)+E(f408(x22963,x22964,x22961,x22965,x22966),f408(x22963,x22964,x22962,x22965,x22966))
% 28.25/28.14 [2297]~E(x22971,x22972)+E(f408(x22973,x22974,x22975,x22971,x22976),f408(x22973,x22974,x22975,x22972,x22976))
% 28.25/28.14 [2298]~E(x22981,x22982)+E(f408(x22983,x22984,x22985,x22986,x22981),f408(x22983,x22984,x22985,x22986,x22982))
% 28.25/28.14 [2299]~E(x22991,x22992)+E(f564(x22991,x22993),f564(x22992,x22993))
% 28.25/28.14 [2300]~E(x23001,x23002)+E(f564(x23003,x23001),f564(x23003,x23002))
% 28.25/28.14 [2301]~E(x23011,x23012)+E(f900(x23011,x23013,x23014,x23015,x23016),f900(x23012,x23013,x23014,x23015,x23016))
% 28.25/28.14 [2302]~E(x23021,x23022)+E(f900(x23023,x23021,x23024,x23025,x23026),f900(x23023,x23022,x23024,x23025,x23026))
% 28.25/28.14 [2303]~E(x23031,x23032)+E(f900(x23033,x23034,x23031,x23035,x23036),f900(x23033,x23034,x23032,x23035,x23036))
% 28.25/28.14 [2304]~E(x23041,x23042)+E(f900(x23043,x23044,x23045,x23041,x23046),f900(x23043,x23044,x23045,x23042,x23046))
% 28.25/28.14 [2305]~E(x23051,x23052)+E(f900(x23053,x23054,x23055,x23056,x23051),f900(x23053,x23054,x23055,x23056,x23052))
% 28.25/28.14 [2306]~E(x23061,x23062)+E(f907(x23061,x23063,x23064,x23065,x23066,x23067),f907(x23062,x23063,x23064,x23065,x23066,x23067))
% 28.25/28.14 [2307]~E(x23071,x23072)+E(f907(x23073,x23071,x23074,x23075,x23076,x23077),f907(x23073,x23072,x23074,x23075,x23076,x23077))
% 28.25/28.14 [2308]~E(x23081,x23082)+E(f907(x23083,x23084,x23081,x23085,x23086,x23087),f907(x23083,x23084,x23082,x23085,x23086,x23087))
% 28.25/28.14 [2309]~E(x23091,x23092)+E(f907(x23093,x23094,x23095,x23091,x23096,x23097),f907(x23093,x23094,x23095,x23092,x23096,x23097))
% 28.25/28.14 [2310]~E(x23101,x23102)+E(f907(x23103,x23104,x23105,x23106,x23101,x23107),f907(x23103,x23104,x23105,x23106,x23102,x23107))
% 28.25/28.14 [2311]~E(x23111,x23112)+E(f907(x23113,x23114,x23115,x23116,x23117,x23111),f907(x23113,x23114,x23115,x23116,x23117,x23112))
% 28.25/28.14 [2312]~E(x23121,x23122)+E(f488(x23121,x23123,x23124),f488(x23122,x23123,x23124))
% 28.25/28.14 [2313]~E(x23131,x23132)+E(f488(x23133,x23131,x23134),f488(x23133,x23132,x23134))
% 28.25/28.14 [2314]~E(x23141,x23142)+E(f488(x23143,x23144,x23141),f488(x23143,x23144,x23142))
% 28.25/28.14 [2315]~E(x23151,x23152)+E(f562(x23151,x23153,x23154,x23155,x23156),f562(x23152,x23153,x23154,x23155,x23156))
% 28.25/28.14 [2316]~E(x23161,x23162)+E(f562(x23163,x23161,x23164,x23165,x23166),f562(x23163,x23162,x23164,x23165,x23166))
% 28.25/28.14 [2317]~E(x23171,x23172)+E(f562(x23173,x23174,x23171,x23175,x23176),f562(x23173,x23174,x23172,x23175,x23176))
% 28.25/28.14 [2318]~E(x23181,x23182)+E(f562(x23183,x23184,x23185,x23181,x23186),f562(x23183,x23184,x23185,x23182,x23186))
% 28.25/28.14 [2319]~E(x23191,x23192)+E(f562(x23193,x23194,x23195,x23196,x23191),f562(x23193,x23194,x23195,x23196,x23192))
% 28.25/28.14 [2320]~E(x23201,x23202)+E(f613(x23201,x23203,x23204),f613(x23202,x23203,x23204))
% 28.25/28.14 [2321]~E(x23211,x23212)+E(f613(x23213,x23211,x23214),f613(x23213,x23212,x23214))
% 28.25/28.14 [2322]~E(x23221,x23222)+E(f613(x23223,x23224,x23221),f613(x23223,x23224,x23222))
% 28.25/28.14 [2323]~E(x23231,x23232)+E(f600(x23231,x23233,x23234),f600(x23232,x23233,x23234))
% 28.25/28.14 [2324]~E(x23241,x23242)+E(f600(x23243,x23241,x23244),f600(x23243,x23242,x23244))
% 28.25/28.14 [2325]~E(x23251,x23252)+E(f600(x23253,x23254,x23251),f600(x23253,x23254,x23252))
% 28.25/28.14 [2326]~E(x23261,x23262)+E(f584(x23261,x23263,x23264,x23265,x23266),f584(x23262,x23263,x23264,x23265,x23266))
% 28.25/28.14 [2327]~E(x23271,x23272)+E(f584(x23273,x23271,x23274,x23275,x23276),f584(x23273,x23272,x23274,x23275,x23276))
% 28.25/28.14 [2328]~E(x23281,x23282)+E(f584(x23283,x23284,x23281,x23285,x23286),f584(x23283,x23284,x23282,x23285,x23286))
% 28.25/28.14 [2329]~E(x23291,x23292)+E(f584(x23293,x23294,x23295,x23291,x23296),f584(x23293,x23294,x23295,x23292,x23296))
% 28.25/28.14 [2330]~E(x23301,x23302)+E(f584(x23303,x23304,x23305,x23306,x23301),f584(x23303,x23304,x23305,x23306,x23302))
% 28.25/28.14 [2331]~E(x23311,x23312)+E(f921(x23311,x23313,x23314,x23315,x23316),f921(x23312,x23313,x23314,x23315,x23316))
% 28.25/28.14 [2332]~E(x23321,x23322)+E(f921(x23323,x23321,x23324,x23325,x23326),f921(x23323,x23322,x23324,x23325,x23326))
% 28.25/28.14 [2333]~E(x23331,x23332)+E(f921(x23333,x23334,x23331,x23335,x23336),f921(x23333,x23334,x23332,x23335,x23336))
% 28.25/28.14 [2334]~E(x23341,x23342)+E(f921(x23343,x23344,x23345,x23341,x23346),f921(x23343,x23344,x23345,x23342,x23346))
% 28.25/28.14 [2335]~E(x23351,x23352)+E(f921(x23353,x23354,x23355,x23356,x23351),f921(x23353,x23354,x23355,x23356,x23352))
% 28.25/28.14 [2336]~E(x23361,x23362)+E(f223(x23361,x23363,x23364,x23365),f223(x23362,x23363,x23364,x23365))
% 28.25/28.14 [2337]~E(x23371,x23372)+E(f223(x23373,x23371,x23374,x23375),f223(x23373,x23372,x23374,x23375))
% 28.25/28.14 [2338]~E(x23381,x23382)+E(f223(x23383,x23384,x23381,x23385),f223(x23383,x23384,x23382,x23385))
% 28.25/28.14 [2339]~E(x23391,x23392)+E(f223(x23393,x23394,x23395,x23391),f223(x23393,x23394,x23395,x23392))
% 28.25/28.14 [2340]~E(x23401,x23402)+E(f427(x23401),f427(x23402))
% 28.25/28.14 [2341]~E(x23411,x23412)+E(f700(x23411,x23413,x23414,x23415,x23416),f700(x23412,x23413,x23414,x23415,x23416))
% 28.25/28.14 [2342]~E(x23421,x23422)+E(f700(x23423,x23421,x23424,x23425,x23426),f700(x23423,x23422,x23424,x23425,x23426))
% 28.25/28.14 [2343]~E(x23431,x23432)+E(f700(x23433,x23434,x23431,x23435,x23436),f700(x23433,x23434,x23432,x23435,x23436))
% 28.25/28.14 [2344]~E(x23441,x23442)+E(f700(x23443,x23444,x23445,x23441,x23446),f700(x23443,x23444,x23445,x23442,x23446))
% 28.25/28.14 [2345]~E(x23451,x23452)+E(f700(x23453,x23454,x23455,x23456,x23451),f700(x23453,x23454,x23455,x23456,x23452))
% 28.25/28.14 [2346]~E(x23461,x23462)+E(f324(x23461),f324(x23462))
% 28.25/28.14 [2347]~E(x23471,x23472)+E(f818(x23471,x23473,x23474,x23475),f818(x23472,x23473,x23474,x23475))
% 28.25/28.14 [2348]~E(x23481,x23482)+E(f818(x23483,x23481,x23484,x23485),f818(x23483,x23482,x23484,x23485))
% 28.25/28.14 [2349]~E(x23491,x23492)+E(f818(x23493,x23494,x23491,x23495),f818(x23493,x23494,x23492,x23495))
% 28.25/28.14 [2350]~E(x23501,x23502)+E(f818(x23503,x23504,x23505,x23501),f818(x23503,x23504,x23505,x23502))
% 28.25/28.14 [2351]~E(x23511,x23512)+E(f356(x23511,x23513,x23514),f356(x23512,x23513,x23514))
% 28.25/28.14 [2352]~E(x23521,x23522)+E(f356(x23523,x23521,x23524),f356(x23523,x23522,x23524))
% 28.25/28.14 [2353]~E(x23531,x23532)+E(f356(x23533,x23534,x23531),f356(x23533,x23534,x23532))
% 28.25/28.14 [2354]~E(x23541,x23542)+E(f493(x23541,x23543,x23544,x23545,x23546),f493(x23542,x23543,x23544,x23545,x23546))
% 28.25/28.14 [2355]~E(x23551,x23552)+E(f493(x23553,x23551,x23554,x23555,x23556),f493(x23553,x23552,x23554,x23555,x23556))
% 28.25/28.14 [2356]~E(x23561,x23562)+E(f493(x23563,x23564,x23561,x23565,x23566),f493(x23563,x23564,x23562,x23565,x23566))
% 28.25/28.14 [2357]~E(x23571,x23572)+E(f493(x23573,x23574,x23575,x23571,x23576),f493(x23573,x23574,x23575,x23572,x23576))
% 28.25/28.14 [2358]~E(x23581,x23582)+E(f493(x23583,x23584,x23585,x23586,x23581),f493(x23583,x23584,x23585,x23586,x23582))
% 28.25/28.14 [2359]~E(x23591,x23592)+E(f424(x23591,x23593,x23594,x23595,x23596),f424(x23592,x23593,x23594,x23595,x23596))
% 28.25/28.14 [2360]~E(x23601,x23602)+E(f424(x23603,x23601,x23604,x23605,x23606),f424(x23603,x23602,x23604,x23605,x23606))
% 28.25/28.14 [2361]~E(x23611,x23612)+E(f424(x23613,x23614,x23611,x23615,x23616),f424(x23613,x23614,x23612,x23615,x23616))
% 28.25/28.14 [2362]~E(x23621,x23622)+E(f424(x23623,x23624,x23625,x23621,x23626),f424(x23623,x23624,x23625,x23622,x23626))
% 28.25/28.14 [2363]~E(x23631,x23632)+E(f424(x23633,x23634,x23635,x23636,x23631),f424(x23633,x23634,x23635,x23636,x23632))
% 28.25/28.14 [2364]~E(x23641,x23642)+E(f199(x23641,x23643,x23644,x23645,x23646,x23647,x23648),f199(x23642,x23643,x23644,x23645,x23646,x23647,x23648))
% 28.25/28.14 [2365]~E(x23651,x23652)+E(f199(x23653,x23651,x23654,x23655,x23656,x23657,x23658),f199(x23653,x23652,x23654,x23655,x23656,x23657,x23658))
% 28.25/28.14 [2366]~E(x23661,x23662)+E(f199(x23663,x23664,x23661,x23665,x23666,x23667,x23668),f199(x23663,x23664,x23662,x23665,x23666,x23667,x23668))
% 28.25/28.14 [2367]~E(x23671,x23672)+E(f199(x23673,x23674,x23675,x23671,x23676,x23677,x23678),f199(x23673,x23674,x23675,x23672,x23676,x23677,x23678))
% 28.25/28.14 [2368]~E(x23681,x23682)+E(f199(x23683,x23684,x23685,x23686,x23681,x23687,x23688),f199(x23683,x23684,x23685,x23686,x23682,x23687,x23688))
% 28.25/28.14 [2369]~E(x23691,x23692)+E(f199(x23693,x23694,x23695,x23696,x23697,x23691,x23698),f199(x23693,x23694,x23695,x23696,x23697,x23692,x23698))
% 28.25/28.14 [2370]~E(x23701,x23702)+E(f199(x23703,x23704,x23705,x23706,x23707,x23708,x23701),f199(x23703,x23704,x23705,x23706,x23707,x23708,x23702))
% 28.25/28.14 [2371]~E(x23711,x23712)+E(f396(x23711,x23713,x23714,x23715),f396(x23712,x23713,x23714,x23715))
% 28.25/28.14 [2372]~E(x23721,x23722)+E(f396(x23723,x23721,x23724,x23725),f396(x23723,x23722,x23724,x23725))
% 28.25/28.14 [2373]~E(x23731,x23732)+E(f396(x23733,x23734,x23731,x23735),f396(x23733,x23734,x23732,x23735))
% 28.25/28.14 [2374]~E(x23741,x23742)+E(f396(x23743,x23744,x23745,x23741),f396(x23743,x23744,x23745,x23742))
% 28.25/28.14 [2375]~E(x23751,x23752)+E(f659(x23751,x23753,x23754),f659(x23752,x23753,x23754))
% 28.25/28.14 [2376]~E(x23761,x23762)+E(f659(x23763,x23761,x23764),f659(x23763,x23762,x23764))
% 28.25/28.14 [2377]~E(x23771,x23772)+E(f659(x23773,x23774,x23771),f659(x23773,x23774,x23772))
% 28.25/28.14 [2378]~E(x23781,x23782)+E(f669(x23781,x23783,x23784,x23785),f669(x23782,x23783,x23784,x23785))
% 28.25/28.14 [2379]~E(x23791,x23792)+E(f669(x23793,x23791,x23794,x23795),f669(x23793,x23792,x23794,x23795))
% 28.25/28.14 [2380]~E(x23801,x23802)+E(f669(x23803,x23804,x23801,x23805),f669(x23803,x23804,x23802,x23805))
% 28.25/28.14 [2381]~E(x23811,x23812)+E(f669(x23813,x23814,x23815,x23811),f669(x23813,x23814,x23815,x23812))
% 28.25/28.14 [2382]~E(x23821,x23822)+E(f428(x23821,x23823,x23824),f428(x23822,x23823,x23824))
% 28.25/28.14 [2383]~E(x23831,x23832)+E(f428(x23833,x23831,x23834),f428(x23833,x23832,x23834))
% 28.25/28.14 [2384]~E(x23841,x23842)+E(f428(x23843,x23844,x23841),f428(x23843,x23844,x23842))
% 28.25/28.14 [2385]~E(x23851,x23852)+E(f743(x23851,x23853,x23854),f743(x23852,x23853,x23854))
% 28.25/28.14 [2386]~E(x23861,x23862)+E(f743(x23863,x23861,x23864),f743(x23863,x23862,x23864))
% 28.25/28.14 [2387]~E(x23871,x23872)+E(f743(x23873,x23874,x23871),f743(x23873,x23874,x23872))
% 28.25/28.14 [2388]~E(x23881,x23882)+E(f735(x23881,x23883,x23884),f735(x23882,x23883,x23884))
% 28.25/28.14 [2389]~E(x23891,x23892)+E(f735(x23893,x23891,x23894),f735(x23893,x23892,x23894))
% 28.25/28.14 [2390]~E(x23901,x23902)+E(f735(x23903,x23904,x23901),f735(x23903,x23904,x23902))
% 28.25/28.14 [2391]~E(x23911,x23912)+E(f726(x23911,x23913,x23914),f726(x23912,x23913,x23914))
% 28.25/28.14 [2392]~E(x23921,x23922)+E(f726(x23923,x23921,x23924),f726(x23923,x23922,x23924))
% 28.25/28.14 [2393]~E(x23931,x23932)+E(f726(x23933,x23934,x23931),f726(x23933,x23934,x23932))
% 28.25/28.14 [2394]~E(x23941,x23942)+E(f432(x23941,x23943,x23944),f432(x23942,x23943,x23944))
% 28.25/28.14 [2395]~E(x23951,x23952)+E(f432(x23953,x23951,x23954),f432(x23953,x23952,x23954))
% 28.25/28.14 [2396]~E(x23961,x23962)+E(f432(x23963,x23964,x23961),f432(x23963,x23964,x23962))
% 28.25/28.14 [2397]~E(x23971,x23972)+E(f388(x23971,x23973,x23974,x23975),f388(x23972,x23973,x23974,x23975))
% 28.25/28.14 [2398]~E(x23981,x23982)+E(f388(x23983,x23981,x23984,x23985),f388(x23983,x23982,x23984,x23985))
% 28.25/28.14 [2399]~E(x23991,x23992)+E(f388(x23993,x23994,x23991,x23995),f388(x23993,x23994,x23992,x23995))
% 28.25/28.14 [2400]~E(x24001,x24002)+E(f388(x24003,x24004,x24005,x24001),f388(x24003,x24004,x24005,x24002))
% 28.25/28.14 [2401]~E(x24011,x24012)+E(f411(x24011,x24013,x24014),f411(x24012,x24013,x24014))
% 28.25/28.14 [2402]~E(x24021,x24022)+E(f411(x24023,x24021,x24024),f411(x24023,x24022,x24024))
% 28.25/28.14 [2403]~E(x24031,x24032)+E(f411(x24033,x24034,x24031),f411(x24033,x24034,x24032))
% 28.25/28.14 [2404]~E(x24041,x24042)+E(f337(x24041,x24043,x24044),f337(x24042,x24043,x24044))
% 28.25/28.14 [2405]~E(x24051,x24052)+E(f337(x24053,x24051,x24054),f337(x24053,x24052,x24054))
% 28.25/28.14 [2406]~E(x24061,x24062)+E(f337(x24063,x24064,x24061),f337(x24063,x24064,x24062))
% 28.25/28.14 [2407]~E(x24071,x24072)+E(f746(x24071,x24073,x24074,x24075,x24076,x24077),f746(x24072,x24073,x24074,x24075,x24076,x24077))
% 28.25/28.14 [2408]~E(x24081,x24082)+E(f746(x24083,x24081,x24084,x24085,x24086,x24087),f746(x24083,x24082,x24084,x24085,x24086,x24087))
% 28.25/28.14 [2409]~E(x24091,x24092)+E(f746(x24093,x24094,x24091,x24095,x24096,x24097),f746(x24093,x24094,x24092,x24095,x24096,x24097))
% 28.25/28.14 [2410]~E(x24101,x24102)+E(f746(x24103,x24104,x24105,x24101,x24106,x24107),f746(x24103,x24104,x24105,x24102,x24106,x24107))
% 28.25/28.14 [2411]~E(x24111,x24112)+E(f746(x24113,x24114,x24115,x24116,x24111,x24117),f746(x24113,x24114,x24115,x24116,x24112,x24117))
% 28.25/28.14 [2412]~E(x24121,x24122)+E(f746(x24123,x24124,x24125,x24126,x24127,x24121),f746(x24123,x24124,x24125,x24126,x24127,x24122))
% 28.25/28.14 [2413]~E(x24131,x24132)+E(f202(x24131,x24133,x24134,x24135),f202(x24132,x24133,x24134,x24135))
% 28.25/28.14 [2414]~E(x24141,x24142)+E(f202(x24143,x24141,x24144,x24145),f202(x24143,x24142,x24144,x24145))
% 28.25/28.14 [2415]~E(x24151,x24152)+E(f202(x24153,x24154,x24151,x24155),f202(x24153,x24154,x24152,x24155))
% 28.25/28.14 [2416]~E(x24161,x24162)+E(f202(x24163,x24164,x24165,x24161),f202(x24163,x24164,x24165,x24162))
% 28.25/28.14 [2417]~E(x24171,x24172)+E(f755(x24171,x24173,x24174,x24175,x24176),f755(x24172,x24173,x24174,x24175,x24176))
% 28.25/28.14 [2418]~E(x24181,x24182)+E(f755(x24183,x24181,x24184,x24185,x24186),f755(x24183,x24182,x24184,x24185,x24186))
% 28.25/28.14 [2419]~E(x24191,x24192)+E(f755(x24193,x24194,x24191,x24195,x24196),f755(x24193,x24194,x24192,x24195,x24196))
% 28.25/28.14 [2420]~E(x24201,x24202)+E(f755(x24203,x24204,x24205,x24201,x24206),f755(x24203,x24204,x24205,x24202,x24206))
% 28.25/28.14 [2421]~E(x24211,x24212)+E(f755(x24213,x24214,x24215,x24216,x24211),f755(x24213,x24214,x24215,x24216,x24212))
% 28.25/28.14 [2422]~E(x24221,x24222)+E(f653(x24221,x24223,x24224,x24225,x24226,x24227,x24228),f653(x24222,x24223,x24224,x24225,x24226,x24227,x24228))
% 28.25/28.14 [2423]~E(x24231,x24232)+E(f653(x24233,x24231,x24234,x24235,x24236,x24237,x24238),f653(x24233,x24232,x24234,x24235,x24236,x24237,x24238))
% 28.25/28.14 [2424]~E(x24241,x24242)+E(f653(x24243,x24244,x24241,x24245,x24246,x24247,x24248),f653(x24243,x24244,x24242,x24245,x24246,x24247,x24248))
% 28.25/28.14 [2425]~E(x24251,x24252)+E(f653(x24253,x24254,x24255,x24251,x24256,x24257,x24258),f653(x24253,x24254,x24255,x24252,x24256,x24257,x24258))
% 28.25/28.14 [2426]~E(x24261,x24262)+E(f653(x24263,x24264,x24265,x24266,x24261,x24267,x24268),f653(x24263,x24264,x24265,x24266,x24262,x24267,x24268))
% 28.25/28.14 [2427]~E(x24271,x24272)+E(f653(x24273,x24274,x24275,x24276,x24277,x24271,x24278),f653(x24273,x24274,x24275,x24276,x24277,x24272,x24278))
% 28.25/28.14 [2428]~E(x24281,x24282)+E(f653(x24283,x24284,x24285,x24286,x24287,x24288,x24281),f653(x24283,x24284,x24285,x24286,x24287,x24288,x24282))
% 28.25/28.14 [2429]~E(x24291,x24292)+E(f115(x24291),f115(x24292))
% 28.25/28.14 [2430]~E(x24301,x24302)+E(f239(x24301,x24303,x24304),f239(x24302,x24303,x24304))
% 28.25/28.14 [2431]~E(x24311,x24312)+E(f239(x24313,x24311,x24314),f239(x24313,x24312,x24314))
% 28.25/28.14 [2432]~E(x24321,x24322)+E(f239(x24323,x24324,x24321),f239(x24323,x24324,x24322))
% 28.25/28.14 [2433]~E(x24331,x24332)+E(f607(x24331,x24333,x24334,x24335,x24336,x24337),f607(x24332,x24333,x24334,x24335,x24336,x24337))
% 28.25/28.14 [2434]~E(x24341,x24342)+E(f607(x24343,x24341,x24344,x24345,x24346,x24347),f607(x24343,x24342,x24344,x24345,x24346,x24347))
% 28.25/28.14 [2435]~E(x24351,x24352)+E(f607(x24353,x24354,x24351,x24355,x24356,x24357),f607(x24353,x24354,x24352,x24355,x24356,x24357))
% 28.25/28.14 [2436]~E(x24361,x24362)+E(f607(x24363,x24364,x24365,x24361,x24366,x24367),f607(x24363,x24364,x24365,x24362,x24366,x24367))
% 28.25/28.14 [2437]~E(x24371,x24372)+E(f607(x24373,x24374,x24375,x24376,x24371,x24377),f607(x24373,x24374,x24375,x24376,x24372,x24377))
% 28.25/28.14 [2438]~E(x24381,x24382)+E(f607(x24383,x24384,x24385,x24386,x24387,x24381),f607(x24383,x24384,x24385,x24386,x24387,x24382))
% 28.25/28.14 [2439]~E(x24391,x24392)+E(f601(x24391,x24393,x24394,x24395),f601(x24392,x24393,x24394,x24395))
% 28.25/28.14 [2440]~E(x24401,x24402)+E(f601(x24403,x24401,x24404,x24405),f601(x24403,x24402,x24404,x24405))
% 28.25/28.14 [2441]~E(x24411,x24412)+E(f601(x24413,x24414,x24411,x24415),f601(x24413,x24414,x24412,x24415))
% 28.25/28.14 [2442]~E(x24421,x24422)+E(f601(x24423,x24424,x24425,x24421),f601(x24423,x24424,x24425,x24422))
% 28.25/28.14 [2443]~E(x24431,x24432)+E(f261(x24431,x24433),f261(x24432,x24433))
% 28.25/28.14 [2444]~E(x24441,x24442)+E(f261(x24443,x24441),f261(x24443,x24442))
% 28.25/28.14 [2445]~E(x24451,x24452)+E(f598(x24451,x24453,x24454),f598(x24452,x24453,x24454))
% 28.25/28.14 [2446]~E(x24461,x24462)+E(f598(x24463,x24461,x24464),f598(x24463,x24462,x24464))
% 28.25/28.14 [2447]~E(x24471,x24472)+E(f598(x24473,x24474,x24471),f598(x24473,x24474,x24472))
% 28.25/28.14 [2448]~E(x24481,x24482)+E(f615(x24481,x24483,x24484,x24485),f615(x24482,x24483,x24484,x24485))
% 28.25/28.14 [2449]~E(x24491,x24492)+E(f615(x24493,x24491,x24494,x24495),f615(x24493,x24492,x24494,x24495))
% 28.25/28.14 [2450]~E(x24501,x24502)+E(f615(x24503,x24504,x24501,x24505),f615(x24503,x24504,x24502,x24505))
% 28.25/28.14 [2451]~E(x24511,x24512)+E(f615(x24513,x24514,x24515,x24511),f615(x24513,x24514,x24515,x24512))
% 28.25/28.14 [2452]~E(x24521,x24522)+E(f622(x24521,x24523,x24524,x24525,x24526,x24527,x24528,x24529),f622(x24522,x24523,x24524,x24525,x24526,x24527,x24528,x24529))
% 28.25/28.14 [2453]~E(x24531,x24532)+E(f622(x24533,x24531,x24534,x24535,x24536,x24537,x24538,x24539),f622(x24533,x24532,x24534,x24535,x24536,x24537,x24538,x24539))
% 28.25/28.14 [2454]~E(x24541,x24542)+E(f622(x24543,x24544,x24541,x24545,x24546,x24547,x24548,x24549),f622(x24543,x24544,x24542,x24545,x24546,x24547,x24548,x24549))
% 28.25/28.14 [2455]~E(x24551,x24552)+E(f622(x24553,x24554,x24555,x24551,x24556,x24557,x24558,x24559),f622(x24553,x24554,x24555,x24552,x24556,x24557,x24558,x24559))
% 28.25/28.14 [2456]~E(x24561,x24562)+E(f622(x24563,x24564,x24565,x24566,x24561,x24567,x24568,x24569),f622(x24563,x24564,x24565,x24566,x24562,x24567,x24568,x24569))
% 28.25/28.14 [2457]~E(x24571,x24572)+E(f622(x24573,x24574,x24575,x24576,x24577,x24571,x24578,x24579),f622(x24573,x24574,x24575,x24576,x24577,x24572,x24578,x24579))
% 28.25/28.14 [2458]~E(x24581,x24582)+E(f622(x24583,x24584,x24585,x24586,x24587,x24588,x24581,x24589),f622(x24583,x24584,x24585,x24586,x24587,x24588,x24582,x24589))
% 28.25/28.14 [2459]~E(x24591,x24592)+E(f622(x24593,x24594,x24595,x24596,x24597,x24598,x24599,x24591),f622(x24593,x24594,x24595,x24596,x24597,x24598,x24599,x24592))
% 28.25/28.14 [2460]~E(x24601,x24602)+E(f824(x24601,x24603,x24604,x24605,x24606),f824(x24602,x24603,x24604,x24605,x24606))
% 28.25/28.14 [2461]~E(x24611,x24612)+E(f824(x24613,x24611,x24614,x24615,x24616),f824(x24613,x24612,x24614,x24615,x24616))
% 28.25/28.14 [2462]~E(x24621,x24622)+E(f824(x24623,x24624,x24621,x24625,x24626),f824(x24623,x24624,x24622,x24625,x24626))
% 28.25/28.14 [2463]~E(x24631,x24632)+E(f824(x24633,x24634,x24635,x24631,x24636),f824(x24633,x24634,x24635,x24632,x24636))
% 28.25/28.14 [2464]~E(x24641,x24642)+E(f824(x24643,x24644,x24645,x24646,x24641),f824(x24643,x24644,x24645,x24646,x24642))
% 28.25/28.14 [2465]~E(x24651,x24652)+E(f753(x24651,x24653,x24654,x24655),f753(x24652,x24653,x24654,x24655))
% 28.25/28.14 [2466]~E(x24661,x24662)+E(f753(x24663,x24661,x24664,x24665),f753(x24663,x24662,x24664,x24665))
% 28.25/28.14 [2467]~E(x24671,x24672)+E(f753(x24673,x24674,x24671,x24675),f753(x24673,x24674,x24672,x24675))
% 28.25/28.14 [2468]~E(x24681,x24682)+E(f753(x24683,x24684,x24685,x24681),f753(x24683,x24684,x24685,x24682))
% 28.25/28.14 [2469]~E(x24691,x24692)+E(f387(x24691,x24693,x24694,x24695),f387(x24692,x24693,x24694,x24695))
% 28.25/28.14 [2470]~E(x24701,x24702)+E(f387(x24703,x24701,x24704,x24705),f387(x24703,x24702,x24704,x24705))
% 28.25/28.14 [2471]~E(x24711,x24712)+E(f387(x24713,x24714,x24711,x24715),f387(x24713,x24714,x24712,x24715))
% 28.25/28.14 [2472]~E(x24721,x24722)+E(f387(x24723,x24724,x24725,x24721),f387(x24723,x24724,x24725,x24722))
% 28.25/28.14 [2473]~E(x24731,x24732)+E(f478(x24731,x24733,x24734),f478(x24732,x24733,x24734))
% 28.25/28.14 [2474]~E(x24741,x24742)+E(f478(x24743,x24741,x24744),f478(x24743,x24742,x24744))
% 28.25/28.14 [2475]~E(x24751,x24752)+E(f478(x24753,x24754,x24751),f478(x24753,x24754,x24752))
% 28.25/28.14 [2476]~E(x24761,x24762)+E(f791(x24761,x24763,x24764,x24765),f791(x24762,x24763,x24764,x24765))
% 28.25/28.14 [2477]~E(x24771,x24772)+E(f791(x24773,x24771,x24774,x24775),f791(x24773,x24772,x24774,x24775))
% 28.25/28.14 [2478]~E(x24781,x24782)+E(f791(x24783,x24784,x24781,x24785),f791(x24783,x24784,x24782,x24785))
% 28.25/28.14 [2479]~E(x24791,x24792)+E(f791(x24793,x24794,x24795,x24791),f791(x24793,x24794,x24795,x24792))
% 28.25/28.14 [2480]~E(x24801,x24802)+E(f594(x24801,x24803,x24804),f594(x24802,x24803,x24804))
% 28.25/28.14 [2481]~E(x24811,x24812)+E(f594(x24813,x24811,x24814),f594(x24813,x24812,x24814))
% 28.25/28.14 [2482]~E(x24821,x24822)+E(f594(x24823,x24824,x24821),f594(x24823,x24824,x24822))
% 28.25/28.14 [2483]~E(x24831,x24832)+E(f826(x24831,x24833),f826(x24832,x24833))
% 28.25/28.14 [2484]~E(x24841,x24842)+E(f826(x24843,x24841),f826(x24843,x24842))
% 28.25/28.14 [2485]~E(x24851,x24852)+E(f381(x24851,x24853,x24854,x24855),f381(x24852,x24853,x24854,x24855))
% 28.25/28.14 [2486]~E(x24861,x24862)+E(f381(x24863,x24861,x24864,x24865),f381(x24863,x24862,x24864,x24865))
% 28.25/28.14 [2487]~E(x24871,x24872)+E(f381(x24873,x24874,x24871,x24875),f381(x24873,x24874,x24872,x24875))
% 28.25/28.14 [2488]~E(x24881,x24882)+E(f381(x24883,x24884,x24885,x24881),f381(x24883,x24884,x24885,x24882))
% 28.25/28.14 [2489]~E(x24891,x24892)+E(f490(x24891,x24893),f490(x24892,x24893))
% 28.25/28.14 [2490]~E(x24901,x24902)+E(f490(x24903,x24901),f490(x24903,x24902))
% 28.25/28.14 [2491]~E(x24911,x24912)+E(f684(x24911,x24913,x24914),f684(x24912,x24913,x24914))
% 28.25/28.14 [2492]~E(x24921,x24922)+E(f684(x24923,x24921,x24924),f684(x24923,x24922,x24924))
% 28.25/28.14 [2493]~E(x24931,x24932)+E(f684(x24933,x24934,x24931),f684(x24933,x24934,x24932))
% 28.25/28.14 [2494]~E(x24941,x24942)+E(f822(x24941,x24943),f822(x24942,x24943))
% 28.25/28.14 [2495]~E(x24951,x24952)+E(f822(x24953,x24951),f822(x24953,x24952))
% 28.25/28.14 [2496]~E(x24961,x24962)+E(f855(x24961,x24963,x24964,x24965,x24966,x24967,x24968,x24969),f855(x24962,x24963,x24964,x24965,x24966,x24967,x24968,x24969))
% 28.25/28.14 [2497]~E(x24971,x24972)+E(f855(x24973,x24971,x24974,x24975,x24976,x24977,x24978,x24979),f855(x24973,x24972,x24974,x24975,x24976,x24977,x24978,x24979))
% 28.25/28.14 [2498]~E(x24981,x24982)+E(f855(x24983,x24984,x24981,x24985,x24986,x24987,x24988,x24989),f855(x24983,x24984,x24982,x24985,x24986,x24987,x24988,x24989))
% 28.25/28.14 [2499]~E(x24991,x24992)+E(f855(x24993,x24994,x24995,x24991,x24996,x24997,x24998,x24999),f855(x24993,x24994,x24995,x24992,x24996,x24997,x24998,x24999))
% 28.25/28.14 [2500]~E(x25001,x25002)+E(f855(x25003,x25004,x25005,x25006,x25001,x25007,x25008,x25009),f855(x25003,x25004,x25005,x25006,x25002,x25007,x25008,x25009))
% 28.25/28.14 [2501]~E(x25011,x25012)+E(f855(x25013,x25014,x25015,x25016,x25017,x25011,x25018,x25019),f855(x25013,x25014,x25015,x25016,x25017,x25012,x25018,x25019))
% 28.25/28.14 [2502]~E(x25021,x25022)+E(f855(x25023,x25024,x25025,x25026,x25027,x25028,x25021,x25029),f855(x25023,x25024,x25025,x25026,x25027,x25028,x25022,x25029))
% 28.25/28.14 [2503]~E(x25031,x25032)+E(f855(x25033,x25034,x25035,x25036,x25037,x25038,x25039,x25031),f855(x25033,x25034,x25035,x25036,x25037,x25038,x25039,x25032))
% 28.25/28.14 [2504]~E(x25041,x25042)+E(f457(x25041,x25043),f457(x25042,x25043))
% 28.25/28.14 [2505]~E(x25051,x25052)+E(f457(x25053,x25051),f457(x25053,x25052))
% 28.25/28.14 [2506]~E(x25061,x25062)+E(f733(x25061,x25063,x25064),f733(x25062,x25063,x25064))
% 28.25/28.14 [2507]~E(x25071,x25072)+E(f733(x25073,x25071,x25074),f733(x25073,x25072,x25074))
% 28.25/28.14 [2508]~E(x25081,x25082)+E(f733(x25083,x25084,x25081),f733(x25083,x25084,x25082))
% 28.25/28.14 [2509]~E(x25091,x25092)+E(f914(x25091,x25093,x25094),f914(x25092,x25093,x25094))
% 28.25/28.14 [2510]~E(x25101,x25102)+E(f914(x25103,x25101,x25104),f914(x25103,x25102,x25104))
% 28.25/28.14 [2511]~E(x25111,x25112)+E(f914(x25113,x25114,x25111),f914(x25113,x25114,x25112))
% 28.25/28.14 [2512]~E(x25121,x25122)+E(f707(x25121,x25123,x25124,x25125),f707(x25122,x25123,x25124,x25125))
% 28.25/28.14 [2513]~E(x25131,x25132)+E(f707(x25133,x25131,x25134,x25135),f707(x25133,x25132,x25134,x25135))
% 28.25/28.14 [2514]~E(x25141,x25142)+E(f707(x25143,x25144,x25141,x25145),f707(x25143,x25144,x25142,x25145))
% 28.25/28.14 [2515]~E(x25151,x25152)+E(f707(x25153,x25154,x25155,x25151),f707(x25153,x25154,x25155,x25152))
% 28.25/28.14 [2516]~E(x25161,x25162)+E(f369(x25161,x25163,x25164,x25165),f369(x25162,x25163,x25164,x25165))
% 28.25/28.14 [2517]~E(x25171,x25172)+E(f369(x25173,x25171,x25174,x25175),f369(x25173,x25172,x25174,x25175))
% 28.25/28.14 [2518]~E(x25181,x25182)+E(f369(x25183,x25184,x25181,x25185),f369(x25183,x25184,x25182,x25185))
% 28.25/28.14 [2519]~E(x25191,x25192)+E(f369(x25193,x25194,x25195,x25191),f369(x25193,x25194,x25195,x25192))
% 28.25/28.14 [2520]~E(x25201,x25202)+E(f724(x25201,x25203,x25204),f724(x25202,x25203,x25204))
% 28.25/28.14 [2521]~E(x25211,x25212)+E(f724(x25213,x25211,x25214),f724(x25213,x25212,x25214))
% 28.25/28.14 [2522]~E(x25221,x25222)+E(f724(x25223,x25224,x25221),f724(x25223,x25224,x25222))
% 28.25/28.14 [2523]~E(x25231,x25232)+E(f196(x25231),f196(x25232))
% 28.25/28.14 [2524]~E(x25241,x25242)+E(f263(x25241,x25243,x25244,x25245),f263(x25242,x25243,x25244,x25245))
% 28.25/28.14 [2525]~E(x25251,x25252)+E(f263(x25253,x25251,x25254,x25255),f263(x25253,x25252,x25254,x25255))
% 28.25/28.14 [2526]~E(x25261,x25262)+E(f263(x25263,x25264,x25261,x25265),f263(x25263,x25264,x25262,x25265))
% 28.25/28.14 [2527]~E(x25271,x25272)+E(f263(x25273,x25274,x25275,x25271),f263(x25273,x25274,x25275,x25272))
% 28.25/28.14 [2528]~E(x25281,x25282)+E(f336(x25281,x25283,x25284),f336(x25282,x25283,x25284))
% 28.25/28.14 [2529]~E(x25291,x25292)+E(f336(x25293,x25291,x25294),f336(x25293,x25292,x25294))
% 28.25/28.14 [2530]~E(x25301,x25302)+E(f336(x25303,x25304,x25301),f336(x25303,x25304,x25302))
% 28.25/28.14 [2531]~E(x25311,x25312)+E(f857(x25311,x25313,x25314),f857(x25312,x25313,x25314))
% 28.25/28.14 [2532]~E(x25321,x25322)+E(f857(x25323,x25321,x25324),f857(x25323,x25322,x25324))
% 28.25/28.14 [2533]~E(x25331,x25332)+E(f857(x25333,x25334,x25331),f857(x25333,x25334,x25332))
% 28.25/28.14 [2534]~E(x25341,x25342)+E(f839(x25341,x25343,x25344),f839(x25342,x25343,x25344))
% 28.25/28.14 [2535]~E(x25351,x25352)+E(f839(x25353,x25351,x25354),f839(x25353,x25352,x25354))
% 28.25/28.14 [2536]~E(x25361,x25362)+E(f839(x25363,x25364,x25361),f839(x25363,x25364,x25362))
% 28.25/28.14 [2537]~E(x25371,x25372)+E(f573(x25371,x25373,x25374,x25375),f573(x25372,x25373,x25374,x25375))
% 28.25/28.14 [2538]~E(x25381,x25382)+E(f573(x25383,x25381,x25384,x25385),f573(x25383,x25382,x25384,x25385))
% 28.25/28.14 [2539]~E(x25391,x25392)+E(f573(x25393,x25394,x25391,x25395),f573(x25393,x25394,x25392,x25395))
% 28.25/28.14 [2540]~E(x25401,x25402)+E(f573(x25403,x25404,x25405,x25401),f573(x25403,x25404,x25405,x25402))
% 28.25/28.14 [2541]~E(x25411,x25412)+E(f372(x25411,x25413),f372(x25412,x25413))
% 28.25/28.14 [2542]~E(x25421,x25422)+E(f372(x25423,x25421),f372(x25423,x25422))
% 28.25/28.14 [2543]~E(x25431,x25432)+E(f862(x25431,x25433,x25434,x25435,x25436,x25437,x25438,x25439),f862(x25432,x25433,x25434,x25435,x25436,x25437,x25438,x25439))
% 28.25/28.14 [2544]~E(x25441,x25442)+E(f862(x25443,x25441,x25444,x25445,x25446,x25447,x25448,x25449),f862(x25443,x25442,x25444,x25445,x25446,x25447,x25448,x25449))
% 28.25/28.14 [2545]~E(x25451,x25452)+E(f862(x25453,x25454,x25451,x25455,x25456,x25457,x25458,x25459),f862(x25453,x25454,x25452,x25455,x25456,x25457,x25458,x25459))
% 28.25/28.14 [2546]~E(x25461,x25462)+E(f862(x25463,x25464,x25465,x25461,x25466,x25467,x25468,x25469),f862(x25463,x25464,x25465,x25462,x25466,x25467,x25468,x25469))
% 28.25/28.14 [2547]~E(x25471,x25472)+E(f862(x25473,x25474,x25475,x25476,x25471,x25477,x25478,x25479),f862(x25473,x25474,x25475,x25476,x25472,x25477,x25478,x25479))
% 28.25/28.14 [2548]~E(x25481,x25482)+E(f862(x25483,x25484,x25485,x25486,x25487,x25481,x25488,x25489),f862(x25483,x25484,x25485,x25486,x25487,x25482,x25488,x25489))
% 28.25/28.14 [2549]~E(x25491,x25492)+E(f862(x25493,x25494,x25495,x25496,x25497,x25498,x25491,x25499),f862(x25493,x25494,x25495,x25496,x25497,x25498,x25492,x25499))
% 28.25/28.14 [2550]~E(x25501,x25502)+E(f862(x25503,x25504,x25505,x25506,x25507,x25508,x25509,x25501),f862(x25503,x25504,x25505,x25506,x25507,x25508,x25509,x25502))
% 28.25/28.14 [2551]~E(x25511,x25512)+E(f200(x25511),f200(x25512))
% 28.25/28.14 [2552]~E(x25521,x25522)+E(f801(x25521,x25523,x25524),f801(x25522,x25523,x25524))
% 28.25/28.14 [2553]~E(x25531,x25532)+E(f801(x25533,x25531,x25534),f801(x25533,x25532,x25534))
% 28.25/28.14 [2554]~E(x25541,x25542)+E(f801(x25543,x25544,x25541),f801(x25543,x25544,x25542))
% 28.25/28.14 [2555]~E(x25551,x25552)+E(f354(x25551,x25553),f354(x25552,x25553))
% 28.25/28.14 [2556]~E(x25561,x25562)+E(f354(x25563,x25561),f354(x25563,x25562))
% 28.25/28.14 [2557]~E(x25571,x25572)+E(f677(x25571,x25573,x25574),f677(x25572,x25573,x25574))
% 28.25/28.14 [2558]~E(x25581,x25582)+E(f677(x25583,x25581,x25584),f677(x25583,x25582,x25584))
% 28.25/28.14 [2559]~E(x25591,x25592)+E(f677(x25593,x25594,x25591),f677(x25593,x25594,x25592))
% 28.25/28.14 [2560]~E(x25601,x25602)+E(f221(x25601,x25603,x25604,x25605),f221(x25602,x25603,x25604,x25605))
% 28.25/28.14 [2561]~E(x25611,x25612)+E(f221(x25613,x25611,x25614,x25615),f221(x25613,x25612,x25614,x25615))
% 28.25/28.14 [2562]~E(x25621,x25622)+E(f221(x25623,x25624,x25621,x25625),f221(x25623,x25624,x25622,x25625))
% 28.25/28.14 [2563]~E(x25631,x25632)+E(f221(x25633,x25634,x25635,x25631),f221(x25633,x25634,x25635,x25632))
% 28.25/28.14 [2564]~E(x25641,x25642)+E(f19(x25641,x25643,x25644,x25645),f19(x25642,x25643,x25644,x25645))
% 28.25/28.14 [2565]~E(x25651,x25652)+E(f19(x25653,x25651,x25654,x25655),f19(x25653,x25652,x25654,x25655))
% 28.25/28.14 [2566]~E(x25661,x25662)+E(f19(x25663,x25664,x25661,x25665),f19(x25663,x25664,x25662,x25665))
% 28.25/28.14 [2567]~E(x25671,x25672)+E(f19(x25673,x25674,x25675,x25671),f19(x25673,x25674,x25675,x25672))
% 28.25/28.14 [2568]~E(x25681,x25682)+E(f788(x25681,x25683,x25684),f788(x25682,x25683,x25684))
% 28.25/28.14 [2569]~E(x25691,x25692)+E(f788(x25693,x25691,x25694),f788(x25693,x25692,x25694))
% 28.25/28.14 [2570]~E(x25701,x25702)+E(f788(x25703,x25704,x25701),f788(x25703,x25704,x25702))
% 28.25/28.14 [2571]~E(x25711,x25712)+E(f728(x25711,x25713),f728(x25712,x25713))
% 28.25/28.14 [2572]~E(x25721,x25722)+E(f728(x25723,x25721),f728(x25723,x25722))
% 28.25/28.14 [2573]~E(x25731,x25732)+E(f859(x25731,x25733,x25734,x25735),f859(x25732,x25733,x25734,x25735))
% 28.25/28.14 [2574]~E(x25741,x25742)+E(f859(x25743,x25741,x25744,x25745),f859(x25743,x25742,x25744,x25745))
% 28.25/28.14 [2575]~E(x25751,x25752)+E(f859(x25753,x25754,x25751,x25755),f859(x25753,x25754,x25752,x25755))
% 28.25/28.14 [2576]~E(x25761,x25762)+E(f859(x25763,x25764,x25765,x25761),f859(x25763,x25764,x25765,x25762))
% 28.25/28.14 [2577]~E(x25771,x25772)+E(f268(x25771,x25773,x25774,x25775),f268(x25772,x25773,x25774,x25775))
% 28.25/28.14 [2578]~E(x25781,x25782)+E(f268(x25783,x25781,x25784,x25785),f268(x25783,x25782,x25784,x25785))
% 28.25/28.14 [2579]~E(x25791,x25792)+E(f268(x25793,x25794,x25791,x25795),f268(x25793,x25794,x25792,x25795))
% 28.25/28.14 [2580]~E(x25801,x25802)+E(f268(x25803,x25804,x25805,x25801),f268(x25803,x25804,x25805,x25802))
% 28.25/28.14 [2581]~E(x25811,x25812)+E(f604(x25811,x25813,x25814,x25815,x25816,x25817),f604(x25812,x25813,x25814,x25815,x25816,x25817))
% 28.25/28.14 [2582]~E(x25821,x25822)+E(f604(x25823,x25821,x25824,x25825,x25826,x25827),f604(x25823,x25822,x25824,x25825,x25826,x25827))
% 28.25/28.14 [2583]~E(x25831,x25832)+E(f604(x25833,x25834,x25831,x25835,x25836,x25837),f604(x25833,x25834,x25832,x25835,x25836,x25837))
% 28.25/28.14 [2584]~E(x25841,x25842)+E(f604(x25843,x25844,x25845,x25841,x25846,x25847),f604(x25843,x25844,x25845,x25842,x25846,x25847))
% 28.25/28.14 [2585]~E(x25851,x25852)+E(f604(x25853,x25854,x25855,x25856,x25851,x25857),f604(x25853,x25854,x25855,x25856,x25852,x25857))
% 28.25/28.14 [2586]~E(x25861,x25862)+E(f604(x25863,x25864,x25865,x25866,x25867,x25861),f604(x25863,x25864,x25865,x25866,x25867,x25862))
% 28.25/28.14 [2587]~E(x25871,x25872)+E(f464(x25871,x25873,x25874,x25875,x25876,x25877),f464(x25872,x25873,x25874,x25875,x25876,x25877))
% 28.25/28.14 [2588]~E(x25881,x25882)+E(f464(x25883,x25881,x25884,x25885,x25886,x25887),f464(x25883,x25882,x25884,x25885,x25886,x25887))
% 28.25/28.14 [2589]~E(x25891,x25892)+E(f464(x25893,x25894,x25891,x25895,x25896,x25897),f464(x25893,x25894,x25892,x25895,x25896,x25897))
% 28.25/28.14 [2590]~E(x25901,x25902)+E(f464(x25903,x25904,x25905,x25901,x25906,x25907),f464(x25903,x25904,x25905,x25902,x25906,x25907))
% 28.25/28.14 [2591]~E(x25911,x25912)+E(f464(x25913,x25914,x25915,x25916,x25911,x25917),f464(x25913,x25914,x25915,x25916,x25912,x25917))
% 28.25/28.14 [2592]~E(x25921,x25922)+E(f464(x25923,x25924,x25925,x25926,x25927,x25921),f464(x25923,x25924,x25925,x25926,x25927,x25922))
% 28.25/28.14 [2593]~E(x25931,x25932)+E(f456(x25931,x25933),f456(x25932,x25933))
% 28.25/28.14 [2594]~E(x25941,x25942)+E(f456(x25943,x25941),f456(x25943,x25942))
% 28.25/28.14 [2595]~E(x25951,x25952)+E(f628(x25951,x25953),f628(x25952,x25953))
% 28.25/28.14 [2596]~E(x25961,x25962)+E(f628(x25963,x25961),f628(x25963,x25962))
% 28.25/28.14 [2597]~E(x25971,x25972)+E(f453(x25971,x25973),f453(x25972,x25973))
% 28.25/28.14 [2598]~E(x25981,x25982)+E(f453(x25983,x25981),f453(x25983,x25982))
% 28.25/28.14 [2599]~E(x25991,x25992)+E(f711(x25991,x25993,x25994),f711(x25992,x25993,x25994))
% 28.25/28.14 [2600]~E(x26001,x26002)+E(f711(x26003,x26001,x26004),f711(x26003,x26002,x26004))
% 28.25/28.14 [2601]~E(x26011,x26012)+E(f711(x26013,x26014,x26011),f711(x26013,x26014,x26012))
% 28.25/28.14 [2602]~E(x26021,x26022)+E(f881(x26021,x26023,x26024,x26025),f881(x26022,x26023,x26024,x26025))
% 28.25/28.14 [2603]~E(x26031,x26032)+E(f881(x26033,x26031,x26034,x26035),f881(x26033,x26032,x26034,x26035))
% 28.25/28.14 [2604]~E(x26041,x26042)+E(f881(x26043,x26044,x26041,x26045),f881(x26043,x26044,x26042,x26045))
% 28.25/28.14 [2605]~E(x26051,x26052)+E(f881(x26053,x26054,x26055,x26051),f881(x26053,x26054,x26055,x26052))
% 28.25/28.14 [2606]~E(x26061,x26062)+E(f352(x26061),f352(x26062))
% 28.25/28.14 [2607]~E(x26071,x26072)+E(f537(x26071,x26073,x26074,x26075,x26076),f537(x26072,x26073,x26074,x26075,x26076))
% 28.25/28.14 [2608]~E(x26081,x26082)+E(f537(x26083,x26081,x26084,x26085,x26086),f537(x26083,x26082,x26084,x26085,x26086))
% 28.25/28.14 [2609]~E(x26091,x26092)+E(f537(x26093,x26094,x26091,x26095,x26096),f537(x26093,x26094,x26092,x26095,x26096))
% 28.25/28.14 [2610]~E(x26101,x26102)+E(f537(x26103,x26104,x26105,x26101,x26106),f537(x26103,x26104,x26105,x26102,x26106))
% 28.25/28.14 [2611]~E(x26111,x26112)+E(f537(x26113,x26114,x26115,x26116,x26111),f537(x26113,x26114,x26115,x26116,x26112))
% 28.25/28.14 [2612]~E(x26121,x26122)+E(f709(x26121,x26123,x26124,x26125,x26126),f709(x26122,x26123,x26124,x26125,x26126))
% 28.25/28.14 [2613]~E(x26131,x26132)+E(f709(x26133,x26131,x26134,x26135,x26136),f709(x26133,x26132,x26134,x26135,x26136))
% 28.25/28.14 [2614]~E(x26141,x26142)+E(f709(x26143,x26144,x26141,x26145,x26146),f709(x26143,x26144,x26142,x26145,x26146))
% 28.25/28.14 [2615]~E(x26151,x26152)+E(f709(x26153,x26154,x26155,x26151,x26156),f709(x26153,x26154,x26155,x26152,x26156))
% 28.25/28.14 [2616]~E(x26161,x26162)+E(f709(x26163,x26164,x26165,x26166,x26161),f709(x26163,x26164,x26165,x26166,x26162))
% 28.25/28.14 [2617]~E(x26171,x26172)+E(f409(x26171,x26173,x26174,x26175,x26176),f409(x26172,x26173,x26174,x26175,x26176))
% 28.25/28.14 [2618]~E(x26181,x26182)+E(f409(x26183,x26181,x26184,x26185,x26186),f409(x26183,x26182,x26184,x26185,x26186))
% 28.25/28.14 [2619]~E(x26191,x26192)+E(f409(x26193,x26194,x26191,x26195,x26196),f409(x26193,x26194,x26192,x26195,x26196))
% 28.25/28.14 [2620]~E(x26201,x26202)+E(f409(x26203,x26204,x26205,x26201,x26206),f409(x26203,x26204,x26205,x26202,x26206))
% 28.25/28.14 [2621]~E(x26211,x26212)+E(f409(x26213,x26214,x26215,x26216,x26211),f409(x26213,x26214,x26215,x26216,x26212))
% 28.25/28.14 [2622]~E(x26221,x26222)+E(f825(x26221,x26223),f825(x26222,x26223))
% 28.25/28.14 [2623]~E(x26231,x26232)+E(f825(x26233,x26231),f825(x26233,x26232))
% 28.25/28.14 [2624]~E(x26241,x26242)+E(f421(x26241,x26243,x26244,x26245),f421(x26242,x26243,x26244,x26245))
% 28.25/28.14 [2625]~E(x26251,x26252)+E(f421(x26253,x26251,x26254,x26255),f421(x26253,x26252,x26254,x26255))
% 28.25/28.14 [2626]~E(x26261,x26262)+E(f421(x26263,x26264,x26261,x26265),f421(x26263,x26264,x26262,x26265))
% 28.25/28.14 [2627]~E(x26271,x26272)+E(f421(x26273,x26274,x26275,x26271),f421(x26273,x26274,x26275,x26272))
% 28.25/28.14 [2628]~E(x26281,x26282)+E(f605(x26281,x26283,x26284,x26285,x26286,x26287),f605(x26282,x26283,x26284,x26285,x26286,x26287))
% 28.25/28.14 [2629]~E(x26291,x26292)+E(f605(x26293,x26291,x26294,x26295,x26296,x26297),f605(x26293,x26292,x26294,x26295,x26296,x26297))
% 28.25/28.14 [2630]~E(x26301,x26302)+E(f605(x26303,x26304,x26301,x26305,x26306,x26307),f605(x26303,x26304,x26302,x26305,x26306,x26307))
% 28.25/28.14 [2631]~E(x26311,x26312)+E(f605(x26313,x26314,x26315,x26311,x26316,x26317),f605(x26313,x26314,x26315,x26312,x26316,x26317))
% 28.25/28.14 [2632]~E(x26321,x26322)+E(f605(x26323,x26324,x26325,x26326,x26321,x26327),f605(x26323,x26324,x26325,x26326,x26322,x26327))
% 28.25/28.14 [2633]~E(x26331,x26332)+E(f605(x26333,x26334,x26335,x26336,x26337,x26331),f605(x26333,x26334,x26335,x26336,x26337,x26332))
% 28.25/28.14 [2634]~E(x26341,x26342)+E(f851(x26341,x26343,x26344,x26345,x26346,x26347,x26348),f851(x26342,x26343,x26344,x26345,x26346,x26347,x26348))
% 28.25/28.14 [2635]~E(x26351,x26352)+E(f851(x26353,x26351,x26354,x26355,x26356,x26357,x26358),f851(x26353,x26352,x26354,x26355,x26356,x26357,x26358))
% 28.25/28.14 [2636]~E(x26361,x26362)+E(f851(x26363,x26364,x26361,x26365,x26366,x26367,x26368),f851(x26363,x26364,x26362,x26365,x26366,x26367,x26368))
% 28.25/28.14 [2637]~E(x26371,x26372)+E(f851(x26373,x26374,x26375,x26371,x26376,x26377,x26378),f851(x26373,x26374,x26375,x26372,x26376,x26377,x26378))
% 28.25/28.14 [2638]~E(x26381,x26382)+E(f851(x26383,x26384,x26385,x26386,x26381,x26387,x26388),f851(x26383,x26384,x26385,x26386,x26382,x26387,x26388))
% 28.25/28.14 [2639]~E(x26391,x26392)+E(f851(x26393,x26394,x26395,x26396,x26397,x26391,x26398),f851(x26393,x26394,x26395,x26396,x26397,x26392,x26398))
% 28.25/28.14 [2640]~E(x26401,x26402)+E(f851(x26403,x26404,x26405,x26406,x26407,x26408,x26401),f851(x26403,x26404,x26405,x26406,x26407,x26408,x26402))
% 28.25/28.14 [2641]~E(x26411,x26412)+E(f621(x26411,x26413,x26414,x26415,x26416,x26417,x26418,x26419),f621(x26412,x26413,x26414,x26415,x26416,x26417,x26418,x26419))
% 28.25/28.14 [2642]~E(x26421,x26422)+E(f621(x26423,x26421,x26424,x26425,x26426,x26427,x26428,x26429),f621(x26423,x26422,x26424,x26425,x26426,x26427,x26428,x26429))
% 28.25/28.14 [2643]~E(x26431,x26432)+E(f621(x26433,x26434,x26431,x26435,x26436,x26437,x26438,x26439),f621(x26433,x26434,x26432,x26435,x26436,x26437,x26438,x26439))
% 28.25/28.14 [2644]~E(x26441,x26442)+E(f621(x26443,x26444,x26445,x26441,x26446,x26447,x26448,x26449),f621(x26443,x26444,x26445,x26442,x26446,x26447,x26448,x26449))
% 28.25/28.14 [2645]~E(x26451,x26452)+E(f621(x26453,x26454,x26455,x26456,x26451,x26457,x26458,x26459),f621(x26453,x26454,x26455,x26456,x26452,x26457,x26458,x26459))
% 28.25/28.14 [2646]~E(x26461,x26462)+E(f621(x26463,x26464,x26465,x26466,x26467,x26461,x26468,x26469),f621(x26463,x26464,x26465,x26466,x26467,x26462,x26468,x26469))
% 28.25/28.14 [2647]~E(x26471,x26472)+E(f621(x26473,x26474,x26475,x26476,x26477,x26478,x26471,x26479),f621(x26473,x26474,x26475,x26476,x26477,x26478,x26472,x26479))
% 28.25/28.14 [2648]~E(x26481,x26482)+E(f621(x26483,x26484,x26485,x26486,x26487,x26488,x26489,x26481),f621(x26483,x26484,x26485,x26486,x26487,x26488,x26489,x26482))
% 28.25/28.14 [2649]~E(x26491,x26492)+E(f576(x26491,x26493),f576(x26492,x26493))
% 28.25/28.14 [2650]~E(x26501,x26502)+E(f576(x26503,x26501),f576(x26503,x26502))
% 28.25/28.14 [2651]~E(x26511,x26512)+E(f756(x26511,x26513),f756(x26512,x26513))
% 28.25/28.14 [2652]~E(x26521,x26522)+E(f756(x26523,x26521),f756(x26523,x26522))
% 28.25/28.14 [2653]~E(x26531,x26532)+E(f498(x26531,x26533,x26534),f498(x26532,x26533,x26534))
% 28.25/28.14 [2654]~E(x26541,x26542)+E(f498(x26543,x26541,x26544),f498(x26543,x26542,x26544))
% 28.25/28.14 [2655]~E(x26551,x26552)+E(f498(x26553,x26554,x26551),f498(x26553,x26554,x26552))
% 28.25/28.14 [2656]~E(x26561,x26562)+E(f290(x26561,x26563,x26564),f290(x26562,x26563,x26564))
% 28.25/28.14 [2657]~E(x26571,x26572)+E(f290(x26573,x26571,x26574),f290(x26573,x26572,x26574))
% 28.25/28.14 [2658]~E(x26581,x26582)+E(f290(x26583,x26584,x26581),f290(x26583,x26584,x26582))
% 28.25/28.14 [2659]~E(x26591,x26592)+E(f894(x26591,x26593,x26594,x26595),f894(x26592,x26593,x26594,x26595))
% 28.25/28.14 [2660]~E(x26601,x26602)+E(f894(x26603,x26601,x26604,x26605),f894(x26603,x26602,x26604,x26605))
% 28.25/28.14 [2661]~E(x26611,x26612)+E(f894(x26613,x26614,x26611,x26615),f894(x26613,x26614,x26612,x26615))
% 28.25/28.14 [2662]~E(x26621,x26622)+E(f894(x26623,x26624,x26625,x26621),f894(x26623,x26624,x26625,x26622))
% 28.25/28.14 [2663]~E(x26631,x26632)+E(f494(x26631,x26633,x26634),f494(x26632,x26633,x26634))
% 28.25/28.14 [2664]~E(x26641,x26642)+E(f494(x26643,x26641,x26644),f494(x26643,x26642,x26644))
% 28.25/28.14 [2665]~E(x26651,x26652)+E(f494(x26653,x26654,x26651),f494(x26653,x26654,x26652))
% 28.25/28.14 [2666]~E(x26661,x26662)+E(f266(x26661,x26663,x26664),f266(x26662,x26663,x26664))
% 28.25/28.14 [2667]~E(x26671,x26672)+E(f266(x26673,x26671,x26674),f266(x26673,x26672,x26674))
% 28.25/28.14 [2668]~E(x26681,x26682)+E(f266(x26683,x26684,x26681),f266(x26683,x26684,x26682))
% 28.25/28.14 [2669]~E(x26691,x26692)+E(f284(x26691,x26693),f284(x26692,x26693))
% 28.25/28.14 [2670]~E(x26701,x26702)+E(f284(x26703,x26701),f284(x26703,x26702))
% 28.25/28.14 [2671]~E(x26711,x26712)+E(f17(x26711,x26713,x26714,x26715),f17(x26712,x26713,x26714,x26715))
% 28.25/28.14 [2672]~E(x26721,x26722)+E(f17(x26723,x26721,x26724,x26725),f17(x26723,x26722,x26724,x26725))
% 28.25/28.14 [2673]~E(x26731,x26732)+E(f17(x26733,x26734,x26731,x26735),f17(x26733,x26734,x26732,x26735))
% 28.25/28.14 [2674]~E(x26741,x26742)+E(f17(x26743,x26744,x26745,x26741),f17(x26743,x26744,x26745,x26742))
% 28.25/28.14 [2675]~E(x26751,x26752)+E(f732(x26751,x26753,x26754),f732(x26752,x26753,x26754))
% 28.25/28.14 [2676]~E(x26761,x26762)+E(f732(x26763,x26761,x26764),f732(x26763,x26762,x26764))
% 28.25/28.14 [2677]~E(x26771,x26772)+E(f732(x26773,x26774,x26771),f732(x26773,x26774,x26772))
% 28.25/28.14 [2678]~E(x26781,x26782)+E(f920(x26781,x26783,x26784),f920(x26782,x26783,x26784))
% 28.25/28.14 [2679]~E(x26791,x26792)+E(f920(x26793,x26791,x26794),f920(x26793,x26792,x26794))
% 28.25/28.14 [2680]~E(x26801,x26802)+E(f920(x26803,x26804,x26801),f920(x26803,x26804,x26802))
% 28.25/28.14 [2681]~E(x26811,x26812)+E(f641(x26811,x26813,x26814,x26815,x26816),f641(x26812,x26813,x26814,x26815,x26816))
% 28.25/28.14 [2682]~E(x26821,x26822)+E(f641(x26823,x26821,x26824,x26825,x26826),f641(x26823,x26822,x26824,x26825,x26826))
% 28.25/28.14 [2683]~E(x26831,x26832)+E(f641(x26833,x26834,x26831,x26835,x26836),f641(x26833,x26834,x26832,x26835,x26836))
% 28.25/28.14 [2684]~E(x26841,x26842)+E(f641(x26843,x26844,x26845,x26841,x26846),f641(x26843,x26844,x26845,x26842,x26846))
% 28.25/28.14 [2685]~E(x26851,x26852)+E(f641(x26853,x26854,x26855,x26856,x26851),f641(x26853,x26854,x26855,x26856,x26852))
% 28.25/28.14 [2686]~E(x26861,x26862)+E(f481(x26861,x26863),f481(x26862,x26863))
% 28.25/28.14 [2687]~E(x26871,x26872)+E(f481(x26873,x26871),f481(x26873,x26872))
% 28.25/28.14 [2688]~E(x26881,x26882)+E(f378(x26881,x26883,x26884),f378(x26882,x26883,x26884))
% 28.25/28.14 [2689]~E(x26891,x26892)+E(f378(x26893,x26891,x26894),f378(x26893,x26892,x26894))
% 28.25/28.14 [2690]~E(x26901,x26902)+E(f378(x26903,x26904,x26901),f378(x26903,x26904,x26902))
% 28.25/28.14 [2691]~E(x26911,x26912)+E(f505(x26911,x26913,x26914,x26915,x26916),f505(x26912,x26913,x26914,x26915,x26916))
% 28.25/28.14 [2692]~E(x26921,x26922)+E(f505(x26923,x26921,x26924,x26925,x26926),f505(x26923,x26922,x26924,x26925,x26926))
% 28.25/28.14 [2693]~E(x26931,x26932)+E(f505(x26933,x26934,x26931,x26935,x26936),f505(x26933,x26934,x26932,x26935,x26936))
% 28.25/28.14 [2694]~E(x26941,x26942)+E(f505(x26943,x26944,x26945,x26941,x26946),f505(x26943,x26944,x26945,x26942,x26946))
% 28.25/28.14 [2695]~E(x26951,x26952)+E(f505(x26953,x26954,x26955,x26956,x26951),f505(x26953,x26954,x26955,x26956,x26952))
% 28.25/28.14 [2696]~E(x26961,x26962)+E(f398(x26961,x26963,x26964,x26965),f398(x26962,x26963,x26964,x26965))
% 28.25/28.14 [2697]~E(x26971,x26972)+E(f398(x26973,x26971,x26974,x26975),f398(x26973,x26972,x26974,x26975))
% 28.25/28.14 [2698]~E(x26981,x26982)+E(f398(x26983,x26984,x26981,x26985),f398(x26983,x26984,x26982,x26985))
% 28.25/28.14 [2699]~E(x26991,x26992)+E(f398(x26993,x26994,x26995,x26991),f398(x26993,x26994,x26995,x26992))
% 28.25/28.14 [2700]~E(x27001,x27002)+E(f578(x27001,x27003,x27004,x27005),f578(x27002,x27003,x27004,x27005))
% 28.25/28.14 [2701]~E(x27011,x27012)+E(f578(x27013,x27011,x27014,x27015),f578(x27013,x27012,x27014,x27015))
% 28.25/28.14 [2702]~E(x27021,x27022)+E(f578(x27023,x27024,x27021,x27025),f578(x27023,x27024,x27022,x27025))
% 28.25/28.14 [2703]~E(x27031,x27032)+E(f578(x27033,x27034,x27035,x27031),f578(x27033,x27034,x27035,x27032))
% 28.25/28.14 [2704]~E(x27041,x27042)+E(f701(x27041,x27043,x27044,x27045,x27046),f701(x27042,x27043,x27044,x27045,x27046))
% 28.25/28.14 [2705]~E(x27051,x27052)+E(f701(x27053,x27051,x27054,x27055,x27056),f701(x27053,x27052,x27054,x27055,x27056))
% 28.25/28.14 [2706]~E(x27061,x27062)+E(f701(x27063,x27064,x27061,x27065,x27066),f701(x27063,x27064,x27062,x27065,x27066))
% 28.25/28.14 [2707]~E(x27071,x27072)+E(f701(x27073,x27074,x27075,x27071,x27076),f701(x27073,x27074,x27075,x27072,x27076))
% 28.25/28.14 [2708]~E(x27081,x27082)+E(f701(x27083,x27084,x27085,x27086,x27081),f701(x27083,x27084,x27085,x27086,x27082))
% 28.25/28.14 [2709]~E(x27091,x27092)+E(f712(x27091,x27093,x27094),f712(x27092,x27093,x27094))
% 28.25/28.14 [2710]~E(x27101,x27102)+E(f712(x27103,x27101,x27104),f712(x27103,x27102,x27104))
% 28.25/28.14 [2711]~E(x27111,x27112)+E(f712(x27113,x27114,x27111),f712(x27113,x27114,x27112))
% 28.25/28.14 [2712]~E(x27121,x27122)+E(f264(x27121,x27123),f264(x27122,x27123))
% 28.25/28.14 [2713]~E(x27131,x27132)+E(f264(x27133,x27131),f264(x27133,x27132))
% 28.25/28.14 [2714]~E(x27141,x27142)+E(f670(x27141,x27143,x27144,x27145,x27146),f670(x27142,x27143,x27144,x27145,x27146))
% 28.25/28.14 [2715]~E(x27151,x27152)+E(f670(x27153,x27151,x27154,x27155,x27156),f670(x27153,x27152,x27154,x27155,x27156))
% 28.25/28.14 [2716]~E(x27161,x27162)+E(f670(x27163,x27164,x27161,x27165,x27166),f670(x27163,x27164,x27162,x27165,x27166))
% 28.25/28.14 [2717]~E(x27171,x27172)+E(f670(x27173,x27174,x27175,x27171,x27176),f670(x27173,x27174,x27175,x27172,x27176))
% 28.25/28.14 [2718]~E(x27181,x27182)+E(f670(x27183,x27184,x27185,x27186,x27181),f670(x27183,x27184,x27185,x27186,x27182))
% 28.25/28.14 [2719]~E(x27191,x27192)+E(f410(x27191,x27193,x27194,x27195,x27196),f410(x27192,x27193,x27194,x27195,x27196))
% 28.25/28.14 [2720]~E(x27201,x27202)+E(f410(x27203,x27201,x27204,x27205,x27206),f410(x27203,x27202,x27204,x27205,x27206))
% 28.25/28.14 [2721]~E(x27211,x27212)+E(f410(x27213,x27214,x27211,x27215,x27216),f410(x27213,x27214,x27212,x27215,x27216))
% 28.25/28.14 [2722]~E(x27221,x27222)+E(f410(x27223,x27224,x27225,x27221,x27226),f410(x27223,x27224,x27225,x27222,x27226))
% 28.25/28.14 [2723]~E(x27231,x27232)+E(f410(x27233,x27234,x27235,x27236,x27231),f410(x27233,x27234,x27235,x27236,x27232))
% 28.25/28.14 [2724]~E(x27241,x27242)+E(f116(x27241),f116(x27242))
% 28.25/28.14 [2725]~E(x27251,x27252)+E(f482(x27251,x27253),f482(x27252,x27253))
% 28.25/28.14 [2726]~E(x27261,x27262)+E(f482(x27263,x27261),f482(x27263,x27262))
% 28.25/28.14 [2727]~E(x27271,x27272)+E(f574(x27271,x27273,x27274,x27275),f574(x27272,x27273,x27274,x27275))
% 28.25/28.14 [2728]~E(x27281,x27282)+E(f574(x27283,x27281,x27284,x27285),f574(x27283,x27282,x27284,x27285))
% 28.25/28.14 [2729]~E(x27291,x27292)+E(f574(x27293,x27294,x27291,x27295),f574(x27293,x27294,x27292,x27295))
% 28.25/28.14 [2730]~E(x27301,x27302)+E(f574(x27303,x27304,x27305,x27301),f574(x27303,x27304,x27305,x27302))
% 28.25/28.14 [2731]~E(x27311,x27312)+E(f401(x27311,x27313,x27314,x27315),f401(x27312,x27313,x27314,x27315))
% 28.25/28.14 [2732]~E(x27321,x27322)+E(f401(x27323,x27321,x27324,x27325),f401(x27323,x27322,x27324,x27325))
% 28.25/28.14 [2733]~E(x27331,x27332)+E(f401(x27333,x27334,x27331,x27335),f401(x27333,x27334,x27332,x27335))
% 28.25/28.14 [2734]~E(x27341,x27342)+E(f401(x27343,x27344,x27345,x27341),f401(x27343,x27344,x27345,x27342))
% 28.25/28.14 [2735]~E(x27351,x27352)+E(f479(x27351,x27353,x27354),f479(x27352,x27353,x27354))
% 28.25/28.14 [2736]~E(x27361,x27362)+E(f479(x27363,x27361,x27364),f479(x27363,x27362,x27364))
% 28.25/28.14 [2737]~E(x27371,x27372)+E(f479(x27373,x27374,x27371),f479(x27373,x27374,x27372))
% 28.25/28.14 [2738]~E(x27381,x27382)+E(f837(x27381,x27383),f837(x27382,x27383))
% 28.25/28.14 [2739]~E(x27391,x27392)+E(f837(x27393,x27391),f837(x27393,x27392))
% 28.25/28.14 [2740]~E(x27401,x27402)+E(f435(x27401,x27403,x27404),f435(x27402,x27403,x27404))
% 28.25/28.14 [2741]~E(x27411,x27412)+E(f435(x27413,x27411,x27414),f435(x27413,x27412,x27414))
% 28.25/28.14 [2742]~E(x27421,x27422)+E(f435(x27423,x27424,x27421),f435(x27423,x27424,x27422))
% 28.25/28.14 [2743]~E(x27431,x27432)+E(f774(x27431,x27433,x27434),f774(x27432,x27433,x27434))
% 28.25/28.14 [2744]~E(x27441,x27442)+E(f774(x27443,x27441,x27444),f774(x27443,x27442,x27444))
% 28.25/28.14 [2745]~E(x27451,x27452)+E(f774(x27453,x27454,x27451),f774(x27453,x27454,x27452))
% 28.25/28.14 [2746]~E(x27461,x27462)+E(f459(x27461,x27463,x27464,x27465,x27466,x27467),f459(x27462,x27463,x27464,x27465,x27466,x27467))
% 28.25/28.14 [2747]~E(x27471,x27472)+E(f459(x27473,x27471,x27474,x27475,x27476,x27477),f459(x27473,x27472,x27474,x27475,x27476,x27477))
% 28.25/28.14 [2748]~E(x27481,x27482)+E(f459(x27483,x27484,x27481,x27485,x27486,x27487),f459(x27483,x27484,x27482,x27485,x27486,x27487))
% 28.25/28.14 [2749]~E(x27491,x27492)+E(f459(x27493,x27494,x27495,x27491,x27496,x27497),f459(x27493,x27494,x27495,x27492,x27496,x27497))
% 28.25/28.14 [2750]~E(x27501,x27502)+E(f459(x27503,x27504,x27505,x27506,x27501,x27507),f459(x27503,x27504,x27505,x27506,x27502,x27507))
% 28.25/28.14 [2751]~E(x27511,x27512)+E(f459(x27513,x27514,x27515,x27516,x27517,x27511),f459(x27513,x27514,x27515,x27516,x27517,x27512))
% 28.25/28.14 [2752]~E(x27521,x27522)+E(f673(x27521,x27523),f673(x27522,x27523))
% 28.25/28.14 [2753]~E(x27531,x27532)+E(f673(x27533,x27531),f673(x27533,x27532))
% 28.25/28.14 [2754]~E(x27541,x27542)+E(f870(x27541,x27543,x27544),f870(x27542,x27543,x27544))
% 28.25/28.14 [2755]~E(x27551,x27552)+E(f870(x27553,x27551,x27554),f870(x27553,x27552,x27554))
% 28.25/28.14 [2756]~E(x27561,x27562)+E(f870(x27563,x27564,x27561),f870(x27563,x27564,x27562))
% 28.25/28.14 [2757]~E(x27571,x27572)+E(f717(x27571,x27573),f717(x27572,x27573))
% 28.25/28.14 [2758]~E(x27581,x27582)+E(f717(x27583,x27581),f717(x27583,x27582))
% 28.25/28.14 [2759]~E(x27591,x27592)+E(f638(x27591,x27593,x27594,x27595,x27596),f638(x27592,x27593,x27594,x27595,x27596))
% 28.25/28.14 [2760]~E(x27601,x27602)+E(f638(x27603,x27601,x27604,x27605,x27606),f638(x27603,x27602,x27604,x27605,x27606))
% 28.25/28.14 [2761]~E(x27611,x27612)+E(f638(x27613,x27614,x27611,x27615,x27616),f638(x27613,x27614,x27612,x27615,x27616))
% 28.25/28.14 [2762]~E(x27621,x27622)+E(f638(x27623,x27624,x27625,x27621,x27626),f638(x27623,x27624,x27625,x27622,x27626))
% 28.25/28.14 [2763]~E(x27631,x27632)+E(f638(x27633,x27634,x27635,x27636,x27631),f638(x27633,x27634,x27635,x27636,x27632))
% 28.25/28.14 [2764]~E(x27641,x27642)+E(f511(x27641,x27643,x27644),f511(x27642,x27643,x27644))
% 28.25/28.14 [2765]~E(x27651,x27652)+E(f511(x27653,x27651,x27654),f511(x27653,x27652,x27654))
% 28.25/28.14 [2766]~E(x27661,x27662)+E(f511(x27663,x27664,x27661),f511(x27663,x27664,x27662))
% 28.25/28.14 [2767]~E(x27671,x27672)+E(f419(x27671,x27673),f419(x27672,x27673))
% 28.25/28.14 [2768]~E(x27681,x27682)+E(f419(x27683,x27681),f419(x27683,x27682))
% 28.25/28.14 [2769]~E(x27691,x27692)+E(f467(x27691,x27693,x27694,x27695),f467(x27692,x27693,x27694,x27695))
% 28.25/28.14 [2770]~E(x27701,x27702)+E(f467(x27703,x27701,x27704,x27705),f467(x27703,x27702,x27704,x27705))
% 28.25/28.14 [2771]~E(x27711,x27712)+E(f467(x27713,x27714,x27711,x27715),f467(x27713,x27714,x27712,x27715))
% 28.25/28.14 [2772]~E(x27721,x27722)+E(f467(x27723,x27724,x27725,x27721),f467(x27723,x27724,x27725,x27722))
% 28.25/28.14 [2773]~E(x27731,x27732)+E(f491(x27731,x27733),f491(x27732,x27733))
% 28.25/28.14 [2774]~E(x27741,x27742)+E(f491(x27743,x27741),f491(x27743,x27742))
% 28.25/28.14 [2775]~E(x27751,x27752)+E(f599(x27751,x27753,x27754),f599(x27752,x27753,x27754))
% 28.25/28.14 [2776]~E(x27761,x27762)+E(f599(x27763,x27761,x27764),f599(x27763,x27762,x27764))
% 28.25/28.14 [2777]~E(x27771,x27772)+E(f599(x27773,x27774,x27771),f599(x27773,x27774,x27772))
% 28.25/28.14 [2778]~E(x27781,x27782)+E(f334(x27781,x27783,x27784),f334(x27782,x27783,x27784))
% 28.25/28.14 [2779]~E(x27791,x27792)+E(f334(x27793,x27791,x27794),f334(x27793,x27792,x27794))
% 28.25/28.14 [2780]~E(x27801,x27802)+E(f334(x27803,x27804,x27801),f334(x27803,x27804,x27802))
% 28.25/28.14 [2781]~E(x27811,x27812)+E(f609(x27811,x27813,x27814,x27815,x27816,x27817),f609(x27812,x27813,x27814,x27815,x27816,x27817))
% 28.25/28.14 [2782]~E(x27821,x27822)+E(f609(x27823,x27821,x27824,x27825,x27826,x27827),f609(x27823,x27822,x27824,x27825,x27826,x27827))
% 28.25/28.14 [2783]~E(x27831,x27832)+E(f609(x27833,x27834,x27831,x27835,x27836,x27837),f609(x27833,x27834,x27832,x27835,x27836,x27837))
% 28.25/28.14 [2784]~E(x27841,x27842)+E(f609(x27843,x27844,x27845,x27841,x27846,x27847),f609(x27843,x27844,x27845,x27842,x27846,x27847))
% 28.25/28.14 [2785]~E(x27851,x27852)+E(f609(x27853,x27854,x27855,x27856,x27851,x27857),f609(x27853,x27854,x27855,x27856,x27852,x27857))
% 28.25/28.14 [2786]~E(x27861,x27862)+E(f609(x27863,x27864,x27865,x27866,x27867,x27861),f609(x27863,x27864,x27865,x27866,x27867,x27862))
% 28.25/28.14 [2787]~E(x27871,x27872)+E(f558(x27871),f558(x27872))
% 28.25/28.14 [2788]~E(x27881,x27882)+E(f588(x27881,x27883),f588(x27882,x27883))
% 28.25/28.14 [2789]~E(x27891,x27892)+E(f588(x27893,x27891),f588(x27893,x27892))
% 28.25/28.14 [2790]~E(x27901,x27902)+E(f843(x27901,x27903,x27904),f843(x27902,x27903,x27904))
% 28.25/28.14 [2791]~E(x27911,x27912)+E(f843(x27913,x27911,x27914),f843(x27913,x27912,x27914))
% 28.25/28.14 [2792]~E(x27921,x27922)+E(f843(x27923,x27924,x27921),f843(x27923,x27924,x27922))
% 28.25/28.14 [2793]~E(x27931,x27932)+E(f575(x27931,x27933,x27934,x27935),f575(x27932,x27933,x27934,x27935))
% 28.25/28.14 [2794]~E(x27941,x27942)+E(f575(x27943,x27941,x27944,x27945),f575(x27943,x27942,x27944,x27945))
% 28.25/28.14 [2795]~E(x27951,x27952)+E(f575(x27953,x27954,x27951,x27955),f575(x27953,x27954,x27952,x27955))
% 28.25/28.14 [2796]~E(x27961,x27962)+E(f575(x27963,x27964,x27965,x27961),f575(x27963,x27964,x27965,x27962))
% 28.25/28.14 [2797]~E(x27971,x27972)+E(f21(x27971,x27973),f21(x27972,x27973))
% 28.25/28.14 [2798]~E(x27981,x27982)+E(f21(x27983,x27981),f21(x27983,x27982))
% 28.25/28.14 [2799]~E(x27991,x27992)+E(f271(x27991,x27993,x27994,x27995),f271(x27992,x27993,x27994,x27995))
% 28.25/28.14 [2800]~E(x28001,x28002)+E(f271(x28003,x28001,x28004,x28005),f271(x28003,x28002,x28004,x28005))
% 28.25/28.14 [2801]~E(x28011,x28012)+E(f271(x28013,x28014,x28011,x28015),f271(x28013,x28014,x28012,x28015))
% 28.25/28.14 [2802]~E(x28021,x28022)+E(f271(x28023,x28024,x28025,x28021),f271(x28023,x28024,x28025,x28022))
% 28.25/28.14 [2803]~E(x28031,x28032)+E(f891(x28031,x28033,x28034,x28035,x28036),f891(x28032,x28033,x28034,x28035,x28036))
% 28.25/28.14 [2804]~E(x28041,x28042)+E(f891(x28043,x28041,x28044,x28045,x28046),f891(x28043,x28042,x28044,x28045,x28046))
% 28.25/28.14 [2805]~E(x28051,x28052)+E(f891(x28053,x28054,x28051,x28055,x28056),f891(x28053,x28054,x28052,x28055,x28056))
% 28.25/28.14 [2806]~E(x28061,x28062)+E(f891(x28063,x28064,x28065,x28061,x28066),f891(x28063,x28064,x28065,x28062,x28066))
% 28.25/28.14 [2807]~E(x28071,x28072)+E(f891(x28073,x28074,x28075,x28076,x28071),f891(x28073,x28074,x28075,x28076,x28072))
% 28.25/28.14 [2808]~E(x28081,x28082)+E(f904(x28081,x28083,x28084),f904(x28082,x28083,x28084))
% 28.25/28.14 [2809]~E(x28091,x28092)+E(f904(x28093,x28091,x28094),f904(x28093,x28092,x28094))
% 28.25/28.14 [2810]~E(x28101,x28102)+E(f904(x28103,x28104,x28101),f904(x28103,x28104,x28102))
% 28.25/28.14 [2811]~E(x28111,x28112)+E(f760(x28111,x28113,x28114,x28115),f760(x28112,x28113,x28114,x28115))
% 28.25/28.14 [2812]~E(x28121,x28122)+E(f760(x28123,x28121,x28124,x28125),f760(x28123,x28122,x28124,x28125))
% 28.25/28.14 [2813]~E(x28131,x28132)+E(f760(x28133,x28134,x28131,x28135),f760(x28133,x28134,x28132,x28135))
% 28.25/28.14 [2814]~E(x28141,x28142)+E(f760(x28143,x28144,x28145,x28141),f760(x28143,x28144,x28145,x28142))
% 28.25/28.14 [2815]~E(x28151,x28152)+E(f919(x28151,x28153,x28154),f919(x28152,x28153,x28154))
% 28.25/28.14 [2816]~E(x28161,x28162)+E(f919(x28163,x28161,x28164),f919(x28163,x28162,x28164))
% 28.25/28.14 [2817]~E(x28171,x28172)+E(f919(x28173,x28174,x28171),f919(x28173,x28174,x28172))
% 28.25/28.14 [2818]~E(x28181,x28182)+E(f745(x28181,x28183,x28184,x28185),f745(x28182,x28183,x28184,x28185))
% 28.25/28.14 [2819]~E(x28191,x28192)+E(f745(x28193,x28191,x28194,x28195),f745(x28193,x28192,x28194,x28195))
% 28.25/28.14 [2820]~E(x28201,x28202)+E(f745(x28203,x28204,x28201,x28205),f745(x28203,x28204,x28202,x28205))
% 28.25/28.14 [2821]~E(x28211,x28212)+E(f745(x28213,x28214,x28215,x28211),f745(x28213,x28214,x28215,x28212))
% 28.25/28.14 [2822]~E(x28221,x28222)+E(f214(x28221,x28223,x28224),f214(x28222,x28223,x28224))
% 28.25/28.14 [2823]~E(x28231,x28232)+E(f214(x28233,x28231,x28234),f214(x28233,x28232,x28234))
% 28.25/28.14 [2824]~E(x28241,x28242)+E(f214(x28243,x28244,x28241),f214(x28243,x28244,x28242))
% 28.25/28.14 [2825]~E(x28251,x28252)+E(f468(x28251,x28253,x28254,x28255,x28256,x28257),f468(x28252,x28253,x28254,x28255,x28256,x28257))
% 28.25/28.14 [2826]~E(x28261,x28262)+E(f468(x28263,x28261,x28264,x28265,x28266,x28267),f468(x28263,x28262,x28264,x28265,x28266,x28267))
% 28.25/28.14 [2827]~E(x28271,x28272)+E(f468(x28273,x28274,x28271,x28275,x28276,x28277),f468(x28273,x28274,x28272,x28275,x28276,x28277))
% 28.25/28.14 [2828]~E(x28281,x28282)+E(f468(x28283,x28284,x28285,x28281,x28286,x28287),f468(x28283,x28284,x28285,x28282,x28286,x28287))
% 28.25/28.14 [2829]~E(x28291,x28292)+E(f468(x28293,x28294,x28295,x28296,x28291,x28297),f468(x28293,x28294,x28295,x28296,x28292,x28297))
% 28.25/28.14 [2830]~E(x28301,x28302)+E(f468(x28303,x28304,x28305,x28306,x28307,x28301),f468(x28303,x28304,x28305,x28306,x28307,x28302))
% 28.25/28.14 [2831]~E(x28311,x28312)+E(f521(x28311,x28313,x28314,x28315),f521(x28312,x28313,x28314,x28315))
% 28.25/28.14 [2832]~E(x28321,x28322)+E(f521(x28323,x28321,x28324,x28325),f521(x28323,x28322,x28324,x28325))
% 28.25/28.14 [2833]~E(x28331,x28332)+E(f521(x28333,x28334,x28331,x28335),f521(x28333,x28334,x28332,x28335))
% 28.25/28.14 [2834]~E(x28341,x28342)+E(f521(x28343,x28344,x28345,x28341),f521(x28343,x28344,x28345,x28342))
% 28.25/28.14 [2835]~E(x28351,x28352)+E(f192(x28351),f192(x28352))
% 28.25/28.14 [2836]~E(x28361,x28362)+E(f582(x28361,x28363,x28364,x28365,x28366,x28367),f582(x28362,x28363,x28364,x28365,x28366,x28367))
% 28.25/28.14 [2837]~E(x28371,x28372)+E(f582(x28373,x28371,x28374,x28375,x28376,x28377),f582(x28373,x28372,x28374,x28375,x28376,x28377))
% 28.25/28.14 [2838]~E(x28381,x28382)+E(f582(x28383,x28384,x28381,x28385,x28386,x28387),f582(x28383,x28384,x28382,x28385,x28386,x28387))
% 28.25/28.14 [2839]~E(x28391,x28392)+E(f582(x28393,x28394,x28395,x28391,x28396,x28397),f582(x28393,x28394,x28395,x28392,x28396,x28397))
% 28.25/28.14 [2840]~E(x28401,x28402)+E(f582(x28403,x28404,x28405,x28406,x28401,x28407),f582(x28403,x28404,x28405,x28406,x28402,x28407))
% 28.25/28.14 [2841]~E(x28411,x28412)+E(f582(x28413,x28414,x28415,x28416,x28417,x28411),f582(x28413,x28414,x28415,x28416,x28417,x28412))
% 28.25/28.14 [2842]~E(x28421,x28422)+E(f499(x28421,x28423,x28424),f499(x28422,x28423,x28424))
% 28.25/28.14 [2843]~E(x28431,x28432)+E(f499(x28433,x28431,x28434),f499(x28433,x28432,x28434))
% 28.25/28.14 [2844]~E(x28441,x28442)+E(f499(x28443,x28444,x28441),f499(x28443,x28444,x28442))
% 28.25/28.14 [2845]~E(x28451,x28452)+E(f737(x28451,x28453,x28454),f737(x28452,x28453,x28454))
% 28.25/28.14 [2846]~E(x28461,x28462)+E(f737(x28463,x28461,x28464),f737(x28463,x28462,x28464))
% 28.25/28.14 [2847]~E(x28471,x28472)+E(f737(x28473,x28474,x28471),f737(x28473,x28474,x28472))
% 28.25/28.14 [2848]~E(x28481,x28482)+E(f721(x28481,x28483,x28484,x28485,x28486),f721(x28482,x28483,x28484,x28485,x28486))
% 28.25/28.14 [2849]~E(x28491,x28492)+E(f721(x28493,x28491,x28494,x28495,x28496),f721(x28493,x28492,x28494,x28495,x28496))
% 28.25/28.14 [2850]~E(x28501,x28502)+E(f721(x28503,x28504,x28501,x28505,x28506),f721(x28503,x28504,x28502,x28505,x28506))
% 28.25/28.14 [2851]~E(x28511,x28512)+E(f721(x28513,x28514,x28515,x28511,x28516),f721(x28513,x28514,x28515,x28512,x28516))
% 28.25/28.14 [2852]~E(x28521,x28522)+E(f721(x28523,x28524,x28525,x28526,x28521),f721(x28523,x28524,x28525,x28526,x28522))
% 28.25/28.14 [2853]~E(x28531,x28532)+E(f229(x28531,x28533),f229(x28532,x28533))
% 28.25/28.14 [2854]~E(x28541,x28542)+E(f229(x28543,x28541),f229(x28543,x28542))
% 28.25/28.14 [2855]~E(x28551,x28552)+E(f888(x28551,x28553,x28554,x28555),f888(x28552,x28553,x28554,x28555))
% 28.25/28.14 [2856]~E(x28561,x28562)+E(f888(x28563,x28561,x28564,x28565),f888(x28563,x28562,x28564,x28565))
% 28.25/28.14 [2857]~E(x28571,x28572)+E(f888(x28573,x28574,x28571,x28575),f888(x28573,x28574,x28572,x28575))
% 28.25/28.14 [2858]~E(x28581,x28582)+E(f888(x28583,x28584,x28585,x28581),f888(x28583,x28584,x28585,x28582))
% 28.25/28.14 [2859]~E(x28591,x28592)+E(f331(x28591,x28593),f331(x28592,x28593))
% 28.25/28.14 [2860]~E(x28601,x28602)+E(f331(x28603,x28601),f331(x28603,x28602))
% 28.25/28.14 [2861]~E(x28611,x28612)+E(f451(x28611,x28613),f451(x28612,x28613))
% 28.25/28.14 [2862]~E(x28621,x28622)+E(f451(x28623,x28621),f451(x28623,x28622))
% 28.25/28.14 [2863]~E(x28631,x28632)+E(f252(x28631,x28633,x28634,x28635,x28636),f252(x28632,x28633,x28634,x28635,x28636))
% 28.25/28.14 [2864]~E(x28641,x28642)+E(f252(x28643,x28641,x28644,x28645,x28646),f252(x28643,x28642,x28644,x28645,x28646))
% 28.25/28.14 [2865]~E(x28651,x28652)+E(f252(x28653,x28654,x28651,x28655,x28656),f252(x28653,x28654,x28652,x28655,x28656))
% 28.25/28.14 [2866]~E(x28661,x28662)+E(f252(x28663,x28664,x28665,x28661,x28666),f252(x28663,x28664,x28665,x28662,x28666))
% 28.25/28.14 [2867]~E(x28671,x28672)+E(f252(x28673,x28674,x28675,x28676,x28671),f252(x28673,x28674,x28675,x28676,x28672))
% 28.25/28.14 [2868]~E(x28681,x28682)+E(f520(x28681,x28683,x28684),f520(x28682,x28683,x28684))
% 28.25/28.14 [2869]~E(x28691,x28692)+E(f520(x28693,x28691,x28694),f520(x28693,x28692,x28694))
% 28.25/28.14 [2870]~E(x28701,x28702)+E(f520(x28703,x28704,x28701),f520(x28703,x28704,x28702))
% 28.25/28.14 [2871]~E(x28711,x28712)+E(f416(x28711,x28713),f416(x28712,x28713))
% 28.25/28.14 [2872]~E(x28721,x28722)+E(f416(x28723,x28721),f416(x28723,x28722))
% 28.25/28.14 [2873]~E(x28731,x28732)+E(f525(x28731,x28733,x28734),f525(x28732,x28733,x28734))
% 28.25/28.14 [2874]~E(x28741,x28742)+E(f525(x28743,x28741,x28744),f525(x28743,x28742,x28744))
% 28.25/28.14 [2875]~E(x28751,x28752)+E(f525(x28753,x28754,x28751),f525(x28753,x28754,x28752))
% 28.25/28.14 [2876]~E(x28761,x28762)+E(f844(x28761,x28763,x28764),f844(x28762,x28763,x28764))
% 28.25/28.14 [2877]~E(x28771,x28772)+E(f844(x28773,x28771,x28774),f844(x28773,x28772,x28774))
% 28.25/28.14 [2878]~E(x28781,x28782)+E(f844(x28783,x28784,x28781),f844(x28783,x28784,x28782))
% 28.25/28.14 [2879]~E(x28791,x28792)+E(f902(x28791,x28793),f902(x28792,x28793))
% 28.25/28.14 [2880]~E(x28801,x28802)+E(f902(x28803,x28801),f902(x28803,x28802))
% 28.25/28.14 [2881]~E(x28811,x28812)+E(f632(x28811,x28813,x28814),f632(x28812,x28813,x28814))
% 28.25/28.14 [2882]~E(x28821,x28822)+E(f632(x28823,x28821,x28824),f632(x28823,x28822,x28824))
% 28.25/28.14 [2883]~E(x28831,x28832)+E(f632(x28833,x28834,x28831),f632(x28833,x28834,x28832))
% 28.25/28.14 [2884]~E(x28841,x28842)+E(f480(x28841,x28843),f480(x28842,x28843))
% 28.25/28.14 [2885]~E(x28851,x28852)+E(f480(x28853,x28851),f480(x28853,x28852))
% 28.25/28.14 [2886]~E(x28861,x28862)+E(f792(x28861,x28863,x28864),f792(x28862,x28863,x28864))
% 28.25/28.14 [2887]~E(x28871,x28872)+E(f792(x28873,x28871,x28874),f792(x28873,x28872,x28874))
% 28.25/28.14 [2888]~E(x28881,x28882)+E(f792(x28883,x28884,x28881),f792(x28883,x28884,x28882))
% 28.25/28.14 [2889]~E(x28891,x28892)+E(f326(x28891),f326(x28892))
% 28.25/28.14 [2890]~E(x28901,x28902)+E(f373(x28901),f373(x28902))
% 28.25/28.14 [2891]~E(x28911,x28912)+E(f566(x28911,x28913,x28914,x28915),f566(x28912,x28913,x28914,x28915))
% 28.25/28.14 [2892]~E(x28921,x28922)+E(f566(x28923,x28921,x28924,x28925),f566(x28923,x28922,x28924,x28925))
% 28.25/28.14 [2893]~E(x28931,x28932)+E(f566(x28933,x28934,x28931,x28935),f566(x28933,x28934,x28932,x28935))
% 28.25/28.14 [2894]~E(x28941,x28942)+E(f566(x28943,x28944,x28945,x28941),f566(x28943,x28944,x28945,x28942))
% 28.25/28.14 [2895]~E(x28951,x28952)+E(f333(x28951),f333(x28952))
% 28.25/28.14 [2896]~E(x28961,x28962)+E(f38(x28961),f38(x28962))
% 28.25/28.14 [2897]~P1(x28971)+P1(x28972)+~E(x28971,x28972)
% 28.25/28.14 [2898]~P2(x28981)+P2(x28982)+~E(x28981,x28982)
% 28.25/28.14 [2899]~P4(x28991)+P4(x28992)+~E(x28991,x28992)
% 28.25/28.14 [2900]~P90(x29001)+P90(x29002)+~E(x29001,x29002)
% 28.25/28.14 [2901]~P74(x29011)+P74(x29012)+~E(x29011,x29012)
% 28.25/28.14 [2902]~P3(x29021)+P3(x29022)+~E(x29021,x29022)
% 28.25/28.14 [2903]P59(x29032,x29033,x29034)+~E(x29031,x29032)+~P59(x29031,x29033,x29034)
% 28.25/28.14 [2904]P59(x29043,x29042,x29044)+~E(x29041,x29042)+~P59(x29043,x29041,x29044)
% 28.25/28.14 [2905]P59(x29053,x29054,x29052)+~E(x29051,x29052)+~P59(x29053,x29054,x29051)
% 28.25/28.14 [2906]~P6(x29061)+P6(x29062)+~E(x29061,x29062)
% 28.25/28.14 [2907]P152(x29072,x29073,x29074)+~E(x29071,x29072)+~P152(x29071,x29073,x29074)
% 28.25/28.14 [2908]P152(x29083,x29082,x29084)+~E(x29081,x29082)+~P152(x29083,x29081,x29084)
% 28.25/28.14 [2909]P152(x29093,x29094,x29092)+~E(x29091,x29092)+~P152(x29093,x29094,x29091)
% 28.25/28.14 [2910]~P78(x29101)+P78(x29102)+~E(x29101,x29102)
% 28.25/28.14 [2911]~P121(x29111)+P121(x29112)+~E(x29111,x29112)
% 28.25/28.14 [2912]~P72(x29121)+P72(x29122)+~E(x29121,x29122)
% 28.25/28.14 [2913]~P113(x29131)+P113(x29132)+~E(x29131,x29132)
% 28.25/28.14 [2914]~P130(x29141)+P130(x29142)+~E(x29141,x29142)
% 28.25/28.14 [2915]~P75(x29151)+P75(x29152)+~E(x29151,x29152)
% 28.25/28.14 [2916]~P141(x29161)+P141(x29162)+~E(x29161,x29162)
% 28.25/28.14 [2917]~P5(x29171)+P5(x29172)+~E(x29171,x29172)
% 28.25/28.14 [2918]P21(x29182,x29183,x29184,x29185)+~E(x29181,x29182)+~P21(x29181,x29183,x29184,x29185)
% 28.25/28.14 [2919]P21(x29193,x29192,x29194,x29195)+~E(x29191,x29192)+~P21(x29193,x29191,x29194,x29195)
% 28.25/28.14 [2920]P21(x29203,x29204,x29202,x29205)+~E(x29201,x29202)+~P21(x29203,x29204,x29201,x29205)
% 28.25/28.14 [2921]P21(x29213,x29214,x29215,x29212)+~E(x29211,x29212)+~P21(x29213,x29214,x29215,x29211)
% 28.25/28.14 [2922]~P114(x29221)+P114(x29222)+~E(x29221,x29222)
% 28.25/28.14 [2923]~P96(x29231)+P96(x29232)+~E(x29231,x29232)
% 28.25/28.14 [2924]~P67(x29241)+P67(x29242)+~E(x29241,x29242)
% 28.25/28.14 [2925]~P68(x29251)+P68(x29252)+~E(x29251,x29252)
% 28.25/28.14 [2926]P26(x29262,x29263,x29264,x29265)+~E(x29261,x29262)+~P26(x29261,x29263,x29264,x29265)
% 28.25/28.14 [2927]P26(x29273,x29272,x29274,x29275)+~E(x29271,x29272)+~P26(x29273,x29271,x29274,x29275)
% 28.25/28.14 [2928]P26(x29283,x29284,x29282,x29285)+~E(x29281,x29282)+~P26(x29283,x29284,x29281,x29285)
% 28.25/28.14 [2929]P26(x29293,x29294,x29295,x29292)+~E(x29291,x29292)+~P26(x29293,x29294,x29295,x29291)
% 28.25/28.14 [2930]P151(x29302,x29303,x29304)+~E(x29301,x29302)+~P151(x29301,x29303,x29304)
% 28.25/28.14 [2931]P151(x29313,x29312,x29314)+~E(x29311,x29312)+~P151(x29313,x29311,x29314)
% 28.25/28.14 [2932]P151(x29323,x29324,x29322)+~E(x29321,x29322)+~P151(x29323,x29324,x29321)
% 28.25/28.14 [2933]~P69(x29331)+P69(x29332)+~E(x29331,x29332)
% 28.25/28.14 [2934]~P102(x29341)+P102(x29342)+~E(x29341,x29342)
% 28.25/28.14 [2935]P41(x29352,x29353,x29354)+~E(x29351,x29352)+~P41(x29351,x29353,x29354)
% 28.25/28.14 [2936]P41(x29363,x29362,x29364)+~E(x29361,x29362)+~P41(x29363,x29361,x29364)
% 28.25/28.14 [2937]P41(x29373,x29374,x29372)+~E(x29371,x29372)+~P41(x29373,x29374,x29371)
% 28.25/28.14 [2938]P15(x29382,x29383,x29384)+~E(x29381,x29382)+~P15(x29381,x29383,x29384)
% 28.25/28.14 [2939]P15(x29393,x29392,x29394)+~E(x29391,x29392)+~P15(x29393,x29391,x29394)
% 28.25/28.14 [2940]P15(x29403,x29404,x29402)+~E(x29401,x29402)+~P15(x29403,x29404,x29401)
% 28.25/28.14 [2941]~P107(x29411)+P107(x29412)+~E(x29411,x29412)
% 28.25/28.14 [2942]~P76(x29421)+P76(x29422)+~E(x29421,x29422)
% 28.25/28.14 [2943]P12(x29432,x29433,x29434,x29435)+~E(x29431,x29432)+~P12(x29431,x29433,x29434,x29435)
% 28.25/28.14 [2944]P12(x29443,x29442,x29444,x29445)+~E(x29441,x29442)+~P12(x29443,x29441,x29444,x29445)
% 28.25/28.14 [2945]P12(x29453,x29454,x29452,x29455)+~E(x29451,x29452)+~P12(x29453,x29454,x29451,x29455)
% 28.25/28.14 [2946]P12(x29463,x29464,x29465,x29462)+~E(x29461,x29462)+~P12(x29463,x29464,x29465,x29461)
% 28.25/28.14 [2947]~P108(x29471)+P108(x29472)+~E(x29471,x29472)
% 28.25/28.14 [2948]~P99(x29481)+P99(x29482)+~E(x29481,x29482)
% 28.25/28.14 [2949]~P100(x29491)+P100(x29492)+~E(x29491,x29492)
% 28.25/28.14 [2950]~P103(x29501)+P103(x29502)+~E(x29501,x29502)
% 28.25/28.14 [2951]~P115(x29511)+P115(x29512)+~E(x29511,x29512)
% 28.25/28.14 [2952]~P106(x29521)+P106(x29522)+~E(x29521,x29522)
% 28.25/28.14 [2953]P32(x29532,x29533,x29534)+~E(x29531,x29532)+~P32(x29531,x29533,x29534)
% 28.25/28.14 [2954]P32(x29543,x29542,x29544)+~E(x29541,x29542)+~P32(x29543,x29541,x29544)
% 28.25/28.14 [2955]P32(x29553,x29554,x29552)+~E(x29551,x29552)+~P32(x29553,x29554,x29551)
% 28.25/28.14 [2956]P14(x29562,x29563)+~E(x29561,x29562)+~P14(x29561,x29563)
% 28.25/28.14 [2957]P14(x29573,x29572)+~E(x29571,x29572)+~P14(x29573,x29571)
% 28.25/28.14 [2958]~P109(x29581)+P109(x29582)+~E(x29581,x29582)
% 28.25/28.14 [2959]~P65(x29591)+P65(x29592)+~E(x29591,x29592)
% 28.25/28.14 [2960]~P104(x29601)+P104(x29602)+~E(x29601,x29602)
% 28.25/28.14 [2961]~P70(x29611)+P70(x29612)+~E(x29611,x29612)
% 28.25/28.14 [2962]~P83(x29621)+P83(x29622)+~E(x29621,x29622)
% 28.25/28.14 [2963]P35(x29632,x29633,x29634,x29635,x29636)+~E(x29631,x29632)+~P35(x29631,x29633,x29634,x29635,x29636)
% 28.25/28.14 [2964]P35(x29643,x29642,x29644,x29645,x29646)+~E(x29641,x29642)+~P35(x29643,x29641,x29644,x29645,x29646)
% 28.25/28.14 [2965]P35(x29653,x29654,x29652,x29655,x29656)+~E(x29651,x29652)+~P35(x29653,x29654,x29651,x29655,x29656)
% 28.25/28.14 [2966]P35(x29663,x29664,x29665,x29662,x29666)+~E(x29661,x29662)+~P35(x29663,x29664,x29665,x29661,x29666)
% 28.25/28.14 [2967]P35(x29673,x29674,x29675,x29676,x29672)+~E(x29671,x29672)+~P35(x29673,x29674,x29675,x29676,x29671)
% 28.25/28.14 [2968]P62(x29682,x29683)+~E(x29681,x29682)+~P62(x29681,x29683)
% 28.25/28.14 [2969]P62(x29693,x29692)+~E(x29691,x29692)+~P62(x29693,x29691)
% 28.25/28.14 [2970]P38(x29702,x29703)+~E(x29701,x29702)+~P38(x29701,x29703)
% 28.25/28.14 [2971]P38(x29713,x29712)+~E(x29711,x29712)+~P38(x29713,x29711)
% 28.25/28.14 [2972]~P73(x29721)+P73(x29722)+~E(x29721,x29722)
% 28.25/28.14 [2973]P11(x29732,x29733,x29734,x29735,x29736)+~E(x29731,x29732)+~P11(x29731,x29733,x29734,x29735,x29736)
% 28.25/28.14 [2974]P11(x29743,x29742,x29744,x29745,x29746)+~E(x29741,x29742)+~P11(x29743,x29741,x29744,x29745,x29746)
% 28.25/28.14 [2975]P11(x29753,x29754,x29752,x29755,x29756)+~E(x29751,x29752)+~P11(x29753,x29754,x29751,x29755,x29756)
% 28.25/28.14 [2976]P11(x29763,x29764,x29765,x29762,x29766)+~E(x29761,x29762)+~P11(x29763,x29764,x29765,x29761,x29766)
% 28.25/28.14 [2977]P11(x29773,x29774,x29775,x29776,x29772)+~E(x29771,x29772)+~P11(x29773,x29774,x29775,x29776,x29771)
% 28.25/28.14 [2978]P27(x29782,x29783,x29784,x29785,x29786)+~E(x29781,x29782)+~P27(x29781,x29783,x29784,x29785,x29786)
% 28.25/28.14 [2979]P27(x29793,x29792,x29794,x29795,x29796)+~E(x29791,x29792)+~P27(x29793,x29791,x29794,x29795,x29796)
% 28.25/28.14 [2980]P27(x29803,x29804,x29802,x29805,x29806)+~E(x29801,x29802)+~P27(x29803,x29804,x29801,x29805,x29806)
% 28.25/28.14 [2981]P27(x29813,x29814,x29815,x29812,x29816)+~E(x29811,x29812)+~P27(x29813,x29814,x29815,x29811,x29816)
% 28.25/28.14 [2982]P27(x29823,x29824,x29825,x29826,x29822)+~E(x29821,x29822)+~P27(x29823,x29824,x29825,x29826,x29821)
% 28.25/28.14 [2983]~P116(x29831)+P116(x29832)+~E(x29831,x29832)
% 28.25/28.14 [2984]~P117(x29841)+P117(x29842)+~E(x29841,x29842)
% 28.25/28.14 [2985]~P71(x29851)+P71(x29852)+~E(x29851,x29852)
% 28.25/28.14 [2986]~P93(x29861)+P93(x29862)+~E(x29861,x29862)
% 28.25/28.14 [2987]~P126(x29871)+P126(x29872)+~E(x29871,x29872)
% 28.25/28.14 [2988]~P101(x29881)+P101(x29882)+~E(x29881,x29882)
% 28.25/28.14 [2989]P33(x29892,x29893,x29894,x29895)+~E(x29891,x29892)+~P33(x29891,x29893,x29894,x29895)
% 28.25/28.14 [2990]P33(x29903,x29902,x29904,x29905)+~E(x29901,x29902)+~P33(x29903,x29901,x29904,x29905)
% 28.25/28.14 [2991]P33(x29913,x29914,x29912,x29915)+~E(x29911,x29912)+~P33(x29913,x29914,x29911,x29915)
% 28.25/28.14 [2992]P33(x29923,x29924,x29925,x29922)+~E(x29921,x29922)+~P33(x29923,x29924,x29925,x29921)
% 28.25/28.14 [2993]P40(x29932,x29933)+~E(x29931,x29932)+~P40(x29931,x29933)
% 28.25/28.14 [2994]P40(x29943,x29942)+~E(x29941,x29942)+~P40(x29943,x29941)
% 28.25/28.14 [2995]~P86(x29951)+P86(x29952)+~E(x29951,x29952)
% 28.25/28.14 [2996]P17(x29962,x29963)+~E(x29961,x29962)+~P17(x29961,x29963)
% 28.25/28.14 [2997]P17(x29973,x29972)+~E(x29971,x29972)+~P17(x29973,x29971)
% 28.25/28.14 [2998]P55(x29982,x29983)+~E(x29981,x29982)+~P55(x29981,x29983)
% 28.25/28.14 [2999]P55(x29993,x29992)+~E(x29991,x29992)+~P55(x29993,x29991)
% 28.25/28.14 [3000]~P79(x30001)+P79(x30002)+~E(x30001,x30002)
% 28.25/28.14 [3001]P56(x30012,x30013)+~E(x30011,x30012)+~P56(x30011,x30013)
% 28.25/28.14 [3002]P56(x30023,x30022)+~E(x30021,x30022)+~P56(x30023,x30021)
% 28.25/28.14 [3003]P57(x30032,x30033,x30034)+~E(x30031,x30032)+~P57(x30031,x30033,x30034)
% 28.25/28.14 [3004]P57(x30043,x30042,x30044)+~E(x30041,x30042)+~P57(x30043,x30041,x30044)
% 28.25/28.14 [3005]P57(x30053,x30054,x30052)+~E(x30051,x30052)+~P57(x30053,x30054,x30051)
% 28.25/28.14 [3006]~P87(x30061)+P87(x30062)+~E(x30061,x30062)
% 28.25/28.14 [3007]~P42(x30071)+P42(x30072)+~E(x30071,x30072)
% 28.25/28.14 [3008]~P145(x30081)+P145(x30082)+~E(x30081,x30082)
% 28.25/28.14 [3009]~P143(x30091)+P143(x30092)+~E(x30091,x30092)
% 28.25/28.14 [3010]~P84(x30101)+P84(x30102)+~E(x30101,x30102)
% 28.25/28.14 [3011]P30(x30112,x30113,x30114)+~E(x30111,x30112)+~P30(x30111,x30113,x30114)
% 28.25/28.14 [3012]P30(x30123,x30122,x30124)+~E(x30121,x30122)+~P30(x30123,x30121,x30124)
% 28.25/28.14 [3013]P30(x30133,x30134,x30132)+~E(x30131,x30132)+~P30(x30133,x30134,x30131)
% 28.25/28.14 [3014]~P129(x30141)+P129(x30142)+~E(x30141,x30142)
% 28.25/28.14 [3015]P19(x30152,x30153,x30154)+~E(x30151,x30152)+~P19(x30151,x30153,x30154)
% 28.25/28.14 [3016]P19(x30163,x30162,x30164)+~E(x30161,x30162)+~P19(x30163,x30161,x30164)
% 28.25/28.14 [3017]P19(x30173,x30174,x30172)+~E(x30171,x30172)+~P19(x30173,x30174,x30171)
% 28.25/28.14 [3018]~P91(x30181)+P91(x30182)+~E(x30181,x30182)
% 28.25/28.14 [3019]~P144(x30191)+P144(x30192)+~E(x30191,x30192)
% 28.25/28.14 [3020]~P118(x30201)+P118(x30202)+~E(x30201,x30202)
% 28.25/28.14 [3021]P52(x30212,x30213,x30214,x30215)+~E(x30211,x30212)+~P52(x30211,x30213,x30214,x30215)
% 28.25/28.14 [3022]P52(x30223,x30222,x30224,x30225)+~E(x30221,x30222)+~P52(x30223,x30221,x30224,x30225)
% 28.25/28.14 [3023]P52(x30233,x30234,x30232,x30235)+~E(x30231,x30232)+~P52(x30233,x30234,x30231,x30235)
% 28.25/28.14 [3024]P52(x30243,x30244,x30245,x30242)+~E(x30241,x30242)+~P52(x30243,x30244,x30245,x30241)
% 28.25/28.14 [3025]~P92(x30251)+P92(x30252)+~E(x30251,x30252)
% 28.25/28.14 [3026]P29(x30262,x30263)+~E(x30261,x30262)+~P29(x30261,x30263)
% 28.25/28.14 [3027]P29(x30273,x30272)+~E(x30271,x30272)+~P29(x30273,x30271)
% 28.25/28.14 [3028]~P89(x30281)+P89(x30282)+~E(x30281,x30282)
% 28.25/28.14 [3029]P64(x30292,x30293)+~E(x30291,x30292)+~P64(x30291,x30293)
% 28.25/28.14 [3030]P64(x30303,x30302)+~E(x30301,x30302)+~P64(x30303,x30301)
% 28.25/28.14 [3031]P44(x30312,x30313,x30314,x30315,x30316,x30317)+~E(x30311,x30312)+~P44(x30311,x30313,x30314,x30315,x30316,x30317)
% 28.25/28.14 [3032]P44(x30323,x30322,x30324,x30325,x30326,x30327)+~E(x30321,x30322)+~P44(x30323,x30321,x30324,x30325,x30326,x30327)
% 28.25/28.14 [3033]P44(x30333,x30334,x30332,x30335,x30336,x30337)+~E(x30331,x30332)+~P44(x30333,x30334,x30331,x30335,x30336,x30337)
% 28.25/28.14 [3034]P44(x30343,x30344,x30345,x30342,x30346,x30347)+~E(x30341,x30342)+~P44(x30343,x30344,x30345,x30341,x30346,x30347)
% 28.25/28.14 [3035]P44(x30353,x30354,x30355,x30356,x30352,x30357)+~E(x30351,x30352)+~P44(x30353,x30354,x30355,x30356,x30351,x30357)
% 28.25/28.14 [3036]P44(x30363,x30364,x30365,x30366,x30367,x30362)+~E(x30361,x30362)+~P44(x30363,x30364,x30365,x30366,x30367,x30361)
% 28.25/28.14 [3037]~P148(x30371)+P148(x30372)+~E(x30371,x30372)
% 28.25/28.14 [3038]~P123(x30381)+P123(x30382)+~E(x30381,x30382)
% 28.25/28.14 [3039]~P80(x30391)+P80(x30392)+~E(x30391,x30392)
% 28.25/28.14 [3040]~P149(x30401)+P149(x30402)+~E(x30401,x30402)
% 28.25/28.14 [3041]P13(x30412,x30413,x30414,x30415,x30416,x30417)+~E(x30411,x30412)+~P13(x30411,x30413,x30414,x30415,x30416,x30417)
% 28.25/28.14 [3042]P13(x30423,x30422,x30424,x30425,x30426,x30427)+~E(x30421,x30422)+~P13(x30423,x30421,x30424,x30425,x30426,x30427)
% 28.25/28.14 [3043]P13(x30433,x30434,x30432,x30435,x30436,x30437)+~E(x30431,x30432)+~P13(x30433,x30434,x30431,x30435,x30436,x30437)
% 28.25/28.14 [3044]P13(x30443,x30444,x30445,x30442,x30446,x30447)+~E(x30441,x30442)+~P13(x30443,x30444,x30445,x30441,x30446,x30447)
% 28.25/28.14 [3045]P13(x30453,x30454,x30455,x30456,x30452,x30457)+~E(x30451,x30452)+~P13(x30453,x30454,x30455,x30456,x30451,x30457)
% 28.25/28.14 [3046]P13(x30463,x30464,x30465,x30466,x30467,x30462)+~E(x30461,x30462)+~P13(x30463,x30464,x30465,x30466,x30467,x30461)
% 28.25/28.14 [3047]~P81(x30471)+P81(x30472)+~E(x30471,x30472)
% 28.25/28.14 [3048]P9(x30482,x30483,x30484)+~E(x30481,x30482)+~P9(x30481,x30483,x30484)
% 28.25/28.14 [3049]P9(x30493,x30492,x30494)+~E(x30491,x30492)+~P9(x30493,x30491,x30494)
% 28.25/28.14 [3050]P9(x30503,x30504,x30502)+~E(x30501,x30502)+~P9(x30503,x30504,x30501)
% 28.25/28.14 [3051]P39(x30512,x30513)+~E(x30511,x30512)+~P39(x30511,x30513)
% 28.25/28.14 [3052]P39(x30523,x30522)+~E(x30521,x30522)+~P39(x30523,x30521)
% 28.25/28.14 [3053]~P77(x30531)+P77(x30532)+~E(x30531,x30532)
% 28.25/28.14 [3054]~P66(x30541)+P66(x30542)+~E(x30541,x30542)
% 28.25/28.14 [3055]P54(x30552,x30553)+~E(x30551,x30552)+~P54(x30551,x30553)
% 28.25/28.14 [3056]P54(x30563,x30562)+~E(x30561,x30562)+~P54(x30563,x30561)
% 28.25/28.14 [3057]~P139(x30571)+P139(x30572)+~E(x30571,x30572)
% 28.25/28.14 [3058]P49(x30582,x30583,x30584)+~E(x30581,x30582)+~P49(x30581,x30583,x30584)
% 28.25/28.14 [3059]P49(x30593,x30592,x30594)+~E(x30591,x30592)+~P49(x30593,x30591,x30594)
% 28.25/28.14 [3060]P49(x30603,x30604,x30602)+~E(x30601,x30602)+~P49(x30603,x30604,x30601)
% 28.25/28.14 [3061]~P119(x30611)+P119(x30612)+~E(x30611,x30612)
% 28.25/28.14 [3062]~P124(x30621)+P124(x30622)+~E(x30621,x30622)
% 28.25/28.14 [3063]P63(x30632,x30633,x30634,x30635)+~E(x30631,x30632)+~P63(x30631,x30633,x30634,x30635)
% 28.25/28.14 [3064]P63(x30643,x30642,x30644,x30645)+~E(x30641,x30642)+~P63(x30643,x30641,x30644,x30645)
% 28.25/28.14 [3065]P63(x30653,x30654,x30652,x30655)+~E(x30651,x30652)+~P63(x30653,x30654,x30651,x30655)
% 28.25/28.14 [3066]P63(x30663,x30664,x30665,x30662)+~E(x30661,x30662)+~P63(x30663,x30664,x30665,x30661)
% 28.25/28.14 [3067]P20(x30672,x30673,x30674)+~E(x30671,x30672)+~P20(x30671,x30673,x30674)
% 28.25/28.14 [3068]P20(x30683,x30682,x30684)+~E(x30681,x30682)+~P20(x30683,x30681,x30684)
% 28.25/28.14 [3069]P20(x30693,x30694,x30692)+~E(x30691,x30692)+~P20(x30693,x30694,x30691)
% 28.25/28.14 [3070]~P146(x30701)+P146(x30702)+~E(x30701,x30702)
% 28.25/28.14 [3071]~P46(x30711)+P46(x30712)+~E(x30711,x30712)
% 28.25/28.14 [3072]~P132(x30721)+P132(x30722)+~E(x30721,x30722)
% 28.25/28.14 [3073]~P122(x30731)+P122(x30732)+~E(x30731,x30732)
% 28.25/28.14 [3074]~P111(x30741)+P111(x30742)+~E(x30741,x30742)
% 28.25/28.14 [3075]~P138(x30751)+P138(x30752)+~E(x30751,x30752)
% 28.25/28.14 [3076]P8(x30762,x30763)+~E(x30761,x30762)+~P8(x30761,x30763)
% 28.25/28.14 [3077]P8(x30773,x30772)+~E(x30771,x30772)+~P8(x30773,x30771)
% 28.25/28.14 [3078]P50(x30782,x30783)+~E(x30781,x30782)+~P50(x30781,x30783)
% 28.25/28.14 [3079]P50(x30793,x30792)+~E(x30791,x30792)+~P50(x30793,x30791)
% 28.25/28.14 [3080]~P135(x30801)+P135(x30802)+~E(x30801,x30802)
% 28.25/28.14 [3081]P18(x30812,x30813,x30814)+~E(x30811,x30812)+~P18(x30811,x30813,x30814)
% 28.25/28.14 [3082]P18(x30823,x30822,x30824)+~E(x30821,x30822)+~P18(x30823,x30821,x30824)
% 28.25/28.14 [3083]P18(x30833,x30834,x30832)+~E(x30831,x30832)+~P18(x30833,x30834,x30831)
% 28.25/28.14 [3084]~P110(x30841)+P110(x30842)+~E(x30841,x30842)
% 28.25/28.14 [3085]~P150(x30851)+P150(x30852)+~E(x30851,x30852)
% 28.25/28.14 [3086]~P7(x30861)+P7(x30862)+~E(x30861,x30862)
% 28.25/28.14 [3087]~P97(x30871)+P97(x30872)+~E(x30871,x30872)
% 28.25/28.14 [3088]P34(x30882,x30883,x30884)+~E(x30881,x30882)+~P34(x30881,x30883,x30884)
% 28.25/28.14 [3089]P34(x30893,x30892,x30894)+~E(x30891,x30892)+~P34(x30893,x30891,x30894)
% 28.25/28.14 [3090]P34(x30903,x30904,x30902)+~E(x30901,x30902)+~P34(x30903,x30904,x30901)
% 28.25/28.14 [3091]P36(x30912,x30913,x30914)+~E(x30911,x30912)+~P36(x30911,x30913,x30914)
% 28.25/28.14 [3092]P36(x30923,x30922,x30924)+~E(x30921,x30922)+~P36(x30923,x30921,x30924)
% 28.25/28.14 [3093]P36(x30933,x30934,x30932)+~E(x30931,x30932)+~P36(x30933,x30934,x30931)
% 28.25/28.14 [3094]~P88(x30941)+P88(x30942)+~E(x30941,x30942)
% 28.25/28.14 [3095]P31(x30952,x30953,x30954)+~E(x30951,x30952)+~P31(x30951,x30953,x30954)
% 28.25/28.14 [3096]P31(x30963,x30962,x30964)+~E(x30961,x30962)+~P31(x30963,x30961,x30964)
% 28.25/28.14 [3097]P31(x30973,x30974,x30972)+~E(x30971,x30972)+~P31(x30973,x30974,x30971)
% 28.25/28.14 [3098]P22(x30982,x30983,x30984,x30985)+~E(x30981,x30982)+~P22(x30981,x30983,x30984,x30985)
% 28.25/28.14 [3099]P22(x30993,x30992,x30994,x30995)+~E(x30991,x30992)+~P22(x30993,x30991,x30994,x30995)
% 28.25/28.14 [3100]P22(x31003,x31004,x31002,x31005)+~E(x31001,x31002)+~P22(x31003,x31004,x31001,x31005)
% 28.25/28.14 [3101]P22(x31013,x31014,x31015,x31012)+~E(x31011,x31012)+~P22(x31013,x31014,x31015,x31011)
% 28.25/28.14 [3102]~P142(x31021)+P142(x31022)+~E(x31021,x31022)
% 28.25/28.14 [3103]~P133(x31031)+P133(x31032)+~E(x31031,x31032)
% 28.25/28.14 [3104]~P98(x31041)+P98(x31042)+~E(x31041,x31042)
% 28.25/28.14 [3105]P60(x31052,x31053,x31054)+~E(x31051,x31052)+~P60(x31051,x31053,x31054)
% 28.25/28.14 [3106]P60(x31063,x31062,x31064)+~E(x31061,x31062)+~P60(x31063,x31061,x31064)
% 28.25/28.14 [3107]P60(x31073,x31074,x31072)+~E(x31071,x31072)+~P60(x31073,x31074,x31071)
% 28.25/28.14 [3108]~P147(x31081)+P147(x31082)+~E(x31081,x31082)
% 28.25/28.14 [3109]P61(x31092,x31093,x31094,x31095,x31096)+~E(x31091,x31092)+~P61(x31091,x31093,x31094,x31095,x31096)
% 28.25/28.14 [3110]P61(x31103,x31102,x31104,x31105,x31106)+~E(x31101,x31102)+~P61(x31103,x31101,x31104,x31105,x31106)
% 28.25/28.14 [3111]P61(x31113,x31114,x31112,x31115,x31116)+~E(x31111,x31112)+~P61(x31113,x31114,x31111,x31115,x31116)
% 28.25/28.14 [3112]P61(x31123,x31124,x31125,x31122,x31126)+~E(x31121,x31122)+~P61(x31123,x31124,x31125,x31121,x31126)
% 28.25/28.14 [3113]P61(x31133,x31134,x31135,x31136,x31132)+~E(x31131,x31132)+~P61(x31133,x31134,x31135,x31136,x31131)
% 28.25/28.14 [3114]~P82(x31141)+P82(x31142)+~E(x31141,x31142)
% 28.25/28.14 [3115]P51(x31152,x31153,x31154)+~E(x31151,x31152)+~P51(x31151,x31153,x31154)
% 28.25/28.14 [3116]P51(x31163,x31162,x31164)+~E(x31161,x31162)+~P51(x31163,x31161,x31164)
% 28.25/28.14 [3117]P51(x31173,x31174,x31172)+~E(x31171,x31172)+~P51(x31173,x31174,x31171)
% 28.25/28.14 [3118]~P105(x31181)+P105(x31182)+~E(x31181,x31182)
% 28.25/28.14 [3119]~P134(x31191)+P134(x31192)+~E(x31191,x31192)
% 28.25/28.14 [3120]P23(x31202,x31203,x31204,x31205,x31206)+~E(x31201,x31202)+~P23(x31201,x31203,x31204,x31205,x31206)
% 28.25/28.14 [3121]P23(x31213,x31212,x31214,x31215,x31216)+~E(x31211,x31212)+~P23(x31213,x31211,x31214,x31215,x31216)
% 28.25/28.14 [3122]P23(x31223,x31224,x31222,x31225,x31226)+~E(x31221,x31222)+~P23(x31223,x31224,x31221,x31225,x31226)
% 28.25/28.14 [3123]P23(x31233,x31234,x31235,x31232,x31236)+~E(x31231,x31232)+~P23(x31233,x31234,x31235,x31231,x31236)
% 28.25/28.14 [3124]P23(x31243,x31244,x31245,x31246,x31242)+~E(x31241,x31242)+~P23(x31243,x31244,x31245,x31246,x31241)
% 28.25/28.14 [3125]P25(x31252,x31253,x31254,x31255,x31256,x31257)+~E(x31251,x31252)+~P25(x31251,x31253,x31254,x31255,x31256,x31257)
% 28.25/28.14 [3126]P25(x31263,x31262,x31264,x31265,x31266,x31267)+~E(x31261,x31262)+~P25(x31263,x31261,x31264,x31265,x31266,x31267)
% 28.25/28.14 [3127]P25(x31273,x31274,x31272,x31275,x31276,x31277)+~E(x31271,x31272)+~P25(x31273,x31274,x31271,x31275,x31276,x31277)
% 28.25/28.14 [3128]P25(x31283,x31284,x31285,x31282,x31286,x31287)+~E(x31281,x31282)+~P25(x31283,x31284,x31285,x31281,x31286,x31287)
% 28.25/28.14 [3129]P25(x31293,x31294,x31295,x31296,x31292,x31297)+~E(x31291,x31292)+~P25(x31293,x31294,x31295,x31296,x31291,x31297)
% 28.25/28.14 [3130]P25(x31303,x31304,x31305,x31306,x31307,x31302)+~E(x31301,x31302)+~P25(x31303,x31304,x31305,x31306,x31307,x31301)
% 28.25/28.14 [3131]P43(x31312,x31313,x31314,x31315)+~E(x31311,x31312)+~P43(x31311,x31313,x31314,x31315)
% 28.25/28.14 [3132]P43(x31323,x31322,x31324,x31325)+~E(x31321,x31322)+~P43(x31323,x31321,x31324,x31325)
% 28.25/28.14 [3133]P43(x31333,x31334,x31332,x31335)+~E(x31331,x31332)+~P43(x31333,x31334,x31331,x31335)
% 28.25/28.14 [3134]P43(x31343,x31344,x31345,x31342)+~E(x31341,x31342)+~P43(x31343,x31344,x31345,x31341)
% 28.25/28.14 [3135]P45(x31352,x31353)+~E(x31351,x31352)+~P45(x31351,x31353)
% 28.25/28.14 [3136]P45(x31363,x31362)+~E(x31361,x31362)+~P45(x31363,x31361)
% 28.25/28.14 [3137]P16(x31372,x31373,x31374)+~E(x31371,x31372)+~P16(x31371,x31373,x31374)
% 28.25/28.14 [3138]P16(x31383,x31382,x31384)+~E(x31381,x31382)+~P16(x31383,x31381,x31384)
% 28.25/28.14 [3139]P16(x31393,x31394,x31392)+~E(x31391,x31392)+~P16(x31393,x31394,x31391)
% 28.25/28.14 [3140]~P94(x31401)+P94(x31402)+~E(x31401,x31402)
% 28.25/28.14 [3141]P24(x31412,x31413,x31414,x31415,x31416,x31417)+~E(x31411,x31412)+~P24(x31411,x31413,x31414,x31415,x31416,x31417)
% 28.25/28.14 [3142]P24(x31423,x31422,x31424,x31425,x31426,x31427)+~E(x31421,x31422)+~P24(x31423,x31421,x31424,x31425,x31426,x31427)
% 28.25/28.14 [3143]P24(x31433,x31434,x31432,x31435,x31436,x31437)+~E(x31431,x31432)+~P24(x31433,x31434,x31431,x31435,x31436,x31437)
% 28.25/28.14 [3144]P24(x31443,x31444,x31445,x31442,x31446,x31447)+~E(x31441,x31442)+~P24(x31443,x31444,x31445,x31441,x31446,x31447)
% 28.25/28.14 [3145]P24(x31453,x31454,x31455,x31456,x31452,x31457)+~E(x31451,x31452)+~P24(x31453,x31454,x31455,x31456,x31451,x31457)
% 28.25/28.14 [3146]P24(x31463,x31464,x31465,x31466,x31467,x31462)+~E(x31461,x31462)+~P24(x31463,x31464,x31465,x31466,x31467,x31461)
% 28.25/28.14 [3147]P28(x31472,x31473)+~E(x31471,x31472)+~P28(x31471,x31473)
% 28.25/28.14 [3148]P28(x31483,x31482)+~E(x31481,x31482)+~P28(x31483,x31481)
% 28.25/28.14 [3149]P53(x31492,x31493,x31494,x31495,x31496,x31497)+~E(x31491,x31492)+~P53(x31491,x31493,x31494,x31495,x31496,x31497)
% 28.25/28.14 [3150]P53(x31503,x31502,x31504,x31505,x31506,x31507)+~E(x31501,x31502)+~P53(x31503,x31501,x31504,x31505,x31506,x31507)
% 28.25/28.14 [3151]P53(x31513,x31514,x31512,x31515,x31516,x31517)+~E(x31511,x31512)+~P53(x31513,x31514,x31511,x31515,x31516,x31517)
% 28.25/28.14 [3152]P53(x31523,x31524,x31525,x31522,x31526,x31527)+~E(x31521,x31522)+~P53(x31523,x31524,x31525,x31521,x31526,x31527)
% 28.25/28.14 [3153]P53(x31533,x31534,x31535,x31536,x31532,x31537)+~E(x31531,x31532)+~P53(x31533,x31534,x31535,x31536,x31531,x31537)
% 28.25/28.14 [3154]P53(x31543,x31544,x31545,x31546,x31547,x31542)+~E(x31541,x31542)+~P53(x31543,x31544,x31545,x31546,x31547,x31541)
% 28.25/28.14 [3155]~P85(x31551)+P85(x31552)+~E(x31551,x31552)
% 28.25/28.14 [3156]~P140(x31561)+P140(x31562)+~E(x31561,x31562)
% 28.25/28.14 [3157]~P120(x31571)+P120(x31572)+~E(x31571,x31572)
% 28.25/28.14 [3158]~P125(x31581)+P125(x31582)+~E(x31581,x31582)
% 28.25/28.14 [3159]~P128(x31591)+P128(x31592)+~E(x31591,x31592)
% 28.25/28.14 [3160]~P131(x31601)+P131(x31602)+~E(x31601,x31602)
% 28.25/28.14 [3161]~P127(x31611)+P127(x31612)+~E(x31611,x31612)
% 28.25/28.14 [3162]~P112(x31621)+P112(x31622)+~E(x31621,x31622)
% 28.25/28.14 [3163]~P95(x31631)+P95(x31632)+~E(x31631,x31632)
% 28.25/28.14 [3164]P10(x31642,x31643,x31644)+~E(x31641,x31642)+~P10(x31641,x31643,x31644)
% 28.25/28.14 [3165]P10(x31653,x31652,x31654)+~E(x31651,x31652)+~P10(x31653,x31651,x31654)
% 28.25/28.14 [3166]P10(x31663,x31664,x31662)+~E(x31661,x31662)+~P10(x31663,x31664,x31661)
% 28.25/28.14 [3167]~P136(x31671)+P136(x31672)+~E(x31671,x31672)
% 28.25/28.14 [3168]P47(x31682,x31683)+~E(x31681,x31682)+~P47(x31681,x31683)
% 28.25/28.14 [3169]P47(x31693,x31692)+~E(x31691,x31692)+~P47(x31693,x31691)
% 28.25/28.14 [3170]~P37(x31701)+P37(x31702)+~E(x31701,x31702)
% 28.25/28.14 [3171]P58(x31712,x31713)+~E(x31711,x31712)+~P58(x31711,x31713)
% 28.25/28.14 [3172]P58(x31723,x31722)+~E(x31721,x31722)+~P58(x31723,x31721)
% 28.25/28.14 [3173]P48(x31732,x31733,x31734)+~E(x31731,x31732)+~P48(x31731,x31733,x31734)
% 28.25/28.14 [3174]P48(x31743,x31742,x31744)+~E(x31741,x31742)+~P48(x31743,x31741,x31744)
% 28.25/28.14 [3175]P48(x31753,x31754,x31752)+~E(x31751,x31752)+~P48(x31753,x31754,x31751)
% 28.25/28.14 [3176]~P137(x31761)+P137(x31762)+~E(x31761,x31762)
% 28.25/28.14
% 28.25/28.14 %-------------------------------------------
% 28.25/28.15 cnf(10537,plain,
% 28.25/28.15 ($false),
% 28.25/28.15 inference(scs_inference,[],[3464,4730,3466,5700]),
% 28.25/28.15 ['proof']).
% 28.25/28.15 % SZS output end Proof
% 28.25/28.15 % Total time :22.600000s
%------------------------------------------------------------------------------