TSTP Solution File: SWW312+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW312+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 : n005.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 00:13:38 EDT 2023
% Result : Theorem 59.73s 59.64s
% Output : CNFRefutation 59.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SWW312+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.15 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 20:32:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.58 start to proof:theBenchmark
% 59.45/59.48 %-------------------------------------------
% 59.45/59.48 % File :CSE---1.6
% 59.45/59.48 % Problem :theBenchmark
% 59.45/59.48 % Transform :cnf
% 59.45/59.48 % Format :tptp:raw
% 59.45/59.48 % Command :java -jar mcs_scs.jar %d %s
% 59.45/59.48
% 59.45/59.48 % Result :Theorem 55.820000s
% 59.45/59.48 % Output :CNFRefutation 55.820000s
% 59.45/59.48 %-------------------------------------------
% 59.45/59.49 %------------------------------------------------------------------------------
% 59.45/59.49 % File : SWW312+1 : TPTP v8.1.2. Released v5.2.0.
% 59.45/59.49 % Domain : Software Verification
% 59.45/59.49 % Problem : Hoare's Logic with Procedures 434967, 5000 axioms selected
% 59.45/59.49 % Version : Especial.
% 59.45/59.49 % English :
% 59.45/59.49
% 59.45/59.49 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 59.45/59.49 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 59.45/59.49 % Source : [Bla11]
% 59.45/59.49 % Names : hoare_434967.5000.p [Bla11]
% 59.45/59.49
% 59.45/59.49 % Status : ContradictoryAxioms
% 59.45/59.49 % Rating : 0.44 v8.1.0, 0.50 v7.5.0, 0.53 v7.4.0, 0.63 v7.3.0, 0.55 v7.1.0, 0.65 v7.0.0, 0.70 v6.4.0, 0.65 v6.3.0, 0.58 v6.2.0, 0.68 v6.1.0, 0.73 v6.0.0, 0.65 v5.5.0, 0.74 v5.4.0, 0.71 v5.3.0, 0.78 v5.2.0
% 59.45/59.49 % Syntax : Number of formulae : 5245 (1716 unt; 0 def)
% 59.45/59.49 % Number of atoms : 12696 (4564 equ)
% 59.45/59.49 % Maximal formula atoms : 13 ( 2 avg)
% 59.45/59.49 % Number of connectives : 8424 ( 973 ~; 150 |; 716 &)
% 59.45/59.49 % ( 885 <=>;5700 =>; 0 <=; 0 <~>)
% 59.45/59.49 % Maximal formula depth : 22 ( 6 avg)
% 59.45/59.49 % Maximal term depth : 19 ( 2 avg)
% 59.45/59.49 % Number of predicates : 146 ( 145 usr; 0 prp; 1-6 aty)
% 59.45/59.49 % Number of functors : 395 ( 395 usr; 49 con; 0-7 aty)
% 59.45/59.49 % Number of variables : 16701 (16558 !; 143 ?)
% 59.45/59.49 % SPC : FOF_CAX_RFO_SEQ
% 59.45/59.49
% 59.45/59.49 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 59.45/59.49 % 2011-03-01 11:41:24
% 59.45/59.49 %------------------------------------------------------------------------------
% 59.45/59.49 %----Relevant facts (4986)
% 59.45/59.49 fof(fact_ext,axiom,
% 59.45/59.49 ! [V_g_2,V_f_2] :
% 59.45/59.49 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 59.45/59.49 => V_f_2 = V_g_2 ) ).
% 59.45/59.49
% 59.45/59.49 fof(fact_empty,axiom,
% 59.45/59.49 ! [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))) ).
% 59.45/59.49
% 59.45/59.49 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 59.45/59.49 ! [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))) ).
% 59.45/59.49
% 59.45/59.49 fof(fact_asm,axiom,
% 59.45/59.49 ! [V_G_2,V_tsa_2,T_b] :
% 59.45/59.49 ( 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))
% 59.45/59.49 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ).
% 59.45/59.49
% 59.45/59.49 fof(fact_weaken,axiom,
% 59.45/59.49 ! [V_tsa_2,V_ts_H_2,V_G_2,T_b] :
% 59.45/59.49 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2)
% 59.45/59.49 => ( 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))
% 59.45/59.49 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ) ).
% 59.45/59.49
% 59.45/59.49 fof(fact_cut,axiom,
% 59.45/59.49 ! [V_G_2,V_tsa_2,V_G_Ha_2,T_b] :
% 59.45/59.49 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
% 59.45/59.49 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2)
% 59.45/59.49 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ) ).
% 59.45/59.49
% 59.45/59.49 fof(fact_hoare__derivs_Oinsert,axiom,
% 59.45/59.49 ! [V_tsa_2,V_t_2,V_G_2,T_b] :
% 59.45/59.49 ( 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))))
% 59.45/59.49 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
% 59.45/59.49 => 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)) ) ) ).
% 59.45/59.49
% 59.45/59.49 fof(fact_empty__subsetI,axiom,
% 59.45/59.49 ! [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)) ).
% 59.45/59.49
% 59.45/59.49 fof(fact_subset__singletonD,axiom,
% 59.45/59.49 ! [V_x_2,V_A_2,T_b] :
% 59.45/59.49 ( 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)))))
% 59.45/59.49 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.45/59.49 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 59.45/59.49
% 59.45/59.49 fof(fact_equalityI,axiom,
% 59.45/59.49 ! [V_B_2,V_A_2,T_b] :
% 59.45/59.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 59.45/59.49 => V_A_2 = V_B_2 ) ) ).
% 59.45/59.49
% 59.45/59.49 fof(fact_order__refl,axiom,
% 59.45/59.49 ! [V_x,T_a] :
% 59.45/59.49 ( class_Orderings_Opreorder(T_a)
% 59.45/59.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 59.45/59.49
% 59.45/59.49 fof(fact_bot__fun__def,axiom,
% 59.45/59.49 ! [V_x_2,T_c,T_b] :
% 59.45/59.50 ( class_Orderings_Obot(T_b)
% 59.45/59.50 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_subset__insertI,axiom,
% 59.45/59.50 ! [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))) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_subset__insertI2,axiom,
% 59.45/59.50 ! [V_b_2,V_B_2,V_A_2,T_b] :
% 59.45/59.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.50 => 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))) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_insert__mono,axiom,
% 59.45/59.50 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 59.45/59.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 59.45/59.50 => 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))) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_subset__empty,axiom,
% 59.45/59.50 ! [V_A_2,T_b] :
% 59.45/59.50 ( 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))))
% 59.45/59.50 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_empty__not__insert,axiom,
% 59.45/59.50 ! [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) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_insert__not__empty,axiom,
% 59.45/59.50 ! [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)) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_doubleton__eq__iff,axiom,
% 59.45/59.50 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 59.45/59.50 ( 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))))
% 59.45/59.50 <=> ( ( V_a_2 = V_c_2
% 59.45/59.50 & V_b_2 = V_d_2 )
% 59.45/59.50 | ( V_a_2 = V_d_2
% 59.45/59.50 & V_b_2 = V_c_2 ) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_linorder__le__cases,axiom,
% 59.45/59.50 ! [V_y,V_x,T_a] :
% 59.45/59.50 ( class_Orderings_Olinorder(T_a)
% 59.45/59.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 59.45/59.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_xt1_I6_J,axiom,
% 59.45/59.50 ! [V_z,V_x,V_y,T_a] :
% 59.45/59.50 ( class_Orderings_Oorder(T_a)
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 59.45/59.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_xt1_I5_J,axiom,
% 59.45/59.50 ! [V_x,V_y,T_a] :
% 59.45/59.50 ( class_Orderings_Oorder(T_a)
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 59.45/59.50 => V_x = V_y ) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_order__trans,axiom,
% 59.45/59.50 ! [V_z,V_y,V_x,T_a] :
% 59.45/59.50 ( class_Orderings_Opreorder(T_a)
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 59.45/59.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_order__antisym,axiom,
% 59.45/59.50 ! [V_y,V_x,T_a] :
% 59.45/59.50 ( class_Orderings_Oorder(T_a)
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 59.45/59.50 => V_x = V_y ) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_xt1_I4_J,axiom,
% 59.45/59.50 ! [V_c,V_a,V_b,T_a] :
% 59.45/59.50 ( class_Orderings_Oorder(T_a)
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 59.45/59.50 => ( V_b = V_c
% 59.45/59.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_ord__le__eq__trans,axiom,
% 59.45/59.50 ! [V_c,V_b,V_a,T_a] :
% 59.45/59.50 ( class_Orderings_Oord(T_a)
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.45/59.50 => ( V_b = V_c
% 59.45/59.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_xt1_I3_J,axiom,
% 59.45/59.50 ! [V_c,V_b,V_a,T_a] :
% 59.45/59.50 ( class_Orderings_Oorder(T_a)
% 59.45/59.50 => ( V_a = V_b
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 59.45/59.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_ord__eq__le__trans,axiom,
% 59.45/59.50 ! [V_c,V_b,V_a,T_a] :
% 59.45/59.50 ( class_Orderings_Oord(T_a)
% 59.45/59.50 => ( V_a = V_b
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 59.45/59.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_order__antisym__conv,axiom,
% 59.45/59.50 ! [V_x_2,V_y_2,T_b] :
% 59.45/59.50 ( class_Orderings_Oorder(T_b)
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 59.45/59.50 <=> V_x_2 = V_y_2 ) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_order__eq__refl,axiom,
% 59.45/59.50 ! [V_y,V_x,T_a] :
% 59.45/59.50 ( class_Orderings_Opreorder(T_a)
% 59.45/59.50 => ( V_x = V_y
% 59.45/59.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_order__eq__iff,axiom,
% 59.45/59.50 ! [V_y_2,V_x_2,T_b] :
% 59.45/59.50 ( class_Orderings_Oorder(T_b)
% 59.45/59.50 => ( V_x_2 = V_y_2
% 59.45/59.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 59.45/59.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_linorder__linear,axiom,
% 59.45/59.50 ! [V_y,V_x,T_a] :
% 59.45/59.50 ( class_Orderings_Olinorder(T_a)
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 59.45/59.50 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_insert__code,axiom,
% 59.45/59.50 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 59.45/59.50 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 59.45/59.50 <=> ( V_y_2 = V_x_2
% 59.45/59.50 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_insert__commute,axiom,
% 59.45/59.50 ! [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)) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_insert__absorb2,axiom,
% 59.45/59.50 ! [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) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_equalityE,axiom,
% 59.45/59.50 ! [T_b,V_B_2,V_A_2] :
% 59.45/59.50 ( V_A_2 = V_B_2
% 59.45/59.50 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.50 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_subset__trans,axiom,
% 59.45/59.50 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 59.45/59.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 59.45/59.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_equalityD2,axiom,
% 59.45/59.50 ! [T_b,V_B_2,V_A_2] :
% 59.45/59.50 ( V_A_2 = V_B_2
% 59.45/59.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_equalityD1,axiom,
% 59.45/59.50 ! [T_b,V_B_2,V_A_2] :
% 59.45/59.50 ( V_A_2 = V_B_2
% 59.45/59.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_set__eq__subset,axiom,
% 59.45/59.50 ! [T_b,V_B_2,V_A_2] :
% 59.45/59.50 ( V_A_2 = V_B_2
% 59.45/59.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_subset__refl,axiom,
% 59.45/59.50 ! [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)) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_bot__least,axiom,
% 59.45/59.50 ! [V_x,T_a] :
% 59.45/59.50 ( class_Orderings_Obot(T_a)
% 59.45/59.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_le__funE,axiom,
% 59.45/59.50 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 59.45/59.50 ( class_Orderings_Oord(T_c)
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 59.45/59.50 => 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))) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_le__funD,axiom,
% 59.45/59.50 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 59.45/59.50 ( class_Orderings_Oord(T_c)
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 59.45/59.50 => 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))) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_le__fun__def,axiom,
% 59.45/59.50 ! [V_g_2,V_f_2,T_b,T_c] :
% 59.45/59.50 ( class_Orderings_Oord(T_c)
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 59.45/59.50 <=> ! [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))) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_bot__apply,axiom,
% 59.45/59.50 ! [V_x_2,T_c,T_b] :
% 59.45/59.50 ( class_Orderings_Obot(T_b)
% 59.45/59.50 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_singleton__inject,axiom,
% 59.45/59.50 ! [V_b_2,V_a_2,T_b] :
% 59.45/59.50 ( 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)))
% 59.45/59.50 => V_a_2 = V_b_2 ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_the__elem__eq,axiom,
% 59.45/59.50 ! [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 ).
% 59.45/59.50
% 59.45/59.50 fof(fact_predicate1D,axiom,
% 59.45/59.50 ! [V_x_2,V_Q_2,V_P_2,T_b] :
% 59.45/59.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
% 59.45/59.50 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 59.45/59.50 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_rev__predicate1D,axiom,
% 59.45/59.50 ! [V_Q_2,T_b,V_x_2,V_P_2] :
% 59.45/59.50 ( hBOOL(hAPP(V_P_2,V_x_2))
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
% 59.45/59.50 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_order__fun_I1_J,axiom,
% 59.45/59.50 ! [V_g_2,V_f_2,T_b,T_c] :
% 59.45/59.50 ( ( class_Orderings_Oorder(T_c)
% 59.45/59.50 & class_Enum_Oenum(T_b) )
% 59.45/59.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 59.45/59.50 <=> 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))) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_Least__le,axiom,
% 59.45/59.50 ! [V_k_2,V_P_2,T_b] :
% 59.45/59.50 ( class_Orderings_Owellorder(T_b)
% 59.45/59.50 => ( hBOOL(hAPP(V_P_2,V_k_2))
% 59.45/59.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Orderings_Oord__class_OLeast(T_b,V_P_2)),V_k_2)) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_le__funI,axiom,
% 59.45/59.50 ! [T_b,V_g_2,V_f_2,T_c] :
% 59.45/59.50 ( class_Orderings_Oord(T_c)
% 59.45/59.50 => ( ! [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)))
% 59.45/59.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_strict__mono__less__eq,axiom,
% 59.45/59.50 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 59.45/59.50 ( ( class_Orderings_Oorder(T_c)
% 59.45/59.50 & class_Orderings_Olinorder(T_b) )
% 59.45/59.50 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 59.45/59.50 => ( 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)))
% 59.45/59.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_the__elem__def,axiom,
% 59.45/59.50 ! [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))))) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_Collect__conv__if,axiom,
% 59.45/59.50 ! [T_b,V_a_2,V_P_2] :
% 59.45/59.50 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 59.45/59.50 => 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))) )
% 59.45/59.50 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 59.45/59.50 => 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)) ) ) ).
% 59.45/59.50
% 59.45/59.50 fof(fact_Collect__conv__if2,axiom,
% 59.45/59.50 ! [T_b,V_a_2,V_P_2] :
% 59.45/59.50 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 59.45/59.51 => 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))) )
% 59.45/59.51 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 59.45/59.51 => 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)) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_singleton__conv,axiom,
% 59.45/59.51 ! [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))) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_singleton__conv2,axiom,
% 59.45/59.51 ! [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))) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Collect__def,axiom,
% 59.45/59.51 ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),V_P_2) = V_P_2 ).
% 59.45/59.51
% 59.45/59.51 fof(fact_all__code,axiom,
% 59.45/59.51 ! [V_P_2,T_b] :
% 59.45/59.51 ( class_Enum_Oenum(T_b)
% 59.45/59.51 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 59.45/59.51 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2)) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_enum__all,axiom,
% 59.45/59.51 ! [V_P_2,T_b] :
% 59.45/59.51 ( class_Enum_Oenum(T_b)
% 59.45/59.51 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2))
% 59.45/59.51 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_LeastI__ex,axiom,
% 59.45/59.51 ! [V_P_2,T_b] :
% 59.45/59.51 ( class_Orderings_Owellorder(T_b)
% 59.45/59.51 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 59.45/59.51 => hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_strict__mono__eq,axiom,
% 59.45/59.51 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 59.45/59.51 ( ( class_Orderings_Oorder(T_c)
% 59.45/59.51 & class_Orderings_Olinorder(T_b) )
% 59.45/59.51 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 59.45/59.51 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 59.45/59.51 <=> V_x_2 = V_y_2 ) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_empty__Collect__eq,axiom,
% 59.45/59.51 ! [V_P_2,T_b] :
% 59.45/59.51 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_P_2)
% 59.45/59.51 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Collect__empty__eq,axiom,
% 59.45/59.51 ! [V_P_2,T_b] :
% 59.45/59.51 ( hAPP(c_Set_OCollect(T_b),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.45/59.51 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_LeastI,axiom,
% 59.45/59.51 ! [V_k_2,V_P_2,T_b] :
% 59.45/59.51 ( class_Orderings_Owellorder(T_b)
% 59.45/59.51 => ( hBOOL(hAPP(V_P_2,V_k_2))
% 59.45/59.51 => hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_empty__def,axiom,
% 59.45/59.51 ! [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)) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_insert__Collect,axiom,
% 59.45/59.51 ! [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)) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_enum__the__def,axiom,
% 59.45/59.51 ! [V_P_2,T_b] : c_Enum_Oenum__the(T_b,V_P_2) = c_HOL_OThe(T_b,V_P_2) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_the__eq__trivial,axiom,
% 59.45/59.51 ! [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 ).
% 59.45/59.51
% 59.45/59.51 fof(fact_the__sym__eq__trivial,axiom,
% 59.45/59.51 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Powp__mono,axiom,
% 59.45/59.51 ! [V_B_2,V_A_2,T_b] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.51 => 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))) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Least__equality,axiom,
% 59.45/59.51 ! [V_x_2,V_P_2,T_b] :
% 59.45/59.51 ( class_Orderings_Oorder(T_b)
% 59.45/59.51 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 59.45/59.51 => ( ! [B_y] :
% 59.45/59.51 ( hBOOL(hAPP(V_P_2,B_y))
% 59.45/59.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 59.45/59.51 => c_Orderings_Oord__class_OLeast(T_b,V_P_2) = V_x_2 ) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Collect__mono,axiom,
% 59.45/59.51 ! [T_b,V_Q_2,V_P_2] :
% 59.45/59.51 ( ! [B_x] :
% 59.45/59.51 ( hBOOL(hAPP(V_P_2,B_x))
% 59.45/59.51 => hBOOL(hAPP(V_Q_2,B_x)) )
% 59.45/59.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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))) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_insert__compr,axiom,
% 59.45/59.51 ! [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))) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_insert__compr__raw,axiom,
% 59.45/59.51 ! [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))) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_inv__imagep__def,axiom,
% 59.45/59.51 ! [V_y_2,V_x_2,V_f_2,V_r_2,T_c,T_b] :
% 59.45/59.51 ( c_Predicate_Oinv__imagep(T_b,T_c,V_r_2,V_f_2,V_x_2,V_y_2)
% 59.45/59.51 <=> hBOOL(hAPP(hAPP(V_r_2,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_insert__def,axiom,
% 59.45/59.51 ! [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) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_image__constant__conv,axiom,
% 59.45/59.51 ! [V_c_2,T_c,T_b,V_A_2] :
% 59.45/59.51 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.45/59.51 => 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)) )
% 59.45/59.51 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.45/59.51 => 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))) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_strict__mono__mono,axiom,
% 59.45/59.51 ! [V_f_2,T_b,T_c] :
% 59.45/59.51 ( ( class_Orderings_Oorder(T_c)
% 59.45/59.51 & class_Orderings_Oorder(T_b) )
% 59.45/59.51 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 59.45/59.51 => c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_equalityCE,axiom,
% 59.45/59.51 ! [V_c_2,T_b,V_B_2,V_A_2] :
% 59.45/59.51 ( V_A_2 = V_B_2
% 59.45/59.51 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 59.45/59.51 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) )
% 59.45/59.51 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 59.45/59.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_sup1CI,axiom,
% 59.45/59.51 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 59.45/59.51 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 59.45/59.51 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 59.45/59.51 => 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)) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_sup1E,axiom,
% 59.45/59.51 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 59.45/59.51 ( 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))
% 59.45/59.51 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 59.45/59.51 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_emptyE,axiom,
% 59.45/59.51 ! [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)))) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_insertCI,axiom,
% 59.45/59.51 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 59.45/59.51 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 59.45/59.51 => V_a_2 = V_b_2 )
% 59.45/59.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_insertE,axiom,
% 59.45/59.51 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 59.45/59.51 => ( V_a_2 != V_b_2
% 59.45/59.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_subsetD,axiom,
% 59.45/59.51 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 59.45/59.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_image__eqI,axiom,
% 59.45/59.51 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
% 59.45/59.51 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 59.45/59.51 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 59.45/59.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_UnCI,axiom,
% 59.45/59.51 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 59.45/59.51 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 59.45/59.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
% 59.45/59.51 => 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))) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_UnE,axiom,
% 59.45/59.51 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 59.45/59.51 ( 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)))
% 59.45/59.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 59.45/59.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_CollectI,axiom,
% 59.45/59.51 ! [T_b,V_a_2,V_P_2] :
% 59.45/59.51 ( hBOOL(hAPP(V_P_2,V_a_2))
% 59.45/59.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_sup1I2,axiom,
% 59.45/59.51 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 59.45/59.51 ( hBOOL(hAPP(V_B_2,V_x_2))
% 59.45/59.51 => 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)) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_sup1I1,axiom,
% 59.45/59.51 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 59.45/59.51 ( hBOOL(hAPP(V_A_2,V_x_2))
% 59.45/59.51 => 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)) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_sup__Un__eq,axiom,
% 59.45/59.51 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 59.45/59.51 ( 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))
% 59.45/59.51 <=> 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))) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_eq__mem,axiom,
% 59.45/59.51 ! [V_y_2,V_x_2,T_b] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 59.45/59.51 <=> V_x_2 = V_y_2 ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_rev__image__eqI,axiom,
% 59.45/59.51 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.51 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 59.45/59.51 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_eq__mem__trans,axiom,
% 59.45/59.51 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 59.45/59.51 ( V_a_2 = V_b_2
% 59.45/59.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 59.45/59.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_eqelem__imp__iff,axiom,
% 59.45/59.51 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 59.45/59.51 ( V_x_2 = V_y_2
% 59.45/59.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.51 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_eqset__imp__iff,axiom,
% 59.45/59.51 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 59.45/59.51 ( V_A_2 = V_B_2
% 59.45/59.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.51 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_imageI,axiom,
% 59.45/59.51 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.51 => 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))) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_UnI2,axiom,
% 59.45/59.51 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 59.45/59.51 => 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))) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_UnI1,axiom,
% 59.45/59.51 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 59.45/59.51 => 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))) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_ball__Un,axiom,
% 59.45/59.51 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 59.45/59.51 ( ! [B_x] :
% 59.45/59.51 ( 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)))
% 59.45/59.51 => hBOOL(hAPP(V_P_2,B_x)) )
% 59.45/59.51 <=> ( ! [B_x] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.45/59.51 => hBOOL(hAPP(V_P_2,B_x)) )
% 59.45/59.51 & ! [B_x] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 59.45/59.51 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_bex__Un,axiom,
% 59.45/59.51 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 59.45/59.51 ( ? [B_x] :
% 59.45/59.51 ( 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)))
% 59.45/59.51 & hBOOL(hAPP(V_P_2,B_x)) )
% 59.45/59.51 <=> ( ? [B_x] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.45/59.51 & hBOOL(hAPP(V_P_2,B_x)) )
% 59.45/59.51 | ? [B_x] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 59.45/59.51 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Un__assoc,axiom,
% 59.45/59.51 ! [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)) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Un__iff,axiom,
% 59.45/59.51 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 59.45/59.51 ( 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)))
% 59.45/59.51 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 59.45/59.51 | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_image__Un,axiom,
% 59.45/59.51 ! [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)) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Un__left__commute,axiom,
% 59.45/59.51 ! [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)) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_image__iff,axiom,
% 59.45/59.51 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 59.45/59.51 <=> ? [B_x] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 59.45/59.51 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Un__left__absorb,axiom,
% 59.45/59.51 ! [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) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Un__commute,axiom,
% 59.45/59.51 ! [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) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_mem__def,axiom,
% 59.45/59.51 ! [V_A_2,V_x_2,T_b] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.51 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Un__absorb,axiom,
% 59.45/59.51 ! [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 ).
% 59.45/59.51
% 59.45/59.51 fof(fact_insert__image,axiom,
% 59.45/59.51 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.51 => 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) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_image__image,axiom,
% 59.45/59.51 ! [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) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_mono__Un,axiom,
% 59.45/59.51 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 59.45/59.51 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2)
% 59.45/59.51 => 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)))) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_pred__equals__eq,axiom,
% 59.45/59.51 ! [V_S_2,V_R_2,T_b] :
% 59.45/59.51 ( 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)
% 59.45/59.51 <=> V_R_2 = V_S_2 ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Un__def,axiom,
% 59.45/59.51 ! [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))) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Least__mono,axiom,
% 59.45/59.51 ! [V_S_2,V_f_2,T_b,T_c] :
% 59.45/59.51 ( ( class_Orderings_Oorder(T_c)
% 59.45/59.51 & class_Orderings_Oorder(T_b) )
% 59.45/59.51 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 59.45/59.51 => ( ? [B_x] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 59.45/59.51 & ! [B_xa] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_S_2))
% 59.45/59.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) )
% 59.45/59.51 => 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))) ) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_image__is__empty,axiom,
% 59.45/59.51 ! [V_A_2,V_f_2,T_b,T_c] :
% 59.45/59.51 ( 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))
% 59.45/59.51 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_image__empty,axiom,
% 59.45/59.51 ! [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)) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_empty__is__image,axiom,
% 59.45/59.51 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.45/59.51 ( 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)
% 59.45/59.51 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_image__insert,axiom,
% 59.45/59.51 ! [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)) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_image__mono,axiom,
% 59.45/59.51 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.51 => 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))) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_subset__image__iff,axiom,
% 59.45/59.51 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 59.45/59.51 ( 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)))
% 59.45/59.51 <=> ? [B_AA] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 59.45/59.51 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_image__constant,axiom,
% 59.45/59.51 ! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.51 => 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))) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Un__empty,axiom,
% 59.45/59.51 ! [V_B_2,V_A_2,T_b] :
% 59.45/59.51 ( 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))
% 59.45/59.51 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.45/59.51 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Un__empty__right,axiom,
% 59.45/59.51 ! [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 ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Un__empty__left,axiom,
% 59.45/59.51 ! [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 ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Un__insert__left,axiom,
% 59.45/59.51 ! [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)) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Un__insert__right,axiom,
% 59.45/59.51 ! [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)) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Un__mono,axiom,
% 59.45/59.51 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 59.45/59.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 59.45/59.51 => 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))) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Un__least,axiom,
% 59.45/59.51 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 59.45/59.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 59.45/59.51 => 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)) ) ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Un__absorb2,axiom,
% 59.45/59.51 ! [V_A_2,V_B_2,T_b] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 59.45/59.51 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Un__absorb1,axiom,
% 59.45/59.51 ! [V_B_2,V_A_2,T_b] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.51 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_subset__Un__eq,axiom,
% 59.45/59.51 ! [V_B_2,V_A_2,T_b] :
% 59.45/59.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.51 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Un__upper2,axiom,
% 59.45/59.51 ! [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))) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_Un__upper1,axiom,
% 59.45/59.51 ! [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))) ).
% 59.45/59.51
% 59.45/59.51 fof(fact_in__inv__imagep,axiom,
% 59.45/59.51 ! [V_y_2,V_x_2,V_f_2,V_r_2,T_c,T_b] :
% 59.45/59.51 ( c_Predicate_Oinv__imagep(T_b,T_c,V_r_2,V_f_2,V_x_2,V_y_2)
% 59.45/59.52 <=> hBOOL(hAPP(hAPP(V_r_2,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_equals0D,axiom,
% 59.45/59.52 ! [V_a_2,T_b,V_A_2] :
% 59.45/59.52 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.45/59.52 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_empty__iff,axiom,
% 59.45/59.52 ! [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)))) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_ex__in__conv,axiom,
% 59.45/59.52 ! [V_A_2,T_b] :
% 59.45/59.52 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.45/59.52 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_all__not__in__conv,axiom,
% 59.45/59.52 ! [V_A_2,T_b] :
% 59.45/59.52 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.45/59.52 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_insert__absorb,axiom,
% 59.45/59.52 ! [V_A_2,V_a_2,T_b] :
% 59.45/59.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.45/59.52 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_insertI2,axiom,
% 59.45/59.52 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 59.45/59.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 59.45/59.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_insert__ident,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 59.45/59.52 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.52 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 59.45/59.52 => ( 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)
% 59.45/59.52 <=> V_A_2 = V_B_2 ) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_insert__iff,axiom,
% 59.45/59.52 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 59.45/59.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 59.45/59.52 <=> ( V_a_2 = V_b_2
% 59.45/59.52 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_insertI1,axiom,
% 59.45/59.52 ! [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))) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_set__mp,axiom,
% 59.45/59.52 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 59.45/59.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_set__rev__mp,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 59.45/59.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_in__mono,axiom,
% 59.45/59.52 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 59.45/59.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Collect__disj__eq,axiom,
% 59.45/59.52 ! [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)) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_monoD,axiom,
% 59.45/59.52 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 59.45/59.52 ( ( class_Orderings_Oorder(T_c)
% 59.45/59.52 & class_Orderings_Oorder(T_b) )
% 59.45/59.52 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 59.45/59.52 => 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))) ) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_bot__empty__eq,axiom,
% 59.45/59.52 ! [V_x_2,T_b] :
% 59.45/59.52 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 59.45/59.52 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_CollectE,axiom,
% 59.45/59.52 ! [V_P_2,V_a_2,T_b] :
% 59.45/59.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 59.45/59.52 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_CollectD,axiom,
% 59.45/59.52 ! [V_P_2,V_a_2,T_b] :
% 59.45/59.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 59.45/59.52 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_mem__Collect__eq,axiom,
% 59.45/59.52 ! [V_P_2,V_a_2,T_b] :
% 59.45/59.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 59.45/59.52 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Collect__mem__eq,axiom,
% 59.45/59.52 ! [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 ).
% 59.45/59.52
% 59.45/59.52 fof(fact_pred__subset__eq,axiom,
% 59.45/59.52 ! [V_S_2,V_R_2,T_b] :
% 59.45/59.52 ( 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)))
% 59.45/59.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_insert__is__Un,axiom,
% 59.45/59.52 ! [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) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_singletonE,axiom,
% 59.45/59.52 ! [V_a_2,V_b_2,T_b] :
% 59.45/59.52 ( 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)))))
% 59.45/59.52 => V_b_2 = V_a_2 ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_singleton__iff,axiom,
% 59.45/59.52 ! [V_a_2,V_b_2,T_b] :
% 59.45/59.52 ( 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)))))
% 59.45/59.52 <=> V_b_2 = V_a_2 ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_subset__insert,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 59.45/59.52 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.52 => ( 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)))
% 59.45/59.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_insert__subset,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 59.45/59.52 ( 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))
% 59.45/59.52 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 59.45/59.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_mono__sup,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 59.45/59.52 ( ( class_Lattices_Osemilattice__sup(T_c)
% 59.45/59.52 & class_Lattices_Osemilattice__sup(T_b) )
% 59.45/59.52 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 59.45/59.52 => 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)))) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__fun__def,axiom,
% 59.45/59.52 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 59.45/59.52 ( class_Lattices_Olattice(T_b)
% 59.45/59.52 => 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)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__apply,axiom,
% 59.45/59.52 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 59.45/59.52 ( class_Lattices_Olattice(T_b)
% 59.45/59.52 => 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)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__eq__bot__iff,axiom,
% 59.45/59.52 ! [V_y_2,V_x_2,T_b] :
% 59.45/59.52 ( class_Lattices_Obounded__lattice__bot(T_b)
% 59.45/59.52 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 59.45/59.52 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 59.45/59.52 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__bot__right,axiom,
% 59.45/59.52 ! [V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Obounded__lattice__bot(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__bot__left,axiom,
% 59.45/59.52 ! [V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Obounded__lattice__bot(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_le__supE,axiom,
% 59.45/59.52 ! [V_x,V_b,V_a,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => ( 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))
% 59.45/59.52 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 59.45/59.52 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__mono,axiom,
% 59.45/59.52 ! [V_d,V_b,V_c,V_a,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 59.45/59.52 => 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))) ) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__least,axiom,
% 59.45/59.52 ! [V_z,V_x,V_y,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 59.45/59.52 => 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)) ) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_le__supI,axiom,
% 59.45/59.52 ! [V_b,V_x,V_a,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 59.45/59.52 => 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)) ) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__absorb1,axiom,
% 59.45/59.52 ! [V_x,V_y,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__absorb2,axiom,
% 59.45/59.52 ! [V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__assoc,axiom,
% 59.45/59.52 ! [V_z,V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => 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)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__sup__aci_I6_J,axiom,
% 59.45/59.52 ! [V_z,V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Olattice(T_a)
% 59.45/59.52 => 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)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup_Oassoc,axiom,
% 59.45/59.52 ! [V_c,V_b,V_a,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => 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)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__left__commute,axiom,
% 59.45/59.52 ! [V_z,V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => 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)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__sup__aci_I7_J,axiom,
% 59.45/59.52 ! [V_z,V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Olattice(T_a)
% 59.45/59.52 => 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)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup_Oleft__commute,axiom,
% 59.45/59.52 ! [V_c,V_a,V_b,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => 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)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__left__idem,axiom,
% 59.45/59.52 ! [V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => 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) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__sup__aci_I8_J,axiom,
% 59.45/59.52 ! [V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Olattice(T_a)
% 59.45/59.52 => 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) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup_Oleft__idem,axiom,
% 59.45/59.52 ! [V_b,V_a,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => 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) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__commute,axiom,
% 59.45/59.52 ! [V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => 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) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__sup__aci_I5_J,axiom,
% 59.45/59.52 ! [V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Olattice(T_a)
% 59.45/59.52 => 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) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup_Ocommute,axiom,
% 59.45/59.52 ! [V_b,V_a,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => 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) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__idem,axiom,
% 59.45/59.52 ! [V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup_Oidem,axiom,
% 59.45/59.52 ! [V_a,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__sup__ord_I3_J,axiom,
% 59.45/59.52 ! [V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Olattice(T_a)
% 59.45/59.52 => 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))) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__ge1,axiom,
% 59.45/59.52 ! [V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => 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))) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__sup__ord_I4_J,axiom,
% 59.45/59.52 ! [V_x,V_y,T_a] :
% 59.45/59.52 ( class_Lattices_Olattice(T_a)
% 59.45/59.52 => 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))) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__ge2,axiom,
% 59.45/59.52 ! [V_x,V_y,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => 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))) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_le__iff__sup,axiom,
% 59.45/59.52 ! [V_y_2,V_x_2,T_b] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_b)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 59.45/59.52 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_le__sup__iff,axiom,
% 59.45/59.52 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_b)
% 59.45/59.52 => ( 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))
% 59.45/59.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 59.45/59.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_le__supI1,axiom,
% 59.45/59.52 ! [V_b,V_a,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 59.45/59.52 => 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))) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_le__supI2,axiom,
% 59.45/59.52 ! [V_a,V_b,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 59.45/59.52 => 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))) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_coinduct3__mono__lemma,axiom,
% 59.45/59.52 ! [V_B_2,V_X_2,V_f_2,T_c,T_b] :
% 59.45/59.52 ( class_Orderings_Oorder(T_b)
% 59.45/59.52 => ( c_Orderings_Oorder__class_Omono(T_b,tc_fun(T_c,tc_HOL_Obool),V_f_2)
% 59.45/59.52 => 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)) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_image__ident,axiom,
% 59.45/59.52 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 59.45/59.52
% 59.45/59.52 fof(fact_image__Pow__mono,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 59.45/59.52 ( 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))
% 59.45/59.52 => 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))) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_subset__insert__iff,axiom,
% 59.45/59.52 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 59.45/59.52 ( 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)))
% 59.45/59.52 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.52 => 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)) )
% 59.45/59.52 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_diff__single__insert,axiom,
% 59.45/59.52 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 59.45/59.52 ( 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))
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.52 => 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))) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_imageE,axiom,
% 59.45/59.52 ! [V_A_2,V_f_2,T_c,V_b_2,T_b] :
% 59.45/59.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 59.45/59.52 => ~ ! [B_x] :
% 59.45/59.52 ( V_b_2 = hAPP(V_f_2,B_x)
% 59.45/59.52 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_image__subsetI,axiom,
% 59.45/59.52 ! [V_B_2,V_f_2,T_c,V_A_2,T_b] :
% 59.45/59.52 ( ! [B_x] :
% 59.45/59.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.45/59.52 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,B_x)),V_B_2)) )
% 59.45/59.52 => 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)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Powp__Pow__eq,axiom,
% 59.45/59.52 ! [V_x_2,V_A_2,T_b] :
% 59.45/59.52 ( 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))
% 59.45/59.52 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_def__coinduct__set,axiom,
% 59.45/59.52 ! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
% 59.45/59.52 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 59.45/59.52 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 59.45/59.52 => ( 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))))
% 59.45/59.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_coinduct__set,axiom,
% 59.45/59.52 ! [V_X_2,V_a_2,V_f_2,T_b] :
% 59.45/59.52 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 59.45/59.52 => ( 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)))))
% 59.45/59.52 => 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))) ) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_if__image__distrib,axiom,
% 59.45/59.52 ! [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))))) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf1E,axiom,
% 59.45/59.52 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 59.45/59.52 ( 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))
% 59.45/59.52 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 59.45/59.52 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf1I,axiom,
% 59.45/59.52 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 59.45/59.52 ( hBOOL(hAPP(V_A_2,V_x_2))
% 59.45/59.52 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 59.45/59.52 => 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)) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_IntE,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 59.45/59.52 ( 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)))
% 59.45/59.52 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 59.45/59.52 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_IntI,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 59.45/59.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 59.45/59.52 => 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))) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_DiffE,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 59.45/59.52 ( 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)))
% 59.45/59.52 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 59.45/59.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_DiffI,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 59.45/59.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 59.45/59.52 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 59.45/59.52 => 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))) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_PowI,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,T_b] :
% 59.45/59.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.52 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__apply,axiom,
% 59.45/59.52 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 59.45/59.52 ( class_Lattices_Olattice(T_b)
% 59.45/59.52 => 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)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_minus__apply,axiom,
% 59.45/59.52 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 59.45/59.52 ( class_Groups_Ominus(T_b)
% 59.45/59.52 => 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)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__assoc,axiom,
% 59.45/59.52 ! [V_z,V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__sup__aci_I2_J,axiom,
% 59.45/59.52 ! [V_z,V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Olattice(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf_Oassoc,axiom,
% 59.45/59.52 ! [V_c,V_b,V_a,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__left__commute,axiom,
% 59.45/59.52 ! [V_z,V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__sup__aci_I3_J,axiom,
% 59.45/59.52 ! [V_z,V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Olattice(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf_Oleft__commute,axiom,
% 59.45/59.52 ! [V_c,V_a,V_b,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__left__idem,axiom,
% 59.45/59.52 ! [V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__sup__aci_I4_J,axiom,
% 59.45/59.52 ! [V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Olattice(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf_Oleft__idem,axiom,
% 59.45/59.52 ! [V_b,V_a,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__commute,axiom,
% 59.45/59.52 ! [V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__sup__aci_I1_J,axiom,
% 59.45/59.52 ! [V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Olattice(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf_Ocommute,axiom,
% 59.45/59.52 ! [V_b,V_a,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_a) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__fun__def,axiom,
% 59.45/59.52 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 59.45/59.52 ( class_Lattices_Olattice(T_b)
% 59.45/59.52 => 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)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_fun__diff__def,axiom,
% 59.45/59.52 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 59.45/59.52 ( class_Groups_Ominus(T_b)
% 59.45/59.52 => 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)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__idem,axiom,
% 59.45/59.52 ! [V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf_Oidem,axiom,
% 59.45/59.52 ! [V_a,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf1D2,axiom,
% 59.45/59.52 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 59.45/59.52 ( 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))
% 59.45/59.52 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf1D1,axiom,
% 59.45/59.52 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 59.45/59.52 ( 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))
% 59.45/59.52 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Diff__Int2,axiom,
% 59.45/59.52 ! [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) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Diff__Int__distrib2,axiom,
% 59.45/59.52 ! [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)) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Int__assoc,axiom,
% 59.45/59.52 ! [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)) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Int__Diff,axiom,
% 59.45/59.52 ! [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)) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Diff__idemp,axiom,
% 59.45/59.52 ! [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) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Diff__Int__distrib,axiom,
% 59.45/59.52 ! [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)) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Int__left__commute,axiom,
% 59.45/59.52 ! [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)) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Int__left__absorb,axiom,
% 59.45/59.52 ! [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) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Int__commute,axiom,
% 59.45/59.52 ! [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) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Int__absorb,axiom,
% 59.45/59.52 ! [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 ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Pow__Int__eq,axiom,
% 59.45/59.52 ! [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)) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Pow__not__empty,axiom,
% 59.45/59.52 ! [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)) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Pow__top,axiom,
% 59.45/59.52 ! [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))) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Cantors__paradox,axiom,
% 59.45/59.52 ! [V_A_2,T_b] :
% 59.45/59.52 ~ ? [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) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Diff__disjoint,axiom,
% 59.45/59.52 ! [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)) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Diff__triv,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,T_b] :
% 59.45/59.52 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.45/59.52 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Un__Diff__Int,axiom,
% 59.45/59.52 ! [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 ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Diff__Un,axiom,
% 59.45/59.52 ! [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)) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Diff__Int,axiom,
% 59.45/59.52 ! [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)) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_gfp__upperbound,axiom,
% 59.45/59.52 ! [V_f_2,V_X_2,T_b] :
% 59.45/59.52 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,V_X_2)))
% 59.45/59.52 => 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))) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_gfp__unfold,axiom,
% 59.45/59.52 ! [V_f_2,T_b] :
% 59.45/59.52 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.45/59.52 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 59.45/59.52 => 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)) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_def__gfp__unfold,axiom,
% 59.45/59.52 ! [V_f_2,V_A_2,T_b] :
% 59.45/59.52 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.45/59.52 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
% 59.45/59.52 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 59.45/59.52 => V_A_2 = hAPP(V_f_2,V_A_2) ) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_le__infE,axiom,
% 59.45/59.52 ! [V_b,V_a,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => ( 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)))
% 59.45/59.52 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 59.45/59.52 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__mono,axiom,
% 59.45/59.52 ! [V_d,V_b,V_c,V_a,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 59.45/59.52 => 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))) ) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__greatest,axiom,
% 59.45/59.52 ! [V_z,V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 59.45/59.52 => 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))) ) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_le__infI,axiom,
% 59.45/59.52 ! [V_b,V_a,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 59.45/59.52 => 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))) ) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__absorb2,axiom,
% 59.45/59.52 ! [V_x,V_y,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__absorb1,axiom,
% 59.45/59.52 ! [V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_le__infI2,axiom,
% 59.45/59.52 ! [V_a,V_x,V_b,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 59.45/59.52 => 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)) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_le__infI1,axiom,
% 59.45/59.52 ! [V_b,V_x,V_a,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 59.45/59.52 => 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)) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_le__inf__iff,axiom,
% 59.45/59.52 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_b)
% 59.45/59.52 => ( 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)))
% 59.45/59.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 59.45/59.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_le__iff__inf,axiom,
% 59.45/59.52 ! [V_y_2,V_x_2,T_b] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_b)
% 59.45/59.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 59.45/59.52 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__le2,axiom,
% 59.45/59.52 ! [V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => 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)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__sup__ord_I2_J,axiom,
% 59.45/59.52 ! [V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Olattice(T_a)
% 59.45/59.52 => 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)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__le1,axiom,
% 59.45/59.52 ! [V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.52 => 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)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__sup__ord_I1_J,axiom,
% 59.45/59.52 ! [V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Olattice(T_a)
% 59.45/59.52 => 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)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__bot__right,axiom,
% 59.45/59.52 ! [V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Obounded__lattice__bot(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__bot__left,axiom,
% 59.45/59.52 ! [V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Obounded__lattice__bot(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__sup__absorb,axiom,
% 59.45/59.52 ! [V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Olattice(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = V_x ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__inf__absorb,axiom,
% 59.45/59.52 ! [V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Olattice(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = V_x ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__sup__distrib1,axiom,
% 59.45/59.52 ! [V_z,V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Odistrib__lattice(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__inf__distrib1,axiom,
% 59.45/59.52 ! [V_z,V_y,V_x,T_a] :
% 59.45/59.52 ( class_Lattices_Odistrib__lattice(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_inf__sup__distrib2,axiom,
% 59.45/59.52 ! [V_x,V_z,V_y,T_a] :
% 59.45/59.52 ( class_Lattices_Odistrib__lattice(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_sup__inf__distrib2,axiom,
% 59.45/59.52 ! [V_x,V_z,V_y,T_a] :
% 59.45/59.52 ( class_Lattices_Odistrib__lattice(T_a)
% 59.45/59.52 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_z),V_x)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_DiffD2,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 59.45/59.52 ( 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)))
% 59.45/59.52 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_DiffD1,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 59.45/59.52 ( 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)))
% 59.45/59.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Diff__iff,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 59.45/59.52 ( 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)))
% 59.45/59.52 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 59.45/59.52 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_IntD2,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 59.45/59.52 ( 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)))
% 59.45/59.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_IntD1,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 59.45/59.52 ( 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)))
% 59.45/59.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Int__iff,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 59.45/59.52 ( 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)))
% 59.45/59.52 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 59.45/59.52 & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Diff__cancel,axiom,
% 59.45/59.52 ! [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)) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Diff__empty,axiom,
% 59.45/59.52 ! [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 ).
% 59.45/59.52
% 59.45/59.52 fof(fact_empty__Diff,axiom,
% 59.45/59.52 ! [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)) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_disjoint__iff__not__equal,axiom,
% 59.45/59.52 ! [V_B_2,V_A_2,T_b] :
% 59.45/59.52 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.45/59.52 <=> ! [B_x] :
% 59.45/59.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.45/59.52 => ! [B_xa] :
% 59.45/59.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 59.45/59.52 => B_x != B_xa ) ) ) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Int__empty__right,axiom,
% 59.45/59.52 ! [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)) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_Int__empty__left,axiom,
% 59.45/59.52 ! [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)) ).
% 59.45/59.52
% 59.45/59.52 fof(fact_double__diff,axiom,
% 59.45/59.52 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 59.45/59.53 => 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 ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Diff__mono,axiom,
% 59.45/59.53 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 59.45/59.53 => 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))) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Diff__subset,axiom,
% 59.45/59.53 ! [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)) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_insert__inter__insert,axiom,
% 59.45/59.53 ! [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)) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Un__Diff,axiom,
% 59.45/59.53 ! [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)) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Un__Diff__cancel2,axiom,
% 59.45/59.53 ! [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) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Un__Diff__cancel,axiom,
% 59.45/59.53 ! [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) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Int__mono,axiom,
% 59.45/59.53 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 59.45/59.53 => 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))) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Int__greatest,axiom,
% 59.45/59.53 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 59.45/59.53 => 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))) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Int__absorb1,axiom,
% 59.45/59.53 ! [V_A_2,V_B_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 59.45/59.53 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Int__absorb2,axiom,
% 59.45/59.53 ! [V_B_2,V_A_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.53 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Int__lower2,axiom,
% 59.45/59.53 ! [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)) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Int__lower1,axiom,
% 59.45/59.53 ! [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)) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Un__Int__crazy,axiom,
% 59.45/59.53 ! [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)) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Un__Int__distrib2,axiom,
% 59.45/59.53 ! [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)) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Int__Un__distrib2,axiom,
% 59.45/59.53 ! [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)) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Un__Int__distrib,axiom,
% 59.45/59.53 ! [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)) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Int__Un__distrib,axiom,
% 59.45/59.53 ! [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)) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Pow__bottom,axiom,
% 59.45/59.53 ! [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))) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Pow__empty,axiom,
% 59.45/59.53 ! [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))) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Pow__insert,axiom,
% 59.45/59.53 ! [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))) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Pow__iff,axiom,
% 59.45/59.53 ! [V_B_2,V_A_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 59.45/59.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_PowD,axiom,
% 59.45/59.53 ! [V_B_2,V_A_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_image__Pow__surj,axiom,
% 59.45/59.53 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 59.45/59.53 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 59.45/59.53 => 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) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_inf__Int__eq,axiom,
% 59.45/59.53 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 59.45/59.53 ( 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))
% 59.45/59.53 <=> 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))) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_weak__coinduct,axiom,
% 59.45/59.53 ! [V_f_2,V_X_2,V_a_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 59.45/59.53 => ( 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)))
% 59.45/59.53 => 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))) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Collect__conj__eq,axiom,
% 59.45/59.53 ! [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)) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Pow__def,axiom,
% 59.45/59.53 ! [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)) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_gfp__lemma2,axiom,
% 59.45/59.53 ! [V_f_2,T_b] :
% 59.45/59.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.45/59.53 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 59.45/59.53 => 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)))) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_gfp__lemma3,axiom,
% 59.45/59.53 ! [V_f_2,T_b] :
% 59.45/59.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.45/59.53 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 59.45/59.53 => 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))) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_distrib__sup__le,axiom,
% 59.45/59.53 ! [V_z,V_y,V_x,T_a] :
% 59.45/59.53 ( class_Lattices_Olattice(T_a)
% 59.45/59.53 => 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)))) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_distrib__inf__le,axiom,
% 59.45/59.53 ! [V_z,V_y,V_x,T_a] :
% 59.45/59.53 ( class_Lattices_Olattice(T_a)
% 59.45/59.53 => 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)))) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_insert__Diff__if,axiom,
% 59.45/59.53 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 59.45/59.53 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 59.45/59.53 => 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) )
% 59.45/59.53 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 59.45/59.53 => 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)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_insert__Diff1,axiom,
% 59.45/59.53 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 59.45/59.53 => 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) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_insert__Diff__single,axiom,
% 59.45/59.53 ! [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) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Diff__insert2,axiom,
% 59.45/59.53 ! [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) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Diff__insert,axiom,
% 59.45/59.53 ! [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)))) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Int__insert__right,axiom,
% 59.45/59.53 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 59.45/59.53 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.45/59.53 => 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)) )
% 59.45/59.53 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.45/59.53 => 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) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Int__insert__left,axiom,
% 59.45/59.53 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 59.45/59.53 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 59.45/59.53 => 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)) )
% 59.45/59.53 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 59.45/59.53 => 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) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Int__insert__right__if0,axiom,
% 59.45/59.53 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 59.45/59.53 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.45/59.53 => 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) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Int__insert__left__if0,axiom,
% 59.45/59.53 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 59.45/59.53 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 59.45/59.53 => 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) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Int__insert__right__if1,axiom,
% 59.45/59.53 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.45/59.53 => 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)) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Int__insert__left__if1,axiom,
% 59.45/59.53 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 59.45/59.53 => 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)) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_image__diff__subset,axiom,
% 59.45/59.53 ! [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)))) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_mono__inf,axiom,
% 59.45/59.53 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 59.45/59.53 ( ( class_Lattices_Osemilattice__inf(T_c)
% 59.45/59.53 & class_Lattices_Osemilattice__inf(T_b) )
% 59.45/59.53 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 59.45/59.53 => 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)))) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Diff__subset__conv,axiom,
% 59.45/59.53 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 59.45/59.53 ( 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))
% 59.45/59.53 <=> 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))) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Diff__partition,axiom,
% 59.45/59.53 ! [V_B_2,V_A_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.53 => 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 ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_image__Int__subset,axiom,
% 59.45/59.53 ! [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)))) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Un__Int__assoc__eq,axiom,
% 59.45/59.53 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 59.45/59.53 ( 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))
% 59.45/59.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_weak__coinduct__image,axiom,
% 59.45/59.53 ! [V_f_2,V_g_2,T_c,V_X_2,V_a_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 59.45/59.53 => ( 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))))
% 59.45/59.53 => 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))) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_set__diff__eq,axiom,
% 59.45/59.53 ! [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)))) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_mono__Int,axiom,
% 59.45/59.53 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 59.45/59.53 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2)
% 59.45/59.53 => 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)))) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Int__Collect,axiom,
% 59.45/59.53 ! [V_P_2,V_A_2,V_x_2,T_b] :
% 59.45/59.53 ( 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))))
% 59.45/59.53 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.53 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Int__def,axiom,
% 59.45/59.53 ! [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))) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_gfp__fun__UnI2,axiom,
% 59.45/59.53 ! [V_X_2,V_a_2,V_f_2,T_b] :
% 59.45/59.53 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 59.45/59.53 => ( 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)))
% 59.45/59.53 => 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))))) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Pow__mono,axiom,
% 59.45/59.53 ! [V_B_2,V_A_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.53 => 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))) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_coinduct,axiom,
% 59.45/59.53 ! [V_X_2,V_f_2,T_b] :
% 59.45/59.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.45/59.53 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 59.45/59.53 => ( 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)))))
% 59.45/59.53 => 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))) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_coinduct__lemma,axiom,
% 59.45/59.53 ! [V_f_2,V_X_2,T_b] :
% 59.45/59.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.45/59.53 => ( 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)))))
% 59.45/59.53 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 59.45/59.53 => 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))))) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_def__coinduct,axiom,
% 59.45/59.53 ! [V_X_2,V_f_2,V_A_2,T_b] :
% 59.45/59.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.45/59.53 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
% 59.45/59.53 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 59.45/59.53 => ( 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))))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),V_A_2)) ) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Un__Pow__subset,axiom,
% 59.45/59.53 ! [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)))) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_insert__Diff,axiom,
% 59.45/59.53 ! [V_A_2,V_a_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.45/59.53 => 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 ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Diff__insert__absorb,axiom,
% 59.45/59.53 ! [V_A_2,V_x_2,T_b] :
% 59.45/59.53 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.53 => 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 ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_flat__lub__def,axiom,
% 59.45/59.53 ! [V_b_2,V_A_2,T_b] :
% 59.45/59.53 ( ( 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)))))
% 59.45/59.53 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 )
% 59.45/59.53 & ( ~ 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)))))
% 59.45/59.53 => 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)))))) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_coinduct3,axiom,
% 59.45/59.53 ! [V_X_2,V_a_2,V_f_2,T_b] :
% 59.45/59.53 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 59.45/59.53 => ( 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))))))
% 59.45/59.53 => 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))) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_def__coinduct3,axiom,
% 59.45/59.53 ! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
% 59.45/59.53 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 59.45/59.53 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 59.45/59.53 => ( 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)))))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_def__Collect__coinduct,axiom,
% 59.45/59.53 ! [V_X_2,V_a_2,V_P_2,T_b,V_A_2] :
% 59.45/59.53 ( 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))
% 59.45/59.53 => ( 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))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 59.45/59.53 => ( ! [B_z] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_member(T_b),B_z),V_X_2))
% 59.45/59.53 => 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)) )
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_diff__eq__diff__less__eq,axiom,
% 59.45/59.53 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 59.45/59.53 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.45/59.53 => ( 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)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 59.45/59.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_fun__upd__image,axiom,
% 59.45/59.53 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 59.45/59.53 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.53 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(hAPP(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)))))) )
% 59.45/59.53 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.53 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(hAPP(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) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_coinduct3__lemma,axiom,
% 59.45/59.53 ! [V_f_2,V_X_2,T_b] :
% 59.45/59.53 ( 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))))))
% 59.45/59.53 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 59.45/59.53 => 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)))))) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_psubset__insert__iff,axiom,
% 59.45/59.53 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 59.45/59.53 ( 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)))
% 59.45/59.53 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 59.45/59.53 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 59.45/59.53 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.53 => 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)) )
% 59.45/59.53 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_Int__Collect__mono,axiom,
% 59.45/59.53 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.53 => ( ! [B_x] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.45/59.53 => ( hBOOL(hAPP(V_P_2,B_x))
% 59.45/59.53 => hBOOL(hAPP(V_Q_2,B_x)) ) )
% 59.45/59.53 => 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)))) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 59.45/59.53 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.53 => ( 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)
% 59.45/59.53 => 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)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_lfp__induct,axiom,
% 59.45/59.53 ! [V_P_2,V_f_2,T_b] :
% 59.45/59.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.45/59.53 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 59.45/59.53 => ( 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))
% 59.45/59.53 => 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)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_fun__upd__triv,axiom,
% 59.45/59.53 ! [V_x_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),hAPP(V_f_2,V_x_2)) = V_f_2 ).
% 59.45/59.53
% 59.45/59.53 fof(fact_fun__upd__idem__iff,axiom,
% 59.45/59.53 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 59.45/59.53 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2) = V_f_2
% 59.45/59.53 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_fun__upd__upd,axiom,
% 59.45/59.53 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_z_2) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_fun__upd__same,axiom,
% 59.45/59.53 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2),V_x_2) = V_y_2 ).
% 59.45/59.53
% 59.45/59.53 fof(fact_fun__upd__apply,axiom,
% 59.45/59.53 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 59.45/59.53 ( ( V_z_2 = V_x_2
% 59.45/59.53 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = V_y_2 )
% 59.45/59.53 & ( V_z_2 != V_x_2
% 59.45/59.53 => hAPP(hAPP(hAPP(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) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_fun__upd__twist,axiom,
% 59.45/59.53 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
% 59.45/59.53 ( V_a_2 != V_c_2
% 59.45/59.53 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_a_2),V_b_2)),V_c_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_c_2),V_d_2)),V_a_2),V_b_2) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_fun__upd__other,axiom,
% 59.45/59.53 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 59.45/59.53 ( V_z_2 != V_x_2
% 59.45/59.53 => hAPP(hAPP(hAPP(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) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_fun__upd__idem,axiom,
% 59.45/59.53 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 59.45/59.53 ( hAPP(V_f_2,V_x_2) = V_y_2
% 59.45/59.53 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_order__less__irrefl,axiom,
% 59.45/59.53 ! [V_x,T_a] :
% 59.45/59.53 ( class_Orderings_Opreorder(T_a)
% 59.45/59.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_linorder__neq__iff,axiom,
% 59.45/59.53 ! [V_y_2,V_x_2,T_b] :
% 59.45/59.53 ( class_Orderings_Olinorder(T_b)
% 59.45/59.53 => ( V_x_2 != V_y_2
% 59.45/59.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 59.45/59.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_not__less__iff__gr__or__eq,axiom,
% 59.45/59.53 ! [V_y_2,V_x_2,T_b] :
% 59.45/59.53 ( class_Orderings_Olinorder(T_b)
% 59.45/59.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 59.45/59.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 59.45/59.53 | V_x_2 = V_y_2 ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_linorder__less__linear,axiom,
% 59.45/59.53 ! [V_y,V_x,T_a] :
% 59.45/59.53 ( class_Orderings_Olinorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 59.45/59.53 | V_x = V_y
% 59.45/59.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_linorder__antisym__conv3,axiom,
% 59.45/59.53 ! [V_x_2,V_y_2,T_b] :
% 59.45/59.53 ( class_Orderings_Olinorder(T_b)
% 59.45/59.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 59.45/59.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 59.45/59.53 <=> V_x_2 = V_y_2 ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_linorder__neqE,axiom,
% 59.45/59.53 ! [V_y,V_x,T_a] :
% 59.45/59.53 ( class_Orderings_Olinorder(T_a)
% 59.45/59.53 => ( V_x != V_y
% 59.45/59.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_less__imp__neq,axiom,
% 59.45/59.53 ! [V_y,V_x,T_a] :
% 59.45/59.53 ( class_Orderings_Oorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 59.45/59.53 => V_x != V_y ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_order__less__not__sym,axiom,
% 59.45/59.53 ! [V_y,V_x,T_a] :
% 59.45/59.53 ( class_Orderings_Opreorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 59.45/59.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_order__less__imp__not__less,axiom,
% 59.45/59.53 ! [V_y,V_x,T_a] :
% 59.45/59.53 ( class_Orderings_Opreorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 59.45/59.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_order__less__imp__not__eq,axiom,
% 59.45/59.53 ! [V_y,V_x,T_a] :
% 59.45/59.53 ( class_Orderings_Oorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 59.45/59.53 => V_x != V_y ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_order__less__imp__not__eq2,axiom,
% 59.45/59.53 ! [V_y,V_x,T_a] :
% 59.45/59.53 ( class_Orderings_Oorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 59.45/59.53 => V_y != V_x ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_order__less__asym_H,axiom,
% 59.45/59.53 ! [V_b,V_a,T_a] :
% 59.45/59.53 ( class_Orderings_Opreorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 59.45/59.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_xt1_I9_J,axiom,
% 59.45/59.53 ! [V_a,V_b,T_a] :
% 59.45/59.53 ( class_Orderings_Oorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 59.45/59.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_ord__eq__less__trans,axiom,
% 59.45/59.53 ! [V_c,V_b,V_a,T_a] :
% 59.45/59.53 ( class_Orderings_Oord(T_a)
% 59.45/59.53 => ( V_a = V_b
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_xt1_I1_J,axiom,
% 59.45/59.53 ! [V_c,V_b,V_a,T_a] :
% 59.45/59.53 ( class_Orderings_Oorder(T_a)
% 59.45/59.53 => ( V_a = V_b
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_psubset__trans,axiom,
% 59.45/59.53 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_ord__less__eq__trans,axiom,
% 59.45/59.53 ! [V_c,V_b,V_a,T_a] :
% 59.45/59.53 ( class_Orderings_Oord(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 59.45/59.53 => ( V_b = V_c
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_xt1_I2_J,axiom,
% 59.45/59.53 ! [V_c,V_a,V_b,T_a] :
% 59.45/59.53 ( class_Orderings_Oorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 59.45/59.53 => ( V_b = V_c
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_order__less__trans,axiom,
% 59.45/59.53 ! [V_z,V_y,V_x,T_a] :
% 59.45/59.53 ( class_Orderings_Opreorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_xt1_I10_J,axiom,
% 59.45/59.53 ! [V_z,V_x,V_y,T_a] :
% 59.45/59.53 ( class_Orderings_Oorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_order__less__asym,axiom,
% 59.45/59.53 ! [V_y,V_x,T_a] :
% 59.45/59.53 ( class_Orderings_Opreorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 59.45/59.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_linorder__cases,axiom,
% 59.45/59.53 ! [V_y,V_x,T_a] :
% 59.45/59.53 ( class_Orderings_Olinorder(T_a)
% 59.45/59.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 59.45/59.53 => ( V_x != V_y
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_diff__eq__diff__less,axiom,
% 59.45/59.53 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 59.45/59.53 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.45/59.53 => ( 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)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 59.45/59.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_fun__upd__def,axiom,
% 59.45/59.53 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 59.45/59.53 ( ( V_x_2 = V_a_2
% 59.45/59.53 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_a_2),V_b_2),V_x_2) = V_b_2 )
% 59.45/59.53 & ( V_x_2 != V_a_2
% 59.45/59.53 => hAPP(hAPP(hAPP(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) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_lfp__const,axiom,
% 59.45/59.53 ! [V_t_2,T_b] :
% 59.45/59.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.45/59.53 => c_Inductive_Ocomplete__lattice__class_Olfp(T_b,hAPP(c_COMBK(T_b,T_b),V_t_2)) = V_t_2 ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 59.45/59.53 ! [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) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 59.45/59.53 ! [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) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_less__fun__def,axiom,
% 59.45/59.53 ! [V_g_2,V_f_2,T_b,T_c] :
% 59.45/59.53 ( class_Orderings_Oord(T_c)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 59.45/59.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 59.45/59.53 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_linorder__not__less,axiom,
% 59.45/59.53 ! [V_y_2,V_x_2,T_b] :
% 59.45/59.53 ( class_Orderings_Olinorder(T_b)
% 59.45/59.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 59.45/59.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_linorder__not__le,axiom,
% 59.45/59.53 ! [V_y_2,V_x_2,T_b] :
% 59.45/59.53 ( class_Orderings_Olinorder(T_b)
% 59.45/59.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 59.45/59.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_linorder__le__less__linear,axiom,
% 59.45/59.53 ! [V_y,V_x,T_a] :
% 59.45/59.53 ( class_Orderings_Olinorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 59.45/59.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_order__less__le,axiom,
% 59.45/59.53 ! [V_y_2,V_x_2,T_b] :
% 59.45/59.53 ( class_Orderings_Oorder(T_b)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 59.45/59.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 59.45/59.53 & V_x_2 != V_y_2 ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_less__le__not__le,axiom,
% 59.45/59.53 ! [V_y_2,V_x_2,T_b] :
% 59.45/59.53 ( class_Orderings_Opreorder(T_b)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 59.45/59.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 59.45/59.53 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_order__le__less,axiom,
% 59.45/59.53 ! [V_y_2,V_x_2,T_b] :
% 59.45/59.53 ( class_Orderings_Oorder(T_b)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 59.45/59.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 59.45/59.53 | V_x_2 = V_y_2 ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_leI,axiom,
% 59.45/59.53 ! [V_y,V_x,T_a] :
% 59.45/59.53 ( class_Orderings_Olinorder(T_a)
% 59.45/59.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_not__leE,axiom,
% 59.45/59.53 ! [V_x,V_y,T_a] :
% 59.45/59.53 ( class_Orderings_Olinorder(T_a)
% 59.45/59.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_linorder__antisym__conv1,axiom,
% 59.45/59.53 ! [V_y_2,V_x_2,T_b] :
% 59.45/59.53 ( class_Orderings_Olinorder(T_b)
% 59.45/59.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 59.45/59.53 <=> V_x_2 = V_y_2 ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_order__neq__le__trans,axiom,
% 59.45/59.53 ! [V_b,V_a,T_a] :
% 59.45/59.53 ( class_Orderings_Oorder(T_a)
% 59.45/59.53 => ( V_a != V_b
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_xt1_I12_J,axiom,
% 59.45/59.53 ! [V_b,V_a,T_a] :
% 59.45/59.53 ( class_Orderings_Oorder(T_a)
% 59.45/59.53 => ( V_a != V_b
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_leD,axiom,
% 59.45/59.53 ! [V_x,V_y,T_a] :
% 59.45/59.53 ( class_Orderings_Olinorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 59.45/59.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_order__less__imp__le,axiom,
% 59.45/59.53 ! [V_y,V_x,T_a] :
% 59.45/59.53 ( class_Orderings_Opreorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_linorder__antisym__conv2,axiom,
% 59.45/59.53 ! [V_y_2,V_x_2,T_b] :
% 59.45/59.53 ( class_Orderings_Olinorder(T_b)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 59.45/59.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 59.45/59.53 <=> V_x_2 = V_y_2 ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_order__le__imp__less__or__eq,axiom,
% 59.45/59.53 ! [V_y,V_x,T_a] :
% 59.45/59.53 ( class_Orderings_Oorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 59.45/59.53 | V_x = V_y ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_order__le__neq__trans,axiom,
% 59.45/59.53 ! [V_b,V_a,T_a] :
% 59.45/59.53 ( class_Orderings_Oorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.45/59.53 => ( V_a != V_b
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_xt1_I11_J,axiom,
% 59.45/59.53 ! [V_a,V_b,T_a] :
% 59.45/59.53 ( class_Orderings_Oorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 59.45/59.53 => ( V_a != V_b
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_order__less__le__trans,axiom,
% 59.45/59.53 ! [V_z,V_y,V_x,T_a] :
% 59.45/59.53 ( class_Orderings_Opreorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_xt1_I7_J,axiom,
% 59.45/59.53 ! [V_z,V_x,V_y,T_a] :
% 59.45/59.53 ( class_Orderings_Oorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_order__le__less__trans,axiom,
% 59.45/59.53 ! [V_z,V_y,V_x,T_a] :
% 59.45/59.53 ( class_Orderings_Opreorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_xt1_I8_J,axiom,
% 59.45/59.53 ! [V_z,V_x,V_y,T_a] :
% 59.45/59.53 ( class_Orderings_Oorder(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_psubsetD,axiom,
% 59.45/59.53 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_not__psubset__empty,axiom,
% 59.45/59.53 ! [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)))) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_less__supI2,axiom,
% 59.45/59.53 ! [V_a,V_b,V_x,T_a] :
% 59.45/59.53 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_less__supI1,axiom,
% 59.45/59.53 ! [V_b,V_a,V_x,T_a] :
% 59.45/59.53 ( class_Lattices_Osemilattice__sup(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_less__infI1,axiom,
% 59.45/59.53 ! [V_b,V_x,V_a,T_a] :
% 59.45/59.53 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 59.45/59.53 => 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)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_less__infI2,axiom,
% 59.45/59.53 ! [V_a,V_x,V_b,T_a] :
% 59.45/59.53 ( class_Lattices_Osemilattice__inf(T_a)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 59.45/59.53 => 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)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_psubset__eq,axiom,
% 59.45/59.53 ! [V_B_2,V_A_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.53 & V_A_2 != V_B_2 ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_subset__iff__psubset__eq,axiom,
% 59.45/59.53 ! [V_B_2,V_A_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.53 | V_A_2 = V_B_2 ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_psubset__imp__subset,axiom,
% 59.45/59.53 ! [V_B_2,V_A_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_psubset__subset__trans,axiom,
% 59.45/59.53 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_subset__psubset__trans,axiom,
% 59.45/59.53 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_strict__mono__less,axiom,
% 59.45/59.53 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 59.45/59.53 ( ( class_Orderings_Oorder(T_c)
% 59.45/59.53 & class_Orderings_Olinorder(T_b) )
% 59.45/59.53 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 59.45/59.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_strict__monoD,axiom,
% 59.45/59.53 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 59.45/59.53 ( ( class_Orderings_Oorder(T_c)
% 59.45/59.53 & class_Orderings_Oorder(T_b) )
% 59.45/59.53 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_lfp__lowerbound,axiom,
% 59.45/59.53 ! [V_A_2,V_f_2,T_b] :
% 59.45/59.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_A_2)),V_A_2))
% 59.45/59.53 => 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)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_not__less__Least,axiom,
% 59.45/59.53 ! [V_P_2,V_k_2,T_b] :
% 59.45/59.53 ( class_Orderings_Owellorder(T_b)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),c_Orderings_Oord__class_OLeast(T_b,V_P_2)))
% 59.45/59.53 => ~ hBOOL(hAPP(V_P_2,V_k_2)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_def__lfp__unfold,axiom,
% 59.45/59.53 ! [V_f_2,V_h_2,T_b] :
% 59.45/59.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.45/59.53 => ( V_h_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
% 59.45/59.53 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 59.45/59.53 => V_h_2 = hAPP(V_f_2,V_h_2) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_lfp__unfold,axiom,
% 59.45/59.53 ! [V_f_2,T_b] :
% 59.45/59.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.45/59.53 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 59.45/59.53 => 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)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_lfp__lemma2,axiom,
% 59.45/59.53 ! [V_f_2,T_b] :
% 59.45/59.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.45/59.53 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 59.45/59.53 => 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))) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_lfp__lemma3,axiom,
% 59.45/59.53 ! [V_f_2,T_b] :
% 59.45/59.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.45/59.53 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 59.45/59.53 => 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)))) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_diff__eq__diff__eq,axiom,
% 59.45/59.53 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 59.45/59.53 ( class_Groups_Oab__group__add(T_b)
% 59.45/59.53 => ( 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)
% 59.45/59.53 => ( V_a_2 = V_b_2
% 59.45/59.53 <=> V_c_2 = V_d_2 ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_def__lfp__induct,axiom,
% 59.45/59.53 ! [V_P_2,V_f_2,V_A_2,T_b] :
% 59.45/59.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.45/59.53 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
% 59.45/59.53 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 59.45/59.53 => ( 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))
% 59.45/59.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_A_2),V_P_2)) ) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_lfp__induct__set,axiom,
% 59.45/59.53 ! [V_P_2,V_f_2,V_a_2,T_b] :
% 59.45/59.53 ( 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)))
% 59.45/59.53 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 59.45/59.53 => ( ! [B_x] :
% 59.45/59.53 ( 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)))))
% 59.45/59.53 => hBOOL(hAPP(V_P_2,B_x)) )
% 59.45/59.53 => hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_def__lfp__induct__set,axiom,
% 59.45/59.53 ! [V_P_2,V_a_2,V_f_2,T_b,V_A_2] :
% 59.45/59.53 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 59.45/59.53 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.45/59.53 => ( ! [B_x] :
% 59.45/59.53 ( 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)))))
% 59.45/59.53 => hBOOL(hAPP(V_P_2,B_x)) )
% 59.45/59.53 => hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 59.45/59.53 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 59.45/59.53 ( 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))
% 59.45/59.53 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.45/59.53 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 59.45/59.53 | ? [B_x,B_y] :
% 59.45/59.53 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 59.45/59.53 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 59.45/59.53 & 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) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_order__fun_I2_J,axiom,
% 59.45/59.53 ! [V_g_2,V_f_2,T_b,T_c] :
% 59.45/59.53 ( ( class_Orderings_Oorder(T_c)
% 59.45/59.53 & class_Enum_Oenum(T_b) )
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 59.45/59.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 59.45/59.53 & 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)))) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_inj__on__Un,axiom,
% 59.45/59.53 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 59.45/59.53 ( 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))
% 59.45/59.53 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.45/59.53 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 59.45/59.53 & 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)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_inj__on__insert,axiom,
% 59.45/59.53 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 59.45/59.53 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 59.45/59.53 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.45/59.53 & ~ 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))))))) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_the__inv__into__def,axiom,
% 59.45/59.53 ! [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))) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_mk__less__def,axiom,
% 59.45/59.53 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 59.45/59.53 ( c_Partial__Function_Omk__less(T_b,V_R_2,V_x_2,V_y_2)
% 59.45/59.53 <=> ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 59.45/59.53 & ~ hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_psubset__imp__ex__mem,axiom,
% 59.45/59.53 ! [V_B_2,V_A_2,T_b] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.53 => ? [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))) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_override__on__def,axiom,
% 59.45/59.53 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 59.45/59.53 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.45/59.53 => 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) )
% 59.45/59.53 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.45/59.53 => 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) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_inj__on__empty,axiom,
% 59.45/59.53 ! [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))) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_inj__on__id2,axiom,
% 59.45/59.53 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_inj__on__def,axiom,
% 59.45/59.53 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.45/59.53 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.45/59.53 <=> ! [B_x] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.45/59.53 => ! [B_xa] :
% 59.45/59.53 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 59.45/59.53 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 59.45/59.53 => B_x = B_xa ) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_the__inv__into__f__eq,axiom,
% 59.45/59.53 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 59.45/59.53 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.45/59.53 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.53 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_the__inv__into__f__f,axiom,
% 59.45/59.53 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 59.45/59.53 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.53 => 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 ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_enum__ex,axiom,
% 59.45/59.53 ! [V_P_2,T_b] :
% 59.45/59.53 ( class_Enum_Oenum(T_b)
% 59.45/59.53 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2))
% 59.45/59.53 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_exists__code,axiom,
% 59.45/59.53 ! [V_P_2,T_b] :
% 59.45/59.53 ( class_Enum_Oenum(T_b)
% 59.45/59.53 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 59.45/59.53 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2)) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_the__inv__into__onto,axiom,
% 59.45/59.53 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.45/59.53 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.45/59.53 => 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 ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_inj__on__the__inv__into,axiom,
% 59.45/59.53 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.45/59.53 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.45/59.53 => 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)) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_inj__on__contraD,axiom,
% 59.45/59.53 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 59.45/59.53 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.45/59.53 => ( V_x_2 != V_y_2
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 59.45/59.53 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_inj__on__iff,axiom,
% 59.45/59.53 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 59.45/59.53 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 59.45/59.53 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 59.45/59.53 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_inj__onD,axiom,
% 59.45/59.53 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 59.45/59.53 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.45/59.53 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 59.45/59.53 => V_x_2 = V_y_2 ) ) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_subset__inj__on,axiom,
% 59.45/59.53 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 59.45/59.53 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 59.45/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.45/59.53 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 59.45/59.53
% 59.45/59.53 fof(fact_inj__on__Int,axiom,
% 59.60/59.53 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.53 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.60/59.53 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 59.60/59.53 => 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)) ) ) ).
% 59.60/59.53
% 59.60/59.53 fof(fact_inj__on__diff,axiom,
% 59.60/59.53 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.53 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.60/59.53 => 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)) ) ).
% 59.60/59.53
% 59.60/59.53 fof(fact_f__the__inv__into__f,axiom,
% 59.60/59.53 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.53 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.60/59.53 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 59.60/59.53 => 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 ) ) ).
% 59.60/59.53
% 59.60/59.53 fof(fact_strict__mono__imp__inj__on,axiom,
% 59.60/59.53 ! [V_A_2,V_f_2,T_b,T_c] :
% 59.60/59.53 ( ( class_Orderings_Oorder(T_c)
% 59.60/59.53 & class_Orderings_Olinorder(T_b) )
% 59.60/59.53 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 59.60/59.53 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 59.60/59.53
% 59.60/59.53 fof(fact_the__inv__into__into,axiom,
% 59.60/59.53 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.53 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.60/59.53 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 59.60/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.60/59.53 => 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)) ) ) ) ).
% 59.60/59.53
% 59.60/59.53 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 59.60/59.53 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.53 ( 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))
% 59.60/59.53 => ( 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)
% 59.60/59.53 <=> V_A_2 = V_B_2 ) ) ).
% 59.60/59.53
% 59.60/59.53 fof(fact_inj__on__strict__subset,axiom,
% 59.60/59.53 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 59.60/59.53 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 59.60/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.60/59.53 => 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))) ) ) ).
% 59.60/59.53
% 59.60/59.53 fof(fact_inj__on__image__Int,axiom,
% 59.60/59.53 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 59.60/59.53 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 59.60/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 59.60/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 59.60/59.53 => 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)) ) ) ) ).
% 59.60/59.53
% 59.60/59.53 fof(fact_inj__on__image__set__diff,axiom,
% 59.60/59.53 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 59.60/59.53 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 59.60/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 59.60/59.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 59.60/59.53 => 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)) ) ) ) ).
% 59.60/59.53
% 59.60/59.53 fof(fact_inj__on__fun__updI,axiom,
% 59.60/59.53 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.60/59.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 59.60/59.54 => c_Fun_Oinj__on(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_A_2) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_override__on__apply__notin,axiom,
% 59.60/59.54 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 59.60/59.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.54 => 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) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_override__on__apply__in,axiom,
% 59.60/59.54 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.54 => 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) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_override__on__emptyset,axiom,
% 59.60/59.54 ! [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 ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inj__on__iff__surj,axiom,
% 59.60/59.54 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 59.60/59.54 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.54 => ( ? [B_f] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 59.60/59.54 & 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)) )
% 59.60/59.54 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_dom__override__on,axiom,
% 59.60/59.54 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Fun_Ooverride__on(T_b,tc_Option_Ooption(T_c),V_f_2,V_g_2,V_A_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)),c_Map_Odom(T_b,T_c,V_f_2)),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)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_b,T_c,V_g_2)))))),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)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_b,T_c,V_g_2))))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_the__inv__into__comp,axiom,
% 59.60/59.54 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 59.60/59.54 => ( 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))))
% 59.60/59.54 => 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) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_quotient__diff1,axiom,
% 59.60/59.54 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 59.60/59.54 ( 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)
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.54 => 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)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_fun__left__comm__idem__remove,axiom,
% 59.60/59.54 ! [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))))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Inf__fin_Oidem,axiom,
% 59.60/59.54 ! [V_x,T_a] :
% 59.60/59.54 ( class_Lattices_Olattice(T_a)
% 59.60/59.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Sup__fin_Oidem,axiom,
% 59.60/59.54 ! [V_x,T_a] :
% 59.60/59.54 ( class_Lattices_Olattice(T_a)
% 59.60/59.54 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_fun__upd__restrict__conv,axiom,
% 59.60/59.54 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 59.60/59.54 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_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),V_y_2) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_restrict__fun__upd,axiom,
% 59.60/59.54 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 59.60/59.54 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 59.60/59.54 => c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_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),V_y_2) )
% 59.60/59.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 59.60/59.54 => c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_subsetI,axiom,
% 59.60/59.54 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.54 ( ! [B_x] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.60/59.54 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
% 59.60/59.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_o__assoc,axiom,
% 59.60/59.54 ! [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) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_o__apply,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_o__eq__dest,axiom,
% 59.60/59.54 ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 59.60/59.54 ( 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)
% 59.60/59.54 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_o__eq__elim,axiom,
% 59.60/59.54 ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 59.60/59.54 ( 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)
% 59.60/59.54 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 59.60/59.54 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 59.60/59.54 => 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) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 59.60/59.54 ! [V_x_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 59.60/59.54 => 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) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 59.60/59.54 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 59.60/59.54 => 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)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_o__def,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_dom__restrict,axiom,
% 59.60/59.54 ! [V_A_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_m_2)),V_A_2) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_restrict__in,axiom,
% 59.60/59.54 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.54 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_restrict__map__insert,axiom,
% 59.60/59.54 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_f_2,V_A_2)),V_a_2),hAPP(V_f_2,V_a_2)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_restrict__restrict,axiom,
% 59.60/59.54 ! [V_B_2,V_A_2,V_m_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_fun__left__comm__idem__insert,axiom,
% 59.60/59.54 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_fun__left__comm__idem__sup,axiom,
% 59.60/59.54 ! [T_b] :
% 59.60/59.54 ( class_Lattices_Osemilattice__sup(T_b)
% 59.60/59.54 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_fun__left__comm__idem__inf,axiom,
% 59.60/59.54 ! [T_b] :
% 59.60/59.54 ( class_Lattices_Osemilattice__inf(T_b)
% 59.60/59.54 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_image__compose,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inj__on__imageI2,axiom,
% 59.60/59.54 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 59.60/59.54 ( 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)
% 59.60/59.54 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_fun__upd__comp,axiom,
% 59.60/59.54 ! [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),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_d),V_g_2),V_x_2),V_y_2)) = hAPP(hAPP(hAPP(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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_quotient__empty,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_quotient__is__empty2,axiom,
% 59.60/59.54 ! [V_r_2,V_A_2,T_b] :
% 59.60/59.54 ( 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)
% 59.60/59.54 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_quotient__is__empty,axiom,
% 59.60/59.54 ! [V_r_2,V_A_2,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_comp__inj__on__iff,axiom,
% 59.60/59.54 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.60/59.54 => ( 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))
% 59.60/59.54 <=> 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) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_comp__inj__on,axiom,
% 59.60/59.54 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.60/59.54 => ( 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))
% 59.60/59.54 => 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) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inj__on__imageI,axiom,
% 59.60/59.54 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 59.60/59.54 ( 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)
% 59.60/59.54 => 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)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_fun__upd__restrict,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,V_D_2,V_m_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_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),V_y_2) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_dom__if,axiom,
% 59.60/59.54 ! [V_g_2,V_f_2,V_P_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_Option_Ooption(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),T_b),c_If(tc_Option_Ooption(T_c))),V_P_2)),V_f_2)),V_g_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)),c_Map_Odom(T_b,T_c,V_f_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)),c_Map_Odom(T_b,T_c,V_g_2)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_fun__upd__None__restrict,axiom,
% 59.60/59.54 ! [V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 59.60/59.54 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 59.60/59.54 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_c)) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) )
% 59.60/59.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 59.60/59.54 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_c)) = c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_singleton__quotient,axiom,
% 59.60/59.54 ! [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))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_quotientI,axiom,
% 59.60/59.54 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.54 => 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))) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_dom__fun__upd,axiom,
% 59.60/59.54 ! [V_x_2,V_f_2,T_c,T_b,V_y_2] :
% 59.60/59.54 ( ( V_y_2 = c_Option_Ooption_ONone(T_b)
% 59.60/59.54 => c_Map_Odom(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) )
% 59.60/59.54 & ( V_y_2 != c_Option_Ooption_ONone(T_b)
% 59.60/59.54 => c_Map_Odom(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Map_Odom(T_c,T_b,V_f_2)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_quotient__disj,axiom,
% 59.60/59.54 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 59.60/59.54 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.60/59.54 => ( 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)))
% 59.60/59.54 => ( 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)))
% 59.60/59.54 => ( V_X_2 = V_Y_2
% 59.60/59.54 | 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)) ) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_K__record__comp,axiom,
% 59.60/59.54 ! [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 ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Diff1__fold__graph,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.54 => 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))) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inv__into__comp,axiom,
% 59.60/59.54 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 59.60/59.54 => ( 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))))
% 59.60/59.54 => 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) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inj__singleton,axiom,
% 59.60/59.54 ! [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))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_fold1Set__sing,axiom,
% 59.60/59.54 ! [V_b_2,V_a_2,V_f_2,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 <=> V_a_2 = V_b_2 ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_top1I,axiom,
% 59.60/59.54 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UNIV__I,axiom,
% 59.60/59.54 ! [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)))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_fold1Set_Ointros,axiom,
% 59.60/59.54 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 59.60/59.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.54 => 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)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_surj__iff__all,axiom,
% 59.60/59.54 ! [V_f_2,T_b,T_c] :
% 59.60/59.54 ( 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))
% 59.60/59.54 <=> ! [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 ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_surj__f__inv__f,axiom,
% 59.60/59.54 ! [V_y_2,V_f_2,T_b,T_c] :
% 59.60/59.54 ( 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))
% 59.60/59.54 => 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 ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_image__surj__f__inv__f,axiom,
% 59.60/59.54 ! [V_A_2,V_f_2,T_b,T_c] :
% 59.60/59.54 ( 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))
% 59.60/59.54 => 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 ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_top__apply,axiom,
% 59.60/59.54 ! [V_x_2,T_c,T_b] :
% 59.60/59.54 ( class_Orderings_Otop(T_b)
% 59.60/59.54 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inv__f__eq,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 59.60/59.54 => 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 ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inv__f__f,axiom,
% 59.60/59.54 ! [V_x_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => 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 ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_iso__tuple__UNIV__I,axiom,
% 59.60/59.54 ! [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)))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Pow__UNIV,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_surj__imp__inj__inv,axiom,
% 59.60/59.54 ! [V_f_2,T_b,T_c] :
% 59.60/59.54 ( 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))
% 59.60/59.54 => 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))) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inv__image__comp,axiom,
% 59.60/59.54 ! [V_X_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => 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 ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_image__inv__f__f,axiom,
% 59.60/59.54 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => 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 ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inj__imp__surj__inv,axiom,
% 59.60/59.54 ! [V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => 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)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_o__inv__o__cancel,axiom,
% 59.60/59.54 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => 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 ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UNIV__not__empty,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_subset__UNIV,axiom,
% 59.60/59.54 ! [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)))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Un__UNIV__right,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Un__UNIV__left,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Int__UNIV__right,axiom,
% 59.60/59.54 ! [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 ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Int__UNIV__left,axiom,
% 59.60/59.54 ! [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 ).
% 59.60/59.54
% 59.60/59.54 fof(fact_injD,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 59.60/59.54 => V_x_2 = V_y_2 ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inj__eq,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 59.60/59.54 <=> V_x_2 = V_y_2 ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_empty__fold__graphE,axiom,
% 59.60/59.54 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 => V_x_2 = V_z_2 ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_fold__graph_OemptyI,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UNIV__def,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_range__composition,axiom,
% 59.60/59.54 ! [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)))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_equiv__class__self,axiom,
% 59.60/59.54 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 59.60/59.54 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.54 => 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)))))) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_empty__upd__none,axiom,
% 59.60/59.54 ! [V_xa_2,V_x_2,T_b,T_c] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))),V_x_2),c_Option_Ooption_ONone(T_b)),V_xa_2) = c_Option_Ooption_ONone(T_b) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_top__greatest,axiom,
% 59.60/59.54 ! [V_x,T_a] :
% 59.60/59.54 ( class_Orderings_Otop(T_a)
% 59.60/59.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_restrict__map__empty,axiom,
% 59.60/59.54 ! [V_x_2,V_D_2,T_b,T_c] : hAPP(c_Map_Orestrict__map(T_c,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_D_2),V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_sup__top__left,axiom,
% 59.60/59.54 ! [V_x,T_a] :
% 59.60/59.54 ( class_Lattices_Obounded__lattice__top(T_a)
% 59.60/59.54 => 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) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_sup__top__right,axiom,
% 59.60/59.54 ! [V_x,T_a] :
% 59.60/59.54 ( class_Lattices_Obounded__lattice__top(T_a)
% 59.60/59.54 => 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) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inf__eq__top__iff,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,T_b] :
% 59.60/59.54 ( class_Lattices_Obounded__lattice__top(T_b)
% 59.60/59.54 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 59.60/59.54 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 59.60/59.54 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inf__top__right,axiom,
% 59.60/59.54 ! [V_x,T_a] :
% 59.60/59.54 ( class_Lattices_Obounded__lattice__top(T_a)
% 59.60/59.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inf__top__left,axiom,
% 59.60/59.54 ! [V_x,T_a] :
% 59.60/59.54 ( class_Lattices_Obounded__lattice__top(T_a)
% 59.60/59.54 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_fold1Set__nonempty,axiom,
% 59.60/59.54 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 59.60/59.54 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_empty__fold1SetE,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_domIff,axiom,
% 59.60/59.54 ! [V_m_2,T_c,V_a_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_c,V_m_2)))
% 59.60/59.54 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_c) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_range__eqI,axiom,
% 59.60/59.54 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
% 59.60/59.54 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 59.60/59.54 => 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))))) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_rangeI,axiom,
% 59.60/59.54 ! [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))))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_restrict__out,axiom,
% 59.60/59.54 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 59.60/59.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.54 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Diff__UNIV,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_comp__surj,axiom,
% 59.60/59.54 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 59.60/59.54 ( 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))
% 59.60/59.54 => ( 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))
% 59.60/59.54 => 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)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_f__inv__into__f,axiom,
% 59.60/59.54 ! [V_A_2,V_f_2,T_c,V_y_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 59.60/59.54 => 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 ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inv__into__into,axiom,
% 59.60/59.54 ! [V_A_2,V_f_2,T_c,V_x_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 59.60/59.54 => 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)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inv__into__injective,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] :
% 59.60/59.54 ( 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)
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 59.60/59.54 => V_x_2 = V_y_2 ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inj__image__eq__iff,axiom,
% 59.60/59.54 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => ( 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)
% 59.60/59.54 <=> V_A_2 = V_B_2 ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inj__comp,axiom,
% 59.60/59.54 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 59.60/59.54 => 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))) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inv__into__f__f,axiom,
% 59.60/59.54 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.54 => 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 ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inv__into__f__eq,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.54 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 59.60/59.54 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_image__inv__into__cancel,axiom,
% 59.60/59.54 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
% 59.60/59.54 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2))
% 59.60/59.54 => 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 ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_fold__graph_OinsertI,axiom,
% 59.60/59.54 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 59.60/59.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.54 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 59.60/59.54 => 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))) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_dom__eq__empty__conv,axiom,
% 59.60/59.54 ! [V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Map_Odom(T_b,T_c,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.54 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_dom__empty,axiom,
% 59.60/59.54 ! [T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_dom__def,axiom,
% 59.60/59.54 ! [V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,V_m_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_Option_Ooption(T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),T_b),c_fequal),V_m_2)),c_Option_Ooption_ONone(T_c)))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_restrict__map__def,axiom,
% 59.60/59.54 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 59.60/59.54 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.54 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) )
% 59.60/59.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.54 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_the__inv__f__f,axiom,
% 59.60/59.54 ! [V_x_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => 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 ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_restrict__map__to__empty,axiom,
% 59.60/59.54 ! [V_x_2,V_m_2,T_b,T_c] : hAPP(c_Map_Orestrict__map(T_c,T_b,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inj__fun,axiom,
% 59.60/59.54 ! [T_d,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => 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))) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_dom__minus,axiom,
% 59.60/59.54 ! [V_A_2,T_c,T_b,V_x_2,V_f_2] :
% 59.60/59.54 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_b)
% 59.60/59.54 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),V_A_2) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_range__ex1__eq,axiom,
% 59.60/59.54 ! [V_b_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => ( 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)))))
% 59.60/59.54 <=> ? [B_x] :
% 59.60/59.54 ( V_b_2 = hAPP(V_f_2,B_x)
% 59.60/59.54 & ! [B_y] :
% 59.60/59.54 ( V_b_2 = hAPP(V_f_2,B_y)
% 59.60/59.54 => B_y = B_x ) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inj__image__mem__iff,axiom,
% 59.60/59.54 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => ( 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)))
% 59.60/59.54 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inj__image__subset__iff,axiom,
% 59.60/59.54 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => ( 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)))
% 59.60/59.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_image__Int,axiom,
% 59.60/59.54 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => 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)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_image__set__diff,axiom,
% 59.60/59.54 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => 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)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inv__into__image__cancel,axiom,
% 59.60/59.54 ! [V_S_2,V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2))
% 59.60/59.54 => 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 ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inj__on__inv__into,axiom,
% 59.60/59.54 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 59.60/59.54 ( 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)))
% 59.60/59.54 => 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) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_o__eq__dest__lhs,axiom,
% 59.60/59.54 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 59.60/59.54 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_c_2
% 59.60/59.54 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Image__Int__subset,axiom,
% 59.60/59.54 ! [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)))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_quotientE,axiom,
% 59.60/59.54 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 59.60/59.54 ( 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)))
% 59.60/59.54 => ~ ! [B_x] :
% 59.60/59.54 ( 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))))
% 59.60/59.54 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Image__Un,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Un__Image,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Image__mono,axiom,
% 59.60/59.54 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 59.60/59.54 => 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))) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Image__empty,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_quotient__def,axiom,
% 59.60/59.54 ! [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)))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inj__vimage__singleton,axiom,
% 59.60/59.54 ! [V_a_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => 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))))) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inj__transfer,axiom,
% 59.60/59.54 ! [V_x_2,V_P_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => ( ! [B_y] :
% 59.60/59.54 ( 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)))))
% 59.60/59.54 => 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))) )
% 59.60/59.54 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimageI,axiom,
% 59.60/59.54 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
% 59.60/59.54 ( hAPP(V_f_2,V_a_2) = V_b_2
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 59.60/59.54 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_SUP1__I,axiom,
% 59.60/59.54 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 59.60/59.54 => 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)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__code,axiom,
% 59.60/59.54 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 59.60/59.54 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_SUP1__iff,axiom,
% 59.60/59.54 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 <=> ? [B_x] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.60/59.54 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__ident,axiom,
% 59.60/59.54 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Image__UN,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__o,axiom,
% 59.60/59.54 ! [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) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__eq,axiom,
% 59.60/59.54 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 59.60/59.54 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimageD,axiom,
% 59.60/59.54 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 59.60/59.54 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimageI2,axiom,
% 59.60/59.54 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 59.60/59.54 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__empty,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__mono,axiom,
% 59.60/59.54 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.60/59.54 => 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))) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__UNIV,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__Un,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__Int,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__compose,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__Diff,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__Collect__eq,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_image__vimage__subset,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_surj__image__vimage__eq,axiom,
% 59.60/59.54 ! [V_A_2,V_f_2,T_b,T_c] :
% 59.60/59.54 ( 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))
% 59.60/59.54 => 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 ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_SUP__UN__eq,axiom,
% 59.60/59.54 ! [V_x_2,V_r_2,T_c,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 <=> 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))) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Image__eq__UN,axiom,
% 59.60/59.54 ! [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))))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__def,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__singleton__eq,axiom,
% 59.60/59.54 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
% 59.60/59.54 ( 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))))))
% 59.60/59.54 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__insert,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__subsetD,axiom,
% 59.60/59.54 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 59.60/59.54 ( 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))
% 59.60/59.54 => ( 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))
% 59.60/59.54 => 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))) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_image__vimage__eq,axiom,
% 59.60/59.54 ! [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)))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inj__vimage__image__eq,axiom,
% 59.60/59.54 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => 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 ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__const,axiom,
% 59.60/59.54 ! [T_c,V_A_2,V_c_2,T_b] :
% 59.60/59.54 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 59.60/59.54 => 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)) )
% 59.60/59.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 59.60/59.54 => 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)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__subsetI,axiom,
% 59.60/59.54 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.54 => ( 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)))
% 59.60/59.54 => 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)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__I,axiom,
% 59.60/59.54 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 59.60/59.54 => 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))) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__Pow__subset,axiom,
% 59.60/59.54 ! [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)))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__eq__UN,axiom,
% 59.60/59.54 ! [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))))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_image__eq__UN,axiom,
% 59.60/59.54 ! [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)))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__equiv__class,axiom,
% 59.60/59.54 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 59.60/59.54 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.60/59.54 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.54 => 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) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__equiv__class2,axiom,
% 59.60/59.54 ! [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] :
% 59.60/59.54 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 59.60/59.54 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 59.60/59.54 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 59.60/59.54 => 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) ) ) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__insert,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__extend__simps_I2_J,axiom,
% 59.60/59.54 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 59.60/59.54 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.54 => 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 )
% 59.60/59.54 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.54 => 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)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__extend__simps_I3_J,axiom,
% 59.60/59.54 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 59.60/59.54 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.54 => 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 )
% 59.60/59.54 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.54 => 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)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_congruent2__implies__congruent,axiom,
% 59.60/59.54 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 59.60/59.54 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 59.60/59.54 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.54 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_ball__UN,axiom,
% 59.60/59.54 ! [V_P_2,V_B_2,V_A_2,T_c,T_b] :
% 59.60/59.54 ( ! [B_x] :
% 59.60/59.54 ( 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)))
% 59.60/59.54 => hBOOL(hAPP(V_P_2,B_x)) )
% 59.60/59.54 <=> ! [B_x] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 59.60/59.54 => ! [B_xa] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 59.60/59.54 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_SUP__commute,axiom,
% 59.60/59.54 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 59.60/59.54 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.60/59.54 => 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))) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__extend__simps_I9_J,axiom,
% 59.60/59.54 ! [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) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__simps_I9_J,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__UN__flatten,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_congruent2__implies__congruent__UN,axiom,
% 59.60/59.54 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 59.60/59.54 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 59.60/59.54 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 59.60/59.54 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 59.60/59.54 => 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)) ) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_SUP__le__iff,axiom,
% 59.60/59.54 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 59.60/59.54 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.60/59.54 => ( 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))
% 59.60/59.54 <=> ! [B_x] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 59.60/59.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_less__SUP__iff,axiom,
% 59.60/59.54 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 59.60/59.54 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.60/59.54 & class_Orderings_Olinorder(T_b) )
% 59.60/59.54 => ( 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)))
% 59.60/59.54 <=> ? [B_x] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 59.60/59.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__iff,axiom,
% 59.60/59.54 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 59.60/59.54 ( 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)))
% 59.60/59.54 <=> ? [B_x] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 59.60/59.54 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_SUP__const,axiom,
% 59.60/59.54 ! [V_M_2,T_b,V_A_2,T_c] :
% 59.60/59.54 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 59.60/59.54 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.54 => 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 ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UNION__empty__conv_I2_J,axiom,
% 59.60/59.54 ! [V_B_2,V_A_2,T_b,T_c] :
% 59.60/59.54 ( 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))
% 59.60/59.54 <=> ! [B_x] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 59.60/59.54 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__constant,axiom,
% 59.60/59.54 ! [V_c_2,T_c,T_b,V_A_2] :
% 59.60/59.54 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.54 => 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)) )
% 59.60/59.54 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.54 => 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 ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__empty2,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UNION__empty__conv_I1_J,axiom,
% 59.60/59.54 ! [V_B_2,V_A_2,T_c,T_b] :
% 59.60/59.54 ( 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)
% 59.60/59.54 <=> ! [B_x] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 59.60/59.54 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__subset__iff,axiom,
% 59.60/59.54 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 <=> ! [B_x] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 59.60/59.54 => 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)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__extend__simps_I10_J,axiom,
% 59.60/59.54 ! [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) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_image__UN,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__simps_I10_J,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__Un__distrib,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__Un,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__simps_I5_J,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__simps_I4_J,axiom,
% 59.60/59.54 ! [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) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__extend__simps_I5_J,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Int__UN__distrib,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__extend__simps_I4_J,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Int__UN__distrib2,axiom,
% 59.60/59.54 ! [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))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_SUPR__apply,axiom,
% 59.60/59.54 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 59.60/59.54 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.60/59.54 => 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)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__simps_I6_J,axiom,
% 59.60/59.54 ! [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) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__extend__simps_I6_J,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_vimage__UN,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_SUP__subset,axiom,
% 59.60/59.54 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 59.60/59.54 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.60/59.54 => 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))) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_le__SUPI,axiom,
% 59.60/59.54 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 59.60/59.54 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 59.60/59.54 => 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))) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__insert__distrib,axiom,
% 59.60/59.54 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 59.60/59.54 => 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)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__upper,axiom,
% 59.60/59.54 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.54 => 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))) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__absorb,axiom,
% 59.60/59.54 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 59.60/59.54 => 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) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__extend__simps_I1_J,axiom,
% 59.60/59.54 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 59.60/59.54 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.54 => 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))) )
% 59.60/59.54 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.54 => 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)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__singleton,axiom,
% 59.60/59.54 ! [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 ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__simps_I1_J,axiom,
% 59.60/59.54 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 59.60/59.54 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.54 => 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)) )
% 59.60/59.54 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.54 => 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)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__simps_I3_J,axiom,
% 59.60/59.54 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 59.60/59.54 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.54 => 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)) )
% 59.60/59.54 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.54 => 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)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__simps_I2_J,axiom,
% 59.60/59.54 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 59.60/59.54 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.54 => 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)) )
% 59.60/59.54 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.54 => 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) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__equiv__class__type2,axiom,
% 59.60/59.54 ! [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] :
% 59.60/59.54 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 59.60/59.54 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 59.60/59.54 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 59.60/59.54 => ( 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)))
% 59.60/59.54 => ( 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)))
% 59.60/59.54 => ( ! [B_x1] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 59.60/59.54 => ! [B_x2] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 59.60/59.54 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 59.60/59.54 => 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)) ) ) ) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__equiv__class__type,axiom,
% 59.60/59.54 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 59.60/59.54 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.60/59.54 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 59.60/59.54 => ( 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)))
% 59.60/59.54 => ( ! [B_x] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.60/59.54 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 59.60/59.54 => 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)) ) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_equiv__class__nondisjoint,axiom,
% 59.60/59.54 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 59.60/59.54 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.60/59.54 => ( 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)))))))
% 59.60/59.54 => 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)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_subset__equiv__class,axiom,
% 59.60/59.54 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
% 59.60/59.54 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.60/59.54 => ( 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))))))
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 59.60/59.54 => 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)) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_insert__fold1SetE,axiom,
% 59.60/59.54 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 => ~ ! [B_a,B_A] :
% 59.60/59.54 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 59.60/59.54 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 59.60/59.54 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_fold1Set_Oequations,axiom,
% 59.60/59.54 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 <=> ? [B_a,B_A] :
% 59.60/59.54 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 59.60/59.54 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 59.60/59.54 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_eq__equiv__class__iff2,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 59.60/59.54 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 59.60/59.54 => ( 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)
% 59.60/59.54 <=> 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)) ) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_equiv__class__subset,axiom,
% 59.60/59.54 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 59.60/59.54 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.60/59.54 => ( 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))
% 59.60/59.54 => 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)))))) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_dom__eq__singleton__conv,axiom,
% 59.60/59.54 ! [V_x_2,V_f_2,T_c,T_b] :
% 59.60/59.54 ( c_Map_Odom(T_b,T_c,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)))
% 59.60/59.54 <=> ? [B_v] : V_f_2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),B_v)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_SUP2__I,axiom,
% 59.60/59.54 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 59.60/59.54 => 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)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_bot__empty__eq2,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,T_c,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 <=> 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)))) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_pred__equals__eq2,axiom,
% 59.60/59.54 ! [V_S_2,V_R_2,T_c,T_b] :
% 59.60/59.54 ( 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)
% 59.60/59.54 <=> V_R_2 = V_S_2 ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inf__Int__eq2,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 <=> 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))) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_SUP__UN__eq2,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 <=> 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))) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_map__upd__Some__unfold,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_b,T_c] :
% 59.60/59.54 ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 59.60/59.54 <=> ( ( V_x_2 = V_a_2
% 59.60/59.54 & V_b_2 = V_y_2 )
% 59.60/59.54 | ( V_x_2 != V_a_2
% 59.60/59.54 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_map__upd__triv,axiom,
% 59.60/59.54 ! [T_c,V_x_2,T_b,V_k_2,V_t_2] :
% 59.60/59.54 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 59.60/59.54 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = V_t_2 ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_map__upd__eqD1,axiom,
% 59.60/59.54 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_c,T_b] :
% 59.60/59.54 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))
% 59.60/59.54 => V_x_2 = V_y_2 ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_congruentD,axiom,
% 59.60/59.54 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 59.60/59.54 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 59.60/59.54 => ( 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))
% 59.60/59.54 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_congruent2D,axiom,
% 59.60/59.54 ! [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] :
% 59.60/59.54 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 59.60/59.54 => ( 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))
% 59.60/59.54 => ( 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))
% 59.60/59.54 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_pred__subset__eq2,axiom,
% 59.60/59.54 ! [V_S_2,V_R_2,T_c,T_b] :
% 59.60/59.54 ( 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)))
% 59.60/59.54 <=> 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)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_sup__Un__eq2,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 <=> 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))) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_enum__all__prod__def,axiom,
% 59.60/59.54 ! [V_P_2,T_b,T_c] :
% 59.60/59.54 ( ( class_Enum_Oenum(T_c)
% 59.60/59.54 & class_Enum_Oenum(T_b) )
% 59.60/59.54 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_P_2))
% 59.60/59.54 <=> 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))))) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_enum__ex__prod__def,axiom,
% 59.60/59.54 ! [V_P_2,T_b,T_c] :
% 59.60/59.54 ( ( class_Enum_Oenum(T_c)
% 59.60/59.54 & class_Enum_Oenum(T_b) )
% 59.60/59.54 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_P_2))
% 59.60/59.54 <=> 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))))) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_domI,axiom,
% 59.60/59.54 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
% 59.60/59.54 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2)
% 59.60/59.54 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Map_Odom(T_c,T_b,V_m_2))) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_image__map__upd,axiom,
% 59.60/59.54 ! [V_y_2,V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 59.60/59.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.54 => hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))),V_A_2) = hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_c),V_m_2),V_A_2) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_insert__dom,axiom,
% 59.60/59.54 ! [T_c,V_y_2,T_b,V_x_2,V_f_2] :
% 59.60/59.54 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 59.60/59.54 => hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Map_Odom(T_c,T_b,V_f_2)) = c_Map_Odom(T_c,T_b,V_f_2) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_rev__ImageI,axiom,
% 59.60/59.54 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.54 => ( 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))
% 59.60/59.54 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Image__iff,axiom,
% 59.60/59.54 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 59.60/59.54 <=> ? [B_x] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 59.60/59.54 & 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)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_dom__const,axiom,
% 59.60/59.54 ! [V_f_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_Option_Ooption(T_c),T_b),c_Option_Ooption_OSome(T_c)),V_f_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_map__upd__nonempty,axiom,
% 59.60/59.54 ! [V_x_2,V_k_2,V_t_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) != hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_enum__all__option__def,axiom,
% 59.60/59.54 ! [V_P_2,T_b] :
% 59.60/59.54 ( class_Enum_Oenum(T_b)
% 59.60/59.54 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_b)),V_P_2))
% 59.60/59.54 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_b)))
% 59.60/59.54 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_HOL_Obool,T_b),V_P_2),c_Option_Ooption_OSome(T_b)))) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_enum__ex__option__def,axiom,
% 59.60/59.54 ! [V_P_2,T_b] :
% 59.60/59.54 ( class_Enum_Oenum(T_b)
% 59.60/59.54 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_b)),V_P_2))
% 59.60/59.54 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_b)))
% 59.60/59.54 | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_HOL_Obool,T_b),V_P_2),c_Option_Ooption_OSome(T_b)))) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Image__singleton__iff,axiom,
% 59.60/59.54 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
% 59.60/59.54 ( 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))))))
% 59.60/59.54 <=> 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)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_equiv__class__eq,axiom,
% 59.60/59.54 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 59.60/59.54 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.60/59.54 => ( 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))
% 59.60/59.54 => 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)))) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_quotient__eqI,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 59.60/59.54 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.60/59.54 => ( 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)))
% 59.60/59.54 => ( 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)))
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 59.60/59.54 => ( 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))
% 59.60/59.54 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_quotient__eq__iff,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 59.60/59.54 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.60/59.54 => ( 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)))
% 59.60/59.54 => ( 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)))
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 59.60/59.54 => ( V_X_2 = V_Y_2
% 59.60/59.54 <=> 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)) ) ) ) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Image__singleton,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_equiv__class__eq__iff,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 59.60/59.54 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.60/59.54 => ( 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))
% 59.60/59.54 <=> ( 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))))
% 59.60/59.54 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.54 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_eq__equiv__class__iff,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 59.60/59.54 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 59.60/59.54 => ( 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))))
% 59.60/59.54 <=> 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)) ) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_eq__equiv__class,axiom,
% 59.60/59.54 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
% 59.60/59.54 ( 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))))
% 59.60/59.54 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 59.60/59.54 => 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)) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_Nitpick_Orefl_H__def,axiom,
% 59.60/59.54 ! [V_r_2,T_b] :
% 59.60/59.54 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 59.60/59.54 <=> ! [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)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UN__equiv__class__inject,axiom,
% 59.60/59.54 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 59.60/59.54 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.60/59.54 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 59.60/59.54 => ( 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)
% 59.60/59.54 => ( 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)))
% 59.60/59.54 => ( 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)))
% 59.60/59.54 => ( ! [B_x] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.60/59.54 => ! [B_y] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 59.60/59.54 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 59.60/59.54 => 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)) ) ) )
% 59.60/59.54 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_UNIV__option__conv,axiom,
% 59.60/59.54 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(T_b)),c_Option_Ooption_ONone(T_b)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_b),c_Option_Ooption_OSome(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_irrefl__def,axiom,
% 59.60/59.54 ! [V_r_2,T_b] :
% 59.60/59.54 ( c_Relation_Oirrefl(T_b,V_r_2)
% 59.60/59.54 <=> ! [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)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_ran__map__upd,axiom,
% 59.60/59.54 ! [V_b_2,T_c,T_b,V_a_2,V_m_2] :
% 59.60/59.54 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_b)
% 59.60/59.54 => c_Map_Oran(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_option_Osimps_I2_J,axiom,
% 59.60/59.54 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_option_Osimps_I3_J,axiom,
% 59.60/59.54 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_not__Some__eq,axiom,
% 59.60/59.54 ! [T_b,V_x_2] :
% 59.60/59.54 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_b),B_y)
% 59.60/59.54 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_not__None__eq,axiom,
% 59.60/59.54 ! [T_b,V_x_2] :
% 59.60/59.54 ( V_x_2 != c_Option_Ooption_ONone(T_b)
% 59.60/59.54 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_sup2CI,axiom,
% 59.60/59.54 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 59.60/59.54 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 59.60/59.54 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 59.60/59.54 => 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)) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_sup2E,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 59.60/59.54 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inf2E,axiom,
% 59.60/59.54 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 59.60/59.54 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_inf2I,axiom,
% 59.60/59.54 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 59.60/59.54 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 59.60/59.54 => 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)) ) ) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_bot2E,axiom,
% 59.60/59.54 ! [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)) ).
% 59.60/59.54
% 59.60/59.54 fof(fact_SUP2__iff,axiom,
% 59.60/59.54 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 59.60/59.54 ( 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))
% 59.60/59.54 <=> ? [B_x] :
% 59.60/59.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.60/59.54 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_predicate2D,axiom,
% 59.60/59.55 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_c,T_b] :
% 59.60/59.55 ( 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))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 59.60/59.55 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_rev__predicate2D,axiom,
% 59.60/59.55 ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_P_2] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 59.60/59.55 => ( 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))
% 59.60/59.55 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_sup2I2,axiom,
% 59.60/59.55 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 59.60/59.55 => 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)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_sup2I1,axiom,
% 59.60/59.55 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 59.60/59.55 => 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)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_inf2D2,axiom,
% 59.60/59.55 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 59.60/59.55 ( 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))
% 59.60/59.55 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_inf2D1,axiom,
% 59.60/59.55 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 59.60/59.55 ( 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))
% 59.60/59.55 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_inj__Some,axiom,
% 59.60/59.55 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_b),c_Option_Ooption_OSome(T_b),V_A_2) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_option_Oinject,axiom,
% 59.60/59.55 ! [V_a_H_2,V_a_2,T_b] :
% 59.60/59.55 ( hAPP(c_Option_Ooption_OSome(T_b),V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_a_H_2)
% 59.60/59.55 <=> V_a_2 = V_a_H_2 ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_ranI,axiom,
% 59.60/59.55 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
% 59.60/59.55 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2)
% 59.60/59.55 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_ran__empty,axiom,
% 59.60/59.55 ! [T_b,T_c] : c_Map_Oran(T_c,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Option_Oset_Osimps_I2_J,axiom,
% 59.60/59.55 ! [V_x_2,T_b] : c_Option_Oset(T_b,hAPP(c_Option_Ooption_OSome(T_b),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))) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_less__by__empty,axiom,
% 59.60/59.55 ! [V_B_2,T_b,V_A_2] :
% 59.60/59.55 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 59.60/59.55 => 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)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_equivp__equiv,axiom,
% 59.60/59.55 ! [V_A_2,T_b] :
% 59.60/59.55 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 59.60/59.55 <=> 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)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_ImageE,axiom,
% 59.60/59.55 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 59.60/59.55 => ~ ! [B_x] :
% 59.60/59.55 ( 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))
% 59.60/59.55 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Field__insert,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_ran__restrictD,axiom,
% 59.60/59.55 ! [V_A_2,V_m_2,T_c,V_y_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),c_Map_Oran(T_c,T_b,c_Map_Orestrict__map(T_c,T_b,V_m_2,V_A_2))))
% 59.60/59.55 => ? [B_x] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 59.60/59.55 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Id__on__def,axiom,
% 59.60/59.55 ! [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)))) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_set__empty__eq,axiom,
% 59.60/59.55 ! [V_xo_2,T_b] :
% 59.60/59.55 ( c_Option_Oset(T_b,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 <=> V_xo_2 = c_Option_Ooption_ONone(T_b) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Option_Oset_Osimps_I1_J,axiom,
% 59.60/59.55 ! [T_b] : c_Option_Oset(T_b,c_Option_Ooption_ONone(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_identity__equivp,axiom,
% 59.60/59.55 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_equivp__def,axiom,
% 59.60/59.55 ! [V_R_2,T_b] :
% 59.60/59.55 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 59.60/59.55 <=> ! [B_x,B_y] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 59.60/59.55 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_equivp__reflp,axiom,
% 59.60/59.55 ! [V_x_2,V_R_2,T_b] :
% 59.60/59.55 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 59.60/59.55 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_equivp__symp,axiom,
% 59.60/59.55 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 59.60/59.55 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 59.60/59.55 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_equivp__transp,axiom,
% 59.60/59.55 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 59.60/59.55 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 59.60/59.55 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Id__on__empty,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Image__Id__on,axiom,
% 59.60/59.55 ! [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) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Field__empty,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_mono__Field,axiom,
% 59.60/59.55 ! [V_s_2,V_r_2,T_b] :
% 59.60/59.55 ( 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))
% 59.60/59.55 => 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))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_comp__cong,axiom,
% 59.60/59.55 ! [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] :
% 59.60/59.55 ( 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))
% 59.60/59.55 => 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) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Field__Un,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Id__on__iff,axiom,
% 59.60/59.55 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 59.60/59.55 ( 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)))
% 59.60/59.55 <=> ( V_x_2 = V_y_2
% 59.60/59.55 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Id__on__eqI,axiom,
% 59.60/59.55 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 59.60/59.55 ( V_a_2 = V_b_2
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.55 => 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))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_elem__set,axiom,
% 59.60/59.55 ! [V_xo_2,V_x_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Option_Oset(T_b,V_xo_2)))
% 59.60/59.55 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_in__rel__def,axiom,
% 59.60/59.55 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 59.60/59.55 <=> 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)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Id__onE,axiom,
% 59.60/59.55 ! [V_A_2,V_c_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2)))
% 59.60/59.55 => ~ ! [B_x] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.60/59.55 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_restrict__upd__same,axiom,
% 59.60/59.55 ! [V_y_2,V_x_2,V_m_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_restrict__complement__singleton__eq,axiom,
% 59.60/59.55 ! [V_x_2,V_f_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,V_f_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),c_Option_Ooption_ONone(T_c)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_fold__graph__permute__diff,axiom,
% 59.60/59.55 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
% 59.60/59.55 ( class_Groups_Oab__semigroup__mult(T_b)
% 59.60/59.55 => ( 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))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 59.60/59.55 => 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)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__range__updI,axiom,
% 59.60/59.55 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
% 59.60/59.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_option_Osimps_I5_J,axiom,
% 59.60/59.55 ! [V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_Option_Ooption_Ooption__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(c_Option_Ooption_OSome(T_c),V_a_2)) = hAPP(V_f2_2,V_a_2) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_option_Orecs_I2_J,axiom,
% 59.60/59.55 ! [V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Option_Ooption_Ooption__rec(T_b,T_c,V_f1_2,V_f2_2,hAPP(c_Option_Ooption_OSome(T_c),V_a_2)) = hAPP(V_f2_2,V_a_2) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite_OemptyI,axiom,
% 59.60/59.55 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite_OinsertI,axiom,
% 59.60/59.55 ! [V_a_2,V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__imageI,axiom,
% 59.60/59.55 ! [V_h_2,T_c,V_F_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 59.60/59.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__Int,axiom,
% 59.60/59.55 ! [V_G_2,V_F_2,T_b] :
% 59.60/59.55 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 59.60/59.55 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2)) )
% 59.60/59.55 => 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))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__Diff,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => 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))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_inj__uminus,axiom,
% 59.60/59.55 ! [V_A_2,T_b] :
% 59.60/59.55 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.60/59.55 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_ComplI,axiom,
% 59.60/59.55 ! [V_A_2,V_c_2,T_b] :
% 59.60/59.55 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 59.60/59.55 => 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))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__Collect__conjI,axiom,
% 59.60/59.55 ! [V_Q_2,V_P_2,T_b] :
% 59.60/59.55 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 59.60/59.55 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) )
% 59.60/59.55 => 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)))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__Collect__subsets,axiom,
% 59.60/59.55 ! [V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => 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)))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__Pow__iff,axiom,
% 59.60/59.55 ! [V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 59.60/59.55 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__code,axiom,
% 59.60/59.55 ! [V_A_2,T_b] :
% 59.60/59.55 ( class_Finite__Set_Ofinite(T_b)
% 59.60/59.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite,axiom,
% 59.60/59.55 ! [V_A_2,T_b] :
% 59.60/59.55 ( class_Finite__Set_Ofinite(T_b)
% 59.60/59.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 59.60/59.55 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.55 ( class_Groups_Oab__semigroup__mult(T_a)
% 59.60/59.55 => 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)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_neg__equal__iff__equal,axiom,
% 59.60/59.55 ! [V_b_2,V_a_2,T_b] :
% 59.60/59.55 ( class_Groups_Ogroup__add(T_b)
% 59.60/59.55 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 59.60/59.55 <=> V_a_2 = V_b_2 ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_minus__equation__iff,axiom,
% 59.60/59.55 ! [V_b_2,V_a_2,T_b] :
% 59.60/59.55 ( class_Groups_Ogroup__add(T_b)
% 59.60/59.55 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
% 59.60/59.55 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_equation__minus__iff,axiom,
% 59.60/59.55 ! [V_b_2,V_a_2,T_b] :
% 59.60/59.55 ( class_Groups_Ogroup__add(T_b)
% 59.60/59.55 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 59.60/59.55 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_minus__minus,axiom,
% 59.60/59.55 ! [V_a,T_a] :
% 59.60/59.55 ( class_Groups_Ogroup__add(T_a)
% 59.60/59.55 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_compl__eq__compl__iff,axiom,
% 59.60/59.55 ! [V_y_2,V_x_2,T_b] :
% 59.60/59.55 ( class_Lattices_Oboolean__algebra(T_b)
% 59.60/59.55 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 59.60/59.55 <=> V_x_2 = V_y_2 ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_mult__left__idem,axiom,
% 59.60/59.55 ! [V_b,V_a,T_a] :
% 59.60/59.55 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 59.60/59.55 => 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) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_uminus__apply,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,T_c,T_b] :
% 59.60/59.55 ( class_Groups_Ouminus(T_b)
% 59.60/59.55 => 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)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_mult__idem,axiom,
% 59.60/59.55 ! [V_x,T_a] :
% 59.60/59.55 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 59.60/59.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_times_Oidem,axiom,
% 59.60/59.55 ! [V_a,T_a] :
% 59.60/59.55 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 59.60/59.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_double__compl,axiom,
% 59.60/59.55 ! [V_x,T_a] :
% 59.60/59.55 ( class_Lattices_Oboolean__algebra(T_a)
% 59.60/59.55 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_fun__Compl__def,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,T_c,T_b] :
% 59.60/59.55 ( class_Groups_Ouminus(T_b)
% 59.60/59.55 => 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)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Compl__eq__Compl__iff,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.55 ( 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)
% 59.60/59.55 <=> V_A_2 = V_B_2 ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_double__complement,axiom,
% 59.60/59.55 ! [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 ).
% 59.60/59.55
% 59.60/59.55 fof(fact_nat__seg__image__imp__finite,axiom,
% 59.60/59.55 ! [V_n_2,V_f_2,T_b,V_A_2] :
% 59.60/59.55 ( 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)))
% 59.60/59.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__Plus__UNIV__iff,axiom,
% 59.60/59.55 ! [T_c,T_b] :
% 59.60/59.55 ( 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))))
% 59.60/59.55 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 59.60/59.55 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__Prod__UNIV,axiom,
% 59.60/59.55 ! [T_c,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 59.60/59.55 => 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)))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__compl,axiom,
% 59.60/59.55 ! [V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 59.60/59.55 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__Field,axiom,
% 59.60/59.55 ! [V_r_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 59.60/59.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_compl__mono,axiom,
% 59.60/59.55 ! [V_y,V_x,T_a] :
% 59.60/59.55 ( class_Lattices_Oboolean__algebra(T_a)
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 59.60/59.55 => 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))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_compl__le__compl__iff,axiom,
% 59.60/59.55 ! [V_y_2,V_x_2,T_b] :
% 59.60/59.55 ( class_Lattices_Oboolean__algebra(T_b)
% 59.60/59.55 => ( 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)))
% 59.60/59.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_le__imp__neg__le,axiom,
% 59.60/59.55 ! [V_b,V_a,T_a] :
% 59.60/59.55 ( class_Groups_Oordered__ab__group__add(T_a)
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.60/59.55 => 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))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_neg__le__iff__le,axiom,
% 59.60/59.55 ! [V_a_2,V_b_2,T_b] :
% 59.60/59.55 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.60/59.55 => ( 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)))
% 59.60/59.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_minus__le__iff,axiom,
% 59.60/59.55 ! [V_b_2,V_a_2,T_b] :
% 59.60/59.55 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.60/59.55 => ( 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))
% 59.60/59.55 <=> 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)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_le__minus__iff,axiom,
% 59.60/59.55 ! [V_b_2,V_a_2,T_b] :
% 59.60/59.55 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.60/59.55 => ( 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)))
% 59.60/59.55 <=> 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))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_less__minus__iff,axiom,
% 59.60/59.55 ! [V_b_2,V_a_2,T_b] :
% 59.60/59.55 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 59.60/59.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_minus__less__iff,axiom,
% 59.60/59.55 ! [V_b_2,V_a_2,T_b] :
% 59.60/59.55 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 59.60/59.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_neg__less__iff__less,axiom,
% 59.60/59.55 ! [V_a_2,V_b_2,T_b] :
% 59.60/59.55 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.60/59.55 => ( 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)))
% 59.60/59.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_ComplE,axiom,
% 59.60/59.55 ! [V_A_2,V_c_2,T_b] :
% 59.60/59.55 ( 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)))
% 59.60/59.55 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_ComplD,axiom,
% 59.60/59.55 ! [V_A_2,V_c_2,T_b] :
% 59.60/59.55 ( 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)))
% 59.60/59.55 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Compl__iff,axiom,
% 59.60/59.55 ! [V_A_2,V_c_2,T_b] :
% 59.60/59.55 ( 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)))
% 59.60/59.55 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_minus__diff__eq,axiom,
% 59.60/59.55 ! [V_b,V_a,T_a] :
% 59.60/59.55 ( class_Groups_Oab__group__add(T_a)
% 59.60/59.55 => 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) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Compl__anti__mono,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.60/59.55 => 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))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Compl__subset__Compl__iff,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.55 ( 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)))
% 59.60/59.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite_Oequations_I1_J,axiom,
% 59.60/59.55 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_vimage__Compl,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__insert,axiom,
% 59.60/59.55 ! [V_A_2,V_a_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 59.60/59.55 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__fun__UNIVD2,axiom,
% 59.60/59.55 ! [T_c,T_b] :
% 59.60/59.55 ( 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))))
% 59.60/59.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__subset,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_rev__finite__subset,axiom,
% 59.60/59.55 ! [V_A_2,V_B_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.60/59.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__UNIV,axiom,
% 59.60/59.55 ! [T_b] :
% 59.60/59.55 ( class_Finite__Set_Ofinite(T_b)
% 59.60/59.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__Un,axiom,
% 59.60/59.55 ! [V_G_2,V_F_2,T_b] :
% 59.60/59.55 ( 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)))
% 59.60/59.55 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 59.60/59.55 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__UnI,axiom,
% 59.60/59.55 ! [V_G_2,V_F_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
% 59.60/59.55 => 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))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__Diff2,axiom,
% 59.60/59.55 ! [V_A_2,V_B_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => ( 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)))
% 59.60/59.55 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__UN,axiom,
% 59.60/59.55 ! [V_B_2,T_c,V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( 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)))
% 59.60/59.55 <=> ! [B_x] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.60/59.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_fold__graph__imp__finite,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 59.60/59.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_fun__left__comm__idem,axiom,
% 59.60/59.55 ! [T_b] :
% 59.60/59.55 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 59.60/59.55 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Collect__neg__eq,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__option__UNIV,axiom,
% 59.60/59.55 ! [T_b] :
% 59.60/59.55 ( 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))))
% 59.60/59.55 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__Collect__disjI,axiom,
% 59.60/59.55 ! [V_Q_2,V_P_2,T_b] :
% 59.60/59.55 ( 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))))
% 59.60/59.55 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 59.60/59.55 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_compl__inf__bot,axiom,
% 59.60/59.55 ! [V_x,T_a] :
% 59.60/59.55 ( class_Lattices_Oboolean__algebra(T_a)
% 59.60/59.55 => 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) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_inf__compl__bot,axiom,
% 59.60/59.55 ! [V_x,T_a] :
% 59.60/59.55 ( class_Lattices_Oboolean__algebra(T_a)
% 59.60/59.55 => 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) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_diff__eq,axiom,
% 59.60/59.55 ! [V_y,V_x,T_a] :
% 59.60/59.55 ( class_Lattices_Oboolean__algebra(T_a)
% 59.60/59.55 => 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)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_compl__top__eq,axiom,
% 59.60/59.55 ! [T_a] :
% 59.60/59.55 ( class_Lattices_Oboolean__algebra(T_a)
% 59.60/59.55 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_compl__bot__eq,axiom,
% 59.60/59.55 ! [T_a] :
% 59.60/59.55 ( class_Lattices_Oboolean__algebra(T_a)
% 59.60/59.55 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_compl__sup,axiom,
% 59.60/59.55 ! [V_y,V_x,T_a] :
% 59.60/59.55 ( class_Lattices_Oboolean__algebra(T_a)
% 59.60/59.55 => 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)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_compl__inf,axiom,
% 59.60/59.55 ! [V_y,V_x,T_a] :
% 59.60/59.55 ( class_Lattices_Oboolean__algebra(T_a)
% 59.60/59.55 => 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)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_compl__sup__top,axiom,
% 59.60/59.55 ! [V_x,T_a] :
% 59.60/59.55 ( class_Lattices_Oboolean__algebra(T_a)
% 59.60/59.55 => 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) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_sup__compl__top,axiom,
% 59.60/59.55 ! [V_x,T_a] :
% 59.60/59.55 ( class_Lattices_Oboolean__algebra(T_a)
% 59.60/59.55 => 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) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_subset__Compl__self__eq,axiom,
% 59.60/59.55 ! [V_A_2,T_b] :
% 59.60/59.55 ( 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)))
% 59.60/59.55 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Compl__UNIV__eq,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Compl__empty__eq,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Compl__disjoint,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Compl__disjoint2,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Compl__partition,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Compl__partition2,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Compl__Un,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Compl__Int,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 59.60/59.55 ! [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) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Compl__Diff__eq,axiom,
% 59.60/59.55 ! [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) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Diff__Compl,axiom,
% 59.60/59.55 ! [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) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Diff__eq,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__surj,axiom,
% 59.60/59.55 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( 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)))
% 59.60/59.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__Diff__insert,axiom,
% 59.60/59.55 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 59.60/59.55 ( 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))))
% 59.60/59.55 <=> 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))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__imageD,axiom,
% 59.60/59.55 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 59.60/59.55 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 59.60/59.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Compl__eq,axiom,
% 59.60/59.55 ! [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))) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Collect__imp__eq,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__Collect__not,axiom,
% 59.60/59.55 ! [V_P_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 59.60/59.55 => ( 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))))
% 59.60/59.55 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__range__imageI,axiom,
% 59.60/59.55 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 59.60/59.55 ( 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)))))
% 59.60/59.55 => 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))))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_disjoint__eq__subset__Compl,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.55 ( 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))
% 59.60/59.55 <=> 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))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_surj__Compl__image__subset,axiom,
% 59.60/59.55 ! [V_A_2,V_f_2,T_b,T_c] :
% 59.60/59.55 ( 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))
% 59.60/59.55 => 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)))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_fold__graph__insert__swap,axiom,
% 59.60/59.55 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
% 59.60/59.55 ( class_Groups_Oab__semigroup__mult(T_b)
% 59.60/59.55 => ( 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))
% 59.60/59.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 59.60/59.55 => 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))) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__surj__inj,axiom,
% 59.60/59.55 ! [V_f_2,V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( 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)))
% 59.60/59.55 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_endo__inj__surj,axiom,
% 59.60/59.55 ! [V_f_2,V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( 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))
% 59.60/59.55 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 59.60/59.55 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__UNIV__surj__inj,axiom,
% 59.60/59.55 ! [V_f_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 59.60/59.55 => ( 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))
% 59.60/59.55 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__UNIV__inj__surj,axiom,
% 59.60/59.55 ! [V_f_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 59.60/59.55 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.55 => 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)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__vimageD,axiom,
% 59.60/59.55 ! [V_F_2,V_h_2,T_c,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 59.60/59.55 => ( 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))
% 59.60/59.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__vimageI,axiom,
% 59.60/59.55 ! [V_h_2,T_c,V_F_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 59.60/59.55 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 59.60/59.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_compl__unique,axiom,
% 59.60/59.55 ! [V_y,V_x,T_a] :
% 59.60/59.55 ( class_Lattices_Oboolean__algebra(T_a)
% 59.60/59.55 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 59.60/59.55 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 59.60/59.55 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_inj__image__Compl__subset,axiom,
% 59.60/59.55 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.60/59.55 => 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)))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_vimage__if,axiom,
% 59.60/59.55 ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
% 59.60/59.55 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 59.60/59.55 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 59.60/59.55 => 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)) )
% 59.60/59.55 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 59.60/59.55 => 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 ) ) )
% 59.60/59.55 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 59.60/59.55 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 59.60/59.55 => 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) )
% 59.60/59.55 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 59.60/59.55 => 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)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_option_Orecs_I1_J,axiom,
% 59.60/59.55 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Option_Ooption_Ooption__rec(T_b,T_c,V_f1_2,V_f2_2,c_Option_Ooption_ONone(T_c)) = V_f1_2 ).
% 59.60/59.55
% 59.60/59.55 fof(fact_option_Osimps_I4_J,axiom,
% 59.60/59.55 ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_Option_Ooption_Ooption__case(T_b,T_c,V_f1_2,V_f2_2),c_Option_Ooption_ONone(T_c)) = V_f1_2 ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding_Oremove,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.55 => 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)) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__image__simple_Oremove,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 59.60/59.55 => 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)))))) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__one_Oremove,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.55 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.60/59.55 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 59.60/59.55 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.60/59.55 => 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)))))) ) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__image_Oreindex,axiom,
% 59.60/59.55 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 59.60/59.55 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 59.60/59.55 => 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) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding_Ounion,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => ( 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))
% 59.60/59.55 => 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)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding_Oinsert__remove,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => 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)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 59.60/59.55 => ( 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))
% 59.60/59.55 => 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)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__one_Ounion__disjoint,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( 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))
% 59.60/59.55 => 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)) ) ) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__Collect__le__nat,axiom,
% 59.60/59.55 ! [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)))) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__Collect__less__nat,axiom,
% 59.60/59.55 ! [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)))) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_termination__basic__simps_I5_J,axiom,
% 59.60/59.55 ! [V_y,V_x] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 59.60/59.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding_Ocommute__left__comp,axiom,
% 59.60/59.55 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 59.60/59.55 => 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)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding_Ocommute__comp,axiom,
% 59.60/59.55 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 59.60/59.55 => 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)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 59.60/59.55 ! [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] :
% 59.60/59.55 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 59.60/59.55 => 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) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__image__simple_Oempty,axiom,
% 59.60/59.55 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 59.60/59.55 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__image_Odistrib,axiom,
% 59.60/59.55 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 59.60/59.55 => 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)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 59.60/59.55 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => 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)) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => 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)) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 59.60/59.55 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => 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)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding_Ocommute__comp_H,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => 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)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__one_Osingleton,axiom,
% 59.60/59.55 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 59.60/59.55 => 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 ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__image__simple_Oinsert,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 59.60/59.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 59.60/59.55 => 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)) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 59.60/59.55 => 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)) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding_Oinsert,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.55 => 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)) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding_Ounion__inter,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => 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)) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__one_Oinsert,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => 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)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__one_Oinsert__remove,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.60/59.55 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 59.60/59.55 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.60/59.55 => 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)))))) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 59.60/59.55 => 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)))))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__one_Ounion__inter,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => ( 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))
% 59.60/59.55 => 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)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__M__bounded__by__nat,axiom,
% 59.60/59.55 ! [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))))) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_square__eq__iff,axiom,
% 59.60/59.55 ! [V_b_2,V_a_2,T_b] :
% 59.60/59.55 ( class_Rings_Oidom(T_b)
% 59.60/59.55 => ( 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)
% 59.60/59.55 <=> ( V_a_2 = V_b_2
% 59.60/59.55 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_minus__mult__minus,axiom,
% 59.60/59.55 ! [V_b,V_a,T_a] :
% 59.60/59.55 ( class_Rings_Oring(T_a)
% 59.60/59.55 => 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) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_minus__mult__commute,axiom,
% 59.60/59.55 ! [V_b,V_a,T_a] :
% 59.60/59.55 ( class_Rings_Oring(T_a)
% 59.60/59.55 => 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)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_minus__mult__left,axiom,
% 59.60/59.55 ! [V_b,V_a,T_a] :
% 59.60/59.55 ( class_Rings_Oring(T_a)
% 59.60/59.55 => 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) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_minus__mult__right,axiom,
% 59.60/59.55 ! [V_b,V_a,T_a] :
% 59.60/59.55 ( class_Rings_Oring(T_a)
% 59.60/59.55 => 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)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Inf__fin_Oremove,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.55 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.60/59.55 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 59.60/59.55 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.60/59.55 => 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)))))) ) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Sup__fin_Oremove,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.55 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.60/59.55 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 59.60/59.55 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.60/59.55 => 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)))))) ) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 59.60/59.55 ! [V_N_2] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 59.60/59.55 <=> ? [B_m] :
% 59.60/59.55 ! [B_x] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 59.60/59.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_infinite__UNIV__nat,axiom,
% 59.60/59.55 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Inf__le__Sup,axiom,
% 59.60/59.55 ! [V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => 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))) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Sup__fin_Osingleton,axiom,
% 59.60/59.55 ! [V_x_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => 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 ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Inf__fin_Osingleton,axiom,
% 59.60/59.55 ! [V_x_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => 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 ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_linorder__neqE__linordered__idom,axiom,
% 59.60/59.55 ! [V_y,V_x,T_a] :
% 59.60/59.55 ( class_Rings_Olinordered__idom(T_a)
% 59.60/59.55 => ( V_x != V_y
% 59.60/59.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 59.60/59.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__nat__set__iff__bounded,axiom,
% 59.60/59.55 ! [V_N_2] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 59.60/59.55 <=> ? [B_m] :
% 59.60/59.55 ! [B_x] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 59.60/59.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_sup__Inf__absorb,axiom,
% 59.60/59.55 ! [V_a_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.55 => 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 ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Sup__fin_Oin__idem,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.55 => 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) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Inf__fin_Oin__idem,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.55 => 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) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_inf__Sup__absorb,axiom,
% 59.60/59.55 ! [V_a_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.55 => 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 ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => 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)) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => 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)) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Sup__fin_Osubset__idem,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 59.60/59.55 => 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) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Inf__fin_Osubset__idem,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 59.60/59.55 => 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) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Sup__fin_Ounion__idem,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => 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)) ) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Inf__fin_Ounion__idem,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => 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)) ) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Sup__fin_Oinsert,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => 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)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Inf__fin_Oinsert,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => 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)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.60/59.55 => 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 )
% 59.60/59.55 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.60/59.55 => 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)))))) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.60/59.55 => 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 )
% 59.60/59.55 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.60/59.55 => 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)))))) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( 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))
% 59.60/59.55 => 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)) ) ) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Sup__fin_Ounion__inter,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => ( 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))
% 59.60/59.55 => 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)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( 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))
% 59.60/59.55 => 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)) ) ) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Inf__fin_Ounion__inter,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => ( 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))
% 59.60/59.55 => 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)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Inf__fin_Oclosed,axiom,
% 59.60/59.55 ! [V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( ! [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))))))
% 59.60/59.55 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Sup__fin_Oclosed,axiom,
% 59.60/59.55 ! [V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( ! [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))))))
% 59.60/59.55 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_ord_OatMost__iff,axiom,
% 59.60/59.55 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 59.60/59.55 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_ord_OatLeast__iff,axiom,
% 59.60/59.55 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 59.60/59.55 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_ord_OlessThan__iff,axiom,
% 59.60/59.55 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 59.60/59.55 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_ord_OgreaterThan__iff,axiom,
% 59.60/59.55 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 59.60/59.55 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 59.60/59.55 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 59.60/59.55 ( 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)))
% 59.60/59.55 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 59.60/59.55 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 59.60/59.55 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 59.60/59.55 ( 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)))
% 59.60/59.55 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 59.60/59.55 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 59.60/59.55 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 59.60/59.55 ( 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)))
% 59.60/59.55 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 59.60/59.55 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 59.60/59.55 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 59.60/59.55 ( 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)))
% 59.60/59.55 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 59.60/59.55 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_nat__less__le,axiom,
% 59.60/59.55 ! [V_n_2,V_m_2] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 59.60/59.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 59.60/59.55 & V_m_2 != V_n_2 ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_le__eq__less__or__eq,axiom,
% 59.60/59.55 ! [V_n_2,V_m_2] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 59.60/59.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 59.60/59.55 | V_m_2 = V_n_2 ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_less__imp__le__nat,axiom,
% 59.60/59.55 ! [V_n,V_m] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.60/59.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_le__neq__implies__less,axiom,
% 59.60/59.55 ! [V_n,V_m] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 59.60/59.55 => ( V_m != V_n
% 59.60/59.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_less__or__eq__imp__le,axiom,
% 59.60/59.55 ! [V_n,V_m] :
% 59.60/59.55 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.60/59.55 | V_m = V_n )
% 59.60/59.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_diff__less__mono,axiom,
% 59.60/59.55 ! [V_c,V_b,V_a] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 59.60/59.55 => 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))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_diff__commute,axiom,
% 59.60/59.55 ! [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) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_diff__mult__distrib2,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_diff__mult__distrib,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_less__imp__diff__less,axiom,
% 59.60/59.55 ! [V_n,V_k,V_j] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 59.60/59.55 => 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)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_diff__less__mono2,axiom,
% 59.60/59.55 ! [V_l,V_n,V_m] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 59.60/59.55 => 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))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_less__not__refl,axiom,
% 59.60/59.55 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_nat__neq__iff,axiom,
% 59.60/59.55 ! [V_n_2,V_m_2] :
% 59.60/59.55 ( V_m_2 != V_n_2
% 59.60/59.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 59.60/59.55 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_linorder__neqE__nat,axiom,
% 59.60/59.55 ! [V_y,V_x] :
% 59.60/59.55 ( V_x != V_y
% 59.60/59.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 59.60/59.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_less__irrefl__nat,axiom,
% 59.60/59.55 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_less__not__refl2,axiom,
% 59.60/59.55 ! [V_m,V_n] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 59.60/59.55 => V_m != V_n ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_less__not__refl3,axiom,
% 59.60/59.55 ! [V_t,V_s] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 59.60/59.55 => V_s != V_t ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_nat__less__cases,axiom,
% 59.60/59.55 ! [V_P_2,V_n_2,V_m_2] :
% 59.60/59.55 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 59.60/59.55 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 59.60/59.55 => ( ( V_m_2 = V_n_2
% 59.60/59.55 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 59.60/59.55 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 59.60/59.55 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 59.60/59.55 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_diff__le__self,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_diff__le__mono2,axiom,
% 59.60/59.55 ! [V_l,V_n,V_m] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 59.60/59.55 => 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))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_diff__le__mono,axiom,
% 59.60/59.55 ! [V_l,V_n,V_m] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 59.60/59.55 => 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))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_diff__diff__cancel,axiom,
% 59.60/59.55 ! [V_n,V_i] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 59.60/59.55 => 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 ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_eq__diff__iff,axiom,
% 59.60/59.55 ! [V_n_2,V_m_2,V_k_2] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 59.60/59.55 => ( 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)
% 59.60/59.55 <=> V_m_2 = V_n_2 ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Nat_Odiff__diff__eq,axiom,
% 59.60/59.55 ! [V_n,V_m,V_k] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 59.60/59.55 => 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) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_le__diff__iff,axiom,
% 59.60/59.55 ! [V_n_2,V_m_2,V_k_2] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 59.60/59.55 => ( 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)))
% 59.60/59.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_le__antisym,axiom,
% 59.60/59.55 ! [V_n,V_m] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 59.60/59.55 => V_m = V_n ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_le__trans,axiom,
% 59.60/59.55 ! [V_k,V_j,V_i] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 59.60/59.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_eq__imp__le,axiom,
% 59.60/59.55 ! [V_n,V_m] :
% 59.60/59.55 ( V_m = V_n
% 59.60/59.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_nat__le__linear,axiom,
% 59.60/59.55 ! [V_n,V_m] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 59.60/59.55 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_le__refl,axiom,
% 59.60/59.55 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_le__square,axiom,
% 59.60/59.55 ! [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))) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_le__cube,axiom,
% 59.60/59.55 ! [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)))) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_mult__le__mono1,axiom,
% 59.60/59.55 ! [V_k,V_j,V_i] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 59.60/59.55 => 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))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_mult__le__mono2,axiom,
% 59.60/59.55 ! [V_k,V_j,V_i] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 59.60/59.55 => 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))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_mult__le__mono,axiom,
% 59.60/59.55 ! [V_l,V_k,V_j,V_i] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 59.60/59.55 => 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))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_less__diff__iff,axiom,
% 59.60/59.55 ! [V_n_2,V_m_2,V_k_2] :
% 59.60/59.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 59.60/59.55 => ( 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)))
% 59.60/59.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__idem_Ounion__idem,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => 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)) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 59.60/59.55 => 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) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__idem_Oinsert__idem,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => 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)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__one_Oclosed,axiom,
% 59.60/59.55 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( ! [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))))))
% 59.60/59.55 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_inf__Sup1__distrib,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Odistrib__lattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => 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))))) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_inf__Sup2__distrib,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Odistrib__lattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => 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))))))) ) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_sup__Inf1__distrib,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Odistrib__lattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => 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))))) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_sup__Inf2__distrib,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Lattices_Odistrib__lattice(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => 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))))))) ) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_nat__mult__assoc,axiom,
% 59.60/59.55 ! [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)) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_nat__mult__commute,axiom,
% 59.60/59.55 ! [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) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__Collect__bounded__ex,axiom,
% 59.60/59.55 ! [V_Q_2,T_c,V_P_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 59.60/59.55 => ( 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)))))
% 59.60/59.55 <=> ! [B_y] :
% 59.60/59.55 ( hBOOL(hAPP(V_P_2,B_y))
% 59.60/59.55 => 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)))) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__image__set,axiom,
% 59.60/59.55 ! [V_f_2,T_c,V_P_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 59.60/59.55 => 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))))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 59.60/59.55 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 59.60/59.55 => 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) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__idem_Oidem__comp,axiom,
% 59.60/59.55 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 59.60/59.55 => 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) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_ran__def,axiom,
% 59.60/59.55 ! [V_m_2,T_b,T_c] : c_Map_Oran(T_c,T_b,V_m_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_Option_Ooption(T_b),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_c),c_fequal),V_m_2))),c_Option_Ooption_OSome(T_b)))) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Pow__Compl,axiom,
% 59.60/59.55 ! [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))))) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.55 => 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) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Inf__fin_Ohom__commute,axiom,
% 59.60/59.55 ! [V_N_2,V_h_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( ! [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))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 59.60/59.55 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => 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)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_Sup__fin_Ohom__commute,axiom,
% 59.60/59.55 ! [V_N_2,V_h_2,T_b] :
% 59.60/59.55 ( class_Lattices_Olattice(T_b)
% 59.60/59.55 => ( ! [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))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 59.60/59.55 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => 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)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__empty__induct,axiom,
% 59.60/59.55 ! [V_P_2,V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(V_P_2,V_A_2))
% 59.60/59.55 => ( ! [B_a,B_A] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 59.60/59.55 => ( hBOOL(hAPP(V_P_2,B_A))
% 59.60/59.55 => 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)))))) ) ) )
% 59.60/59.55 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => 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)) ) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__subset__induct,axiom,
% 59.60/59.55 ! [V_P_2,V_A_2,V_F_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 59.60/59.55 => ( ! [B_a,B_F] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 59.60/59.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 59.60/59.55 => ( hBOOL(hAPP(V_P_2,B_F))
% 59.60/59.55 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 59.60/59.55 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 59.60/59.55 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => 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)) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_finite__conv__nat__seg__image,axiom,
% 59.60/59.55 ! [V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 <=> ? [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))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__one__idem_Oidem,axiom,
% 59.60/59.55 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 59.60/59.55 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__one__idem_Oin__idem,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.55 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_image__eq__fold__image,axiom,
% 59.60/59.55 ! [V_f_2,T_c,V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => 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) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_fold1__Un,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Groups_Oab__semigroup__mult(T_b)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( 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))
% 59.60/59.55 => 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)) ) ) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_card__Diff2__less,axiom,
% 59.60/59.55 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 59.60/59.55 => 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))) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_card__Diff1__less,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.55 => 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))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 59.60/59.55 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 59.60/59.55 => ( ! [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))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 59.60/59.55 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => 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)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 59.60/59.55 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 59.60/59.55 => ( ! [B_x] :
% 59.60/59.55 ( 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)))
% 59.60/59.55 => hAPP(V_g_2,B_x) = V_z_2 )
% 59.60/59.55 => 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)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_fold1__insert,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.55 ( class_Groups_Oab__semigroup__mult(T_b)
% 59.60/59.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.55 => 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)) ) ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_fold__image__empty,axiom,
% 59.60/59.55 ! [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 ).
% 59.60/59.55
% 59.60/59.55 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 59.60/59.55 ! [V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 59.60/59.55 => ( 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)))
% 59.60/59.55 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_card__image,axiom,
% 59.60/59.55 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.60/59.55 => 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) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_fold1__singleton,axiom,
% 59.60/59.55 ! [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 ).
% 59.60/59.55
% 59.60/59.55 fof(fact_fold1__singleton__def,axiom,
% 59.60/59.55 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 59.60/59.55 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 59.60/59.55 => 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 ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 59.60/59.55 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 59.60/59.55 => 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) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__image_Oeq__fold,axiom,
% 59.60/59.55 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 59.60/59.55 => 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) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_folding__one_Oeq__fold,axiom,
% 59.60/59.55 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 59.60/59.55 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 59.60/59.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_card__insert__le,axiom,
% 59.60/59.55 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => 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)))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_card__seteq,axiom,
% 59.60/59.55 ! [V_A_2,V_B_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.60/59.55 => ( 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)))
% 59.60/59.55 => V_A_2 = V_B_2 ) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_card__mono,axiom,
% 59.60/59.55 ! [V_A_2,V_B_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.60/59.55 => 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))) ) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_card__image__le,axiom,
% 59.60/59.55 ! [V_f_2,T_c,V_A_2,T_b] :
% 59.60/59.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.55 => 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))) ) ).
% 59.60/59.55
% 59.60/59.55 fof(fact_inj__on__iff__eq__card,axiom,
% 59.60/59.55 ! [V_f_2,T_c,V_A_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.60/59.56 <=> 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) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_eq__card__imp__inj__on,axiom,
% 59.60/59.56 ! [V_f_2,T_c,V_A_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( 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)
% 59.60/59.56 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_pigeonhole,axiom,
% 59.60/59.56 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.56 ( 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)))
% 59.60/59.56 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card__quotient__disjoint,axiom,
% 59.60/59.56 ! [V_r_2,V_A_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( 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)
% 59.60/59.56 => 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) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_psubset__card__mono,axiom,
% 59.60/59.56 ! [V_A_2,V_B_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.60/59.56 => 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))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_fold1__def,axiom,
% 59.60/59.56 ! [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)) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Sup__fin_OF__eq,axiom,
% 59.60/59.56 ! [V_A_2,T_b] :
% 59.60/59.56 ( class_Lattices_Olattice(T_b)
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => 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) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Inf__fin_OF__eq,axiom,
% 59.60/59.56 ! [V_A_2,T_b] :
% 59.60/59.56 ( class_Lattices_Olattice(T_b)
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => 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) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card__bij__eq,axiom,
% 59.60/59.56 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.56 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.60/59.56 => ( 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))
% 59.60/59.56 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 59.60/59.56 => ( 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))
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 59.60/59.56 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card__Diff__subset,axiom,
% 59.60/59.56 ! [V_A_2,V_B_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 59.60/59.56 => 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)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card__Diff__subset__Int,axiom,
% 59.60/59.56 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.56 ( 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)))
% 59.60/59.56 => 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))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__card__le__card__Diff,axiom,
% 59.60/59.56 ! [V_A_2,V_B_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_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)))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card__psubset,axiom,
% 59.60/59.56 ! [V_A_2,V_B_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.60/59.56 => ( 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)))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_fold__image__insert,axiom,
% 59.60/59.56 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 59.60/59.56 ( class_Groups_Oab__semigroup__mult(T_c)
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.56 => 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)) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_fold1__belowI,axiom,
% 59.60/59.56 ! [V_a_2,V_A_2,T_b] :
% 59.60/59.56 ( class_Lattices_Osemilattice__inf(T_b)
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.56 => 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)) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_below__fold1__iff,axiom,
% 59.60/59.56 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.56 ( class_Lattices_Osemilattice__inf(T_b)
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> ! [B_x] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_fold1__insert__idem,axiom,
% 59.60/59.56 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.56 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 59.60/59.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => 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)) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_fold1__Un2,axiom,
% 59.60/59.56 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.56 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.56 => 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)) ) ) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card__Diff1__le,axiom,
% 59.60/59.56 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => 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))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card__inj__on__le,axiom,
% 59.60/59.56 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 59.60/59.56 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.60/59.56 => ( 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))
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_inj__on__iff__card__le,axiom,
% 59.60/59.56 ! [V_B_2,T_c,V_A_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 59.60/59.56 => ( ? [B_f] :
% 59.60/59.56 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 59.60/59.56 & 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)) )
% 59.60/59.56 <=> 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_fold__image__reindex,axiom,
% 59.60/59.56 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 59.60/59.56 ( class_Groups_Oab__semigroup__mult(T_d)
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 59.60/59.56 => 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) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_semilattice__big_OF__eq,axiom,
% 59.60/59.56 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 59.60/59.56 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__monoid__big_OF__eq,axiom,
% 59.60/59.56 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 59.60/59.56 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 59.60/59.56 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 59.60/59.56 => 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) )
% 59.60/59.56 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 59.60/59.56 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_fold1__in,axiom,
% 59.60/59.56 ! [V_A_2,T_b] :
% 59.60/59.56 ( class_Groups_Oab__semigroup__mult(T_b)
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.56 => ( ! [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))))))
% 59.60/59.56 => 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)) ) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card__Diff__singleton,axiom,
% 59.60/59.56 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.56 => 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)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card__Diff__singleton__if,axiom,
% 59.60/59.56 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.56 => 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)) )
% 59.60/59.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.56 => 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) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_hom__fold1__commute,axiom,
% 59.60/59.56 ! [V_N_2,V_h_2,T_b] :
% 59.60/59.56 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 59.60/59.56 => ( ! [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))
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 59.60/59.56 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.56 => 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)) ) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card__Diff__insert,axiom,
% 59.60/59.56 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.60/59.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 59.60/59.56 => 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)) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card__UNIV__unit,axiom,
% 59.60/59.56 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) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_one__reorient,axiom,
% 59.60/59.56 ! [V_x_2,T_b] :
% 59.60/59.56 ( class_Groups_Oone(T_b)
% 59.60/59.56 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 59.60/59.56 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult_Ocomm__neutral,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Groups_Ocomm__monoid__mult(T_a)
% 59.60/59.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__1__right,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Groups_Omonoid__mult(T_a)
% 59.60/59.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__1,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Groups_Ocomm__monoid__mult(T_a)
% 59.60/59.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__1__left,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Groups_Omonoid__mult(T_a)
% 59.60/59.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__mult__1,axiom,
% 59.60/59.56 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__1__eq__mult__iff,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2] :
% 59.60/59.56 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 59.60/59.56 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 59.60/59.56 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__mult__1__right,axiom,
% 59.60/59.56 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__mult__eq__1__iff,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2] :
% 59.60/59.56 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 59.60/59.56 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 59.60/59.56 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__1__mult,axiom,
% 59.60/59.56 ! [V_n,V_m,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__semidom(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_square__eq__1__iff,axiom,
% 59.60/59.56 ! [V_x_2,T_b] :
% 59.60/59.56 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 59.60/59.56 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 59.60/59.56 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 59.60/59.56 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_fold__image__distrib,axiom,
% 59.60/59.56 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 59.60/59.56 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => 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)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 59.60/59.56 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 59.60/59.56 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 59.60/59.56 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 59.60/59.56 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_fold__image__Un__Int,axiom,
% 59.60/59.56 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 59.60/59.56 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_fold__Un__disjoint,axiom,
% 59.60/59.56 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 59.60/59.56 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.56 => ( 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))
% 59.60/59.56 => 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)) ) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 59.60/59.56 ! [V_x,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__ring__1(T_a)
% 59.60/59.56 => 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) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_fold__image__Un__one,axiom,
% 59.60/59.56 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 59.60/59.56 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 59.60/59.56 => ( ! [B_x] :
% 59.60/59.56 ( 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)))
% 59.60/59.56 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 59.60/59.56 => 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)) ) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card_Oremove,axiom,
% 59.60/59.56 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.56 => 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)))))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card_Oinsert__remove,axiom,
% 59.60/59.56 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => 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)))))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card__Suc__Diff1,axiom,
% 59.60/59.56 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.56 => 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) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_lessI,axiom,
% 59.60/59.56 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__mono,axiom,
% 59.60/59.56 ! [V_n,V_m] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__iff__Suc__add,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 59.60/59.56 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__add__Suc2,axiom,
% 59.60/59.56 ! [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)))) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__add__Suc1,axiom,
% 59.60/59.56 ! [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)))) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_inj__on__add__nat,axiom,
% 59.60/59.56 ! [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) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_inj__Suc,axiom,
% 59.60/59.56 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_n__not__Suc__n,axiom,
% 59.60/59.56 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__n__not__n,axiom,
% 59.60/59.56 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__add__commute,axiom,
% 59.60/59.56 ! [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) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__Suc__right,axiom,
% 59.60/59.56 ! [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)) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__add__left__commute,axiom,
% 59.60/59.56 ! [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)) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__Suc,axiom,
% 59.60/59.56 ! [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)) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__Suc__shift,axiom,
% 59.60/59.56 ! [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)) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat_Oinject,axiom,
% 59.60/59.56 ! [V_nat_H_2,V_nat_2] :
% 59.60/59.56 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 59.60/59.56 <=> V_nat_2 = V_nat_H_2 ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__add__assoc,axiom,
% 59.60/59.56 ! [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)) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__add__left__cancel,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2,V_k_2] :
% 59.60/59.56 ( 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)
% 59.60/59.56 <=> V_m_2 = V_n_2 ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__add__right__cancel,axiom,
% 59.60/59.56 ! [V_n_2,V_k_2,V_m_2] :
% 59.60/59.56 ( 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)
% 59.60/59.56 <=> V_m_2 = V_n_2 ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__inject,axiom,
% 59.60/59.56 ! [V_y,V_x] :
% 59.60/59.56 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 59.60/59.56 => V_x = V_y ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mono__Suc,axiom,
% 59.60/59.56 c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 59.60/59.56 ! [V_d,V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 59.60/59.56 ! [V_d,V_c,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 59.60/59.56 ! [V_d,V_c,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 59.60/59.56 ! [V_c,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Oab__semigroup__add(T_a)
% 59.60/59.56 => 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)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__left__cancel,axiom,
% 59.60/59.56 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 59.60/59.56 ( class_Groups_Ocancel__semigroup__add(T_b)
% 59.60/59.56 => ( 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)
% 59.60/59.56 <=> V_b_2 = V_c_2 ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__right__cancel,axiom,
% 59.60/59.56 ! [V_c_2,V_a_2,V_b_2,T_b] :
% 59.60/59.56 ( class_Groups_Ocancel__semigroup__add(T_b)
% 59.60/59.56 => ( 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)
% 59.60/59.56 <=> V_b_2 = V_c_2 ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__left__imp__eq,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Ocancel__semigroup__add(T_a)
% 59.60/59.56 => ( 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)
% 59.60/59.56 => V_b = V_c ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__imp__eq,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 59.60/59.56 => ( 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)
% 59.60/59.56 => V_b = V_c ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__right__imp__eq,axiom,
% 59.60/59.56 ! [V_c,V_a,V_b,T_a] :
% 59.60/59.56 ( class_Groups_Ocancel__semigroup__add(T_a)
% 59.60/59.56 => ( 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)
% 59.60/59.56 => V_b = V_c ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_crossproduct__eq,axiom,
% 59.60/59.56 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 59.60/59.56 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 59.60/59.56 => ( 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))
% 59.60/59.56 <=> ( V_w_2 = V_x_2
% 59.60/59.56 | V_y_2 = V_z_2 ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 59.60/59.56 ! [V_b,V_m,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_crossproduct__noteq,axiom,
% 59.60/59.56 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 59.60/59.56 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 59.60/59.56 => ( ( V_a_2 != V_b_2
% 59.60/59.56 & V_c_2 != V_d_2 )
% 59.60/59.56 <=> 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)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 59.60/59.56 ! [V_z,V_y,V_x,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__Suc__right,axiom,
% 59.60/59.56 ! [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)) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__Suc,axiom,
% 59.60/59.56 ! [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)) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__Suc__diff__eq1,axiom,
% 59.60/59.56 ! [V_m,V_j,V_k] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 59.60/59.56 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__Suc__diff__eq2,axiom,
% 59.60/59.56 ! [V_m,V_j,V_k] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 59.60/59.56 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__le__cancel__right,axiom,
% 59.60/59.56 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 59.60/59.56 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__le__cancel__left,axiom,
% 59.60/59.56 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 59.60/59.56 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__right__mono,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.60/59.56 => 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))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__left__mono,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.60/59.56 => 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))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__mono,axiom,
% 59.60/59.56 ! [V_d,V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__le__imp__le__right,axiom,
% 59.60/59.56 ! [V_b,V_c,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__le__imp__le__left,axiom,
% 59.60/59.56 ! [V_b,V_a,V_c,T_a] :
% 59.60/59.56 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__less__imp__less__left,axiom,
% 59.60/59.56 ! [V_b,V_a,V_c,T_a] :
% 59.60/59.56 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__less__imp__less__right,axiom,
% 59.60/59.56 ! [V_b,V_c,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__strict__mono,axiom,
% 59.60/59.56 ! [V_d,V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__strict__left__mono,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 59.60/59.56 => 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))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__strict__right__mono,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 59.60/59.56 => 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))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__less__cancel__left,axiom,
% 59.60/59.56 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 59.60/59.56 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__less__cancel__right,axiom,
% 59.60/59.56 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 59.60/59.56 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mono__iff__le__Suc,axiom,
% 59.60/59.56 ! [V_f_2,T_b] :
% 59.60/59.56 ( class_Orderings_Oorder(T_b)
% 59.60/59.56 => ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,T_b,V_f_2)
% 59.60/59.56 <=> ! [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)))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__class_Odistrib,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring(T_a)
% 59.60/59.56 => 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)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_combine__common__factor,axiom,
% 59.60/59.56 ! [V_c,V_b,V_e,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Osemiring(T_a)
% 59.60/59.56 => 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) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__diff__cancel,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Ogroup__add(T_a)
% 59.60/59.56 => 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 ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__add__cancel,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Ogroup__add(T_a)
% 59.60/59.56 => 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 ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_minus__add__distrib,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Oab__group__add(T_a)
% 59.60/59.56 => 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)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_minus__add,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Ogroup__add(T_a)
% 59.60/59.56 => 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)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__minus__cancel,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Ogroup__add(T_a)
% 59.60/59.56 => 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 ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_minus__add__cancel,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Ogroup__add(T_a)
% 59.60/59.56 => 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 ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_not__less__eq,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2] :
% 59.60/59.56 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__Suc__eq,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 59.60/59.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 59.60/59.56 | V_m_2 = V_n_2 ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__less__eq,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2] :
% 59.60/59.56 ( 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)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_not__less__less__Suc__eq,axiom,
% 59.60/59.56 ! [V_m_2,V_n_2] :
% 59.60/59.56 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 59.60/59.56 <=> V_n_2 = V_m_2 ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__antisym,axiom,
% 59.60/59.56 ! [V_m,V_n] :
% 59.60/59.56 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 59.60/59.56 => V_m = V_n ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__SucI,axiom,
% 59.60/59.56 ! [V_n,V_m] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__lessI,axiom,
% 59.60/59.56 ! [V_n,V_m] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.60/59.56 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__trans__Suc,axiom,
% 59.60/59.56 ! [V_k,V_j,V_i] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__SucE,axiom,
% 59.60/59.56 ! [V_n,V_m] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 59.60/59.56 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.60/59.56 => V_m = V_n ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__lessD,axiom,
% 59.60/59.56 ! [V_n,V_m] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__less__SucD,axiom,
% 59.60/59.56 ! [V_n,V_m] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__leD,axiom,
% 59.60/59.56 ! [V_n,V_m] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le__SucE,axiom,
% 59.60/59.56 ! [V_n,V_m] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 59.60/59.56 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 59.60/59.56 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le__SucI,axiom,
% 59.60/59.56 ! [V_n,V_m] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__le__mono,axiom,
% 59.60/59.56 ! [V_m_2,V_n_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le__Suc__eq,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 59.60/59.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 59.60/59.56 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_not__less__eq__eq,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2] :
% 59.60/59.56 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__n__not__le__n,axiom,
% 59.60/59.56 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_termination__basic__simps_I1_J,axiom,
% 59.60/59.56 ! [V_z,V_y,V_x] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 59.60/59.56 => 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))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_termination__basic__simps_I2_J,axiom,
% 59.60/59.56 ! [V_y,V_z,V_x] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 59.60/59.56 => 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))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_not__add__less1,axiom,
% 59.60/59.56 ! [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)) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_not__add__less2,axiom,
% 59.60/59.56 ! [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)) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__add__left__cancel__less,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2,V_k_2] :
% 59.60/59.56 ( 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)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_trans__less__add1,axiom,
% 59.60/59.56 ! [V_m,V_j,V_i] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 59.60/59.56 => 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))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_trans__less__add2,axiom,
% 59.60/59.56 ! [V_m,V_j,V_i] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 59.60/59.56 => 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))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__less__mono1,axiom,
% 59.60/59.56 ! [V_k,V_j,V_i] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 59.60/59.56 => 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))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__less__mono,axiom,
% 59.60/59.56 ! [V_l,V_k,V_j,V_i] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 59.60/59.56 => 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))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__add__eq__less,axiom,
% 59.60/59.56 ! [V_n,V_m,V_l,V_k] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 59.60/59.56 => ( 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)
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__lessD1,axiom,
% 59.60/59.56 ! [V_k,V_j,V_i] :
% 59.60/59.56 ( 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))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__Suc__Suc,axiom,
% 59.60/59.56 ! [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) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__diff__diff,axiom,
% 59.60/59.56 ! [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) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__mult__cancel1,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2,V_k_2] :
% 59.60/59.56 ( 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)
% 59.60/59.56 <=> V_m_2 = V_n_2 ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_termination__basic__simps_I4_J,axiom,
% 59.60/59.56 ! [V_y,V_z,V_x] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_termination__basic__simps_I3_J,axiom,
% 59.60/59.56 ! [V_z,V_y,V_x] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__leE,axiom,
% 59.60/59.56 ! [V_n,V_k,V_m] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 59.60/59.56 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 59.60/59.56 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__leD1,axiom,
% 59.60/59.56 ! [V_n,V_k,V_m] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__leD2,axiom,
% 59.60/59.56 ! [V_n,V_k,V_m] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__le__mono,axiom,
% 59.60/59.56 ! [V_l,V_k,V_j,V_i] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__le__mono1,axiom,
% 59.60/59.56 ! [V_k,V_j,V_i] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_trans__le__add2,axiom,
% 59.60/59.56 ! [V_m,V_j,V_i] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_trans__le__add1,axiom,
% 59.60/59.56 ! [V_m,V_j,V_i] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__add__left__cancel__le,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2,V_k_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le__iff__add,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 59.60/59.56 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le__add1,axiom,
% 59.60/59.56 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le__add2,axiom,
% 59.60/59.56 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__add__inverse2,axiom,
% 59.60/59.56 ! [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 ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__add__inverse,axiom,
% 59.60/59.56 ! [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 ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__diff__left,axiom,
% 59.60/59.56 ! [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)) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__cancel,axiom,
% 59.60/59.56 ! [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) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__cancel2,axiom,
% 59.60/59.56 ! [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) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__mult__distrib,axiom,
% 59.60/59.56 ! [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)) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__mult__distrib2,axiom,
% 59.60/59.56 ! [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)) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 59.60/59.56 ! [V_m,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 59.60/59.56 ! [V_a,V_m,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 59.60/59.56 ! [V_m,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 59.60/59.56 ! [V_y,V_x,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__ring__1(T_a)
% 59.60/59.56 => 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)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__less__le__mono,axiom,
% 59.60/59.56 ! [V_d,V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__le__less__mono,axiom,
% 59.60/59.56 ! [V_d,V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__add__one,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__semidom(T_a)
% 59.60/59.56 => 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)))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_eq__add__iff2,axiom,
% 59.60/59.56 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 59.60/59.56 ( class_Rings_Oring(T_b)
% 59.60/59.56 => ( 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)
% 59.60/59.56 <=> 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) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_eq__add__iff1,axiom,
% 59.60/59.56 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 59.60/59.56 ( class_Rings_Oring(T_b)
% 59.60/59.56 => ( 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)
% 59.60/59.56 <=> 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 ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__def,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Ogroup__add(T_a)
% 59.60/59.56 => 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)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_ab__diff__minus,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Oab__group__add(T_a)
% 59.60/59.56 => 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)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__minus__eq__add,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Ogroup__add(T_a)
% 59.60/59.56 => 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) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__le__lessD,axiom,
% 59.60/59.56 ! [V_n,V_m] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le__less__Suc__eq,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 59.60/59.56 <=> V_n_2 = V_m_2 ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__leI,axiom,
% 59.60/59.56 ! [V_n,V_m] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le__imp__less__Suc,axiom,
% 59.60/59.56 ! [V_n,V_m] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__le__eq,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__Suc__eq__le,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__eq__Suc__le,axiom,
% 59.60/59.56 ! [V_m_2,V_n_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__less__Suc,axiom,
% 59.60/59.56 ! [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))) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__mult__less__cancel1,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2,V_k_2] :
% 59.60/59.56 ( 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)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__diff__le,axiom,
% 59.60/59.56 ! [V_m,V_n] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 59.60/59.56 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__mult__le__cancel1,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2,V_k_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__diff__conv,axiom,
% 59.60/59.56 ! [V_k_2,V_j_2,V_i_2] :
% 59.60/59.56 ( 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)))
% 59.60/59.56 <=> 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)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__diff__inverse,axiom,
% 59.60/59.56 ! [V_n,V_m] :
% 59.60/59.56 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.60/59.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__diff__right,axiom,
% 59.60/59.56 ! [V_i,V_j,V_k] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 59.60/59.56 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le__diff__conv,axiom,
% 59.60/59.56 ! [V_i_2,V_k_2,V_j_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le__add__diff,axiom,
% 59.60/59.56 ! [V_m,V_n,V_k] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le__add__diff__inverse,axiom,
% 59.60/59.56 ! [V_m,V_n] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 59.60/59.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__diff__assoc,axiom,
% 59.60/59.56 ! [V_i,V_j,V_k] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 59.60/59.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le__diff__conv2,axiom,
% 59.60/59.56 ! [V_i_2,V_j_2,V_k_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le__add__diff__inverse2,axiom,
% 59.60/59.56 ! [V_m,V_n] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 59.60/59.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le__imp__diff__is__add,axiom,
% 59.60/59.56 ! [V_k_2,V_j_2,V_i_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 59.60/59.56 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 59.60/59.56 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__add__assoc,axiom,
% 59.60/59.56 ! [V_i,V_j,V_k] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 59.60/59.56 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__diff__assoc2,axiom,
% 59.60/59.56 ! [V_i,V_j,V_k] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 59.60/59.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__add__assoc2,axiom,
% 59.60/59.56 ! [V_i,V_j,V_k] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 59.60/59.56 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__Suc__1,axiom,
% 59.60/59.56 ! [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 ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__eq__Suc__le__raw,axiom,
% 59.60/59.56 ! [V_n_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le__add__iff2,axiom,
% 59.60/59.56 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 59.60/59.56 ( class_Rings_Oordered__ring(T_b)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> 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))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le__add__iff1,axiom,
% 59.60/59.56 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 59.60/59.56 ( class_Rings_Oordered__ring(T_b)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> 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)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__add__iff2,axiom,
% 59.60/59.56 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 59.60/59.56 ( class_Rings_Oordered__ring(T_b)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> 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))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__add__iff1,axiom,
% 59.60/59.56 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 59.60/59.56 ( class_Rings_Oordered__ring(T_b)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> 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)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 59.60/59.56 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 59.60/59.56 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 59.60/59.56 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 59.60/59.56 ! [V_rx,V_ly,V_lx,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 59.60/59.56 ! [V_rx,V_ly,V_lx,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 59.60/59.56 ! [V_ry,V_rx,V_lx,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 59.60/59.56 ! [V_ry,V_rx,V_lx,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card__insert__disjoint,axiom,
% 59.60/59.56 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.56 => 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)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card__insert__if,axiom,
% 59.60/59.56 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.56 => 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) )
% 59.60/59.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.56 => 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)) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card_Ounion__inter,axiom,
% 59.60/59.56 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.56 => 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)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card__Un__Int,axiom,
% 59.60/59.56 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.56 => 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))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card__insert,axiom,
% 59.60/59.56 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => 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)))))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card__Un__disjoint,axiom,
% 59.60/59.56 ! [V_B_2,V_A_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.60/59.56 => ( 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))
% 59.60/59.56 => 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)) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_card_Oinsert,axiom,
% 59.60/59.56 ! [V_x_2,V_A_2,T_b] :
% 59.60/59.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.60/59.56 => 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)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__less__add__iff2,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__less__add__iff1,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__le__add__iff1,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__diff__add__eq1,axiom,
% 59.60/59.56 ! [V_n,V_m,V_u,V_i,V_j] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 59.60/59.56 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__eq__add__iff1,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 59.60/59.56 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
% 59.60/59.56 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) = V_n_2 ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__le__add__iff2,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__diff__add__eq2,axiom,
% 59.60/59.56 ! [V_n,V_m,V_u,V_j,V_i] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 59.60/59.56 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)),V_u)),V_n)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_left__add__mult__distrib,axiom,
% 59.60/59.56 ! [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) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__eq__add__iff2,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 59.60/59.56 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
% 59.60/59.56 <=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 59.60/59.56 ! [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) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__eq__plus1,axiom,
% 59.60/59.56 ! [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)) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__eq__plus1__left,axiom,
% 59.60/59.56 ! [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) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_finite__fun__UNIVD1,axiom,
% 59.60/59.56 ! [T_c,T_b] :
% 59.60/59.56 ( 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))))
% 59.60/59.56 => ( 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))
% 59.60/59.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__Max__commute,axiom,
% 59.60/59.56 ! [V_k_2,V_N_2,T_b] :
% 59.60/59.56 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 59.60/59.56 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.56 => 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))))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__Min__commute,axiom,
% 59.60/59.56 ! [V_k_2,V_N_2,T_b] :
% 59.60/59.56 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 59.60/59.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 59.60/59.56 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.56 => 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))))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__zeroE,axiom,
% 59.60/59.56 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le0,axiom,
% 59.60/59.56 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_zero__less__Suc,axiom,
% 59.60/59.56 ! [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))) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_bot__nat__def,axiom,
% 59.60/59.56 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_zero__reorient,axiom,
% 59.60/59.56 ! [V_x_2,T_b] :
% 59.60/59.56 ( class_Groups_Ozero(T_b)
% 59.60/59.56 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 59.60/59.56 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__0__iff,axiom,
% 59.60/59.56 ! [V_a_2,V_b_2,T_b] :
% 59.60/59.56 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 59.60/59.56 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
% 59.60/59.56 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__0__left,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Groups_Omonoid__add(T_a)
% 59.60/59.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__0,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 59.60/59.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_double__zero__sym,axiom,
% 59.60/59.56 ! [V_a_2,T_b] :
% 59.60/59.56 ( class_Groups_Olinordered__ab__group__add(T_b)
% 59.60/59.56 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 59.60/59.56 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__0__right,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Groups_Omonoid__add(T_a)
% 59.60/59.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add_Ocomm__neutral,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 59.60/59.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.60/59.56 => 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) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__zero__left,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Rings_Omult__zero(T_a)
% 59.60/59.56 => 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) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__zero__right,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Rings_Omult__zero(T_a)
% 59.60/59.56 => 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) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__eq__0__iff,axiom,
% 59.60/59.56 ! [V_b_2,V_a_2,T_b] :
% 59.60/59.56 ( class_Rings_Oring__no__zero__divisors(T_b)
% 59.60/59.56 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 59.60/59.56 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 59.60/59.56 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_no__zero__divisors,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ono__zero__divisors(T_a)
% 59.60/59.56 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 59.60/59.56 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 59.60/59.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_divisors__zero,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Ono__zero__divisors(T_a)
% 59.60/59.56 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 59.60/59.56 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 59.60/59.56 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_right__minus__eq,axiom,
% 59.60/59.56 ! [V_b_2,V_a_2,T_b] :
% 59.60/59.56 ( class_Groups_Ogroup__add(T_b)
% 59.60/59.56 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 59.60/59.56 <=> V_a_2 = V_b_2 ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_eq__iff__diff__eq__0,axiom,
% 59.60/59.56 ! [V_b_2,V_a_2,T_b] :
% 59.60/59.56 ( class_Groups_Oab__group__add(T_b)
% 59.60/59.56 => ( V_a_2 = V_b_2
% 59.60/59.56 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__self,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Groups_Ogroup__add(T_a)
% 59.60/59.56 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__0__right,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Groups_Ogroup__add(T_a)
% 59.60/59.56 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_one__neq__zero,axiom,
% 59.60/59.56 ! [T_a] :
% 59.60/59.56 ( class_Rings_Ozero__neq__one(T_a)
% 59.60/59.56 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_zero__neq__one,axiom,
% 59.60/59.56 ! [T_a] :
% 59.60/59.56 ( class_Rings_Ozero__neq__one(T_a)
% 59.60/59.56 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_minus__zero,axiom,
% 59.60/59.56 ! [T_a] :
% 59.60/59.56 ( class_Groups_Ogroup__add(T_a)
% 59.60/59.56 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_neg__0__equal__iff__equal,axiom,
% 59.60/59.56 ! [V_a_2,T_b] :
% 59.60/59.56 ( class_Groups_Ogroup__add(T_b)
% 59.60/59.56 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 59.60/59.56 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_equal__neg__zero,axiom,
% 59.60/59.56 ! [V_a_2,T_b] :
% 59.60/59.56 ( class_Groups_Olinordered__ab__group__add(T_b)
% 59.60/59.56 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 59.60/59.56 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_neg__equal__0__iff__equal,axiom,
% 59.60/59.56 ! [V_a_2,T_b] :
% 59.60/59.56 ( class_Groups_Ogroup__add(T_b)
% 59.60/59.56 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 59.60/59.56 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_neg__equal__zero,axiom,
% 59.60/59.56 ! [V_a_2,T_b] :
% 59.60/59.56 ( class_Groups_Olinordered__ab__group__add(T_b)
% 59.60/59.56 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 59.60/59.56 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Zero__not__Suc,axiom,
% 59.60/59.56 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat_Osimps_I2_J,axiom,
% 59.60/59.56 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__not__Zero,axiom,
% 59.60/59.56 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat_Osimps_I3_J,axiom,
% 59.60/59.56 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Zero__neq__Suc,axiom,
% 59.60/59.56 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Suc__neq__Zero,axiom,
% 59.60/59.56 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_not__less0,axiom,
% 59.60/59.56 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_neq0__conv,axiom,
% 59.60/59.56 ! [V_n_2] :
% 59.60/59.56 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__nat__zero__code,axiom,
% 59.60/59.56 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_gr__implies__not0,axiom,
% 59.60/59.56 ! [V_n,V_m] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.60/59.56 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_gr0I,axiom,
% 59.60/59.56 ! [V_n] :
% 59.60/59.56 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_plus__nat_Oadd__0,axiom,
% 59.60/59.56 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Nat_Oadd__0__right,axiom,
% 59.60/59.56 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__is__0,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2] :
% 59.60/59.56 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.60/59.56 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.60/59.56 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__eq__self__zero,axiom,
% 59.60/59.56 ! [V_n,V_m] :
% 59.60/59.56 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 59.60/59.56 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le__0__eq,axiom,
% 59.60/59.56 ! [V_n_2] :
% 59.60/59.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 59.60/59.56 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 59.60/59.56 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__0__eq__0,axiom,
% 59.60/59.56 ! [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) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_minus__nat_Odiff__0,axiom,
% 59.60/59.56 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diff__self__eq__0,axiom,
% 59.60/59.56 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_diffs0__imp__equal,axiom,
% 59.60/59.56 ! [V_n,V_m] :
% 59.60/59.56 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.60/59.56 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.60/59.56 => V_m = V_n ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__cancel2,axiom,
% 59.60/59.56 ! [V_n_2,V_k_2,V_m_2] :
% 59.60/59.56 ( 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)
% 59.60/59.56 <=> ( V_m_2 = V_n_2
% 59.60/59.56 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__cancel1,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2,V_k_2] :
% 59.60/59.56 ( 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)
% 59.60/59.56 <=> ( V_m_2 = V_n_2
% 59.60/59.56 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__is__0,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2] :
% 59.60/59.56 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.60/59.56 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.60/59.56 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__0__right,axiom,
% 59.60/59.56 ! [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) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__0,axiom,
% 59.60/59.56 ! [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) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 59.60/59.56 ! [V_n_2,V_m_2,V_k_2] :
% 59.60/59.56 ( 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)
% 59.60/59.56 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.60/59.56 | V_m_2 = V_n_2 ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_sum__squares__eq__zero__iff,axiom,
% 59.60/59.56 ! [V_y_2,V_x_2,T_b] :
% 59.60/59.56 ( class_Rings_Olinordered__ring__strict(T_b)
% 59.60/59.56 => ( 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)
% 59.60/59.56 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 59.60/59.56 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_Least__Suc,axiom,
% 59.60/59.56 ! [V_n_2,V_P_2] :
% 59.60/59.56 ( hBOOL(hAPP(V_P_2,V_n_2))
% 59.60/59.56 => ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 59.60/59.56 => 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))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_sum__squares__le__zero__iff,axiom,
% 59.60/59.56 ! [V_y_2,V_x_2,T_b] :
% 59.60/59.56 ( class_Rings_Olinordered__ring__strict(T_b)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 59.60/59.56 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_sum__squares__ge__zero,axiom,
% 59.60/59.56 ! [V_y,V_x,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__ring(T_a)
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_sum__squares__gt__zero__iff,axiom,
% 59.60/59.56 ! [V_y_2,V_x_2,T_b] :
% 59.60/59.56 ( class_Rings_Olinordered__ring__strict(T_b)
% 59.60/59.56 => ( 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))))
% 59.60/59.56 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 59.60/59.56 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_not__sum__squares__lt__zero,axiom,
% 59.60/59.56 ! [V_y,V_x,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__ring(T_a)
% 59.60/59.56 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 59.60/59.56 ! [V_a_2,T_b] :
% 59.60/59.56 ( class_Groups_Olinordered__ab__group__add(T_b)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 59.60/59.56 ! [V_a_2,T_b] :
% 59.60/59.56 ( class_Groups_Olinordered__ab__group__add(T_b)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__nonneg__nonneg,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__nonneg__eq__0__iff,axiom,
% 59.60/59.56 ! [V_y_2,V_x_2,T_b] :
% 59.60/59.56 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 59.60/59.56 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 59.60/59.56 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 59.60/59.56 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__increasing,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__increasing2,axiom,
% 59.60/59.56 ! [V_a,V_b,V_c,T_a] :
% 59.60/59.56 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__nonpos__nonpos,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_zero__le__square,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__ring(T_a)
% 59.60/59.56 => 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))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_zero__le__mult__iff,axiom,
% 59.60/59.56 ! [V_b_2,V_a_2,T_b] :
% 59.60/59.56 ( class_Rings_Olinordered__ring__strict(T_b)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 59.60/59.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 59.60/59.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.60/59.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__le__0__iff,axiom,
% 59.60/59.56 ! [V_b_2,V_a_2,T_b] :
% 59.60/59.56 ( class_Rings_Olinordered__ring__strict(T_b)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 59.60/59.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 59.60/59.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.60/59.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__nonneg__nonneg,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Oordered__cancel__semiring(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__nonneg__nonpos,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Oordered__cancel__semiring(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__nonneg__nonpos2,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Oordered__cancel__semiring(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__nonpos__nonneg,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Oordered__cancel__semiring(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__nonpos__nonpos,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Oordered__ring(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__right__mono,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Oordered__semiring(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__left__mono,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Oordered__semiring(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__mult__left__mono,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Oordered__comm__semiring(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__right__mono__neg,axiom,
% 59.60/59.56 ! [V_c,V_a,V_b,T_a] :
% 59.60/59.56 ( class_Rings_Oordered__ring(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__left__mono__neg,axiom,
% 59.60/59.56 ! [V_c,V_a,V_b,T_a] :
% 59.60/59.56 ( class_Rings_Oordered__ring(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__mono_H,axiom,
% 59.60/59.56 ! [V_d,V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Oordered__semiring(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__mono,axiom,
% 59.60/59.56 ! [V_d,V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Oordered__semiring(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_split__mult__pos__le,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Oordered__ring(T_a)
% 59.60/59.56 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.60/59.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 59.60/59.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 59.60/59.56 => 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))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_split__mult__neg__le,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Oordered__cancel__semiring(T_a)
% 59.60/59.56 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.60/59.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 59.60/59.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 59.60/59.56 => 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))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_pos__add__strict,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__semidom(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 59.60/59.56 ! [V_a_2,T_b] :
% 59.60/59.56 ( class_Groups_Olinordered__ab__group__add(T_b)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 59.60/59.56 ! [V_a_2,T_b] :
% 59.60/59.56 ( class_Groups_Olinordered__ab__group__add(T_b)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__pos__pos,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_add__neg__neg,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__strict__left__mono__neg,axiom,
% 59.60/59.56 ! [V_c,V_a,V_b,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__strict__right__mono__neg,axiom,
% 59.60/59.56 ! [V_c,V_a,V_b,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_comm__mult__strict__left__mono,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__strict__left__mono,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__strict__right__mono,axiom,
% 59.60/59.56 ! [V_c,V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__neg__neg,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__neg__pos,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__less__cancel__left__neg,axiom,
% 59.60/59.56 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 59.60/59.56 ( class_Rings_Olinordered__ring__strict(T_b)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_zero__less__mult__pos2,axiom,
% 59.60/59.56 ! [V_a,V_b,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_zero__less__mult__pos,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.60/59.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__pos__neg2,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__pos__neg,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__pos__pos,axiom,
% 59.60/59.56 ! [V_b,V_a,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 59.60/59.56 => 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))) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__less__cancel__left__pos,axiom,
% 59.60/59.56 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 59.60/59.56 ( class_Rings_Olinordered__ring__strict(T_b)
% 59.60/59.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__less__cancel__left__disj,axiom,
% 59.60/59.56 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 59.60/59.56 ( class_Rings_Olinordered__ring__strict(T_b)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.60/59.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 59.60/59.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.60/59.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_mult__less__cancel__right__disj,axiom,
% 59.60/59.56 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 59.60/59.56 ( class_Rings_Olinordered__ring__strict(T_b)
% 59.60/59.56 => ( 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)))
% 59.60/59.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.60/59.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 59.60/59.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.60/59.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_not__square__less__zero,axiom,
% 59.60/59.56 ! [V_a,T_a] :
% 59.60/59.56 ( class_Rings_Olinordered__ring(T_a)
% 59.60/59.56 => ~ 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))) ) ).
% 59.60/59.56
% 59.60/59.56 fof(fact_le__iff__diff__le__0,axiom,
% 59.60/59.56 ! [V_b_2,V_a_2,T_b] :
% 59.60/59.56 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.60/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 59.60/59.57 <=> 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))) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_less__iff__diff__less__0,axiom,
% 59.60/59.57 ! [V_b_2,V_a_2,T_b] :
% 59.60/59.57 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.60/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 59.60/59.57 <=> 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))) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_add__scale__eq__noteq,axiom,
% 59.60/59.57 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 59.60/59.57 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 59.60/59.57 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 59.60/59.57 => ( ( V_a = V_b
% 59.60/59.57 & V_c != V_d )
% 59.60/59.57 => 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)) ) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_zero__le__one,axiom,
% 59.60/59.57 ! [T_a] :
% 59.60/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.60/59.57 => 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))) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_not__one__le__zero,axiom,
% 59.60/59.57 ! [T_a] :
% 59.60/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.60/59.57 => ~ 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))) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_zero__less__one,axiom,
% 59.60/59.57 ! [T_a] :
% 59.60/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.60/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_not__one__less__zero,axiom,
% 59.60/59.57 ! [T_a] :
% 59.60/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.60/59.57 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_minus__le__self__iff,axiom,
% 59.60/59.57 ! [V_a_2,T_b] :
% 59.60/59.57 ( class_Groups_Olinordered__ab__group__add(T_b)
% 59.60/59.57 => ( 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))
% 59.60/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_neg__le__0__iff__le,axiom,
% 59.60/59.57 ! [V_a_2,T_b] :
% 59.60/59.57 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.60/59.57 => ( 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)))
% 59.60/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_le__minus__self__iff,axiom,
% 59.60/59.57 ! [V_a_2,T_b] :
% 59.60/59.57 ( class_Groups_Olinordered__ab__group__add(T_b)
% 59.60/59.57 => ( 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)))
% 59.60/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_neg__0__le__iff__le,axiom,
% 59.60/59.57 ! [V_a_2,T_b] :
% 59.60/59.57 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.60/59.57 => ( 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)))
% 59.60/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_neg__less__nonneg,axiom,
% 59.60/59.57 ! [V_a_2,T_b] :
% 59.60/59.57 ( class_Groups_Olinordered__ab__group__add(T_b)
% 59.60/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 59.60/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_neg__less__0__iff__less,axiom,
% 59.60/59.57 ! [V_a_2,T_b] :
% 59.60/59.57 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.60/59.57 => ( 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)))
% 59.60/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_neg__0__less__iff__less,axiom,
% 59.60/59.57 ! [V_a_2,T_b] :
% 59.60/59.57 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.60/59.57 => ( 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)))
% 59.60/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_less__minus__self__iff,axiom,
% 59.60/59.57 ! [V_a_2,T_b] :
% 59.60/59.57 ( class_Rings_Olinordered__idom(T_b)
% 59.60/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 59.60/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_minus__Min__eq__Max,axiom,
% 59.60/59.57 ! [V_S_2,T_b] :
% 59.60/59.57 ( class_Groups_Olinordered__ab__group__add(T_b)
% 59.60/59.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 59.60/59.57 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.57 => 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)) ) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_minus__Max__eq__Min,axiom,
% 59.60/59.57 ! [V_S_2,T_b] :
% 59.60/59.57 ( class_Groups_Olinordered__ab__group__add(T_b)
% 59.60/59.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 59.60/59.57 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.60/59.57 => 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)) ) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_right__minus,axiom,
% 59.60/59.57 ! [V_a,T_a] :
% 59.60/59.57 ( class_Groups_Ogroup__add(T_a)
% 59.60/59.57 => 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) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 59.60/59.57 ! [V_b_2,V_a_2,T_b] :
% 59.60/59.57 ( class_Groups_Ogroup__add(T_b)
% 59.60/59.57 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 59.60/59.57 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_left__minus,axiom,
% 59.60/59.57 ! [V_a,T_a] :
% 59.60/59.57 ( class_Groups_Ogroup__add(T_a)
% 59.60/59.57 => 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) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_ab__left__minus,axiom,
% 59.60/59.57 ! [V_a,T_a] :
% 59.60/59.57 ( class_Groups_Oab__group__add(T_a)
% 59.60/59.57 => 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) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_minus__unique,axiom,
% 59.60/59.57 ! [V_b,V_a,T_a] :
% 59.60/59.57 ( class_Groups_Ogroup__add(T_a)
% 59.60/59.57 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 59.60/59.57 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_diff__0,axiom,
% 59.60/59.57 ! [V_a,T_a] :
% 59.60/59.57 ( class_Groups_Ogroup__add(T_a)
% 59.60/59.57 => 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) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_less__Suc__eq__0__disj,axiom,
% 59.60/59.57 ! [V_n_2,V_m_2] :
% 59.60/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 59.60/59.57 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.60/59.57 | ? [B_j] :
% 59.60/59.57 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 59.60/59.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_less__Suc0,axiom,
% 59.60/59.57 ! [V_n_2] :
% 59.60/59.57 ( 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))))
% 59.60/59.57 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_gr0__conv__Suc,axiom,
% 59.60/59.57 ! [V_n_2] :
% 59.60/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 59.60/59.57 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_one__is__add,axiom,
% 59.60/59.57 ! [V_n_2,V_m_2] :
% 59.60/59.57 ( 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)
% 59.60/59.57 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 59.60/59.57 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 59.60/59.57 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.60/59.57 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_add__is__1,axiom,
% 59.60/59.57 ! [V_n_2,V_m_2] :
% 59.60/59.57 ( 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))
% 59.60/59.57 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 59.60/59.57 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 59.60/59.57 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.60/59.57 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_add__gr__0,axiom,
% 59.60/59.57 ! [V_n_2,V_m_2] :
% 59.60/59.57 ( 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)))
% 59.60/59.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 59.60/59.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_card_Oempty,axiom,
% 59.60/59.57 ! [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) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_card__infinite,axiom,
% 59.60/59.57 ! [V_A_2,T_b] :
% 59.60/59.57 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.60/59.57 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_mult__eq__1__iff,axiom,
% 59.60/59.57 ! [V_n_2,V_m_2] :
% 59.60/59.57 ( 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))
% 59.60/59.57 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 59.60/59.57 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_zero__less__diff,axiom,
% 59.60/59.57 ! [V_m_2,V_n_2] :
% 59.60/59.57 ( 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)))
% 59.60/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_diff__less,axiom,
% 59.60/59.57 ! [V_m,V_n] :
% 59.60/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 59.60/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 59.60/59.57 => 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)) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_mult__less__mono2,axiom,
% 59.60/59.57 ! [V_k,V_j,V_i] :
% 59.60/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 59.60/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 59.60/59.57 => 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))) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_mult__less__mono1,axiom,
% 59.60/59.57 ! [V_k,V_j,V_i] :
% 59.60/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 59.60/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 59.60/59.57 => 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))) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_mult__less__cancel2,axiom,
% 59.60/59.57 ! [V_n_2,V_k_2,V_m_2] :
% 59.60/59.57 ( 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)))
% 59.60/59.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 59.60/59.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_mult__less__cancel1,axiom,
% 59.60/59.57 ! [V_n_2,V_m_2,V_k_2] :
% 59.60/59.57 ( 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)))
% 59.60/59.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 59.60/59.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_nat__0__less__mult__iff,axiom,
% 59.60/59.57 ! [V_n_2,V_m_2] :
% 59.60/59.57 ( 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)))
% 59.60/59.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 59.60/59.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_nat__mult__less__cancel1,axiom,
% 59.60/59.57 ! [V_n_2,V_m_2,V_k_2] :
% 59.60/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 59.60/59.57 => ( 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)))
% 59.60/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_nat__mult__eq__cancel1,axiom,
% 59.60/59.57 ! [V_n_2,V_m_2,V_k_2] :
% 59.60/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 59.60/59.57 => ( 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)
% 59.60/59.57 <=> V_m_2 = V_n_2 ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_diff__add__0,axiom,
% 59.60/59.57 ! [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) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_diff__is__0__eq,axiom,
% 59.60/59.57 ! [V_n_2,V_m_2] :
% 59.60/59.57 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.60/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_diff__is__0__eq_H,axiom,
% 59.60/59.57 ! [V_n,V_m] :
% 59.60/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 59.60/59.57 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_One__nat__def,axiom,
% 59.60/59.57 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_Max_Osingleton,axiom,
% 59.60/59.57 ! [V_x_2,T_b] :
% 59.60/59.57 ( class_Orderings_Olinorder(T_b)
% 59.60/59.57 => 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 ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_Min_Osingleton,axiom,
% 59.60/59.57 ! [V_x_2,T_b] :
% 59.60/59.57 ( class_Orderings_Olinorder(T_b)
% 59.60/59.57 => 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 ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_mult__eq__self__implies__10,axiom,
% 59.60/59.57 ! [V_n,V_m] :
% 59.60/59.57 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 59.60/59.57 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 59.60/59.57 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 59.60/59.57
% 59.60/59.57 fof(fact_Suc__pred_H,axiom,
% 59.60/59.57 ! [V_n] :
% 59.60/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 59.60/59.57 => 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))) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_add__eq__if,axiom,
% 59.73/59.57 ! [V_n,V_m] :
% 59.73/59.57 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 59.73/59.57 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.57 => 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)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_add__pos__nonneg,axiom,
% 59.73/59.57 ! [V_b,V_a,T_a] :
% 59.73/59.57 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 59.73/59.57 => 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))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_add__nonneg__pos,axiom,
% 59.73/59.57 ! [V_b,V_a,T_a] :
% 59.73/59.57 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 59.73/59.57 => 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))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_add__strict__increasing,axiom,
% 59.73/59.57 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.57 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 59.73/59.57 => 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))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_add__strict__increasing2,axiom,
% 59.73/59.57 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.57 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 59.73/59.57 => 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))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_add__neg__nonpos,axiom,
% 59.73/59.57 ! [V_b,V_a,T_a] :
% 59.73/59.57 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.57 => 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))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_add__nonpos__neg,axiom,
% 59.73/59.57 ! [V_b,V_a,T_a] :
% 59.73/59.57 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.57 => 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))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mult__le__cancel__left__pos,axiom,
% 59.73/59.57 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 59.73/59.57 ( class_Rings_Olinordered__ring__strict(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.57 => ( 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)))
% 59.73/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mult__le__cancel__left__neg,axiom,
% 59.73/59.57 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 59.73/59.57 ( class_Rings_Olinordered__ring__strict(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.57 => ( 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)))
% 59.73/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mult__strict__mono,axiom,
% 59.73/59.57 ! [V_d,V_c,V_b,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semiring__strict(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.73/59.57 => 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))) ) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mult__strict__mono_H,axiom,
% 59.73/59.57 ! [V_d,V_c,V_b,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semiring__strict(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.73/59.57 => 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))) ) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mult__less__le__imp__less,axiom,
% 59.73/59.57 ! [V_d,V_c,V_b,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semiring__strict(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.73/59.57 => 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))) ) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mult__le__less__imp__less,axiom,
% 59.73/59.57 ! [V_d,V_c,V_b,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semiring__strict(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.73/59.57 => 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))) ) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mult__right__less__imp__less,axiom,
% 59.73/59.57 ! [V_b,V_c,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semiring(T_a)
% 59.73/59.57 => ( 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)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mult__less__imp__less__right,axiom,
% 59.73/59.57 ! [V_b,V_c,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semiring__strict(T_a)
% 59.73/59.57 => ( 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)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mult__left__less__imp__less,axiom,
% 59.73/59.57 ! [V_b,V_a,V_c,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semiring(T_a)
% 59.73/59.57 => ( 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)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mult__less__imp__less__left,axiom,
% 59.73/59.57 ! [V_b,V_a,V_c,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semiring__strict(T_a)
% 59.73/59.57 => ( 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)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mult__right__le__imp__le,axiom,
% 59.73/59.57 ! [V_b,V_c,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semiring__strict(T_a)
% 59.73/59.57 => ( 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)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mult__left__le__imp__le,axiom,
% 59.73/59.57 ! [V_b,V_a,V_c,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semiring__strict(T_a)
% 59.73/59.57 => ( 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)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mult__eq__if,axiom,
% 59.73/59.57 ! [V_n,V_m] :
% 59.73/59.57 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 59.73/59.57 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.57 => 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)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mult__left__le__one__le,axiom,
% 59.73/59.57 ! [V_y,V_x,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 59.73/59.57 => 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)) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mult__right__le__one__le,axiom,
% 59.73/59.57 ! [V_y,V_x,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 59.73/59.57 => 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)) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zero__less__two,axiom,
% 59.73/59.57 ! [T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => 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)))) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_card__eq__0__iff,axiom,
% 59.73/59.57 ! [V_A_2,T_b] :
% 59.73/59.57 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.57 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.57 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_card__ge__0__finite,axiom,
% 59.73/59.57 ! [V_A_2,T_b] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Suc__pred,axiom,
% 59.73/59.57 ! [V_n] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 59.73/59.57 => 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 ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_diff__Suc__less,axiom,
% 59.73/59.57 ! [V_i,V_n] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 59.73/59.57 => 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)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_n__less__m__mult__n,axiom,
% 59.73/59.57 ! [V_m,V_n] :
% 59.73/59.57 ( 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))
% 59.73/59.57 => ( 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))
% 59.73/59.57 => 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))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_n__less__n__mult__m,axiom,
% 59.73/59.57 ! [V_m,V_n] :
% 59.73/59.57 ( 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))
% 59.73/59.57 => ( 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))
% 59.73/59.57 => 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))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_one__less__mult,axiom,
% 59.73/59.57 ! [V_m,V_n] :
% 59.73/59.57 ( 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))
% 59.73/59.57 => ( 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))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_nat__diff__split__asm,axiom,
% 59.73/59.57 ! [V_b_2,V_a_2,V_P_2] :
% 59.73/59.57 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 59.73/59.57 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 59.73/59.57 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 59.73/59.57 | ? [B_d] :
% 59.73/59.57 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 59.73/59.57 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_nat__diff__split,axiom,
% 59.73/59.57 ! [V_b_2,V_a_2,V_P_2] :
% 59.73/59.57 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 59.73/59.57 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 59.73/59.57 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 59.73/59.57 & ! [B_d] :
% 59.73/59.57 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 59.73/59.57 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_one__le__mult__iff,axiom,
% 59.73/59.57 ! [V_n_2,V_m_2] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
% 59.73/59.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2))
% 59.73/59.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mult__le__cancel1,axiom,
% 59.73/59.57 ! [V_n_2,V_m_2,V_k_2] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mult__le__cancel2,axiom,
% 59.73/59.57 ! [V_n_2,V_k_2,V_m_2] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_nat__mult__le__cancel1,axiom,
% 59.73/59.57 ! [V_n_2,V_m_2,V_k_2] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 59.73/59.57 => ( 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)))
% 59.73/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Min__le,axiom,
% 59.73/59.57 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.57 ( class_Orderings_Olinorder(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.57 => 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)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Max__ge,axiom,
% 59.73/59.57 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.57 ( class_Orderings_Olinorder(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.57 => 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))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Max__in,axiom,
% 59.73/59.57 ! [V_A_2,T_b] :
% 59.73/59.57 ( class_Orderings_Olinorder(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Min__in,axiom,
% 59.73/59.57 ! [V_A_2,T_b] :
% 59.73/59.57 ( class_Orderings_Olinorder(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_card__less__Suc2,axiom,
% 59.73/59.57 ! [V_i_2,V_M_2] :
% 59.73/59.57 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 59.73/59.57 => 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))))) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_card__less,axiom,
% 59.73/59.57 ! [V_i_2,V_M_2] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 59.73/59.57 => 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) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_card__less__Suc,axiom,
% 59.73/59.57 ! [V_i_2,V_M_2] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 59.73/59.57 => 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))))) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_convex__bound__le,axiom,
% 59.73/59.57 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semiring__1(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 59.73/59.57 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 59.73/59.57 => 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)) ) ) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_card__gt__0__iff,axiom,
% 59.73/59.57 ! [V_A_2,T_b] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.57 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_finite__UNIV__card__ge__0,axiom,
% 59.73/59.57 ! [T_b] :
% 59.73/59.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 59.73/59.57 => 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))))) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Suc__diff__1,axiom,
% 59.73/59.57 ! [V_n] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 59.73/59.57 => 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 ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Max__mono,axiom,
% 59.73/59.57 ! [V_N_2,V_M_2,T_b] :
% 59.73/59.57 ( class_Orderings_Olinorder(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 59.73/59.57 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 59.73/59.57 => 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))) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Min__antimono,axiom,
% 59.73/59.57 ! [V_N_2,V_M_2,T_b] :
% 59.73/59.57 ( class_Orderings_Olinorder(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 59.73/59.57 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 59.73/59.57 => 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))) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_card__def,axiom,
% 59.73/59.57 ! [V_A_2,T_b] :
% 59.73/59.57 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 => 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) )
% 59.73/59.57 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_card_Oeq__fold__g,axiom,
% 59.73/59.57 ! [V_A_2,T_b] :
% 59.73/59.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 => 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) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_convex__bound__lt,axiom,
% 59.73/59.57 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 59.73/59.57 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 59.73/59.57 => 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)) ) ) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_even__less__0__iff,axiom,
% 59.73/59.57 ! [V_a_2,T_b] :
% 59.73/59.57 ( class_Rings_Olinordered__idom(T_b)
% 59.73/59.57 => ( 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)))
% 59.73/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_card_Ounion__inter__neutral,axiom,
% 59.73/59.57 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.57 => ( ( ? [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)))
% 59.73/59.57 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 59.73/59.57 => 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)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_card__Suc__eq,axiom,
% 59.73/59.57 ! [V_k_2,V_A_2,T_b] :
% 59.73/59.57 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 59.73/59.57 <=> ? [B_b,B_B] :
% 59.73/59.57 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 59.73/59.57 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 59.73/59.57 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 59.73/59.57 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.57 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_option_Osize_I2_J,axiom,
% 59.73/59.57 ! [V_a_2,V_fa_2,T_b] : c_Option_Ooption_Ooption__size(T_b,V_fa_2,hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_card__Pow,axiom,
% 59.73/59.57 ! [V_A_2,T_b] :
% 59.73/59.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 => 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)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_double__eq__0__iff,axiom,
% 59.73/59.57 ! [V_a_2,T_b] :
% 59.73/59.57 ( class_Groups_Olinordered__ab__group__add(T_b)
% 59.73/59.57 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.57 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_card__Plus__conv__if,axiom,
% 59.73/59.57 ! [V_B_2,T_c,V_A_2,T_b] :
% 59.73/59.57 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 59.73/59.57 => 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)) )
% 59.73/59.57 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 59.73/59.57 => 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) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 59.73/59.57 ! [V_q,V_y,V_x,T_a] :
% 59.73/59.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.73/59.57 => 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)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 59.73/59.57 ! [V_q,V_p,V_x,T_a] :
% 59.73/59.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.73/59.57 => 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)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 59.73/59.57 ! [V_x,T_a] :
% 59.73/59.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.73/59.57 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 59.73/59.57 ! [V_q,V_x,T_a] :
% 59.73/59.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.73/59.57 => 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)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 59.73/59.57 ! [V_q,V_x,T_a] :
% 59.73/59.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.73/59.57 => 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)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 59.73/59.57 ! [V_q,V_x,T_a] :
% 59.73/59.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.73/59.57 => 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)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 59.73/59.57 ! [V_x,T_a] :
% 59.73/59.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.73/59.57 => 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) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 59.73/59.57 ! [V_q,V_p,V_x,T_a] :
% 59.73/59.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.73/59.57 => 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)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_option_Osize_I1_J,axiom,
% 59.73/59.57 ! [V_fa_2,T_b] : c_Option_Ooption_Ooption__size(T_b,V_fa_2,c_Option_Ooption_ONone(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__eq__if,axiom,
% 59.73/59.57 ! [V_p,V_m] :
% 59.73/59.57 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.57 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 59.73/59.57 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.57 => 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)))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_finite__PlusD_I2_J,axiom,
% 59.73/59.57 ! [V_B_2,V_A_2,T_c,T_b] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_finite__PlusD_I1_J,axiom,
% 59.73/59.57 ! [V_B_2,V_A_2,T_c,T_b] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_finite__Plus,axiom,
% 59.73/59.57 ! [V_B_2,T_c,V_A_2,T_b] :
% 59.73/59.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 59.73/59.57 => 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))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_finite__Plus__iff,axiom,
% 59.73/59.57 ! [V_B_2,V_A_2,T_c,T_b] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_card__Plus,axiom,
% 59.73/59.57 ! [V_B_2,T_c,V_A_2,T_b] :
% 59.73/59.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 59.73/59.57 => 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)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__strict__mono,axiom,
% 59.73/59.57 ! [V_n,V_b,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_one__less__power,axiom,
% 59.73/59.57 ! [V_n,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__le__imp__le__exp,axiom,
% 59.73/59.57 ! [V_n,V_m,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 59.73/59.57 => ( 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)))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__increasing__iff,axiom,
% 59.73/59.57 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 59.73/59.57 => ( 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)))
% 59.73/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__decreasing,axiom,
% 59.73/59.57 ! [V_a,V_N,V_n,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__strict__decreasing,axiom,
% 59.73/59.57 ! [V_a,V_N,V_n,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zpower__zadd__distrib,axiom,
% 59.73/59.57 ! [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)) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zpower__zpower,axiom,
% 59.73/59.57 ! [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)) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_field__power__not__zero,axiom,
% 59.73/59.57 ! [V_n,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 59.73/59.57 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.57 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__mult__distrib,axiom,
% 59.73/59.57 ! [V_n,V_b,V_a,T_a] :
% 59.73/59.57 ( class_Groups_Ocomm__monoid__mult(T_a)
% 59.73/59.57 => 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)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__commutes,axiom,
% 59.73/59.57 ! [V_n,V_a,T_a] :
% 59.73/59.57 ( class_Groups_Omonoid__mult(T_a)
% 59.73/59.57 => 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)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__one,axiom,
% 59.73/59.57 ! [V_n,T_a] :
% 59.73/59.57 ( class_Groups_Omonoid__mult(T_a)
% 59.73/59.57 => 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) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__mult,axiom,
% 59.73/59.57 ! [V_n,V_m,V_a,T_a] :
% 59.73/59.57 ( class_Groups_Omonoid__mult(T_a)
% 59.73/59.57 => 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) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__one__right,axiom,
% 59.73/59.57 ! [V_a,T_a] :
% 59.73/59.57 ( class_Groups_Omonoid__mult(T_a)
% 59.73/59.57 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__mono,axiom,
% 59.73/59.57 ! [V_n,V_b,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zero__le__power,axiom,
% 59.73/59.57 ! [V_n,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.57 => 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))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zero__less__power,axiom,
% 59.73/59.57 ! [V_n,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__eq__0__iff,axiom,
% 59.73/59.57 ! [V_n_2,V_a_2,T_b] :
% 59.73/59.57 ( ( class_Power_Opower(T_b)
% 59.73/59.57 & class_Rings_Omult__zero(T_b)
% 59.73/59.57 & class_Rings_Ono__zero__divisors(T_b)
% 59.73/59.57 & class_Rings_Ozero__neq__one(T_b) )
% 59.73/59.57 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.57 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.57 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_one__le__power,axiom,
% 59.73/59.57 ! [V_n,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__0__Suc,axiom,
% 59.73/59.57 ! [V_n,T_a] :
% 59.73/59.57 ( ( class_Power_Opower(T_a)
% 59.73/59.57 & class_Rings_Osemiring__0(T_a) )
% 59.73/59.57 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__inject__exp,axiom,
% 59.73/59.57 ! [V_n_2,V_m_2,V_a_2,T_b] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 59.73/59.57 => ( 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)
% 59.73/59.57 <=> V_m_2 = V_n_2 ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__Suc2,axiom,
% 59.73/59.57 ! [V_n,V_a,T_a] :
% 59.73/59.57 ( class_Groups_Omonoid__mult(T_a)
% 59.73/59.57 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__Suc,axiom,
% 59.73/59.57 ! [V_n,V_a,T_a] :
% 59.73/59.57 ( class_Power_Opower(T_a)
% 59.73/59.57 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__0,axiom,
% 59.73/59.57 ! [V_a,T_a] :
% 59.73/59.57 ( class_Power_Opower(T_a)
% 59.73/59.57 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__add,axiom,
% 59.73/59.57 ! [V_n,V_m,V_a,T_a] :
% 59.73/59.57 ( class_Groups_Omonoid__mult(T_a)
% 59.73/59.57 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__Suc__0,axiom,
% 59.73/59.57 ! [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)) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 59.73/59.57 ! [V_m_2,V_x_2] :
% 59.73/59.57 ( 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))
% 59.73/59.57 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.57 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_nat__zero__less__power__iff,axiom,
% 59.73/59.57 ! [V_n_2,V_x_2] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 59.73/59.57 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_nat__power__less__imp__less,axiom,
% 59.73/59.57 ! [V_n,V_m,V_i] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 59.73/59.57 => ( 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)))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__less__imp__less__base,axiom,
% 59.73/59.57 ! [V_b,V_n,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__le__imp__le__base,axiom,
% 59.73/59.57 ! [V_b,V_n,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__inject__base,axiom,
% 59.73/59.57 ! [V_b,V_n,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 59.73/59.57 => V_a = V_b ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__gt1__lemma,axiom,
% 59.73/59.57 ! [V_n,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__less__power__Suc,axiom,
% 59.73/59.57 ! [V_n,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__0__left,axiom,
% 59.73/59.57 ! [V_n,T_a] :
% 59.73/59.57 ( ( class_Power_Opower(T_a)
% 59.73/59.57 & class_Rings_Osemiring__0(T_a) )
% 59.73/59.57 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.57 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 59.73/59.57 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.57 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__gt1,axiom,
% 59.73/59.57 ! [V_n,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__strict__increasing__iff,axiom,
% 59.73/59.57 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 59.73/59.57 => ( 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)))
% 59.73/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__less__imp__less__exp,axiom,
% 59.73/59.57 ! [V_n,V_m,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__strict__increasing,axiom,
% 59.73/59.57 ! [V_a,V_N,V_n,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__increasing,axiom,
% 59.73/59.57 ! [V_a,V_N,V_n,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__minus,axiom,
% 59.73/59.57 ! [V_n,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Oring__1(T_a)
% 59.73/59.57 => 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)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_nat__one__le__power,axiom,
% 59.73/59.57 ! [V_n,V_i] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__Suc__less,axiom,
% 59.73/59.57 ! [V_n,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__eq__imp__eq__base,axiom,
% 59.73/59.57 ! [V_b,V_n,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 59.73/59.57 => V_a = V_b ) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__Suc__less__one,axiom,
% 59.73/59.57 ! [V_n,V_a,T_a] :
% 59.73/59.57 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_UNIV__Plus__UNIV,axiom,
% 59.73/59.57 ! [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)) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_nat_Osize_I2_J,axiom,
% 59.73/59.57 ! [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))) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_in__measure,axiom,
% 59.73/59.57 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 <=> 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))) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Plus__eq__empty__conv,axiom,
% 59.73/59.57 ! [V_B_2,V_A_2,T_c,T_b] :
% 59.73/59.57 ( 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))
% 59.73/59.57 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.57 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power__power__power,axiom,
% 59.73/59.57 ! [T_b] :
% 59.73/59.57 ( class_Power_Opower(T_b)
% 59.73/59.57 => 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)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mlex__leq,axiom,
% 59.73/59.57 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 => ( 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))
% 59.73/59.57 => 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))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zadd__zmult__distrib,axiom,
% 59.73/59.57 ! [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)) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zadd__zmult__distrib2,axiom,
% 59.73/59.57 ! [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)) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zmult__zminus,axiom,
% 59.73/59.57 ! [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)) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zmult__assoc,axiom,
% 59.73/59.57 ! [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)) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zmult__commute,axiom,
% 59.73/59.57 ! [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) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zdiff__zmult__distrib,axiom,
% 59.73/59.57 ! [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)) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zdiff__zmult__distrib2,axiom,
% 59.73/59.57 ! [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)) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zmult__1__right,axiom,
% 59.73/59.57 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zmult__1,axiom,
% 59.73/59.57 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 59.73/59.57
% 59.73/59.57 fof(fact_pos__zmult__eq__1__iff,axiom,
% 59.73/59.57 ! [V_n_2,V_m_2] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 59.73/59.57 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 59.73/59.57 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 59.73/59.57 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zmult__zless__mono2,axiom,
% 59.73/59.57 ! [V_k,V_j,V_i] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 59.73/59.57 => 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))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power_Opower_Opower__0,axiom,
% 59.73/59.57 ! [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 ).
% 59.73/59.57
% 59.73/59.57 fof(fact_power_Opower_Opower__Suc,axiom,
% 59.73/59.57 ! [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)) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_nat_Osize_I1_J,axiom,
% 59.73/59.57 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_mlex__less,axiom,
% 59.73/59.57 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 => 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))) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_nat_Osize_I4_J,axiom,
% 59.73/59.57 ! [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))) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_option_Osize_I4_J,axiom,
% 59.73/59.57 ! [V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),hAPP(c_Option_Ooption_OSome(T_a),V_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_option_Osize_I3_J,axiom,
% 59.73/59.57 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Ints__odd__less__0,axiom,
% 59.73/59.57 ! [V_a_2,T_b] :
% 59.73/59.57 ( class_Rings_Olinordered__idom(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 59.73/59.57 => ( 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)))
% 59.73/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_in__lex__prod,axiom,
% 59.73/59.57 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 <=> ( 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))
% 59.73/59.57 | ( V_a_2 = V_a_H_2
% 59.73/59.57 & 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)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_in__finite__psubset,axiom,
% 59.73/59.57 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.73/59.57 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_odd__less__0,axiom,
% 59.73/59.57 ! [V_z_2] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_odd__nonzero,axiom,
% 59.73/59.57 ! [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) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_le__imp__0__less,axiom,
% 59.73/59.57 ! [V_z] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 59.73/59.57 => 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))) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zadd__0__right,axiom,
% 59.73/59.57 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zadd__0,axiom,
% 59.73/59.57 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zadd__zminus__inverse2,axiom,
% 59.73/59.57 ! [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) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_less__bin__lemma,axiom,
% 59.73/59.57 ! [V_l_2,V_k_2] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 59.73/59.57 <=> 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))) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zminus__0,axiom,
% 59.73/59.57 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) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_int__one__le__iff__zero__less,axiom,
% 59.73/59.57 ! [V_z_2] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 59.73/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_int__0__neq__1,axiom,
% 59.73/59.57 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_int__0__less__1,axiom,
% 59.73/59.57 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))) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zle__diff1__eq,axiom,
% 59.73/59.57 ! [V_z_2,V_w_2] :
% 59.73/59.57 ( 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))))
% 59.73/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zminus__zminus,axiom,
% 59.73/59.57 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zless__linear,axiom,
% 59.73/59.57 ! [V_y,V_x] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 59.73/59.57 | V_x = V_y
% 59.73/59.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_nat__size,axiom,
% 59.73/59.57 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zless__le,axiom,
% 59.73/59.57 ! [V_w_2,V_z_2] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 59.73/59.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 59.73/59.57 & V_z_2 != V_w_2 ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zminus__zadd__distrib,axiom,
% 59.73/59.57 ! [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)) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zadd__strict__right__mono,axiom,
% 59.73/59.57 ! [V_k,V_j,V_i] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 59.73/59.57 => 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))) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zadd__commute,axiom,
% 59.73/59.57 ! [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) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zadd__left__commute,axiom,
% 59.73/59.57 ! [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)) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zadd__assoc,axiom,
% 59.73/59.57 ! [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)) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zadd__left__mono,axiom,
% 59.73/59.57 ! [V_k,V_j,V_i] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 59.73/59.57 => 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))) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zadd__zless__mono,axiom,
% 59.73/59.57 ! [V_z,V_z_H,V_w,V_w_H] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 59.73/59.57 => 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))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_diff__int__def,axiom,
% 59.73/59.57 ! [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)) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_diff__int__def__symmetric,axiom,
% 59.73/59.57 ! [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) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zle__add1__eq__le,axiom,
% 59.73/59.57 ! [V_z_2,V_w_2] :
% 59.73/59.57 ( 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))))
% 59.73/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_add1__zle__eq,axiom,
% 59.73/59.57 ! [V_z_2,V_w_2] :
% 59.73/59.57 ( 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))
% 59.73/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zless__imp__add1__zle,axiom,
% 59.73/59.57 ! [V_z,V_w] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 59.73/59.57 => 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)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zless__add1__eq,axiom,
% 59.73/59.57 ! [V_z_2,V_w_2] :
% 59.73/59.57 ( 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))))
% 59.73/59.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 59.73/59.57 | V_w_2 = V_z_2 ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Ints__0,axiom,
% 59.73/59.57 ! [T_b] :
% 59.73/59.57 ( class_Rings_Oring__1(T_b)
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Ints__add,axiom,
% 59.73/59.57 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.57 ( class_Rings_Oring__1(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 59.73/59.57 => 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))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Ints__mult,axiom,
% 59.73/59.57 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.57 ( class_Rings_Oring__1(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 59.73/59.57 => 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))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_nat_Osize_I3_J,axiom,
% 59.73/59.57 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) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Ints__diff,axiom,
% 59.73/59.57 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.57 ( class_Rings_Oring__1(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 59.73/59.57 => 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))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Ints__1,axiom,
% 59.73/59.57 ! [T_b] :
% 59.73/59.57 ( class_Rings_Oring__1(T_b)
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Ints__minus,axiom,
% 59.73/59.57 ! [V_a_2,T_b] :
% 59.73/59.57 ( class_Rings_Oring__1(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 59.73/59.57 => 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))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Ints__power,axiom,
% 59.73/59.57 ! [V_n_2,V_a_2,T_b] :
% 59.73/59.57 ( class_Rings_Oring__1(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 59.73/59.57 => 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))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Ints__double__eq__0__iff,axiom,
% 59.73/59.57 ! [V_a_2,T_b] :
% 59.73/59.57 ( class_Int_Oring__char__0(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 59.73/59.57 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.57 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Ints__odd__nonzero,axiom,
% 59.73/59.57 ! [V_a_2,T_b] :
% 59.73/59.57 ( class_Int_Oring__char__0(T_b)
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 59.73/59.57 => 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) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_self__quotient__aux1,axiom,
% 59.73/59.57 ! [V_q,V_r,V_a] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 59.73/59.57 => ( 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))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_self__quotient__aux2,axiom,
% 59.73/59.57 ! [V_q,V_r,V_a] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 59.73/59.57 => ( 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))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_q__pos__lemma,axiom,
% 59.73/59.57 ! [V_r_H,V_q_H,V_b_H] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_q__neg__lemma,axiom,
% 59.73/59.57 ! [V_r_H,V_q_H,V_b_H] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_unique__quotient__lemma,axiom,
% 59.73/59.57 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zdiv__mono2__lemma,axiom,
% 59.73/59.57 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 59.73/59.57 ( 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)
% 59.73/59.57 => ( 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)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zle__antisym,axiom,
% 59.73/59.57 ! [V_w,V_z] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 59.73/59.57 => V_z = V_w ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zle__trans,axiom,
% 59.73/59.57 ! [V_k,V_j,V_i] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zle__linear,axiom,
% 59.73/59.57 ! [V_w,V_z] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 59.73/59.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zle__refl,axiom,
% 59.73/59.57 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 59.73/59.57 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 59.73/59.57 ( 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)
% 59.73/59.57 => ( 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)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_unique__quotient__lemma__neg,axiom,
% 59.73/59.57 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 59.73/59.57 ! [V_n,V_x] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 59.73/59.57 => 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))) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_same__fstI,axiom,
% 59.73/59.57 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_P_2] :
% 59.73/59.57 ( hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.57 => ( 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)))
% 59.73/59.57 => 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))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 59.73/59.57 ! [V_y,V_x] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 59.73/59.57 => 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))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 59.73/59.57 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))) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 59.73/59.57 ! [V_y,V_x] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 59.73/59.57 => 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))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 59.73/59.57 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))) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_tsub__def,axiom,
% 59.73/59.57 ! [V_x,V_y] :
% 59.73/59.57 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 59.73/59.57 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 59.73/59.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 59.73/59.57 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_int__power__div__base,axiom,
% 59.73/59.57 ! [V_k,V_m] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 59.73/59.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m)),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_divmod__int__relI,axiom,
% 59.73/59.57 ! [V_r,V_q,V_b,V_a] :
% 59.73/59.57 ( 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)
% 59.73/59.57 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 59.73/59.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 59.73/59.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 59.73/59.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 59.73/59.57 => 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))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_setprod__gen__delta,axiom,
% 59.73/59.57 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 59.73/59.57 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 59.73/59.57 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 59.73/59.57 => 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)))) )
% 59.73/59.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 59.73/59.57 => 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)) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_ex__least__nat__less,axiom,
% 59.73/59.57 ! [V_n_2,V_P_2] :
% 59.73/59.57 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 59.73/59.57 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 59.73/59.57 => ? [B_k] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 59.73/59.57 & ! [B_i] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 59.73/59.57 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 59.73/59.57 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_max__ext__additive,axiom,
% 59.73/59.57 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 => ( 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)))
% 59.73/59.57 => 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))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_divmod__int__rel__div,axiom,
% 59.73/59.57 ! [V_r,V_q,V_b,V_a] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zdiv__zero,axiom,
% 59.73/59.57 ! [V_b] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zdiv__zminus__zminus,axiom,
% 59.73/59.57 ! [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) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zdiv__zminus2,axiom,
% 59.73/59.57 ! [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) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_div__by__0,axiom,
% 59.73/59.57 ! [V_a,T_a] :
% 59.73/59.57 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_div__0,axiom,
% 59.73/59.57 ! [V_a,T_a] :
% 59.73/59.57 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_div__by__1,axiom,
% 59.73/59.57 ! [V_a,T_a] :
% 59.73/59.57 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_setprod__timesf,axiom,
% 59.73/59.57 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 59.73/59.57 ( class_Groups_Ocomm__monoid__mult(T_b)
% 59.73/59.57 => 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)) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_setprod__1,axiom,
% 59.73/59.57 ! [V_A_2,T_c,T_b] :
% 59.73/59.57 ( class_Groups_Ocomm__monoid__mult(T_b)
% 59.73/59.57 => 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) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_divmod__int__rel__0,axiom,
% 59.73/59.57 ! [V_b] :
% 59.73/59.57 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.57 => 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)))) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_self__remainder,axiom,
% 59.73/59.57 ! [V_r,V_q,V_a] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.57 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_unique__quotient,axiom,
% 59.73/59.57 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 => ( 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)))
% 59.73/59.57 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.57 => V_q = V_q_H ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_unique__remainder,axiom,
% 59.73/59.57 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 => ( 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)))
% 59.73/59.57 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.57 => V_r = V_r_H ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_setprod__zero__iff,axiom,
% 59.73/59.57 ! [V_f_2,V_A_2,T_b,T_c] :
% 59.73/59.57 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 59.73/59.57 & class_Rings_Ono__zero__divisors(T_c) )
% 59.73/59.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 => ( 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)
% 59.73/59.57 <=> ? [B_x] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.57 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_setprod__zero,axiom,
% 59.73/59.57 ! [V_f_2,V_A_2,T_b,T_c] :
% 59.73/59.57 ( class_Rings_Ocomm__semiring__1(T_c)
% 59.73/59.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 => ( ? [B_x] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.57 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 59.73/59.57 => 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) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_setprod__empty,axiom,
% 59.73/59.57 ! [V_f_2,T_c,T_b] :
% 59.73/59.57 ( class_Groups_Ocomm__monoid__mult(T_b)
% 59.73/59.57 => 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) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_setprod_Oempty,axiom,
% 59.73/59.57 ! [V_g_2,T_c,T_b] :
% 59.73/59.57 ( class_Groups_Ocomm__monoid__mult(T_b)
% 59.73/59.57 => 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) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_setprod__infinite,axiom,
% 59.73/59.57 ! [V_f_2,V_A_2,T_b,T_c] :
% 59.73/59.57 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.57 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 => 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) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_setprod_Oinfinite,axiom,
% 59.73/59.57 ! [V_g_2,V_A_2,T_b,T_c] :
% 59.73/59.57 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.57 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 => 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) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_setprod__eq__1__iff,axiom,
% 59.73/59.57 ! [V_f_2,V_F_2,T_b] :
% 59.73/59.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 59.73/59.57 => ( 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)
% 59.73/59.57 <=> ! [B_x] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 59.73/59.57 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 59.73/59.57 ! [V_y,V_x] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_div__neg__pos__less0,axiom,
% 59.73/59.57 ! [V_b,V_a] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 59.73/59.57 ! [V_a_2,V_b_2] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 59.73/59.57 ! [V_a_2,V_b_2] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zdiv__self,axiom,
% 59.73/59.57 ! [V_a] :
% 59.73/59.57 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_setprod_Odistrib,axiom,
% 59.73/59.57 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 59.73/59.57 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.57 => 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)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_div__mult__mult1__if,axiom,
% 59.73/59.57 ! [V_b,V_a,V_c,T_a] :
% 59.73/59.57 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.57 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) )
% 59.73/59.57 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_div__mult__self2__is__id,axiom,
% 59.73/59.57 ! [V_a,V_b,T_a] :
% 59.73/59.57 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.57 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_div__mult__self1__is__id,axiom,
% 59.73/59.57 ! [V_a,V_b,T_a] :
% 59.73/59.57 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.57 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_div__mult__mult2,axiom,
% 59.73/59.57 ! [V_b,V_a,V_c,T_a] :
% 59.73/59.57 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.57 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_div__mult__mult1,axiom,
% 59.73/59.57 ! [V_b,V_a,V_c,T_a] :
% 59.73/59.57 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.57 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_div__self,axiom,
% 59.73/59.57 ! [V_a,T_a] :
% 59.73/59.57 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.57 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_setprod__pos__nat__iff,axiom,
% 59.73/59.57 ! [V_f_2,V_S_2,T_b] :
% 59.73/59.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 59.73/59.57 => ( 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)))
% 59.73/59.57 <=> ! [B_x] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 59.73/59.57 => 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))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_setprod__reindex__cong,axiom,
% 59.73/59.57 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 59.73/59.57 ( class_Groups_Ocomm__monoid__mult(T_d)
% 59.73/59.57 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.73/59.57 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 59.73/59.57 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 59.73/59.57 => 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) ) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_setprod__reindex,axiom,
% 59.73/59.57 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 59.73/59.57 ( class_Groups_Ocomm__monoid__mult(T_d)
% 59.73/59.57 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 59.73/59.57 => 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) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_self__quotient,axiom,
% 59.73/59.57 ! [V_r,V_q,V_a] :
% 59.73/59.57 ( 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)))
% 59.73/59.57 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.57 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zdiv__mono1__neg,axiom,
% 59.73/59.57 ! [V_b,V_a_H,V_a] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zdiv__mono1,axiom,
% 59.73/59.57 ! [V_b,V_a_H,V_a] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_div__neg__neg__trivial,axiom,
% 59.73/59.57 ! [V_b,V_a] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 59.73/59.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zdiv__mono2__neg,axiom,
% 59.73/59.57 ! [V_b,V_b_H,V_a] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_div__nonpos__pos__le0,axiom,
% 59.73/59.57 ! [V_b,V_a] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 59.73/59.57 ! [V_a_2,V_b_2] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
% 59.73/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_div__pos__pos__trivial,axiom,
% 59.73/59.57 ! [V_b,V_a] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 59.73/59.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_div__nonneg__neg__le0,axiom,
% 59.73/59.57 ! [V_b,V_a] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zdiv__mono2,axiom,
% 59.73/59.57 ! [V_b,V_b_H,V_a] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 59.73/59.57 ! [V_b_2,V_a_2] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
% 59.73/59.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 59.73/59.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 59.73/59.57 ! [V_i_2,V_k_2] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2)))
% 59.73/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 59.73/59.57 ! [V_a_2,V_b_2] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
% 59.73/59.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zdiv__eq__0__iff,axiom,
% 59.73/59.57 ! [V_k_2,V_i_2] :
% 59.73/59.57 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.57 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.57 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 59.73/59.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 59.73/59.57 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_int__div__less__self,axiom,
% 59.73/59.57 ! [V_k,V_x] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 59.73/59.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 59.73/59.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x)) ) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_zdiv__zmult2__eq,axiom,
% 59.73/59.57 ! [V_b,V_a,V_c] :
% 59.73/59.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 59.73/59.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c) ) ).
% 59.73/59.57
% 59.73/59.57 fof(fact_setprod__delta_H,axiom,
% 59.73/59.57 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 59.73/59.57 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 59.73/59.57 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 59.73/59.58 => 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) )
% 59.73/59.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 59.73/59.58 => 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) ) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_setprod__delta,axiom,
% 59.73/59.58 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 59.73/59.58 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 59.73/59.58 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 59.73/59.58 => 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) )
% 59.73/59.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 59.73/59.58 => 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) ) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_setprod__constant,axiom,
% 59.73/59.58 ! [V_y_2,V_A_2,T_b,T_c] :
% 59.73/59.58 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__mult__self2,axiom,
% 59.73/59.58 ! [V_c,V_a,V_b,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__mult__self1,axiom,
% 59.73/59.58 ! [V_c,V_a,V_b,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__add__self1,axiom,
% 59.73/59.58 ! [V_a,V_b,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__add__self2,axiom,
% 59.73/59.58 ! [V_a,V_b,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_setprod__insert,axiom,
% 59.73/59.58 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 59.73/59.58 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.58 => 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)) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_setprod_Oinsert,axiom,
% 59.73/59.58 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 59.73/59.58 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.58 => 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)) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_setprod__Un__Int,axiom,
% 59.73/59.58 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 59.73/59.58 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.58 => 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)) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_setprod_Ounion__inter,axiom,
% 59.73/59.58 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 59.73/59.58 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.58 => 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)) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_setprod_Oreindex,axiom,
% 59.73/59.58 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 59.73/59.58 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.58 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 59.73/59.58 => 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) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_setprod_Oeq__fold,axiom,
% 59.73/59.58 ! [V_g_2,V_A_2,T_b,T_c] :
% 59.73/59.58 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.58 => 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) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_setprod_OF__eq,axiom,
% 59.73/59.58 ! [V_g_2,V_A_2,T_b,T_c] :
% 59.73/59.58 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.58 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.58 => 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) )
% 59.73/59.58 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.58 => 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) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_setprod_Oinsert__remove,axiom,
% 59.73/59.58 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 59.73/59.58 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.58 => 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)))))) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_setprod_Ounion__disjoint,axiom,
% 59.73/59.58 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 59.73/59.58 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.58 => ( 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))
% 59.73/59.58 => 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)) ) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_setprod__Un__disjoint,axiom,
% 59.73/59.58 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 59.73/59.58 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.58 => ( 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))
% 59.73/59.58 => 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)) ) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_split__zdiv,axiom,
% 59.73/59.58 ! [V_k_2,V_n_2,V_P_2] :
% 59.73/59.58 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 59.73/59.58 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 59.73/59.58 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 59.73/59.58 => ! [B_i] :
% 59.73/59.58 ( ? [B_j] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 59.73/59.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 59.73/59.58 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 59.73/59.58 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 59.73/59.58 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => ! [B_i] :
% 59.73/59.58 ( ? [B_j] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 59.73/59.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 59.73/59.58 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__int__rel__div__eq,axiom,
% 59.73/59.58 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 59.73/59.58 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)
% 59.73/59.58 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 59.73/59.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 59.73/59.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 59.73/59.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 59.73/59.58 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 59.73/59.58 ! [V_y,V_x] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 59.73/59.58 => 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))) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_tsub__eq,axiom,
% 59.73/59.58 ! [V_x,V_y] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 59.73/59.58 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_setprod_Oremove,axiom,
% 59.73/59.58 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 59.73/59.58 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.58 => 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)))))) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zminus1__lemma,axiom,
% 59.73/59.58 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => 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))))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_max__extp__max__ext__eq,axiom,
% 59.73/59.58 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 59.73/59.58 ( 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)
% 59.73/59.58 <=> 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))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_z3div__def,axiom,
% 59.73/59.58 ! [V_k,V_l] :
% 59.73/59.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 59.73/59.58 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 59.73/59.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 59.73/59.58 => 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))) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_norm__frac_Osimps,axiom,
% 59.73/59.58 ! [V_a_2,V_b_2] :
% 59.73/59.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => 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)) )
% 59.73/59.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 59.73/59.58 => 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)) )
% 59.73/59.58 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 59.73/59.58 => 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))) ) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_setprod__Un__one,axiom,
% 59.73/59.58 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 59.73/59.58 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 59.73/59.58 => ( ! [B_x] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 59.73/59.58 => 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)) ) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 59.73/59.58 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 59.73/59.58 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.58 => ( ! [B_x] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 59.73/59.58 => 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)) ) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmult2__lemma,axiom,
% 59.73/59.58 ! [V_c,V_r,V_q,V_b,V_a] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 59.73/59.58 => 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)))) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__add__cong,axiom,
% 59.73/59.58 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 59.73/59.58 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 59.73/59.58 => 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) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__simps_I1_J,axiom,
% 59.73/59.58 ! [V_b,V_c,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__simps_I2_J,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__add__eq,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__add__left__eq,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__add__right__eq,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__add__self1,axiom,
% 59.73/59.58 ! [V_a,V_b,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__add__self2,axiom,
% 59.73/59.58 ! [V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__mult__cong,axiom,
% 59.73/59.58 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 59.73/59.58 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 59.73/59.58 => 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) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__simps_I4_J,axiom,
% 59.73/59.58 ! [V_b,V_c,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__mult__mult2,axiom,
% 59.73/59.58 ! [V_b,V_c,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__mult__mult1,axiom,
% 59.73/59.58 ! [V_b,V_a,V_c,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__mult__eq,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__mult__left__eq,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__mult__right__eq,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__self,axiom,
% 59.73/59.58 ! [V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__by__0,axiom,
% 59.73/59.58 ! [V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__0,axiom,
% 59.73/59.58 ! [V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__mod__trivial,axiom,
% 59.73/59.58 ! [V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__diff__cong,axiom,
% 59.73/59.58 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Oring__div(T_a)
% 59.73/59.58 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 59.73/59.58 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 59.73/59.58 => 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) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__diff__eq,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Oring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__diff__left__eq,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Oring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__diff__right__eq,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Oring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__minus__eq,axiom,
% 59.73/59.58 ! [V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Oring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__minus__cong,axiom,
% 59.73/59.58 ! [V_a_H,V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Oring__div(T_a)
% 59.73/59.58 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 59.73/59.58 => 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) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__le__mono,axiom,
% 59.73/59.58 ! [V_k,V_n,V_m] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 59.73/59.58 => 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))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__le__dividend,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__mult2__eq,axiom,
% 59.73/59.58 ! [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) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__zero,axiom,
% 59.73/59.58 ! [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) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__self,axiom,
% 59.73/59.58 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__zmult1__eq,axiom,
% 59.73/59.58 ! [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) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__simps_I3_J,axiom,
% 59.73/59.58 ! [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) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zdiff__zmod__right,axiom,
% 59.73/59.58 ! [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) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zdiff__zmod__left,axiom,
% 59.73/59.58 ! [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) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__zminus2,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__zminus__zminus,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zminus__zmod,axiom,
% 59.73/59.58 ! [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) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zpower__zmod,axiom,
% 59.73/59.58 ! [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) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__mult__self1__is__0,axiom,
% 59.73/59.58 ! [V_a,V_b,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__mult__self2__is__0,axiom,
% 59.73/59.58 ! [V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__mult__self1,axiom,
% 59.73/59.58 ! [V_b,V_c,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__mult__self2,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__by__1,axiom,
% 59.73/59.58 ! [V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__div__trivial,axiom,
% 59.73/59.58 ! [V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__1,axiom,
% 59.73/59.58 ! [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 ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__less,axiom,
% 59.73/59.58 ! [V_n,V_m] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.73/59.58 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_nat__mult__div__cancel__disj,axiom,
% 59.73/59.58 ! [V_n,V_m,V_k] :
% 59.73/59.58 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.58 => 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) )
% 59.73/59.58 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.58 => 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) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__le__nonneg__dividend,axiom,
% 59.73/59.58 ! [V_k,V_m] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 59.73/59.58 => 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)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 59.73/59.58 ! [V_y,V_x] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 59.73/59.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_pos__mod__bound,axiom,
% 59.73/59.58 ! [V_a,V_b] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_neg__mod__bound,axiom,
% 59.73/59.58 ! [V_a,V_b] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__eq__0__iff,axiom,
% 59.73/59.58 ! [V_d_2,V_m_2] :
% 59.73/59.58 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__zminus1__not__zero,axiom,
% 59.73/59.58 ! [V_l,V_k] :
% 59.73/59.58 ( 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)
% 59.73/59.58 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__zminus2__not__zero,axiom,
% 59.73/59.58 ! [V_l,V_k] :
% 59.73/59.58 ( 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)
% 59.73/59.58 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__zdiv__trivial,axiom,
% 59.73/59.58 ! [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) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_DIVISION__BY__ZERO,axiom,
% 59.73/59.58 ! [V_a] :
% 59.73/59.58 ( 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)
% 59.73/59.58 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zdiv__zadd1__eq,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 59.73/59.58 ! [V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)) = V_a ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__div__equality2,axiom,
% 59.73/59.58 ! [V_a,V_b,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__div__equality,axiom,
% 59.73/59.58 ! [V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__mod__equality2,axiom,
% 59.73/59.58 ! [V_c,V_a,V_b,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__mod__equality,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.58 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.58 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__le__mono2,axiom,
% 59.73/59.58 ! [V_k,V_n,V_m] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 59.73/59.58 => 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))) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_nat__mult__div__cancel1,axiom,
% 59.73/59.58 ! [V_n,V_m,V_k] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__mult__self__is__m,axiom,
% 59.73/59.58 ! [V_m,V_n] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 59.73/59.58 => 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 ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__mult__self1__is__m,axiom,
% 59.73/59.58 ! [V_m,V_n] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 59.73/59.58 => 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 ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__less__dividend,axiom,
% 59.73/59.58 ! [V_m,V_n] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_pos__mod__sign,axiom,
% 59.73/59.58 ! [V_a,V_b] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_pos__mod__conj,axiom,
% 59.73/59.58 ! [V_a,V_b] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))
% 59.73/59.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__pos__pos__trivial,axiom,
% 59.73/59.58 ! [V_b,V_a] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 59.73/59.58 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_neg__mod__sign,axiom,
% 59.73/59.58 ! [V_a,V_b] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_neg__mod__conj,axiom,
% 59.73/59.58 ! [V_a,V_b] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__neg__neg__trivial,axiom,
% 59.73/59.58 ! [V_b,V_a] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 59.73/59.58 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__zminus1__eq__if,axiom,
% 59.73/59.58 ! [V_b,V_a] :
% 59.73/59.58 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => 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) )
% 59.73/59.58 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__zminus2__eq__if,axiom,
% 59.73/59.58 ! [V_b,V_a] :
% 59.73/59.58 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => 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) )
% 59.73/59.58 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => 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) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__zdiv__equality,axiom,
% 59.73/59.58 ! [V_b,V_a] : V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zdiv__zmult1__eq,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zdiv__zmod__equality,axiom,
% 59.73/59.58 ! [V_k,V_a,V_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zdiv__zmod__equality2,axiom,
% 59.73/59.58 ! [V_k,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__zdiv__equality_H,axiom,
% 59.73/59.58 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)),V_n)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmult__div__cancel,axiom,
% 59.73/59.58 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__int__rel__mod,axiom,
% 59.73/59.58 ! [V_r,V_q,V_b,V_a] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__geq,axiom,
% 59.73/59.58 ! [V_m,V_n] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 59.73/59.58 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__if,axiom,
% 59.73/59.58 ! [V_m,V_n] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 59.73/59.58 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.73/59.58 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 59.73/59.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.73/59.58 => 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)) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_split__div,axiom,
% 59.73/59.58 ! [V_k_2,V_n_2,V_P_2] :
% 59.73/59.58 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 59.73/59.58 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.58 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 59.73/59.58 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.58 => ! [B_i,B_j] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 59.73/59.58 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
% 59.73/59.58 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__pos__neg__trivial,axiom,
% 59.73/59.58 ! [V_b,V_a] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__int__rel__div__mod,axiom,
% 59.73/59.58 ! [V_a,V_b] :
% 59.73/59.58 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => 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)))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_le__div__geq,axiom,
% 59.73/59.58 ! [V_m,V_n] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_split__div_H,axiom,
% 59.73/59.58 ! [V_n_2,V_m_2,V_P_2] :
% 59.73/59.58 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 59.73/59.58 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.58 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 59.73/59.58 | ? [B_q] :
% 59.73/59.58 ( 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))
% 59.73/59.58 & 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))))
% 59.73/59.58 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_split__div__lemma,axiom,
% 59.73/59.58 ! [V_m_2,V_q_2,V_n_2] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 59.73/59.58 => ( ( 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))
% 59.73/59.58 & 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)))) )
% 59.73/59.58 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__int__rel__mod__eq,axiom,
% 59.73/59.58 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 59.73/59.58 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1)),V_y)
% 59.73/59.58 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 59.73/59.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 59.73/59.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 59.73/59.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 59.73/59.58 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmult2__lemma__aux2,axiom,
% 59.73/59.58 ! [V_q,V_r,V_b,V_c] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmult2__lemma__aux1,axiom,
% 59.73/59.58 ! [V_q,V_r,V_b,V_c] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmult2__lemma__aux4,axiom,
% 59.73/59.58 ! [V_q,V_b,V_r,V_c] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 59.73/59.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmult2__lemma__aux3,axiom,
% 59.73/59.58 ! [V_q,V_b,V_r,V_c] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 59.73/59.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_split__zmod,axiom,
% 59.73/59.58 ! [V_k_2,V_n_2,V_P_2] :
% 59.73/59.58 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 59.73/59.58 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 59.73/59.58 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 59.73/59.58 => ! [B_i,B_j] :
% 59.73/59.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 59.73/59.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 59.73/59.58 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 59.73/59.58 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 59.73/59.58 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => ! [B_i,B_j] :
% 59.73/59.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 59.73/59.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 59.73/59.58 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmod__zmult2__eq,axiom,
% 59.73/59.58 ! [V_b,V_a,V_c] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 59.73/59.58 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zdiv__zminus1__eq__if,axiom,
% 59.73/59.58 ! [V_a,V_b] :
% 59.73/59.58 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => 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)) )
% 59.73/59.58 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => 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)) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zdiv__zminus2__eq__if,axiom,
% 59.73/59.58 ! [V_a,V_b] :
% 59.73/59.58 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => 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)) )
% 59.73/59.58 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => 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)) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zadd1__lemma,axiom,
% 59.73/59.58 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => ( 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)))
% 59.73/59.58 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => 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)))) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_split__neg__lemma,axiom,
% 59.73/59.58 ! [V_n_2,V_P_2,V_k_2] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => ( 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)))
% 59.73/59.58 <=> ! [B_i,B_j] :
% 59.73/59.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 59.73/59.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 59.73/59.58 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_split__pos__lemma,axiom,
% 59.73/59.58 ! [V_n_2,V_P_2,V_k_2] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 59.73/59.58 => ( 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)))
% 59.73/59.58 <=> ! [B_i,B_j] :
% 59.73/59.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 59.73/59.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 59.73/59.58 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 59.73/59.58 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_zmult1__lemma,axiom,
% 59.73/59.58 ! [V_a,V_r,V_q,V_c,V_b] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => 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)))) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_z3mod__def,axiom,
% 59.73/59.58 ! [V_k,V_l] :
% 59.73/59.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 59.73/59.58 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 59.73/59.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_norm__frac_Opsimps,axiom,
% 59.73/59.58 ! [V_b_2,V_a_2] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => 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)) )
% 59.73/59.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 59.73/59.58 => 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)) )
% 59.73/59.58 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 59.73/59.58 => 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))) ) ) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_negDivAlg__div__mod,axiom,
% 59.73/59.58 ! [V_l,V_k] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_posDivAlg__div__mod,axiom,
% 59.73/59.58 ! [V_l,V_k] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__int__mod__div,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_accp__downward,axiom,
% 59.73/59.58 ! [V_a_2,V_b_2,V_r_2,T_b] :
% 59.73/59.58 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 59.73/59.58 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_accp_Oequations,axiom,
% 59.73/59.58 ! [V_a_2,V_r_2,T_b] :
% 59.73/59.58 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 59.73/59.58 <=> ! [B_x] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 59.73/59.58 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_accp_Osimps,axiom,
% 59.73/59.58 ! [V_a_2,V_r_2,T_b] :
% 59.73/59.58 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 59.73/59.58 <=> ! [B_x] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 59.73/59.58 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 59.73/59.58 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__less,axiom,
% 59.73/59.58 ! [V_n,V_m] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.73/59.58 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__add1__eq,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__less__eq__dividend,axiom,
% 59.73/59.58 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_m)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__mult__distrib,axiom,
% 59.73/59.58 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__mult__distrib2,axiom,
% 59.73/59.58 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__Suc,axiom,
% 59.73/59.58 ! [V_n,V_m] :
% 59.73/59.58 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 59.73/59.58 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 59.73/59.58 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 59.73/59.58 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__1,axiom,
% 59.73/59.58 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__less__divisor,axiom,
% 59.73/59.58 ! [V_m,V_n] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 59.73/59.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__eq__0__iff,axiom,
% 59.73/59.58 ! [V_d_2,V_m_2] :
% 59.73/59.58 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.58 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__geq,axiom,
% 59.73/59.58 ! [V_n,V_m] :
% 59.73/59.58 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.73/59.58 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__if,axiom,
% 59.73/59.58 ! [V_n,V_m] :
% 59.73/59.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.73/59.58 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 59.73/59.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.73/59.58 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__mult__self3,axiom,
% 59.73/59.58 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__mult2__eq,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__mult1__eq,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_le__mod__geq,axiom,
% 59.73/59.58 ! [V_m,V_n] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 59.73/59.58 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_Divides_Omod__div__equality_H,axiom,
% 59.73/59.58 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mult__div__cancel,axiom,
% 59.73/59.58 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__mod__equality_H,axiom,
% 59.73/59.58 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__le__divisor,axiom,
% 59.73/59.58 ! [V_m,V_n] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 59.73/59.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__mult__self4,axiom,
% 59.73/59.58 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_posDivAlg__0,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_accp__subset,axiom,
% 59.73/59.58 ! [V_R2_2,V_R1_2,T_b] :
% 59.73/59.58 ( 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))
% 59.73/59.58 => 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))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__lemma,axiom,
% 59.73/59.58 ! [V_q,V_b,V_r,V_c] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 59.73/59.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_split__mod,axiom,
% 59.73/59.58 ! [V_k_2,V_n_2,V_P_2] :
% 59.73/59.58 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 59.73/59.58 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.58 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 59.73/59.58 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.58 => ! [B_i,B_j] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 59.73/59.58 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
% 59.73/59.58 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_Suc__times__mod__eq,axiom,
% 59.73/59.58 ! [V_m,V_k] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 59.73/59.58 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_negDivAlg__correct,axiom,
% 59.73/59.58 ! [V_b,V_a] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.58 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__int__correct,axiom,
% 59.73/59.58 ! [V_a,V_b] :
% 59.73/59.58 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_posDivAlg__correct,axiom,
% 59.73/59.58 ! [V_b,V_a] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.58 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__int__def,axiom,
% 59.73/59.58 ! [V_b,V_a] :
% 59.73/59.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 59.73/59.58 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.58 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 59.73/59.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.58 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => 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)) )
% 59.73/59.58 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.58 => 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))) ) ) ) ) )
% 59.73/59.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 59.73/59.58 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.58 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 59.73/59.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.58 => 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))) ) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__nat__step,axiom,
% 59.73/59.58 ! [V_m,V_n] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_norm__frac_Opinduct,axiom,
% 59.73/59.58 ! [V_P_2,V_a1_2,V_a0_2] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => ( ! [B_a,B_b] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => 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))) )
% 59.73/59.58 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 59.73/59.58 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 59.73/59.58 ! [V_a,V_r,V_q,V_c,V_b] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 59.73/59.58 => 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)))) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 59.73/59.58 ! [V_c,V_r,V_q,V_b,V_a] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 59.73/59.58 => 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)))) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__eq,axiom,
% 59.73/59.58 ! [V_r,V_q,V_n,V_m] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__nat__def,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 59.73/59.58 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__nat__eq,axiom,
% 59.73/59.58 ! [V_qr,V_n,V_m] :
% 59.73/59.58 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 59.73/59.58 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__nat__rel__unique,axiom,
% 59.73/59.58 ! [V_qr_H,V_qr,V_n,V_m] :
% 59.73/59.58 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 59.73/59.58 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 59.73/59.58 => V_qr = V_qr_H ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__nat__rel,axiom,
% 59.73/59.58 ! [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)))) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__eq,axiom,
% 59.73/59.58 ! [V_r,V_q,V_n,V_m] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__nat__zero,axiom,
% 59.73/59.58 ! [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) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__nat__div__mod,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__nat__base,axiom,
% 59.73/59.58 ! [V_n,V_m] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_negateSnd__eq,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__int__rel__neg,axiom,
% 59.73/59.58 ! [V_qr,V_b,V_a] :
% 59.73/59.58 ( 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))
% 59.73/59.58 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 59.73/59.58 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => ( 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)))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 59.73/59.58 => 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)))) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__neg__neg,axiom,
% 59.73/59.58 ! [V_b,V_a] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => 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)))) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__neg__neg,axiom,
% 59.73/59.58 ! [V_b,V_a] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => 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)))) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__nat__if,axiom,
% 59.73/59.58 ! [V_m_2,V_n_2] :
% 59.73/59.58 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.58 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 59.73/59.58 => 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) )
% 59.73/59.58 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.58 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__pos__neg,axiom,
% 59.73/59.58 ! [V_b,V_a] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => 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)))) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__pos__neg,axiom,
% 59.73/59.58 ! [V_b,V_a] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => 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)))) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__int__def,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__int__def,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__neg__pos,axiom,
% 59.73/59.58 ! [V_b,V_a] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__neg__pos,axiom,
% 59.73/59.58 ! [V_b,V_a] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__pos__pos,axiom,
% 59.73/59.58 ! [V_b,V_a] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__pos__pos,axiom,
% 59.73/59.58 ! [V_b,V_a] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_pair__imageI,axiom,
% 59.73/59.58 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 59.73/59.58 ( 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))
% 59.73/59.58 => 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))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_prod__size__simp,axiom,
% 59.73/59.58 ! [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))) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_split__comp,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_split__def,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_split__comp__eq,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_splitI,axiom,
% 59.73/59.58 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 59.73/59.58 => 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))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_prod__caseI,axiom,
% 59.73/59.58 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 59.73/59.58 => 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))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mem__splitI,axiom,
% 59.73/59.58 ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
% 59.73/59.58 => 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)))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_splitD,axiom,
% 59.73/59.58 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_splitD_H,axiom,
% 59.73/59.58 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 59.73/59.58 ( 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))
% 59.73/59.58 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_Id__on__def_H,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_split__paired__The,axiom,
% 59.73/59.58 ! [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)))) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_The__split__eq,axiom,
% 59.73/59.58 ! [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) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_inj__graph,axiom,
% 59.73/59.58 ! [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))) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__nat__def,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__nat__def,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_The__split,axiom,
% 59.73/59.58 ! [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))) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__nat__rel__def,axiom,
% 59.73/59.58 ! [V_qr_2,V_n_2,V_m_2] :
% 59.73/59.58 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 59.73/59.58 <=> ( 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))
% 59.73/59.58 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.58 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 59.73/59.58 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.58 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 59.73/59.58 => ( 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)))
% 59.73/59.58 & 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)) ) )
% 59.73/59.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 59.73/59.58 => ( 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)))
% 59.73/59.58 & 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))) ) ) ) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_Pair__inject,axiom,
% 59.73/59.58 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 59.73/59.58 ( 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)
% 59.73/59.58 => ~ ( V_a = V_a_H
% 59.73/59.58 => V_b != V_b_H ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_Pair__eq,axiom,
% 59.73/59.58 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 59.73/59.58 ( 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)
% 59.73/59.58 <=> ( V_a_2 = V_a_H_2
% 59.73/59.58 & V_b_2 = V_b_H_2 ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_split__paired__All,axiom,
% 59.73/59.58 ! [T_c,T_b,V_P_2] :
% 59.73/59.58 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 59.73/59.58 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_split__weak__cong,axiom,
% 59.73/59.58 ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 59.73/59.58 ( V_p_2 = V_q_2
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_finite__psubset__def,axiom,
% 59.73/59.58 ! [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)))) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divmod__int__rel__def,axiom,
% 59.73/59.58 ! [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))))))) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_prod_Osimps_I2_J,axiom,
% 59.73/59.58 ! [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) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_split__conv,axiom,
% 59.73/59.58 ! [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) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_fst__eqD,axiom,
% 59.73/59.58 ! [V_a,V_y,V_x,T_b,T_a] :
% 59.73/59.58 ( 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
% 59.73/59.58 => V_x = V_a ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_fst__conv,axiom,
% 59.73/59.58 ! [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 ).
% 59.73/59.58
% 59.73/59.58 fof(fact_snd__eqD,axiom,
% 59.73/59.58 ! [V_a,V_y,V_x,T_a,T_b] :
% 59.73/59.58 ( 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
% 59.73/59.58 => V_y = V_a ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_snd__conv,axiom,
% 59.73/59.58 ! [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 ).
% 59.73/59.58
% 59.73/59.58 fof(fact_prod__eqI,axiom,
% 59.73/59.58 ! [V_q,V_p,T_b,T_a] :
% 59.73/59.58 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 59.73/59.58 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 59.73/59.58 => V_p = V_q ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_Pair__fst__snd__eq,axiom,
% 59.73/59.58 ! [T_c,T_b,V_t_2,V_s_2] :
% 59.73/59.58 ( V_s_2 = V_t_2
% 59.73/59.58 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 59.73/59.58 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_split__eta,axiom,
% 59.73/59.58 ! [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 ).
% 59.73/59.58
% 59.73/59.58 fof(fact_fst__def,axiom,
% 59.73/59.58 ! [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) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_snd__def,axiom,
% 59.73/59.58 ! [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) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_swap__inj__on,axiom,
% 59.73/59.58 ! [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) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_split__twice,axiom,
% 59.73/59.58 ! [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) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_pair__collapse,axiom,
% 59.73/59.58 ! [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 ).
% 59.73/59.58
% 59.73/59.58 fof(fact_surjective__pairing,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_prod__case__beta,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_split__beta,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_Nitpick_OFrac__def,axiom,
% 59.73/59.58 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)))) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_exI__realizer,axiom,
% 59.73/59.58 ! [T_b,T_c,V_x_2,V_y_2,V_P_2] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
% 59.73/59.58 => 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)))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_conjI__realizer,axiom,
% 59.73/59.58 ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_P_2] :
% 59.73/59.58 ( hBOOL(hAPP(V_P_2,V_p_2))
% 59.73/59.58 => ( hBOOL(hAPP(V_Q_2,V_q_2))
% 59.73/59.58 => ( 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))))
% 59.73/59.58 & 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)))) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_int__ge__less__than2__def,axiom,
% 59.73/59.58 ! [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)))) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_int__ge__less__than__def,axiom,
% 59.73/59.58 ! [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)))) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_Nitpick_Oprod__def,axiom,
% 59.73/59.58 ! [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)))) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__pos__neg__1__number__of,axiom,
% 59.73/59.58 ! [V_w] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => 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))))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__pos__neg__1__number__of,axiom,
% 59.73/59.58 ! [V_w] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => 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))))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_inv__image__def,axiom,
% 59.73/59.58 ! [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))) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_prod_Orecs,axiom,
% 59.73/59.58 ! [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) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_less__eq__number__of__int__code,axiom,
% 59.73/59.58 ! [V_l_2,V_k_2] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_less__number__of__int__code,axiom,
% 59.73/59.58 ! [V_l_2,V_k_2] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_plus__numeral__code_I9_J,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_number__of__is__id,axiom,
% 59.73/59.58 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 59.73/59.58
% 59.73/59.58 fof(fact_number__of__reorient,axiom,
% 59.73/59.58 ! [V_x_2,V_w_2,T_b] :
% 59.73/59.58 ( class_Int_Onumber(T_b)
% 59.73/59.58 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 59.73/59.58 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_eq__number__of,axiom,
% 59.73/59.58 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.58 ( ( class_Int_Onumber__ring(T_b)
% 59.73/59.58 & class_Int_Oring__char__0(T_b) )
% 59.73/59.58 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 59.73/59.58 <=> V_x_2 = V_y_2 ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_times__numeral__code_I5_J,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_minus__numeral__code_I5_J,axiom,
% 59.73/59.58 ! [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)) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_le__number__of__eq__not__less,axiom,
% 59.73/59.58 ! [V_w_2,V_v_2,T_b] :
% 59.73/59.58 ( ( class_Int_Onumber(T_b)
% 59.73/59.58 & class_Orderings_Olinorder(T_b) )
% 59.73/59.58 => ( 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)))
% 59.73/59.58 <=> ~ 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))) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_left__distrib__number__of,axiom,
% 59.73/59.58 ! [V_v,V_b,V_a,T_b] :
% 59.73/59.58 ( ( class_Int_Onumber(T_b)
% 59.73/59.58 & class_Rings_Osemiring(T_b) )
% 59.73/59.58 => 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))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_right__distrib__number__of,axiom,
% 59.73/59.58 ! [V_c,V_b,V_v,T_b] :
% 59.73/59.58 ( ( class_Int_Onumber(T_b)
% 59.73/59.58 & class_Rings_Osemiring(T_b) )
% 59.73/59.58 => 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)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_right__diff__distrib__number__of,axiom,
% 59.73/59.58 ! [V_c,V_b,V_v,T_b] :
% 59.73/59.58 ( ( class_Int_Onumber(T_b)
% 59.73/59.58 & class_Rings_Oring(T_b) )
% 59.73/59.58 => 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)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_left__diff__distrib__number__of,axiom,
% 59.73/59.58 ! [V_v,V_b,V_a,T_b] :
% 59.73/59.58 ( ( class_Int_Onumber(T_b)
% 59.73/59.58 & class_Rings_Oring(T_b) )
% 59.73/59.58 => 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))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_le__number__of,axiom,
% 59.73/59.58 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.58 ( ( class_Int_Onumber__ring(T_b)
% 59.73/59.58 & class_Rings_Olinordered__idom(T_b) )
% 59.73/59.58 => ( 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)))
% 59.73/59.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_less__number__of,axiom,
% 59.73/59.58 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.58 ( ( class_Int_Onumber__ring(T_b)
% 59.73/59.58 & class_Rings_Olinordered__idom(T_b) )
% 59.73/59.58 => ( 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)))
% 59.73/59.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_add__number__of__left,axiom,
% 59.73/59.58 ! [V_z,V_w,V_v,T_a] :
% 59.73/59.58 ( class_Int_Onumber__ring(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_add__number__of__eq,axiom,
% 59.73/59.58 ! [V_w,V_v,T_a] :
% 59.73/59.58 ( class_Int_Onumber__ring(T_a)
% 59.73/59.58 => 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)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_number__of__add,axiom,
% 59.73/59.58 ! [V_w,V_v,T_a] :
% 59.73/59.58 ( class_Int_Onumber__ring(T_a)
% 59.73/59.58 => 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)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mult__number__of__left,axiom,
% 59.73/59.58 ! [V_z,V_w,V_v,T_a] :
% 59.73/59.58 ( class_Int_Onumber__ring(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_arith__simps_I32_J,axiom,
% 59.73/59.58 ! [V_w,V_v,T_a] :
% 59.73/59.58 ( class_Int_Onumber__ring(T_a)
% 59.73/59.58 => 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)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_number__of__mult,axiom,
% 59.73/59.58 ! [V_w,V_v,T_a] :
% 59.73/59.58 ( class_Int_Onumber__ring(T_a)
% 59.73/59.58 => 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)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_number__of__diff,axiom,
% 59.73/59.58 ! [V_w,V_v,T_a] :
% 59.73/59.58 ( class_Int_Onumber__ring(T_a)
% 59.73/59.58 => 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)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_number__of__minus,axiom,
% 59.73/59.58 ! [V_w,T_a] :
% 59.73/59.58 ( class_Int_Onumber__ring(T_a)
% 59.73/59.58 => 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)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_arith__simps_I30_J,axiom,
% 59.73/59.58 ! [V_w,T_a] :
% 59.73/59.58 ( class_Int_Onumber__ring(T_a)
% 59.73/59.58 => 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)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_Ints__number__of,axiom,
% 59.73/59.58 ! [V_w_2,T_b] :
% 59.73/59.58 ( class_Int_Onumber__ring(T_b)
% 59.73/59.58 => 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))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_add__number__of__diff1,axiom,
% 59.73/59.58 ! [V_c,V_w,V_v,T_a] :
% 59.73/59.58 ( class_Int_Onumber__ring(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_minus__number__of__mult,axiom,
% 59.73/59.58 ! [V_z,V_w,T_a] :
% 59.73/59.58 ( class_Int_Onumber__ring(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_diff__number__of__eq,axiom,
% 59.73/59.58 ! [V_w,V_v,T_a] :
% 59.73/59.58 ( class_Int_Onumber__ring(T_a)
% 59.73/59.58 => 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))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_minus__numeral__code_I6_J,axiom,
% 59.73/59.58 ! [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))) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_in__inv__image,axiom,
% 59.73/59.58 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 <=> 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)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_add__number__of__diff2,axiom,
% 59.73/59.58 ! [V_w,V_c,V_v,T_a] :
% 59.73/59.58 ( class_Int_Onumber__ring(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_mod__pos__pos__1__number__of,axiom,
% 59.73/59.58 ! [V_w] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => 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))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_div__pos__pos__1__number__of,axiom,
% 59.73/59.58 ! [V_w] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => 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))) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_rp__inv__image__def,axiom,
% 59.73/59.58 ! [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))) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_lfp__induct2,axiom,
% 59.73/59.58 ! [V_P_2,V_f_2,V_b_2,V_a_2,T_c,T_b] :
% 59.73/59.58 ( 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)))
% 59.73/59.58 => ( 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)
% 59.73/59.58 => ( ! [B_a,B_b] :
% 59.73/59.58 ( 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))))))
% 59.73/59.58 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) )
% 59.73/59.58 => hBOOL(hAPP(hAPP(V_P_2,V_a_2),V_b_2)) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_power__number__of__odd__number__of,axiom,
% 59.73/59.58 ! [V_v_2,V_w_2,T_b] :
% 59.73/59.58 ( class_Int_Onumber__ring(T_b)
% 59.73/59.58 => ( ( 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)))
% 59.73/59.58 => 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))) )
% 59.73/59.58 & ( ~ 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)))
% 59.73/59.58 => 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) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_setprod__diff1,axiom,
% 59.73/59.58 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 59.73/59.58 ( class_Fields_Ofield(T_c)
% 59.73/59.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.58 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 59.73/59.58 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.58 => 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)) )
% 59.73/59.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.58 => 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) ) ) ) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_pair__lessI2,axiom,
% 59.73/59.58 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 59.73/59.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 59.73/59.58 => 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)) ) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_rel__simps_I34_J,axiom,
% 59.73/59.58 ! [V_l_2,V_k_2] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 59.73/59.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_less__eq__int__code_I16_J,axiom,
% 59.73/59.58 ! [V_k2_2,V_k1_2] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 59.73/59.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_less__int__code_I16_J,axiom,
% 59.73/59.58 ! [V_k2_2,V_k1_2] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 59.73/59.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_rel__simps_I17_J,axiom,
% 59.73/59.58 ! [V_l_2,V_k_2] :
% 59.73/59.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 59.73/59.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divide__zero__left,axiom,
% 59.73/59.58 ! [V_a,T_a] :
% 59.73/59.58 ( class_Rings_Odivision__ring(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divide__zero,axiom,
% 59.73/59.58 ! [V_a,T_a] :
% 59.73/59.58 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_add__divide__distrib,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.58 ( class_Rings_Odivision__ring(T_a)
% 59.73/59.58 => 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)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_times__divide__eq__right,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.58 ( class_Rings_Odivision__ring(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_rel__simps_I51_J,axiom,
% 59.73/59.58 ! [V_l_2,V_k_2] :
% 59.73/59.58 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 59.73/59.58 <=> V_k_2 = V_l_2 ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_power__divide,axiom,
% 59.73/59.58 ! [V_n,V_b,V_a,T_a] :
% 59.73/59.58 ( class_Fields_Ofield__inverse__zero(T_a)
% 59.73/59.58 => 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)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_minus__divide__left,axiom,
% 59.73/59.58 ! [V_b,V_a,T_a] :
% 59.73/59.58 ( class_Rings_Odivision__ring(T_a)
% 59.73/59.58 => 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) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_divide__1,axiom,
% 59.73/59.58 ! [V_a,T_a] :
% 59.73/59.58 ( class_Rings_Odivision__ring(T_a)
% 59.73/59.58 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_diff__divide__distrib,axiom,
% 59.73/59.58 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.58 ( class_Rings_Odivision__ring(T_a)
% 59.73/59.58 => 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)) ) ).
% 59.73/59.58
% 59.73/59.58 fof(fact_eq__divide__imp,axiom,
% 59.73/59.58 ! [V_b,V_a,V_c,T_a] :
% 59.73/59.58 ( class_Rings_Odivision__ring(T_a)
% 59.73/59.58 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.58 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 59.73/59.58 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__eq__imp,axiom,
% 59.73/59.59 ! [V_a,V_b,V_c,T_a] :
% 59.73/59.59 ( class_Rings_Odivision__ring(T_a)
% 59.73/59.59 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 59.73/59.59 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nonzero__divide__eq__eq,axiom,
% 59.73/59.59 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 59.73/59.59 ( class_Rings_Odivision__ring(T_b)
% 59.73/59.59 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 59.73/59.59 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nonzero__eq__divide__eq,axiom,
% 59.73/59.59 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 59.73/59.59 ( class_Rings_Odivision__ring(T_b)
% 59.73/59.59 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 59.73/59.59 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_right__inverse__eq,axiom,
% 59.73/59.59 ! [V_a_2,V_b_2,T_b] :
% 59.73/59.59 ( class_Rings_Odivision__ring(T_b)
% 59.73/59.59 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
% 59.73/59.59 <=> V_a_2 = V_b_2 ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__self,axiom,
% 59.73/59.59 ! [V_a,T_a] :
% 59.73/59.59 ( class_Rings_Odivision__ring(T_a)
% 59.73/59.59 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__self__if,axiom,
% 59.73/59.59 ! [V_a,T_a] :
% 59.73/59.59 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 59.73/59.59 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 59.73/59.59 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nonzero__minus__divide__divide,axiom,
% 59.73/59.59 ! [V_a,V_b,T_a] :
% 59.73/59.59 ( class_Rings_Odivision__ring(T_a)
% 59.73/59.59 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nonzero__minus__divide__right,axiom,
% 59.73/59.59 ! [V_a,V_b,T_a] :
% 59.73/59.59 ( class_Rings_Odivision__ring(T_a)
% 59.73/59.59 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nonzero__power__divide,axiom,
% 59.73/59.59 ! [V_n,V_a,V_b,T_a] :
% 59.73/59.59 ( class_Fields_Ofield(T_a)
% 59.73/59.59 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => 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)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power__one__over,axiom,
% 59.73/59.59 ! [V_n,V_a,T_a] :
% 59.73/59.59 ( class_Fields_Ofield__inverse__zero(T_a)
% 59.73/59.59 => 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) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_bin__less__0__simps_I4_J,axiom,
% 59.73/59.59 ! [V_w_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Bit1__def,axiom,
% 59.73/59.59 ! [V_k] : c_Int_OBit1(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)),V_k) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_setprod__dividef,axiom,
% 59.73/59.59 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 59.73/59.59 ( class_Fields_Ofield__inverse__zero(T_c)
% 59.73/59.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.59 => 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)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_eq__divide__eq__number__of1,axiom,
% 59.73/59.59 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 59.73/59.59 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 59.73/59.59 & class_Int_Onumber(T_b) )
% 59.73/59.59 => ( 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))
% 59.73/59.59 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 => 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 )
% 59.73/59.59 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_eq__divide__eq__number__of,axiom,
% 59.73/59.59 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 59.73/59.59 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 59.73/59.59 & class_Int_Onumber(T_b) )
% 59.73/59.59 => ( 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)
% 59.73/59.59 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 => 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 )
% 59.73/59.59 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__eq__eq__number__of,axiom,
% 59.73/59.59 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 59.73/59.59 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 59.73/59.59 & class_Int_Onumber(T_b) )
% 59.73/59.59 => ( 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)
% 59.73/59.59 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 => 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) )
% 59.73/59.59 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__eq__eq__number__of1,axiom,
% 59.73/59.59 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 59.73/59.59 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 59.73/59.59 & class_Int_Onumber(T_b) )
% 59.73/59.59 => ( 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
% 59.73/59.59 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 => 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)) )
% 59.73/59.59 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_number__of__Bit1,axiom,
% 59.73/59.59 ! [V_w,T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power__number__of__odd,axiom,
% 59.73/59.59 ! [V_z_2,V_w_2,T_b] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_b)
% 59.73/59.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 59.73/59.59 => 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))) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 59.73/59.59 => 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) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_zpower__number__of__odd,axiom,
% 59.73/59.59 ! [V_z_2,V_w_2] :
% 59.73/59.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 59.73/59.59 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z_2))),c_COMBI(tc_Int_Oint))) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 59.73/59.59 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__less__eq__number__of1,axiom,
% 59.73/59.59 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 59.73/59.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 59.73/59.59 & class_Int_Onumber(T_b) )
% 59.73/59.59 => ( 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))
% 59.73/59.59 <=> ( ( 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)))
% 59.73/59.59 => 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)))) )
% 59.73/59.59 & ( ~ 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)))
% 59.73/59.59 => ( ( 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)))
% 59.73/59.59 => 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)) )
% 59.73/59.59 & ( ~ 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)))
% 59.73/59.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__less__eq__number__of,axiom,
% 59.73/59.59 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 59.73/59.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 59.73/59.59 & class_Int_Onumber(T_b) )
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => 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))) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => 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)) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => 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))) ) ) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__divide__eq__number__of,axiom,
% 59.73/59.59 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 59.73/59.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 59.73/59.59 & class_Int_Onumber(T_b) )
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => 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)) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => 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))) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => 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))) ) ) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__divide__eq__number__of1,axiom,
% 59.73/59.59 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 59.73/59.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 59.73/59.59 & class_Int_Onumber(T_b) )
% 59.73/59.59 => ( 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))))
% 59.73/59.59 <=> ( ( 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)))
% 59.73/59.59 => 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)) )
% 59.73/59.59 & ( ~ 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)))
% 59.73/59.59 => ( ( 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)))
% 59.73/59.59 => 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)))) )
% 59.73/59.59 & ( ~ 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)))
% 59.73/59.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power__diff,axiom,
% 59.73/59.59 ! [V_m,V_n,V_a,T_a] :
% 59.73/59.59 ( class_Fields_Ofield(T_a)
% 59.73/59.59 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 59.73/59.59 => 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)) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_pair__lessI1,axiom,
% 59.73/59.59 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 59.73/59.59 => 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)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_le__divide__eq__number__of1,axiom,
% 59.73/59.59 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 59.73/59.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 59.73/59.59 & class_Int_Onumber(T_b) )
% 59.73/59.59 => ( 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))))
% 59.73/59.59 <=> ( ( 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)))
% 59.73/59.59 => 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)) )
% 59.73/59.59 & ( ~ 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)))
% 59.73/59.59 => ( ( 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)))
% 59.73/59.59 => 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)))) )
% 59.73/59.59 & ( ~ 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)))
% 59.73/59.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_le__divide__eq__number__of,axiom,
% 59.73/59.59 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 59.73/59.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 59.73/59.59 & class_Int_Onumber(T_b) )
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => 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)) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => 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))) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => 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))) ) ) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__le__eq__number__of,axiom,
% 59.73/59.59 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 59.73/59.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 59.73/59.59 & class_Int_Onumber(T_b) )
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => 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))) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => 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)) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => 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))) ) ) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__le__eq__number__of1,axiom,
% 59.73/59.59 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 59.73/59.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 59.73/59.59 & class_Int_Onumber(T_b) )
% 59.73/59.59 => ( 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))
% 59.73/59.59 <=> ( ( 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)))
% 59.73/59.59 => 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)))) )
% 59.73/59.59 & ( ~ 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)))
% 59.73/59.59 => ( ( 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)))
% 59.73/59.59 => 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)) )
% 59.73/59.59 & ( ~ 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)))
% 59.73/59.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_expand__Suc,axiom,
% 59.73/59.59 ! [V_v] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)))
% 59.73/59.59 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__left__mono__neg,axiom,
% 59.73/59.59 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.59 => ( 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)))
% 59.73/59.59 => 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))) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__left__mono,axiom,
% 59.73/59.59 ! [V_c,V_a,V_b,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.73/59.59 => ( 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)))
% 59.73/59.59 => 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))) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_neg__divide__le__eq,axiom,
% 59.73/59.59 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_b)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => ( 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))
% 59.73/59.59 <=> 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)) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_neg__le__divide__eq,axiom,
% 59.73/59.59 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_b)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mult__imp__le__div__pos,axiom,
% 59.73/59.59 ! [V_x,V_z,V_y,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 59.73/59.59 => ( 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))
% 59.73/59.59 => 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_times__divide__times__eq,axiom,
% 59.73/59.59 ! [V_w,V_z,V_y,V_x,T_a] :
% 59.73/59.59 ( class_Fields_Ofield__inverse__zero(T_a)
% 59.73/59.59 => 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)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_minus__divide__right,axiom,
% 59.73/59.59 ! [V_b,V_a,T_a] :
% 59.73/59.59 ( class_Fields_Ofield__inverse__zero(T_a)
% 59.73/59.59 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_minus__divide__divide,axiom,
% 59.73/59.59 ! [V_b,V_a,T_a] :
% 59.73/59.59 ( class_Fields_Ofield__inverse__zero(T_a)
% 59.73/59.59 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__right__mono__neg,axiom,
% 59.73/59.59 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.59 => 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__right__mono,axiom,
% 59.73/59.59 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.73/59.59 => 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__le__0__iff,axiom,
% 59.73/59.59 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.59 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 59.73/59.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 59.73/59.59 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_zero__le__divide__iff,axiom,
% 59.73/59.59 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.59 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 59.73/59.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 59.73/59.59 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_zero__less__divide__iff,axiom,
% 59.73/59.59 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.59 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 59.73/59.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 59.73/59.59 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__less__0__iff,axiom,
% 59.73/59.59 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.59 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 59.73/59.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 59.73/59.59 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__pos__pos,axiom,
% 59.73/59.59 ! [V_y,V_x,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 59.73/59.59 => 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__pos__neg,axiom,
% 59.73/59.59 ! [V_y,V_x,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.59 => 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__neg__pos,axiom,
% 59.73/59.59 ! [V_y,V_x,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 59.73/59.59 => 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__neg__neg,axiom,
% 59.73/59.59 ! [V_y,V_x,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.59 => 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__strict__right__mono,axiom,
% 59.73/59.59 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.73/59.59 => 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__strict__right__mono__neg,axiom,
% 59.73/59.59 ! [V_c,V_a,V_b,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.59 => 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_frac__eq__eq,axiom,
% 59.73/59.59 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 59.73/59.59 ( class_Fields_Ofield(T_b)
% 59.73/59.59 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 => ( 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)
% 59.73/59.59 <=> 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) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mult__divide__mult__cancel__left,axiom,
% 59.73/59.59 ! [V_b,V_a,V_c,T_a] :
% 59.73/59.59 ( class_Fields_Ofield__inverse__zero(T_a)
% 59.73/59.59 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => 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) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mult__divide__mult__cancel__right,axiom,
% 59.73/59.59 ! [V_b,V_a,V_c,T_a] :
% 59.73/59.59 ( class_Fields_Ofield__inverse__zero(T_a)
% 59.73/59.59 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => 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) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__eq__eq,axiom,
% 59.73/59.59 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 59.73/59.59 ( class_Fields_Ofield__inverse__zero(T_b)
% 59.73/59.59 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 59.73/59.59 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) )
% 59.73/59.59 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_eq__divide__eq,axiom,
% 59.73/59.59 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 59.73/59.59 ( class_Fields_Ofield__inverse__zero(T_b)
% 59.73/59.59 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 59.73/59.59 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 )
% 59.73/59.59 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__nonpos__neg,axiom,
% 59.73/59.59 ! [V_y,V_x,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.59 => 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__nonpos__pos,axiom,
% 59.73/59.59 ! [V_y,V_x,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 59.73/59.59 => 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_frac__le,axiom,
% 59.73/59.59 ! [V_z,V_w,V_y,V_x,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 59.73/59.59 => 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))) ) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_frac__less,axiom,
% 59.73/59.59 ! [V_z,V_w,V_y,V_x,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 59.73/59.59 => 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))) ) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_frac__less2,axiom,
% 59.73/59.59 ! [V_z,V_w,V_y,V_x,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 59.73/59.59 => 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))) ) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__nonneg__neg,axiom,
% 59.73/59.59 ! [V_y,V_x,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.59 => 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__nonneg__pos,axiom,
% 59.73/59.59 ! [V_y,V_x,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 59.73/59.59 => 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__divide__eq,axiom,
% 59.73/59.59 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 59.73/59.59 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => 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)) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => 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))) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__less__eq,axiom,
% 59.73/59.59 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 59.73/59.59 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 59.73/59.59 => ( 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))
% 59.73/59.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => 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))) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => 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)) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_pos__less__divide__eq,axiom,
% 59.73/59.59 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_b)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> 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)) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_pos__divide__less__eq,axiom,
% 59.73/59.59 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_b)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => ( 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))
% 59.73/59.59 <=> 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mult__imp__div__pos__less,axiom,
% 59.73/59.59 ! [V_z,V_x,V_y,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 59.73/59.59 => ( 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)))
% 59.73/59.59 => 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)) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mult__imp__less__div__pos,axiom,
% 59.73/59.59 ! [V_x,V_z,V_y,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 59.73/59.59 => ( 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))
% 59.73/59.59 => 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_neg__less__divide__eq,axiom,
% 59.73/59.59 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_b)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_neg__divide__less__eq,axiom,
% 59.73/59.59 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_b)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => ( 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))
% 59.73/59.59 <=> 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)) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__strict__left__mono,axiom,
% 59.73/59.59 ! [V_c,V_a,V_b,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 59.73/59.59 => ( 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)))
% 59.73/59.59 => 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))) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__strict__left__mono__neg,axiom,
% 59.73/59.59 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.59 => ( 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)))
% 59.73/59.59 => 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))) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__frac__eq,axiom,
% 59.73/59.59 ! [V_w,V_x,V_z,V_y,T_a] :
% 59.73/59.59 ( class_Fields_Ofield(T_a)
% 59.73/59.59 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => 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)) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__add__eq__iff,axiom,
% 59.73/59.59 ! [V_y,V_x,V_z,T_a] :
% 59.73/59.59 ( class_Fields_Ofield(T_a)
% 59.73/59.59 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => 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) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__frac__num,axiom,
% 59.73/59.59 ! [V_z,V_x,V_y,T_a] :
% 59.73/59.59 ( class_Fields_Ofield__inverse__zero(T_a)
% 59.73/59.59 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => 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) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__divide__eq__iff,axiom,
% 59.73/59.59 ! [V_y,V_x,V_z,T_a] :
% 59.73/59.59 ( class_Fields_Ofield(T_a)
% 59.73/59.59 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => 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) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__num__frac,axiom,
% 59.73/59.59 ! [V_x,V_z,V_y,T_a] :
% 59.73/59.59 ( class_Fields_Ofield__inverse__zero(T_a)
% 59.73/59.59 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => 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) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_diff__frac__eq,axiom,
% 59.73/59.59 ! [V_w,V_x,V_z,V_y,T_a] :
% 59.73/59.59 ( class_Fields_Ofield(T_a)
% 59.73/59.59 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => 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)) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__diff__eq__iff,axiom,
% 59.73/59.59 ! [V_y,V_x,V_z,T_a] :
% 59.73/59.59 ( class_Fields_Ofield(T_a)
% 59.73/59.59 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => 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) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_diff__divide__eq__iff,axiom,
% 59.73/59.59 ! [V_y,V_x,V_z,T_a] :
% 59.73/59.59 ( class_Fields_Ofield(T_a)
% 59.73/59.59 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.59 => 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) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_gt__half__sum,axiom,
% 59.73/59.59 ! [V_b,V_a,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 59.73/59.59 => 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)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__half__sum,axiom,
% 59.73/59.59 ! [V_b,V_a,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 59.73/59.59 => 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))))) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_le__divide__eq,axiom,
% 59.73/59.59 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 59.73/59.59 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => 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)) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => 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))) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__le__eq,axiom,
% 59.73/59.59 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 59.73/59.59 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 59.73/59.59 => ( 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))
% 59.73/59.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => 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))) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => 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)) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 59.73/59.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_pos__le__divide__eq,axiom,
% 59.73/59.59 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_b)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> 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)) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_pos__divide__le__eq,axiom,
% 59.73/59.59 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_b)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 59.73/59.59 => ( 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))
% 59.73/59.59 <=> 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mult__imp__div__pos__le,axiom,
% 59.73/59.59 ! [V_z,V_x,V_y,T_a] :
% 59.73/59.59 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 59.73/59.59 => ( 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)))
% 59.73/59.59 => 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)) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_pair__leqI2,axiom,
% 59.73/59.59 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 59.73/59.59 => 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)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_smin__insertI,axiom,
% 59.73/59.59 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 59.73/59.59 => ( 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))
% 59.73/59.59 => ( 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))
% 59.73/59.59 => 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)) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_smax__insertI,axiom,
% 59.73/59.59 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 59.73/59.59 => ( 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))
% 59.73/59.59 => ( 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))
% 59.73/59.59 => 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)) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_pair__leqI1,axiom,
% 59.73/59.59 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 59.73/59.59 => 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)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_setprod__Un,axiom,
% 59.73/59.59 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 59.73/59.59 ( class_Fields_Ofield(T_c)
% 59.73/59.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.59 => ( ! [B_x] :
% 59.73/59.59 ( 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)))
% 59.73/59.59 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 59.73/59.59 => 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))) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_smax__emptyI,axiom,
% 59.73/59.59 ! [V_Y_2] :
% 59.73/59.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 59.73/59.59 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 59.73/59.59 => 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)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_smin__emptyI,axiom,
% 59.73/59.59 ! [V_X_2] :
% 59.73/59.59 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 59.73/59.59 => 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)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_max__strict__def,axiom,
% 59.73/59.59 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_wmax__insertI,axiom,
% 59.73/59.59 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 59.73/59.59 => ( 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))
% 59.73/59.59 => ( 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))
% 59.73/59.59 => 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)) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_wmin__insertI,axiom,
% 59.73/59.59 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 59.73/59.59 => ( 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))
% 59.73/59.59 => ( 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))
% 59.73/59.59 => 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)) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_max__weak__def,axiom,
% 59.73/59.59 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)))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__number__of__Bit1,axiom,
% 59.73/59.59 ! [V_w_2] :
% 59.73/59.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 59.73/59.59 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 59.73/59.59 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_wmax__emptyI,axiom,
% 59.73/59.59 ! [V_X_2] :
% 59.73/59.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 59.73/59.59 => 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)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_not__neg__0,axiom,
% 59.73/59.59 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_not__neg__1,axiom,
% 59.73/59.59 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_not__neg__eq__ge__0,axiom,
% 59.73/59.59 ! [V_x_2] :
% 59.73/59.59 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_neg__def,axiom,
% 59.73/59.59 ! [V_Z_2] :
% 59.73/59.59 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_neg__number__of__Bit1,axiom,
% 59.73/59.59 ! [V_w_2] :
% 59.73/59.59 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 59.73/59.59 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_neg__imp__number__of__eq__0,axiom,
% 59.73/59.59 ! [V_v] :
% 59.73/59.59 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.59 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_eq__nat__number__of,axiom,
% 59.73/59.59 ! [V_v_H_2,V_v_2] :
% 59.73/59.59 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)
% 59.73/59.59 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 59.73/59.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 59.73/59.59 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 59.73/59.59 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 59.73/59.59 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__number__of__add__left,axiom,
% 59.73/59.59 ! [V_k,V_v_H,V_v] :
% 59.73/59.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.59 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_k) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_wmin__emptyI,axiom,
% 59.73/59.59 ! [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)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_min__weak__def,axiom,
% 59.73/59.59 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)))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Suc__nat__number__of__add,axiom,
% 59.73/59.59 ! [V_n,V_v] :
% 59.73/59.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.59 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.59 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))),V_n) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Suc__nat__number__of,axiom,
% 59.73/59.59 ! [V_v] :
% 59.73/59.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.59 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.59 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_one__mod__nat__number__of,axiom,
% 59.73/59.59 ! [V_v_H] :
% 59.73/59.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 59.73/59.59 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 59.73/59.59 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_min__rpair__set,axiom,
% 59.73/59.59 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)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 59.73/59.59 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))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__0,axiom,
% 59.73/59.59 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 59.73/59.59 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_eq__nat__nat__iff,axiom,
% 59.73/59.59 ! [V_z_H_2,V_z_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 59.73/59.59 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 59.73/59.59 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 59.73/59.59 ! [V_y_2,V_x_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 59.73/59.59 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 59.73/59.59 <=> V_x_2 = V_y_2 ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_all__nat,axiom,
% 59.73/59.59 ! [V_P_2] :
% 59.73/59.59 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 59.73/59.59 <=> ! [B_x] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 59.73/59.59 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_ex__nat,axiom,
% 59.73/59.59 ! [V_P_2] :
% 59.73/59.59 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 59.73/59.59 <=> ? [B_x] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 59.73/59.59 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__number__of__def,axiom,
% 59.73/59.59 ! [V_v] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__number__of,axiom,
% 59.73/59.59 ! [V_w] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 59.73/59.59 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_neg__nat,axiom,
% 59.73/59.59 ! [V_z] :
% 59.73/59.59 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 59.73/59.59 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__le__0,axiom,
% 59.73/59.59 ! [V_z] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.59 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__0__iff,axiom,
% 59.73/59.59 ! [V_i_2] :
% 59.73/59.59 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_zless__nat__conj,axiom,
% 59.73/59.59 ! [V_z_2,V_w_2] :
% 59.73/59.59 ( 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)))
% 59.73/59.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 59.73/59.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__mono__iff,axiom,
% 59.73/59.59 ! [V_w_2,V_z_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 59.73/59.59 ! [V_y_2,V_x_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__1,axiom,
% 59.73/59.59 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 59.73/59.59 ! [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)))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_succ__def,axiom,
% 59.73/59.59 ! [V_k] : c_Int_Osucc(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_zero__less__nat__eq,axiom,
% 59.73/59.59 ! [V_z_2] :
% 59.73/59.59 ( 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)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__less__eq__zless,axiom,
% 59.73/59.59 ! [V_z_2,V_w_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 59.73/59.59 ! [V_y_2,V_x_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__le__eq__zle,axiom,
% 59.73/59.59 ! [V_z_2,V_w_2] :
% 59.73/59.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 59.73/59.59 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__add__distrib,axiom,
% 59.73/59.59 ! [V_z_H,V_z] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 59.73/59.59 => 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)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 59.73/59.59 ! [V_y,V_x] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 59.73/59.59 => 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)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__mult__distrib,axiom,
% 59.73/59.59 ! [V_z_H,V_z] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 59.73/59.59 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 59.73/59.59 ! [V_y,V_x] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 59.73/59.59 => 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)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__diff__distrib,axiom,
% 59.73/59.59 ! [V_z,V_z_H] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 59.73/59.59 => 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)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__mod__distrib,axiom,
% 59.73/59.59 ! [V_y,V_x] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 59.73/59.59 => 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)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 59.73/59.59 ! [V_y,V_x] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 59.73/59.59 => 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)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__div__distrib,axiom,
% 59.73/59.59 ! [V_y,V_x] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 59.73/59.59 => 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)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 59.73/59.59 ! [V_y,V_x] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 59.73/59.59 => 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)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 59.73/59.59 ! [V_n,V_x] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 59.73/59.59 => 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)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__power__eq,axiom,
% 59.73/59.59 ! [V_n,V_z] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 59.73/59.59 => 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) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 59.73/59.59 ! [V_y,V_x] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 59.73/59.59 => 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)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_diff__nat__eq__if,axiom,
% 59.73/59.59 ! [V_z_2,V_z_H_2] :
% 59.73/59.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 59.73/59.59 => 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) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 59.73/59.59 => 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)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_one__less__nat__eq,axiom,
% 59.73/59.59 ! [V_z_2] :
% 59.73/59.59 ( 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)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 59.73/59.59 ! [V_z] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 59.73/59.59 => 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)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_number__of__succ,axiom,
% 59.73/59.59 ! [V_k,T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Osucc(V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__mult__distrib__neg,axiom,
% 59.73/59.59 ! [V_z_H,V_z] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.59 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_H))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rp__inv__image__rp,axiom,
% 59.73/59.59 ! [V_f_2,T_c,V_P_2,T_b] :
% 59.73/59.59 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 59.73/59.59 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_P_2),V_f_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mod__nat__number__of,axiom,
% 59.73/59.59 ! [V_v_H,V_v] :
% 59.73/59.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.59 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.59 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 59.73/59.59 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 59.73/59.59 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_div__nat__number__of,axiom,
% 59.73/59.59 ! [V_v_H,V_v] :
% 59.73/59.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.59 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.59 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power__nat__number__of__number__of,axiom,
% 59.73/59.59 ! [V_w,V_v] :
% 59.73/59.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.59 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.59 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w))) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power__nat__number__of,axiom,
% 59.73/59.59 ! [V_n,V_v] :
% 59.73/59.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.59 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.59 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),V_n)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_one__div__nat__number__of,axiom,
% 59.73/59.59 ! [V_v_H] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_min__strict__def,axiom,
% 59.73/59.59 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_max__rpair__set,axiom,
% 59.73/59.59 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)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__aux__def,axiom,
% 59.73/59.59 ! [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) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_diff__nat__number__of,axiom,
% 59.73/59.59 ! [V_v_2,V_v_H_2] :
% 59.73/59.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_v_H_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_transfer__morphism__nat__int,axiom,
% 59.73/59.59 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))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_le__number__of__Suc,axiom,
% 59.73/59.59 ! [V_n_2,V_v_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_le__Suc__number__of,axiom,
% 59.73/59.59 ! [V_v_2,V_n_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_diff__bin__simps_I1_J,axiom,
% 59.73/59.59 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 59.73/59.59
% 59.73/59.59 fof(fact_minus__Pls,axiom,
% 59.73/59.59 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I19_J,axiom,
% 59.73/59.59 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I2_J,axiom,
% 59.73/59.59 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Pls__def,axiom,
% 59.73/59.59 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mult__Pls,axiom,
% 59.73/59.59 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__Pls__right,axiom,
% 59.73/59.59 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__Pls,axiom,
% 59.73/59.59 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I46_J,axiom,
% 59.73/59.59 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I39_J,axiom,
% 59.73/59.59 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_succ__pred,axiom,
% 59.73/59.59 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 59.73/59.59
% 59.73/59.59 fof(fact_semiring__norm_I112_J,axiom,
% 59.73/59.59 ! [T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_number__of__Pls,axiom,
% 59.73/59.59 ! [T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__numeral__0,axiom,
% 59.73/59.59 ! [V_a,T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)),V_a) = V_a ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__numeral__0__right,axiom,
% 59.73/59.59 ! [V_a,T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = V_a ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_bin__less__0__simps_I1_J,axiom,
% 59.73/59.59 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__number__of__Pls,axiom,
% 59.73/59.59 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_semiring__norm_I113_J,axiom,
% 59.73/59.59 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_zero__is__num__zero,axiom,
% 59.73/59.59 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I22_J,axiom,
% 59.73/59.59 ! [V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I12_J,axiom,
% 59.73/59.59 ! [V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Suc__diff__number__of,axiom,
% 59.73/59.59 ! [V_m,V_v] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_not__neg__number__of__Pls,axiom,
% 59.73/59.59 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_succ__Pls,axiom,
% 59.73/59.59 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_le__iff__pred__less,axiom,
% 59.73/59.59 ! [V_l_2,V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_minus__Bit1,axiom,
% 59.73/59.59 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_pred__def,axiom,
% 59.73/59.59 ! [V_k] : c_Int_Opred(V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__number__of__diff__1,axiom,
% 59.73/59.59 ! [V_v] :
% 59.73/59.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mult__numeral__1__right,axiom,
% 59.73/59.59 ! [V_a,T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mult__numeral__1,axiom,
% 59.73/59.59 ! [V_a,T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))),V_a) = V_a ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__Numeral0,axiom,
% 59.73/59.59 ! [V_x,T_a] :
% 59.73/59.59 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 59.73/59.59 & class_Int_Onumber__ring(T_a) )
% 59.73/59.59 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_numeral__1__eq__1,axiom,
% 59.73/59.59 ! [T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_semiring__norm_I110_J,axiom,
% 59.73/59.59 ! [T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_eq__0__number__of,axiom,
% 59.73/59.59 ! [V_v_2] :
% 59.73/59.59 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_eq__number__of__0,axiom,
% 59.73/59.59 ! [V_v_2] :
% 59.73/59.59 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I29_J,axiom,
% 59.73/59.59 ! [V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I5_J,axiom,
% 59.73/59.59 ! [V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__nat__number__of,axiom,
% 59.73/59.59 ! [V_v_H_2,V_v_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
% 59.73/59.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 59.73/59.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 59.73/59.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__Numeral1,axiom,
% 59.73/59.59 ! [V_x,T_a] :
% 59.73/59.59 ( ( class_Fields_Ofield(T_a)
% 59.73/59.59 & class_Int_Onumber__ring(T_a) )
% 59.73/59.59 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_x ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_divide__numeral__1,axiom,
% 59.73/59.59 ! [V_a,T_a] :
% 59.73/59.59 ( ( class_Fields_Ofield(T_a)
% 59.73/59.59 & class_Int_Onumber__ring(T_a) )
% 59.73/59.59 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_le__nat__number__of,axiom,
% 59.73/59.59 ! [V_v_H_2,V_v_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
% 59.73/59.59 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 59.73/59.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_one__is__num__one,axiom,
% 59.73/59.59 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Numeral1__eq1__nat,axiom,
% 59.73/59.59 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__numeral__1__eq__1,axiom,
% 59.73/59.59 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_le__special_I1_J,axiom,
% 59.73/59.59 ! [V_y_2,T_b] :
% 59.73/59.59 ( ( class_Int_Onumber__ring(T_b)
% 59.73/59.59 & class_Rings_Olinordered__idom(T_b) )
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_le__special_I3_J,axiom,
% 59.73/59.59 ! [V_x_2,T_b] :
% 59.73/59.59 ( ( class_Int_Onumber__ring(T_b)
% 59.73/59.59 & class_Rings_Olinordered__idom(T_b) )
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__special_I1_J,axiom,
% 59.73/59.59 ! [V_y_2,T_b] :
% 59.73/59.59 ( ( class_Int_Onumber__ring(T_b)
% 59.73/59.59 & class_Rings_Olinordered__idom(T_b) )
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__special_I3_J,axiom,
% 59.73/59.59 ! [V_x_2,T_b] :
% 59.73/59.59 ( ( class_Int_Onumber__ring(T_b)
% 59.73/59.59 & class_Rings_Olinordered__idom(T_b) )
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__0__number__of,axiom,
% 59.73/59.59 ! [V_v_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_numeral__1__eq__Suc__0,axiom,
% 59.73/59.59 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_numeral__3__eq__3,axiom,
% 59.73/59.59 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power3__eq__cube,axiom,
% 59.73/59.59 ! [V_a,T_a] :
% 59.73/59.59 ( class_Groups_Omonoid__mult(T_a)
% 59.73/59.59 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 59.73/59.59 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Suc3__eq__add__3,axiom,
% 59.73/59.59 ! [V_n] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__nat__number__of,axiom,
% 59.73/59.59 ! [V_v_H,V_v] :
% 59.73/59.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 59.73/59.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H)) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 59.73/59.59 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_number__of__pred,axiom,
% 59.73/59.59 ! [V_w,T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Opred(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_le__special_I2_J,axiom,
% 59.73/59.59 ! [V_y_2,T_b] :
% 59.73/59.59 ( ( class_Int_Onumber__ring(T_b)
% 59.73/59.59 & class_Rings_Olinordered__idom(T_b) )
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_le__special_I4_J,axiom,
% 59.73/59.59 ! [V_x_2,T_b] :
% 59.73/59.59 ( ( class_Int_Onumber__ring(T_b)
% 59.73/59.59 & class_Rings_Olinordered__idom(T_b) )
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__special_I2_J,axiom,
% 59.73/59.59 ! [V_y_2,T_b] :
% 59.73/59.59 ( ( class_Int_Onumber__ring(T_b)
% 59.73/59.59 & class_Rings_Olinordered__idom(T_b) )
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__special_I4_J,axiom,
% 59.73/59.59 ! [V_x_2,T_b] :
% 59.73/59.59 ( ( class_Int_Onumber__ring(T_b)
% 59.73/59.59 & class_Rings_Olinordered__idom(T_b) )
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__special_I2_J,axiom,
% 59.73/59.59 ! [V_w,T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__special_I3_J,axiom,
% 59.73/59.59 ! [V_v,T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 59.73/59.59 ! [V_m,V_n] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mult__nat__number__of,axiom,
% 59.73/59.59 ! [V_v_H,V_v] :
% 59.73/59.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__number__of__mult__left,axiom,
% 59.73/59.59 ! [V_k,V_v_H,V_v] :
% 59.73/59.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_neg__number__of__pred__iff__0,axiom,
% 59.73/59.59 ! [V_v_2] :
% 59.73/59.59 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 59.73/59.59 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 59.73/59.59 ! [V_v,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 59.73/59.59 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),V_n) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 59.73/59.59 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 59.73/59.59 ! [V_v,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Suc__div__eq__add3__div,axiom,
% 59.73/59.59 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),V_n) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_div__Suc__eq__div__add3,axiom,
% 59.73/59.59 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__1__add__number__of,axiom,
% 59.73/59.59 ! [V_v] :
% 59.73/59.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__number__of__add__1,axiom,
% 59.73/59.59 ! [V_v] :
% 59.73/59.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 59.73/59.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_diff__special_I2_J,axiom,
% 59.73/59.59 ! [V_v,T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_diff__special_I1_J,axiom,
% 59.73/59.59 ! [V_w,T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Suc__eq__number__of,axiom,
% 59.73/59.59 ! [V_v_2,V_n_2] :
% 59.73/59.59 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_eq__number__of__Suc,axiom,
% 59.73/59.59 ! [V_n_2,V_v_2] :
% 59.73/59.59 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__number__of__Suc,axiom,
% 59.73/59.59 ! [V_n_2,V_v_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__Suc__number__of,axiom,
% 59.73/59.59 ! [V_v_2,V_n_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_number__of2,axiom,
% 59.73/59.59 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__case__add__eq__if,axiom,
% 59.73/59.59 ! [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)))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__case__number__of,axiom,
% 59.73/59.59 ! [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))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__rec__add__eq__if,axiom,
% 59.73/59.59 ! [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))))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__rec__0,axiom,
% 59.73/59.59 ! [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 ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__rec__Suc,axiom,
% 59.73/59.59 ! [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)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__case__0,axiom,
% 59.73/59.59 ! [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 ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__case__Suc,axiom,
% 59.73/59.59 ! [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) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 59.73/59.59 ! [V_n_2,V_m_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 59.73/59.59 <=> 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)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_diff__Suc,axiom,
% 59.73/59.59 ! [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)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__rec__number__of,axiom,
% 59.73/59.59 ! [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)))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_eq__special_I4_J,axiom,
% 59.73/59.59 ! [V_x_2,T_b] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_b)
% 59.73/59.59 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 59.73/59.59 <=> 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))))) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_eq__special_I2_J,axiom,
% 59.73/59.59 ! [V_y_2,T_b] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_b)
% 59.73/59.59 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 59.73/59.59 <=> 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)))) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_neg__zmod__mult__2,axiom,
% 59.73/59.59 ! [V_b,V_a] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.59 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_zmod__number__of__Bit1,axiom,
% 59.73/59.59 ! [V_v,V_w] :
% 59.73/59.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 59.73/59.59 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 59.73/59.59 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_iszero__number__of__Bit0,axiom,
% 59.73/59.59 ! [V_w_2,T_b] :
% 59.73/59.59 ( ( class_Int_Onumber__ring(T_b)
% 59.73/59.59 & class_Int_Oring__char__0(T_b) )
% 59.73/59.59 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 59.73/59.59 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I50_J,axiom,
% 59.73/59.59 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I49_J,axiom,
% 59.73/59.59 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_diff__bin__simps_I7_J,axiom,
% 59.73/59.59 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_minus__Bit0,axiom,
% 59.73/59.59 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(V_k)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mult__Bit0,axiom,
% 59.73/59.59 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__eq__int__code_I13_J,axiom,
% 59.73/59.59 ! [V_k2_2,V_k1_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I31_J,axiom,
% 59.73/59.59 ! [V_l_2,V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I14_J,axiom,
% 59.73/59.59 ! [V_l_2,V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__int__code_I13_J,axiom,
% 59.73/59.59 ! [V_k2_2,V_k1_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I48_J,axiom,
% 59.73/59.59 ! [V_l_2,V_k_2] :
% 59.73/59.59 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 59.73/59.59 <=> V_k_2 = V_l_2 ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__Bit0__Bit0,axiom,
% 59.73/59.59 ! [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)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Bit0__def,axiom,
% 59.73/59.59 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I44_J,axiom,
% 59.73/59.59 ! [V_k_2] :
% 59.73/59.59 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 59.73/59.59 <=> V_k_2 = c_Int_OPls ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I38_J,axiom,
% 59.73/59.59 ! [V_l_2] :
% 59.73/59.59 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 59.73/59.59 <=> c_Int_OPls = V_l_2 ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Bit0__Pls,axiom,
% 59.73/59.59 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 59.73/59.59
% 59.73/59.59 fof(fact_iszero__def,axiom,
% 59.73/59.59 ! [V_z_2,T_b] :
% 59.73/59.59 ( class_Rings_Osemiring__1(T_b)
% 59.73/59.59 => ( c_Int_Oiszero(T_b,V_z_2)
% 59.73/59.59 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_iszero__0,axiom,
% 59.73/59.59 ! [T_a] :
% 59.73/59.59 ( class_Rings_Osemiring__1(T_a)
% 59.73/59.59 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_not__iszero__1,axiom,
% 59.73/59.59 ! [T_a] :
% 59.73/59.59 ( class_Rings_Osemiring__1(T_a)
% 59.73/59.59 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_bin__less__0__simps_I3_J,axiom,
% 59.73/59.59 ! [V_w_2] :
% 59.73/59.59 ( 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)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I27_J,axiom,
% 59.73/59.59 ! [V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I21_J,axiom,
% 59.73/59.59 ! [V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__eq__int__code_I14_J,axiom,
% 59.73/59.59 ! [V_k2_2,V_k1_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I32_J,axiom,
% 59.73/59.59 ! [V_l_2,V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I4_J,axiom,
% 59.73/59.59 ! [V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I10_J,axiom,
% 59.73/59.59 ! [V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I16_J,axiom,
% 59.73/59.59 ! [V_l_2,V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__int__code_I15_J,axiom,
% 59.73/59.59 ! [V_k2_2,V_k1_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__Bit1__Bit0,axiom,
% 59.73/59.59 ! [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)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__Bit0__Bit1,axiom,
% 59.73/59.59 ! [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)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_diff__bin__simps_I3_J,axiom,
% 59.73/59.59 ! [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)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_diff__bin__simps_I10_J,axiom,
% 59.73/59.59 ! [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)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_diff__bin__simps_I9_J,axiom,
% 59.73/59.59 ! [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)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_zdiv__number__of__Bit0,axiom,
% 59.73/59.59 ! [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)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_neg__number__of__Bit0,axiom,
% 59.73/59.59 ! [V_w_2] :
% 59.73/59.59 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 59.73/59.59 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_pred__Bit0,axiom,
% 59.73/59.59 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_pred__Bit1,axiom,
% 59.73/59.59 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_succ__Bit1,axiom,
% 59.73/59.59 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_succ__Bit0,axiom,
% 59.73/59.59 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__number__of__Bit0,axiom,
% 59.73/59.59 ! [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))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_number__of__Bit0,axiom,
% 59.73/59.59 ! [V_w,T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => 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)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__eq__int__code_I15_J,axiom,
% 59.73/59.59 ! [V_k2_2,V_k1_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I33_J,axiom,
% 59.73/59.59 ! [V_l_2,V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__int__code_I14_J,axiom,
% 59.73/59.59 ! [V_k2_2,V_k1_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I15_J,axiom,
% 59.73/59.59 ! [V_l_2,V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_card__UNIV__bool,axiom,
% 59.73/59.59 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))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mult__Bit1,axiom,
% 59.73/59.59 ! [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) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_diff__bin__simps_I8_J,axiom,
% 59.73/59.59 ! [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)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__Bit1__Bit1,axiom,
% 59.73/59.59 ! [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))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power__number__of__even,axiom,
% 59.73/59.59 ! [V_w_2,V_z_2,T_b] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_b)
% 59.73/59.59 => 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))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_zpower__number__of__even,axiom,
% 59.73/59.59 ! [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))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_iszero__Numeral0,axiom,
% 59.73/59.59 ! [T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_iszero__number__of__Bit1,axiom,
% 59.73/59.59 ! [V_w,T_a] :
% 59.73/59.59 ( ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 & class_Int_Oring__char__0(T_a) )
% 59.73/59.59 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_double__number__of__Bit0,axiom,
% 59.73/59.59 ! [V_w,T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => 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)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_number__of1,axiom,
% 59.73/59.59 ! [V_n] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n))))
% 59.73/59.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n)))) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power__number__of__even__number__of,axiom,
% 59.73/59.59 ! [V_w_2,V_v_2,T_b] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_b)
% 59.73/59.59 => 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))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mult__2,axiom,
% 59.73/59.59 ! [V_z,T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => 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) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mult__2__right,axiom,
% 59.73/59.59 ! [V_z,T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => 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) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_one__add__one__is__two,axiom,
% 59.73/59.59 ! [T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => 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))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_zero__eq__power2,axiom,
% 59.73/59.59 ! [V_a_2,T_b] :
% 59.73/59.59 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 59.73/59.59 => ( 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)
% 59.73/59.59 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_zero__power2,axiom,
% 59.73/59.59 ! [T_a] :
% 59.73/59.59 ( class_Rings_Osemiring__1(T_a)
% 59.73/59.59 => 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) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_semiring__norm_I115_J,axiom,
% 59.73/59.59 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))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_numeral__2__eq__2,axiom,
% 59.73/59.59 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))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 59.73/59.59 ! [V_x,T_a] :
% 59.73/59.59 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.73/59.59 => 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)))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power2__eq__square,axiom,
% 59.73/59.59 ! [V_a,T_a] :
% 59.73/59.59 ( class_Groups_Omonoid__mult(T_a)
% 59.73/59.59 => 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) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 59.73/59.59 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__2__eq__Suc_H,axiom,
% 59.73/59.59 ! [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)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__2__eq__Suc,axiom,
% 59.73/59.59 ! [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)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_one__power2,axiom,
% 59.73/59.59 ! [T_a] :
% 59.73/59.59 ( class_Rings_Osemiring__1(T_a)
% 59.73/59.59 => 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) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power2__minus,axiom,
% 59.73/59.59 ! [V_a,T_a] :
% 59.73/59.59 ( class_Rings_Oring__1(T_a)
% 59.73/59.59 => 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)))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__mult__2,axiom,
% 59.73/59.59 ! [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) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__mult__2__right,axiom,
% 59.73/59.59 ! [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) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power__even__eq,axiom,
% 59.73/59.59 ! [V_n,V_a,T_a] :
% 59.73/59.59 ( class_Groups_Omonoid__mult(T_a)
% 59.73/59.59 => 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)))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 59.73/59.59 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)))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__1__add__1,axiom,
% 59.73/59.59 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))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mod2__Suc__Suc,axiom,
% 59.73/59.59 ! [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)))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_div2__Suc__Suc,axiom,
% 59.73/59.59 ! [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))))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_zmod__number__of__Bit0,axiom,
% 59.73/59.59 ! [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))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__self__div__2,axiom,
% 59.73/59.59 ! [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 ).
% 59.73/59.59
% 59.73/59.59 fof(fact_not__iszero__Numeral1,axiom,
% 59.73/59.59 ! [T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_eq__number__of__eq,axiom,
% 59.73/59.59 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_b)
% 59.73/59.59 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 59.73/59.59 <=> 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)))) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_half__gt__zero__iff,axiom,
% 59.73/59.59 ! [V_r_2,T_b] :
% 59.73/59.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 59.73/59.59 & class_Int_Onumber__ring(T_b) )
% 59.73/59.59 => ( 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))))))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_half__gt__zero,axiom,
% 59.73/59.59 ! [V_r,T_a] :
% 59.73/59.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 59.73/59.59 & class_Int_Onumber__ring(T_a) )
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 59.73/59.59 => 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)))))) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_zero__le__power2,axiom,
% 59.73/59.59 ! [V_a,T_a] :
% 59.73/59.59 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.59 => 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)))))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power2__le__imp__le,axiom,
% 59.73/59.59 ! [V_y,V_x,T_a] :
% 59.73/59.59 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.59 => ( 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))))))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 59.73/59.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power2__eq__imp__eq,axiom,
% 59.73/59.59 ! [V_y,V_x,T_a] :
% 59.73/59.59 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.59 => ( 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))))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 59.73/59.59 => V_x = V_y ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power2__less__0,axiom,
% 59.73/59.59 ! [V_a,T_a] :
% 59.73/59.59 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.59 => ~ 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))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_zero__less__power2,axiom,
% 59.73/59.59 ! [V_a_2,T_b] :
% 59.73/59.59 ( class_Rings_Olinordered__idom(T_b)
% 59.73/59.59 => ( 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))))))
% 59.73/59.59 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_sum__power2__eq__zero__iff,axiom,
% 59.73/59.59 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.59 ( class_Rings_Olinordered__idom(T_b)
% 59.73/59.59 => ( 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)
% 59.73/59.59 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power2__eq__square__number__of,axiom,
% 59.73/59.59 ! [V_w,T_b] :
% 59.73/59.59 ( ( class_Groups_Omonoid__mult(T_b)
% 59.73/59.59 & class_Int_Onumber(T_b) )
% 59.73/59.59 => 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)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_less__2__cases,axiom,
% 59.73/59.59 ! [V_n] :
% 59.73/59.59 ( 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)))))
% 59.73/59.59 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.59 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_nat__2,axiom,
% 59.73/59.59 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))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power2__eq__1__iff,axiom,
% 59.73/59.59 ! [V_a_2,T_b] :
% 59.73/59.59 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 59.73/59.59 => ( 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)
% 59.73/59.59 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 59.73/59.59 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 59.73/59.59 ! [V_n,V_x,T_a] :
% 59.73/59.59 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.73/59.59 => 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)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power__minus__even,axiom,
% 59.73/59.59 ! [V_n,V_a,T_a] :
% 59.73/59.59 ( class_Rings_Oring__1(T_a)
% 59.73/59.59 => 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)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power2__less__imp__less,axiom,
% 59.73/59.59 ! [V_y,V_x,T_a] :
% 59.73/59.59 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.59 => ( 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))))))
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 59.73/59.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_sum__power2__ge__zero,axiom,
% 59.73/59.59 ! [V_y,V_x,T_a] :
% 59.73/59.59 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.59 => 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))))))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_sum__power2__le__zero__iff,axiom,
% 59.73/59.59 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.59 ( class_Rings_Olinordered__idom(T_b)
% 59.73/59.59 => ( 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)))
% 59.73/59.59 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_not__sum__power2__lt__zero,axiom,
% 59.73/59.59 ! [V_y,V_x,T_a] :
% 59.73/59.59 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.59 => ~ 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))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_sum__power2__gt__zero__iff,axiom,
% 59.73/59.59 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.59 ( class_Rings_Olinordered__idom(T_b)
% 59.73/59.59 => ( 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)))))))
% 59.73/59.59 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power2__sum,axiom,
% 59.73/59.59 ! [V_y,V_x,T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => 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)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_zero__le__even__power_H,axiom,
% 59.73/59.59 ! [V_n,V_a,T_a] :
% 59.73/59.59 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.59 => 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)))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 59.73/59.59 ! [V_n,V_x,T_a] :
% 59.73/59.59 ( class_Rings_Ocomm__semiring__1(T_a)
% 59.73/59.59 => 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))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power__odd__eq,axiom,
% 59.73/59.59 ! [V_n,V_a,T_a] :
% 59.73/59.59 ( class_Groups_Omonoid__mult(T_a)
% 59.73/59.59 => 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))))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power__minus1__even,axiom,
% 59.73/59.59 ! [V_n,T_a] :
% 59.73/59.59 ( class_Rings_Oring__1(T_a)
% 59.73/59.59 => 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) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_zdiv__number__of__Bit1,axiom,
% 59.73/59.59 ! [V_v,V_w] :
% 59.73/59.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 59.73/59.59 => 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)) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 59.73/59.59 => 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)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mod2__gr__0,axiom,
% 59.73/59.59 ! [V_m_2] :
% 59.73/59.59 ( 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))))))
% 59.73/59.59 <=> 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) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_div__2__gt__zero,axiom,
% 59.73/59.59 ! [V_n] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 59.73/59.59 => 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)))))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power2__diff,axiom,
% 59.73/59.59 ! [V_y,V_x,T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => 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)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 59.73/59.59 ! [V_n,V_a,T_a] :
% 59.73/59.59 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.59 => ( 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)))))
% 59.73/59.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_odd__power__less__zero,axiom,
% 59.73/59.59 ! [V_n,V_a,T_a] :
% 59.73/59.59 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.59 => 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))) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_power__minus1__odd,axiom,
% 59.73/59.59 ! [V_n,T_a] :
% 59.73/59.59 ( class_Rings_Oring__1(T_a)
% 59.73/59.59 => 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)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 59.73/59.59 ! [V_n] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 59.73/59.59 => 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)))))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_eq__special_I1_J,axiom,
% 59.73/59.59 ! [V_y_2,T_b] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_b)
% 59.73/59.59 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 59.73/59.59 <=> 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)))) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_eq__special_I3_J,axiom,
% 59.73/59.59 ! [V_x_2,T_b] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_b)
% 59.73/59.59 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 <=> 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)))) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_pos__zmod__mult__2,axiom,
% 59.73/59.59 ! [V_b,V_a] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 59.73/59.59 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_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))) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_neg__zdiv__mult__2,axiom,
% 59.73/59.59 ! [V_b,V_a] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.59 => 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) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_pos__zdiv__mult__2,axiom,
% 59.73/59.59 ! [V_b,V_a] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 59.73/59.59 => 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) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_adjust__def,axiom,
% 59.73/59.59 ! [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))))))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_adjust__eq,axiom,
% 59.73/59.59 ! [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))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 59.73/59.59 ! [V_w] :
% 59.73/59.59 ( 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)))
% 59.73/59.59 => ( ( 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)))
% 59.73/59.59 => 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)) )
% 59.73/59.59 & ( ~ 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)))
% 59.73/59.59 => 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)))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_posDivAlg_Osimps,axiom,
% 59.73/59.59 ! [V_b,V_a] :
% 59.73/59.59 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 59.73/59.59 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 59.73/59.59 => 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) )
% 59.73/59.59 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 59.73/59.59 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 59.73/59.59 => 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))) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_posDivAlg__eqn,axiom,
% 59.73/59.59 ! [V_a,V_b] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 59.73/59.59 => 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) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 59.73/59.59 => 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_posDivAlg__eqn__number__of,axiom,
% 59.73/59.59 ! [V_w,V_v] :
% 59.73/59.59 ( 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)))
% 59.73/59.59 => ( ( 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)))
% 59.73/59.59 => 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)) )
% 59.73/59.59 & ( ~ 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)))
% 59.73/59.59 => 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)))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_posDivAlg_Opsimps,axiom,
% 59.73/59.59 ! [V_b_2,V_a_2] :
% 59.73/59.59 ( 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)))
% 59.73/59.59 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 59.73/59.59 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 59.73/59.59 => 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) )
% 59.73/59.59 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 59.73/59.59 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 59.73/59.59 => 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))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_of__int__num,axiom,
% 59.73/59.59 ! [V_k_2,T_b] :
% 59.73/59.59 ( class_Rings_Oring__1(T_b)
% 59.73/59.59 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.59 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 59.73/59.59 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.59 => 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))) )
% 59.73/59.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.59 => 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))))) ) ) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 59.73/59.59 ! [V_w] :
% 59.73/59.59 ( 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)))
% 59.73/59.59 => ( ( 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))))
% 59.73/59.59 => 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))) )
% 59.73/59.59 & ( ~ 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))))
% 59.73/59.59 => 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)))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_negDivAlg__eqn__number__of,axiom,
% 59.73/59.59 ! [V_w,V_v] :
% 59.73/59.59 ( 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)))
% 59.73/59.59 => ( ( 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))))
% 59.73/59.59 => 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))) )
% 59.73/59.59 & ( ~ 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))))
% 59.73/59.59 => 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)))) ) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_of__int__m1,axiom,
% 59.73/59.59 ! [T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => 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) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I47_J,axiom,
% 59.73/59.59 ! [V_k_2] :
% 59.73/59.59 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 59.73/59.59 <=> V_k_2 = c_Int_OMin ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I43_J,axiom,
% 59.73/59.59 ! [V_l_2] :
% 59.73/59.59 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 59.73/59.59 <=> c_Int_OMin = V_l_2 ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Bit1__Min,axiom,
% 59.73/59.59 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 59.73/59.59
% 59.73/59.59 fof(fact_of__int__eq__iff,axiom,
% 59.73/59.59 ! [V_z_2,V_w_2,T_b] :
% 59.73/59.59 ( class_Int_Oring__char__0(T_b)
% 59.73/59.59 => ( 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)
% 59.73/59.59 <=> V_w_2 = V_z_2 ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I7_J,axiom,
% 59.73/59.59 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I24_J,axiom,
% 59.73/59.59 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_int__number__of__def,axiom,
% 59.73/59.59 ! [V_w] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),V_w) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_number__of__eq,axiom,
% 59.73/59.59 ! [V_k,T_a] :
% 59.73/59.59 ( class_Int_Onumber__ring(T_a)
% 59.73/59.59 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I37_J,axiom,
% 59.73/59.59 c_Int_OPls != c_Int_OMin ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I40_J,axiom,
% 59.73/59.59 c_Int_OMin != c_Int_OPls ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I45_J,axiom,
% 59.73/59.59 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I42_J,axiom,
% 59.73/59.59 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_of__int__setprod,axiom,
% 59.73/59.59 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.59 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 59.73/59.59 & class_Rings_Oring__1(T_b) )
% 59.73/59.59 => 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) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_bin__less__0__simps_I2_J,axiom,
% 59.73/59.59 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I20_J,axiom,
% 59.73/59.59 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I23_J,axiom,
% 59.73/59.59 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I30_J,axiom,
% 59.73/59.59 ! [V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I26_J,axiom,
% 59.73/59.59 ! [V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I6_J,axiom,
% 59.73/59.59 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I3_J,axiom,
% 59.73/59.59 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I9_J,axiom,
% 59.73/59.59 ! [V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I13_J,axiom,
% 59.73/59.59 ! [V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I28_J,axiom,
% 59.73/59.59 ! [V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_rel__simps_I8_J,axiom,
% 59.73/59.59 ! [V_k_2] :
% 59.73/59.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 59.73/59.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_eq__number__of__Pls__Min,axiom,
% 59.73/59.59 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) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_Int_OMin__def,axiom,
% 59.73/59.59 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_mult__Min,axiom,
% 59.73/59.59 ! [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) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_neg__number__of__Min,axiom,
% 59.73/59.59 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_pred__Pls,axiom,
% 59.73/59.59 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__Min__right,axiom,
% 59.73/59.59 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_add__Min,axiom,
% 59.73/59.59 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_pred__Min,axiom,
% 59.73/59.59 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_of__int__0,axiom,
% 59.73/59.59 ! [T_a] :
% 59.73/59.59 ( class_Rings_Oring__1(T_a)
% 59.73/59.59 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_of__int__0__eq__iff,axiom,
% 59.73/59.59 ! [V_z_2,T_b] :
% 59.73/59.59 ( class_Int_Oring__char__0(T_b)
% 59.73/59.59 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 59.73/59.59 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_of__int__eq__0__iff,axiom,
% 59.73/59.59 ! [V_z_2,T_b] :
% 59.73/59.59 ( class_Int_Oring__char__0(T_b)
% 59.73/59.59 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.59 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 59.73/59.59
% 59.73/59.59 fof(fact_of__int__le__iff,axiom,
% 59.73/59.60 ! [V_z_2,V_w_2,T_b] :
% 59.73/59.60 ( class_Rings_Olinordered__idom(T_b)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__int__less__iff,axiom,
% 59.73/59.60 ! [V_z_2,V_w_2,T_b] :
% 59.73/59.60 ( class_Rings_Olinordered__idom(T_b)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_nonzero__number__of__Min,axiom,
% 59.73/59.60 ! [T_a] :
% 59.73/59.60 ( class_Int_Onumber__ring(T_a)
% 59.73/59.60 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__int__add,axiom,
% 59.73/59.60 ! [V_z,V_w,T_a] :
% 59.73/59.60 ( class_Rings_Oring__1(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__int__number__of__eq,axiom,
% 59.73/59.60 ! [V_v,T_a] :
% 59.73/59.60 ( class_Int_Onumber__ring(T_a)
% 59.73/59.60 => 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__int__mult,axiom,
% 59.73/59.60 ! [V_z,V_w,T_a] :
% 59.73/59.60 ( class_Rings_Oring__1(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_succ__Min,axiom,
% 59.73/59.60 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__int__1,axiom,
% 59.73/59.60 ! [T_a] :
% 59.73/59.60 ( class_Rings_Oring__1(T_a)
% 59.73/59.60 => 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__int__diff,axiom,
% 59.73/59.60 ! [V_z,V_w,T_a] :
% 59.73/59.60 ( class_Rings_Oring__1(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_diff__bin__simps_I2_J,axiom,
% 59.73/59.60 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__int__minus,axiom,
% 59.73/59.60 ! [V_z,T_a] :
% 59.73/59.60 ( class_Rings_Oring__1(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Ints__of__int,axiom,
% 59.73/59.60 ! [V_z_2,T_b] :
% 59.73/59.60 ( class_Rings_Oring__1(T_b)
% 59.73/59.60 => 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))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__int__power,axiom,
% 59.73/59.60 ! [V_n,V_z,T_a] :
% 59.73/59.60 ( class_Rings_Oring__1(T_a)
% 59.73/59.60 => 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_mult__minus1,axiom,
% 59.73/59.60 ! [V_z,T_a] :
% 59.73/59.60 ( class_Int_Onumber__ring(T_a)
% 59.73/59.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_z) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_mult__minus1__right,axiom,
% 59.73/59.60 ! [V_z,T_a] :
% 59.73/59.60 ( class_Int_Onumber__ring(T_a)
% 59.73/59.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_number__of__Min,axiom,
% 59.73/59.60 ! [T_a] :
% 59.73/59.60 ( class_Int_Onumber__ring(T_a)
% 59.73/59.60 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_arith__simps_I31_J,axiom,
% 59.73/59.60 ! [T_a] :
% 59.73/59.60 ( class_Int_Onumber__ring(T_a)
% 59.73/59.60 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_divide__minus1,axiom,
% 59.73/59.60 ! [V_x,T_a] :
% 59.73/59.60 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 59.73/59.60 & class_Int_Onumber__ring(T_a) )
% 59.73/59.60 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_rel__simps_I11_J,axiom,
% 59.73/59.60 ! [V_k_2] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_rel__simps_I25_J,axiom,
% 59.73/59.60 ! [V_k_2] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zmod__minus1__right,axiom,
% 59.73/59.60 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_diff__bin__simps_I4_J,axiom,
% 59.73/59.60 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_minus__Min,axiom,
% 59.73/59.60 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zmult__eq__1__iff,axiom,
% 59.73/59.60 ! [V_n_2,V_m_2] :
% 59.73/59.60 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 59.73/59.60 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 59.73/59.60 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 59.73/59.60 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 59.73/59.60 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 59.73/59.60 ! [V_n,V_m] :
% 59.73/59.60 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 59.73/59.60 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 59.73/59.60 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_diff__bin__simps_I5_J,axiom,
% 59.73/59.60 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_diff__bin__simps_I6_J,axiom,
% 59.73/59.60 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zdiv__minus1__right,axiom,
% 59.73/59.60 ! [V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_minus1__divide,axiom,
% 59.73/59.60 ! [V_x,T_a] :
% 59.73/59.60 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 59.73/59.60 & class_Int_Onumber__ring(T_a) )
% 59.73/59.60 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_x)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_div__eq__minus1,axiom,
% 59.73/59.60 ! [V_b] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.60 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__int__le__0__iff,axiom,
% 59.73/59.60 ! [V_z_2,T_b] :
% 59.73/59.60 ( class_Rings_Olinordered__idom(T_b)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__int__0__le__iff,axiom,
% 59.73/59.60 ! [V_z_2,T_b] :
% 59.73/59.60 ( class_Rings_Olinordered__idom(T_b)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__int__0__less__iff,axiom,
% 59.73/59.60 ! [V_z_2,T_b] :
% 59.73/59.60 ( class_Rings_Olinordered__idom(T_b)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__int__less__0__iff,axiom,
% 59.73/59.60 ! [V_z_2,T_b] :
% 59.73/59.60 ( class_Rings_Olinordered__idom(T_b)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_negDivAlg__minus1,axiom,
% 59.73/59.60 ! [V_b] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_div__pos__neg__trivial,axiom,
% 59.73/59.60 ! [V_b,V_a] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.60 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zmod__minus1,axiom,
% 59.73/59.60 ! [V_b] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.60 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_power__m1__even,axiom,
% 59.73/59.60 ! [V_n,T_a] :
% 59.73/59.60 ( class_Int_Onumber__ring(T_a)
% 59.73/59.60 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_power__m1__odd,axiom,
% 59.73/59.60 ! [V_n,T_a] :
% 59.73/59.60 ( class_Int_Onumber__ring(T_a)
% 59.73/59.60 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_negDivAlg_Osimps,axiom,
% 59.73/59.60 ! [V_b,V_a] :
% 59.73/59.60 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)))
% 59.73/59.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 59.73/59.60 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) )
% 59.73/59.60 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)))
% 59.73/59.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 59.73/59.60 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_negDivAlg__eqn,axiom,
% 59.73/59.60 ! [V_a,V_b] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 59.73/59.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)))
% 59.73/59.60 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) )
% 59.73/59.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)))
% 59.73/59.60 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_negDivAlg_Opsimps,axiom,
% 59.73/59.60 ! [V_b_2,V_a_2] :
% 59.73/59.60 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
% 59.73/59.60 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)))
% 59.73/59.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 59.73/59.60 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)) )
% 59.73/59.60 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)))
% 59.73/59.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 59.73/59.60 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OnegDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_posDivAlg_Opinduct,axiom,
% 59.73/59.60 ! [V_P_2,V_a1_2,V_a0_2] :
% 59.73/59.60 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 59.73/59.60 => ( ! [B_a,B_b] :
% 59.73/59.60 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
% 59.73/59.60 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 59.73/59.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 59.73/59.60 => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 59.73/59.60 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 59.73/59.60 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_int__of__code,axiom,
% 59.73/59.60 ! [V_k] :
% 59.73/59.60 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 59.73/59.60 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 59.73/59.60 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 59.73/59.60 => ( ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 59.73/59.60 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) )
% 59.73/59.60 & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 59.73/59.60 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__double,axiom,
% 59.73/59.60 ! [V_x,T_a] :
% 59.73/59.60 ( class_Rings_Osemiring__1(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 59.73/59.60 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_negative__zle,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_negative__zless,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__int__of__nat__eq,axiom,
% 59.73/59.60 ! [V_n,T_a] :
% 59.73/59.60 ( class_Rings_Oring__1(T_a)
% 59.73/59.60 => 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__int__int__eq,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 59.73/59.60 ! [V_A_2,V_x_2] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 59.73/59.60 <=> 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))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_not__neg__int,axiom,
% 59.73/59.60 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_code__numeral__zero__minus__one,axiom,
% 59.73/59.60 hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__eq__iff,axiom,
% 59.73/59.60 ! [V_n_2,V_m_2,T_b] :
% 59.73/59.60 ( class_Nat_Osemiring__char__0(T_b)
% 59.73/59.60 => ( 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)
% 59.73/59.60 <=> V_m_2 = V_n_2 ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_nat__int,axiom,
% 59.73/59.60 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 59.73/59.60 ! [V_A_2] :
% 59.73/59.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 59.73/59.60 <=> 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))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_inj__int,axiom,
% 59.73/59.60 c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 59.73/59.60 ! [V_A_2,V_f_2,T_b] :
% 59.73/59.60 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.60 & class_Groups_Ocomm__monoid__mult(T_b) )
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_int__setprod,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_int__eq__0__conv,axiom,
% 59.73/59.60 ! [V_n_2] :
% 59.73/59.60 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.60 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_int__0,axiom,
% 59.73/59.60 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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 59.73/59.60 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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zero__zle__int,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 59.73/59.60 ! [V_P_2] :
% 59.73/59.60 ( ! [B_x] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 59.73/59.60 => hBOOL(hAPP(V_P_2,B_x)) )
% 59.73/59.60 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 59.73/59.60 ! [V_P_2] :
% 59.73/59.60 ( ? [B_x] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 59.73/59.60 & hBOOL(hAPP(V_P_2,B_x)) )
% 59.73/59.60 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_int__less__0__conv,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zless__int,axiom,
% 59.73/59.60 ! [V_n_2,V_m_2] :
% 59.73/59.60 ( 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)))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2] :
% 59.73/59.60 ( 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)))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zle__int,axiom,
% 59.73/59.60 ! [V_n_2,V_m_2] :
% 59.73/59.60 ( 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)))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2] :
% 59.73/59.60 ( 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)))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zadd__int,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zadd__int__left,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zle__iff__zadd,axiom,
% 59.73/59.60 ! [V_z_2,V_w_2] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 59.73/59.60 <=> ? [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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__0__le__iff,axiom,
% 59.73/59.60 ! [V_n,T_a] :
% 59.73/59.60 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.60 => 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))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zero__le__imp__of__nat,axiom,
% 59.73/59.60 ! [V_m,T_a] :
% 59.73/59.60 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.60 => 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))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_negative__eq__positive,axiom,
% 59.73/59.60 ! [V_m_2,V_n_2] :
% 59.73/59.60 ( 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)
% 59.73/59.60 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.60 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__less__0__iff,axiom,
% 59.73/59.60 ! [V_m,T_a] :
% 59.73/59.60 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.60 => ~ 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))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_not__int__zless__negative,axiom,
% 59.73/59.60 ! [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)))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_int__mult,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zmult__int,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__0,axiom,
% 59.73/59.60 ! [T_a] :
% 59.73/59.60 ( class_Rings_Osemiring__1(T_a)
% 59.73/59.60 => 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__less__imp__less,axiom,
% 59.73/59.60 ! [V_n,V_m,T_a] :
% 59.73/59.60 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_less__imp__of__nat__less,axiom,
% 59.73/59.60 ! [V_n,V_m,T_a] :
% 59.73/59.60 ( class_Rings_Olinordered__semidom(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 59.73/59.60 => 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))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__less__iff,axiom,
% 59.73/59.60 ! [V_n_2,V_m_2,T_b] :
% 59.73/59.60 ( class_Rings_Olinordered__semidom(T_b)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_int__1,axiom,
% 59.73/59.60 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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 59.73/59.60 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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__le__iff,axiom,
% 59.73/59.60 ! [V_n_2,V_m_2,T_b] :
% 59.73/59.60 ( class_Rings_Olinordered__semidom(T_b)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__add,axiom,
% 59.73/59.60 ! [V_n,V_m,T_a] :
% 59.73/59.60 ( class_Rings_Osemiring__1(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__mult,axiom,
% 59.73/59.60 ! [V_n,V_m,T_a] :
% 59.73/59.60 ( class_Rings_Osemiring__1(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zmod__int,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_not__neg__nat,axiom,
% 59.73/59.60 ! [V_z] :
% 59.73/59.60 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 59.73/59.60 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zdiv__int,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__1,axiom,
% 59.73/59.60 ! [T_a] :
% 59.73/59.60 ( class_Rings_Osemiring__1(T_a)
% 59.73/59.60 => 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 59.73/59.60 ! [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 ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Ints__of__nat,axiom,
% 59.73/59.60 ! [V_n_2,T_b] :
% 59.73/59.60 ( class_Rings_Oring__1(T_b)
% 59.73/59.60 => 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))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__power,axiom,
% 59.73/59.60 ! [V_n,V_m,T_a] :
% 59.73/59.60 ( class_Rings_Osemiring__1(T_a)
% 59.73/59.60 => 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zpower__int,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_int__power,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_inj__of__nat,axiom,
% 59.73/59.60 ! [T_b] :
% 59.73/59.60 ( class_Nat_Osemiring__char__0(T_b)
% 59.73/59.60 => 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))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 59.73/59.60 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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_int__le__0__conv,axiom,
% 59.73/59.60 ! [V_n_2] :
% 59.73/59.60 ( 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)))
% 59.73/59.60 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_int__Suc0__eq__1,axiom,
% 59.73/59.60 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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zless__iff__Suc__zadd,axiom,
% 59.73/59.60 ! [V_z_2,V_w_2] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 59.73/59.60 <=> ? [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))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_int__nat__eq,axiom,
% 59.73/59.60 ! [V_z] :
% 59.73/59.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 59.73/59.60 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 59.73/59.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 59.73/59.60 => 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) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_int__eq__iff,axiom,
% 59.73/59.60 ! [V_z_2,V_m_2] :
% 59.73/59.60 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 59.73/59.60 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 59.73/59.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_nat__0__le,axiom,
% 59.73/59.60 ! [V_z] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 59.73/59.60 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zless__nat__eq__int__zless,axiom,
% 59.73/59.60 ! [V_z_2,V_m_2] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 59.73/59.60 <=> 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_int__zle__neg,axiom,
% 59.73/59.60 ! [V_m_2,V_n_2] :
% 59.73/59.60 ( 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))))
% 59.73/59.60 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.60 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_int__Suc,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_negative__zle__0,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_nat__zminus__int,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__setprod,axiom,
% 59.73/59.60 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.60 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 59.73/59.60 & class_Rings_Osemiring__1(T_b) )
% 59.73/59.60 => 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zdiff__int,axiom,
% 59.73/59.60 ! [V_m,V_n] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__Suc,axiom,
% 59.73/59.60 ! [V_m,T_a] :
% 59.73/59.60 ( class_Rings_Osemiring__1(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_neg__zminus__int,axiom,
% 59.73/59.60 ! [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))))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__diff,axiom,
% 59.73/59.60 ! [V_m,V_n,T_a] :
% 59.73/59.60 ( class_Rings_Oring__1(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 59.73/59.60 => 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)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zero__code__numeral__code,axiom,
% 59.73/59.60 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zero__less__int__conv,axiom,
% 59.73/59.60 ! [V_n_2] :
% 59.73/59.60 ( 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)))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_nat__eq__iff,axiom,
% 59.73/59.60 ! [V_m_2,V_w_2] :
% 59.73/59.60 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 59.73/59.60 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 59.73/59.60 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 59.73/59.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 59.73/59.60 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_nat__eq__iff2,axiom,
% 59.73/59.60 ! [V_w_2,V_m_2] :
% 59.73/59.60 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 59.73/59.60 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 59.73/59.60 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 59.73/59.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 59.73/59.60 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_split__nat,axiom,
% 59.73/59.60 ! [V_i_2,V_P_2] :
% 59.73/59.60 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
% 59.73/59.60 <=> ( ! [B_n] :
% 59.73/59.60 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 59.73/59.60 => hBOOL(hAPP(V_P_2,B_n)) )
% 59.73/59.60 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.60 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zmult__zless__mono2__lemma,axiom,
% 59.73/59.60 ! [V_k,V_j,V_i] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 59.73/59.60 => 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))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_not__zle__0__negative,axiom,
% 59.73/59.60 ! [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))))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_negative__zless__0,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_int__eq__iff__number__of,axiom,
% 59.73/59.60 ! [V_v_2,V_m_2] :
% 59.73/59.60 ( 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)
% 59.73/59.60 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 59.73/59.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 59.73/59.60 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)))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__0__less__iff,axiom,
% 59.73/59.60 ! [V_n_2,T_b] :
% 59.73/59.60 ( class_Rings_Olinordered__semidom(T_b)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_int__nat__number__of,axiom,
% 59.73/59.60 ! [V_v] :
% 59.73/59.60 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.60 => 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) )
% 59.73/59.60 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.60 => 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) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__nat,axiom,
% 59.73/59.60 ! [V_z,T_a] :
% 59.73/59.60 ( class_Rings_Oring__1(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 59.73/59.60 => 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) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_nat__less__iff,axiom,
% 59.73/59.60 ! [V_m_2,V_w_2] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 59.73/59.60 <=> 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))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zdiff__int__split,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2,V_P_2] :
% 59.73/59.60 ( 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))))
% 59.73/59.60 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 59.73/59.60 => 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)))) )
% 59.73/59.60 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 59.73/59.60 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 59.73/59.60 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 59.73/59.60 ! [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)))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__number__of__eq,axiom,
% 59.73/59.60 ! [V_v,T_a] :
% 59.73/59.60 ( class_Int_Onumber__ring(T_a)
% 59.73/59.60 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.60 => 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) )
% 59.73/59.60 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.60 => 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) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__number__of__lemma,axiom,
% 59.73/59.60 ! [V_v,T_a] :
% 59.73/59.60 ( class_Int_Onumber__ring(T_a)
% 59.73/59.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.60 => 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) )
% 59.73/59.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 59.73/59.60 => 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) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__int__of__nat,axiom,
% 59.73/59.60 ! [V_k,T_a] :
% 59.73/59.60 ( class_Rings_Oring__1(T_a)
% 59.73/59.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.60 => 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)))) )
% 59.73/59.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.60 => 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)) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_one__code__numeral__code,axiom,
% 59.73/59.60 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_div__mod__code__numeral__def,axiom,
% 59.73/59.60 ! [V_m,V_n] : c_Code__Numeral_Odiv__mod__code__numeral(V_n,V_m) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_negDivAlg_Opinduct,axiom,
% 59.73/59.60 ! [V_P_2,V_a1_2,V_a0_2] :
% 59.73/59.60 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 59.73/59.60 => ( ! [B_a,B_b] :
% 59.73/59.60 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
% 59.73/59.60 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_a),B_b)))
% 59.73/59.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 59.73/59.60 => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 59.73/59.60 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 59.73/59.60 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 59.73/59.60 ! [V_n_2,T_b] :
% 59.73/59.60 ( class_Rings_Osemiring__1(T_b)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__Suc__number__of,axiom,
% 59.73/59.60 ! [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)))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.73/59.60 <=> 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))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2] :
% 59.73/59.60 ( V_A_2 = V_B_2
% 59.73/59.60 <=> 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.73/59.60 <=> 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))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2] :
% 59.73/59.60 ( 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)
% 59.73/59.60 <=> V_x_2 = V_y_2 ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_int__int__eq,axiom,
% 59.73/59.60 ! [V_n_2,V_m_2] :
% 59.73/59.60 ( 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)
% 59.73/59.60 <=> V_m_2 = V_n_2 ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__0L,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__0R,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_infinite__UNIV__int,axiom,
% 59.73/59.60 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 59.73/59.60 ! [T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__of__mono,axiom,
% 59.73/59.60 ! [V_n_2,V_m_2,V_f_2,T_b,T_c] :
% 59.73/59.60 ( ( class_Orderings_Olinorder(T_c)
% 59.73/59.60 & class_Orderings_Olinorder(T_b) )
% 59.73/59.60 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 59.73/59.60 => 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)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__add__distrib__left,axiom,
% 59.73/59.60 ! [V_z,V_y,V_x,T_a] :
% 59.73/59.60 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__diff__distrib__left,axiom,
% 59.73/59.60 ! [V_z,V_y,V_x,T_a] :
% 59.73/59.60 ( class_Groups_Oordered__ab__group__add(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_inf__min,axiom,
% 59.73/59.60 ! [T_b] :
% 59.73/59.60 ( ( class_Lattices_Osemilattice__inf(T_b)
% 59.73/59.60 & class_Orderings_Olinorder(T_b) )
% 59.73/59.60 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__Suc__Suc,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_inf__nat__def,axiom,
% 59.73/59.60 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf_Oidem,axiom,
% 59.73/59.60 ! [V_a,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf_Ocommute,axiom,
% 59.73/59.60 ! [V_b,V_a,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf__commute,axiom,
% 59.73/59.60 ! [V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 59.73/59.60 ! [V_b,V_a,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf__left__idem,axiom,
% 59.73/59.60 ! [V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 59.73/59.60 ! [V_c,V_a,V_b,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf__left__commute,axiom,
% 59.73/59.60 ! [V_z,V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf_Oassoc,axiom,
% 59.73/59.60 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf__assoc,axiom,
% 59.73/59.60 ! [V_z,V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Min_Oidem,axiom,
% 59.73/59.60 ! [V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oless__infI2,axiom,
% 59.73/59.60 ! [V_a,V_x,V_b,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 59.73/59.60 => 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)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oless__infI1,axiom,
% 59.73/59.60 ! [V_b,V_x,V_a,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 59.73/59.60 => 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)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__less__iff__disj,axiom,
% 59.73/59.60 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( 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))
% 59.73/59.60 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 59.73/59.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__less__iff__conj,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 59.73/59.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__le__iff__disj,axiom,
% 59.73/59.60 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( 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))
% 59.73/59.60 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 59.73/59.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Ole__infE,axiom,
% 59.73/59.60 ! [V_b,V_a,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 59.73/59.60 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf__mono,axiom,
% 59.73/59.60 ! [V_d,V_b,V_c,V_a,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 59.73/59.60 => 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))) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf__greatest,axiom,
% 59.73/59.60 ! [V_z,V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 59.73/59.60 => 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))) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Ole__infI,axiom,
% 59.73/59.60 ! [V_b,V_a,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 59.73/59.60 => 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))) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf__absorb2,axiom,
% 59.73/59.60 ! [V_x,V_y,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 59.73/59.60 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf__absorb1,axiom,
% 59.73/59.60 ! [V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 59.73/59.60 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Ole__infI2,axiom,
% 59.73/59.60 ! [V_a,V_x,V_b,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 59.73/59.60 => 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)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Ole__infI1,axiom,
% 59.73/59.60 ! [V_b,V_x,V_a,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 59.73/59.60 => 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)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Ole__inf__iff,axiom,
% 59.73/59.60 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 59.73/59.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Ole__iff__inf,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 59.73/59.60 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf__le2,axiom,
% 59.73/59.60 ! [V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf__le1,axiom,
% 59.73/59.60 ! [V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__diff,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__number__of,axiom,
% 59.73/59.60 ! [V_v,V_u,T_b] :
% 59.73/59.60 ( ( class_Int_Onumber(T_b)
% 59.73/59.60 & class_Orderings_Oord(T_b) )
% 59.73/59.60 => ( ( 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)))
% 59.73/59.60 => 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) )
% 59.73/59.60 & ( ~ 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)))
% 59.73/59.60 => 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) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Min_Oin__idem,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.60 => 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) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Omono__inf,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 59.73/59.60 ( ( class_Lattices_Osemilattice__inf(T_c)
% 59.73/59.60 & class_Orderings_Olinorder(T_b) )
% 59.73/59.60 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 59.73/59.60 => 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)))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 59.73/59.60 ! [V_i_2,V_inc_2,T_b] :
% 59.73/59.60 ( class_Rings_Osemiring__1(T_b)
% 59.73/59.60 => 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 ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 59.73/59.60 ! [V_i_2,V_n_2,V_inc_2,T_b] :
% 59.73/59.60 ( class_Rings_Osemiring__1(T_b)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Min_OF__eq,axiom,
% 59.73/59.60 ! [V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => 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) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__Suc1,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__Suc2,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Ofold1__belowI,axiom,
% 59.73/59.60 ! [V_a_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.60 => 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)) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( 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)))
% 59.73/59.60 <=> ! [B_x] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_fold1__below__iff,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( 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))
% 59.73/59.60 <=> ? [B_x] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_strict__below__fold1__iff,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( 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)))
% 59.73/59.60 <=> ! [B_x] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_fold1__strict__below__iff,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( 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))
% 59.73/59.60 <=> ? [B_x] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Min__insert,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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)) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Min_Osubset__idem,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 59.73/59.60 => 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) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Min__Un,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.60 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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)) ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Min_Oinsert,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_fold1__antimono,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.60 => 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))) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Min_Oinsert__remove,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.73/59.60 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 59.73/59.60 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.73/59.60 => 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)))))) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Min_Ounion__inter,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.60 => ( 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))
% 59.73/59.60 => 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)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Min_Ounion__disjoint,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.60 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( 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))
% 59.73/59.60 => 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)) ) ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Min_Oremove,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.60 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.73/59.60 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 59.73/59.60 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.73/59.60 => 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)))))) ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__number__of__Suc,axiom,
% 59.73/59.60 ! [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)))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_nat__of__aux__code,axiom,
% 59.73/59.60 ! [V_n,V_i] :
% 59.73/59.60 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 59.73/59.60 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 59.73/59.60 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 59.73/59.60 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,V_n)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2] :
% 59.73/59.60 ( c_Nat__Transfer_Onat__set(V_A_2)
% 59.73/59.60 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 59.73/59.60 => 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))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2] :
% 59.73/59.60 ( c_Nat__Transfer_Onat__set(V_A_2)
% 59.73/59.60 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 59.73/59.60 => 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))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_dual__max,axiom,
% 59.73/59.60 ! [T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 59.73/59.60 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2] :
% 59.73/59.60 ( c_Nat__Transfer_Onat__set(V_A_2)
% 59.73/59.60 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 59.73/59.60 => 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)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2] :
% 59.73/59.60 ( c_Nat__Transfer_Onat__set(V_A_2)
% 59.73/59.60 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 59.73/59.60 => 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)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_nat__set__def,axiom,
% 59.73/59.60 ! [V_S_2] :
% 59.73/59.60 ( c_Nat__Transfer_Onat__set(V_S_2)
% 59.73/59.60 <=> ! [B_x] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 59.73/59.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2] :
% 59.73/59.60 ( c_Nat__Transfer_Onat__set(V_A_2)
% 59.73/59.60 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.73/59.60 <=> 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))) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2] :
% 59.73/59.60 ( c_Nat__Transfer_Onat__set(V_A_2)
% 59.73/59.60 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 59.73/59.60 => ( V_A_2 = V_B_2
% 59.73/59.60 <=> 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) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2] :
% 59.73/59.60 ( c_Nat__Transfer_Onat__set(V_A_2)
% 59.73/59.60 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.73/59.60 <=> 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))) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2] :
% 59.73/59.60 ( c_Nat__Transfer_Onat__set(V_A_2)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 59.73/59.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 59.73/59.60 ! [V_A_2] :
% 59.73/59.60 ( c_Nat__Transfer_Onat__set(V_A_2)
% 59.73/59.60 => 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 ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 59.73/59.60 ! [V_A_2] :
% 59.73/59.60 ( c_Nat__Transfer_Onat__set(V_A_2)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 59.73/59.60 <=> 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))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 59.73/59.60 ! [V_A_2] :
% 59.73/59.60 ( c_Nat__Transfer_Onat__set(V_A_2)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 59.73/59.60 ! [V_f_2,V_A_2,T_b] :
% 59.73/59.60 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.60 & class_Groups_Ocomm__monoid__mult(T_b) )
% 59.73/59.60 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 59.73/59.60 => 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)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__ord__min,axiom,
% 59.73/59.60 ! [T_b] :
% 59.73/59.60 ( class_Orderings_Oord(T_b)
% 59.73/59.60 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 59.73/59.60 ! [V_A_2,V_x_2] :
% 59.73/59.60 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 59.73/59.60 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 59.73/59.60 <=> 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))) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Min_Oclosed,axiom,
% 59.73/59.60 ! [V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( ! [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))))))
% 59.73/59.60 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_code__numeral_Osize_I1_J,axiom,
% 59.73/59.60 c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 59.73/59.60 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 59.73/59.60 ! [V_y,V_x] :
% 59.73/59.60 ( c_Nat__Transfer_Ois__nat(V_x)
% 59.73/59.60 => ( c_Nat__Transfer_Ois__nat(V_y)
% 59.73/59.60 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 59.73/59.60 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 59.73/59.60 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 59.73/59.60 ! [V_y,V_x] :
% 59.73/59.60 ( c_Nat__Transfer_Ois__nat(V_x)
% 59.73/59.60 => ( c_Nat__Transfer_Ois__nat(V_y)
% 59.73/59.60 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 59.73/59.60 ! [V_y,V_x] :
% 59.73/59.60 ( c_Nat__Transfer_Ois__nat(V_x)
% 59.73/59.60 => ( c_Nat__Transfer_Ois__nat(V_y)
% 59.73/59.60 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 59.73/59.60 ! [V_y,V_x] :
% 59.73/59.60 ( c_Nat__Transfer_Ois__nat(V_x)
% 59.73/59.60 => ( c_Nat__Transfer_Ois__nat(V_y)
% 59.73/59.60 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 59.73/59.60 ! [V_n,V_x] :
% 59.73/59.60 ( c_Nat__Transfer_Ois__nat(V_x)
% 59.73/59.60 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 59.73/59.60 ! [V_y,V_x] :
% 59.73/59.60 ( c_Nat__Transfer_Ois__nat(V_x)
% 59.73/59.60 => ( c_Nat__Transfer_Ois__nat(V_y)
% 59.73/59.60 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_is__nat__def,axiom,
% 59.73/59.60 ! [V_x_2] :
% 59.73/59.60 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2] :
% 59.73/59.60 ( c_Nat__Transfer_Onat__set(V_A_2)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 59.73/59.60 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 59.73/59.60 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 59.73/59.60 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 59.73/59.60 ! [V_f_2,V_A_2,T_b] :
% 59.73/59.60 ( ! [B_x] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.60 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_code__numeral_Osize_I2_J,axiom,
% 59.73/59.60 ! [V_code__numeral] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_card__greaterThanLessThan__int,axiom,
% 59.73/59.60 ! [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)))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_equiv__intrel__iff,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2] :
% 59.73/59.60 ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_finite__greaterThanLessThan__int,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_code__numeral_Oinject,axiom,
% 59.73/59.60 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 59.73/59.60 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 59.73/59.60 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_equiv__intrel,axiom,
% 59.73/59.60 c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 59.73/59.60 ! [V_code__numeral_H_1] : c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_1) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 59.73/59.60 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_greaterThanLessThan__empty,axiom,
% 59.73/59.60 ! [V_k_2,V_l_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 59.73/59.60 => 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)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.60 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Suc__code__numeral__minus__one,axiom,
% 59.73/59.60 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_n)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = V_n ).
% 59.73/59.60
% 59.73/59.60 fof(fact_intrel__iff,axiom,
% 59.73/59.60 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel))
% 59.73/59.60 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__int,axiom,
% 59.73/59.60 ! [V_j_2,V_i_2,T_b] :
% 59.73/59.60 ( class_Rings_Oring__1(T_b)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_One__int__def,axiom,
% 59.73/59.60 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_mult,axiom,
% 59.73/59.60 ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_v_2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_u_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_le,axiom,
% 59.73/59.60 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_finite__greaterThanLessThan,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_card__greaterThanLessThan,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_minus,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_y_2),V_x_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Zero__int__def,axiom,
% 59.73/59.60 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_int__def,axiom,
% 59.73/59.60 ! [V_m_2] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_add,axiom,
% 59.73/59.60 ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),V_v_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_nat,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_less,axiom,
% 59.73/59.60 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_minus__int__def,axiom,
% 59.73/59.60 ! [V_z_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_2) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_code__numeral_Osize_I4_J,axiom,
% 59.73/59.60 ! [V_code__numeral] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_eq__Abs__Integ,axiom,
% 59.73/59.60 ! [V_z_2] :
% 59.73/59.60 ~ ! [B_x,B_y] : V_z_2 != hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Integ__def,axiom,
% 59.73/59.60 c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Rep__Integ,axiom,
% 59.73/59.60 ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_x_2)),c_Int_OInteg)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Rep__Integ__inject,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2] :
% 59.73/59.60 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 59.73/59.60 <=> V_x_2 = V_y_2 ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Rep__Integ__inverse,axiom,
% 59.73/59.60 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 59.73/59.60
% 59.73/59.60 fof(fact_code__numeral_Osize_I3_J,axiom,
% 59.73/59.60 hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_nat__def,axiom,
% 59.73/59.60 ! [V_z_2] : hAPP(c_Int_Onat,V_z_2) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nats__number__of,axiom,
% 59.73/59.60 ! [V_w_2,T_b] :
% 59.73/59.60 ( class_Int_Onumber__ring(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 59.73/59.60 => 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))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_ivl__disj__un_I4_J,axiom,
% 59.73/59.60 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 59.73/59.60 => 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) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_less__than__iff,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than))
% 59.73/59.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.60 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.73/59.60 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 59.73/59.60 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.73/59.60 => 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)))))) ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_finite__greaterThanAtMost,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_finite__greaterThanAtMost__int,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_greaterThanAtMost__empty,axiom,
% 59.73/59.60 ! [V_k_2,V_l_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 59.73/59.60 => 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)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 59.73/59.60 ! [V_l_2,V_k_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => ( 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)
% 59.73/59.60 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 59.73/59.60 ! [V_l_2,V_k_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => ( 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))
% 59.73/59.60 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_ivl__disj__un_I20_J,axiom,
% 59.73/59.60 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 59.73/59.60 => 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) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_ivl__disj__int_I14_J,axiom,
% 59.73/59.60 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_pair__less__def,axiom,
% 59.73/59.60 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_card__greaterThanAtMost,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.60 => 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) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 59.73/59.60 ! [V_x_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => 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 ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 59.73/59.60 ! [V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => 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) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nats__0,axiom,
% 59.73/59.60 ! [T_b] :
% 59.73/59.60 ( class_Rings_Osemiring__1(T_b)
% 59.73/59.60 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nats__add,axiom,
% 59.73/59.60 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.60 ( class_Rings_Osemiring__1(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 59.73/59.60 => 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))) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nats__mult,axiom,
% 59.73/59.60 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.60 ( class_Rings_Osemiring__1(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 59.73/59.60 => 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))) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Nats__1,axiom,
% 59.73/59.60 ! [T_b] :
% 59.73/59.60 ( class_Rings_Osemiring__1(T_b)
% 59.73/59.60 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_of__nat__in__Nats,axiom,
% 59.73/59.60 ! [V_n_2,T_b] :
% 59.73/59.60 ( class_Rings_Osemiring__1(T_b)
% 59.73/59.60 => 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))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_measure__def,axiom,
% 59.73/59.60 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_ivl__disj__int_I10_J,axiom,
% 59.73/59.60 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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)) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 59.73/59.60 => 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) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.60 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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)) ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_card__greaterThanAtMost__int,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_ivl__disj__un_I16_J,axiom,
% 59.73/59.60 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 59.73/59.60 => 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) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.73/59.60 => 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 )
% 59.73/59.60 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.73/59.60 => 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)))))) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.60 => ( 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))
% 59.73/59.60 => 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)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.60 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( 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))
% 59.73/59.60 => 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)) ) ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_mlex__prod__def,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 59.73/59.60 ! [V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( ! [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))))))
% 59.73/59.60 => 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)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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))))) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.60 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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))))))) ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_type__definition__Integ,axiom,
% 59.73/59.60 c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_max__diff__distrib__left,axiom,
% 59.73/59.60 ! [V_z,V_y,V_x,T_a] :
% 59.73/59.60 ( class_Groups_Oordered__ab__group__add(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_sup__max,axiom,
% 59.73/59.60 ! [T_b] :
% 59.73/59.60 ( ( class_Lattices_Osemilattice__sup(T_b)
% 59.73/59.60 & class_Orderings_Olinorder(T_b) )
% 59.73/59.60 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Max_Oidem,axiom,
% 59.73/59.60 ! [V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup__assoc,axiom,
% 59.73/59.60 ! [V_z,V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup_Oassoc,axiom,
% 59.73/59.60 ! [V_c,V_b,V_a,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup__left__commute,axiom,
% 59.73/59.60 ! [V_z,V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 59.73/59.60 ! [V_c,V_a,V_b,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup__left__idem,axiom,
% 59.73/59.60 ! [V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 59.73/59.60 ! [V_b,V_a,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup__commute,axiom,
% 59.73/59.60 ! [V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup_Ocommute,axiom,
% 59.73/59.60 ! [V_b,V_a,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup_Oidem,axiom,
% 59.73/59.60 ! [V_a,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_max__Suc__Suc,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_max__add__distrib__left,axiom,
% 59.73/59.60 ! [V_z,V_y,V_x,T_a] :
% 59.73/59.60 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_max__of__mono,axiom,
% 59.73/59.60 ! [V_n_2,V_m_2,V_f_2,T_b,T_c] :
% 59.73/59.60 ( ( class_Orderings_Olinorder(T_c)
% 59.73/59.60 & class_Orderings_Olinorder(T_b) )
% 59.73/59.60 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 59.73/59.60 => 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)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 59.73/59.60 ! [T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_max__0R,axiom,
% 59.73/59.60 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 59.73/59.60
% 59.73/59.60 fof(fact_max__0L,axiom,
% 59.73/59.60 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oless__supI2,axiom,
% 59.73/59.60 ! [V_a,V_b,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 59.73/59.60 => 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))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oless__supI1,axiom,
% 59.73/59.60 ! [V_b,V_a,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 59.73/59.60 => 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))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_max__less__iff__conj,axiom,
% 59.73/59.60 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( 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))
% 59.73/59.60 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 59.73/59.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_less__max__iff__disj,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 59.73/59.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_le__max__iff__disj,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 59.73/59.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Ole__supE,axiom,
% 59.73/59.60 ! [V_x,V_b,V_a,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( 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))
% 59.73/59.60 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 59.73/59.60 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup__mono,axiom,
% 59.73/59.60 ! [V_d,V_b,V_c,V_a,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 59.73/59.60 => 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))) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup__least,axiom,
% 59.73/59.60 ! [V_z,V_x,V_y,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 59.73/59.60 => 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)) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Ole__supI,axiom,
% 59.73/59.60 ! [V_b,V_x,V_a,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 59.73/59.60 => 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)) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup__absorb1,axiom,
% 59.73/59.60 ! [V_x,V_y,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 59.73/59.60 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup__absorb2,axiom,
% 59.73/59.60 ! [V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 59.73/59.60 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Ole__supI2,axiom,
% 59.73/59.60 ! [V_a,V_b,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 59.73/59.60 => 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))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Ole__supI1,axiom,
% 59.73/59.60 ! [V_b,V_a,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 59.73/59.60 => 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))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Ole__sup__iff,axiom,
% 59.73/59.60 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( 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))
% 59.73/59.60 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 59.73/59.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Ole__iff__sup,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 59.73/59.60 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_le__maxI2,axiom,
% 59.73/59.60 ! [V_x,V_y,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_le__maxI1,axiom,
% 59.73/59.60 ! [V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 59.73/59.60 ! [V_x,V_z,V_y,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 59.73/59.60 ! [V_x,V_z,V_y,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 59.73/59.60 ! [V_z,V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 59.73/59.60 ! [V_z,V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 59.73/59.60 ! [V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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 ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup__inf__absorb,axiom,
% 59.73/59.60 ! [V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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 ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_max__number__of,axiom,
% 59.73/59.60 ! [V_v,V_u,T_b] :
% 59.73/59.60 ( ( class_Int_Onumber(T_b)
% 59.73/59.60 & class_Orderings_Oord(T_b) )
% 59.73/59.60 => ( ( 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)))
% 59.73/59.60 => 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) )
% 59.73/59.60 & ( ~ 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)))
% 59.73/59.60 => 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) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Odistrib__sup__le,axiom,
% 59.73/59.60 ! [V_z,V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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)))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Odistrib__inf__le,axiom,
% 59.73/59.60 ! [V_z,V_y,V_x,T_a] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_a)
% 59.73/59.60 => 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)))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_minus__max__eq__min,axiom,
% 59.73/59.60 ! [V_y,V_x,T_a] :
% 59.73/59.60 ( class_Groups_Olinordered__ab__group__add(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_minus__min__eq__max,axiom,
% 59.73/59.60 ! [V_y,V_x,T_a] :
% 59.73/59.60 ( class_Groups_Olinordered__ab__group__add(T_a)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_nat__minus__add__max,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_max__Suc1,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_max__Suc2,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_max__ord__max,axiom,
% 59.73/59.60 ! [T_b] :
% 59.73/59.60 ( class_Orderings_Oord(T_b)
% 59.73/59.60 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Max_Oin__idem,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.60 => 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) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Omono__sup,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 59.73/59.60 ( ( class_Lattices_Osemilattice__sup(T_c)
% 59.73/59.60 & class_Orderings_Olinorder(T_b) )
% 59.73/59.60 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 59.73/59.60 => 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)))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Int__greaterThanAtMost,axiom,
% 59.73/59.60 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Int__greaterThanLessThan,axiom,
% 59.73/59.60 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Max_OF__eq,axiom,
% 59.73/59.60 ! [V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => 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) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_dual__min,axiom,
% 59.73/59.60 ! [T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => 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) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Max__insert,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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)) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Max_Osubset__idem,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 59.73/59.60 => 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) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 59.73/59.60 ! [V_a_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.60 => 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 ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Max__Un,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.60 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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)) ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Max_Oinsert,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Max_Oinsert__remove,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.73/59.60 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 59.73/59.60 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.73/59.60 => 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)))))) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Max_Ounion__disjoint,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.60 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( 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))
% 59.73/59.60 => 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)) ) ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Max_Ounion__inter,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.60 => ( 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))
% 59.73/59.60 => 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)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Max_Oremove,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.60 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.73/59.60 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 59.73/59.60 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.73/59.60 => 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)))))) ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_max__Suc__number__of,axiom,
% 59.73/59.60 ! [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)))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_max__number__of__Suc,axiom,
% 59.73/59.60 ! [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)))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_type__definition_OAbs__image,axiom,
% 59.73/59.60 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 59.73/59.60 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_type__definition_ORep__range,axiom,
% 59.73/59.60 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 59.73/59.60 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 59.73/59.60 => 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 ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.60 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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))))))) ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_sup__nat__def,axiom,
% 59.73/59.60 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.60 => 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) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 59.73/59.60 ! [V_x_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => 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 ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 59.73/59.60 ! [V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => 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) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_type__definition_ORep__inject,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 59.73/59.60 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 59.73/59.60 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 59.73/59.60 <=> V_x_2 = V_y_2 ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_type__definition_ORep__inverse,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 59.73/59.60 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 59.73/59.60 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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)) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 59.73/59.60 => 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) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 59.73/59.60 ! [V_a_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.60 => 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 ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.60 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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)) ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.73/59.60 => 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 )
% 59.73/59.60 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.73/59.60 => 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)))))) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.60 => ( 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))
% 59.73/59.60 => 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)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 59.73/59.60 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.60 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( 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))
% 59.73/59.60 => 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)) ) ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.60 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.73/59.60 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 59.73/59.60 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 59.73/59.60 => 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)))))) ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OInf__le__Sup,axiom,
% 59.73/59.60 ! [V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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))) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_type__definition_OAbs__inject,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 59.73/59.60 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 59.73/59.60 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 59.73/59.60 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_type__definition_OAbs__inverse,axiom,
% 59.73/59.60 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 59.73/59.60 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 59.73/59.60 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_type__definition_ORep,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 59.73/59.60 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 59.73/59.60 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 59.73/59.60 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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))))) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 59.73/59.60 ! [V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( ! [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))))))
% 59.73/59.60 => 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)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Max_Oclosed,axiom,
% 59.73/59.60 ! [V_A_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => ( ! [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))))))
% 59.73/59.60 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 59.73/59.60 ! [V_N_2,V_h_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( ! [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))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 59.73/59.60 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 59.73/59.60 ! [V_N_2,V_h_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( ! [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))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 59.73/59.60 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Max_Ohom__commute,axiom,
% 59.73/59.60 ! [V_N_2,V_h_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( ! [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))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 59.73/59.60 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Min_Ohom__commute,axiom,
% 59.73/59.60 ! [V_N_2,V_h_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( ! [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))
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 59.73/59.60 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.60 => 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)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_decr__mult__lemma,axiom,
% 59.73/59.60 ! [V_k_2,V_P_2,V_d_2] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 59.73/59.60 => ( ! [B_x] :
% 59.73/59.60 ( hBOOL(hAPP(V_P_2,B_x))
% 59.73/59.60 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 59.73/59.60 => ! [B_x] :
% 59.73/59.60 ( hBOOL(hAPP(V_P_2,B_x))
% 59.73/59.60 => 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)))) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_negD,axiom,
% 59.73/59.60 ! [V_x] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.60 => ? [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))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_incr__mult__lemma,axiom,
% 59.73/59.60 ! [V_k_2,V_P_2,V_d_2] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 59.73/59.60 => ( ! [B_x] :
% 59.73/59.60 ( hBOOL(hAPP(V_P_2,B_x))
% 59.73/59.60 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 59.73/59.60 => ! [B_x] :
% 59.73/59.60 ( hBOOL(hAPP(V_P_2,B_x))
% 59.73/59.60 => 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)))) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_strong__setprod__reindex__cong,axiom,
% 59.73/59.60 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 59.73/59.60 ( class_Groups_Ocomm__monoid__mult(T_d)
% 59.73/59.60 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.73/59.60 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 59.73/59.60 => ( ! [B_x] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.60 => 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) )
% 59.73/59.60 => 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) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_setprod__mono__one__left,axiom,
% 59.73/59.60 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 59.73/59.60 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 59.73/59.60 => ( ! [B_x] :
% 59.73/59.60 ( 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)))
% 59.73/59.60 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 59.73/59.60 => 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) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_setprod__mono__one__right,axiom,
% 59.73/59.60 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 59.73/59.60 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 59.73/59.60 => ( ! [B_x] :
% 59.73/59.60 ( 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)))
% 59.73/59.60 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 59.73/59.60 => 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) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_zero__less__imp__eq__int,axiom,
% 59.73/59.60 ! [V_k] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 59.73/59.60 => ? [B_n] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 59.73/59.60 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_ivl__disj__un_I19_J,axiom,
% 59.73/59.60 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 59.73/59.60 => 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) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_ivl__disj__un_I3_J,axiom,
% 59.73/59.60 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 59.73/59.60 => 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) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_finite__atLeastLessThan,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_finite__atLeastAtMost,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_finite__atLeastAtMost__int,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_finite__atLeastLessThan__int,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_image__add__atLeastLessThan,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_image__Suc__atLeastLessThan,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_image__Suc__atLeastAtMost,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_image__add__atLeastAtMost,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastLessThan__eq__iff,axiom,
% 59.73/59.60 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 59.73/59.60 => ( 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)
% 59.73/59.60 <=> ( V_a_2 = V_c_2
% 59.73/59.60 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 59.73/59.60 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( 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)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 59.73/59.60 => V_a_2 = V_c_2 ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 59.73/59.60 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( 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)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 59.73/59.60 => V_b_2 = V_d_2 ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_ivl__disj__int_I15_J,axiom,
% 59.73/59.60 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_ivl__disj__un_I21_J,axiom,
% 59.73/59.60 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 59.73/59.60 => 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) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 59.73/59.60 ! [V_n_2,V_m_2] :
% 59.73/59.60 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 59.73/59.60 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 59.73/59.60 => 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))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastLessThan0,axiom,
% 59.73/59.60 ! [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)) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_ivl__disj__un_I6_J,axiom,
% 59.73/59.60 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 59.73/59.60 => 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) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_card__atLeastLessThan,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2] :
% 59.73/59.60 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 59.73/59.60 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_ivl__disj__un_I18_J,axiom,
% 59.73/59.60 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 59.73/59.60 => 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) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastatMost__empty__iff,axiom,
% 59.73/59.60 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => ( 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))
% 59.73/59.60 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastatMost__empty__iff2,axiom,
% 59.73/59.60 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => ( 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)
% 59.73/59.60 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastatMost__empty,axiom,
% 59.73/59.60 ! [V_a_2,V_b_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
% 59.73/59.60 => 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)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastatMost__subset__iff,axiom,
% 59.73/59.60 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 59.73/59.60 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 59.73/59.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastLessThan__empty,axiom,
% 59.73/59.60 ! [V_a_2,V_b_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 59.73/59.60 => 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)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastLessThan__empty__iff,axiom,
% 59.73/59.60 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => ( 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))
% 59.73/59.60 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 59.73/59.60 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => ( 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)
% 59.73/59.60 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastAtMost__singleton_H,axiom,
% 59.73/59.60 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => ( V_a_2 = V_b_2
% 59.73/59.60 => 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))) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 59.73/59.60 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 <=> ( V_a_2 = V_b_2
% 59.73/59.60 & V_b_2 = V_c_2 ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastAtMost__singleton,axiom,
% 59.73/59.60 ! [V_a_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => 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))) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastLessThan__subset__iff,axiom,
% 59.73/59.60 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 59.73/59.60 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 59.73/59.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_ivl__disj__un_I17_J,axiom,
% 59.73/59.60 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 59.73/59.60 => 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) ) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_image__uminus__atLeastAtMost,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.60 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_ivl__diff,axiom,
% 59.73/59.60 ! [V_m_2,V_n_2,V_i_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
% 59.73/59.60 => 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) ) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_UN__UN__finite__eq,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_ivl__disj__int_I11_J,axiom,
% 59.73/59.60 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 59.73/59.60 ! [V_y_2,V_x_2] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 59.73/59.60 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_card__atLeastAtMost,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastAtMostSuc__conv,axiom,
% 59.73/59.60 ! [V_n_2,V_m_2] :
% 59.73/59.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastLessThan__singleton,axiom,
% 59.73/59.60 ! [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))) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 59.73/59.60 ! [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) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_Int__atLeastAtMost,axiom,
% 59.73/59.60 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 59.73/59.60 ( class_Orderings_Olinorder(T_b)
% 59.73/59.60 => 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)) ) ).
% 59.73/59.60
% 59.73/59.60 fof(fact_atLeastatMost__psubset__iff,axiom,
% 59.73/59.60 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 59.73/59.60 ( class_Orderings_Oorder(T_b)
% 59.73/59.60 => ( 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)))
% 59.73/59.60 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 59.73/59.60 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 59.73/59.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
% 59.73/59.60 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2))
% 59.73/59.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) )
% 59.73/59.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_atLeastLessThan__add__Un,axiom,
% 59.73/59.61 ! [V_k_2,V_j_2,V_i_2] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Int__atLeastLessThan,axiom,
% 59.73/59.61 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__un_I22_J,axiom,
% 59.73/59.61 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 59.73/59.61 => 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) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__int_I16_J,axiom,
% 59.73/59.61 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oorder(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__int_I12_J,axiom,
% 59.73/59.61 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oorder(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__int_I13_J,axiom,
% 59.73/59.61 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oorder(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_subset__card__intvl__is__intvl,axiom,
% 59.73/59.61 ! [V_k_2,V_A_2] :
% 59.73/59.61 ( 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)))))
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__int_I9_J,axiom,
% 59.73/59.61 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oorder(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 59.73/59.61 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_image__uminus__atLeastLessThan,axiom,
% 59.73/59.61 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_image__add__int__atLeastLessThan,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_card__atLeastLessThan__int,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_atLeastLessThanSuc,axiom,
% 59.73/59.61 ! [V_n_2,V_m_2] :
% 59.73/59.61 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 59.73/59.61 => 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)) )
% 59.73/59.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 59.73/59.61 => 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_simp__from__to,axiom,
% 59.73/59.61 ! [V_i_2,V_j_2] :
% 59.73/59.61 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 59.73/59.61 => 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)) )
% 59.73/59.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 59.73/59.61 => 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__un_I15_J,axiom,
% 59.73/59.61 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 59.73/59.61 => 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) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_card__atLeastAtMost__int,axiom,
% 59.73/59.61 ! [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))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 59.73/59.61 ! [V_x_2,V_y_2,V_c_2] :
% 59.73/59.61 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 59.73/59.61 => 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)) )
% 59.73/59.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 59.73/59.61 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 59.73/59.61 => 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))) )
% 59.73/59.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 59.73/59.61 => 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)) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__un_I5_J,axiom,
% 59.73/59.61 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 59.73/59.61 => 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) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_bset_I8_J,axiom,
% 59.73/59.61 ! [V_B_2,V_t_2,V_D_2] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 59.73/59.61 => ( 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))
% 59.73/59.61 => ! [B_x] :
% 59.73/59.61 ( ! [B_xa] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => ! [B_xb] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 59.73/59.61 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 59.73/59.61 => 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))) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_aset_I6_J,axiom,
% 59.73/59.61 ! [V_A_2,V_t_2,V_D_2] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 59.73/59.61 => ( 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))
% 59.73/59.61 => ! [B_x] :
% 59.73/59.61 ( ! [B_xa] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => ! [B_xb] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 59.73/59.61 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 59.73/59.61 => 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)) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_bset_I3_J,axiom,
% 59.73/59.61 ! [V_B_2,V_t_2,V_D_2] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 59.73/59.61 => ( 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))
% 59.73/59.61 => ( ! [B_x] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => ! [B_xa] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 59.73/59.61 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 59.73/59.61 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ex__nat__less,axiom,
% 59.73/59.61 ! [V_P_2,V_n_2] :
% 59.73/59.61 ( ? [B_m] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 59.73/59.61 & hBOOL(hAPP(V_P_2,B_m)) )
% 59.73/59.61 <=> ? [B_x] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_all__nat__less,axiom,
% 59.73/59.61 ! [V_P_2,V_n_2] :
% 59.73/59.61 ( ! [B_m] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 59.73/59.61 => hBOOL(hAPP(V_P_2,B_m)) )
% 59.73/59.61 <=> ! [B_x] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_all__nat__less__eq,axiom,
% 59.73/59.61 ! [V_P_2,V_n_2] :
% 59.73/59.61 ( ! [B_m] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 59.73/59.61 => hBOOL(hAPP(V_P_2,B_m)) )
% 59.73/59.61 <=> ! [B_x] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ex__nat__less__eq,axiom,
% 59.73/59.61 ! [V_P_2,V_n_2] :
% 59.73/59.61 ( ? [B_m] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 59.73/59.61 & hBOOL(hAPP(V_P_2,B_m)) )
% 59.73/59.61 <=> ? [B_x] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_aset_I3_J,axiom,
% 59.73/59.61 ! [V_A_2,V_t_2,V_D_2] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 59.73/59.61 => ( 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))
% 59.73/59.61 => ( ! [B_x] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => ! [B_xa] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 59.73/59.61 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 59.73/59.61 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_aset_I5_J,axiom,
% 59.73/59.61 ! [V_A_2,V_t_2,V_D_2] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 59.73/59.61 => ! [B_x] :
% 59.73/59.61 ( ! [B_xa] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => ! [B_xb] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 59.73/59.61 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 59.73/59.61 => 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)) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_bset_I7_J,axiom,
% 59.73/59.61 ! [V_B_2,V_t_2,V_D_2] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 59.73/59.61 => ! [B_x] :
% 59.73/59.61 ( ! [B_xa] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => ! [B_xb] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 59.73/59.61 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 59.73/59.61 => 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))) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_aset_I4_J,axiom,
% 59.73/59.61 ! [V_A_2,V_t_2,V_D_2] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 59.73/59.61 => ! [B_x] :
% 59.73/59.61 ( ! [B_xa] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => ! [B_xb] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 59.73/59.61 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 59.73/59.61 => ( B_x != V_t_2
% 59.73/59.61 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_bset_I4_J,axiom,
% 59.73/59.61 ! [V_B_2,V_t_2,V_D_2] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 59.73/59.61 => ! [B_x] :
% 59.73/59.61 ( ! [B_xa] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => ! [B_xb] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 59.73/59.61 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 59.73/59.61 => ( B_x != V_t_2
% 59.73/59.61 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_aset_I8_J,axiom,
% 59.73/59.61 ! [V_t_2,V_A_2,V_D_2] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 59.73/59.61 => ! [B_x] :
% 59.73/59.61 ( ! [B_xa] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => ! [B_xb] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 59.73/59.61 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 59.73/59.61 => 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))) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_bset_I6_J,axiom,
% 59.73/59.61 ! [V_t_2,V_B_2,V_D_2] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 59.73/59.61 => ! [B_x] :
% 59.73/59.61 ( ! [B_xa] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => ! [B_xb] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 59.73/59.61 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 59.73/59.61 => 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)) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_UN__finite2__subset,axiom,
% 59.73/59.61 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 59.73/59.61 ( ! [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)))
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_periodic__finite__ex,axiom,
% 59.73/59.61 ! [V_P_2,V_d_2] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 59.73/59.61 => ( ! [B_x,B_k] :
% 59.73/59.61 ( hBOOL(hAPP(V_P_2,B_x))
% 59.73/59.61 <=> 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)))) )
% 59.73/59.61 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 59.73/59.61 <=> ? [B_x] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_aset_I7_J,axiom,
% 59.73/59.61 ! [V_t_2,V_A_2,V_D_2] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 59.73/59.61 => ! [B_x] :
% 59.73/59.61 ( ! [B_xa] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => ! [B_xb] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 59.73/59.61 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 59.73/59.61 => 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))) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_bset_I5_J,axiom,
% 59.73/59.61 ! [V_t_2,V_B_2,V_D_2] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 59.73/59.61 => ! [B_x] :
% 59.73/59.61 ( ! [B_xa] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => ! [B_xb] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 59.73/59.61 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 59.73/59.61 => 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)) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 59.73/59.61 ! [V_u_2] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_finite__lessThan,axiom,
% 59.73/59.61 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_lessThan__eq__iff,axiom,
% 59.73/59.61 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 59.73/59.61 <=> V_x_2 = V_y_2 ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_card__lessThan,axiom,
% 59.73/59.61 ! [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 ).
% 59.73/59.61
% 59.73/59.61 fof(fact_UN__lessThan__UNIV,axiom,
% 59.73/59.61 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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_atLeast0LessThan,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_lessThan__0,axiom,
% 59.73/59.61 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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_lessThan__Suc,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_lessThan__iff,axiom,
% 59.73/59.61 ! [V_k_2,V_i_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oord(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 59.73/59.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_lessThan__subset__iff,axiom,
% 59.73/59.61 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => ( 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)))
% 59.73/59.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_lessThan__strict__subset__iff,axiom,
% 59.73/59.61 ! [V_n_2,V_m_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => ( 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)))
% 59.73/59.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_single__Diff__lessThan,axiom,
% 59.73/59.61 ! [V_k_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oorder(T_b)
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__un_I8_J,axiom,
% 59.73/59.61 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 59.73/59.61 => 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) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__int_I4_J,axiom,
% 59.73/59.61 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oorder(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__int_I2_J,axiom,
% 59.73/59.61 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oorder(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 59.73/59.61 ! [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))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_arith__series__int,axiom,
% 59.73/59.61 ! [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)))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_UN__finite2__eq,axiom,
% 59.73/59.61 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 59.73/59.61 ( ! [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)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_UN__finite__subset,axiom,
% 59.73/59.61 ! [V_C_2,V_A_2,T_b] :
% 59.73/59.61 ( ! [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))
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_of__int__setsum,axiom,
% 59.73/59.61 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.61 ( class_Rings_Oring__1(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__0,axiom,
% 59.73/59.61 ! [V_A_2,T_c,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__negf,axiom,
% 59.73/59.61 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.61 ( class_Groups_Oab__group__add(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__divide__distrib,axiom,
% 59.73/59.61 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.61 ( class_Fields_Ofield(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__addf,axiom,
% 59.73/59.61 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__product,axiom,
% 59.73/59.61 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.61 ( class_Rings_Osemiring__0(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__left__distrib,axiom,
% 59.73/59.61 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.61 ( class_Rings_Osemiring__0(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__right__distrib,axiom,
% 59.73/59.61 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 59.73/59.61 ( class_Rings_Osemiring__0(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__commute,axiom,
% 59.73/59.61 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__subtractf,axiom,
% 59.73/59.61 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 59.73/59.61 ( class_Groups_Oab__group__add(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_of__nat__setsum,axiom,
% 59.73/59.61 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.61 ( class_Rings_Osemiring__1(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum_Oempty,axiom,
% 59.73/59.61 ! [V_g_2,T_c,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__empty,axiom,
% 59.73/59.61 ! [V_f_2,T_c,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum_Oinfinite,axiom,
% 59.73/59.61 ! [V_g_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => 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) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__infinite,axiom,
% 59.73/59.61 ! [V_f_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => 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) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum_Odistrib,axiom,
% 59.73/59.61 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 59.73/59.61 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 59.73/59.61 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 59.73/59.61 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 59.73/59.61 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__reindex,axiom,
% 59.73/59.61 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_d)
% 59.73/59.61 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 59.73/59.61 => 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) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__add__nat__ivl,axiom,
% 59.73/59.61 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 59.73/59.61 => 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)) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__diff__nat__ivl,axiom,
% 59.73/59.61 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 59.73/59.61 ( class_Groups_Oab__group__add(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 59.73/59.61 => 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)) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__delta,axiom,
% 59.73/59.61 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 59.73/59.61 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 59.73/59.61 => 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) )
% 59.73/59.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 59.73/59.61 => 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) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__delta_H,axiom,
% 59.73/59.61 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 59.73/59.61 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 59.73/59.61 => 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) )
% 59.73/59.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 59.73/59.61 => 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) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__setsum__restrict,axiom,
% 59.73/59.61 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_d)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 59.73/59.61 => 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) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__constant,axiom,
% 59.73/59.61 ! [V_A_2,V_y_2,T_c,T_b] :
% 59.73/59.61 ( class_Rings_Osemiring__1(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__lessThan__Suc,axiom,
% 59.73/59.61 ! [V_n_2,V_f_2,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__insert,axiom,
% 59.73/59.61 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 59.73/59.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 59.73/59.61 => 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)) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum_Oinsert,axiom,
% 59.73/59.61 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.61 => 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)) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__Un__Int,axiom,
% 59.73/59.61 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.61 => 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)) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__diff,axiom,
% 59.73/59.61 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Oab__group__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 59.73/59.61 => 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)) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum_Oreindex,axiom,
% 59.73/59.61 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 59.73/59.61 => 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) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum_Oeq__fold,axiom,
% 59.73/59.61 ! [V_g_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => 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) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum_OF__eq,axiom,
% 59.73/59.61 ! [V_g_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => 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) )
% 59.73/59.61 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => 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) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 59.73/59.61 ! [V_k_2,V_f_2,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.61 => 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__head__upt__Suc,axiom,
% 59.73/59.61 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 59.73/59.61 => 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))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__head__Suc,axiom,
% 59.73/59.61 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 59.73/59.61 => 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))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__restrict__set_H,axiom,
% 59.73/59.61 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => 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) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__restrict__set,axiom,
% 59.73/59.61 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => 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) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__image__gen,axiom,
% 59.73/59.61 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 59.73/59.61 => 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum_Oinsert__remove,axiom,
% 59.73/59.61 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => 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)))))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__Un__disjoint,axiom,
% 59.73/59.61 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.61 => ( 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))
% 59.73/59.61 => 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)) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__Un,axiom,
% 59.73/59.61 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Oab__group__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.61 => 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))) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__op__ivl__Suc,axiom,
% 59.73/59.61 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 59.73/59.61 => 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) )
% 59.73/59.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 59.73/59.61 => 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)) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__cl__ivl__Suc,axiom,
% 59.73/59.61 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 59.73/59.61 => 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) )
% 59.73/59.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 59.73/59.61 => 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))) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__head,axiom,
% 59.73/59.61 ! [V_P_2,V_n_2,V_m_2,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 59.73/59.61 => 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))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__ub__add__nat,axiom,
% 59.73/59.61 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => ( 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))))
% 59.73/59.61 => 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)))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__cases,axiom,
% 59.73/59.61 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => 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))))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__diff1_H,axiom,
% 59.73/59.61 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.61 => 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)))))) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum_Oremove,axiom,
% 59.73/59.61 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.61 => 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)))))) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__diff1,axiom,
% 59.73/59.61 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Oab__group__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.61 => 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)) )
% 59.73/59.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.61 => 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) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__diff1__ring,axiom,
% 59.73/59.61 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Rings_Oring(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.61 => 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)) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_geometric__sum,axiom,
% 59.73/59.61 ! [V_n_2,V_x_2,T_b] :
% 59.73/59.61 ( class_Fields_Ofield(T_b)
% 59.73/59.61 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 59.73/59.61 => 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))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_gauss__sum,axiom,
% 59.73/59.61 ! [V_n_2,T_b] :
% 59.73/59.61 ( class_Rings_Ocomm__semiring__1(T_b)
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__natinterval__difff,axiom,
% 59.73/59.61 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 59.73/59.61 ( class_Groups_Oab__group__add(T_b)
% 59.73/59.61 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 59.73/59.61 => 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)))) )
% 59.73/59.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 59.73/59.61 => 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) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_arith__series__general,axiom,
% 59.73/59.61 ! [V_n_2,V_d_2,V_a_2,T_b] :
% 59.73/59.61 ( class_Rings_Ocomm__semiring__1(T_b)
% 59.73/59.61 => 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)))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__mono2,axiom,
% 59.73/59.61 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.73/59.61 => ( ! [B_b] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 59.73/59.61 => 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))) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__bounded,axiom,
% 59.73/59.61 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 59.73/59.61 & class_Rings_Osemiring__1(T_c) )
% 59.73/59.61 => ( ! [B_i] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 59.73/59.61 => 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))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 59.73/59.61 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.61 => ( ! [B_x] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 59.73/59.61 => 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)) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__eq__0__iff,axiom,
% 59.73/59.61 ! [V_f_2,V_F_2,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 59.73/59.61 => ( 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)
% 59.73/59.61 <=> ! [B_x] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 59.73/59.61 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_card__eq__setsum,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_int__setsum,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__eq__Suc0__iff,axiom,
% 59.73/59.61 ! [V_f_2,V_A_2,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => ( 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))
% 59.73/59.61 <=> ? [B_x] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.61 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 59.73/59.61 & ! [B_xa] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 59.73/59.61 => ( B_x != B_xa
% 59.73/59.61 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__eq__1__iff,axiom,
% 59.73/59.61 ! [V_f_2,V_A_2,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => ( 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)
% 59.73/59.61 <=> ? [B_x] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.61 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 59.73/59.61 & ! [B_xa] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 59.73/59.61 => ( B_x != B_xa
% 59.73/59.61 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 59.73/59.61 ! [V_k_2,V_f_2] :
% 59.73/59.61 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__diff__nat,axiom,
% 59.73/59.61 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 59.73/59.61 => 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 59.73/59.61 ! [V_A_2,V_f_2,T_b] :
% 59.73/59.61 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 & class_Groups_Ocomm__monoid__mult(T_b) )
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__diff1__nat,axiom,
% 59.73/59.61 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 59.73/59.61 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.61 => 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)) )
% 59.73/59.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.61 => 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) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__Un__nat,axiom,
% 59.73/59.61 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.61 => 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))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 59.73/59.61 ! [V_f_2,V_A_2,T_b] :
% 59.73/59.61 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 & class_Groups_Ocomm__monoid__mult(T_b) )
% 59.73/59.61 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 59.73/59.61 => 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_arith__series__nat,axiom,
% 59.73/59.61 ! [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)))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 59.73/59.61 ! [V_f_2,V_A_2,T_b] :
% 59.73/59.61 ( ! [B_x] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.61 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__multicount,axiom,
% 59.73/59.61 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 59.73/59.61 => ( ! [B_x] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 59.73/59.61 => 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 )
% 59.73/59.61 => 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)) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__Un__zero,axiom,
% 59.73/59.61 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 59.73/59.61 => ( ! [B_x] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 59.73/59.61 => 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)) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__mono3,axiom,
% 59.73/59.61 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 59.73/59.61 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.73/59.61 => ( ! [B_x] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 59.73/59.61 => 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))) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__reindex__nonzero,axiom,
% 59.73/59.61 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_d)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 59.73/59.61 => ( ! [B_x] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 59.73/59.61 => ! [B_y] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 59.73/59.61 => ( B_x != B_y
% 59.73/59.61 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 59.73/59.61 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 59.73/59.61 => 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) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_UN__le__eq__Un0,axiom,
% 59.73/59.61 ! [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))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_finite__atMost,axiom,
% 59.73/59.61 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_atMost__eq__iff,axiom,
% 59.73/59.61 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 59.73/59.61 <=> V_x_2 = V_y_2 ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_atLeast0AtMost,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_lessThan__Suc__atMost,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_card__atMost,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_atMost__Suc,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_atMost__iff,axiom,
% 59.73/59.61 ! [V_k_2,V_i_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oord(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 59.73/59.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_atMost__subset__iff,axiom,
% 59.73/59.61 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oorder(T_b)
% 59.73/59.61 => ( 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)))
% 59.73/59.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_UN__atMost__UNIV,axiom,
% 59.73/59.61 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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__atMost__Suc,axiom,
% 59.73/59.61 ! [V_n_2,V_f_2,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_atMost__0,axiom,
% 59.73/59.61 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))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Int__atLeastAtMostR1,axiom,
% 59.73/59.61 ! [V_d_2,V_c_2,V_b_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Int__atLeastAtMostL1,axiom,
% 59.73/59.61 ! [V_d_2,V_b_2,V_a_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__un_I9_J,axiom,
% 59.73/59.61 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 59.73/59.61 => 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) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_UN__le__add__shift,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__int_I3_J,axiom,
% 59.73/59.61 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oorder(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__int_I1_J,axiom,
% 59.73/59.61 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oorder(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__un_I2_J,axiom,
% 59.73/59.61 ! [V_u_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__un_I10_J,axiom,
% 59.73/59.61 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 59.73/59.61 => 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) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__un_I7_J,axiom,
% 59.73/59.61 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 59.73/59.61 => 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) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 59.73/59.61 ! [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))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__multicount__gen,axiom,
% 59.73/59.61 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 59.73/59.61 => ( ! [B_x] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 59.73/59.61 => 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) )
% 59.73/59.61 => 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) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__nonneg__0,axiom,
% 59.73/59.61 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 59.73/59.61 => ( ! [B_i] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 59.73/59.61 => ( 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)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 59.73/59.61 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__nonneg__leq__bound,axiom,
% 59.73/59.61 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 59.73/59.61 => ( ! [B_i] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 59.73/59.61 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_greaterThan__0,axiom,
% 59.73/59.61 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))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_sum__diff__distrib,axiom,
% 59.73/59.61 ! [V_n_2,V_P_2,V_Q_2] :
% 59.73/59.61 ( ! [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)))
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__mono__zero__right,axiom,
% 59.73/59.61 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 59.73/59.61 => ( ! [B_x] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 59.73/59.61 => 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) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_greaterThan__eq__iff,axiom,
% 59.73/59.61 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 59.73/59.61 <=> V_x_2 = V_y_2 ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_greaterThan__iff,axiom,
% 59.73/59.61 ! [V_k_2,V_i_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oord(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 59.73/59.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_greaterThan__subset__iff,axiom,
% 59.73/59.61 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => ( 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)))
% 59.73/59.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Compl__atMost,axiom,
% 59.73/59.61 ! [V_k_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Compl__greaterThan,axiom,
% 59.73/59.61 ! [V_k_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__int_I7_J,axiom,
% 59.73/59.61 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oorder(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__un_I11_J,axiom,
% 59.73/59.61 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 59.73/59.61 => 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) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_image__uminus__lessThan,axiom,
% 59.73/59.61 ! [V_x_2,T_b] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_image__uminus__greaterThan,axiom,
% 59.73/59.61 ! [V_x_2,T_b] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__int_I5_J,axiom,
% 59.73/59.61 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oorder(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_greaterThan__Suc,axiom,
% 59.73/59.61 ! [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)))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__un_I12_J,axiom,
% 59.73/59.61 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 59.73/59.61 => 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) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__mono__zero__left,axiom,
% 59.73/59.61 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 59.73/59.61 => ( ! [B_x] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 59.73/59.61 => 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) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__un_I13_J,axiom,
% 59.73/59.61 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 59.73/59.61 => 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) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_atLeast__eq__iff,axiom,
% 59.73/59.61 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 59.73/59.61 <=> V_x_2 = V_y_2 ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_atLeast__iff,axiom,
% 59.73/59.61 ! [V_k_2,V_i_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oord(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 59.73/59.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_atLeast__subset__iff,axiom,
% 59.73/59.61 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oorder(T_b)
% 59.73/59.61 => ( 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)))
% 59.73/59.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_atLeast__0,axiom,
% 59.73/59.61 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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Compl__lessThan,axiom,
% 59.73/59.61 ! [V_k_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Compl__atLeast,axiom,
% 59.73/59.61 ! [V_k_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_atLeast__Suc__greaterThan,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__un_I14_J,axiom,
% 59.73/59.61 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 59.73/59.61 => 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) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__int_I8_J,axiom,
% 59.73/59.61 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oorder(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Int__atLeastAtMostL2,axiom,
% 59.73/59.61 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Int__atLeastAtMostR2,axiom,
% 59.73/59.61 ! [V_d_2,V_c_2,V_a_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_UN__atLeast__UNIV,axiom,
% 59.73/59.61 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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__int_I6_J,axiom,
% 59.73/59.61 ! [V_u_2,V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oorder(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_image__uminus__atMost,axiom,
% 59.73/59.61 ! [V_x_2,T_b] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_image__uminus__atLeast,axiom,
% 59.73/59.61 ! [V_x_2,T_b] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add(T_b)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_atLeast__Suc,axiom,
% 59.73/59.61 ! [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)))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_atMost__Int__atLeast,axiom,
% 59.73/59.61 ! [V_n_2,T_b] :
% 59.73/59.61 ( class_Orderings_Oorder(T_b)
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_ivl__disj__un_I1_J,axiom,
% 59.73/59.61 ! [V_l_2,T_b] :
% 59.73/59.61 ( class_Orderings_Olinorder(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__strict__mono,axiom,
% 59.73/59.61 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 59.73/59.61 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.61 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.61 => ( ! [B_x] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 59.73/59.61 => 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))) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_field__le__mult__one__interval,axiom,
% 59.73/59.61 ! [V_y,V_x,T_a] :
% 59.73/59.61 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 59.73/59.61 => ( ! [B_z] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 59.73/59.61 => 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)) ) )
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 59.73/59.61 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 59.73/59.61 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 & class_Groups_Ocomm__monoid__mult(T_b) )
% 59.73/59.61 => ( V_A_2 = V_B_2
% 59.73/59.61 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 59.73/59.61 => ( ! [B_x] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 59.73/59.61 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 59.73/59.61 => 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) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_sgn__if,axiom,
% 59.73/59.61 ! [V_x,T_a] :
% 59.73/59.61 ( class_Groups_Osgn__if(T_a)
% 59.73/59.61 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.61 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 59.73/59.61 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.61 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 59.73/59.61 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 59.73/59.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 59.73/59.61 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_sgn__neg,axiom,
% 59.73/59.61 ! [V_a,T_a] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.61 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_sgn__1__neg,axiom,
% 59.73/59.61 ! [V_a_2,T_b] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_b)
% 59.73/59.61 => ( 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))
% 59.73/59.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_sgn0,axiom,
% 59.73/59.61 ! [T_a] :
% 59.73/59.61 ( class_Groups_Osgn__if(T_a)
% 59.73/59.61 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_sgn__0__0,axiom,
% 59.73/59.61 ! [V_a_2,T_b] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_b)
% 59.73/59.61 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.61 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_sgn__sgn,axiom,
% 59.73/59.61 ! [V_a,T_a] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_sgn__times,axiom,
% 59.73/59.61 ! [V_b,V_a,T_a] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_sgn__less,axiom,
% 59.73/59.61 ! [V_a_2,T_b] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_b)
% 59.73/59.61 => ( 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)))
% 59.73/59.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_sgn__greater,axiom,
% 59.73/59.61 ! [V_a_2,T_b] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_b)
% 59.73/59.61 => ( 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)))
% 59.73/59.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_sgn__pos,axiom,
% 59.73/59.61 ! [V_a,T_a] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.61 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_sgn__1__pos,axiom,
% 59.73/59.61 ! [V_a_2,T_b] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_b)
% 59.73/59.61 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 59.73/59.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_zsgn__def,axiom,
% 59.73/59.61 ! [V_i] :
% 59.73/59.61 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.61 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 59.73/59.61 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.61 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 59.73/59.61 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 59.73/59.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 59.73/59.61 => 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)) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_decr__lemma,axiom,
% 59.73/59.61 ! [V_z,V_x,V_d] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_incr__lemma,axiom,
% 59.73/59.61 ! [V_x,V_z,V_d] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 59.73/59.61 => 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)))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__abs,axiom,
% 59.73/59.61 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__abs__ge__zero,axiom,
% 59.73/59.61 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__minus__commute,axiom,
% 59.73/59.61 ! [V_b,V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__not__less__zero,axiom,
% 59.73/59.61 ! [V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => ~ 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_zero__less__abs__iff,axiom,
% 59.73/59.61 ! [V_a_2,T_b] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 59.73/59.61 => ( 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)))
% 59.73/59.61 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__of__pos,axiom,
% 59.73/59.61 ! [V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.61 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__ge__zero,axiom,
% 59.73/59.61 ! [V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__le__zero__iff,axiom,
% 59.73/59.61 ! [V_a_2,T_b] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 59.73/59.61 => ( 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)))
% 59.73/59.61 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__of__nonneg,axiom,
% 59.73/59.61 ! [V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.61 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__setsum__abs,axiom,
% 59.73/59.61 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__of__nat,axiom,
% 59.73/59.61 ! [V_n,T_a] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__int__eq,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__setprod,axiom,
% 59.73/59.61 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.61 ( class_Fields_Olinordered__field(T_b)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__one,axiom,
% 59.73/59.61 ! [T_a] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.61 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__divide,axiom,
% 59.73/59.61 ! [V_b,V_a,T_a] :
% 59.73/59.61 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__minus__cancel,axiom,
% 59.73/59.61 ! [V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__idempotent,axiom,
% 59.73/59.61 ! [V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__mult,axiom,
% 59.73/59.61 ! [V_b,V_a,T_a] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__mult__self,axiom,
% 59.73/59.61 ! [V_a,T_a] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__add__abs,axiom,
% 59.73/59.61 ! [V_b,V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_power__abs,axiom,
% 59.73/59.61 ! [V_n,V_a,T_a] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__eq__0,axiom,
% 59.73/59.61 ! [V_a_2,T_b] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 59.73/59.61 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 59.73/59.61 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__zero,axiom,
% 59.73/59.61 ! [T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__le__D1,axiom,
% 59.73/59.61 ! [V_b,V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__ge__self,axiom,
% 59.73/59.61 ! [V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__triangle__ineq3,axiom,
% 59.73/59.61 ! [V_b,V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => 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)))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__triangle__ineq2,axiom,
% 59.73/59.61 ! [V_b,V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => 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)))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__triangle__ineq2__sym,axiom,
% 59.73/59.61 ! [V_b,V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => 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)))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__mult__less,axiom,
% 59.73/59.61 ! [V_d,V_b,V_c,V_a,T_a] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 59.73/59.61 => 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))) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__triangle__ineq,axiom,
% 59.73/59.61 ! [V_b,V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => 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)))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__ge__minus__self,axiom,
% 59.73/59.61 ! [V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__le__iff,axiom,
% 59.73/59.61 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 59.73/59.61 => ( 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))
% 59.73/59.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 59.73/59.61 & 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)) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__leI,axiom,
% 59.73/59.61 ! [V_b,V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__le__D2,axiom,
% 59.73/59.61 ! [V_b,V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__less__iff,axiom,
% 59.73/59.61 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_b)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 59.73/59.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 59.73/59.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_nonzero__abs__divide,axiom,
% 59.73/59.61 ! [V_a,V_b,T_a] :
% 59.73/59.61 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.61 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 59.73/59.61 => 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__power__minus,axiom,
% 59.73/59.61 ! [V_n,V_a,T_a] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__zmult__eq__1,axiom,
% 59.73/59.61 ! [V_n,V_m] :
% 59.73/59.61 ( 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)
% 59.73/59.61 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__sgn,axiom,
% 59.73/59.61 ! [V_k,T_a] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_mult__sgn__abs,axiom,
% 59.73/59.61 ! [V_x,T_a] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.61 => 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 ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__mult__pos,axiom,
% 59.73/59.61 ! [V_y,V_x,T_a] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 59.73/59.61 => 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__eq__mult,axiom,
% 59.73/59.61 ! [V_b,V_a,T_a] :
% 59.73/59.61 ( class_Rings_Oordered__ring__abs(T_a)
% 59.73/59.61 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 59.73/59.61 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 59.73/59.61 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 59.73/59.61 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 59.73/59.61 => 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__diff__triangle__ineq,axiom,
% 59.73/59.61 ! [V_d,V_c,V_b,V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => 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))))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__triangle__ineq4,axiom,
% 59.73/59.61 ! [V_b,V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => 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)))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__minus__le__zero,axiom,
% 59.73/59.61 ! [V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__of__nonpos,axiom,
% 59.73/59.61 ! [V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.61 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__if,axiom,
% 59.73/59.61 ! [V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oabs__if(T_a)
% 59.73/59.61 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.61 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 59.73/59.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.61 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__of__neg,axiom,
% 59.73/59.61 ! [V_a,T_a] :
% 59.73/59.61 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 59.73/59.61 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_zero__le__power__abs,axiom,
% 59.73/59.61 ! [V_n,V_a,T_a] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__div__pos,axiom,
% 59.73/59.61 ! [V_x,V_y,T_a] :
% 59.73/59.61 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 59.73/59.61 => 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__minus__one,axiom,
% 59.73/59.61 ! [T_a] :
% 59.73/59.61 ( ( class_Int_Onumber__ring(T_a)
% 59.73/59.61 & class_Rings_Olinordered__idom(T_a) )
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_zabs__less__one__iff,axiom,
% 59.73/59.61 ! [V_z_2] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_zabs__def,axiom,
% 59.73/59.61 ! [V_i] :
% 59.73/59.61 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.61 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 59.73/59.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 59.73/59.61 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_nat__abs__mult__distrib,axiom,
% 59.73/59.61 ! [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))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_zero__le__zpower__abs,axiom,
% 59.73/59.61 ! [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))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__number__of,axiom,
% 59.73/59.61 ! [V_x,T_a] :
% 59.73/59.61 ( ( class_Int_Onumber__ring(T_a)
% 59.73/59.61 & class_Rings_Olinordered__idom(T_a) )
% 59.73/59.61 => ( ( 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)))
% 59.73/59.61 => 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)) )
% 59.73/59.61 & ( ~ 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)))
% 59.73/59.61 => 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) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__power__minus__one,axiom,
% 59.73/59.61 ! [V_n,T_a] :
% 59.73/59.61 ( ( class_Int_Onumber__ring(T_a)
% 59.73/59.61 & class_Rings_Olinordered__idom(T_a) )
% 59.73/59.61 => 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) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_zero__less__zpower__abs__iff,axiom,
% 59.73/59.61 ! [V_n_2,V_x_2] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.61 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_abs__power2,axiom,
% 59.73/59.61 ! [V_a,T_a] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.61 => 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)))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_power2__abs,axiom,
% 59.73/59.61 ! [V_a,T_a] :
% 59.73/59.61 ( class_Rings_Olinordered__idom(T_a)
% 59.73/59.61 => 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)))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 59.73/59.61 ! [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 ).
% 59.73/59.61
% 59.73/59.61 fof(fact_divmod__int__pdivmod,axiom,
% 59.73/59.61 ! [V_l_2,V_k_2] :
% 59.73/59.61 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.61 => 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)) )
% 59.73/59.61 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.61 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.61 => 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) )
% 59.73/59.61 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.61 => 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)))) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 59.73/59.61 ! [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)))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_divmod__int__code,axiom,
% 59.73/59.61 ! [V_l_2,V_k_2] :
% 59.73/59.61 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.61 => 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)) )
% 59.73/59.61 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.61 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.61 => 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) )
% 59.73/59.61 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.61 => 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)))) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_fst__apsnd,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_apsnd__conv,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_apsnd__compose,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_snd__apsnd,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_apsnd__eq__conv,axiom,
% 59.73/59.61 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 59.73/59.61 ( 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)
% 59.73/59.61 <=> 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_negateSnd__def,axiom,
% 59.73/59.61 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_nat__gcd_Osimps,axiom,
% 59.73/59.61 ! [V_x,V_y] :
% 59.73/59.61 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.61 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 59.73/59.61 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.61 => 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_pdivmod__def,axiom,
% 59.73/59.61 ! [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))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_pdivmod__posDivAlg,axiom,
% 59.73/59.61 ! [V_k,V_l] :
% 59.73/59.61 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.61 => 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)) )
% 59.73/59.61 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 59.73/59.61 => 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_nat__gcd_Opsimps,axiom,
% 59.73/59.61 ! [V_y_2,V_x_2] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.61 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 59.73/59.61 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.61 => 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)) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 59.73/59.61 ! [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)))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_nat__gcd_Opinduct,axiom,
% 59.73/59.61 ! [V_P_2,V_a1_2,V_a0_2] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => ( ! [B_x,B_y] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.61 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 59.73/59.61 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
% 59.73/59.61 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_apfst__apsnd,axiom,
% 59.73/59.61 ! [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))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_apsnd__apfst,axiom,
% 59.73/59.61 ! [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))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_snd__apfst,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_apfst__conv,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_apfst__compose,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_apfst__eq__conv,axiom,
% 59.73/59.61 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 59.73/59.61 ( 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)
% 59.73/59.61 <=> 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_fst__apfst,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_apsnd__apfst__commute,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 59.73/59.61 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 59.73/59.61 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 & class_Groups_Ocomm__monoid__mult(T_b) )
% 59.73/59.61 => ( V_A_2 = V_B_2
% 59.73/59.61 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 59.73/59.61 => ( ! [B_x] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 59.73/59.61 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 59.73/59.61 => 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) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_accp__acc__eq,axiom,
% 59.73/59.61 ! [V_x_2,V_r_2,T_b] :
% 59.73/59.61 ( 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))
% 59.73/59.61 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_rel__comp__def,axiom,
% 59.73/59.61 ! [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))))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_rel__compI,axiom,
% 59.73/59.61 ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 59.73/59.61 ( 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))
% 59.73/59.61 => ( 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))
% 59.73/59.61 => 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))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_rel__comp__empty1,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_rel__comp__empty2,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_O__assoc,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_rel__comp__mono,axiom,
% 59.73/59.61 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 59.73/59.61 ( 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))
% 59.73/59.61 => ( 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))
% 59.73/59.61 => 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))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_rel__comp__distrib,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_rel__comp__distrib2,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_rel__comp__UNION__distrib,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_rel__comp__UNION__distrib2,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_union__comp__emptyR,axiom,
% 59.73/59.61 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 59.73/59.61 ( 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))
% 59.73/59.61 => ( 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))
% 59.73/59.61 => 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_union__comp__emptyL,axiom,
% 59.73/59.61 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 59.73/59.61 ( 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))
% 59.73/59.61 => ( 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))
% 59.73/59.61 => 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_acc__subset,axiom,
% 59.73/59.61 ! [V_R2_2,V_R1_2,T_b] :
% 59.73/59.61 ( 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))
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_acc_Osimps,axiom,
% 59.73/59.61 ! [V_r_2,V_a_2,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 59.73/59.61 <=> ! [B_x] :
% 59.73/59.61 ( 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))
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_acc__downward,axiom,
% 59.73/59.61 ! [V_a_2,V_r_2,V_b_2,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 59.73/59.61 => ( 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))
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_max__ext__compat,axiom,
% 59.73/59.61 ! [V_S_2,V_R_2,T_b] :
% 59.73/59.61 ( 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))
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_min__ext__compat,axiom,
% 59.73/59.61 ! [V_S_2,V_R_2,T_b] :
% 59.73/59.61 ( 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))
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_pred__comp__rel__comp__eq,axiom,
% 59.73/59.61 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 59.73/59.61 ( 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))
% 59.73/59.61 <=> 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_reduction__pairI,axiom,
% 59.73/59.61 ! [V_S_2,V_R_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_R_2)
% 59.73/59.61 => ( 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))
% 59.73/59.61 => 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_max__extp_Oequations,axiom,
% 59.73/59.61 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 59.73/59.61 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 59.73/59.61 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 59.73/59.61 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.61 & ! [B_x] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 59.73/59.61 => ? [B_xa] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 59.73/59.61 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__less__than,axiom,
% 59.73/59.61 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_pred__comp_Ointros,axiom,
% 59.73/59.61 ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
% 59.73/59.61 => 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__empty,axiom,
% 59.73/59.61 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__inv__image,axiom,
% 59.73/59.61 ! [V_f_2,T_c,V_r_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.61 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__lex__prod,axiom,
% 59.73/59.61 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 59.73/59.61 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 59.73/59.61 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__measure,axiom,
% 59.73/59.61 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__comp__self,axiom,
% 59.73/59.61 ! [V_R_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_R_2)
% 59.73/59.61 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__finite__psubset,axiom,
% 59.73/59.61 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__mlex,axiom,
% 59.73/59.61 ! [V_f_2,V_R_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_R_2)
% 59.73/59.61 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__Int2,axiom,
% 59.73/59.61 ! [V_r_H_2,V_r_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__Int1,axiom,
% 59.73/59.61 ! [V_r_H_2,V_r_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__subset,axiom,
% 59.73/59.61 ! [V_p_2,V_r_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.61 => ( 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))
% 59.73/59.61 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_min__ext__wf,axiom,
% 59.73/59.61 ! [V_r_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.61 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_pred__comp_Oequations,axiom,
% 59.73/59.61 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 59.73/59.61 ( 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))
% 59.73/59.61 <=> ? [B_b] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 59.73/59.61 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_max__ext__wf,axiom,
% 59.73/59.61 ! [V_r_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.61 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__pair__less,axiom,
% 59.73/59.61 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__less,axiom,
% 59.73/59.61 c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__irrefl,axiom,
% 59.73/59.61 ! [V_a_2,V_r_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.61 => ~ 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__asym,axiom,
% 59.73/59.61 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.61 => ( 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))
% 59.73/59.61 => ~ 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__not__sym,axiom,
% 59.73/59.61 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.61 => ( 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))
% 59.73/59.61 => ~ 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)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__not__refl,axiom,
% 59.73/59.61 ! [V_a_2,V_r_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.61 => ~ 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__int__ge__less__than,axiom,
% 59.73/59.61 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__int__ge__less__than2,axiom,
% 59.73/59.61 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__acc__iff,axiom,
% 59.73/59.61 ! [V_r_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.61 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_acc__wfD,axiom,
% 59.73/59.61 ! [V_x_2,V_r_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__no__loop,axiom,
% 59.73/59.61 ! [V_R_2,T_b] :
% 59.73/59.61 ( 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))
% 59.73/59.61 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__union__merge,axiom,
% 59.73/59.61 ! [V_S_2,V_R_2,T_b] :
% 59.73/59.61 ( 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))
% 59.73/59.61 <=> 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 59.73/59.61 ! [V_r_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.61 <=> ~ ? [B_f] :
% 59.73/59.61 ! [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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wfE__pf,axiom,
% 59.73/59.61 ! [V_A_2,V_R_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_R_2)
% 59.73/59.61 => ( 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)))
% 59.73/59.61 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__union__compatible,axiom,
% 59.73/59.61 ! [V_S_2,V_R_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_R_2)
% 59.73/59.61 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 59.73/59.61 => ( 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))
% 59.73/59.61 => 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)) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf,axiom,
% 59.73/59.61 ! [T_b] :
% 59.73/59.61 ( class_Orderings_Owellorder(T_b)
% 59.73/59.61 => 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)))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_reduction__pair__def,axiom,
% 59.73/59.61 ! [V_P_2,T_b] :
% 59.73/59.61 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 59.73/59.61 <=> ( 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))
% 59.73/59.61 & 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))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_reduction__pair__lemma,axiom,
% 59.73/59.61 ! [V_S_2,V_R_2,V_P_2,T_b] :
% 59.73/59.61 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 59.73/59.61 => ( 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)))
% 59.73/59.61 => ( 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)))
% 59.73/59.61 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 59.73/59.61 => 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)) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__lenlex,axiom,
% 59.73/59.61 ! [V_r_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.61 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__if__measure,axiom,
% 59.73/59.61 ! [T_b,V_g_2,V_f_2,V_P_2] :
% 59.73/59.61 ( ! [B_x] :
% 59.73/59.61 ( hBOOL(hAPP(V_P_2,B_x))
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,hAPP(V_g_2,B_x))),hAPP(V_f_2,B_x))) )
% 59.73/59.61 => 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))))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_max__ext_Ointros,axiom,
% 59.73/59.61 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 59.73/59.61 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.61 => ( ! [B_x] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 59.73/59.61 => ? [B_xa] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 59.73/59.61 & 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)) ) )
% 59.73/59.61 => 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))) ) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_pred__nat__def,axiom,
% 59.73/59.61 c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__lex,axiom,
% 59.73/59.61 ! [V_r_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.61 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__lexn,axiom,
% 59.73/59.61 ! [V_n_2,V_r_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.61 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_lex__def,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_lexn_Osimps_I1_J,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__pred__nat,axiom,
% 59.73/59.61 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__same__fst,axiom,
% 59.73/59.61 ! [T_b,V_R_2,T_c,V_P_2] :
% 59.73/59.61 ( ! [B_x] :
% 59.73/59.61 ( hBOOL(hAPP(V_P_2,B_x))
% 59.73/59.61 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 59.73/59.61 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 59.73/59.61 ! [T_a] : c_Nitpick_Ozero__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Range__Collect__split,axiom,
% 59.73/59.61 ! [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))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_RangeI,axiom,
% 59.73/59.61 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 59.73/59.61 ( 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))
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Range__Id__on,axiom,
% 59.73/59.61 ! [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 ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Range__Diff__subset,axiom,
% 59.73/59.61 ! [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)))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Range__empty__iff,axiom,
% 59.73/59.61 ! [V_r_2,T_b,T_c] :
% 59.73/59.61 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.61 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Range__empty,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Range__Un__eq,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_finite__Range,axiom,
% 59.73/59.61 ! [V_r_2,T_c,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 59.73/59.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_snd__eq__Range,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Range__iff,axiom,
% 59.73/59.61 ! [V_r_2,T_c,V_a_2,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 59.73/59.61 <=> ? [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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Range__insert,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Range__Int__subset,axiom,
% 59.73/59.61 ! [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)))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Nitpick_Oone__frac__def,axiom,
% 59.73/59.61 ! [T_a] : c_Nitpick_Oone__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 59.73/59.61 ! [V_n,T_a] : c_Nitpick_Onumber__of__frac(T_a,V_n) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_n),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_RangeP__Range__eq,axiom,
% 59.73/59.61 ! [V_x_2,V_r_2,T_c,T_b] :
% 59.73/59.61 ( 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))
% 59.73/59.61 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_RangeP_Ointros,axiom,
% 59.73/59.61 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 59.73/59.61 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_RangeP_Oequations,axiom,
% 59.73/59.61 ! [V_a2_2,V_r_2,T_c,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 59.73/59.61 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Nitpick_Ofrac__def,axiom,
% 59.73/59.61 ! [V_b,V_a,T_a] : hAPP(hAPP(c_Nitpick_Ofrac(T_a),V_a),V_b) = c_Nitpick_OAbs__Frac(T_a,c_Nitpick_Onorm__frac(V_a,V_b)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_RangeE,axiom,
% 59.73/59.61 ! [V_r_2,T_c,V_b_2,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 59.73/59.61 => ~ ! [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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_wf__Un,axiom,
% 59.73/59.61 ! [V_s_2,V_r_2,T_b] :
% 59.73/59.61 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.61 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 59.73/59.61 => ( 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))
% 59.73/59.61 => 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)) ) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_DomainI,axiom,
% 59.73/59.61 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 59.73/59.61 ( 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))
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Domain__Id__on,axiom,
% 59.73/59.61 ! [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 ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Domain__empty__iff,axiom,
% 59.73/59.61 ! [V_r_2,T_c,T_b] :
% 59.73/59.61 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.61 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Domain__empty,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Domain__mono,axiom,
% 59.73/59.61 ! [V_s_2,V_r_2,T_c,T_b] :
% 59.73/59.61 ( 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))
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Domain__Un__eq,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_finite__Domain,axiom,
% 59.73/59.61 ! [V_r_2,T_c,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 59.73/59.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_fst__eq__Domain,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Domain__iff,axiom,
% 59.73/59.61 ! [V_r_2,T_c,V_a_2,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 59.73/59.61 <=> ? [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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Domain__insert,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Domain__Int__subset,axiom,
% 59.73/59.61 ! [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)))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Domain__Diff__subset,axiom,
% 59.73/59.61 ! [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)))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Field__def,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Domain__Collect__split,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_DomainP__Domain__eq,axiom,
% 59.73/59.61 ! [V_x_2,V_r_2,T_c,T_b] :
% 59.73/59.61 ( 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))
% 59.73/59.61 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_DomainE,axiom,
% 59.73/59.61 ! [V_r_2,T_c,V_a_2,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 59.73/59.61 => ~ ! [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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_image__split__eq__Sigma,axiom,
% 59.73/59.61 ! [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))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_DomainP_Ointros,axiom,
% 59.73/59.61 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 59.73/59.61 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_SigmaI,axiom,
% 59.73/59.61 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.61 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 59.73/59.61 => 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))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Sigma__empty1,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Times__eq__cancel2,axiom,
% 59.73/59.61 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 59.73/59.61 => ( 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))
% 59.73/59.61 <=> V_A_2 = V_B_2 ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_card__cartesian__product,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setsum__cartesian__product,axiom,
% 59.73/59.61 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Sigma__empty2,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Times__empty,axiom,
% 59.73/59.61 ! [V_B_2,V_A_2,T_c,T_b] :
% 59.73/59.61 ( 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))
% 59.73/59.61 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.61 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Compl__Times__UNIV1,axiom,
% 59.73/59.61 ! [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))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Compl__Times__UNIV2,axiom,
% 59.73/59.61 ! [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)))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_setprod__cartesian__product,axiom,
% 59.73/59.61 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 59.73/59.61 ( class_Groups_Ocomm__monoid__mult(T_b)
% 59.73/59.61 => 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))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Sigma__Un__distrib1,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Times__Un__distrib1,axiom,
% 59.73/59.61 ! [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))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Sigma__Un__distrib2,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_rel__comp__subset__Sigma,axiom,
% 59.73/59.61 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 59.73/59.61 ( 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))))
% 59.73/59.61 => ( 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))))
% 59.73/59.61 => 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)))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_swap__product,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_finite__cartesian__product,axiom,
% 59.73/59.61 ! [V_B_2,T_c,V_A_2,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 59.73/59.61 => 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)))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_equiv__type,axiom,
% 59.73/59.61 ! [V_r_2,V_A_2,T_b] :
% 59.73/59.61 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.73/59.61 => 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)))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Sigma__Int__distrib1,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Times__Int__distrib1,axiom,
% 59.73/59.61 ! [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))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Sigma__Int__distrib2,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Id__on__subset__Times,axiom,
% 59.73/59.61 ! [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)))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Sigma__Diff__distrib2,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Times__Diff__distrib1,axiom,
% 59.73/59.61 ! [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))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Sigma__Diff__distrib1,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_DomainP_Oequations,axiom,
% 59.73/59.61 ! [V_a1_2,V_r_2,T_c,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 59.73/59.61 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_UNIV__Times__UNIV,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_SigmaE2,axiom,
% 59.73/59.61 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.61 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_SigmaD2,axiom,
% 59.73/59.61 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_SigmaD1,axiom,
% 59.73/59.61 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_mem__Sigma__iff,axiom,
% 59.73/59.61 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 59.73/59.61 ( 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)))
% 59.73/59.61 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.61 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_card__cartesian__product__singleton,axiom,
% 59.73/59.61 ! [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) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Times__subset__cancel2,axiom,
% 59.73/59.61 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 59.73/59.61 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 59.73/59.61 => ( 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))))
% 59.73/59.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Image__subset,axiom,
% 59.73/59.61 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 59.73/59.61 ( 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))))
% 59.73/59.61 => 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)) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_finite__cartesian__productD1,axiom,
% 59.73/59.61 ! [V_B_2,V_A_2,T_c,T_b] :
% 59.73/59.61 ( 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))))
% 59.73/59.61 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 59.73/59.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_finite__cartesian__productD2,axiom,
% 59.73/59.61 ! [V_B_2,V_A_2,T_c,T_b] :
% 59.73/59.61 ( 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))))
% 59.73/59.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_SetCompr__Sigma__eq,axiom,
% 59.73/59.61 ! [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)) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_Collect__split,axiom,
% 59.73/59.61 ! [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))) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_fst__image__times,axiom,
% 59.73/59.61 ! [V_A_2,T_c,T_b,V_B_2] :
% 59.73/59.61 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.61 => 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)) )
% 59.73/59.61 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.61 => 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 ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_snd__image__times,axiom,
% 59.73/59.61 ! [V_B_2,T_c,T_b,V_A_2] :
% 59.73/59.61 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.61 => 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)) )
% 59.73/59.61 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.61 => 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 ) ) ).
% 59.73/59.61
% 59.73/59.61 fof(fact_insert__times__insert,axiom,
% 59.73/59.61 ! [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)))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_finite__equiv__class,axiom,
% 59.73/59.62 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( 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))))
% 59.73/59.62 => ( 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)))
% 59.73/59.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_vimage__Times,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_UN__Times__distrib,axiom,
% 59.73/59.62 ! [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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Sigma__def,axiom,
% 59.73/59.62 ! [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))))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_finite__quotient,axiom,
% 59.73/59.62 ! [V_r_2,V_A_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( 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))))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 59.73/59.62 ( class_Rings_Osemiring__0(T_d)
% 59.73/59.62 => ( 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)))
% 59.73/59.62 => 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))))))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 59.73/59.62 ! [V_A_2,V_I_2,T_c,T_b] :
% 59.73/59.62 ? [B_f] :
% 59.73/59.62 ( 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))
% 59.73/59.62 & 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fold__image__Sigma,axiom,
% 59.73/59.62 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 59.73/59.62 ( class_Groups_Ocomm__monoid__mult(T_d)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 59.73/59.62 => 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)) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_image__id,axiom,
% 59.73/59.62 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 59.73/59.62
% 59.73/59.62 fof(fact_apfst__id,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_inj__on__id,axiom,
% 59.73/59.62 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_vimage__id,axiom,
% 59.73/59.62 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 59.73/59.62
% 59.73/59.62 fof(fact_id__def,axiom,
% 59.73/59.62 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 59.73/59.62
% 59.73/59.62 fof(fact_id__apply,axiom,
% 59.73/59.62 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 59.73/59.62
% 59.73/59.62 fof(fact_id__o,axiom,
% 59.73/59.62 ! [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 ).
% 59.73/59.62
% 59.73/59.62 fof(fact_o__id,axiom,
% 59.73/59.62 ! [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 ).
% 59.73/59.62
% 59.73/59.62 fof(fact_o__eq__id__dest,axiom,
% 59.73/59.62 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 59.73/59.62 ( 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)
% 59.73/59.62 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_apsnd__id,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_of__int__eq__id,axiom,
% 59.73/59.62 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_surj__id,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_inv__id,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_folding_Oempty,axiom,
% 59.73/59.62 ! [V_F_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 59.73/59.62 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_split__Pair,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_setsum__reindex__id,axiom,
% 59.73/59.62 ! [V_B_2,V_f_2,T_b,T_c] :
% 59.73/59.62 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.62 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_setprod__reindex__id,axiom,
% 59.73/59.62 ! [V_B_2,V_f_2,T_b,T_c] :
% 59.73/59.62 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.62 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_surj__iff,axiom,
% 59.73/59.62 ! [V_f_2,T_b,T_c] :
% 59.73/59.62 ( 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))
% 59.73/59.62 <=> 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) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_inv__o__cancel,axiom,
% 59.73/59.62 ! [V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.73/59.62 => 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) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_inj__iff,axiom,
% 59.73/59.62 ! [V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.73/59.62 <=> 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) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_setprod__Sigma,axiom,
% 59.73/59.62 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 59.73/59.62 ( class_Groups_Ocomm__monoid__mult(T_d)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 59.73/59.62 => 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)) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_setsum__Sigma,axiom,
% 59.73/59.62 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 59.73/59.62 ( class_Groups_Ocomm__monoid__add(T_d)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 59.73/59.62 => 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)) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_card__SigmaI,axiom,
% 59.73/59.62 ! [V_B_2,T_c,V_A_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_finite__SigmaI,axiom,
% 59.73/59.62 ! [V_B_2,T_c,V_A_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ! [B_a] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_SigmaE,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ~ ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => ! [B_y] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 59.73/59.62 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__pair__surj,axiom,
% 59.73/59.62 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ( 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))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__pair__imageI,axiom,
% 59.73/59.62 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__pair__ident,axiom,
% 59.73/59.62 ! [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 ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__pair__simp,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fst__map__pair,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_snd__prod__fun,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_snd__comp__map__pair,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fst__comp__map__pair,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__pair_Ocompositionality,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__pair__compose,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__pair_Ocomp,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__pair_Oidentity,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_apfst__def,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_apsnd__def,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__pair_Oid,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__pair__def,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__pair__surj__on,axiom,
% 59.73/59.62 ! [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] :
% 59.73/59.62 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 59.73/59.62 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_wf__map__pair__image,axiom,
% 59.73/59.62 ! [V_f_2,T_c,V_r_2,T_b] :
% 59.73/59.62 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.62 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__pair__inj__on,axiom,
% 59.73/59.62 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.73/59.62 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_prod__fun__imageE,axiom,
% 59.73/59.62 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ~ ! [B_x,B_y] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ~ 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_refl__on__def,axiom,
% 59.73/59.62 ! [V_r_2,V_A_2,T_b] :
% 59.73/59.62 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 59.73/59.62 <=> ( 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))))
% 59.73/59.62 & ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => 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)) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_int__val__lemma,axiom,
% 59.73/59.62 ! [V_k_2,V_f_2,V_n_2] :
% 59.73/59.62 ( ! [B_i] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 59.73/59.62 => 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))) )
% 59.73/59.62 => ( 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))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 59.73/59.62 => ? [B_i] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 59.73/59.62 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_refl__on__Id__on,axiom,
% 59.73/59.62 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_refl__on__empty,axiom,
% 59.73/59.62 ! [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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_refl__on__Un,axiom,
% 59.73/59.62 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 59.73/59.62 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 59.73/59.62 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_refl__on__Int,axiom,
% 59.73/59.62 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 59.73/59.62 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 59.73/59.62 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_refl__onD,axiom,
% 59.73/59.62 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 59.73/59.62 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_refl__onD1,axiom,
% 59.73/59.62 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 59.73/59.62 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 59.73/59.62 => ( 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))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_refl__onD2,axiom,
% 59.73/59.62 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 59.73/59.62 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 59.73/59.62 => ( 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))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_reflp__def,axiom,
% 59.73/59.62 ! [V_r_2,T_b] :
% 59.73/59.62 ( c_Predicate_Oreflp(T_b,V_r_2)
% 59.73/59.62 <=> 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_refl__onI,axiom,
% 59.73/59.62 ! [V_A_2,V_r_2,T_b] :
% 59.73/59.62 ( 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))))
% 59.73/59.62 => ( ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => 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)) )
% 59.73/59.62 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_nat0__intermed__int__val,axiom,
% 59.73/59.62 ! [V_k_2,V_f_2,V_n_2] :
% 59.73/59.62 ( ! [B_i] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 59.73/59.62 => 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))) )
% 59.73/59.62 => ( 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))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 59.73/59.62 => ? [B_i] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 59.73/59.62 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_reflpE,axiom,
% 59.73/59.62 ! [V_x_2,V_r_2,T_b] :
% 59.73/59.62 ( c_Predicate_Oreflp(T_b,V_r_2)
% 59.73/59.62 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_wfP__def,axiom,
% 59.73/59.62 ! [V_r_2,T_b] :
% 59.73/59.62 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 59.73/59.62 <=> 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_setprod__pos__nat,axiom,
% 59.73/59.62 ! [V_f_2,V_S_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 59.73/59.62 => ( ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 59.73/59.62 => 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))) )
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Rep__Integ__induct,axiom,
% 59.73/59.62 ! [V_P_2,V_y_2] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 59.73/59.62 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
% 59.73/59.62 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_wfP__empty,axiom,
% 59.73/59.62 ! [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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_wfP__accp__iff,axiom,
% 59.73/59.62 ! [V_r_2,T_b] :
% 59.73/59.62 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 59.73/59.62 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_accp__wfPD,axiom,
% 59.73/59.62 ! [V_x_2,V_r_2,T_b] :
% 59.73/59.62 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 59.73/59.62 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_wfP__subset,axiom,
% 59.73/59.62 ! [V_p_2,V_r_2,T_b] :
% 59.73/59.62 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 59.73/59.62 => ( 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))
% 59.73/59.62 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_wf__in__rel,axiom,
% 59.73/59.62 ! [V_R_2,T_b] :
% 59.73/59.62 ( c_Wellfounded_Owf(T_b,V_R_2)
% 59.73/59.62 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_wfP__wf__eq,axiom,
% 59.73/59.62 ! [V_r_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_wfP__acyclicP,axiom,
% 59.73/59.62 ! [V_r_2,T_b] :
% 59.73/59.62 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Rep__Integ__cases,axiom,
% 59.73/59.62 ! [V_y_2] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 59.73/59.62 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_pigeonhole__infinite,axiom,
% 59.73/59.62 ! [V_f_2,T_c,V_A_2,T_b] :
% 59.73/59.62 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 59.73/59.62 => ? [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 & ~ 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)))))) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_acyclic__subset,axiom,
% 59.73/59.62 ! [V_r_2,V_s_2,T_b] :
% 59.73/59.62 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 59.73/59.62 => ( 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))
% 59.73/59.62 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_wf__acyclic,axiom,
% 59.73/59.62 ! [V_r_2,T_b] :
% 59.73/59.62 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.62 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 59.73/59.62 ! [V_r_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 59.73/59.62 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.62 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_finite__acyclic__wf,axiom,
% 59.73/59.62 ! [V_r_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 59.73/59.62 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 59.73/59.62 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Nitpick_Owf_H__def,axiom,
% 59.73/59.62 ! [V_r_2,T_b] :
% 59.73/59.62 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 59.73/59.62 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 59.73/59.62 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 59.73/59.62 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_refl__on__def_H,axiom,
% 59.73/59.62 ! [V_r_2,V_A_2,T_b] :
% 59.73/59.62 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 59.73/59.62 <=> ( ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 59.73/59.62 => 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)) )
% 59.73/59.62 & ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => 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)) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Abs__Integ__induct,axiom,
% 59.73/59.62 ! [V_x_2,V_P_2] :
% 59.73/59.62 ( ! [B_y] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 59.73/59.62 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 59.73/59.62 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_ball__empty,axiom,
% 59.73/59.62 ! [V_P_2,T_b,B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 59.73/59.62 => hBOOL(hAPP(V_P_2,B_x)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Powp__def,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 59.73/59.62 <=> ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 59.73/59.62 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_congruent__def,axiom,
% 59.73/59.62 ! [V_f_2,V_r_2,T_c,T_b] :
% 59.73/59.62 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 59.73/59.62 <=> ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Abs__Integ__cases,axiom,
% 59.73/59.62 ! [V_x_2] :
% 59.73/59.62 ~ ! [B_y] :
% 59.73/59.62 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 59.73/59.62 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_finite__UN__I,axiom,
% 59.73/59.62 ! [V_B_2,T_c,V_A_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ! [B_a] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_inj__on__diff__nat,axiom,
% 59.73/59.62 ! [V_k_2,V_N_2] :
% 59.73/59.62 ( ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 59.73/59.62 => 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) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_wfP__SUP,axiom,
% 59.73/59.62 ! [T_b,V_r_2,T_c] :
% 59.73/59.62 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 59.73/59.62 => ( ! [B_i,B_j] :
% 59.73/59.62 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 59.73/59.62 => 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)) )
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_finite__map__freshness,axiom,
% 59.73/59.62 ! [V_f_2,T_c,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,V_f_2)))
% 59.73/59.62 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 59.73/59.62 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_c) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_mem__splitI2,axiom,
% 59.73/59.62 ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 59.73/59.62 ( ! [B_a,B_b] :
% 59.73/59.62 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_mem__splitE,axiom,
% 59.73/59.62 ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ~ ! [B_x,B_y] :
% 59.73/59.62 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 59.73/59.62 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_setsum__SucD,axiom,
% 59.73/59.62 ! [V_n_2,V_A_2,V_f_2,T_b] :
% 59.73/59.62 ( 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)
% 59.73/59.62 => ? [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 & 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Eps__split,axiom,
% 59.73/59.62 ! [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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_some__sym__eq__trivial,axiom,
% 59.73/59.62 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 59.73/59.62
% 59.73/59.62 fof(fact_some__eq__trivial,axiom,
% 59.73/59.62 ! [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 ).
% 59.73/59.62
% 59.73/59.62 fof(fact_some__eq__ex,axiom,
% 59.73/59.62 ! [T_b,V_P_2] :
% 59.73/59.62 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
% 59.73/59.62 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_someI__ex,axiom,
% 59.73/59.62 ! [T_b,V_P_2] :
% 59.73/59.62 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 59.73/59.62 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_someI,axiom,
% 59.73/59.62 ! [T_b,V_x_2,V_P_2] :
% 59.73/59.62 ( hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.62 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_tfl__some,axiom,
% 59.73/59.62 ! [T_b,B_P] :
% 59.73/59.62 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 59.73/59.62 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_exE__some,axiom,
% 59.73/59.62 ! [T_b,V_c_2,V_P_2] :
% 59.73/59.62 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 59.73/59.62 => ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_P_2)
% 59.73/59.62 => hBOOL(hAPP(V_P_2,V_c_2)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_split__paired__Eps,axiom,
% 59.73/59.62 ! [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)))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Eps__split__eq,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_inv__into__def,axiom,
% 59.73/59.62 ! [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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_inv__def,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_nat__mod__eq__lemma,axiom,
% 59.73/59.62 ! [V_y,V_n,V_x] :
% 59.73/59.62 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 59.73/59.62 => ? [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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_wfI__pf,axiom,
% 59.73/59.62 ! [V_R_2,T_b] :
% 59.73/59.62 ( ! [B_A] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 59.73/59.62 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Sigma__mono,axiom,
% 59.73/59.62 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 59.73/59.62 => ( ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => 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))) )
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_acc_OaccI,axiom,
% 59.73/59.62 ! [V_r_2,V_x_2,T_b] :
% 59.73/59.62 ( ! [B_y] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_not__acc__down,axiom,
% 59.73/59.62 ! [V_R_2,V_x_2,T_b] :
% 59.73/59.62 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 59.73/59.62 => ~ ! [B_z] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fold__image__1,axiom,
% 59.73/59.62 ! [V_f_2,V_S_2,T_b,T_c] :
% 59.73/59.62 ( class_Groups_Ocomm__monoid__mult(T_c)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 59.73/59.62 => ( ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 59.73/59.62 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 59.73/59.62 => 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) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_card_Oneutral,axiom,
% 59.73/59.62 ! [V_A_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 59.73/59.62 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_max__ext_Osimps,axiom,
% 59.73/59.62 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 59.73/59.62 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 59.73/59.62 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 & ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 59.73/59.62 => ? [B_xa] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 59.73/59.62 & 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)) ) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_mod__induct__0,axiom,
% 59.73/59.62 ! [V_i_2,V_P_2,V_p_2] :
% 59.73/59.62 ( ! [B_i] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 59.73/59.62 => ( hBOOL(hAPP(V_P_2,B_i))
% 59.73/59.62 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 59.73/59.62 => ( hBOOL(hAPP(V_P_2,V_i_2))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 59.73/59.62 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fold__image__cong,axiom,
% 59.73/59.62 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 59.73/59.62 ( class_Groups_Oab__semigroup__mult(T_c)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 59.73/59.62 => 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) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Min__eqI,axiom,
% 59.73/59.62 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Orderings_Olinorder(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ! [B_y] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.62 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Max__eqI,axiom,
% 59.73/59.62 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Orderings_Olinorder(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ! [B_y] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.62 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_wf__no__infinite__down__chainE,axiom,
% 59.73/59.62 ! [V_f_2,V_r_2,T_b] :
% 59.73/59.62 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.62 => ~ ! [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)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_setsum__reindex__cong,axiom,
% 59.73/59.62 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 59.73/59.62 ( class_Groups_Ocomm__monoid__add(T_d)
% 59.73/59.62 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 59.73/59.62 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 59.73/59.62 => ( ! [B_a] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 59.73/59.62 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 59.73/59.62 => 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) ) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_scomp__unfold,axiom,
% 59.73/59.62 ! [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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_scomp__scomp,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_scomp__Pair,axiom,
% 59.73/59.62 ! [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 ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Pair__scomp,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_scomp__apply,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_scomp__def,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_iterate_Osimps,axiom,
% 59.73/59.62 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 59.73/59.62 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 59.73/59.62 => 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) )
% 59.73/59.62 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_setsum__ivl__cong,axiom,
% 59.73/59.62 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
% 59.73/59.62 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.62 & class_Orderings_Oord(T_b) )
% 59.73/59.62 => ( V_a_2 = V_c_2
% 59.73/59.62 => ( V_b_2 = V_d_2
% 59.73/59.62 => ( ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 59.73/59.62 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 59.73/59.62 => 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)) ) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_less__eq,axiom,
% 59.73/59.62 ! [V_n_2,V_m_2] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_wf__trancl,axiom,
% 59.73/59.62 ! [V_r_2,T_b] :
% 59.73/59.62 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.62 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_less__than__def,axiom,
% 59.73/59.62 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_acyclic__def,axiom,
% 59.73/59.62 ! [V_r_2,T_b] :
% 59.73/59.62 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 59.73/59.62 <=> ! [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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl_Or__into__trancl,axiom,
% 59.73/59.62 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__subset__Field2,axiom,
% 59.73/59.62 ! [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))))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__Int__subset,axiom,
% 59.73/59.62 ! [V_s_2,V_r_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ( 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))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_r__into__trancl_H,axiom,
% 59.73/59.62 ! [V_r_2,V_p_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__empty,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__domain,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__range,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_finite__trancl,axiom,
% 59.73/59.62 ! [V_r_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 59.73/59.62 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__trans,axiom,
% 59.73/59.62 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ( 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)))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 59.73/59.62 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ( 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))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__into__trancl2,axiom,
% 59.73/59.62 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ( 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)))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_r__r__into__trancl,axiom,
% 59.73/59.62 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ( 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))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__mono,axiom,
% 59.73/59.62 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 59.73/59.62 => ( 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))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__unfold,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__subset__Sigma,axiom,
% 59.73/59.62 ! [V_A_2,V_r_2,T_b] :
% 59.73/59.62 ( 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))))
% 59.73/59.62 => 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)))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_log_Osimps,axiom,
% 59.73/59.62 ! [V_i,V_b] :
% 59.73/59.62 ( ( ( 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)))
% 59.73/59.62 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 59.73/59.62 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 59.73/59.62 & ( ~ ( 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)))
% 59.73/59.62 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_minus__shift__def,axiom,
% 59.73/59.62 ! [V_r,V_l,V_k] :
% 59.73/59.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 59.73/59.62 => 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) )
% 59.73/59.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_inc__shift__def,axiom,
% 59.73/59.62 ! [V_k,V_v] :
% 59.73/59.62 ( ( V_v = V_k
% 59.73/59.62 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 59.73/59.62 & ( V_v != V_k
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_range,axiom,
% 59.73/59.62 ! [V_s,V_k] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => 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)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__insert,axiom,
% 59.73/59.62 ! [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)))))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_reflcl__set__eq,axiom,
% 59.73/59.62 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 <=> 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)))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_r__into__rtrancl,axiom,
% 59.73/59.62 ! [V_r_2,V_p_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 59.73/59.62 ! [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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_IdI,axiom,
% 59.73/59.62 ! [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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__into__rtrancl,axiom,
% 59.73/59.62 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__mono,axiom,
% 59.73/59.62 ! [V_s_2,V_r_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__subset,axiom,
% 59.73/59.62 ! [V_S_2,V_R_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ( 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)))
% 59.73/59.62 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__subset__rtrancl,axiom,
% 59.73/59.62 ! [V_s_2,V_r_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Image__closed__trancl,axiom,
% 59.73/59.62 ! [V_X_2,V_r_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__Un__subset,axiom,
% 59.73/59.62 ! [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)))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__Int__subset,axiom,
% 59.73/59.62 ! [V_r_2,V_s_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ( 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))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Image__Id,axiom,
% 59.73/59.62 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Id__O__R,axiom,
% 59.73/59.62 ! [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 ).
% 59.73/59.62
% 59.73/59.62 fof(fact_R__O__Id,axiom,
% 59.73/59.62 ! [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 ).
% 59.73/59.62
% 59.73/59.62 fof(fact_refl__rtrancl,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__r__diff__Id,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_r__comp__rtrancl__eq,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__idemp__self__comp,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__unfold,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_in__rtrancl__UnI,axiom,
% 59.73/59.62 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 59.73/59.62 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 59.73/59.62 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 59.73/59.62 => 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)))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__reflcl__absorb,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__reflcl,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__Un__rtrancl,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__idemp,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__trans,axiom,
% 59.73/59.62 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ( 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)))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 59.73/59.62 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ( 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))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 59.73/59.62 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ( 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)))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Range__rtrancl,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__empty,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Domain__rtrancl,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__rtrancl__absorb,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__trancl__absorb,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__reflcl,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_reflcl__trancl,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__unfold__right,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__unfold__left,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_pair__in__Id__conv,axiom,
% 59.73/59.62 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 <=> V_a_2 = V_b_2 ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__trancl__trancl,axiom,
% 59.73/59.62 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ( 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)))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__rtrancl__trancl,axiom,
% 59.73/59.62 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ( 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)))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__into__trancl1,axiom,
% 59.73/59.62 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ( 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))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtranclD,axiom,
% 59.73/59.62 ! [V_R_2,V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ( V_a_2 = V_b_2
% 59.73/59.62 | ( V_a_2 != V_b_2
% 59.73/59.62 & 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))) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__into__trancl2,axiom,
% 59.73/59.62 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ( 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)))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__eq__or__trancl,axiom,
% 59.73/59.62 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 <=> ( V_x_2 = V_y_2
% 59.73/59.62 | ( V_x_2 != V_y_2
% 59.73/59.62 & 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))) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Domain__Id,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Range__Id,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_refl__Id,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_pair__leq__def,axiom,
% 59.73/59.62 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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Not__Domain__rtrancl,axiom,
% 59.73/59.62 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 59.73/59.62 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 59.73/59.62 => ( 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)))
% 59.73/59.62 <=> V_x_2 = V_y_2 ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_acc__downwards__aux,axiom,
% 59.73/59.62 ! [V_r_2,V_a_2,V_b_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_acc__downwards,axiom,
% 59.73/59.62 ! [V_b_2,V_r_2,V_a_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 59.73/59.62 => ( 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)))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_wf__insert,axiom,
% 59.73/59.62 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.62 & ~ 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_acyclic__insert,axiom,
% 59.73/59.62 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 59.73/59.62 & ~ 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_refl__reflcl,axiom,
% 59.73/59.62 ! [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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Id__def,axiom,
% 59.73/59.62 ! [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))))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_irrefl__diff__Id,axiom,
% 59.73/59.62 ! [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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_pred__nat__trancl__eq__le,axiom,
% 59.73/59.62 ! [V_n_2,V_m_2] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__subset__Sigma__aux,axiom,
% 59.73/59.62 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ( 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))))
% 59.73/59.62 => ( V_a_2 = V_b_2
% 59.73/59.62 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_irrefl__tranclI,axiom,
% 59.73/59.62 ! [V_x_2,V_r_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ~ 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_sequence__trans,axiom,
% 59.73/59.62 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 59.73/59.62 ( ! [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)))
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_total__on__diff__Id,axiom,
% 59.73/59.62 ! [V_r_2,V_A_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_converse__Id,axiom,
% 59.73/59.62 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__converse,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__converse,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_converse__iff,axiom,
% 59.73/59.62 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 <=> 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)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_converseI,axiom,
% 59.73/59.62 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_converseD,axiom,
% 59.73/59.62 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => 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)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_refl__on__converse,axiom,
% 59.73/59.62 ! [V_r_2,V_A_2,T_b] :
% 59.73/59.62 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 59.73/59.62 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_converse__rel__comp,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_converse__Un,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_finite__converse,axiom,
% 59.73/59.62 ! [V_r_2,T_c,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 59.73/59.62 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_total__on__converse,axiom,
% 59.73/59.62 ! [V_r_2,V_A_2,T_b] :
% 59.73/59.62 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 59.73/59.62 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_converse__converse,axiom,
% 59.73/59.62 ! [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 ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Field__converse,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_converse__Id__on,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_converse__Int,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_converse__inv__image,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_converse__UNION,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_acyclic__converse,axiom,
% 59.73/59.62 ! [V_r_2,T_b] :
% 59.73/59.62 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 59.73/59.62 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_wf__converse__trancl,axiom,
% 59.73/59.62 ! [V_r_2,T_b] :
% 59.73/59.62 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 59.73/59.62 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_equiv__comp__eq,axiom,
% 59.73/59.62 ! [V_r_2,V_A_2,T_b] :
% 59.73/59.62 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.73/59.62 => 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 ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Range__converse,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Domain__converse,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Range__def,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_total__on__empty,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__converseI,axiom,
% 59.73/59.62 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => 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)))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__converseD,axiom,
% 59.73/59.62 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 59.73/59.62 ( 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))))
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__converseD,axiom,
% 59.73/59.62 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 59.73/59.62 ( 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))))
% 59.73/59.62 => 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)))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__converseI,axiom,
% 59.73/59.62 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 59.73/59.62 ( 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))))
% 59.73/59.62 => 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)))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Image__subset__eq,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 <=> 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))))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_refl__on__comp__subset,axiom,
% 59.73/59.62 ! [V_r_2,V_A_2,T_b] :
% 59.73/59.62 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_comp__equivI,axiom,
% 59.73/59.62 ! [V_A_2,V_r_2,T_b] :
% 59.73/59.62 ( 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
% 59.73/59.62 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 59.73/59.62 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_finite__acyclic__wf__converse,axiom,
% 59.73/59.62 ! [V_r_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 59.73/59.62 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 59.73/59.62 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_total__on__def,axiom,
% 59.73/59.62 ! [V_r_2,V_A_2,T_b] :
% 59.73/59.62 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 59.73/59.62 <=> ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => ! [B_xa] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 59.73/59.62 => ( B_x != B_xa
% 59.73/59.62 => ( 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))
% 59.73/59.62 | 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)) ) ) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_converse__def,axiom,
% 59.73/59.62 ! [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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 59.73/59.62 ! [V_R_2,V_p_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 59.73/59.62 => 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)))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_acyclicI,axiom,
% 59.73/59.62 ! [V_r_2,T_b] :
% 59.73/59.62 ( ! [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)))
% 59.73/59.62 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Image__Int__eq,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 59.73/59.62 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 59.73/59.62 => 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)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_single__valued__subset,axiom,
% 59.73/59.62 ! [V_s_2,V_r_2,T_c,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 59.73/59.62 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_single__valued__rel__comp,axiom,
% 59.73/59.62 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 59.73/59.62 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 59.73/59.62 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_wf__exp,axiom,
% 59.73/59.62 ! [V_R_2,V_n_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_funpow__swap1,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_funpow__mult,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_comp__funpow,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rel__pow__commute,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rel__pow__1,axiom,
% 59.73/59.62 ! [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 ).
% 59.73/59.62
% 59.73/59.62 fof(fact_single__valued__rel__pow,axiom,
% 59.73/59.62 ! [V_n_2,V_R_2,T_b] :
% 59.73/59.62 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 59.73/59.62 => 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)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_single__valued__Id,axiom,
% 59.73/59.62 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rel__pow__imp__rtrancl,axiom,
% 59.73/59.62 ! [V_R_2,V_n_2,V_p_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__power,axiom,
% 59.73/59.62 ! [V_R_2,V_p_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 59.73/59.62 <=> ? [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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_single__valued__Id__on,axiom,
% 59.73/59.62 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_relpow_Osimps_I2_J,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rel__pow__add,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_relpow_Osimps_I1_J,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rel__pow__0__I,axiom,
% 59.73/59.62 ! [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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rel__pow__0__E,axiom,
% 59.73/59.62 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => V_x_2 = V_y_2 ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rel__pow__Suc__I2,axiom,
% 59.73/59.62 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ( 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)))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rel__pow__Suc__I,axiom,
% 59.73/59.62 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ( 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))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_funpow_Osimps_I2_J,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_funpow__add,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_single__valued__def,axiom,
% 59.73/59.62 ! [V_r_2,T_c,T_b] :
% 59.73/59.62 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 59.73/59.62 <=> ! [B_x,B_y] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ! [B_z] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => B_y = B_z ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_single__valuedD,axiom,
% 59.73/59.62 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 59.73/59.62 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 59.73/59.62 => ( 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))
% 59.73/59.62 => ( 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))
% 59.73/59.62 => V_y_2 = V_z_2 ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_funpow_Osimps_I1_J,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_trancl__power,axiom,
% 59.73/59.62 ! [V_R_2,V_p_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 59.73/59.62 <=> ? [B_n] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 59.73/59.62 & 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_single__valued__confluent,axiom,
% 59.73/59.62 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 59.73/59.62 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 59.73/59.62 => ( 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)))
% 59.73/59.62 => ( 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)))
% 59.73/59.62 => ( 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)))
% 59.73/59.62 | 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))) ) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_funpow__code__def,axiom,
% 59.73/59.62 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rel__pow__E,axiom,
% 59.73/59.62 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.62 => V_x_2 != V_z_2 )
% 59.73/59.62 => ~ ! [B_y,B_m] :
% 59.73/59.62 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 59.73/59.62 => ( 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)))
% 59.73/59.62 => ~ 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)) ) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rel__pow__E2,axiom,
% 59.73/59.62 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.62 => V_x_2 != V_z_2 )
% 59.73/59.62 => ~ ! [B_y,B_m] :
% 59.73/59.62 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 59.73/59.62 => ( 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))
% 59.73/59.62 => ~ 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))) ) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 59.73/59.62 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( 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))))
% 59.73/59.62 => ( ! [B_x] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ! [B_y] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => B_y = B_x ) )
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rtrancl__Un__separatorE,axiom,
% 59.73/59.62 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( 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))))
% 59.73/59.62 => ( ! [B_x] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ! [B_y] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => B_x = B_y ) )
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rel__pow__Suc__D2,axiom,
% 59.73/59.62 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ? [B_y] :
% 59.73/59.62 ( 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))
% 59.73/59.62 & 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rel__pow__Suc__E,axiom,
% 59.73/59.62 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ~ ! [B_y] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ~ 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rel__pow__Suc__E2,axiom,
% 59.73/59.62 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ~ ! [B_y] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ~ 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_tranclD,axiom,
% 59.73/59.62 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ? [B_z] :
% 59.73/59.62 ( 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))
% 59.73/59.62 & 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_tranclD2,axiom,
% 59.73/59.62 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ? [B_z] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 & 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_IdE,axiom,
% 59.73/59.62 ! [V_p_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 59.73/59.62 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_nat__intermed__int__val,axiom,
% 59.73/59.62 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 59.73/59.62 ( ! [B_i] :
% 59.73/59.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 59.73/59.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 59.73/59.62 => 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))) )
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 59.73/59.62 => ? [B_i] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 59.73/59.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 59.73/59.62 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 59.73/59.62 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Orderings_Olinorder(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.62 => 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) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 59.73/59.62 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Orderings_Olinorder(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.62 => 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) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fold__empty,axiom,
% 59.73/59.62 ! [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 ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fold__image__def,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_folding_Oeq__fold,axiom,
% 59.73/59.62 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fold__def,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_union__fold__insert,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fold__sup__insert,axiom,
% 59.73/59.62 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Lattices_Osemilattice__sup(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fold__inf__insert,axiom,
% 59.73/59.62 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Lattices_Osemilattice__inf(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_min__max_Ofold__inf__insert,axiom,
% 59.73/59.62 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Orderings_Olinorder(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_min__max_Ofold__sup__insert,axiom,
% 59.73/59.62 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Orderings_Olinorder(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 59.73/59.62 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 59.73/59.62 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_sup__SUPR__fold__sup,axiom,
% 59.73/59.62 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 59.73/59.62 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_sup__le__fold__sup,axiom,
% 59.73/59.62 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Lattices_Osemilattice__sup(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.62 => 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))) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fold__inf__le__inf,axiom,
% 59.73/59.62 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Lattices_Osemilattice__inf(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.62 => 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))) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 59.73/59.62 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Orderings_Olinorder(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.62 => 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))) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 59.73/59.62 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Orderings_Olinorder(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.62 => 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))) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fold1__eq__fold__idem,axiom,
% 59.73/59.62 ! [V_a_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 59.73/59.62 ! [V_a_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Lattices_Olattice(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 59.73/59.62 ! [V_a_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Lattices_Olattice(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 59.73/59.62 ! [V_a_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Orderings_Olinorder(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 59.73/59.62 ! [V_a_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Orderings_Olinorder(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 59.73/59.62 ! [V_a_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Orderings_Olinorder(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 59.73/59.62 ! [V_a_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Orderings_Olinorder(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_minus__fold__remove,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_folding__one_Oeq__fold_H,axiom,
% 59.73/59.62 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.62 => 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) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_SUPR__fold__sup,axiom,
% 59.73/59.62 ! [V_f_2,V_A_2,T_b,T_c] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fold1__eq__fold,axiom,
% 59.73/59.62 ! [V_a_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Groups_Oab__semigroup__mult(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.62 => 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) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 59.73/59.62 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Lattices_Olattice(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.62 => 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) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 59.73/59.62 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Lattices_Olattice(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.62 => 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) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Min_Oeq__fold_H,axiom,
% 59.73/59.62 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Orderings_Olinorder(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.62 => 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) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Max_Oeq__fold_H,axiom,
% 59.73/59.62 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Orderings_Olinorder(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.62 => 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) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 59.73/59.62 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.62 => 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)))))) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 59.73/59.62 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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)))))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 59.73/59.62 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 59.73/59.62 => 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)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 59.73/59.62 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 59.73/59.62 => 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)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fun__left__comm,axiom,
% 59.73/59.62 ! [T_b] :
% 59.73/59.62 ( class_Groups_Oab__semigroup__mult(T_b)
% 59.73/59.62 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 59.73/59.62 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 59.73/59.62 => V_y_2 = V_x_2 ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 59.73/59.62 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 59.73/59.62 => 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)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 59.73/59.62 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 59.73/59.62 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 59.73/59.62 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 59.73/59.62 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 59.73/59.62 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.62 => 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)) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 59.73/59.62 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.62 => 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) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 59.73/59.62 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.62 => ? [B_y_H] :
% 59.73/59.62 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 59.73/59.62 & 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)) ) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INFI__fold__inf,axiom,
% 59.73/59.62 ! [V_f_2,V_A_2,T_b,T_c] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__D,axiom,
% 59.73/59.62 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__E,axiom,
% 59.73/59.62 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 59.73/59.62 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INF1__E,axiom,
% 59.73/59.62 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 59.73/59.62 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INF1__D,axiom,
% 59.73/59.62 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INF2__E,axiom,
% 59.73/59.62 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 59.73/59.62 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INF2__D,axiom,
% 59.73/59.62 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_finite__INT,axiom,
% 59.73/59.62 ! [V_A_2,T_c,V_I_2,T_b] :
% 59.73/59.62 ( ? [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 59.73/59.62 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Compl__UN,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Compl__INT,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__extend__simps_I9_J,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__simps_I9_J,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_UN__simps_I7_J,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_UN__extend__simps_I7_J,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INF__INT__eq,axiom,
% 59.73/59.62 ! [V_x_2,V_r_2,T_c,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 <=> 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__extend__simps_I5_J,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__simps_I5_J,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__iff,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 <=> ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,T_c,T_b] :
% 59.73/59.62 ( 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)
% 59.73/59.62 <=> ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 59.73/59.62 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,T_b,T_c] :
% 59.73/59.62 ( 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))
% 59.73/59.62 <=> ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 59.73/59.62 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INF__commute,axiom,
% 59.73/59.62 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Pow__INT__eq,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INFI__apply,axiom,
% 59.73/59.62 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => 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)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__Int__distrib,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INF__INT__eq2,axiom,
% 59.73/59.62 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 <=> 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_vimage__INT,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__simps_I10_J,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__extend__simps_I10_J,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INFI__bool__eq,axiom,
% 59.73/59.62 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__insert__distrib,axiom,
% 59.73/59.62 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 59.73/59.62 => 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)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__absorb,axiom,
% 59.73/59.62 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 59.73/59.62 => 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) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INF__const,axiom,
% 59.73/59.62 ! [V_M_2,T_b,V_A_2,T_c] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 59.73/59.62 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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 ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__extend__simps_I2_J,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 59.73/59.62 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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 )
% 59.73/59.62 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__extend__simps_I1_J,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 59.73/59.62 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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 )
% 59.73/59.62 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__empty,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__constant,axiom,
% 59.73/59.62 ! [V_c_2,T_c,T_b,V_A_2] :
% 59.73/59.62 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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)) )
% 59.73/59.62 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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 ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INF__less__iff,axiom,
% 59.73/59.62 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 59.73/59.62 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 & class_Orderings_Olinorder(T_b) )
% 59.73/59.62 => ( 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))
% 59.73/59.62 <=> ? [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 59.73/59.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_le__INF__iff,axiom,
% 59.73/59.62 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => ( 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)))
% 59.73/59.62 <=> ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__subset__iff,axiom,
% 59.73/59.62 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 <=> ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__lower,axiom,
% 59.73/59.62 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__Un,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Collect__ball__eq,axiom,
% 59.73/59.62 ! [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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__insert,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_converse__INTER,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Un__INT__distrib2,axiom,
% 59.73/59.62 ! [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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__extend__simps_I6_J,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Un__INT__distrib,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__extend__simps_I7_J,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__simps_I6_J,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__simps_I7_J,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Image__INT__subset,axiom,
% 59.73/59.62 ! [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)))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INF__subset,axiom,
% 59.73/59.62 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INTER__def,axiom,
% 59.73/59.62 ! [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)))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__simps_I1_J,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 59.73/59.62 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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)) )
% 59.73/59.62 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__simps_I2_J,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 59.73/59.62 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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)) )
% 59.73/59.62 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__extend__simps_I3_J,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 59.73/59.62 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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) )
% 59.73/59.62 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__simps_I3_J,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 59.73/59.62 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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)) )
% 59.73/59.62 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__extend__simps_I4_J,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 59.73/59.62 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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 )
% 59.73/59.62 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INF__leI,axiom,
% 59.73/59.62 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__greaterThan__UNIV,axiom,
% 59.73/59.62 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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__simps_I4_J,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 59.73/59.62 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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)) )
% 59.73/59.62 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Image__INT__eq,axiom,
% 59.73/59.62 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 59.73/59.62 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 59.73/59.62 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_inf__INFI__fold__inf,axiom,
% 59.73/59.62 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inf__fold__inf,axiom,
% 59.73/59.62 ! [V_A_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Sup__fold__sup,axiom,
% 59.73/59.62 ! [V_A_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_finite__Inter,axiom,
% 59.73/59.62 ! [V_M_2,T_b] :
% 59.73/59.62 ( ? [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 59.73/59.62 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 59.73/59.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_UnionI,axiom,
% 59.73/59.62 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_InterE,axiom,
% 59.73/59.62 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_InterD,axiom,
% 59.73/59.62 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INF2__iff,axiom,
% 59.73/59.62 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 <=> ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__extend__simps_I8_J,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INT__simps_I8_J,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INF1__iff,axiom,
% 59.73/59.62 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 <=> ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_INTER__eq__Inter__image,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inter__image__eq,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Un__Inter,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Union__upper,axiom,
% 59.73/59.62 ! [V_A_2,V_B_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Sup__le__iff,axiom,
% 59.73/59.62 ! [V_b_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => ( 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))
% 59.73/59.62 <=> ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_le__Inf__iff,axiom,
% 59.73/59.62 ! [V_A_2,V_b_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => ( 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)))
% 59.73/59.62 <=> ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_less__Sup__iff,axiom,
% 59.73/59.62 ! [V_S_2,V_a_2,T_b] :
% 59.73/59.62 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 & class_Orderings_Olinorder(T_b) )
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 59.73/59.62 <=> ? [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 59.73/59.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inf__less__iff,axiom,
% 59.73/59.62 ! [V_a_2,V_S_2,T_b] :
% 59.73/59.62 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 & class_Orderings_Olinorder(T_b) )
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 59.73/59.62 <=> ? [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 59.73/59.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Field__Union,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Union__Pow__eq,axiom,
% 59.73/59.62 ! [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 ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Union__disjoint,axiom,
% 59.73/59.62 ! [V_A_2,V_C_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 <=> ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Domain__Union,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_UN__simps_I8_J,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_UN__extend__simps_I8_J,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Range__Union,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Int__Union2,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Int__Union,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_vimage__Union,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Sigma__Union,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_image__Union,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inter__lower,axiom,
% 59.73/59.62 ! [V_A_2,V_B_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 59.73/59.62 => 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)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Sup__Inf,axiom,
% 59.73/59.62 ! [V_A_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => 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)))))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inf__Sup,axiom,
% 59.73/59.62 ! [V_A_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => 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))))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Union__empty,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Union__mono,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Union__quotient,axiom,
% 59.73/59.62 ! [V_r_2,V_A_2,T_b] :
% 59.73/59.62 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.73/59.62 => 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 ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Union__insert,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_finite__UnionD,axiom,
% 59.73/59.62 ! [V_A_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 59.73/59.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_subset__Pow__Union,axiom,
% 59.73/59.62 ! [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)))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inter__anti__mono,axiom,
% 59.73/59.62 ! [V_A_2,V_B_2,T_b] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inter__empty,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inter__eq,axiom,
% 59.73/59.62 ! [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)))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Union__UNIV,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Union__Un__distrib,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inter__insert,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_UNION__eq__Union__image,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Union__image__eq,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Sup__upper,axiom,
% 59.73/59.62 ! [V_A_2,V_x_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.62 => 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))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inter__UNIV,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inf__lower,axiom,
% 59.73/59.62 ! [V_A_2,V_x_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inter__Un__distrib,axiom,
% 59.73/59.62 ! [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)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Sup__empty,axiom,
% 59.73/59.62 ! [T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => 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) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Sup__singleton,axiom,
% 59.73/59.62 ! [V_a_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => 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 ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Sup__insert,axiom,
% 59.73/59.62 ! [V_A_2,V_a_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => 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)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Int__Inter__image,axiom,
% 59.73/59.62 ! [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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Sup__UNIV,axiom,
% 59.73/59.62 ! [T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => 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) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inf__singleton,axiom,
% 59.73/59.62 ! [V_a_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => 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 ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inf__empty,axiom,
% 59.73/59.62 ! [T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => 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) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inf__UNIV,axiom,
% 59.73/59.62 ! [T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => 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) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inf__insert,axiom,
% 59.73/59.62 ! [V_A_2,V_a_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => 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)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Un__eq__Union,axiom,
% 59.73/59.62 ! [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))))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Un__Union__image,axiom,
% 59.73/59.62 ! [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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Union__Int__subset,axiom,
% 59.73/59.62 ! [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)))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Int__eq__Inter,axiom,
% 59.73/59.62 ! [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))))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inter__Un__subset,axiom,
% 59.73/59.62 ! [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)))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Sup__binary,axiom,
% 59.73/59.62 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => 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) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inf__binary,axiom,
% 59.73/59.62 ! [V_b_2,V_a_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => 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) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_sup__Sup__fold__sup,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Sup__fin__Sup,axiom,
% 59.73/59.62 ! [V_A_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_inf__Inf__fold__inf,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => 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) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inf__fin__Inf,axiom,
% 59.73/59.62 ! [V_A_2,T_b] :
% 59.73/59.62 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_image__INT,axiom,
% 59.73/59.62 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 59.73/59.62 => ( ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 59.73/59.62 => 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)) )
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 59.73/59.62 => 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)) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_card__partition,axiom,
% 59.73/59.62 ! [V_k_2,V_C_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 59.73/59.62 => ( ! [B_c] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 59.73/59.62 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 59.73/59.62 => ( ! [B_c1] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 59.73/59.62 => ! [B_c2] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 59.73/59.62 => ( B_c1 != B_c2
% 59.73/59.62 => 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)) ) ) )
% 59.73/59.62 => 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)) ) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inter__def,axiom,
% 59.73/59.62 ! [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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Union__def,axiom,
% 59.73/59.62 ! [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))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_finite__Union,axiom,
% 59.73/59.62 ! [V_A_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 59.73/59.62 => ( ! [B_M] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 59.73/59.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_insert__partition,axiom,
% 59.73/59.62 ! [V_F_2,V_x_2,T_b] :
% 59.73/59.62 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 59.73/59.62 => ( ! [B_x] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ! [B_xa] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ( B_x != B_xa
% 59.73/59.62 => 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)) ) ) )
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_inj__on__Inter,axiom,
% 59.73/59.62 ! [V_f_2,T_c,T_b,V_S_2] :
% 59.73/59.62 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 59.73/59.62 => ( ! [B_A] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 59.73/59.62 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_Inter__subset,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.62 ( ! [B_X] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 59.73/59.62 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_inj__on__INTER,axiom,
% 59.73/59.62 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 59.73/59.62 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => ( ! [B_i] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 59.73/59.62 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 59.73/59.62 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 59.73/59.62 => ( 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))
% 59.73/59.62 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.62 => ~ ! [B_y] :
% 59.73/59.62 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 59.73/59.62 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 59.73/59.62 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Orderings_Olinorder(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 59.73/59.62 => 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))) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 59.73/59.62 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Orderings_Olinorder(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 59.73/59.62 => 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))) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_InterI,axiom,
% 59.73/59.62 ! [V_A_2,V_C_2,T_b] :
% 59.73/59.62 ( ! [B_X] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_inf__le__fold__inf,axiom,
% 59.73/59.62 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Lattices_Osemilattice__inf(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 59.73/59.62 => 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))) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_fold__sup__le__sup,axiom,
% 59.73/59.62 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 59.73/59.62 ( class_Lattices_Osemilattice__sup(T_b)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.62 => ( ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 59.73/59.62 => 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))) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_mod__div__decomp,axiom,
% 59.73/59.62 ! [V_b,V_a,T_a] :
% 59.73/59.62 ( class_Divides_Osemiring__div(T_a)
% 59.73/59.62 => 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)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_wf__eq__minimal,axiom,
% 59.73/59.62 ! [V_r_2,T_b] :
% 59.73/59.62 ( c_Wellfounded_Owf(T_b,V_r_2)
% 59.73/59.62 <=> ! [B_Q] :
% 59.73/59.62 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 59.73/59.62 => ? [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 59.73/59.62 & ! [B_y] :
% 59.73/59.62 ( 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))
% 59.73/59.62 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 59.73/59.62 => 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)) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 59.73/59.62 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 59.73/59.62 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 59.73/59.62 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 59.73/59.62 => 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) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 59.73/59.62 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 59.73/59.62 => 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 59.73/59.62 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 59.73/59.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 59.73/59.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 59.73/59.62 => 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) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_transfer__nat__int__set__cong,axiom,
% 59.73/59.62 ! [V_P_H_2,V_P_2] :
% 59.73/59.62 ( ! [B_x] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 59.73/59.62 => ( hBOOL(hAPP(V_P_2,B_x))
% 59.73/59.62 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 59.73/59.62 => 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)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_UnionE,axiom,
% 59.73/59.62 ! [V_C_2,V_A_2,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ~ ! [B_X] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 59.73/59.62 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__add__upd__left,axiom,
% 59.73/59.62 ! [V_u1_2,V_e1_2,V_e2_2,T_c,V_m_2,T_b] :
% 59.73/59.62 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_e2_2)))
% 59.73/59.62 => c_Map_Omap__add(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_e1_2),V_m_2),hAPP(c_Option_Ooption_OSome(T_c),V_u1_2)),V_e2_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__add(T_b,T_c,V_e1_2,V_e2_2)),V_m_2),hAPP(c_Option_Ooption_OSome(T_c),V_u1_2)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_converseE,axiom,
% 59.73/59.62 ! [V_r_2,V_yx_2,T_c,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ~ ! [B_x,B_y] :
% 59.73/59.62 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 59.73/59.62 => ~ 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)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_empty__map__add,axiom,
% 59.73/59.62 ! [V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)),V_m_2) = V_m_2 ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__add__empty,axiom,
% 59.73/59.62 ! [V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))) = V_m_2 ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__add__def,axiom,
% 59.73/59.62 ! [V_x_2,V_m2_2,V_m1_2,T_b,T_c] : hAPP(c_Map_Omap__add(T_c,T_b,V_m1_2,V_m2_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_b,hAPP(V_m1_2,V_x_2),c_Option_Ooption_OSome(T_b)),hAPP(V_m2_2,V_x_2)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__add__None,axiom,
% 59.73/59.62 ! [V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 59.73/59.62 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_b)
% 59.73/59.62 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 59.73/59.62 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_b) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__add__find__right,axiom,
% 59.73/59.62 ! [V_m_2,T_c,V_xx_2,T_b,V_k_2,V_n_2] :
% 59.73/59.62 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2)
% 59.73/59.62 => hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__add__assoc,axiom,
% 59.73/59.62 ! [V_m3_2,V_m2_2,V_m1_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m1_2,c_Map_Omap__add(T_b,T_c,V_m2_2,V_m3_2)) = c_Map_Omap__add(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2),V_m3_2) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__add__dom__app__simps_I1_J,axiom,
% 59.73/59.62 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
% 59.73/59.62 => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__add__dom__app__simps_I3_J,axiom,
% 59.73/59.62 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
% 59.73/59.62 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
% 59.73/59.62 => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l1_2,V_m_2) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__add__dom__app__simps_I2_J,axiom,
% 59.73/59.62 ! [V_l2_2,V_l1_2,T_c,V_m_2,T_b] :
% 59.73/59.62 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l1_2)))
% 59.73/59.62 => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__add__SomeD,axiom,
% 59.73/59.62 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 59.73/59.62 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 59.73/59.62 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 59.73/59.62 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 59.73/59.62 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__add__Some__iff,axiom,
% 59.73/59.62 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 59.73/59.62 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 59.73/59.62 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 59.73/59.62 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 59.73/59.62 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_dom__map__add,axiom,
% 59.73/59.62 ! [V_n_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m_2,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_n_2)),c_Map_Odom(T_b,T_c,V_m_2)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__add__upd,axiom,
% 59.73/59.62 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__add(T_b,T_c,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_inj__on__map__add__dom,axiom,
% 59.73/59.62 ! [V_m_H_2,V_m_2,T_c,T_b] :
% 59.73/59.62 ( c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_c),c_Map_Omap__add(T_b,T_c,V_m_2,V_m_H_2),c_Map_Odom(T_b,T_c,V_m_H_2))
% 59.73/59.62 <=> c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_c),V_m_H_2,c_Map_Odom(T_b,T_c,V_m_H_2)) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__add__comm,axiom,
% 59.73/59.62 ! [V_m2_2,V_m1_2,T_c,T_b] :
% 59.73/59.62 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_m1_2)),c_Map_Odom(T_b,T_c,V_m2_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.62 => c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2) = c_Map_Omap__add(T_b,T_c,V_m2_2,V_m1_2) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_finite__range__map__of__map__add,axiom,
% 59.73/59.62 ! [V_l_2,V_f_2,T_c,T_b] :
% 59.73/59.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
% 59.73/59.62 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),c_Map_Omap__add(T_c,T_b,V_f_2,hAPP(c_Map_Omap__of(T_c,T_b),V_l_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_rel__compE,axiom,
% 59.73/59.62 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 59.73/59.62 ( 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)))
% 59.73/59.62 => ~ ! [B_x,B_y,B_z] :
% 59.73/59.62 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 59.73/59.62 => ( 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))
% 59.73/59.62 => ~ 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)) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_finite__dom__map__of,axiom,
% 59.73/59.62 ! [V_l_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,hAPP(c_Map_Omap__of(T_b,T_c),V_l_2)))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_finite__range__map__of,axiom,
% 59.73/59.62 ! [V_xys_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),hAPP(c_Map_Omap__of(T_c,T_b),V_xys_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__add__map__of__foldr,axiom,
% 59.73/59.62 ! [V_ps_2,V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m_2,hAPP(c_Map_Omap__of(T_b,T_c),V_ps_2)) = c_List_Ofoldr(tc_prod(T_b,T_c),tc_fun(T_b,tc_Option_Ooption(T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))))),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),T_b),c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),T_b,tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)))))),c_Option_Ooption_OSome(T_c))),V_ps_2,V_m_2) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_,axiom,
% 59.73/59.62 ! [V_y_2,V_x_2,T_b] : c_Smallcheck_Oorelse(T_b,V_x_2,V_y_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_b,V_y_2,c_Option_Ooption_OSome(T_b)),V_x_2) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_full__small__int__def,axiom,
% 59.73/59.62 ! [V_d_2,V_f_2] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,V_f_2,V_d_2) = c_Smallcheck_Ofull__small_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_small_H_Osimps,axiom,
% 59.73/59.62 ! [V_f_2,V_i_2,V_d_2] :
% 59.73/59.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 59.73/59.62 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 59.73/59.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 59.73/59.62 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_small_H_Opsimps,axiom,
% 59.73/59.62 ! [V_i_2,V_d_2,V_f_2] :
% 59.73/59.62 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_f_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2))))
% 59.73/59.62 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 59.73/59.62 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 59.73/59.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 59.73/59.62 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_small__int__def,axiom,
% 59.73/59.62 ! [V_d_2,V_f_2] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),V_f_2),V_d_2) = c_Smallcheck_Osmall_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_small__prod__def,axiom,
% 59.73/59.62 ! [V_d_2,V_f_2,T_b,T_c] :
% 59.73/59.62 ( ( class_Smallcheck_Osmall(T_c)
% 59.73/59.62 & class_Smallcheck_Osmall(T_b) )
% 59.73/59.62 => hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(T_b,T_c)),V_f_2),V_d_2) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(T_b),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_b),c_Smallcheck_Osmall__class_Osmall(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c)))),V_d_2)),V_d_2) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_small_H_Opinduct,axiom,
% 59.73/59.62 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] :
% 59.73/59.62 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_a0_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a1_2),V_a2_2))))
% 59.73/59.62 => ( ! [B_f,B_d,B_i] :
% 59.73/59.62 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),B_f),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i))))
% 59.73/59.62 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 59.73/59.62 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
% 59.73/59.62 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) )
% 59.73/59.62 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) )
% 59.73/59.62 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__of__mapk__SomeI,axiom,
% 59.73/59.62 ! [V_x_2,V_k_2,V_t_2,T_d,V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.73/59.62 => ( hAPP(hAPP(c_Map_Omap__of(T_b,T_d),V_t_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_d),V_x_2)
% 59.73/59.62 => hAPP(hAPP(c_Map_Omap__of(T_c,T_d),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_b),c_Product__Type_OPair(T_c,T_d)),V_f_2))),V_t_2)),hAPP(V_f_2,V_k_2)) = hAPP(c_Option_Ooption_OSome(T_d),V_x_2) ) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_inj__mapI,axiom,
% 59.73/59.62 ! [V_f_2,T_c,T_b] :
% 59.73/59.62 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.73/59.62 => 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))) ) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_foldr__map,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__map,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_List_Omap_Ocompositionality,axiom,
% 59.73/59.62 ! [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) ).
% 59.73/59.62
% 59.73/59.62 fof(fact_map__comp__map,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_List_Omap_Ocomp,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_List_Omap_Oid,axiom,
% 59.73/59.63 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_List_Omap_Oidentity,axiom,
% 59.73/59.63 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__ident,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__injective,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 59.73/59.63 ( 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)
% 59.73/59.63 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 59.73/59.63 => V_xs_2 = V_ys_2 ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_inj__mapD,axiom,
% 59.73/59.63 ! [V_f_2,T_c,T_b] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_inj__map__eq__map,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 59.73/59.63 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.73/59.63 => ( 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)
% 59.73/59.63 <=> V_xs_2 = V_ys_2 ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_inj__map,axiom,
% 59.73/59.63 ! [V_f_2,T_c,T_b] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__map,axiom,
% 59.73/59.63 ! [V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Map_Omap__of(T_b,T_c),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))),V_xs_2)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),hAPP(c_Map_Omap__of(T_b,T_d),V_xs_2)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__comp__def,axiom,
% 59.73/59.63 ! [V_k_2,V_g_2,V_f_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,V_f_2,V_g_2,V_k_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_c,c_Option_Ooption_ONone(T_b),V_f_2),hAPP(V_g_2,V_k_2)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_option__map__o__empty,axiom,
% 59.73/59.63 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_d,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_COMBK(tc_Option_Ooption(T_c),T_d),c_Option_Ooption_ONone(T_c))),V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_option__map__eq__Some,axiom,
% 59.73/59.63 ! [V_y_2,V_xo_2,V_f_2,T_b,T_c] :
% 59.73/59.63 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_xo_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 59.73/59.63 <=> ? [B_z] :
% 59.73/59.63 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_c),B_z)
% 59.73/59.63 & hAPP(V_f_2,B_z) = V_y_2 ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_option__map__Some,axiom,
% 59.73/59.63 ! [V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) = hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_x_2)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_option__map__is__None,axiom,
% 59.73/59.63 ! [V_opt_2,V_f_2,T_b,T_c] :
% 59.73/59.63 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_b)
% 59.73/59.63 <=> V_opt_2 = c_Option_Ooption_ONone(T_c) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_option__map__None,axiom,
% 59.73/59.63 ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),c_Option_Ooption_ONone(T_c)) = c_Option_Ooption_ONone(T_b) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_infinite__UNIV__listI,axiom,
% 59.73/59.63 ! [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)))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_dom__option__map,axiom,
% 59.73/59.63 ! [V_m_2,V_f_2,T_d,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_d),tc_Option_Ooption(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),tc_fun(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c)),T_b),c_Option_Omap(T_d,T_c)),V_f_2)),V_m_2)) = c_Map_Odom(T_b,T_d,V_m_2) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Option_Omap_Oid,axiom,
% 59.73/59.63 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Option_Omap_Oidentity,axiom,
% 59.73/59.63 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_option__map__comp,axiom,
% 59.73/59.63 ! [V_opt_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_Option_Omap(T_d,T_c),V_g_2),V_opt_2)) = hAPP(hAPP(c_Option_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_opt_2) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Option_Omap_Ocompositionality,axiom,
% 59.73/59.63 ! [V_option_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_Option_Omap(T_d,T_c),V_g_2),V_option_2)) = hAPP(hAPP(c_Option_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_option_2) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Option_Omap_Ocomp,axiom,
% 59.73/59.63 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),hAPP(c_Option_Omap(T_d,T_c),V_f_2)),hAPP(c_Option_Omap(T_b,T_d),V_g_2)) = hAPP(c_Option_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__comp__simps_I1_J,axiom,
% 59.73/59.63 ! [V_m1_2,T_c,T_d,T_b,V_k_2,V_m2_2] :
% 59.73/59.63 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 59.73/59.63 => c_Map_Omap__comp(T_b,T_d,T_c,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_d) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__comp__Some__iff,axiom,
% 59.73/59.63 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
% 59.73/59.63 ( c_Map_Omap__comp(T_c,T_b,T_d,V_m1_2,V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2)
% 59.73/59.63 <=> ? [B_k_H] :
% 59.73/59.63 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H)
% 59.73/59.63 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__comp__simps_I2_J,axiom,
% 59.73/59.63 ! [V_m1_2,T_c,T_d,V_k_H_2,T_b,V_k_2,V_m2_2] :
% 59.73/59.63 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_k_H_2)
% 59.73/59.63 => c_Map_Omap__comp(T_b,T_d,T_c,V_m1_2,V_m2_2,V_k_2) = hAPP(V_m1_2,V_k_H_2) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_option__map__o__map__upd,axiom,
% 59.73/59.63 ! [V_b_2,V_a_2,V_m_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_d)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_d),V_b_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),V_m_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),hAPP(V_f_2,V_b_2))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__comp__empty_I1_J,axiom,
% 59.73/59.63 ! [V_x_2,V_m_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_d),c_Option_Ooption_ONone(T_c)),V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__comp__empty_I2_J,axiom,
% 59.73/59.63 ! [V_x_2,V_m_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_m_2,V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__comp__None__iff,axiom,
% 59.73/59.63 ! [V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
% 59.73/59.63 ( c_Map_Omap__comp(T_c,T_b,T_d,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 59.73/59.63 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c)
% 59.73/59.63 | ? [B_k_H] :
% 59.73/59.63 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H)
% 59.73/59.63 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_b) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Option_Omap__def,axiom,
% 59.73/59.63 ! [V_f_2,T_c,T_b] : hAPP(c_Option_Omap(T_b,T_c),V_f_2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_c),T_b,c_Option_Ooption_ONone(T_c),hAPP(hAPP(c_COMBB(T_c,tc_Option_Ooption(T_c),T_b),c_Option_Ooption_OSome(T_c)),V_f_2)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__map__restrict,axiom,
% 59.73/59.63 ! [V_ks_2,V_f_2,T_c,T_b] : hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_ks_2)) = c_Map_Orestrict__map(T_b,T_c,hAPP(c_Fun_Ocomp(T_c,tc_Option_Ooption(T_c),T_b,c_Option_Ooption_OSome(T_c)),V_f_2),hAPP(c_List_Oset(T_b),V_ks_2)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of_Osimps_I2_J,axiom,
% 59.73/59.63 ! [V_ps_2,V_p_2,T_c,T_b] : hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),V_p_2),V_ps_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_Map_Omap__of(T_b,T_c),V_ps_2)),hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Option_Ooption_OSome(T_c),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_finite__set,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__eq__conv,axiom,
% 59.73/59.63 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 59.73/59.63 ( 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)
% 59.73/59.63 <=> ! [B_x] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 59.73/59.63 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map_Osimps_I2_J,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__map,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_foldr_Osimps_I2_J,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list_Oinject,axiom,
% 59.73/59.63 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 59.73/59.63 ( 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)
% 59.73/59.63 <=> ( V_a_2 = V_a_H_2
% 59.73/59.63 & V_list_2 = V_list_H_2 ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_not__Cons__self2,axiom,
% 59.73/59.63 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 59.73/59.63
% 59.73/59.63 fof(fact_not__Cons__self,axiom,
% 59.73/59.63 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__ConsD,axiom,
% 59.73/59.63 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 => ( V_y_2 = V_x_2
% 59.73/59.63 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__subset__Cons,axiom,
% 59.73/59.63 ! [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)))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__inj__on,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 59.73/59.63 ( 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)
% 59.73/59.63 => ( 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)))
% 59.73/59.63 => V_xs_2 = V_ys_2 ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_inj__on__map__eq__map,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => ( 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)
% 59.73/59.63 <=> V_xs_2 = V_ys_2 ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__fun__upd,axiom,
% 59.73/59.63 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 59.73/59.63 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 => hAPP(hAPP(c_List_Omap(T_b,T_c),hAPP(hAPP(hAPP(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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__Cons__code_I2_J,axiom,
% 59.73/59.63 ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
% 59.73/59.63 ( ( V_l = V_k
% 59.73/59.63 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(c_Option_Ooption_OSome(T_c),V_v) )
% 59.73/59.63 & ( V_l != V_k
% 59.73/59.63 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_ps),V_k) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__eq__dom,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 59.73/59.63 ( hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2) = hAPP(c_Map_Omap__of(T_b,T_c),V_ys_2)
% 59.73/59.63 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_ys_2)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__SomeD,axiom,
% 59.73/59.63 ! [V_y_2,V_k_2,V_xs_2,T_b,T_c] :
% 59.73/59.63 ( hAPP(hAPP(c_Map_Omap__of(T_c,T_b),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_k_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xs_2))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__is__SomeD,axiom,
% 59.73/59.63 ! [V_y_2,V_x_2,V_xys_2,T_b,T_c] :
% 59.73/59.63 ( hAPP(hAPP(c_Map_Omap__of(T_c,T_b),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 59.73/59.63 => 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_List_Oset(tc_prod(T_c,T_b)),V_xys_2))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_dom__map__of__conv__image__fst,axiom,
% 59.73/59.63 ! [V_xys_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(c_Map_Omap__of(T_b,T_c),V_xys_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_inj__on__mapI,axiom,
% 59.73/59.63 ! [V_A_2,V_f_2,T_c,T_b] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__eq__None__iff,axiom,
% 59.73/59.63 ! [V_x_2,V_xys_2,T_b,T_c] :
% 59.73/59.63 ( hAPP(hAPP(c_Map_Omap__of(T_c,T_b),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_b)
% 59.73/59.63 <=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xys_2)))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__map__keys,axiom,
% 59.73/59.63 ! [V_m_2,T_c,V_xs_2,T_b] :
% 59.73/59.63 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Map_Odom(T_b,T_c,V_m_2)
% 59.73/59.63 => hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),T_c,T_b),c_Option_Othe(T_c)),V_m_2))),V_xs_2)) = V_m_2 ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__Cons__def,axiom,
% 59.73/59.63 ! [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)))))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_the_Osimps,axiom,
% 59.73/59.63 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ).
% 59.73/59.63
% 59.73/59.63 fof(fact_sublists__powset,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_pick_Osimps,axiom,
% 59.73/59.63 ! [V_xs,V_x,T_a,V_i] :
% 59.73/59.63 ( ( 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)))
% 59.73/59.63 => 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) )
% 59.73/59.63 & ( ~ 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)))
% 59.73/59.63 => 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))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_select__weight__cons__zero,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_pick__member,axiom,
% 59.73/59.63 ! [V_xs_2,T_b,V_i_2] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 => 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)))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listsum__simps_I2_J,axiom,
% 59.73/59.63 ! [V_xs,V_x,T_a] :
% 59.73/59.63 ( class_Groups_Omonoid__add(T_a)
% 59.73/59.63 => 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)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listsum__0,axiom,
% 59.73/59.63 ! [V_xs_2,T_c,T_b] :
% 59.73/59.63 ( class_Groups_Omonoid__add(T_b)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listsum__addf,axiom,
% 59.73/59.63 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 59.73/59.63 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listsum__const__mult,axiom,
% 59.73/59.63 ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
% 59.73/59.63 ( class_Rings_Osemiring__0(T_b)
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listsum__mult__const,axiom,
% 59.73/59.63 ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
% 59.73/59.63 ( class_Rings_Osemiring__0(T_b)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listsum__subtractf,axiom,
% 59.73/59.63 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 59.73/59.63 ( class_Groups_Oab__group__add(T_b)
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listsum__abs,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] :
% 59.73/59.63 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 59.73/59.63 => 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)))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_uminus__listsum__map,axiom,
% 59.73/59.63 ! [V_xs_2,V_f_2,T_c,T_b] :
% 59.73/59.63 ( class_Groups_Oab__group__add(T_b)
% 59.73/59.63 => 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)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_select__weight__def,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_select__weight__member,axiom,
% 59.73/59.63 ! [V_s_2,V_xs_2,T_b] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 => 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)))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_product__list__set,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_ran__distinct,axiom,
% 59.73/59.63 ! [V_al_2,T_c,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_al_2)))
% 59.73/59.63 => c_Map_Oran(T_b,T_c,hAPP(c_Map_Omap__of(T_b,T_c),V_al_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_al_2)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__set__sublists,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.63 => 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)))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 59.73/59.63 ! [V_ns_2] :
% 59.73/59.63 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 <=> ! [B_x] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 59.73/59.63 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__product,axiom,
% 59.73/59.63 ! [V_ys,T_b,V_xs,T_a] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 59.73/59.63 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 59.73/59.63 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct_Osimps_I2_J,axiom,
% 59.73/59.63 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 59.73/59.63 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__map,axiom,
% 59.73/59.63 ! [V_xs_2,V_f_2,T_c,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 59.73/59.63 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 59.73/59.63 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] :
% 59.73/59.63 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.63 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.63 => 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)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 59.73/59.63 ! [V_f_2,V_xs_2,T_b,T_c] :
% 59.73/59.63 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.63 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.63 => 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)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__inject__set,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2)))
% 59.73/59.63 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_ys_2)))
% 59.73/59.63 => ( hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2) = hAPP(c_Map_Omap__of(T_b,T_c),V_ys_2)
% 59.73/59.63 <=> hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2) = hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_ys_2) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Some__eq__map__of__iff,axiom,
% 59.73/59.63 ! [V_x_2,V_y_2,V_xys_2,T_c,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2)))
% 59.73/59.63 => ( hAPP(c_Option_Ooption_OSome(T_c),V_y_2) = hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_xys_2),V_x_2)
% 59.73/59.63 <=> 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)),V_xys_2))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__eq__Some__iff,axiom,
% 59.73/59.63 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2)))
% 59.73/59.63 => ( hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),V_y_2)
% 59.73/59.63 <=> 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)),V_xys_2))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__is__SomeI,axiom,
% 59.73/59.63 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2)))
% 59.73/59.63 => ( 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)),V_xys_2)))
% 59.73/59.63 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),V_y_2) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__map__of__compr,axiom,
% 59.73/59.63 ! [V_xs_2,T_c,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2)))
% 59.73/59.63 => hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_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_Option_Ooption(T_c)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),T_b),c_fequal),hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2)))),c_Option_Ooption_OSome(T_c)))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 59.73/59.63 ! [V_f_2,V_A_2,T_b,T_c] :
% 59.73/59.63 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.63 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.63 => 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))))) )
% 59.73/59.63 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.63 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_finite__lists__length__le,axiom,
% 59.73/59.63 ! [V_n_2,V_A_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.63 => 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))))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__eq__imp__length__eq,axiom,
% 59.73/59.63 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 59.73/59.63 ( 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)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__map,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lexn__length,axiom,
% 59.73/59.63 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2
% 59.73/59.63 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_impossible__Cons,axiom,
% 59.73/59.63 ! [V_x,V_ys,V_xs,T_a] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__sublists,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_neq__if__length__neq,axiom,
% 59.73/59.63 ! [V_ys,V_xs,T_a] :
% 59.73/59.63 ( 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)
% 59.73/59.63 => V_xs != V_ys ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_card__length,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__card,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_card__distinct,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] :
% 59.73/59.63 ( 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)
% 59.73/59.63 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lexn_Osimps_I2_J,axiom,
% 59.73/59.63 ! [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)))))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__pos__if__in__set,axiom,
% 59.73/59.63 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list_Osize_I4_J,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Cons__in__lex,axiom,
% 59.73/59.63 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 <=> ( ( 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))
% 59.73/59.63 & 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) )
% 59.73/59.63 | ( V_x_2 = V_y_2
% 59.73/59.63 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listsum__triv,axiom,
% 59.73/59.63 ! [V_xs_2,V_r_2,T_c,T_b] :
% 59.73/59.63 ( class_Rings_Osemiring__1(T_b)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lenlex__conv,axiom,
% 59.73/59.63 ! [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)))))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lenlex__def,axiom,
% 59.73/59.63 ! [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)))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_finite__lists__length__eq,axiom,
% 59.73/59.63 ! [V_n_2,V_A_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.63 => 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))))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Nitpick_Ocard_H__def,axiom,
% 59.73/59.63 ! [V_A_2,T_b] :
% 59.73/59.63 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.63 => 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)))) )
% 59.73/59.63 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.63 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__n__lists,axiom,
% 59.73/59.63 ! [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)))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__n__lists,axiom,
% 59.73/59.63 ! [V_n,V_xs,T_a] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 59.73/59.63 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__n__lists,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__n__lists__elem,axiom,
% 59.73/59.63 ! [V_xs_2,V_n_2,V_ys_2,T_b] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__sublist,axiom,
% 59.73/59.63 ! [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)))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lexord__cons__cons,axiom,
% 59.73/59.63 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 <=> ( 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))
% 59.73/59.63 | ( V_a_2 = V_b_2
% 59.73/59.63 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__sublistI,axiom,
% 59.73/59.63 ! [V_I_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.63 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_in__set__sublistD,axiom,
% 59.73/59.63 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_notin__set__sublistI,axiom,
% 59.73/59.63 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 => ~ 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)))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__sublist__subset,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lexord__lex,axiom,
% 59.73/59.63 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 & 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) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list_Osize_I2_J,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Cons__acc__listrel1I,axiom,
% 59.73/59.63 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 59.73/59.63 => ( 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))))
% 59.73/59.63 => 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)))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__size__map,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel1__mono,axiom,
% 59.73/59.63 ! [V_s_2,V_r_2,T_b] :
% 59.73/59.63 ( 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))
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel1__converse,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 59.73/59.63 ! [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)))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel1I2,axiom,
% 59.73/59.63 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 59.73/59.63 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 59.73/59.63 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel1__eq__len,axiom,
% 59.73/59.63 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_in__listrel1__converse,axiom,
% 59.73/59.63 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 59.73/59.63 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__size__estimation,axiom,
% 59.73/59.63 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 59.73/59.63 => 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))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__size__estimation_H,axiom,
% 59.73/59.63 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 59.73/59.63 => 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))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel1I1,axiom,
% 59.73/59.63 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 59.73/59.63 ( 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))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Cons__listrel1__Cons,axiom,
% 59.73/59.63 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 <=> ( ( 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))
% 59.73/59.63 & V_xs_2 = V_ys_2 )
% 59.73/59.63 | ( V_x_2 = V_y_2
% 59.73/59.63 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__size__conv__listsum,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel__Cons,axiom,
% 59.73/59.63 ! [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))))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_greaterThanLessThan__upto,axiom,
% 59.73/59.63 ! [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)))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel__rtrancl__refl,axiom,
% 59.73/59.63 ! [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)))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel__mono,axiom,
% 59.73/59.63 ! [V_s_2,V_r_2,T_b] :
% 59.73/59.63 ( 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))
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__upto,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_atLeastAtMost__upto,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__upto,axiom,
% 59.73/59.63 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 59.73/59.63 ! [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)))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 59.73/59.63 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 59.73/59.63 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 59.73/59.63 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 59.73/59.63 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel__eq__len,axiom,
% 59.73/59.63 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel__rtrancl__trans,axiom,
% 59.73/59.63 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 59.73/59.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_atLeastLessThan__upto,axiom,
% 59.73/59.63 ! [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)))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 59.73/59.63 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel1__subset__listrel,axiom,
% 59.73/59.63 ! [V_r_H_2,V_r_2,T_b] :
% 59.73/59.63 ( 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))
% 59.73/59.63 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 59.73/59.63 => 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))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_greaterThanAtMost__upto,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 59.73/59.63 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel_OCons,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 59.73/59.63 ( 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))
% 59.73/59.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nat__list__def,axiom,
% 59.73/59.63 ! [V_l_2] :
% 59.73/59.63 ( c_List_Onat__list(V_l_2)
% 59.73/59.63 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrelp__listrel__eq,axiom,
% 59.73/59.63 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 59.73/59.63 ( 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)
% 59.73/59.63 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrelp_Oequations_I2_J,axiom,
% 59.73/59.63 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 59.73/59.63 ( 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))
% 59.73/59.63 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 59.73/59.63 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrelp_OCons,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 59.73/59.63 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 59.73/59.63 => 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)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel__iff__zip,axiom,
% 59.73/59.63 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 <=> ( 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)
% 59.73/59.63 & ! [B_x] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 => 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)) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel__Cons2,axiom,
% 59.73/59.63 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 => ~ ! [B_x,B_xs] :
% 59.73/59.63 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 59.73/59.63 => ( 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))
% 59.73/59.63 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__zip,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_zip__same__conv__map,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__zipI2,axiom,
% 59.73/59.63 ! [V_xs,T_b,V_ys,T_a] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 59.73/59.63 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__zipI1,axiom,
% 59.73/59.63 ! [V_ys,T_b,V_xs,T_a] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 59.73/59.63 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__zip__inject,axiom,
% 59.73/59.63 ! [V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
% 59.73/59.63 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
% 59.73/59.63 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
% 59.73/59.63 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 59.73/59.63 => ( hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2))
% 59.73/59.63 => V_ys_2 = V_zs_2 ) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__fst__zip,axiom,
% 59.73/59.63 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 59.73/59.63 ( 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)
% 59.73/59.63 => 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 ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__snd__zip,axiom,
% 59.73/59.63 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 59.73/59.63 ( 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)
% 59.73/59.63 => 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 ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_zip__map__fst__snd,axiom,
% 59.73/59.63 ! [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 ).
% 59.73/59.63
% 59.73/59.63 fof(fact_zip__Cons__Cons,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_zip__eq__conv,axiom,
% 59.73/59.63 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 59.73/59.63 ( 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)
% 59.73/59.63 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 59.73/59.63 <=> ( 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
% 59.73/59.63 & 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 ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__zip__map2,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__zip__map,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__eq__iff__zip__eq,axiom,
% 59.73/59.63 ! [T_b,V_ys_2,V_xs_2] :
% 59.73/59.63 ( V_xs_2 = V_ys_2
% 59.73/59.63 <=> ( 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)
% 59.73/59.63 & ! [B_x] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_zip__same,axiom,
% 59.73/59.63 ! [V_xs_2,V_b_2,V_a_2,T_b] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 & V_a_2 = V_b_2 ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__zip__leftD,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__zip__rightD,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_in__set__zipE,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__zip__is__None,axiom,
% 59.73/59.63 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
% 59.73/59.63 ( 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)
% 59.73/59.63 => ( hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) = c_Option_Ooption_ONone(T_c)
% 59.73/59.63 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__zip__is__Some,axiom,
% 59.73/59.63 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
% 59.73/59.63 ( 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)
% 59.73/59.63 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 <=> ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),B_y) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_zip__map2,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_zip__map1,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_zip__map__map,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_dom__map__of__zip,axiom,
% 59.73/59.63 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 59.73/59.63 ( 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)
% 59.73/59.63 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.63 => c_Map_Odom(T_b,T_c,hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) = hAPP(c_List_Oset(T_b),V_xs_2) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__zip__upd,axiom,
% 59.73/59.63 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
% 59.73/59.63 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
% 59.73/59.63 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
% 59.73/59.63 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
% 59.73/59.63 => ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_z_2))
% 59.73/59.63 => hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2)) ) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__zip__map,axiom,
% 59.73/59.63 ! [V_f_2,T_c,V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),hAPP(V_f_2,V_x_2)) )
% 59.73/59.63 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel__Cons1,axiom,
% 59.73/59.63 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 => ~ ! [B_y,B_ys] :
% 59.73/59.63 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 59.73/59.63 => ( 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))
% 59.73/59.63 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__zip__enum__inject,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,T_b,T_c] :
% 59.73/59.63 ( ( class_Enum_Oenum(T_c)
% 59.73/59.63 & class_Enum_Oenum(T_b) )
% 59.73/59.63 => ( 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)),c_Enum_Oenum__class_Oenum(T_c))
% 59.73/59.63 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_Enum_Oenum__class_Oenum(T_c))
% 59.73/59.63 => ( hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_c,c_Option_Othe(T_b)),hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),c_Enum_Oenum__class_Oenum(T_c)),V_xs_2))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_c,c_Option_Othe(T_b)),hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),c_Enum_Oenum__class_Oenum(T_c)),V_ys_2)))
% 59.73/59.63 => V_xs_2 = V_ys_2 ) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_enum__prod__def,axiom,
% 59.73/59.63 ! [T_b,T_a] :
% 59.73/59.63 ( ( class_Enum_Oenum(T_a)
% 59.73/59.63 & class_Enum_Oenum(T_b) )
% 59.73/59.63 => c_Enum_Oenum__class_Oenum(tc_prod(T_a,T_b)) = c_Enum_Oproduct(T_a,T_b,c_Enum_Oenum__class_Oenum(T_a),c_Enum_Oenum__class_Oenum(T_b)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_enum__distinct,axiom,
% 59.73/59.63 ! [T_a] :
% 59.73/59.63 ( class_Enum_Oenum(T_a)
% 59.73/59.63 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_enum__option__def,axiom,
% 59.73/59.63 ! [T_b] :
% 59.73/59.63 ( class_Enum_Oenum(T_b)
% 59.73/59.63 => c_Enum_Oenum__class_Oenum(tc_Option_Ooption(T_b)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(T_b)),c_Option_Ooption_ONone(T_b)),hAPP(hAPP(c_List_Omap(T_b,tc_Option_Ooption(T_b)),c_Option_Ooption_OSome(T_b)),c_Enum_Oenum__class_Oenum(T_b))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_in__enum,axiom,
% 59.73/59.63 ! [V_x_2,T_b] :
% 59.73/59.63 ( class_Enum_Oenum(T_b)
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_Enum_Oenum__class_Oenum(T_b)))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_UNIV__enum,axiom,
% 59.73/59.63 ! [T_b] :
% 59.73/59.63 ( class_Enum_Oenum(T_b)
% 59.73/59.63 => c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),c_Enum_Oenum__class_Oenum(T_b)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_enum__UNIV,axiom,
% 59.73/59.63 ! [T_b] :
% 59.73/59.63 ( class_Enum_Oenum(T_b)
% 59.73/59.63 => hAPP(c_List_Oset(T_b),c_Enum_Oenum__class_Oenum(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_enum__fun__code,axiom,
% 59.73/59.63 ! [T_c,T_b] :
% 59.73/59.63 ( ( class_Enum_Oenum(T_b)
% 59.73/59.63 & class_HOL_Oequal(T_b)
% 59.73/59.63 & class_Enum_Oenum(T_c) )
% 59.73/59.63 => c_Enum_Oenum__class_Oenum(tc_fun(T_b,T_c)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,T_c),tc_List_Olist(T_c)),c_Fun_Ocomp(tc_Option_Ooption(T_c),T_c,T_b,c_Option_Othe(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)),tc_List_Olist(T_c)),c_Map_Omap__of(T_b,T_c)),hAPP(c_List_Ozip(T_b,T_c),c_Enum_Oenum__class_Oenum(T_b))))),c_Enum_On__lists(T_c,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b)),c_Enum_Oenum__class_Oenum(T_c))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_enum__fun__def,axiom,
% 59.73/59.63 ! [T_c,T_b] :
% 59.73/59.63 ( ( class_Enum_Oenum(T_b)
% 59.73/59.63 & class_Enum_Oenum(T_c) )
% 59.73/59.63 => c_Enum_Oenum__class_Oenum(tc_fun(T_b,T_c)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,T_c),tc_List_Olist(T_c)),c_Fun_Ocomp(tc_Option_Ooption(T_c),T_c,T_b,c_Option_Othe(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)),tc_List_Olist(T_c)),c_Map_Omap__of(T_b,T_c)),hAPP(c_List_Ozip(T_b,T_c),c_Enum_Oenum__class_Oenum(T_b))))),c_Enum_On__lists(T_c,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b)),c_Enum_Oenum__class_Oenum(T_c))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_enum__ex__fun__def,axiom,
% 59.73/59.63 ! [V_P_2,T_b,T_c] :
% 59.73/59.63 ( ( class_Enum_Oenum(T_c)
% 59.73/59.63 & class_Enum_Oenum(T_b) )
% 59.73/59.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_b,T_c)),V_P_2))
% 59.73/59.63 <=> c_Enum_Oex__n__lists(T_c,hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_HOL_Obool,tc_List_Olist(T_c)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,T_c),tc_List_Olist(T_c)),c_Fun_Ocomp(tc_Option_Ooption(T_c),T_c,T_b,c_Option_Othe(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)),tc_List_Olist(T_c)),c_Map_Omap__of(T_b,T_c)),hAPP(c_List_Ozip(T_b,T_c),c_Enum_Oenum__class_Oenum(T_b))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_enum__ex__fun__code,axiom,
% 59.73/59.63 ! [V_P_2,T_b,T_c] :
% 59.73/59.63 ( ( class_Enum_Oenum(T_c)
% 59.73/59.63 & class_Enum_Oenum(T_b)
% 59.73/59.63 & class_HOL_Oequal(T_b) )
% 59.73/59.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_b,T_c)),V_P_2))
% 59.73/59.63 <=> c_Enum_Oex__n__lists(T_c,hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_HOL_Obool,tc_List_Olist(T_c)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,T_c),tc_List_Olist(T_c)),c_Fun_Ocomp(tc_Option_Ooption(T_c),T_c,T_b,c_Option_Othe(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)),tc_List_Olist(T_c)),c_Map_Omap__of(T_b,T_c)),hAPP(c_List_Ozip(T_b,T_c),c_Enum_Oenum__class_Oenum(T_b))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_ex__n__lists__def,axiom,
% 59.73/59.63 ! [V_n_2,V_P_2,T_b] :
% 59.73/59.63 ( class_Enum_Oenum(T_b)
% 59.73/59.63 => ( c_Enum_Oex__n__lists(T_b,V_P_2,V_n_2)
% 59.73/59.63 <=> ? [B_x] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,c_Enum_Oenum__class_Oenum(T_b)))))
% 59.73/59.63 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_enum__all__fun__def,axiom,
% 59.73/59.63 ! [V_P_2,T_b,T_c] :
% 59.73/59.63 ( ( class_Enum_Oenum(T_c)
% 59.73/59.63 & class_Enum_Oenum(T_b) )
% 59.73/59.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_b,T_c)),V_P_2))
% 59.73/59.63 <=> c_Enum_Oall__n__lists(T_c,hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_HOL_Obool,tc_List_Olist(T_c)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,T_c),tc_List_Olist(T_c)),c_Fun_Ocomp(tc_Option_Ooption(T_c),T_c,T_b,c_Option_Othe(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)),tc_List_Olist(T_c)),c_Map_Omap__of(T_b,T_c)),hAPP(c_List_Ozip(T_b,T_c),c_Enum_Oenum__class_Oenum(T_b))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_enum__all__fun__code,axiom,
% 59.73/59.63 ! [V_P_2,T_b,T_c] :
% 59.73/59.63 ( ( class_Enum_Oenum(T_c)
% 59.73/59.63 & class_Enum_Oenum(T_b)
% 59.73/59.63 & class_HOL_Oequal(T_b) )
% 59.73/59.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_b,T_c)),V_P_2))
% 59.73/59.63 <=> c_Enum_Oall__n__lists(T_c,hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_HOL_Obool,tc_List_Olist(T_c)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,T_c),tc_List_Olist(T_c)),c_Fun_Ocomp(tc_Option_Ooption(T_c),T_c,T_b,c_Option_Othe(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)),tc_List_Olist(T_c)),c_Map_Omap__of(T_b,T_c)),hAPP(c_List_Ozip(T_b,T_c),c_Enum_Oenum__class_Oenum(T_b))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_all__n__lists__def,axiom,
% 59.73/59.63 ! [V_n_2,V_P_2,T_b] :
% 59.73/59.63 ( class_Enum_Oenum(T_b)
% 59.73/59.63 => ( c_Enum_Oall__n__lists(T_b,V_P_2,V_n_2)
% 59.73/59.63 <=> ! [B_x] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,c_Enum_Oenum__class_Oenum(T_b)))))
% 59.73/59.63 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__zip,axiom,
% 59.73/59.63 ! [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)))))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel__subset,axiom,
% 59.73/59.63 ! [V_A_2,V_r_2,T_b] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 => 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))))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__zip,axiom,
% 59.73/59.63 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => ( 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)))
% 59.73/59.63 => 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)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__eq__iff__nth__eq,axiom,
% 59.73/59.63 ! [T_b,V_ys_2,V_xs_2] :
% 59.73/59.63 ( V_xs_2 = V_ys_2
% 59.73/59.63 <=> ( 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)
% 59.73/59.63 & ! [B_i] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lists__mono,axiom,
% 59.73/59.63 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth_Osimps,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__Cons__Suc,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__Cons__0,axiom,
% 59.73/59.63 ! [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 ).
% 59.73/59.63
% 59.73/59.63 fof(fact_all__set__conv__all__nth,axiom,
% 59.73/59.63 ! [V_P_2,V_xs_2,T_b] :
% 59.73/59.63 ( ! [B_x] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 => hBOOL(hAPP(V_P_2,B_x)) )
% 59.73/59.63 <=> ! [B_i] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__map,axiom,
% 59.73/59.63 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 59.73/59.63 => 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)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__conv__nth,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.63 <=> ! [B_i] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => ! [B_j] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => ( B_i != B_j
% 59.73/59.63 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__eq__iff__index__eq,axiom,
% 59.73/59.63 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 59.73/59.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 59.73/59.63 => ( 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)
% 59.73/59.63 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lists__UNIV,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_equiv__listrel,axiom,
% 59.73/59.63 ! [V_r_2,V_A_2,T_b] :
% 59.73/59.63 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 59.73/59.63 => 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)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel__refl__on,axiom,
% 59.73/59.63 ! [V_r_2,V_A_2,T_b] :
% 59.73/59.63 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 59.73/59.63 => 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)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_elem__le__listsum__nat,axiom,
% 59.73/59.63 ! [V_ns,V_k] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_in__set__conv__nth,axiom,
% 59.73/59.63 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 <=> ? [B_i] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__mem,axiom,
% 59.73/59.63 ! [V_xs_2,T_b,V_n_2] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__Cons_H,axiom,
% 59.73/59.63 ! [V_xs,V_x,T_a,V_n] :
% 59.73/59.63 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 59.73/59.63 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 => 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))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__conv__nth,axiom,
% 59.73/59.63 ! [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))))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Cons__in__lists__iff,axiom,
% 59.73/59.63 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.63 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_in__lists__conv__set,axiom,
% 59.73/59.63 ! [V_A_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 59.73/59.63 <=> ! [B_x] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__Cons__number__of,axiom,
% 59.73/59.63 ! [V_xs,V_x,T_a,V_v] :
% 59.73/59.63 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 => 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 )
% 59.73/59.63 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 => 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))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lists__eq__set,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listsum__setsum__nth,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] :
% 59.73/59.63 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__sublist,axiom,
% 59.73/59.63 ! [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))))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel__iff__nth,axiom,
% 59.73/59.63 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 <=> ( 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)
% 59.73/59.63 & ! [B_n] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => 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)) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lists__accD,axiom,
% 59.73/59.63 ! [V_r_2,V_xs_2,T_b] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 => 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)))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lists__accI,axiom,
% 59.73/59.63 ! [V_r_2,V_xs_2,T_b] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 => 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)))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lexord__take__index__conv,axiom,
% 59.73/59.63 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 <=> ( ( 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)))
% 59.73/59.63 & 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 )
% 59.73/59.63 | ? [B_i] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 59.73/59.63 & 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)) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_pick__same,axiom,
% 59.73/59.63 ! [V_xs_2,T_b,V_l_2] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__take,axiom,
% 59.73/59.63 ! [V_xs,T_a,V_n,V_i] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__map,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__Suc__Cons,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__zip,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_in__set__takeD,axiom,
% 59.73/59.63 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__take__subset,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_sublist__upt__eq__take,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 59.73/59.63 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_times__code__numeral__code,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 59.73/59.63 ! [V_m_2,V_n_2] :
% 59.73/59.63 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 59.73/59.63 <=> V_n_2 = V_m_2 ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__take,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_zero__code__numeral__def,axiom,
% 59.73/59.63 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__take,axiom,
% 59.73/59.63 ! [V_i,V_xs,T_a] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 59.73/59.63 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__take,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__all,axiom,
% 59.73/59.63 ! [V_n,V_xs,T_a] :
% 59.73/59.63 ( 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))
% 59.73/59.63 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_one__code__numeral__def,axiom,
% 59.73/59.63 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_less__code__numeral__code,axiom,
% 59.73/59.63 ! [V_m_2,V_n_2] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 59.73/59.63 ! [V_y_2,V_x_2] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 59.73/59.63 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 59.73/59.63 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 59.73/59.63 <=> V_x_2 = V_y_2 ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_number__of__code__numeral__def,axiom,
% 59.73/59.63 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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__take__subset__set__take,axiom,
% 59.73/59.63 ! [V_xs_2,T_b,V_n_2,V_m_2] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 59.73/59.63 => 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)))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_plus__code__numeral__code,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_less__eq__code__numeral__code,axiom,
% 59.73/59.63 ! [V_m_2,V_n_2] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_code__numeral__not__eq__zero,axiom,
% 59.73/59.63 ! [V_i_2] :
% 59.73/59.63 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 59.73/59.63 <=> 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)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listsum__update__nat,axiom,
% 59.73/59.63 ! [V_n,V_ns,V_k] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => 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)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__list__update,axiom,
% 59.73/59.63 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.63 => ( ~ 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))))))
% 59.73/59.63 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__update__id,axiom,
% 59.73/59.63 ! [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 ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__list__update__neq,axiom,
% 59.73/59.63 ! [V_x,V_xs,T_a,V_j,V_i] :
% 59.73/59.63 ( V_i != V_j
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__update,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__list__update,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__update__beyond,axiom,
% 59.73/59.63 ! [V_x,V_i,V_xs,T_a] :
% 59.73/59.63 ( 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))
% 59.73/59.63 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__update__overwrite,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__update__swap,axiom,
% 59.73/59.63 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 59.73/59.63 ( V_i != V_i_H
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_update__zip,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_zip__update,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__update_Osimps_I2_J,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__update__code_I3_J,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__update__code_I2_J,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__update__subsetI,axiom,
% 59.73/59.63 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 59.73/59.63 ( 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))
% 59.73/59.63 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 59.73/59.63 => 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)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__update__subset__insert,axiom,
% 59.73/59.63 ! [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)))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__list__update__eq,axiom,
% 59.73/59.63 ! [V_x,V_xs,T_a,V_i] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => 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 ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__update__same__conv,axiom,
% 59.73/59.63 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 59.73/59.63 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 59.73/59.63 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__list__update,axiom,
% 59.73/59.63 ! [V_x,V_j,V_xs,T_a,V_i] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => ( ( V_i = V_j
% 59.73/59.63 => 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 )
% 59.73/59.63 & ( V_i != V_j
% 59.73/59.63 => 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) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__update__memI,axiom,
% 59.73/59.63 ! [V_x_2,V_xs_2,T_b,V_n_2] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 59.73/59.63 => 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)))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel1__iff__update,axiom,
% 59.73/59.63 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 <=> ? [B_y,B_n] :
% 59.73/59.63 ( 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))
% 59.73/59.63 & 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)))
% 59.73/59.63 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__upd__upds__conv__if,axiom,
% 59.73/59.63 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_c,V_x_2,T_b] :
% 59.73/59.63 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))))
% 59.73/59.63 => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),V_xs_2,V_ys_2) = c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2) )
% 59.73/59.63 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))))
% 59.73/59.63 => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),V_xs_2,V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__upds__apply__nontin,axiom,
% 59.73/59.63 ! [V_ys_2,V_f_2,T_c,V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 => hAPP(c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__add__upds,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,V_m2_2,V_m1_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m1_2,c_Map_Omap__upds(T_b,T_c,V_m2_2,V_xs_2,V_ys_2)) = c_Map_Omap__upds(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2),V_xs_2,V_ys_2) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__upds__Cons,axiom,
% 59.73/59.63 ! [V_bs_2,V_b_2,V_as_2,V_a_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_as_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_b_2),V_bs_2)) = c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)),V_as_2,V_bs_2) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__upds__list__update2__drop,axiom,
% 59.73/59.63 ! [V_y_2,V_m_2,V_ys_2,T_c,V_i_2,V_xs_2,T_b] :
% 59.73/59.63 ( 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_i_2))
% 59.73/59.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
% 59.73/59.63 => c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__upds__twist,axiom,
% 59.73/59.63 ! [V_bs_2,V_b_2,V_m_2,T_c,V_as_2,V_a_2,T_b] :
% 59.73/59.63 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_as_2)))
% 59.73/59.63 => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)),V_as_2,V_bs_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_m_2,V_as_2,V_bs_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_restrict__map__upds,axiom,
% 59.73/59.63 ! [V_m_2,V_D_2,V_ys_2,T_c,V_xs_2,T_b] :
% 59.73/59.63 ( 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)
% 59.73/59.63 => ( 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_D_2))
% 59.73/59.63 => c_Map_Orestrict__map(T_b,T_c,c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2),V_D_2) = c_Map_Omap__upds(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(c_List_Oset(T_b),V_xs_2))),V_xs_2,V_ys_2) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_dom__map__upds,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__upds(T_b,T_c,V_m_2,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),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))),c_Map_Odom(T_b,T_c,V_m_2)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_select__def,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_subtract__code__numeral__code,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nat__of__inverse,axiom,
% 59.73/59.63 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 59.73/59.63
% 59.73/59.63 fof(fact_of__nat__nat__of,axiom,
% 59.73/59.63 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nat__of__of__nat,axiom,
% 59.73/59.63 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 59.73/59.63 ! [V_l_2,V_k_2] :
% 59.73/59.63 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 59.73/59.63 <=> V_k_2 = V_l_2 ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_code__numeral_Onat__of__inject,axiom,
% 59.73/59.63 ! [V_y_2,V_x_2] :
% 59.73/59.63 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 59.73/59.63 <=> V_x_2 = V_y_2 ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_type__definition__code__numeral,axiom,
% 59.73/59.63 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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_less__code__numeral__def,axiom,
% 59.73/59.63 ! [V_m_2,V_n_2] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 59.73/59.63 <=> 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nat__of,axiom,
% 59.73/59.63 ! [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)))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nat__of__number,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_int__of__def,axiom,
% 59.73/59.63 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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_less__eq__code__numeral__def,axiom,
% 59.73/59.63 ! [V_m_2,V_n_2] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 59.73/59.63 <=> 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nat__of__code,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nat__of__aux__def,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Suc__code__numeral__def,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_minus__code__numeral__def,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_of__nat__inverse,axiom,
% 59.73/59.63 ! [V_y_2] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 59.73/59.63 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_plus__code__numeral__def,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_div__code__numeral__def,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_minus__code__numeral__code,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_subtract__code__numeral__def,axiom,
% 59.73/59.63 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_times__code__numeral__def,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_mod__code__numeral__def,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_code__numeral__decr,axiom,
% 59.73/59.63 ! [V_k] :
% 59.73/59.63 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_select__weigth__select,axiom,
% 59.73/59.63 ! [T_b,V_xs_2] :
% 59.73/59.63 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listsum__mono,axiom,
% 59.73/59.63 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 59.73/59.63 ( ( class_Groups_Omonoid__add(T_c)
% 59.73/59.63 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 59.73/59.63 => ( ! [B_x] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 59.73/59.63 => 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)))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lists_ONil,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel__Nil2,axiom,
% 59.73/59.63 ! [V_r_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel__Nil1,axiom,
% 59.73/59.63 ! [V_r_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__eq__Nil,axiom,
% 59.73/59.63 ! [V_xs_2,V_n_2,T_b] :
% 59.73/59.63 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 59.73/59.63 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__0,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__Nil,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_n__lists_Osimps_I1_J,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_n__lists__Nil,axiom,
% 59.73/59.63 ! [T_a,V_n] :
% 59.73/59.63 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 => 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))) )
% 59.73/59.63 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_sublists_Osimps_I1_J,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list_Osimps_I3_J,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list_Osimps_I2_J,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_zip__Nil,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_zip_Osimps_I1_J,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_sublist__empty,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_upto__empty,axiom,
% 59.73/59.63 ! [V_i,V_j] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 59.73/59.63 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__empty,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] :
% 59.73/59.63 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 59.73/59.63 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__empty2,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] :
% 59.73/59.63 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 59.73/59.63 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_sublist__nil,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listsum__simps_I1_J,axiom,
% 59.73/59.63 ! [T_a] :
% 59.73/59.63 ( class_Groups_Omonoid__add(T_a)
% 59.73/59.63 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_foldr_Osimps_I1_J,axiom,
% 59.73/59.63 ! [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 ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__Cons__code_I1_J,axiom,
% 59.73/59.63 ! [V_k,T_a,T_b] : hAPP(hAPP(c_Map_Omap__of(T_b,T_a),c_List_Olist_ONil(tc_prod(T_b,T_a))),V_k) = c_Option_Ooption_ONone(T_a) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_product_Osimps_I1_J,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list_Osize_I1_J,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrelp_Oequations_I1_J,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrelp_ONil,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct_Osimps_I1_J,axiom,
% 59.73/59.63 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list_Osize_I3_J,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__0__conv,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] :
% 59.73/59.63 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__is__Nil__conv,axiom,
% 59.73/59.63 ! [V_xs_2,V_f_2,T_b,T_c] :
% 59.73/59.63 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 59.73/59.63 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map_Osimps_I1_J,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Nil__is__map__conv,axiom,
% 59.73/59.63 ! [V_xs_2,V_f_2,T_c,T_b] :
% 59.73/59.63 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 59.73/59.63 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of_Osimps_I1_J,axiom,
% 59.73/59.63 ! [V_x_1,T_b,T_a] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),c_List_Olist_ONil(tc_prod(T_a,T_b))),V_x_1) = c_Option_Ooption_ONone(T_b) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__upds__Nil1,axiom,
% 59.73/59.63 ! [V_bs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,c_List_Olist_ONil(T_b),V_bs_2) = V_m_2 ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__upds__Nil2,axiom,
% 59.73/59.63 ! [V_as_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_as_2,c_List_Olist_ONil(T_c)) = V_m_2 ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__update__code_I1_J,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__update_Osimps_I1_J,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__update__nonempty,axiom,
% 59.73/59.63 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 59.73/59.63 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 59.73/59.63 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__greater__0__conv,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__1__Cons,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_not__listrel1__Nil,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_not__Nil__listrel1,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel_ONil,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lexord__Nil__right,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Nil2__notin__lex,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Nil__notin__lex,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__Cons,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_upto_Osimps,axiom,
% 59.73/59.63 ! [V_j,V_i] :
% 59.73/59.63 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 59.73/59.63 => 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)) )
% 59.73/59.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 59.73/59.63 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_sublist__singleton,axiom,
% 59.73/59.63 ! [V_x_2,T_b,V_A_2] :
% 59.73/59.63 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 59.73/59.63 => 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)) )
% 59.73/59.63 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 59.73/59.63 => 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) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lists__empty,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__Cons_H,axiom,
% 59.73/59.63 ! [V_xs,V_x,T_a,V_n] :
% 59.73/59.63 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 => 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) )
% 59.73/59.63 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 => 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)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_upto__rec__number__of,axiom,
% 59.73/59.63 ! [V_n,V_m] :
% 59.73/59.63 ( ( 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)))
% 59.73/59.63 => 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))) )
% 59.73/59.63 & ( ~ 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)))
% 59.73/59.63 => 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) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_select,axiom,
% 59.73/59.63 ! [V_s_2,T_b,V_xs_2] :
% 59.73/59.63 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel__Nil,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__Cons__sing__Nil,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__Cons__number__of,axiom,
% 59.73/59.63 ! [V_xs,V_x,T_a,V_v] :
% 59.73/59.63 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 => 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) )
% 59.73/59.63 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 => 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)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_upto_Opsimps,axiom,
% 59.73/59.63 ! [V_j_2,V_i_2] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 59.73/59.63 => 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)) )
% 59.73/59.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 59.73/59.63 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_anamorph_Osimps,axiom,
% 59.73/59.63 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 59.73/59.63 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 59.73/59.63 => 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) )
% 59.73/59.63 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 59.73/59.63 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = hAPP(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)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listset_Osimps_I1_J,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_zip__Cons1,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list_Osimps_I5_J,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list_Osimps_I4_J,axiom,
% 59.73/59.63 ! [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 ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listset_Osimps_I2_J,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_zip__Cons,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_upto_Opinduct,axiom,
% 59.73/59.63 ! [V_P_2,V_a1_2,V_a0_2] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => ( ! [B_i,B_j] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 59.73/59.63 => 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)) )
% 59.73/59.63 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
% 59.73/59.63 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__upds__append1,axiom,
% 59.73/59.63 ! [V_x_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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)))
% 59.73/59.63 => c_Map_Omap__upds(T_b,T_c,V_m_2,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) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_append1__eq__conv,axiom,
% 59.73/59.63 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 <=> ( V_xs_2 = V_ys_2
% 59.73/59.63 & V_x_2 = V_y_2 ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Cons__eq__append__conv,axiom,
% 59.73/59.63 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( 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)
% 59.73/59.63 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 59.73/59.63 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 59.73/59.63 | ? [B_ys_H] :
% 59.73/59.63 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 59.73/59.63 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_append__eq__Cons__conv,axiom,
% 59.73/59.63 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 59.73/59.63 ( 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)
% 59.73/59.63 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 59.73/59.63 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 59.73/59.63 | ? [B_ys_H] :
% 59.73/59.63 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 59.73/59.63 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_eq__Nil__appendI,axiom,
% 59.73/59.63 ! [T_a,V_ys,V_xs] :
% 59.73/59.63 ( V_xs = V_ys
% 59.73/59.63 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_append__self__conv2,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 59.73/59.63 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_append__self__conv,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 59.73/59.63 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_append__is__Nil__conv,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 59.73/59.63 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 59.73/59.63 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_self__append__conv2,axiom,
% 59.73/59.63 ! [V_xs_2,T_b,V_ys_2] :
% 59.73/59.63 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 59.73/59.63 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_self__append__conv,axiom,
% 59.73/59.63 ! [V_ys_2,T_b,V_xs_2] :
% 59.73/59.63 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 59.73/59.63 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_append__Nil2,axiom,
% 59.73/59.63 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Nil__is__append__conv,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 59.73/59.63 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 59.73/59.63 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_append__Nil,axiom,
% 59.73/59.63 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 59.73/59.63
% 59.73/59.63 fof(fact_fun__upds__append__drop,axiom,
% 59.73/59.63 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 59.73/59.63 ( 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)
% 59.73/59.63 => c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2),V_ys_2) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_fun__upds__append2__drop,axiom,
% 59.73/59.63 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 59.73/59.63 ( 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)
% 59.73/59.63 => c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_zs_2)) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__append,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__append,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_zip__append,axiom,
% 59.73/59.63 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 59.73/59.63 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_us)
% 59.73/59.63 => ( 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)
% 59.73/59.63 => 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)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__append,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),V_xs_2),V_ys_2)) = c_Map_Omap__add(T_b,T_c,hAPP(c_Map_Omap__of(T_b,T_c),V_ys_2),hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_append__assoc,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_append__eq__append__conv2,axiom,
% 59.73/59.63 ! [V_tsa_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( 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)
% 59.73/59.63 <=> ? [B_us] :
% 59.73/59.63 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 59.73/59.63 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_tsa_2 )
% 59.73/59.63 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 59.73/59.63 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_same__append__eq,axiom,
% 59.73/59.63 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( 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)
% 59.73/59.63 <=> V_ys_2 = V_zs_2 ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_append__same__eq,axiom,
% 59.73/59.63 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 59.73/59.63 ( 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)
% 59.73/59.63 <=> V_ys_2 = V_zs_2 ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_append__eq__appendI,axiom,
% 59.73/59.63 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 59.73/59.63 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 59.73/59.63 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 59.73/59.63 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_foldr__append,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listsum__append,axiom,
% 59.73/59.63 ! [V_ys,V_xs,T_a] :
% 59.73/59.63 ( class_Groups_Omonoid__add(T_a)
% 59.73/59.63 => 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)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__append,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_append__in__lists__conv,axiom,
% 59.73/59.63 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 59.73/59.63 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Cons__eq__appendI,axiom,
% 59.73/59.63 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 59.73/59.63 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 59.73/59.63 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 59.73/59.63 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_append__Cons,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_sublists_Osimps_I2_J,axiom,
% 59.73/59.63 ! [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))))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__append__length,axiom,
% 59.73/59.63 ! [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 ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__append__length__plus,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__append,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__update__append1,axiom,
% 59.73/59.63 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__update__length,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_append__listrel1I,axiom,
% 59.73/59.63 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 & V_us_2 = V_vs_2 )
% 59.73/59.63 | ( V_xs_2 = V_ys_2
% 59.73/59.63 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) )
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lexord__append__leftI,axiom,
% 59.73/59.63 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__append,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 59.73/59.63 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.63 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 59.73/59.63 & 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)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__append,axiom,
% 59.73/59.63 ! [V_ys,V_xs,T_a,V_n] :
% 59.73/59.63 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 59.73/59.63 => 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) )
% 59.73/59.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 59.73/59.63 => 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))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__update__append,axiom,
% 59.73/59.63 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 59.73/59.63 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 59.73/59.63 => 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) )
% 59.73/59.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 59.73/59.63 => 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)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_product_Osimps_I2_J,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_sublist__append,axiom,
% 59.73/59.63 ! [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)))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel1I,axiom,
% 59.73/59.63 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 59.73/59.63 ( 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))
% 59.73/59.63 => ( 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))
% 59.73/59.63 => ( 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))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lexord__append__left__rightI,axiom,
% 59.73/59.63 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
% 59.73/59.63 ( 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))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__Suc__conv__app__nth,axiom,
% 59.73/59.63 ! [V_xs,T_a,V_i] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 59.73/59.63 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 & V_x_2 = V_y_2 )
% 59.73/59.63 | ( V_xs_2 = V_ys_2
% 59.73/59.63 & 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)) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_sublist__Cons,axiom,
% 59.73/59.63 ! [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)))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listrel1E,axiom,
% 59.73/59.63 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 => ~ ! [B_x,B_y] :
% 59.73/59.63 ( 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))
% 59.73/59.63 => ! [B_us,B_vs] :
% 59.73/59.63 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 59.73/59.63 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lexord__append__leftD,axiom,
% 59.73/59.63 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 => ( ! [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))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rotate1__def,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_upd__conv__take__nth__drop,axiom,
% 59.73/59.63 ! [V_a,V_xs,T_a,V_i] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_append__take__drop__id,axiom,
% 59.73/59.63 ! [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 ).
% 59.73/59.63
% 59.73/59.63 fof(fact_drop__map,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rotate1__is__Nil__conv,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] :
% 59.73/59.63 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 59.73/59.63 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_drop__Nil,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__drop__subset,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__rotate1,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__drop,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct1__rotate,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 59.73/59.63 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__drop,axiom,
% 59.73/59.63 ! [V_i,V_xs,T_a] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 59.73/59.63 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_drop__drop,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_drop__0,axiom,
% 59.73/59.63 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__rotate1,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_in__set__dropD,axiom,
% 59.73/59.63 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_drop__zip,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__drop,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_drop__take,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__via__drop,axiom,
% 59.73/59.63 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 59.73/59.63 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 59.73/59.63 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_drop__1__Cons,axiom,
% 59.73/59.63 ! [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 ).
% 59.73/59.63
% 59.73/59.63 fof(fact_drop__Suc__Cons,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__drop__subset__set__drop,axiom,
% 59.73/59.63 ! [V_xs_2,T_b,V_m_2,V_n_2] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 59.73/59.63 => 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)))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_drop__all,axiom,
% 59.73/59.63 ! [V_n,V_xs,T_a] :
% 59.73/59.63 ( 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))
% 59.73/59.63 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_drop__eq__Nil,axiom,
% 59.73/59.63 ! [V_xs_2,V_n_2,T_b] :
% 59.73/59.63 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 59.73/59.63 <=> 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)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_drop__append,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_append__eq__conv__conj,axiom,
% 59.73/59.63 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 59.73/59.63 <=> ( 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)
% 59.73/59.63 & 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) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_drop__Cons,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_drop__Cons_H,axiom,
% 59.73/59.63 ! [V_xs,V_x,T_a,V_n] :
% 59.73/59.63 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 => 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) )
% 59.73/59.63 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 => 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) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__drop,axiom,
% 59.73/59.63 ! [V_xs,T_a,V_i,V_n] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => 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)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_append__eq__append__conv__if,axiom,
% 59.73/59.63 ! [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] :
% 59.73/59.63 ( 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)
% 59.73/59.63 <=> ( ( 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)))
% 59.73/59.63 => ( 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)
% 59.73/59.63 & 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) ) )
% 59.73/59.63 & ( ~ 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)))
% 59.73/59.63 => ( 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
% 59.73/59.63 & 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 ) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__drop_H,axiom,
% 59.73/59.63 ! [V_xs,T_a,V_i] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rotate__simps,axiom,
% 59.73/59.63 ! [V_xs,V_x,T_b,T_a] :
% 59.73/59.63 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 59.73/59.63 & 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_drop__Cons__number__of,axiom,
% 59.73/59.63 ! [V_xs,V_x,T_a,V_v] :
% 59.73/59.63 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 => 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) )
% 59.73/59.63 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 => 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) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__add,axiom,
% 59.73/59.63 ! [V_xs,T_a,V_j,V_i] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rotate1__length01,axiom,
% 59.73/59.63 ! [V_xs,T_a] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_zip__append2,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_zip__append1,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_id__take__nth__drop,axiom,
% 59.73/59.63 ! [V_xs,T_a,V_i] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__hd__drop,axiom,
% 59.73/59.63 ! [V_xs,T_a,V_n] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_hd__drop__conv__nth,axiom,
% 59.73/59.63 ! [V_n,T_a,V_xs] :
% 59.73/59.63 ( V_xs != c_List_Olist_ONil(T_a)
% 59.73/59.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 59.73/59.63 => 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) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_hd_Osimps,axiom,
% 59.73/59.63 ! [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 ).
% 59.73/59.63
% 59.73/59.63 fof(fact_hd__map,axiom,
% 59.73/59.63 ! [V_f_2,T_c,T_b,V_xs_2] :
% 59.73/59.63 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 59.73/59.63 => 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)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_hd__append,axiom,
% 59.73/59.63 ! [V_ys,T_a,V_xs] :
% 59.73/59.63 ( ( V_xs = c_List_Olist_ONil(T_a)
% 59.73/59.63 => 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) )
% 59.73/59.63 & ( V_xs != c_List_Olist_ONil(T_a)
% 59.73/59.63 => 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) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_hd__append2,axiom,
% 59.73/59.63 ! [V_ys,T_a,V_xs] :
% 59.73/59.63 ( V_xs != c_List_Olist_ONil(T_a)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_hd__in__set,axiom,
% 59.73/59.63 ! [T_b,V_xs_2] :
% 59.73/59.63 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_hd__conv__nth,axiom,
% 59.73/59.63 ! [T_a,V_xs] :
% 59.73/59.63 ( V_xs != c_List_Olist_ONil(T_a)
% 59.73/59.63 => 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)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rotate1__hd__tl,axiom,
% 59.73/59.63 ! [T_a,V_xs] :
% 59.73/59.63 ( V_xs != c_List_Olist_ONil(T_a)
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_hd__rotate__conv__nth,axiom,
% 59.73/59.63 ! [V_n,T_a,V_xs] :
% 59.73/59.63 ( V_xs != c_List_Olist_ONil(T_a)
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_tl__drop,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_drop__tl,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rotate__conv__mod,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_drop__Suc,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_tl__append2,axiom,
% 59.73/59.63 ! [V_ys,T_a,V_xs] :
% 59.73/59.63 ( V_xs != c_List_Olist_ONil(T_a)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rotate__map,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__tl,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rotate__is__Nil__conv,axiom,
% 59.73/59.63 ! [V_xs_2,V_n_2,T_b] :
% 59.73/59.63 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 59.73/59.63 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_tl_Osimps_I1_J,axiom,
% 59.73/59.63 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__rotate,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__rotate,axiom,
% 59.73/59.63 ! [V_xs_2,V_n_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
% 59.73/59.63 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__tl,axiom,
% 59.73/59.63 ! [V_xs,T_a] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 59.73/59.63 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rotate__rotate,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__rotate,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_tl_Osimps_I2_J,axiom,
% 59.73/59.63 ! [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 ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__tl,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rotate1__rotate__swap,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rotate__def,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rotate__Suc,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_tl__append,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rotate0,axiom,
% 59.73/59.63 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rotate__add,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rotate__id,axiom,
% 59.73/59.63 ! [V_xs,T_a,V_n] :
% 59.73/59.63 ( 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)
% 59.73/59.63 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rotate__length01,axiom,
% 59.73/59.63 ! [V_n,V_xs,T_a] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__tl,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_tl__take,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__Suc,axiom,
% 59.73/59.63 ! [V_n,T_a,V_xs] :
% 59.73/59.63 ( V_xs != c_List_Olist_ONil(T_a)
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_rotate__drop__take,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_fold1__set,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] :
% 59.73/59.63 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 59.73/59.63 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 59.73/59.63 => 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)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lexord__append__rightI,axiom,
% 59.73/59.63 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 59.73/59.63 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_foldl__Cons,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_foldl__assoc,axiom,
% 59.73/59.63 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 59.73/59.63 ( class_Groups_Osemigroup__add(T_b)
% 59.73/59.63 => 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)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_foldl__absorb0,axiom,
% 59.73/59.63 ! [V_zs_2,V_x_2,T_b] :
% 59.73/59.63 ( class_Groups_Omonoid__add(T_b)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_foldr__conv__foldl,axiom,
% 59.73/59.63 ! [V_a_2,V_xs_2,T_b] :
% 59.73/59.63 ( class_Groups_Oab__semigroup__add(T_b)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_start__le__sum,axiom,
% 59.73/59.63 ! [V_ns_2,V_n_2,V_m_2] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_foldl__Nil,axiom,
% 59.73/59.63 ! [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 ).
% 59.73/59.63
% 59.73/59.63 fof(fact_foldl__map,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_foldl__append,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_listsum__foldl,axiom,
% 59.73/59.63 ! [T_b] :
% 59.73/59.63 ( class_Groups_Omonoid__add(T_b)
% 59.73/59.63 => 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)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_foldl__foldr1,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] :
% 59.73/59.63 ( class_Groups_Omonoid__add(T_b)
% 59.73/59.63 => 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)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_foldl__foldr1__lemma,axiom,
% 59.73/59.63 ! [V_xs_2,V_a_2,T_b] :
% 59.73/59.63 ( class_Groups_Omonoid__add(T_b)
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_sum__eq__0__conv,axiom,
% 59.73/59.63 ! [V_ns_2,V_m_2] :
% 59.73/59.63 ( 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)
% 59.73/59.63 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 & ! [B_x] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 59.73/59.63 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 59.73/59.63 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 59.73/59.63 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Sup__set__fold,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] :
% 59.73/59.63 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Inf__set__fold,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] :
% 59.73/59.63 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Sup__fin__set__fold,axiom,
% 59.73/59.63 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( class_Lattices_Olattice(T_b)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Inf__fin__set__fold,axiom,
% 59.73/59.63 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( class_Lattices_Olattice(T_b)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Min__fin__set__fold,axiom,
% 59.73/59.63 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( class_Orderings_Olinorder(T_b)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Max__fin__set__fold,axiom,
% 59.73/59.63 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( class_Orderings_Olinorder(T_b)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 59.73/59.63 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( class_Orderings_Olinorder(T_b)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 59.73/59.63 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( class_Orderings_Olinorder(T_b)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_SUPR__set__fold,axiom,
% 59.73/59.63 ! [V_f_2,V_xs_2,T_c,T_b] :
% 59.73/59.63 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_INFI__set__fold,axiom,
% 59.73/59.63 ! [V_f_2,V_xs_2,T_c,T_b] :
% 59.73/59.63 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__upds__fold__map__upd,axiom,
% 59.73/59.63 ! [V_vs_2,V_ks_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_ks_2,V_vs_2) = hAPP(c_List_Ofoldl(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_prod(T_b,T_c),tc_fun(T_b,tc_Option_Ooption(T_c))),tc_fun(T_b,tc_Option_Ooption(T_c))),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(T_b,tc_Option_Ooption(T_c))),c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(T_b,tc_Option_Ooption(T_c))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)),T_c))),c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c))))),c_Option_Ooption_OSome(T_c))),V_m_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_ks_2),V_vs_2)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_elem__le__sum,axiom,
% 59.73/59.63 ! [V_ns_2,V_n_2] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lexord__Nil__left,axiom,
% 59.73/59.63 ! [V_r_2,V_y_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_last__list__update,axiom,
% 59.73/59.63 ! [V_x,V_k,T_a,V_xs] :
% 59.73/59.63 ( V_xs != c_List_Olist_ONil(T_a)
% 59.73/59.63 => ( ( 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))
% 59.73/59.63 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 59.73/59.63 & ( 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))
% 59.73/59.63 => 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) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_last__appendL,axiom,
% 59.73/59.63 ! [V_xs,T_a,V_ys] :
% 59.73/59.63 ( V_ys = c_List_Olist_ONil(T_a)
% 59.73/59.63 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_last__appendR,axiom,
% 59.73/59.63 ! [V_xs,T_a,V_ys] :
% 59.73/59.63 ( V_ys != c_List_Olist_ONil(T_a)
% 59.73/59.63 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_last__append,axiom,
% 59.73/59.63 ! [V_xs,T_a,V_ys] :
% 59.73/59.63 ( ( V_ys = c_List_Olist_ONil(T_a)
% 59.73/59.63 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 59.73/59.63 & ( V_ys != c_List_Olist_ONil(T_a)
% 59.73/59.63 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_last__map,axiom,
% 59.73/59.63 ! [V_f_2,T_c,T_b,V_xs_2] :
% 59.73/59.63 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 59.73/59.63 => 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)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_last_Osimps,axiom,
% 59.73/59.63 ! [V_x,T_a,V_xs] :
% 59.73/59.63 ( ( V_xs = c_List_Olist_ONil(T_a)
% 59.73/59.63 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 59.73/59.63 & ( V_xs != c_List_Olist_ONil(T_a)
% 59.73/59.63 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_last__ConsR,axiom,
% 59.73/59.63 ! [V_x,T_a,V_xs] :
% 59.73/59.63 ( V_xs != c_List_Olist_ONil(T_a)
% 59.73/59.63 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_last__ConsL,axiom,
% 59.73/59.63 ! [V_x,T_a,V_xs] :
% 59.73/59.63 ( V_xs = c_List_Olist_ONil(T_a)
% 59.73/59.63 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_last__in__set,axiom,
% 59.73/59.63 ! [T_b,V_as_2] :
% 59.73/59.63 ( V_as_2 != c_List_Olist_ONil(T_b)
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_last__snoc,axiom,
% 59.73/59.63 ! [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 ).
% 59.73/59.63
% 59.73/59.63 fof(fact_last__drop,axiom,
% 59.73/59.63 ! [V_xs,T_a,V_n] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 59.73/59.63 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_last__conv__nth,axiom,
% 59.73/59.63 ! [T_a,V_xs] :
% 59.73/59.63 ( V_xs != c_List_Olist_ONil(T_a)
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__zip__enum__is__Some,axiom,
% 59.73/59.63 ! [V_x,V_ys,T_b,T_a] :
% 59.73/59.63 ( class_Enum_Oenum(T_a)
% 59.73/59.63 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))
% 59.73/59.63 => ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a)),V_ys)),V_x) = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lexord__irreflexive,axiom,
% 59.73/59.63 ! [V_y_2,V_r_2,T_b] :
% 59.73/59.63 ( ! [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))
% 59.73/59.63 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lexord__linear,axiom,
% 59.73/59.63 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 59.73/59.63 ( ! [B_a,B_b] :
% 59.73/59.63 ( 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))
% 59.73/59.63 | B_a = B_b
% 59.73/59.63 | 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)) )
% 59.73/59.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 59.73/59.63 | V_x_2 = V_y_2
% 59.73/59.63 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_lists_Osimps,axiom,
% 59.73/59.63 ! [V_A_2,V_a_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 59.73/59.63 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 59.73/59.63 | ? [B_a,B_l] :
% 59.73/59.63 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 59.73/59.63 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 59.73/59.63 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_weak__map__of__SomeI,axiom,
% 59.73/59.63 ! [V_l_2,V_x_2,V_k_2,T_c,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_k_2),V_x_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_l_2)))
% 59.73/59.63 => ? [B_x] : hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_l_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_x) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_list__size__pointwise,axiom,
% 59.73/59.63 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 59.73/59.63 ( ! [B_x] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 59.73/59.63 => 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))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_butlast__take,axiom,
% 59.73/59.63 ! [V_xs,T_a,V_n] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_butlast__drop,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_drop__butlast,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_butlast__append,axiom,
% 59.73/59.63 ! [V_xs,T_a,V_ys] :
% 59.73/59.63 ( ( V_ys = c_List_Olist_ONil(T_a)
% 59.73/59.63 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 59.73/59.63 & ( V_ys != c_List_Olist_ONil(T_a)
% 59.73/59.63 => 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)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__butlast,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_butlast_Osimps_I1_J,axiom,
% 59.73/59.63 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__butlast,axiom,
% 59.73/59.63 ! [T_a,V_xs] :
% 59.73/59.63 ( V_xs != c_List_Olist_ONil(T_a)
% 59.73/59.63 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 59.73/59.63 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_in__set__butlastD,axiom,
% 59.73/59.63 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 59.73/59.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_butlast_Osimps_I2_J,axiom,
% 59.73/59.63 ! [V_x,T_a,V_xs] :
% 59.73/59.63 ( ( V_xs = c_List_Olist_ONil(T_a)
% 59.73/59.63 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 59.73/59.63 & ( V_xs != c_List_Olist_ONil(T_a)
% 59.73/59.63 => 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)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_in__set__butlast__appendI,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 59.73/59.63 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 59.73/59.63 => 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))))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_butlast__snoc,axiom,
% 59.73/59.63 ! [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 ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__butlast,axiom,
% 59.73/59.63 ! [V_xs,T_a,V_n] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__butlast,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_butlast__conv__take,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_butlast__list__update,axiom,
% 59.73/59.63 ! [V_x,V_xs,T_a,V_k] :
% 59.73/59.63 ( ( 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))
% 59.73/59.63 => 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) )
% 59.73/59.63 & ( 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))
% 59.73/59.63 => 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) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_append__butlast__last__id,axiom,
% 59.73/59.63 ! [T_a,V_xs] :
% 59.73/59.63 ( V_xs != c_List_Olist_ONil(T_a)
% 59.73/59.63 => 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 ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_snoc__eq__iff__butlast,axiom,
% 59.73/59.63 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 59.73/59.63 ( 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
% 59.73/59.63 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 59.73/59.63 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 59.73/59.63 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__take__lemma,axiom,
% 59.73/59.63 ! [V_ys,V_xs,T_a,V_k] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => ( 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)))
% 59.73/59.63 => ( ! [B_i] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 59.73/59.63 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 59.73/59.63 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__transpose,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_transpose_Osimps_I1_J,axiom,
% 59.73/59.63 ! [T_a] : c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_transpose_Osimps_I2_J,axiom,
% 59.73/59.63 ! [V_xss,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss)) = c_List_Otranspose(T_a,V_xss) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_transpose__map__map,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_transpose__empty,axiom,
% 59.73/59.63 ! [V_xs_2,T_b] :
% 59.73/59.63 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 59.73/59.63 <=> ! [B_x] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 59.73/59.63 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_transpose_Opsimps_I2_J,axiom,
% 59.73/59.63 ! [V_xss_2,T_b] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_transpose__max__length,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_filter__append,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__filter__map,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_filter__map,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_filter__empty__conv,axiom,
% 59.73/59.63 ! [V_xs_2,V_P_2,T_b] :
% 59.73/59.63 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 59.73/59.63 <=> ! [B_x] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_filter_Osimps_I1_J,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_filter__is__subset,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_sum__length__filter__compl,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__filter__le,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__filter,axiom,
% 59.73/59.63 ! [V_P_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.63 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_filter__filter,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_filter__id__conv,axiom,
% 59.73/59.63 ! [V_xs_2,V_P_2,T_b] :
% 59.73/59.63 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = V_xs_2
% 59.73/59.63 <=> ! [B_x] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_filter_Osimps_I2_J,axiom,
% 59.73/59.63 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 59.73/59.63 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.63 => 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)) )
% 59.73/59.63 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.63 => 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) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__filter,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__filter__less,axiom,
% 59.73/59.63 ! [V_P_2,V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.63 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.63 => 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))) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__minus__filter__out,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_filter__in__sublist,axiom,
% 59.73/59.63 ! [V_s_2,V_xs_2,T_b] :
% 59.73/59.63 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.63 => 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) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__filter__conv__card,axiom,
% 59.73/59.63 ! [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))))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_nth__transpose,axiom,
% 59.73/59.63 ! [V_xs_2,T_b,V_i_2] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
% 59.73/59.63 => 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)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_transpose__aux__max,axiom,
% 59.73/59.63 ! [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)))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_transpose_Opsimps_I1_J,axiom,
% 59.73/59.63 ! [T_b] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__filter__def,axiom,
% 59.73/59.63 ! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_c,c_Option_Othe(T_b)),V_f_2)),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_c),c_fequal),V_f_2)),c_Option_Ooption_ONone(T_b)))),V_xs_2)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_transpose__aux__filter__head,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__concat,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_foldl__conv__concat,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_concat__conv__foldl,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__filter__simps_I2_J,axiom,
% 59.73/59.63 ! [V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_concat_Osimps_I1_J,axiom,
% 59.73/59.63 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_concat_Osimps_I2_J,axiom,
% 59.73/59.63 ! [V_xs,V_x,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),V_x),c_List_Oconcat(T_a,V_xs)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_concat__eq__Nil__conv,axiom,
% 59.73/59.63 ! [V_xss_2,T_b] :
% 59.73/59.63 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 59.73/59.63 <=> ! [B_x] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 59.73/59.63 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_Nil__eq__concat__conv,axiom,
% 59.73/59.63 ! [V_xss_2,T_b] :
% 59.73/59.63 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 59.73/59.63 <=> ! [B_x] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 59.73/59.63 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_filter__concat,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__concat,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__of__filter__in,axiom,
% 59.73/59.63 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_b,T_c] :
% 59.73/59.63 ( hAPP(hAPP(c_Map_Omap__of(T_c,T_b),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2)
% 59.73/59.63 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2))
% 59.73/59.63 => hAPP(hAPP(c_Map_Omap__of(T_c,T_b),hAPP(c_List_Ofilter(tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__filter__simps_I1_J,axiom,
% 59.73/59.63 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(T_b),T_b,c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2))),hAPP(V_f_2,V_x_2)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__concat,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_concat__append,axiom,
% 59.73/59.63 ! [V_ys,V_xs,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Oappend(tc_List_Olist(T_a)),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oconcat(T_a,V_xs)),c_List_Oconcat(T_a,V_ys)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_sublist__shift__lemma__Suc,axiom,
% 59.73/59.63 ! [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)))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_pick__drop__zero,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_select__weigth__drop__zero,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_transpose_Osimps_I3_J,axiom,
% 59.73/59.63 ! [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))))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_concat__injective,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 59.73/59.63 => ( 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)
% 59.73/59.63 => ( ! [B_x] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 => 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)) )
% 59.73/59.63 => V_xs_2 = V_ys_2 ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_concat__eq__concat__iff,axiom,
% 59.73/59.63 ! [V_ys_2,V_xs_2,T_b] :
% 59.73/59.63 ( ! [B_x] :
% 59.73/59.63 ( 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))))
% 59.73/59.63 => 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)) )
% 59.73/59.63 => ( 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)
% 59.73/59.63 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 59.73/59.63 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_concat__map__singleton,axiom,
% 59.73/59.63 ! [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) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_n__lists_Osimps_I2_J,axiom,
% 59.73/59.63 ! [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))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_transpose_Opsimps_I3_J,axiom,
% 59.73/59.63 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 59.73/59.63 ( 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)))
% 59.73/59.63 => 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))))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_transpose__aux__filter__tail,axiom,
% 59.73/59.63 ! [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)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__filter__map__filter,axiom,
% 59.73/59.63 ! [V_xs_2,V_P_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2)) = c_List_Omap__filter(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBS(T_c,tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),T_c),c_If(tc_Option_Ooption(T_b))),V_P_2)),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_c),c_Option_Ooption_OSome(T_b)),V_f_2))),c_Option_Ooption_ONone(T_b)),V_xs_2) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_sublist__def,axiom,
% 59.73/59.63 ! [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))))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_sublist__shift__lemma,axiom,
% 59.73/59.63 ! [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))))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_map__Suc__upt,axiom,
% 59.73/59.63 ! [V_n_2,V_m_2] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(V_m_2,V_n_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_drop__upt,axiom,
% 59.73/59.63 ! [V_j,V_i,V_m] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_j)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m),V_j) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_hd__upt,axiom,
% 59.73/59.63 ! [V_j,V_i] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 59.73/59.63 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_upt__Suc,axiom,
% 59.73/59.63 ! [V_j,V_i] :
% 59.73/59.63 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 59.73/59.63 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) )
% 59.73/59.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 59.73/59.63 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_upt__Suc__append,axiom,
% 59.73/59.63 ! [V_j,V_i] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 59.73/59.63 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_upt__add__eq__append,axiom,
% 59.73/59.63 ! [V_k,V_j,V_i] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 59.73/59.63 => c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),c_List_Oupt(V_j,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_upt__0,axiom,
% 59.73/59.63 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_upt__conv__Nil,axiom,
% 59.73/59.63 ! [V_i,V_j] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 59.73/59.63 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_upt__eq__Nil__conv,axiom,
% 59.73/59.63 ! [V_j_2,V_i_2] :
% 59.73/59.63 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 59.73/59.63 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.63 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_set__upt,axiom,
% 59.73/59.63 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_atLeastLessThan__upt,axiom,
% 59.73/59.63 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_distinct__upt,axiom,
% 59.73/59.63 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_take__upt,axiom,
% 59.73/59.63 ! [V_n,V_m,V_i] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n))
% 59.73/59.63 => hAPP(hAPP(c_List_Otake(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_n)) = c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_upt__conv__Cons,axiom,
% 59.73/59.63 ! [V_j,V_i] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 59.73/59.63 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_upt__rec,axiom,
% 59.73/59.63 ! [V_j,V_i] :
% 59.73/59.63 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 59.73/59.63 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) )
% 59.73/59.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 59.73/59.63 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_length__upt,axiom,
% 59.73/59.63 ! [V_j,V_i] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_upt__rec__number__of,axiom,
% 59.73/59.63 ! [V_n,V_m] :
% 59.73/59.63 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
% 59.73/59.63 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) )
% 59.73/59.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
% 59.73/59.63 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_upt__eq__Cons__conv,axiom,
% 59.73/59.63 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 59.73/59.63 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 59.73/59.63 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 59.73/59.63 & V_i_2 = V_x_2
% 59.73/59.63 & c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_j_2) = V_xs_2 ) ) ).
% 59.73/59.63
% 59.73/59.63 fof(fact_last__upt,axiom,
% 59.73/59.63 ! [V_j,V_i] :
% 59.73/59.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 59.73/59.63 => c_List_Olast(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_map__nth,axiom,
% 59.73/59.64 ! [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 ).
% 59.73/59.64
% 59.73/59.64 fof(fact_atLeastAtMost__upt,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_atLeast__upt,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 59.73/59.64 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 59.73/59.64 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.64 => 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))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 59.73/59.64 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 59.73/59.64 ( class_Groups_Ocomm__monoid__add(T_b)
% 59.73/59.64 => 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))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_nth__upt,axiom,
% 59.73/59.64 ! [V_j,V_k,V_i] :
% 59.73/59.64 ( 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))
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_greaterThanAtMost__upt,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_greaterThanLessThan__upt,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_nth__map__upt,axiom,
% 59.73/59.64 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_atMost__upto,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_transpose__rectangle,axiom,
% 59.73/59.64 ! [V_n_2,T_b,V_xs_2] :
% 59.73/59.64 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 59.73/59.64 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 59.73/59.64 => ( ! [B_i] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => 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 )
% 59.73/59.64 => 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)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_length__remdups__concat,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_distinct__remdups,axiom,
% 59.73/59.64 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_length__remdups__leq,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_remdups__filter,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_remdups__map__remdups,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_set__remdups,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_remdups__remdups,axiom,
% 59.73/59.64 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_distinct__remdups__id,axiom,
% 59.73/59.64 ! [V_xs,T_a] :
% 59.73/59.64 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 59.73/59.64 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_remdups__id__iff__distinct,axiom,
% 59.73/59.64 ! [V_xs_2,T_b] :
% 59.73/59.64 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
% 59.73/59.64 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_length__remdups__eq,axiom,
% 59.73/59.64 ! [V_xs_2,T_b] :
% 59.73/59.64 ( 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)
% 59.73/59.64 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_remdups_Osimps_I1_J,axiom,
% 59.73/59.64 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_remdups__eq__nil__right__iff,axiom,
% 59.73/59.64 ! [V_x_2,T_b] :
% 59.73/59.64 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
% 59.73/59.64 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_remdups__eq__nil__iff,axiom,
% 59.73/59.64 ! [V_x_2,T_b] :
% 59.73/59.64 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
% 59.73/59.64 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_remdups_Osimps_I2_J,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => 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) )
% 59.73/59.64 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => 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)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_length__remdups__card__conv,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 59.73/59.64 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 59.73/59.64 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 59.73/59.64 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_listsum__map__filter,axiom,
% 59.73/59.64 ! [V_f_2,V_P_2,V_xs_2,T_b,T_c] :
% 59.73/59.64 ( class_Groups_Omonoid__add(T_c)
% 59.73/59.64 => ( ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => ( ~ hBOOL(hAPP(V_P_2,B_x))
% 59.73/59.64 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
% 59.73/59.64 => 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)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_return__list__def,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 59.73/59.64 ! [V_l] :
% 59.73/59.64 ( c_List_Onat__list(V_l)
% 59.73/59.64 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_embed__list__def,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_listsum__map__remove1,axiom,
% 59.73/59.64 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 59.73/59.64 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => 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)))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_set__remove1__eq,axiom,
% 59.73/59.64 ! [V_x_2,V_xs_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.64 => 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)))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_remove1_Osimps_I2_J,axiom,
% 59.73/59.64 ! [V_xs,T_a,V_y,V_x] :
% 59.73/59.64 ( ( V_x = V_y
% 59.73/59.64 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 59.73/59.64 & ( V_x != V_y
% 59.73/59.64 => 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)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_remove1__remdups,axiom,
% 59.73/59.64 ! [V_x,V_xs,T_a] :
% 59.73/59.64 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_distinct__remove1,axiom,
% 59.73/59.64 ! [V_x,V_xs,T_a] :
% 59.73/59.64 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 59.73/59.64 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_remove1_Osimps_I1_J,axiom,
% 59.73/59.64 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_remove1__commute,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_remove1__idem,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_notin__set__remove1,axiom,
% 59.73/59.64 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => ~ 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)))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_in__set__remove1,axiom,
% 59.73/59.64 ! [V_xs_2,T_b,V_b_2,V_a_2] :
% 59.73/59.64 ( V_a_2 != V_b_2
% 59.73/59.64 => ( 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))))
% 59.73/59.64 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_set__remove1__subset,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_remove1__filter__not,axiom,
% 59.73/59.64 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 59.73/59.64 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_filter__remove1,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_remove1__append,axiom,
% 59.73/59.64 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => 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) )
% 59.73/59.64 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => 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)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_length__remove1,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => 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)) )
% 59.73/59.64 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => 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) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__list__of__set__remove,axiom,
% 59.73/59.64 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.64 => 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)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_partition__set,axiom,
% 59.73/59.64 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( 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)
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_partition__filter2,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_partition__filter1,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__list__of__set__empty,axiom,
% 59.73/59.64 ! [T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__list__of__set__range,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_partition__P,axiom,
% 59.73/59.64 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( 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)
% 59.73/59.64 => ( ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 59.73/59.64 => hBOOL(hAPP(V_P_2,B_x)) )
% 59.73/59.64 & ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 59.73/59.64 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_partition_Osimps_I1_J,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_partition__filter__conv,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_partition_Osimps_I2_J,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__list__of__set__insert,axiom,
% 59.73/59.64 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.64 => 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)))))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 59.73/59.64 ! [V_xs_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sort__foldl__insort,axiom,
% 59.73/59.64 ! [V_xs_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_insort__key_Osimps_I1_J,axiom,
% 59.73/59.64 ! [V_x_2,V_f_2,T_b,T_c] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_c)
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sort__key__simps_I2_J,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_c)
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_insort__key_Osimps_I2_J,axiom,
% 59.73/59.64 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( ( 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)))
% 59.73/59.64 => 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)) )
% 59.73/59.64 & ( ~ 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)))
% 59.73/59.64 => 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)) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_distinct__sort,axiom,
% 59.73/59.64 ! [V_xs_2,V_f_2,T_b,T_c] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_c)
% 59.73/59.64 => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))
% 59.73/59.64 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_insort__not__Nil,axiom,
% 59.73/59.64 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_c)
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sort__key__simps_I1_J,axiom,
% 59.73/59.64 ! [V_f_2,T_b,T_c] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_c)
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_length__insort,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_c)
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_length__sort,axiom,
% 59.73/59.64 ! [V_xs_2,V_f_2,T_b,T_c] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_c)
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_insort__left__comm,axiom,
% 59.73/59.64 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_insort__key__left__comm,axiom,
% 59.73/59.64 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 59.73/59.64 => 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)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_fun__left__comm__insort,axiom,
% 59.73/59.64 ! [T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => 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))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_set__insort,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_c)
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_set__sort,axiom,
% 59.73/59.64 ! [V_xs_2,V_f_2,T_b,T_c] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_c)
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_filter__insort__triv,axiom,
% 59.73/59.64 ! [V_xs_2,V_f_2,T_b,V_x_2,V_P_2,T_c] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_c)
% 59.73/59.64 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 => 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) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_filter__sort,axiom,
% 59.73/59.64 ! [V_xs_2,V_f_2,V_P_2,T_b,T_c] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_c)
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_remove1__insort,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => 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 ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_distinct__insort,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_c)
% 59.73/59.64 => ( 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)))
% 59.73/59.64 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_insort__key__remove1,axiom,
% 59.73/59.64 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_c)
% 59.73/59.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 59.73/59.64 => ( 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
% 59.73/59.64 => 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 ) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_insort__insert__insort__key,axiom,
% 59.73/59.64 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( ~ 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))))
% 59.73/59.64 => 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) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted_ONil,axiom,
% 59.73/59.64 ! [T_a] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_a)
% 59.73/59.64 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__single,axiom,
% 59.73/59.64 ! [V_x,T_a] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_a)
% 59.73/59.64 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__insort,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( 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))
% 59.73/59.64 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__sort,axiom,
% 59.73/59.64 ! [V_xs_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__sort__key,axiom,
% 59.73/59.64 ! [V_xs_2,V_f_2,T_c,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => 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))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__insort__key,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( 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)))
% 59.73/59.64 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__insort__insert__key,axiom,
% 59.73/59.64 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 59.73/59.64 => 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))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__map__remove1,axiom,
% 59.73/59.64 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 59.73/59.64 => 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))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__map__same,axiom,
% 59.73/59.64 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => 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))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__filter,axiom,
% 59.73/59.64 ! [V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 59.73/59.64 => 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))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__remove1,axiom,
% 59.73/59.64 ! [V_a,V_xs,T_a] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_a)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 59.73/59.64 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__same,axiom,
% 59.73/59.64 ! [V_xs_2,V_g_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__upt,axiom,
% 59.73/59.64 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__tl,axiom,
% 59.73/59.64 ! [V_xs,T_a] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_a)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 59.73/59.64 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__upto,axiom,
% 59.73/59.64 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__insort__insert,axiom,
% 59.73/59.64 ! [V_x_2,V_xs_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 59.73/59.64 => 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)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__drop,axiom,
% 59.73/59.64 ! [V_n,V_xs,T_a] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_a)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 59.73/59.64 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted_Oequations_I1_J,axiom,
% 59.73/59.64 ! [T_a] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_a)
% 59.73/59.64 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_distinct__insort__insert,axiom,
% 59.73/59.64 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_c)
% 59.73/59.64 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.64 => 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))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__remdups,axiom,
% 59.73/59.64 ! [V_l,T_a] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_a)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 59.73/59.64 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__take,axiom,
% 59.73/59.64 ! [V_n,V_xs,T_a] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_a)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 59.73/59.64 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__many__eq,axiom,
% 59.73/59.64 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( 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)))
% 59.73/59.64 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 59.73/59.64 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__many,axiom,
% 59.73/59.64 ! [V_zs,V_y,V_x,T_a] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_a)
% 59.73/59.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 59.73/59.64 => 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))) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__butlast,axiom,
% 59.73/59.64 ! [V_xs,T_a] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_a)
% 59.73/59.64 => ( V_xs != c_List_Olist_ONil(T_a)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 59.73/59.64 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__distinct__set__unique,axiom,
% 59.73/59.64 ! [V_ys_2,V_xs_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 59.73/59.64 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 59.73/59.64 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 59.73/59.64 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 59.73/59.64 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__Cons,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 59.73/59.64 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 59.73/59.64 & ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__append,axiom,
% 59.73/59.64 ! [V_ys_2,V_xs_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 59.73/59.64 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 59.73/59.64 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 59.73/59.64 & ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => ! [B_xa] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 59.73/59.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_filter__insort,axiom,
% 59.73/59.64 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 59.73/59.64 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 => 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)) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted_Oequations_I2_J,axiom,
% 59.73/59.64 ! [V_a1_2,V_a2_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 59.73/59.64 <=> ( ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 59.73/59.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 59.73/59.64 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_insort__insert__triv,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_set__insort__insert,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__list__of__set,axiom,
% 59.73/59.64 ! [V_A_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.64 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 59.73/59.64 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 59.73/59.64 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_insort__remove1,axiom,
% 59.73/59.64 ! [V_xs_2,V_a_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 59.73/59.64 => 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 ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__equals__nth__mono,axiom,
% 59.73/59.64 ! [V_xs_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 59.73/59.64 <=> ! [B_j] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => ! [B_i] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 59.73/59.64 => 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))) ) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__nth__mono,axiom,
% 59.73/59.64 ! [V_j,V_i,V_xs,T_a] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_a)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 59.73/59.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 59.73/59.64 => ( 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)))
% 59.73/59.64 => 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))) ) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_map__sorted__distinct__set__unique,axiom,
% 59.73/59.64 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_c)
% 59.73/59.64 => ( 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)))
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 59.73/59.64 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 59.73/59.64 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 59.73/59.64 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 59.73/59.64 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_insort__insert__key__triv,axiom,
% 59.73/59.64 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( 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))))
% 59.73/59.64 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_insort__insert__insort,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => 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) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_transpose__column,axiom,
% 59.73/59.64 ! [V_i_2,V_xs_2,T_b] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => ( 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)))
% 59.73/59.64 => 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) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_nth__nth__transpose__sorted,axiom,
% 59.73/59.64 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => ( 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))))
% 59.73/59.64 => ( 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))))
% 59.73/59.64 => 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) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_inj__on__rev,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_foldr__foldl,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_foldl__foldr,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rev__append,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_singleton__rev__conv,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( 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)
% 59.73/59.64 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rev__singleton__conv,axiom,
% 59.73/59.64 ! [V_x_2,V_xs_2,T_b] :
% 59.73/59.64 ( 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))
% 59.73/59.64 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_distinct__rev,axiom,
% 59.73/59.64 ! [V_xs_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 59.73/59.64 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rev_Osimps_I1_J,axiom,
% 59.73/59.64 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_Nil__is__rev__conv,axiom,
% 59.73/59.64 ! [V_xs_2,T_b] :
% 59.73/59.64 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 59.73/59.64 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rev__is__Nil__conv,axiom,
% 59.73/59.64 ! [V_xs_2,T_b] :
% 59.73/59.64 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 59.73/59.64 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_length__rev,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rev__rev__ident,axiom,
% 59.73/59.64 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rev__swap,axiom,
% 59.73/59.64 ! [V_ys_2,V_xs_2,T_b] :
% 59.73/59.64 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 59.73/59.64 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rev__is__rev__conv,axiom,
% 59.73/59.64 ! [V_ys_2,V_xs_2,T_b] :
% 59.73/59.64 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 59.73/59.64 <=> V_xs_2 = V_ys_2 ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_listsum__rev,axiom,
% 59.73/59.64 ! [V_xs,T_a] :
% 59.73/59.64 ( class_Groups_Ocomm__monoid__add(T_a)
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_set__rev,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_zip__rev,axiom,
% 59.73/59.64 ! [V_ys,T_b,V_xs,T_a] :
% 59.73/59.64 ( 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)
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rev__filter,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rev__concat,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rev__map,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rev__eq__Cons__iff,axiom,
% 59.73/59.64 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 59.73/59.64 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 59.73/59.64 <=> 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))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rev_Osimps_I2_J,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_hd__rev,axiom,
% 59.73/59.64 ! [T_a,V_xs] :
% 59.73/59.64 ( V_xs != c_List_Olist_ONil(T_a)
% 59.73/59.64 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_last__rev,axiom,
% 59.73/59.64 ! [T_a,V_xs] :
% 59.73/59.64 ( V_xs != c_List_Olist_ONil(T_a)
% 59.73/59.64 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__transpose,axiom,
% 59.73/59.64 ! [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)))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rev__foldl__cons,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rev__drop,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rev__take,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rotate__rev,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rev__nth,axiom,
% 59.73/59.64 ! [V_xs,T_a,V_n] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => 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))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rev__update,axiom,
% 59.73/59.64 ! [V_y,V_xs,T_a,V_k] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__rev__nth__mono,axiom,
% 59.73/59.64 ! [V_j,V_i,V_xs,T_a] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_a)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 59.73/59.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 59.73/59.64 => ( 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)))
% 59.73/59.64 => 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))) ) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_foldr__max__sorted,axiom,
% 59.73/59.64 ! [V_y_2,V_xs_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 59.73/59.64 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 59.73/59.64 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 59.73/59.64 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 59.73/59.64 => 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) ) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_length__transpose__sorted,axiom,
% 59.73/59.64 ! [V_xs_2,T_b] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 59.73/59.64 => 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) )
% 59.73/59.64 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 59.73/59.64 => 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))) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_transpose__column__length,axiom,
% 59.73/59.64 ! [V_i_2,V_xs_2,T_b] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => ( 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)))
% 59.73/59.64 => 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)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_transpose__transpose,axiom,
% 59.73/59.64 ! [V_xs_2,T_b] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__nth__monoI,axiom,
% 59.73/59.64 ! [V_xs,T_a] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_a)
% 59.73/59.64 => ( ! [B_i,B_j] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 59.73/59.64 => ( 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)))
% 59.73/59.64 => 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))) ) )
% 59.73/59.64 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__takeWhile,axiom,
% 59.73/59.64 ! [V_P_2,V_xs_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 59.73/59.64 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_zip__takeWhile__snd,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_zip__takeWhile__fst,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_takeWhile__map,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_takeWhile__eq__all__conv,axiom,
% 59.73/59.64 ! [V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = V_xs_2
% 59.73/59.64 <=> ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_set__takeWhileD,axiom,
% 59.73/59.64 ! [V_xs_2,V_P_2,V_x_2,T_b] :
% 59.73/59.64 ( 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))))
% 59.73/59.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_length__takeWhile__le,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_distinct__takeWhile,axiom,
% 59.73/59.64 ! [V_P_2,V_xs_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.64 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_takeWhile__eq__take,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 59.73/59.64 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 59.73/59.64 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 => 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)) )
% 59.73/59.64 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 => 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) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_takeWhile__tail,axiom,
% 59.73/59.64 ! [V_l_2,V_xs_2,T_b,V_x_2,V_P_2] :
% 59.73/59.64 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_takeWhile__append1,axiom,
% 59.73/59.64 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 => 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) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_nth__length__takeWhile,axiom,
% 59.73/59.64 ! [V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => ~ 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))))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_takeWhile__nth,axiom,
% 59.73/59.64 ! [V_xs_2,V_P_2,T_b,V_j_2] :
% 59.73/59.64 ( 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))))
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_map__upds__def,axiom,
% 59.73/59.64 ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_b,T_c,V_m_2,hAPP(c_Map_Omap__of(T_b,T_c),hAPP(c_List_Orev(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_takeWhile__not__last,axiom,
% 59.73/59.64 ! [T_b,V_xs_2] :
% 59.73/59.64 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 59.73/59.64 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.64 => 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) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 59.73/59.64 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( 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)))
% 59.73/59.64 => 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) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_takeWhile__neq__rev,axiom,
% 59.73/59.64 ! [V_x_2,V_xs_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => 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))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_dropWhile__neq__rev,axiom,
% 59.73/59.64 ! [V_x_2,V_xs_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => 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))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_takeWhile__dropWhile__id,axiom,
% 59.73/59.64 ! [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 ).
% 59.73/59.64
% 59.73/59.64 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 59.73/59.64 ! [V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) = c_List_Olist_ONil(T_b)
% 59.73/59.64 <=> ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 59.73/59.64 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 59.73/59.64 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 => 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) )
% 59.73/59.64 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 => 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) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_distinct__dropWhile,axiom,
% 59.73/59.64 ! [V_P_2,V_xs_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 59.73/59.64 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_hd__dropWhile,axiom,
% 59.73/59.64 ! [V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) != c_List_Olist_ONil(T_b)
% 59.73/59.64 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_length__dropWhile__le,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted__dropWhile,axiom,
% 59.73/59.64 ! [V_P_2,V_xs_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 59.73/59.64 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_P_2,V_xs_2)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_dropWhile__map,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_dropWhile__append1,axiom,
% 59.73/59.64 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 => 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) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 59.73/59.64 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( 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)
% 59.73/59.64 <=> ( 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))
% 59.73/59.64 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_dropWhile__eq__drop,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_dropWhile__nth,axiom,
% 59.73/59.64 ! [V_xs_2,V_P_2,T_b,V_j_2] :
% 59.73/59.64 ( 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))))
% 59.73/59.64 => 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)))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_takeWhile__eq__filter,axiom,
% 59.73/59.64 ! [V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( ! [B_x] :
% 59.73/59.64 ( 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))))
% 59.73/59.64 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 59.73/59.64 => c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 59.73/59.64 ! [V_P_2,V_xs_2,T_b,V_n_2] :
% 59.73/59.64 ( ! [B_i] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 59.73/59.64 => ( 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)))
% 59.73/59.64 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) )
% 59.73/59.64 => ( ( 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)))
% 59.73/59.64 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) )
% 59.73/59.64 => c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_length__takeWhile__less__P__nth,axiom,
% 59.73/59.64 ! [V_xs_2,T_b,V_P_2,V_j_2] :
% 59.73/59.64 ( ! [B_i] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 59.73/59.64 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 59.73/59.64 => ( 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)))
% 59.73/59.64 => 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)))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_lists__IntI,axiom,
% 59.73/59.64 ! [V_B_2,V_A_2,V_l_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2)))
% 59.73/59.64 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2)))
% 59.73/59.64 => 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)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_listsp_ONil,axiom,
% 59.73/59.64 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_append__in__listsp__conv,axiom,
% 59.73/59.64 ! [V_ys_2,V_xs_2,V_A_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 59.73/59.64 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 59.73/59.64 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_listsp_Oequations_I2_J,axiom,
% 59.73/59.64 ! [V_a2_2,V_a1_2,V_A_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2)))
% 59.73/59.64 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 59.73/59.64 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_listsp_Oequations_I1_J,axiom,
% 59.73/59.64 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_listsp__inf__eq,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_listsp__infI,axiom,
% 59.73/59.64 ! [V_B_2,V_l_2,V_A_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2))
% 59.73/59.64 => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2))
% 59.73/59.64 => 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)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_listsp__conj__eq,axiom,
% 59.73/59.64 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 59.73/59.64 ( 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))
% 59.73/59.64 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2))
% 59.73/59.64 & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_in__listsp__conv__set,axiom,
% 59.73/59.64 ! [V_xs_2,V_A_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 59.73/59.64 <=> ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_listsp__mono,axiom,
% 59.73/59.64 ! [V_B_2,V_A_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 59.73/59.64 => 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))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_listsp__lists__eq,axiom,
% 59.73/59.64 ! [V_x_2,V_A_2,T_b] :
% 59.73/59.64 ( 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))
% 59.73/59.64 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_lists__Int__eq,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__def,axiom,
% 59.73/59.64 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 59.73/59.64 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 59.73/59.64 <=> ( 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)
% 59.73/59.64 & ! [B_x] :
% 59.73/59.64 ( 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))))
% 59.73/59.64 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted_Osimps,axiom,
% 59.73/59.64 ! [V_a_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_b,V_a_2)
% 59.73/59.64 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 59.73/59.64 | ? [B_xs,B_x] :
% 59.73/59.64 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 59.73/59.64 & ! [B_xa] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs)))
% 59.73/59.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
% 59.73/59.64 & c_List_Olinorder__class_Osorted(T_b,B_xs) ) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__update__cong2,axiom,
% 59.73/59.64 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 59.73/59.64 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 59.73/59.64 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 59.73/59.64 => ( 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)))
% 59.73/59.64 => 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)) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__update__cong,axiom,
% 59.73/59.64 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_c,V_xs_2,T_b,V_i_2] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 59.73/59.64 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 59.73/59.64 => 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)) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__conv__all__nth,axiom,
% 59.73/59.64 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 59.73/59.64 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 59.73/59.64 <=> ( 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)
% 59.73/59.64 & ! [B_i] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => 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))) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__nthD,axiom,
% 59.73/59.64 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 59.73/59.64 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 59.73/59.64 => ( 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)))
% 59.73/59.64 => 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))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__nthD2,axiom,
% 59.73/59.64 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 59.73/59.64 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 59.73/59.64 => ( 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)))
% 59.73/59.64 => 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))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__map2,axiom,
% 59.73/59.64 ! [V_bs_2,V_f_2,T_d,V_as_2,V_P_2,T_c,T_b] :
% 59.73/59.64 ( 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))
% 59.73/59.64 <=> 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__map1,axiom,
% 59.73/59.64 ! [V_bs_2,V_as_2,V_f_2,T_d,V_P_2,T_c,T_b] :
% 59.73/59.64 ( 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)
% 59.73/59.64 <=> 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__eq,axiom,
% 59.73/59.64 ! [T_b,V_ys_2,V_xs_2] :
% 59.73/59.64 ( V_xs_2 = V_ys_2
% 59.73/59.64 <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__lengthD,axiom,
% 59.73/59.64 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 59.73/59.64 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__dropI,axiom,
% 59.73/59.64 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_c,T_b] :
% 59.73/59.64 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,V_bs_2)
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__Nil2,axiom,
% 59.73/59.64 ! [V_xs_2,V_P_2,T_c,T_b] :
% 59.73/59.64 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,c_List_Olist_ONil(T_c))
% 59.73/59.64 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__Nil,axiom,
% 59.73/59.64 ! [V_ys_2,V_P_2,T_c,T_b] :
% 59.73/59.64 ( c_List_Olist__all2(T_b,T_c,V_P_2,c_List_Olist_ONil(T_b),V_ys_2)
% 59.73/59.64 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__takeI,axiom,
% 59.73/59.64 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 59.73/59.64 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__Cons,axiom,
% 59.73/59.64 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_c,T_b] :
% 59.73/59.64 ( 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))
% 59.73/59.64 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 59.73/59.64 & c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__appendI,axiom,
% 59.73/59.64 ! [V_d_2,V_c_2,V_b_2,V_a_2,V_P_2,T_c,T_b] :
% 59.73/59.64 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2)
% 59.73/59.64 => ( c_List_Olist__all2(T_b,T_c,V_P_2,V_c_2,V_d_2)
% 59.73/59.64 => 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)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__append,axiom,
% 59.73/59.64 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
% 59.73/59.64 ( 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)
% 59.73/59.64 => ( 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))
% 59.73/59.64 <=> ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 59.73/59.64 & c_List_Olist__all2(T_b,T_c,V_P_2,V_us_2,V_vs_2) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__rev,axiom,
% 59.73/59.64 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 59.73/59.64 ( 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))
% 59.73/59.64 <=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__rev1,axiom,
% 59.73/59.64 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 59.73/59.64 ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
% 59.73/59.64 <=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2I,axiom,
% 59.73/59.64 ! [V_P_2,V_b_2,V_a_2,T_c,T_b] :
% 59.73/59.64 ( ! [B_x] :
% 59.73/59.64 ( 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))))
% 59.73/59.64 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) )
% 59.73/59.64 => ( 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)
% 59.73/59.64 => c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_all__nth__imp__all__set,axiom,
% 59.73/59.64 ! [V_x_2,V_P_2,V_xs_2,T_b] :
% 59.73/59.64 ( ! [B_i] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 59.73/59.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_map__removeAll__inj__on,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_not__in__set__insert,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_removeAll__id,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_removeAll__filter__not__eq,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_removeAll__filter__not,axiom,
% 59.73/59.64 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 59.73/59.64 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_removeAll_Osimps_I1_J,axiom,
% 59.73/59.64 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_distinct__insert,axiom,
% 59.73/59.64 ! [V_x,V_xs,T_a] :
% 59.73/59.64 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 59.73/59.64 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_distinct__removeAll,axiom,
% 59.73/59.64 ! [V_x,V_xs,T_a] :
% 59.73/59.64 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 59.73/59.64 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_insert__remdups,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_removeAll_Osimps_I2_J,axiom,
% 59.73/59.64 ! [V_xs,T_a,V_y,V_x] :
% 59.73/59.64 ( ( V_x = V_y
% 59.73/59.64 => 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) )
% 59.73/59.64 & ( V_x != V_y
% 59.73/59.64 => 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)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_removeAll__append,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_distinct__remove1__removeAll,axiom,
% 59.73/59.64 ! [V_x,V_xs,T_a] :
% 59.73/59.64 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 59.73/59.64 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_in__set__insert,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_List_Oset__insert,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_insert__Nil,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_map__removeAll__inj,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 59.73/59.64 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_set__removeAll,axiom,
% 59.73/59.64 ! [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)))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_List_Oinsert__def,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 )
% 59.73/59.64 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => 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) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_concat__map__maps,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_maps__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_maps__simps_I2_J,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_maps__simps_I1_J,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_distinct__concat,axiom,
% 59.73/59.64 ! [V_xs_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2))
% 59.73/59.64 => ( ! [B_ys] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 59.73/59.64 => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) )
% 59.73/59.64 => ( ! [B_ys] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 59.73/59.64 => ! [B_zs] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 59.73/59.64 => ( B_ys != B_zs
% 59.73/59.64 => 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)) ) ) )
% 59.73/59.64 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_measures__lesseq,axiom,
% 59.73/59.64 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => ( 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)))
% 59.73/59.64 => 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)))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_wf__measures,axiom,
% 59.73/59.64 ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_in__measures_I1_J,axiom,
% 59.73/59.64 ! [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))))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_measures__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_measures__less,axiom,
% 59.73/59.64 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => 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)))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_in__measures_I2_J,axiom,
% 59.73/59.64 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] :
% 59.73/59.64 ( 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))))
% 59.73/59.64 <=> ( 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)))
% 59.73/59.64 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 59.73/59.64 & 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))) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_foldl__apply,axiom,
% 59.73/59.64 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] :
% 59.73/59.64 ( ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => 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)) )
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_zip__obtain__same__length,axiom,
% 59.73/59.64 ! [V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
% 59.73/59.64 ( ( 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))
% 59.73/59.64 => 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)))) )
% 59.73/59.64 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_map__of__eqI,axiom,
% 59.73/59.64 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 59.73/59.64 ( hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2)) = hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_ys_2))
% 59.73/59.64 => ( ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2))))
% 59.73/59.64 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2),B_x) = hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_ys_2),B_x) )
% 59.73/59.64 => hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2) = hAPP(c_Map_Omap__of(T_b,T_c),V_ys_2) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_pos__not__random__dseq__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_dropWhile__append2,axiom,
% 59.73/59.64 ! [V_ys_2,V_P_2,V_xs_2,T_b] :
% 59.73/59.64 ( ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => hBOOL(hAPP(V_P_2,B_x)) )
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all2__all__nthI,axiom,
% 59.73/59.64 ! [V_P_2,V_b_2,T_c,V_a_2,T_b] :
% 59.73/59.64 ( 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)
% 59.73/59.64 => ( ! [B_n] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => 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))) )
% 59.73/59.64 => c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_finite__sorted__distinct__unique,axiom,
% 59.73/59.64 ! [V_A_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 59.73/59.64 => ? [B_x] :
% 59.73/59.64 ( hAPP(c_List_Oset(T_b),B_x) = V_A_2
% 59.73/59.64 & c_List_Olinorder__class_Osorted(T_b,B_x)
% 59.73/59.64 & hBOOL(hAPP(c_List_Odistinct(T_b),B_x))
% 59.73/59.64 & ! [B_y] :
% 59.73/59.64 ( ( hAPP(c_List_Oset(T_b),B_y) = V_A_2
% 59.73/59.64 & c_List_Olinorder__class_Osorted(T_b,B_y)
% 59.73/59.64 & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) )
% 59.73/59.64 => B_y = B_x ) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_takeWhile__append2,axiom,
% 59.73/59.64 ! [V_ys_2,V_P_2,V_xs_2,T_b] :
% 59.73/59.64 ( ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => hBOOL(hAPP(V_P_2,B_x)) )
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_insort__is__Cons,axiom,
% 59.73/59.64 ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_c)
% 59.73/59.64 => ( ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 59.73/59.64 => 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) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_filter__eq__Cons__iff,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_b] :
% 59.73/59.64 ( 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)
% 59.73/59.64 <=> ? [B_us,B_vs] :
% 59.73/59.64 ( 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))
% 59.73/59.64 & ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 59.73/59.64 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 59.73/59.64 & hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_Cons__eq__filter__iff,axiom,
% 59.73/59.64 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( 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)
% 59.73/59.64 <=> ? [B_us,B_vs] :
% 59.73/59.64 ( 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))
% 59.73/59.64 & ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 59.73/59.64 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 59.73/59.64 & hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__ball__nth,axiom,
% 59.73/59.64 ! [V_P_2,V_xs_2,T_b,V_n_2] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => ( ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => hBOOL(hAPP(V_P_2,B_x)) )
% 59.73/59.64 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sorted_OCons,axiom,
% 59.73/59.64 ! [V_x_2,V_xs_2,T_b] :
% 59.73/59.64 ( class_Orderings_Olinorder(T_b)
% 59.73/59.64 => ( ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
% 59.73/59.64 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 59.73/59.64 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__ex__length,axiom,
% 59.73/59.64 ! [V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 59.73/59.64 <=> ? [B_n] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__ex__simps_I1_J,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 59.73/59.64 ( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 59.73/59.64 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 | c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__ex__rev,axiom,
% 59.73/59.64 ! [V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( c_List_Olist__ex(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 59.73/59.64 <=> c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__ex__append,axiom,
% 59.73/59.64 ! [V_ys_2,V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 59.73/59.64 <=> ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 59.73/59.64 | c_List_Olist__ex(T_b,V_P_2,V_ys_2) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__ex__iff,axiom,
% 59.73/59.64 ! [V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 59.73/59.64 <=> ? [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__ex__simps_I2_J,axiom,
% 59.73/59.64 ! [V_P_2,T_b] : ~ c_List_Olist__ex(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_in__set__conv__decomp__first,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 <=> ? [B_ys] :
% 59.73/59.64 ( ? [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))
% 59.73/59.64 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_in__set__conv__decomp__last,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 <=> ? [B_ys,B_zs] :
% 59.73/59.64 ( 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))
% 59.73/59.64 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_in__set__conv__decomp,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 <=> ? [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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_Nitpick_Oof__frac__def,axiom,
% 59.73/59.64 ! [V_q,T_a,T_b] :
% 59.73/59.64 ( ( class_Rings_Oinverse(T_b)
% 59.73/59.64 & class_Rings_Oring__1(T_b) )
% 59.73/59.64 => 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))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_Nitpick_Oless__frac__def,axiom,
% 59.73/59.64 ! [V_r_2,V_q_2,T_b] :
% 59.73/59.64 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 59.73/59.64 <=> 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))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 59.73/59.64 ! [V_r_2,V_q_2,T_b] :
% 59.73/59.64 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 59.73/59.64 <=> 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))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_Nitpick_Odenom__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_Nitpick_Onum__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_setprod__pos,axiom,
% 59.73/59.64 ! [V_f_2,V_A_2,T_b,T_c] :
% 59.73/59.64 ( class_Rings_Olinordered__semidom(T_c)
% 59.73/59.64 => ( ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 59.73/59.64 => 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))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all__length,axiom,
% 59.73/59.64 ! [V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 59.73/59.64 <=> ! [B_n] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all__simps_I2_J,axiom,
% 59.73/59.64 ! [V_P_2,T_b] : c_List_Olist__all(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all__iff,axiom,
% 59.73/59.64 ! [V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 59.73/59.64 <=> ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all__append,axiom,
% 59.73/59.64 ! [V_ys_2,V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 59.73/59.64 <=> ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 59.73/59.64 & c_List_Olist__all(T_b,V_P_2,V_ys_2) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all__rev,axiom,
% 59.73/59.64 ! [V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( c_List_Olist__all(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 59.73/59.64 <=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_Ball__set__list__all,axiom,
% 59.73/59.64 ! [V_P_2,V_xs_2,T_b] :
% 59.73/59.64 ( ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => hBOOL(hAPP(V_P_2,B_x)) )
% 59.73/59.64 <=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all__simps_I1_J,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 59.73/59.64 ( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 59.73/59.64 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 & c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all__iff__raw,axiom,
% 59.73/59.64 ! [V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 59.73/59.64 <=> ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__ex1__simps_I2_J,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 59.73/59.64 ( c_List_Olist__ex1(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 59.73/59.64 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 => 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) )
% 59.73/59.64 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 => c_List_Olist__ex1(T_b,V_P_2,V_xs_2) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_internal__split__def,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_exists1__code,axiom,
% 59.73/59.64 ! [V_P_2,T_b] :
% 59.73/59.64 ( class_Enum_Oenum(T_b)
% 59.73/59.64 => ( ? [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(V_P_2,B_x))
% 59.73/59.64 & ! [B_y] :
% 59.73/59.64 ( hBOOL(hAPP(V_P_2,B_y))
% 59.73/59.64 => B_y = B_x ) )
% 59.73/59.64 <=> c_List_Olist__ex1(T_b,V_P_2,c_Enum_Oenum__class_Oenum(T_b)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__ex1__simps_I1_J,axiom,
% 59.73/59.64 ! [V_P_2,T_b] : ~ c_List_Olist__ex1(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_internal__split__conv,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__ex1__iff,axiom,
% 59.73/59.64 ! [V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
% 59.73/59.64 <=> ? [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 & hBOOL(hAPP(V_P_2,B_x))
% 59.73/59.64 & ! [B_y] :
% 59.73/59.64 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 & hBOOL(hAPP(V_P_2,B_y)) )
% 59.73/59.64 => B_y = B_x ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_setprod__nonneg,axiom,
% 59.73/59.64 ! [V_f_2,V_A_2,T_b,T_c] :
% 59.73/59.64 ( class_Rings_Olinordered__semidom(T_c)
% 59.73/59.64 => ( ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 59.73/59.64 => 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))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_bool_Osize_I2_J,axiom,
% 59.73/59.64 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_bool_Osize_I1_J,axiom,
% 59.73/59.64 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_finite__less__ub,axiom,
% 59.73/59.64 ! [V_u_2,V_f_2] :
% 59.73/59.64 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
% 59.73/59.64 => 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)))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_finite__induct,axiom,
% 59.73/59.64 ! [V_P_2,V_F_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 59.73/59.64 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 59.73/59.64 => ( ! [B_x,B_F] :
% 59.73/59.64 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 59.73/59.64 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
% 59.73/59.64 => ( hBOOL(hAPP(V_P_2,B_F))
% 59.73/59.64 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) )
% 59.73/59.64 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_measure__function__int,axiom,
% 59.73/59.64 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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_equal__fun__def,axiom,
% 59.73/59.64 ! [V_g_2,V_f_2,T_b,T_c] :
% 59.73/59.64 ( ( class_HOL_Oequal(T_c)
% 59.73/59.64 & class_Enum_Oenum(T_b) )
% 59.73/59.64 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 59.73/59.64 <=> ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_Enum_Oenum__class_Oenum(T_b))))
% 59.73/59.64 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_measure__snd,axiom,
% 59.73/59.64 ! [T_c,V_f_2,T_b] :
% 59.73/59.64 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 59.73/59.64 => 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))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_measure__fst,axiom,
% 59.73/59.64 ! [T_c,V_f_2,T_b] :
% 59.73/59.64 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 59.73/59.64 => 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))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_measure__size,axiom,
% 59.73/59.64 ! [T_b] :
% 59.73/59.64 ( class_Nat_Osize(T_b)
% 59.73/59.64 => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__equal,axiom,
% 59.73/59.64 ! [T_b] :
% 59.73/59.64 ( class_HOL_Oequal(T_b)
% 59.73/59.64 => c_fequal = c_HOL_Oequal__class_Oequal(T_b) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_equal__eq,axiom,
% 59.73/59.64 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.64 ( class_HOL_Oequal(T_b)
% 59.73/59.64 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_b),V_x_2),V_y_2))
% 59.73/59.64 <=> V_x_2 = V_y_2 ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_equal__refl,axiom,
% 59.73/59.64 ! [V_x,T_a] :
% 59.73/59.64 ( class_HOL_Oequal(T_a)
% 59.73/59.64 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_equal,axiom,
% 59.73/59.64 ! [T_b] :
% 59.73/59.64 ( class_HOL_Oequal(T_b)
% 59.73/59.64 => c_HOL_Oequal__class_Oequal(T_b) = c_fequal ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_is__measure_Osimps,axiom,
% 59.73/59.64 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_is__measure_Oequations,axiom,
% 59.73/59.64 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_is__measure_Ointros,axiom,
% 59.73/59.64 ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_transfer__morphism__int__nat,axiom,
% 59.73/59.64 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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 59.73/59.64 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 59.73/59.64 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 59.73/59.64 => 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) )
% 59.73/59.64 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 59.73/59.64 => 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)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_equal__int__def,axiom,
% 59.73/59.64 ! [V_l_2,V_k_2] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2))
% 59.73/59.64 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__int__code_I1_J,axiom,
% 59.73/59.64 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__int__code_I16_J,axiom,
% 59.73/59.64 ! [V_k2_2,V_k1_2] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 59.73/59.64 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__number__of__int__code,axiom,
% 59.73/59.64 ! [V_l_2,V_k_2] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
% 59.73/59.64 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__int__code_I13_J,axiom,
% 59.73/59.64 ! [V_k2_2,V_k1_2] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 59.73/59.64 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__int__code_I6_J,axiom,
% 59.73/59.64 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__int__code_I15_J,axiom,
% 59.73/59.64 ! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OBit0(V_k2))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__int__code_I14_J,axiom,
% 59.73/59.64 ! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OBit1(V_k2))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__int__code_I9_J,axiom,
% 59.73/59.64 ! [V_k1_2] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls))
% 59.73/59.64 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__int__code_I3_J,axiom,
% 59.73/59.64 ! [V_k2_2] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2)))
% 59.73/59.64 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__int__code_I10_J,axiom,
% 59.73/59.64 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__int__code_I4_J,axiom,
% 59.73/59.64 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__int__code_I11_J,axiom,
% 59.73/59.64 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__int__code_I7_J,axiom,
% 59.73/59.64 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__int__code_I12_J,axiom,
% 59.73/59.64 ! [V_k1_2] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin))
% 59.73/59.64 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__int__code_I8_J,axiom,
% 59.73/59.64 ! [V_k2_2] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2)))
% 59.73/59.64 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__int__code_I2_J,axiom,
% 59.73/59.64 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__int__code_I5_J,axiom,
% 59.73/59.64 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_bool_Osize_I4_J,axiom,
% 59.73/59.64 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_bool_Osize_I3_J,axiom,
% 59.73/59.64 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 59.73/59.64 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__int__refl,axiom,
% 59.73/59.64 ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_pos__empty__def,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_pos__bind__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_size__code,axiom,
% 59.73/59.64 ! [V_xq_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)),V_xq_2) = hAPP(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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_lazy__sequence__size__code,axiom,
% 59.73/59.64 ! [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) = hAPP(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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_seq__case,axiom,
% 59.73/59.64 ! [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) = hAPP(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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_yieldn__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_lazy__sequence_Osize_I2_J,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_lazy__sequence_Osimps_I5_J,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_lazy__sequence_Oinject,axiom,
% 59.73/59.64 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] :
% 59.73/59.64 ( 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)
% 59.73/59.64 <=> ( V_a_2 = V_a_H_2
% 59.73/59.64 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact__01,axiom,
% 59.73/59.64 ! [V_xq,V_x,T_a] : hAPP(c_Lazy__Sequence_Oyield(T_a),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq)) = hAPP(c_Option_Ooption_OSome(tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_Product__Type_OPair(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_x),V_xq)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_lazy__sequence_Osize_I4_J,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_pos__map__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 59.73/59.64 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 59.73/59.64 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 59.73/59.64 => 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) )
% 59.73/59.64 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 59.73/59.64 => 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)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_pos__single__def,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_New__DSequence_Opos__single__def,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_neg__bind__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact__02,axiom,
% 59.73/59.64 ! [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)))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_neg__map__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_small__lazy__list_Osimps,axiom,
% 59.73/59.64 ! [V_d_2,T_b] :
% 59.73/59.64 ( class_Lazy__Sequence_Osmall__lazy(T_b)
% 59.73/59.64 => 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)))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_small__lazy__prod__def,axiom,
% 59.73/59.64 ! [V_d,T_b,T_a] :
% 59.73/59.64 ( ( class_Lazy__Sequence_Osmall__lazy(T_a)
% 59.73/59.64 & class_Lazy__Sequence_Osmall__lazy(T_b) )
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact__03,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_neg__single__def,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_New__DSequence_Opos__union__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_pos__union__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_small__lazy_H_Osimps,axiom,
% 59.73/59.64 ! [V_i,V_d] :
% 59.73/59.64 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 59.73/59.64 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 59.73/59.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 59.73/59.64 => 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)))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_small__lazy_H_Opsimps,axiom,
% 59.73/59.64 ! [V_i_2,V_d_2] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 59.73/59.64 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 59.73/59.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 59.73/59.64 => 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)))) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_small__lazy__int__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_small__lazy_H_Opinduct,axiom,
% 59.73/59.64 ! [V_P_2,V_a1_2,V_a0_2] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => ( ! [B_d,B_i] :
% 59.73/59.64 ( 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)))
% 59.73/59.64 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 59.73/59.64 => 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)))) )
% 59.73/59.64 => hBOOL(hAPP(hAPP(V_P_2,B_d),B_i)) ) )
% 59.73/59.64 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_hb__flat_Osimps_I2_J,axiom,
% 59.73/59.64 ! [V_xqq_2,V_xq_2,T_b] : c_Lazy__Sequence_Ohb__flat(T_b,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_xq_2,V_xqq_2)) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(T_b),hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)),tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)),c_Lazy__Sequence_Ohit__bound(T_b),c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),V_xq_2),c_Lazy__Sequence_Ohb__flat(T_b,V_xqq_2)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_New__DSequence_Oneg__union__def,axiom,
% 59.73/59.64 ! [V_i_2,V_y_2,V_x_2,T_b] : hAPP(c_New__DSequence_Oneg__union(T_b,V_x_2,V_y_2),V_i_2) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(T_b),hAPP(V_x_2,V_i_2),hAPP(V_y_2,V_i_2)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_hb__bind__def,axiom,
% 59.73/59.64 ! [V_f_2,V_xq_2,T_b,T_c] : c_Lazy__Sequence_Ohb__bind(T_c,T_b,V_xq_2,V_f_2) = c_Lazy__Sequence_Ohb__flat(T_b,c_Lazy__Sequence_Ohb__map(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)),V_f_2,V_xq_2)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_hb__map_Osimps_I2_J,axiom,
% 59.73/59.64 ! [V_xq_2,V_x_2,V_f_2,T_b,T_c] : c_Lazy__Sequence_Ohb__map(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(T_c),V_x_2,V_xq_2)) = c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(T_b),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_x_2),c_Lazy__Sequence_Ohb__map(T_c,T_b,V_f_2,V_xq_2)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_neg__union__def,axiom,
% 59.73/59.64 ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_b] : c_New__Random__Sequence_Oneg__union(T_b,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_New__DSequence_Oneg__map__def,axiom,
% 59.73/59.64 ! [V_i_2,V_xq_2,V_f_2,T_b,T_c] : c_New__DSequence_Oneg__map(T_c,T_b,V_f_2,V_xq_2,V_i_2) = c_Lazy__Sequence_Ohb__map(T_c,T_b,V_f_2,hAPP(V_xq_2,V_i_2)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_length__splice,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_acyclicP__converse,axiom,
% 59.73/59.64 ! [V_r_2,T_b] :
% 59.73/59.64 ( 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))))
% 59.73/59.64 <=> 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))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_splice_Osimps_I1_J,axiom,
% 59.73/59.64 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ).
% 59.73/59.64
% 59.73/59.64 fof(fact_splice__Nil2,axiom,
% 59.73/59.64 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ).
% 59.73/59.64
% 59.73/59.64 fof(fact_converse__pred__comp,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_conversep__noteq,axiom,
% 59.73/59.64 ! [V_y_2,V_x_2,T_b] :
% 59.73/59.64 ( 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))
% 59.73/59.64 <=> V_x_2 != V_y_2 ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_conversepD,axiom,
% 59.73/59.64 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 59.73/59.64 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_conversep_Ointros,axiom,
% 59.73/59.64 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 59.73/59.64 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_conversep_Oequations,axiom,
% 59.73/59.64 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
% 59.73/59.64 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_conversep__iff,axiom,
% 59.73/59.64 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 59.73/59.64 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_conversep__conversep,axiom,
% 59.73/59.64 ! [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 ).
% 59.73/59.64
% 59.73/59.64 fof(fact_conversep__eq,axiom,
% 59.73/59.64 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ).
% 59.73/59.64
% 59.73/59.64 fof(fact_converse__join,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_converse__meet,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_splice_Osimps_I3_J,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_conversep__converse__eq,axiom,
% 59.73/59.64 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 59.73/59.64 ( 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))
% 59.73/59.64 <=> 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))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_splice_Osimps_I2_J,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_tl__replicate,axiom,
% 59.73/59.64 ! [V_x,T_a,V_n] :
% 59.73/59.64 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.64 => 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_eq__comp__r,axiom,
% 59.73/59.64 ! [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 ).
% 59.73/59.64
% 59.73/59.64 fof(fact_replicate__append__same,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_map__replicate__const,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_replicate__length__filter,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_length__replicate,axiom,
% 59.73/59.64 ! [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 ).
% 59.73/59.64
% 59.73/59.64 fof(fact_replicate__Suc,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_replicate__app__Cons__same,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_rev__replicate,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_replicate__add,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_append__replicate__commute,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_last__replicate,axiom,
% 59.73/59.64 ! [V_x,T_a,V_n] :
% 59.73/59.64 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.64 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_take__replicate,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_hd__replicate,axiom,
% 59.73/59.64 ! [V_x,T_a,V_n] :
% 59.73/59.64 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.64 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_drop__replicate,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_nth__replicate,axiom,
% 59.73/59.64 ! [V_x,T_a,V_n,V_i] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 59.73/59.64 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_replicate__eq__replicate,axiom,
% 59.73/59.64 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] :
% 59.73/59.64 ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2)
% 59.73/59.64 <=> ( V_m_2 = V_n_2
% 59.73/59.64 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.64 => V_x_2 = V_y_2 ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_Bex__set__replicate,axiom,
% 59.73/59.64 ! [V_P_2,V_a_2,V_n_2,T_b] :
% 59.73/59.64 ( ? [B_x] :
% 59.73/59.64 ( 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))))
% 59.73/59.64 & hBOOL(hAPP(V_P_2,B_x)) )
% 59.73/59.64 <=> ( hBOOL(hAPP(V_P_2,V_a_2))
% 59.73/59.64 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_Ball__set__replicate,axiom,
% 59.73/59.64 ! [V_P_2,V_a_2,V_n_2,T_b] :
% 59.73/59.64 ( ! [B_x] :
% 59.73/59.64 ( 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))))
% 59.73/59.64 => hBOOL(hAPP(V_P_2,B_x)) )
% 59.73/59.64 <=> ( hBOOL(hAPP(V_P_2,V_a_2))
% 59.73/59.64 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_map__replicate,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_replicate__empty,axiom,
% 59.73/59.64 ! [V_x_2,V_n_2,T_b] :
% 59.73/59.64 ( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b)
% 59.73/59.64 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_empty__replicate,axiom,
% 59.73/59.64 ! [V_x_2,V_n_2,T_b] :
% 59.73/59.64 ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2)
% 59.73/59.64 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_replicate__0,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_concat__replicate__trivial,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_filter__replicate,axiom,
% 59.73/59.64 ! [V_n_2,T_b,V_x_2,V_P_2] :
% 59.73/59.64 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 => 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) )
% 59.73/59.64 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 59.73/59.64 => 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) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_in__set__replicate,axiom,
% 59.73/59.64 ! [V_y_2,V_n_2,V_x_2,T_b] :
% 59.73/59.64 ( 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))))
% 59.73/59.64 <=> ( V_x_2 = V_y_2
% 59.73/59.64 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_zip__replicate,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_map__replicate__trivial,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_set__replicate__conv__if,axiom,
% 59.73/59.64 ! [V_x_2,T_b,V_n_2] :
% 59.73/59.64 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.64 => 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)) )
% 59.73/59.64 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.64 => 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))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_set__replicate,axiom,
% 59.73/59.64 ! [V_x_2,T_b,V_n_2] :
% 59.73/59.64 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 59.73/59.64 => 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))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_set__replicate__Suc,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_field__le__epsilon,axiom,
% 59.73/59.64 ! [V_y,V_x,T_a] :
% 59.73/59.64 ( class_Fields_Olinordered__field(T_a)
% 59.73/59.64 => ( ! [B_e] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
% 59.73/59.64 => 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))) )
% 59.73/59.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_refl__on__INTER,axiom,
% 59.73/59.64 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 59.73/59.64 ( ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 59.73/59.64 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_List_Omember__def,axiom,
% 59.73/59.64 ! [V_x_2,V_xs_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2))
% 59.73/59.64 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_in__set__member,axiom,
% 59.73/59.64 ! [V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 <=> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_member__rec_I1_J,axiom,
% 59.73/59.64 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 59.73/59.64 ( 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))
% 59.73/59.64 <=> ( V_x_2 = V_y_2
% 59.73/59.64 | hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_member__set,axiom,
% 59.73/59.64 ! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_member__rec_I2_J,axiom,
% 59.73/59.64 ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_pair__box_Osize_I1_J,axiom,
% 59.73/59.64 ! [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))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__ex1__iff__raw,axiom,
% 59.73/59.64 ! [V_xs_2,V_P_2,T_b] :
% 59.73/59.64 ( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
% 59.73/59.64 <=> ? [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 & hBOOL(hAPP(V_P_2,B_x))
% 59.73/59.64 & ! [B_y] :
% 59.73/59.64 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 59.73/59.64 & hBOOL(hAPP(V_P_2,B_y)) )
% 59.73/59.64 => B_y = B_x ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_pair__box_Oinject,axiom,
% 59.73/59.64 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 59.73/59.64 ( 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)
% 59.73/59.64 <=> ( V_a_2 = V_a_H_2
% 59.73/59.64 & V_b_2 = V_b_H_2 ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_pair__box_Osize_I2_J,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_pair__box_Osimps_I2_J,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_pair__box_Orecs,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_THE__default__def,axiom,
% 59.73/59.64 ! [V_d_2,T_b,V_P_2] :
% 59.73/59.64 ( ( ? [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(V_P_2,B_x))
% 59.73/59.64 & ! [B_y] :
% 59.73/59.64 ( hBOOL(hAPP(V_P_2,B_y))
% 59.73/59.64 => B_y = B_x ) )
% 59.73/59.64 => c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = c_HOL_OThe(T_b,V_P_2) )
% 59.73/59.64 & ( ~ ? [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(V_P_2,B_x))
% 59.73/59.64 & ! [B_y] :
% 59.73/59.64 ( hBOOL(hAPP(V_P_2,B_y))
% 59.73/59.64 => B_y = B_x ) )
% 59.73/59.64 => c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = V_d_2 ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_setsum__UNION__zero,axiom,
% 59.73/59.64 ! [V_f_2,V_S_2,T_b,T_c] :
% 59.73/59.64 ( class_Groups_Ocomm__monoid__add(T_c)
% 59.73/59.64 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2))
% 59.73/59.64 => ( ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2))
% 59.73/59.64 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 59.73/59.64 => ( ! [B_T1] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2))
% 59.73/59.64 => ! [B_T2] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2))
% 59.73/59.64 => ( B_T1 != B_T2
% 59.73/59.64 => ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1))
% 59.73/59.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2))
% 59.73/59.64 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) )
% 59.73/59.64 => 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) ) ) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_SUP2__E,axiom,
% 59.73/59.64 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 59.73/59.64 ( 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))
% 59.73/59.64 => ~ ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.64 => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_INF2__I,axiom,
% 59.73/59.64 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,T_b] :
% 59.73/59.64 ( ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 59.73/59.64 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) )
% 59.73/59.64 => 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)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_finite__maxlen,axiom,
% 59.73/59.64 ! [V_M_2,T_b] :
% 59.73/59.64 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2))
% 59.73/59.64 => ? [B_n] :
% 59.73/59.64 ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2))
% 59.73/59.64 => 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)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_lazy__sequence_Osize_I1_J,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_hb__map_Osimps_I1_J,axiom,
% 59.73/59.64 ! [V_f_2,T_b,T_c] : c_Lazy__Sequence_Ohb__map(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(T_c))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(T_b)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_lazy__sequence_Osimps_I2_J,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_lazy__sequence_Osimps_I3_J,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact__04,axiom,
% 59.73/59.64 ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq ).
% 59.73/59.64
% 59.73/59.64 fof(fact_hb__flat_Osimps_I1_J,axiom,
% 59.73/59.64 ! [T_a] : c_Lazy__Sequence_Ohb__flat(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(T_a)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_lazy__sequence_Osimps_I4_J,axiom,
% 59.73/59.64 ! [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 ).
% 59.73/59.64
% 59.73/59.64 fof(fact__05,axiom,
% 59.73/59.64 ! [T_a] : hAPP(c_Lazy__Sequence_Oyield(T_a),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a)) = c_Option_Ooption_ONone(tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a))) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_lazy__sequence_Osize_I3_J,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__all__iff__all__interval__int,axiom,
% 59.73/59.64 ! [V_j_2,V_i_2,V_P_2] :
% 59.73/59.64 ( c_List_Olist__all(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
% 59.73/59.64 <=> c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_list__ex__iff__not__all__inverval__int,axiom,
% 59.73/59.64 ! [V_j_2,V_i_2,V_P_2] :
% 59.73/59.64 ( c_List_Olist__ex(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
% 59.73/59.64 <=> ~ 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) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_all__interval__int__def,axiom,
% 59.73/59.64 ! [V_j_2,V_i_2,V_P_2] :
% 59.73/59.64 ( c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2)
% 59.73/59.64 <=> ! [B_x] :
% 59.73/59.64 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2)))
% 59.73/59.64 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_code__numeral_Orecs_I2_J,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_Random_Osimps,axiom,
% 59.73/59.64 ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
% 59.73/59.64 ( ( 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)))
% 59.73/59.64 => 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)) )
% 59.73/59.64 & ( ~ 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)))
% 59.73/59.64 => 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))))))) ) ) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_code__numeral_Orecs_I1_J,axiom,
% 59.73/59.64 ! [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 ).
% 59.73/59.64
% 59.73/59.64 fof(fact_Random__Sequence_Oempty__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_Random__Sequence_Osingle__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_Random__Sequence_Omap__def,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_option__map__o__sum__case,axiom,
% 59.73/59.64 ! [V_h_2,V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_e),tc_Option_Ooption(T_d),tc_sum(T_b,T_c),hAPP(c_Option_Omap(T_e,T_d),V_f_2)),c_Sum__Type_Osum_Osum__case(T_b,tc_Option_Ooption(T_e),T_c,V_g_2,V_h_2)) = c_Sum__Type_Osum_Osum__case(T_b,tc_Option_Ooption(T_d),T_c,hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_e),tc_Option_Ooption(T_d),T_b,hAPP(c_Option_Omap(T_e,T_d),V_f_2)),V_g_2),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_e),tc_Option_Ooption(T_d),T_c,hAPP(c_Option_Omap(T_e,T_d),V_f_2)),V_h_2)) ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sum__case__KK,axiom,
% 59.73/59.64 ! [V_x_2,V_a_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_Osum_Osum__case(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_a_2),hAPP(c_COMBK(T_b,T_d),V_a_2)),V_x_2) = V_a_2 ).
% 59.73/59.64
% 59.73/59.64 fof(fact_sum__case__inject,axiom,
% 59.73/59.64 ! [V_g2_2,V_g1_2,V_f2_2,V_f1_2,T_c,T_d,T_b] :
% 59.73/59.64 ( c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_f1_2,V_f2_2) = c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_g1_2,V_g2_2)
% 59.73/59.64 => ~ ( V_f1_2 = V_g1_2
% 59.73/59.64 => V_f2_2 != V_g2_2 ) ) ).
% 59.73/59.64
% 59.73/59.64 %----Arity declarations (233)
% 59.73/59.64 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 59.73/59.64 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 59.73/59.64 ! [T_2,T_1] :
% 59.73/59.64 ( class_Lattices_Obounded__lattice(T_1)
% 59.73/59.64 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 59.73/59.64 ! [T_2,T_1] :
% 59.73/59.64 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 59.73/59.64 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 59.73/59.64 ! [T_2,T_1] :
% 59.73/59.64 ( class_Lattices_Obounded__lattice(T_1)
% 59.73/59.64 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 59.73/59.64 ! [T_2,T_1] :
% 59.73/59.64 ( class_Lattices_Obounded__lattice(T_1)
% 59.73/59.64 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 59.73/59.64 ! [T_2,T_1] :
% 59.73/59.64 ( class_Lattices_Olattice(T_1)
% 59.73/59.64 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 59.73/59.64 ! [T_2,T_1] :
% 59.73/59.64 ( class_Lattices_Olattice(T_1)
% 59.73/59.64 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 59.73/59.64 ! [T_2,T_1] :
% 59.73/59.64 ( class_Lattices_Odistrib__lattice(T_1)
% 59.73/59.64 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 59.73/59.64 ! [T_2,T_1] :
% 59.73/59.64 ( class_Lattices_Oboolean__algebra(T_1)
% 59.73/59.64 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__Orderings_Opreorder,axiom,
% 59.73/59.64 ! [T_2,T_1] :
% 59.73/59.64 ( class_Orderings_Opreorder(T_1)
% 59.73/59.64 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 59.73/59.64 ! [T_1,T_2] :
% 59.73/59.64 ( ( class_Finite__Set_Ofinite(T_2)
% 59.73/59.64 & class_Finite__Set_Ofinite(T_1) )
% 59.73/59.64 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__Lattices_Olattice,axiom,
% 59.73/59.64 ! [T_2,T_1] :
% 59.73/59.64 ( class_Lattices_Olattice(T_1)
% 59.73/59.64 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__Orderings_Oorder,axiom,
% 59.73/59.64 ! [T_2,T_1] :
% 59.73/59.64 ( class_Orderings_Oorder(T_1)
% 59.73/59.64 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__Orderings_Otop,axiom,
% 59.73/59.64 ! [T_2,T_1] :
% 59.73/59.64 ( class_Orderings_Otop(T_1)
% 59.73/59.64 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__Orderings_Oord,axiom,
% 59.73/59.64 ! [T_2,T_1] :
% 59.73/59.64 ( class_Orderings_Oord(T_1)
% 59.73/59.64 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__Orderings_Obot,axiom,
% 59.73/59.64 ! [T_2,T_1] :
% 59.73/59.64 ( class_Orderings_Obot(T_1)
% 59.73/59.64 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__Groups_Ouminus,axiom,
% 59.73/59.64 ! [T_2,T_1] :
% 59.73/59.64 ( class_Groups_Ouminus(T_1)
% 59.73/59.64 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__Groups_Ominus,axiom,
% 59.73/59.64 ! [T_2,T_1] :
% 59.73/59.64 ( class_Groups_Ominus(T_1)
% 59.73/59.64 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__HOL_Oequal,axiom,
% 59.73/59.64 ! [T_1,T_2] :
% 59.73/59.64 ( ( class_Enum_Oenum(T_2)
% 59.73/59.64 & class_HOL_Oequal(T_1) )
% 59.73/59.64 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_fun__Enum_Oenum,axiom,
% 59.73/59.64 ! [T_1,T_2] :
% 59.73/59.64 ( ( class_Enum_Oenum(T_2)
% 59.73/59.64 & class_Enum_Oenum(T_1) )
% 59.73/59.64 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 59.73/59.64 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 59.73/59.64 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 59.73/59.64 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 59.73/59.64 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 59.73/59.64 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 59.73/59.64 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 59.73/59.64 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 59.73/59.64 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 59.73/59.64 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 59.73/59.64 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 59.73/59.64 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 59.73/59.64 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 59.73/59.64 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 59.73/59.64 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 59.73/59.64 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 59.73/59.64 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 59.73/59.64 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 59.73/59.64 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 59.73/59.64 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 59.73/59.64 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 59.73/59.64 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 59.73/59.64 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom,
% 59.73/59.64 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 59.73/59.64 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 59.73/59.64 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 59.73/59.64 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 59.73/59.64 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 59.73/59.64 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 59.73/59.64 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 59.73/59.64 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 59.73/59.64 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 59.73/59.64 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 59.73/59.64 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 59.73/59.64 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 59.73/59.64 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 59.73/59.64 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 59.73/59.64 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 59.73/59.64 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 59.73/59.64 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 59.73/59.64 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 59.73/59.64 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 59.73/59.64 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 59.73/59.64 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 59.73/59.64 class_Orderings_Opreorder(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 59.73/59.64 class_Orderings_Olinorder(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 59.73/59.64 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 59.73/59.64 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 59.73/59.64 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Smallcheck_Osmall,axiom,
% 59.73/59.64 class_Smallcheck_Osmall(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 59.73/59.64 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 59.73/59.64 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 59.73/59.64 class_Lattices_Olattice(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 59.73/59.64 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 59.73/59.64 class_Divides_Oring__div(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 59.73/59.64 class_Rings_Omult__zero(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 59.73/59.64 class_Orderings_Oorder(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 59.73/59.64 class_Int_Oring__char__0(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 59.73/59.64 class_Int_Onumber__ring(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 59.73/59.64 class_Rings_Osemiring(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 59.73/59.64 class_Orderings_Oord(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 59.73/59.64 class_Groups_Ouminus(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 59.73/59.64 class_Groups_Osgn__if(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 59.73/59.64 class_Groups_Oabs__if(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 59.73/59.64 class_Rings_Oring__1(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 59.73/59.64 class_Groups_Ominus(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Power_Opower,axiom,
% 59.73/59.64 class_Power_Opower(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 59.73/59.64 class_Groups_Ozero(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Oring,axiom,
% 59.73/59.64 class_Rings_Oring(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 59.73/59.64 class_Rings_Oidom(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Int_Onumber,axiom,
% 59.73/59.64 class_Int_Onumber(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__Groups_Oone,axiom,
% 59.73/59.64 class_Groups_Oone(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Int__Oint__HOL_Oequal,axiom,
% 59.73/59.64 class_HOL_Oequal(tc_Int_Oint) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 59.73/59.64 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 59.73/59.64 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 59.73/59.64 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 59.73/59.64 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 59.73/59.64 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 59.73/59.64 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 59.73/59.64 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 59.73/59.64 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 59.73/59.64 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 59.73/59.64 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 59.73/59.64 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 59.73/59.64 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 59.73/59.64 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 59.73/59.64 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 59.73/59.64 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 59.73/59.64 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 59.73/59.64 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 59.73/59.64 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 59.73/59.64 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 59.73/59.64 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 59.73/59.64 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 59.73/59.64 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 59.73/59.64 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 59.73/59.64 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 59.73/59.64 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 59.73/59.64 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 59.73/59.64 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 59.73/59.64 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 59.73/59.64 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 59.73/59.64 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 59.73/59.64 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 59.73/59.64 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 59.73/59.64 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 59.73/59.64 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 59.73/59.64 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 59.73/59.64 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 59.73/59.64 class_Lattices_Olattice(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 59.73/59.64 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 59.73/59.64 class_Orderings_Oorder(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 59.73/59.64 class_Rings_Osemiring(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 59.73/59.64 class_Orderings_Oord(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 59.73/59.64 class_Orderings_Obot(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 59.73/59.64 class_Groups_Ominus(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Power_Opower,axiom,
% 59.73/59.64 class_Power_Opower(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 59.73/59.64 class_Groups_Ozero(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 59.73/59.64 class_Int_Onumber(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 59.73/59.64 class_Groups_Oone(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__HOL_Oequal,axiom,
% 59.73/59.64 class_HOL_Oequal(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nat__Onat__Nat_Osize,axiom,
% 59.73/59.64 class_Nat_Osize(tc_Nat_Onat) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 59.73/59.64 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 59.73/59.64 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 59.73/59.64 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 59.73/59.64 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 59.73/59.64 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 59.73/59.64 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 59.73/59.64 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 59.73/59.64 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 59.73/59.64 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 59.73/59.64 class_Lattices_Olattice(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 59.73/59.64 class_Orderings_Oorder(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 59.73/59.64 class_Orderings_Otop(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 59.73/59.64 class_Orderings_Oord(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 59.73/59.64 class_Orderings_Obot(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 59.73/59.64 class_Groups_Ouminus(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 59.73/59.64 class_Groups_Ominus(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__HOL_Oequal,axiom,
% 59.73/59.64 class_HOL_Oequal(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 59.73/59.64 class_Enum_Oenum(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_HOL__Obool__Nat_Osize,axiom,
% 59.73/59.64 class_Nat_Osize(tc_HOL_Obool) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
% 59.73/59.64 ! [T_1] :
% 59.73/59.64 ( class_Lazy__Sequence_Osmall__lazy(T_1)
% 59.73/59.64 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_List__Olist__HOL_Oequal,axiom,
% 59.73/59.64 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_List__Olist__Nat_Osize,axiom,
% 59.73/59.64 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 59.73/59.64 ! [T_1,T_2] :
% 59.73/59.64 ( ( class_Finite__Set_Ofinite(T_2)
% 59.73/59.64 & class_Finite__Set_Ofinite(T_1) )
% 59.73/59.64 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_sum__HOL_Oequal,axiom,
% 59.73/59.64 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_sum__Enum_Oenum,axiom,
% 59.73/59.64 ! [T_1,T_2] :
% 59.73/59.64 ( ( class_Enum_Oenum(T_2)
% 59.73/59.64 & class_Enum_Oenum(T_1) )
% 59.73/59.64 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_sum__Nat_Osize,axiom,
% 59.73/59.64 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 59.73/59.64 ! [T_1] :
% 59.73/59.64 ( class_Finite__Set_Ofinite(T_1)
% 59.73/59.64 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Option__Ooption__HOL_Oequal,axiom,
% 59.73/59.64 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 59.73/59.64 ! [T_1] :
% 59.73/59.64 ( class_Enum_Oenum(T_1)
% 59.73/59.64 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Option__Ooption__Nat_Osize,axiom,
% 59.73/59.64 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nitpick__Opair____box__HOL_Oequal,axiom,
% 59.73/59.64 ! [T_1,T_2] : class_HOL_Oequal(tc_Nitpick_Opair__box(T_2,T_1)) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom,
% 59.73/59.64 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
% 59.73/59.64 ! [T_1,T_2] :
% 59.73/59.64 ( ( class_Lazy__Sequence_Osmall__lazy(T_2)
% 59.73/59.64 & class_Lazy__Sequence_Osmall__lazy(T_1) )
% 59.73/59.64 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 59.73/59.64 ! [T_1,T_2] :
% 59.73/59.64 ( ( class_Finite__Set_Ofinite(T_2)
% 59.73/59.64 & class_Finite__Set_Ofinite(T_1) )
% 59.73/59.64 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_prod__Smallcheck_Osmall,axiom,
% 59.73/59.64 ! [T_1,T_2] :
% 59.73/59.64 ( ( class_Smallcheck_Osmall(T_2)
% 59.73/59.64 & class_Smallcheck_Osmall(T_1) )
% 59.73/59.64 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_prod__HOL_Oequal,axiom,
% 59.73/59.64 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_prod__Enum_Oenum,axiom,
% 59.73/59.64 ! [T_1,T_2] :
% 59.73/59.64 ( ( class_Enum_Oenum(T_2)
% 59.73/59.64 & class_Enum_Oenum(T_1) )
% 59.73/59.64 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_prod__Nat_Osize,axiom,
% 59.73/59.64 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
% 59.73/59.64 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 59.73/59.64 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom,
% 59.73/59.64 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom,
% 59.73/59.64 class_HOL_Oequal(tc_Product__Type_Ounit) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 59.73/59.64 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
% 59.73/59.64 class_Nat_Osize(tc_Product__Type_Ounit) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom,
% 59.73/59.64 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
% 59.73/59.64 class_Nat_Osize(tc_Code__Evaluation_Oterm) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom,
% 59.73/59.64 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
% 59.73/59.64 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 59.73/59.64 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 59.73/59.64 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 59.73/59.64 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 59.73/59.64 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 59.73/59.64 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 59.73/59.64 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 59.73/59.64 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 59.73/59.64 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 59.73/59.64 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 59.73/59.64 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 59.73/59.64 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 59.73/59.64 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 59.73/59.64 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 59.73/59.64 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 59.73/59.64 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 59.73/59.64 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 59.73/59.64 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 59.73/59.64 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 59.73/59.64 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 59.73/59.64 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 59.73/59.64 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 59.73/59.64 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 59.73/59.64 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 59.73/59.64 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 59.73/59.64 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 59.73/59.64 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 59.73/59.64 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 59.73/59.64 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 59.73/59.64 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 59.73/59.64 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 59.73/59.64 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 59.73/59.64 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 59.73/59.64 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 59.73/59.64 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 59.73/59.64 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 59.73/59.64 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 59.73/59.64 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 59.73/59.64 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 59.73/59.64 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 59.73/59.64 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom,
% 59.73/59.64 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
% 59.73/59.64 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom,
% 59.73/59.64 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 59.73/59.64
% 59.73/59.64 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
% 59.73/59.64 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 59.73/59.64
% 59.73/59.64 %----Helper facts (20)
% 59.73/59.64 fof(help_c__COMBI__1,axiom,
% 59.73/59.64 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__COMBK__1,axiom,
% 59.73/59.64 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__COMBB__1,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__COMBC__1,axiom,
% 59.73/59.64 ! [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) ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__COMBS__1,axiom,
% 59.73/59.64 ! [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)) ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__fequal__1,axiom,
% 59.73/59.64 ! [V_y_2,V_x_2] :
% 59.73/59.64 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 59.73/59.64 | V_x_2 = V_y_2 ) ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__fequal__2,axiom,
% 59.73/59.64 ! [V_y_2,V_x_2] :
% 59.73/59.64 ( V_x_2 != V_y_2
% 59.73/59.64 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__fFalse__1,axiom,
% 59.73/59.64 ~ hBOOL(c_fFalse) ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__fTrue__1,axiom,
% 59.73/59.64 hBOOL(c_fTrue) ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__fNot__1,axiom,
% 59.73/59.64 ! [V_P_2] :
% 59.73/59.64 ( ~ hBOOL(hAPP(c_fNot,V_P_2))
% 59.73/59.64 | ~ hBOOL(V_P_2) ) ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__fNot__2,axiom,
% 59.73/59.64 ! [V_P_2] :
% 59.73/59.64 ( ~ ~ hBOOL(V_P_2)
% 59.73/59.64 | hBOOL(hAPP(c_fNot,V_P_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__fconj__1,axiom,
% 59.73/59.64 ! [V_Q_2,V_P_2] :
% 59.73/59.64 ( ~ hBOOL(V_P_2)
% 59.73/59.64 | ~ hBOOL(V_Q_2)
% 59.73/59.64 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__fconj__2,axiom,
% 59.73/59.64 ! [V_Q_2,V_P_2] :
% 59.73/59.64 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 59.73/59.64 | hBOOL(V_P_2) ) ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__fconj__3,axiom,
% 59.73/59.64 ! [V_Q_2,V_P_2] :
% 59.73/59.64 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 59.73/59.64 | hBOOL(V_Q_2) ) ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__fdisj__1,axiom,
% 59.73/59.64 ! [V_Q_2,V_P_2] :
% 59.73/59.64 ( ~ hBOOL(V_P_2)
% 59.73/59.64 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__fdisj__2,axiom,
% 59.73/59.64 ! [V_P_2,V_Q_2] :
% 59.73/59.64 ( ~ hBOOL(V_Q_2)
% 59.73/59.64 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__fdisj__3,axiom,
% 59.73/59.64 ! [V_Q_2,V_P_2] :
% 59.73/59.64 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
% 59.73/59.64 | hBOOL(V_P_2)
% 59.73/59.64 | hBOOL(V_Q_2) ) ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__fimplies__1,axiom,
% 59.73/59.64 ! [V_Q_2,V_P_2] :
% 59.73/59.64 ( hBOOL(V_P_2)
% 59.73/59.64 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__fimplies__2,axiom,
% 59.73/59.64 ! [V_P_2,V_Q_2] :
% 59.73/59.64 ( ~ hBOOL(V_Q_2)
% 59.73/59.64 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 59.73/59.64
% 59.73/59.64 fof(help_c__fimplies__3,axiom,
% 59.73/59.64 ! [V_Q_2,V_P_2] :
% 59.73/59.64 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
% 59.73/59.64 | ~ hBOOL(V_P_2)
% 59.73/59.64 | hBOOL(V_Q_2) ) ).
% 59.73/59.64
% 59.73/59.64 %----Conjectures (6)
% 59.73/59.64 fof(conj_0,hypothesis,
% 59.73/59.64 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ).
% 59.73/59.64
% 59.73/59.64 fof(conj_1,hypothesis,
% 59.73/59.64 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts) ).
% 59.73/59.64
% 59.73/59.64 fof(conj_2,hypothesis,
% 59.73/59.64 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga)) ).
% 59.73/59.64
% 59.73/59.64 fof(conj_3,hypothesis,
% 59.73/59.64 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ).
% 59.73/59.64
% 59.73/59.64 fof(conj_4,hypothesis,
% 59.73/59.64 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts) ).
% 59.73/59.64
% 59.73/59.64 fof(conj_5,conjecture,
% 59.73/59.64 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)) ).
% 59.73/59.64
% 59.73/59.64 %------------------------------------------------------------------------------
% 59.73/59.64 %-------------------------------------------
% 59.73/59.64 % Proof found
% 59.73/59.64 % SZS status Theorem for theBenchmark
% 59.73/59.64 % SZS output start Proof
% 59.73/59.65 %ClaNum:10248(EqnAxiom:2937)
% 59.73/59.65 %VarNum:80242(SingletonVarNum:23571)
% 59.73/59.65 %MaxLitNum:8
% 59.73/59.65 %MaxfuncDepth:13
% 59.73/59.65 %SharedTerms:1011
% 59.73/59.65 %goalClause: 4583
% 59.73/59.65 %singleGoalClaCount:1
% 59.73/59.65 [2941]P1(a187)
% 59.73/59.65 [2942]P2(a879)
% 59.73/59.65 [2943]P2(a881)
% 59.73/59.65 [2944]P2(a1)
% 59.73/59.65 [2945]P2(a93)
% 59.73/59.65 [2946]P3(a879)
% 59.73/59.65 [2947]P3(a881)
% 59.73/59.65 [2948]P106(a881)
% 59.73/59.65 [2949]P106(a1)
% 59.73/59.65 [2950]P106(a93)
% 59.73/59.65 [2951]P107(a879)
% 59.73/59.65 [2952]P107(a881)
% 59.73/59.65 [2953]P107(a1)
% 59.73/59.65 [2954]P107(a93)
% 59.73/59.65 [2955]P108(a879)
% 59.73/59.65 [2956]P108(a881)
% 59.73/59.65 [2957]P108(a1)
% 59.73/59.65 [2958]P108(a93)
% 59.73/59.65 [2959]P4(a879)
% 59.73/59.65 [2960]P4(a884)
% 59.73/59.65 [2961]P109(a881)
% 59.73/59.65 [2962]P60(a879)
% 59.73/59.65 [2963]P60(a881)
% 59.73/59.65 [2964]P60(a1)
% 59.73/59.65 [2965]P61(a879)
% 59.73/59.65 [2966]P61(a881)
% 59.73/59.65 [2967]P61(a1)
% 59.73/59.65 [2968]P62(a879)
% 59.73/59.65 [2969]P63(a879)
% 59.73/59.65 [2970]P63(a881)
% 59.73/59.65 [2971]P63(a1)
% 59.73/59.65 [2972]P63(a93)
% 59.73/59.65 [2973]P102(a879)
% 59.73/59.65 [2974]P102(a881)
% 59.73/59.65 [2975]P102(a1)
% 59.73/59.65 [2976]P5(a879)
% 59.73/59.65 [2977]P100(a879)
% 59.73/59.65 [2978]P100(a881)
% 59.73/59.65 [2979]P100(a1)
% 59.73/59.65 [2980]P80(a1)
% 59.73/59.65 [2981]P64(a1)
% 59.73/59.65 [2982]P110(a879)
% 59.73/59.65 [2983]P101(a879)
% 59.73/59.65 [2984]P70(a881)
% 59.73/59.65 [2985]P70(a1)
% 59.73/59.65 [2986]P70(a93)
% 59.73/59.65 [2987]P65(a879)
% 59.73/59.65 [2988]P65(a884)
% 59.73/59.65 [2989]P72(a1)
% 59.73/59.65 [2990]P84(a879)
% 59.73/59.65 [2991]P85(a879)
% 59.73/59.65 [2992]P85(a1)
% 59.73/59.65 [2993]P111(a1)
% 59.73/59.65 [2994]P118(a1)
% 59.73/59.65 [2995]P119(a1)
% 59.73/59.65 [2996]P81(a881)
% 59.73/59.65 [2997]P81(a1)
% 59.73/59.65 [2998]P81(a93)
% 59.73/59.65 [2999]P73(a881)
% 59.73/59.65 [3000]P73(a1)
% 59.73/59.65 [3001]P73(a93)
% 59.73/59.65 [3002]P82(a881)
% 59.73/59.65 [3003]P82(a1)
% 59.73/59.65 [3004]P82(a93)
% 59.73/59.65 [3005]P122(a881)
% 59.73/59.65 [3006]P122(a1)
% 59.73/59.65 [3007]P122(a93)
% 59.73/59.65 [3008]P136(a1)
% 59.73/59.65 [3009]P112(a1)
% 59.73/59.65 [3010]P114(a881)
% 59.73/59.65 [3011]P114(a1)
% 59.73/59.65 [3012]P114(a93)
% 59.73/59.65 [3013]P71(a881)
% 59.73/59.65 [3014]P71(a1)
% 59.73/59.65 [3015]P71(a93)
% 59.73/59.65 [3016]P74(a881)
% 59.73/59.65 [3017]P74(a1)
% 59.73/59.65 [3018]P74(a93)
% 59.73/59.65 [3019]P75(a881)
% 59.73/59.65 [3020]P75(a1)
% 59.73/59.65 [3021]P75(a93)
% 59.73/59.65 [3022]P138(a881)
% 59.73/59.65 [3023]P138(a1)
% 59.73/59.65 [3024]P86(a881)
% 59.73/59.65 [3025]P86(a1)
% 59.73/59.65 [3026]P86(a93)
% 59.73/59.65 [3027]P87(a881)
% 59.73/59.65 [3028]P87(a1)
% 59.73/59.65 [3029]P87(a93)
% 59.73/59.65 [3030]P89(a881)
% 59.73/59.65 [3031]P89(a1)
% 59.73/59.65 [3032]P89(a93)
% 59.73/59.65 [3033]P115(a881)
% 59.73/59.65 [3034]P115(a1)
% 59.73/59.65 [3035]P115(a93)
% 59.73/59.65 [3036]P139(a881)
% 59.73/59.65 [3037]P139(a1)
% 59.73/59.65 [3038]P139(a93)
% 59.73/59.65 [3039]P125(a1)
% 59.73/59.65 [3040]P78(a881)
% 59.73/59.65 [3041]P78(a1)
% 59.73/59.65 [3042]P78(a93)
% 59.73/59.65 [3043]P93(a881)
% 59.73/59.65 [3044]P93(a1)
% 59.73/59.65 [3045]P93(a93)
% 59.73/59.65 [3046]P83(a881)
% 59.73/59.65 [3047]P83(a1)
% 59.73/59.65 [3048]P83(a93)
% 59.73/59.65 [3049]P77(a881)
% 59.73/59.65 [3050]P77(a1)
% 59.73/59.65 [3051]P77(a93)
% 59.73/59.65 [3052]P79(a1)
% 59.73/59.65 [3053]P126(a881)
% 59.73/59.65 [3054]P126(a1)
% 59.73/59.65 [3055]P126(a93)
% 59.73/59.65 [3056]P140(a1)
% 59.73/59.65 [3057]P131(a881)
% 59.73/59.65 [3058]P131(a1)
% 59.73/59.65 [3059]P131(a93)
% 59.73/59.65 [3060]P141(a881)
% 59.73/59.65 [3061]P141(a1)
% 59.73/59.65 [3062]P141(a93)
% 59.73/59.65 [3063]P123(a1)
% 59.73/59.65 [3064]P124(a1)
% 59.73/59.65 [3065]P90(a881)
% 59.73/59.65 [3066]P90(a1)
% 59.73/59.65 [3067]P90(a93)
% 59.73/59.65 [3068]P132(a881)
% 59.73/59.65 [3069]P132(a1)
% 59.73/59.65 [3070]P132(a93)
% 59.73/59.65 [3071]P134(a881)
% 59.73/59.65 [3072]P134(a1)
% 59.73/59.65 [3073]P134(a93)
% 59.73/59.65 [3074]P133(a881)
% 59.73/59.65 [3075]P133(a1)
% 59.73/59.65 [3076]P133(a93)
% 59.73/59.65 [3077]P120(a881)
% 59.73/59.65 [3078]P120(a1)
% 59.73/59.65 [3079]P120(a93)
% 59.73/59.65 [3080]P127(a881)
% 59.73/59.65 [3081]P127(a1)
% 59.73/59.65 [3082]P127(a93)
% 59.73/59.65 [3083]P128(a881)
% 59.73/59.65 [3084]P128(a1)
% 59.73/59.65 [3085]P128(a93)
% 59.73/59.65 [3086]P129(a1)
% 59.73/59.65 [3087]P130(a1)
% 59.73/59.65 [3088]P113(a881)
% 59.73/59.65 [3089]P113(a1)
% 59.73/59.65 [3090]P113(a93)
% 59.73/59.65 [3091]P142(a881)
% 59.73/59.65 [3092]P142(a1)
% 59.73/59.65 [3093]P142(a93)
% 59.73/59.65 [3094]P137(a1)
% 59.73/59.65 [3095]P94(a1)
% 59.73/59.65 [3096]P58(a881)
% 59.73/59.65 [3097]P58(a1)
% 59.73/59.65 [3098]P58(a93)
% 59.73/59.65 [3099]P59(a1)
% 59.73/59.65 [3100]P95(a881)
% 59.73/59.65 [3101]P95(a1)
% 59.73/59.65 [3102]P95(a93)
% 59.73/59.65 [3103]P97(a1)
% 59.73/59.65 [3104]P143(a881)
% 59.73/59.65 [3105]P143(a1)
% 59.73/59.65 [3106]P143(a93)
% 59.73/59.65 [3107]P103(a881)
% 59.73/59.65 [3108]P103(a1)
% 59.73/59.65 [3109]P103(a93)
% 59.73/59.65 [3110]P91(a1)
% 59.73/59.65 [3111]P88(a1)
% 59.73/59.65 [3112]P135(a1)
% 59.73/59.65 [3113]P76(a1)
% 59.73/59.65 [3114]P144(a884)
% 59.73/59.65 [3115]P144(a1)
% 59.73/59.65 [3116]P96(a879)
% 59.73/59.65 [3117]P96(a881)
% 59.73/59.65 [3118]P96(a884)
% 59.73/59.65 [3119]P96(a1)
% 59.73/59.65 [3120]P96(a93)
% 59.73/59.65 [3121]P96(a331)
% 59.73/59.65 [3122]P92(a881)
% 59.73/59.65 [3123]P92(a1)
% 59.73/59.65 [3124]P92(a93)
% 59.73/59.65 [3125]P105(a879)
% 59.73/59.65 [3126]P105(a881)
% 59.73/59.65 [3127]P105(a884)
% 59.73/59.65 [3128]P105(a93)
% 59.73/59.65 [3129]P105(a331)
% 59.73/59.65 [3130]P104(a884)
% 59.73/59.65 [3131]P104(a1)
% 59.73/59.65 [3132]P99(a879)
% 59.73/59.65 [3151]P36(a881,a248)
% 59.73/59.65 [3152]P36(a881,a325)
% 59.73/59.65 [3229]P16(a878,a890,a891)
% 59.73/59.65 [3230]P16(a878,a892,a891)
% 59.73/59.65 [3231]P37(a881,a881,a106)
% 59.73/59.65 [4533]~E(a91,a78)
% 59.73/59.65 [4534]~E(a91,a78)
% 59.73/59.65 [4535]~P1(a247)
% 59.73/59.65 [2938]E(f2(a1),a78)
% 59.73/59.65 [2939]E(f94(a93),a3)
% 59.73/59.65 [2940]E(f23(a93),a24)
% 59.73/59.65 [3133]E(f188(a881),f2(a881))
% 59.73/59.65 [3134]E(f95(a881),f240(a881))
% 59.73/59.65 [3135]E(f104(a881),f241(a881))
% 59.73/59.65 [3136]E(f96(a1),f25(a1))
% 59.73/59.65 [3137]E(f79(a247),f2(a881))
% 59.73/59.65 [3138]E(f79(a187),f2(a881))
% 59.73/59.65 [3139]P6(f73(a1))
% 59.73/59.65 [3140]P6(f2(a1))
% 59.73/59.65 [3199]P36(f887(a881,a881),a26)
% 59.73/59.65 [3557]E(f328(a881,a881,a248,a248),a26)
% 59.73/59.65 [4536]~E(f73(a1),f2(a1))
% 59.73/59.65 [3141]E(f105(f2(a881)),f2(a881))
% 59.73/59.65 [3142]E(f4(f2(a93)),f2(a881))
% 59.73/59.65 [3154]E(f335(f74(a1),a78),a78)
% 59.73/59.65 [3157]E(f335(a106,f2(a881)),f73(a881))
% 59.73/59.65 [3158]E(f335(a98,f73(a1)),f73(a881))
% 59.73/59.65 [3159]E(f335(a3,f73(a881)),f73(a93))
% 59.73/59.65 [3160]E(f335(a98,f2(a1)),f2(a881))
% 59.73/59.65 [3161]E(f335(a3,f2(a881)),f2(a93))
% 59.73/59.65 [3162]E(f335(f97(a881),a78),f2(a881))
% 59.73/59.65 [3163]E(f335(f97(a1),a78),f2(a1))
% 59.73/59.65 [3164]E(f335(f97(a93),a78),f2(a93))
% 59.73/59.65 [3165]E(f335(a98,f2(a1)),f2(a881))
% 59.73/59.65 [3166]E(f335(f189(a879),a247),f2(a881))
% 59.73/59.65 [3167]E(f335(f189(a879),a187),f2(a881))
% 59.73/59.65 [3168]E(f335(f97(a881),a78),f2(a881))
% 59.73/59.65 [3172]E(f335(f74(a1),f73(a1)),a91)
% 59.73/59.65 [3177]E(f335(f94(a1),f73(a881)),f73(a1))
% 59.73/59.65 [3178]E(f335(f94(a1),f2(a881)),f2(a1))
% 59.73/59.65 [3179]E(f335(f74(a1),f2(a1)),f2(a1))
% 59.73/59.65 [3180]E(f335(f189(a881),f2(a881)),f2(a881))
% 59.73/59.65 [3181]E(f335(f189(a93),f2(a93)),f2(a881))
% 59.73/59.65 [3182]E(f335(f94(a1),f73(a881)),f73(a1))
% 59.73/59.65 [3183]E(f335(f94(a1),f2(a881)),f2(a1))
% 59.73/59.65 [3196]E(f335(a98,f73(a1)),f335(a106,f2(a881)))
% 59.73/59.65 [3197]E(f326(f887(a881,a881),a26),a27)
% 59.73/59.65 [3198]E(f327(f887(a881,a881),a26),a28)
% 59.73/59.65 [3220]E(f335(f250(a881),f2(a881)),f188(f888(a881,a879)))
% 59.73/59.65 [3221]E(f335(f251(a881),f2(a881)),f252(f888(a881,a879)))
% 59.73/59.65 [3233]P38(f188(f888(a1,a879)))
% 59.73/59.65 [3269]E(f335(f335(f23(a93),f2(a93)),f73(a93)),f2(a93))
% 59.73/59.65 [3317]E(f335(f335(f147(a1,a881),a98),f107(a1)),f107(a881))
% 59.73/59.65 [3350]P1(f335(f335(f243(a1),a91),f2(a1)))
% 59.73/59.65 [3375]P1(f335(f335(f242(a1),f2(a1)),f73(a1)))
% 59.73/59.65 [3376]P1(f335(f335(f242(a1),f2(a1)),f2(a1)))
% 59.73/59.65 [3377]P1(f335(f335(f243(a1),f2(a1)),f73(a1)))
% 59.73/59.65 [3588]E(f335(f335(f291(a881,a881,a881),a325),f310(a881,a325)),a248)
% 59.73/59.65 [3627]P39(a1,a881,a98,f335(f242(a1),f2(a1)))
% 59.73/59.65 [3631]E(f335(f335(f33(a881,f888(a881,a879)),f252(f888(a881,a879))),f250(a881)),f252(f888(a881,a879)))
% 59.73/59.65 [3632]E(f335(f335(f33(a881,f888(a881,a879)),f252(f888(a881,a879))),f303(a881)),f252(f888(a881,a879)))
% 59.73/59.65 [3633]E(f335(f335(f33(a881,f888(a881,a879)),f252(f888(a881,a879))),f251(a881)),f252(f888(a881,a879)))
% 59.73/59.65 [3634]E(f335(f335(f34(a881,f888(a881,a879)),f252(f888(a881,a879))),f306(a881)),f188(f888(a881,a879)))
% 59.73/59.65 [3649]P26(a881,a1,f94(a1),f252(f888(a881,a879)))
% 59.73/59.65 [3665]P39(a881,a1,f94(a1),f335(f16(a879,a881),a187))
% 59.73/59.65 [3800]E(f335(f68(a881,a93,a1,a3),a98),f97(a93))
% 59.73/59.65 [4029]P54(a93,a881,a20,a3,f252(f888(a881,a879)))
% 59.73/59.65 [4036]P54(a1,f888(f887(a881,a881),a879),a101,a84,a92)
% 59.73/59.65 [4307]E(f269(a1,a1,a1,a1,f25(a1),f74(a1)),a45)
% 59.73/59.65 [4547]~E(f335(f97(a1),a91),f335(f97(a1),a78))
% 59.73/59.65 [4548]~P1(f335(a193,f73(a1)))
% 59.73/59.65 [4549]~P1(f335(a193,f2(a1)))
% 59.73/59.65 [4576]~P1(f335(f335(f243(a1),a78),f2(a1)))
% 59.73/59.65 [3213]E(f335(f335(f23(a1),a91),a91),a78)
% 59.73/59.65 [3214]E(f335(f335(f75(a1),a78),a78),a78)
% 59.73/59.65 [3215]E(f335(f335(f75(a1),a78),a91),a91)
% 59.73/59.65 [3228]E(f335(f94(a1),f335(a106,f2(a881))),f73(a1))
% 59.73/59.65 [3300]E(f335(f29(a884),f252(f888(a884,a879))),f73(a881))
% 59.73/59.65 [3322]P1(f335(a193,f335(f97(a1),a91)))
% 59.73/59.65 [3323]P1(f335(f335(f242(a1),a78),a78))
% 59.73/59.65 [3324]P1(f335(f335(f242(a1),a91),a78))
% 59.73/59.65 [3325]P1(f335(f335(f242(a1),a91),a91))
% 59.73/59.65 [3326]P1(f335(f335(f243(a1),a91),a78))
% 59.73/59.65 [3327]P1(f335(f335(f86(a1),a78),a78))
% 59.73/59.65 [3328]P1(f335(f335(f86(a1),a91),a91))
% 59.73/59.65 [3386]E(f335(f335(f312(a881),f2(a881)),f188(f888(a881,a879))),f335(f303(a881),f2(a881)))
% 59.73/59.65 [3442]P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),a78)))
% 59.73/59.65 [3454]E(f335(f313(a881,a881,a106),f252(f888(a881,a879))),f335(f306(a881),f2(a881)))
% 59.73/59.65 [3460]E(f335(f313(a1,a881,a98),f188(f888(a1,a879))),f188(f888(a881,a879)))
% 59.73/59.65 [3468]E(f335(f313(a881,a1,f94(a1)),f188(f888(a881,a879))),f188(f888(a1,a879)))
% 59.73/59.65 [3492]P8(f887(a881,a881),f252(f888(f887(a881,a881),a879)),a102)
% 59.73/59.65 [3808]E(f335(f68(a881,a1,a93,f94(a1)),a20),a21)
% 59.73/59.65 [3870]P36(a881,f335(f249(f887(a881,a881)),f335(f268(a881,a881,a879),f243(a881))))
% 59.73/59.65 [4565]~P1(f335(a193,f335(f97(a1),a78)))
% 59.73/59.65 [4566]~P1(f335(f335(f242(a1),a78),a91))
% 59.73/59.65 [4567]~P1(f335(f335(f243(a1),a78),a78))
% 59.73/59.65 [4568]~P1(f335(f335(f243(a1),a78),a91))
% 59.73/59.65 [4569]~P1(f335(f335(f243(a1),a91),a91))
% 59.73/59.65 [4570]~P1(f335(f335(f86(a1),a78),a91))
% 59.73/59.65 [4571]~P1(f335(f335(f86(a1),a91),a78))
% 59.73/59.65 [4580]~P1(f335(f56(a881),f252(f888(a881,a879))))
% 59.73/59.65 [4581]~P1(f335(f56(a1),f252(f888(a1,a879))))
% 59.73/59.65 [3653]P16(a878,a890,f335(f335(f312(f880(a878)),a893),f188(f888(f880(a878),a879))))
% 59.73/59.65 [3654]P16(a878,a892,f335(f335(f312(f880(a878)),a893),f188(f888(f880(a878),a879))))
% 59.73/59.65 [4481]E(f335(f268(a1,a1,a879),f335(f335(f8(f888(a1,a879),f888(a1,a879),a1),f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f243(a1),f2(a1))))),f335(f335(f7(a1,a1,f888(a1,a879)),f335(f335(f8(f888(a1,f888(a1,a879)),f888(a1,f888(a1,a879)),a1),f7(a1,a1,a879)),f335(f335(f8(f888(a1,a1),f888(a1,f888(a1,a879)),a1),f335(f8(a1,f888(a1,a879),a1),a332)),a220))),f73(a1)))),a216)
% 59.73/59.65 [4583]~P16(a878,a892,f335(f335(f312(f880(a878)),a893),a891))
% 59.73/59.65 [3495]E(f335(f335(f23(a1),f335(f335(f75(a1),a91),a91)),a91),a91)
% 59.73/59.65 [3530]E(f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91),f335(f74(a1),a91))
% 59.73/59.65 [3570]E(f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91),f335(f335(f23(a1),a78),a91))
% 59.73/59.65 [3683]P1(f335(f335(f242(f888(f880(a878),a879)),a890),a892))
% 59.73/59.65 [3733]E(f335(f335(f55(f887(a881,a881)),f252(f888(f887(a881,a881),a879))),a102),a92)
% 59.73/59.65 [3762]E(f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f73(a881))
% 59.73/59.65 [3763]E(f335(f97(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f73(a1))
% 59.73/59.65 [3764]E(f335(f97(a93),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f73(a93))
% 59.73/59.65 [3765]E(f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f73(a881))
% 59.73/59.65 [3768]E(f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(a106,f2(a881)))
% 59.73/59.65 [4163]E(f335(f335(f104(f888(f887(f887(a881,a881),f887(a881,a881)),a879)),a26),f310(f887(a881,a881),f188(f888(f887(f887(a881,a881),f887(a881,a881)),a879)))),a65)
% 59.73/59.65 [4236]E(f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),f73(a881)),f2(a881))),f188(f888(f887(a881,a881),a879))))),f73(a1))
% 59.73/59.65 [4237]E(f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),f2(a881)),f2(a881))),f188(f888(f887(a881,a881),a879))))),f2(a1))
% 59.73/59.65 [4252]E(f335(f249(f887(a881,a881)),f335(f268(a881,a881,a879),f335(f335(f8(a881,f888(a881,a879),a881),f335(f7(a881,a881,a879),a332)),a106))),a325)
% 59.73/59.65 [4220]E(f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),f335(a106,f335(a106,f2(a881))))
% 59.73/59.65 [4221]E(f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),f335(a106,f335(a106,f2(a881))))
% 59.73/59.65 [4224]E(f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),f335(f335(f75(a881),f73(a881)),f73(a881)))
% 59.73/59.65 [4225]E(f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),f335(f29(a879),f252(f888(a879,a879))))
% 59.73/59.65 [4293]P6(f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))
% 59.73/59.65 [4366]P27(f888(f887(a881,a881),a879),f335(f335(f264(f888(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),a879),f888(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),a879)),a27),a66))
% 59.73/59.65 [4367]P27(f888(f887(a881,a881),a879),f335(f335(f264(f888(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),a879),f888(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),a879)),a28),a64))
% 59.73/59.65 [4408]E(f335(f335(f104(f888(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),a879)),f327(f887(a881,a881),a65)),f335(f335(f312(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879))),f335(f335(f264(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),f188(f888(f887(a881,a881),a879))),f188(f888(f887(a881,a881),a879)))),f188(f888(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),a879)))),a64)
% 59.73/59.65 [4409]E(f335(f335(f104(f888(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),a879)),f326(f887(a881,a881),a65)),f335(f335(f312(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879))),f335(f335(f264(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),f188(f888(f887(a881,a881),a879))),f188(f888(f887(a881,a881),a879)))),f188(f888(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),a879)))),a66)
% 59.73/59.65 [4295]E(f335(a98,f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(a106,f335(a106,f2(a881))))
% 59.73/59.65 [4342]E(f335(a98,f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))
% 59.73/59.65 [4343]E(f335(f94(a1),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))
% 59.73/59.65 [4378]P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))
% 59.73/59.65 [4379]E(f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),a91)),f335(a106,f335(a106,f335(a106,f2(a881)))))
% 59.73/59.65 [4423]P6(f335(f97(a1),f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),a91)))
% 59.73/59.65 [4450]E(f335(a98,f335(f97(a1),f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),a91))),f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),a91)))
% 59.73/59.65 [4451]E(f335(f94(a1),f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),a91))),f335(f97(a1),f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),a91)))
% 59.73/59.65 [4466]P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),a91))))
% 59.73/59.65 [3153]P7(x31531,a332)
% 59.73/59.65 [3558]P26(a881,a881,a106,x35581)
% 59.73/59.65 [3143]P96(f880(x31431))
% 59.73/59.65 [3144]P96(f885(x31441))
% 59.73/59.65 [3145]P96(f882(x31451))
% 59.73/59.65 [3146]P96(f883(x31461))
% 59.73/59.65 [3147]P105(f880(x31471))
% 59.73/59.65 [3148]P105(f885(x31481))
% 59.73/59.65 [3149]P105(f882(x31491))
% 59.73/59.65 [3150]P105(f883(x31501))
% 59.73/59.65 [3169]P36(a1,f99(x31691))
% 59.73/59.65 [3170]P36(a1,f100(x31701))
% 59.73/59.65 [3217]P36(f888(x32171,a879),f309(x32171))
% 59.73/59.65 [3245]E(f253(x32451,x32451,a332),a332)
% 59.73/59.65 [3260]E(f39(a1,x32601,x32601),f2(a1))
% 59.73/59.65 [3319]P17(x33191,f888(x33191,a879),f312(x33191))
% 59.73/59.65 [4537]~E(f335(a106,x45371),x45371)
% 59.73/59.65 [4538]~E(f335(a106,x45381),x45381)
% 59.73/59.65 [4539]~E(f335(a106,x45391),f2(a881))
% 59.73/59.65 [4540]~E(f335(a106,x45401),f2(a881))
% 59.73/59.65 [4541]~E(f335(a106,x45411),f2(a881))
% 59.73/59.65 [4542]~E(f335(a106,x45421),f2(a881))
% 59.73/59.65 [4543]~E(f335(a106,x45431),f2(a881))
% 59.73/59.65 [4544]~E(f335(a106,x45441),f2(a881))
% 59.73/59.65 [3155]E(f335(f189(a881),x31551),x31551)
% 59.73/59.65 [3156]E(f335(f97(a1),x31561),x31561)
% 59.73/59.65 [3171]E(f335(a84,f336(x31711)),x31711)
% 59.73/59.65 [3184]E(f108(x31841,f107(x31841)),f107(x31841))
% 59.73/59.65 [3185]E(f145(x31851,f107(x31851)),f107(x31851))
% 59.73/59.65 [3193]E(f335(f161(x31931),f107(x31931)),f107(x31931))
% 59.73/59.65 [3194]E(f335(f165(x31941),f107(x31941)),f107(x31941))
% 59.73/59.65 [3195]E(f335(f162(x31951),f107(x31951)),f107(x31951))
% 59.73/59.65 [3200]E(f335(f97(a1),x32001),f335(f96(a1),x32001))
% 59.73/59.65 [3201]E(f335(a84,f335(a101,x32011)),x32011)
% 59.73/59.65 [3202]E(f335(a3,f335(a20,x32021)),x32021)
% 59.73/59.65 [3203]E(f335(a3,f335(a20,x32031)),x32031)
% 59.73/59.65 [3204]E(f335(a20,f335(a3,x32041)),x32041)
% 59.73/59.65 [3205]P6(f335(f94(a1),x32051))
% 59.73/59.65 [3210]E(f335(f189(f885(x32101)),f200(x32101)),f2(a881))
% 59.73/59.65 [3211]E(f335(f189(f882(x32111)),f107(x32111)),f2(a881))
% 59.73/59.65 [3212]E(f335(f189(f883(x32121)),f113(x32121)),f2(a881))
% 59.73/59.65 [3225]E(f234(x32251,f200(x32251)),f188(f888(x32251,a879)))
% 59.73/59.65 [3236]E(f335(f335(f23(a881),x32361),f2(a881)),x32361)
% 59.73/59.65 [3237]E(f335(f335(f76(a881),x32371),f73(a881)),x32371)
% 59.73/59.65 [3238]E(f335(f335(f76(a1),x32381),f73(a1)),x32381)
% 59.73/59.65 [3239]E(f335(f335(f75(a881),x32391),f2(a881)),x32391)
% 59.73/59.65 [3240]E(f335(f335(f75(a1),x32401),f2(a1)),x32401)
% 59.73/59.65 [3241]E(f335(f335(f241(a881),x32411),f2(a881)),x32411)
% 59.73/59.65 [3242]E(f335(f335(f76(a881),x32421),f2(a881)),f2(a881))
% 59.73/59.65 [3243]E(f335(f335(f30(a1),x32431),f2(a1)),f2(a1))
% 59.73/59.65 [3244]E(f335(f335(f240(a881),x32441),f2(a881)),f2(a881))
% 59.73/59.65 [3251]E(f335(f166(x32511),f107(x32511)),f188(f888(x32511,a879)))
% 59.73/59.65 [3255]P1(f335(f130(x32551),f107(x32551)))
% 59.73/59.65 [3261]E(f335(f147(x32611,x32611),f5(x32611)),f25(f882(x32611)))
% 59.73/59.65 [3262]E(f335(f147(x32621,x32621),f25(x32621)),f25(f882(x32621)))
% 59.73/59.65 [3263]E(f335(f201(x32631,x32631),f5(x32631)),f25(f885(x32631)))
% 59.73/59.65 [3264]E(f335(f201(x32641,x32641),f25(x32641)),f25(f885(x32641)))
% 59.73/59.65 [3265]E(f39(a1,x32651,f2(a1)),x32651)
% 59.73/59.65 [3266]E(f335(f242(a881),f335(a106,x32661)),f335(f243(a881),x32661))
% 59.73/59.65 [3267]E(f335(f250(a881),f335(a106,x32671)),f335(f303(a881),x32671))
% 59.73/59.65 [3268]E(f335(f251(a881),f335(a106,x32681)),f335(f306(a881),x32681))
% 59.73/59.65 [3270]E(f39(a1,f2(a1),x32701),f2(a1))
% 59.73/59.65 [3284]E(f335(f335(f75(a881),x32841),f73(a881)),f335(a106,x32841))
% 59.73/59.65 [3294]E(f335(f304(a881,x32941),f2(a881)),f188(f888(a881,a879)))
% 59.73/59.65 [3307]E(f305(a881,f2(a881),x33071),f335(f303(a881),x33071))
% 59.73/59.65 [3353]E(f335(f335(f23(a881),f335(a106,x33531)),f73(a881)),x33531)
% 59.73/59.65 [3366]E(f41(f2(a1),x33661),f335(f335(f264(a1,a1),f2(a1)),f2(a1)))
% 59.73/59.65 [3370]E(f335(f335(f75(a881),f335(a20,x33701)),f2(a881)),f335(a20,x33701))
% 59.73/59.65 [3416]P1(f335(f335(f243(a881),x34161),f335(a106,x34161)))
% 59.73/59.65 [3428]P1(f335(f335(f243(a881),f2(a881)),f335(a106,x34281)))
% 59.73/59.65 [3440]E(f335(f335(f183(f882(x34401),f882(x34401)),f2(a881)),f161(x34401)),f25(f882(x34401)))
% 59.73/59.65 [3664]E(f87(x36641,x36641,f252(f888(x36641,a879)),f25(x36641)),f25(x36641))
% 59.73/59.65 [3720]E(f335(f335(f23(a93),f335(a3,f335(a106,f335(a20,x37201)))),f73(a93)),x37201)
% 59.73/59.65 [3792]P1(f335(f335(f242(a1),f335(f74(a1),f335(f94(a1),x37921))),f2(a1)))
% 59.73/59.65 [3942]P1(f335(f335(f243(a1),f335(f74(a1),f335(f94(a1),f335(a106,x39421)))),f2(a1)))
% 59.73/59.65 [4554]~E(f252(f888(x45541,a879)),f188(f888(x45541,a879)))
% 59.73/59.65 [4577]~P1(f335(f335(f243(a881),x45771),f2(a881)))
% 59.73/59.65 [4578]~P1(f335(f335(f243(a881),x45781),f2(a881)))
% 59.73/59.65 [4579]~P1(f335(f335(f243(a881),x45791),f2(a881)))
% 59.73/59.65 [4591]~P1(f335(f335(f243(a1),f335(f94(a1),x45911)),f2(a1)))
% 59.73/59.65 [3216]E(f173(x32161,f107(f882(x32161))),f107(f882(x32161)))
% 59.73/59.65 [3218]E(f335(f335(f76(a1),a78),x32181),a78)
% 59.73/59.65 [3219]E(f335(f335(f75(a1),a78),x32191),x32191)
% 59.73/59.65 [3222]E(f335(a98,f335(f94(a1),x32221)),x32221)
% 59.73/59.65 [3223]E(f335(f335(f23(a1),x32231),a78),x32231)
% 59.73/59.65 [3224]E(f335(f335(f75(a1),x32241),a78),x32241)
% 59.73/59.65 [3227]E(f335(f335(f23(a881),x32271),x32271),f2(a881))
% 59.73/59.65 [3234]E(f335(f74(a1),f335(f74(a1),x32341)),x32341)
% 59.73/59.65 [3235]E(f335(f29(a881),f335(f250(a881),x32351)),x32351)
% 59.73/59.65 [3246]E(f335(f335(f76(a881),f73(a881)),x32461),x32461)
% 59.73/59.65 [3247]E(f335(f335(f76(a1),f73(a1)),x32471),x32471)
% 59.73/59.65 [3248]E(f335(f335(f75(a881),f2(a881)),x32481),x32481)
% 59.73/59.65 [3249]E(f335(f335(f75(a1),f2(a1)),x32491),x32491)
% 59.73/59.65 [3250]E(f335(f335(f241(a881),f2(a881)),x32501),x32501)
% 59.73/59.65 [3256]E(f335(f335(f23(a881),f2(a881)),x32561),f2(a881))
% 59.73/59.65 [3257]E(f335(f335(f76(a881),f2(a881)),x32571),f2(a881))
% 59.73/59.65 [3258]E(f335(f335(f30(a1),f2(a1)),x32581),f2(a1))
% 59.73/59.65 [3259]E(f335(f335(f240(a881),f2(a881)),x32591),f2(a881))
% 59.73/59.65 [3271]E(f122(x32711,f335(f74(a1),x32711)),f125(a1,x32711))
% 59.73/59.65 [3277]E(f335(f304(a881,f2(a881)),x32771),f335(f250(a881),x32771))
% 59.73/59.65 [3278]E(f335(f335(f76(a1),a91),x32781),f335(f74(a1),x32781))
% 59.73/59.65 [3285]E(f335(a98,f335(f97(a1),x32851)),f335(f97(a881),x32851))
% 59.73/59.65 [3286]E(f335(a98,f335(f97(a1),x32861)),f335(f97(a881),x32861))
% 59.73/59.65 [3287]E(f335(a20,f335(f97(a93),x32871)),f335(f97(a881),x32871))
% 59.73/59.65 [3288]E(f335(f29(a881),f335(f303(a881),x32881)),f335(a106,x32881))
% 59.73/59.65 [3298]E(f335(f335(f75(a881),f73(a881)),x32981),f335(a106,x32981))
% 59.73/59.65 [3302]E(f335(f96(a1),f335(f94(a1),x33021)),f335(f94(a1),x33021))
% 59.73/59.65 [3303]E(f335(f70(a1),f335(f94(a1),x33031)),f335(f94(a1),x33031))
% 59.73/59.65 [3306]E(f200(f887(x33061,f883(x33061))),f335(f128(x33061),f113(x33061)))
% 59.73/59.65 [3309]E(f335(f29(x33091),f188(f888(x33091,a879))),f2(a881))
% 59.73/59.65 [3311]E(f335(f335(f30(a881),x33111),f335(a106,f2(a881))),x33111)
% 59.73/59.65 [3320]E(f39(a881,x33201,f335(a106,f2(a881))),f2(a881))
% 59.73/59.65 [3321]E(f39(a1,x33211,f335(f97(a1),a91)),f2(a1))
% 59.73/59.65 [3330]E(f335(f335(f75(a1),a91),x33301),f335(f335(f75(a1),x33301),a91))
% 59.73/59.65 [3337]E(f335(f335(f30(a1),x33371),f335(f97(a1),a91)),f335(f74(a1),x33371))
% 59.73/59.65 [3341]E(f132(a881,f335(f304(a881,x33411),f2(a881))),f107(a881))
% 59.73/59.65 [3342]E(f335(f335(f75(a1),x33421),f73(a1)),f335(f335(f23(a1),x33421),a91))
% 59.73/59.65 [3343]E(f335(f335(f23(a1),x33431),f73(a1)),f335(f335(f75(a1),x33431),a91))
% 59.73/59.65 [3347]P1(f335(f335(f242(a881),x33471),x33471))
% 59.73/59.65 [3348]P1(f335(f335(f242(a1),x33481),x33481))
% 59.73/59.65 [3349]P1(f335(f335(f86(a1),x33491),x33491))
% 59.73/59.65 [3354]E(f335(f74(a1),f335(f97(a1),x33541)),f335(f97(a1),f335(f74(a1),x33541)))
% 59.73/59.65 [3355]P1(f335(f56(a881),f335(f250(a881),x33551)))
% 59.73/59.65 [3356]P1(f335(f56(a881),f335(f303(a881),x33561)))
% 59.73/59.65 [3364]E(f154(x33641,f252(f888(x33641,a879))),f252(f888(f882(x33641),a879)))
% 59.73/59.65 [3368]P1(f335(f335(f242(a881),f2(a881)),x33681))
% 59.73/59.65 [3369]P1(f335(f335(f242(a881),f2(a881)),x33691))
% 59.73/59.65 [3379]E(f335(f335(f75(a881),f105(x33791)),f335(a106,f2(a881))),f105(f335(a106,x33791)))
% 59.73/59.65 [3381]E(f335(f249(x33811),f335(f16(a879,x33811),a247)),f188(f888(x33811,a879)))
% 59.73/59.65 [3382]E(f335(f249(x33821),f335(f16(a879,x33821),a187)),f252(f888(x33821,a879)))
% 59.73/59.65 [3385]E(f335(f335(f312(a881),x33851),f335(f250(a881),x33851)),f335(f250(a881),f335(a106,x33851)))
% 59.73/59.65 [3397]E(f335(f335(f75(a1),f73(a1)),f335(f94(a1),x33971)),f335(f94(a1),f335(a106,x33971)))
% 59.73/59.65 [3399]E(f335(f335(f144(f882(x33991)),f107(x33991)),f107(f882(x33991))),f48(x33991,f107(x33991)))
% 59.73/59.65 [3419]E(f188(f888(f887(x34191,x34191),a879)),f261(x34191,f188(f888(x34191,a879))))
% 59.73/59.65 [3420]E(f335(f311(x34201),f252(f888(x34201,a879))),f252(f888(f888(x34201,a879),a879)))
% 59.73/59.65 [3421]E(f335(f74(f888(x34211,a879)),f188(f888(x34211,a879))),f252(f888(x34211,a879)))
% 59.73/59.65 [3422]E(f335(f74(f888(x34221,a879)),f252(f888(x34221,a879))),f188(f888(x34221,a879)))
% 59.73/59.65 [3423]P1(f335(f56(x34231),f188(f888(x34231,a879))))
% 59.73/59.65 [3424]P1(f335(f56(x34241),f188(f888(x34241,a879))))
% 59.73/59.65 [3426]E(f335(f304(a881,x34261),f335(a106,x34261)),f335(f335(f312(a881),x34261),f188(f888(a881,a879))))
% 59.73/59.65 [3427]E(f80(f887(a881,a881),f42(x34271,f2(a881))),f335(f335(f264(a881,a881),f2(a881)),x34271))
% 59.73/59.65 [3441]E(f335(f335(f312(a881),f335(a106,x34411)),f335(f303(a881),x34411)),f335(f303(a881),f335(a106,x34411)))
% 59.73/59.65 [3445]P36(x34451,f188(f888(f887(x34451,x34451),a879)))
% 59.73/59.65 [3447]P1(f335(f335(f242(a1),f2(a1)),f335(f94(a1),x34471)))
% 59.73/59.65 [3448]P1(f335(f335(f242(a1),f2(a1)),f335(f94(a1),x34481)))
% 59.73/59.65 [3456]E(f335(f335(f75(a881),f335(f189(a881),x34561)),f335(a106,f2(a881))),f335(f189(a881),f335(a106,x34561)))
% 59.73/59.65 [3508]E(f335(f313(x35081,x35081,f25(x35081)),f252(f888(x35081,a879))),f252(f888(x35081,a879)))
% 59.73/59.65 [3565]P38(f335(f313(a881,a1,f94(a1)),x35651))
% 59.73/59.65 [3604]P46(x36041,f188(f888(x36041,a879)),f188(f888(f887(x36041,x36041),a879)))
% 59.73/59.65 [3623]E(f335(f335(f264(a1,a1),f335(f97(a1),a91)),f335(f335(f23(a1),x36231),f73(a1))),f44(f335(f97(a1),a91),x36231))
% 59.73/59.65 [3624]P1(f335(f335(f337(a881),f335(a20,x36241)),f252(f888(a881,a879))))
% 59.73/59.65 [3677]P57(x36771,f335(f16(f888(x36771,a879),x36771),f335(f16(a879,x36771),a247)))
% 59.73/59.65 [3864]E(f335(f135(f882(x38641),f882(x38641),f127(x38641),f107(x38641)),f107(f882(x38641))),f107(x38641))
% 59.73/59.65 [3882]P1(f335(f335(f337(f888(f887(a881,a881),a879)),f336(x38821)),a92))
% 59.73/59.65 [3907]P1(f335(f335(f337(f888(f887(a881,a881),a879)),f335(a101,x39071)),a92))
% 59.73/59.65 [4045]P26(x40451,f888(x40451,a879),f335(f335(f7(x40451,f888(x40451,a879),f888(x40451,a879)),f312(x40451)),f188(f888(x40451,a879))),f252(f888(x40451,a879)))
% 59.73/59.65 [4550]~E(f335(f335(f75(a1),x45501),x45501),a91)
% 59.73/59.65 [4551]~E(f335(f335(f75(a1),x45511),x45511),a91)
% 59.73/59.65 [4563]~E(f335(a3,f335(a106,f335(a20,x45631))),f2(a93))
% 59.73/59.65 [4564]~E(f335(a3,f335(a106,f335(a20,x45641))),f2(a93))
% 59.73/59.65 [4572]~P1(f335(a193,f335(f94(a1),x45721)))
% 59.73/59.65 [4574]~P1(f335(f335(f243(a881),x45741),x45741))
% 59.73/59.65 [4575]~P1(f335(f335(f243(a881),x45751),x45751))
% 59.73/59.65 [4584]~P1(f335(f335(f242(a881),f335(a106,x45841)),x45841))
% 59.73/59.65 [3371]E(f335(a98,f335(f74(a1),f335(f94(a1),x33711))),f2(a881))
% 59.73/59.65 [3374]E(f335(f335(f75(a1),f335(f74(a1),x33741)),x33741),f2(a1))
% 59.73/59.65 [3378]E(f335(f29(a1),f335(f304(a1,f2(a1)),x33781)),f335(a98,x33781))
% 59.73/59.65 [3390]E(f335(f335(f254(a881),f335(a106,f2(a881))),x33901),f335(a106,f2(a881)))
% 59.73/59.65 [3489]E(f335(f287(x34891),f188(f888(f887(x34891,x34891),a879))),f188(f888(x34891,a879)))
% 59.73/59.65 [3491]P1(f335(f56(a1),f335(f304(a1,f2(a1)),x34911)))
% 59.73/59.65 [3497]E(f32(f888(x34971,a879),f188(f888(f888(x34971,a879),a879))),f252(f888(x34971,a879)))
% 59.73/59.65 [3498]E(f32(f888(x34981,a879),f252(f888(f888(x34981,a879),a879))),f188(f888(x34981,a879)))
% 59.73/59.65 [3499]E(f31(f888(x34991,a879),f188(f888(f888(x34991,a879),a879))),f188(f888(x34991,a879)))
% 59.73/59.65 [3500]E(f31(f888(x35001,a879),f252(f888(f888(x35001,a879),a879))),f252(f888(x35001,a879)))
% 59.73/59.65 [3547]E(f335(f335(f312(f882(x35471)),f107(x35471)),f188(f888(f882(x35471),a879))),f154(x35471,f188(f888(x35471,a879))))
% 59.73/59.65 [3548]E(f335(f335(f312(f882(x35481)),f107(x35481)),f188(f888(f882(x35481),a879))),f155(x35481,f107(f888(x35481,a879))))
% 59.73/59.65 [3574]E(f335(f335(f75(a1),f335(f74(a1),x35741)),f335(f74(a1),x35741)),f335(f74(a1),f335(f335(f75(a1),x35741),x35741)))
% 59.73/59.65 [3587]E(f335(f335(f75(a881),f4(x35871)),f335(a106,f2(a881))),f4(f335(a3,f335(a106,f335(a20,x35871)))))
% 59.73/59.65 [3613]E(f335(f29(a1),f335(f313(a881,a1,f94(a1)),x36131)),f335(f29(a881),x36131))
% 59.73/59.65 [3614]P1(f335(f335(f242(a881),x36141),f335(f335(f76(a881),x36141),x36141)))
% 59.73/59.65 [3655]E(f335(f313(a1,a881,a98),f305(a1,f2(a1),f335(f94(a1),x36551))),f335(f303(a881),x36551))
% 59.73/59.65 [3672]E(f335(f335(f30(a881),f335(a106,f2(a881))),f335(f97(a881),x36721)),f335(a98,f335(f335(f30(a1),f73(a1)),f335(f97(a1),x36721))))
% 59.73/59.65 [3674]E(f335(f166(a881),f132(a881,f335(f304(a881,f2(a881)),f335(a106,x36741)))),f335(f303(a881),x36741))
% 59.73/59.65 [3675]E(f335(f335(f75(a881),f335(f189(a93),x36751)),f335(a106,f2(a881))),f335(f189(a93),f335(a3,f335(a106,f335(a20,x36751)))))
% 59.73/59.65 [3694]E(f335(f313(a1,a881,a98),f335(f313(a881,a1,f94(a1)),x36941)),x36941)
% 59.73/59.65 [3726]E(f335(f335(f312(a881),f2(a881)),f335(f313(a881,a881,a106),f335(f250(a881),x37261))),f335(f250(a881),f335(a106,x37261)))
% 59.73/59.65 [3732]P52(x37321,x37321,f310(x37321,f188(f888(f887(x37321,x37321),a879))))
% 59.73/59.65 [3738]P1(f335(a193,f335(f74(a1),f335(f94(a1),f335(a106,x37381)))))
% 59.73/59.65 [3749]E(f335(f335(f23(f888(a881,a879)),f335(f251(a881),x37491)),f335(f335(f312(a881),x37491),f188(f888(a881,a879)))),f335(f251(a881),f335(a106,x37491)))
% 59.73/59.65 [3766]E(f335(f335(f75(a1),f335(f335(f23(a1),a78),x37661)),f335(f335(f23(a1),a78),x37661)),f335(f335(f23(a1),a78),f335(f335(f75(a1),x37661),x37661)))
% 59.73/59.65 [3769]P46(x37691,f252(f888(x37691,a879)),f310(x37691,f188(f888(f887(x37691,x37691),a879))))
% 59.73/59.65 [3781]E(f335(f335(f312(f888(x37811,a879)),f188(f888(x37811,a879))),f188(f888(f888(x37811,a879),a879))),f335(f311(x37811),f188(f888(x37811,a879))))
% 59.73/59.65 [3809]E(f335(f335(f23(f888(a881,a879)),f335(f306(a881),x38091)),f335(f335(f312(a881),f335(a106,x38091)),f188(f888(a881,a879)))),f335(f306(a881),f335(a106,x38091)))
% 59.73/59.65 [3819]E(f335(f335(f312(f885(x38191)),f200(x38191)),f335(f313(x38191,f885(x38191),f235(x38191)),f252(f888(x38191,a879)))),f252(f888(f885(x38191),a879)))
% 59.73/59.65 [3919]E(f335(f97(a881),f335(f335(f75(a1),x39191),x39191)),f335(f335(f81(a881,a881),f335(f97(a881),x39191)),f335(f335(f18(a881,a881,a881),f75(a881)),f5(a881))))
% 59.73/59.65 [4316]P17(x43161,f888(x43161,a879),f335(f335(f8(f888(x43161,a879),f888(f888(x43161,a879),f888(x43161,a879)),x43161),f335(f7(f888(x43161,a879),f888(x43161,a879),f888(x43161,a879)),f23(f888(x43161,a879)))),f335(f335(f7(x43161,f888(x43161,a879),f888(x43161,a879)),f312(x43161)),f188(f888(x43161,a879)))))
% 59.73/59.65 [4407]E(f335(f249(f887(a1,a1)),f335(f268(a1,a1,a879),f335(f335(f8(f888(a1,a879),f888(a1,a879),a1),f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f242(a1),x44071)))),f243(a1)))),f99(x44071))
% 59.73/59.65 [4441]E(f335(f249(f887(a1,a1)),f335(f268(a1,a1,a879),f335(f335(f18(a1,f888(a1,a879),f888(a1,a879)),f335(f335(f8(f888(a879,a879),f888(f888(a1,a879),f888(a1,a879)),a1),f8(a879,a879,a1)),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f242(a1),x44411)))),f243(a1)))),f100(x44411))
% 59.73/59.65 [4496]E(f335(f249(f887(f888(x44961,a879),f888(x44961,a879))),f335(f268(f888(x44961,a879),f888(x44961,a879),a879),f335(f335(f7(f888(x44961,a879),f888(f888(x44961,a879),a879),f888(f888(x44961,a879),a879)),f335(f335(f8(f888(f888(x44961,a879),f888(a879,a879)),f888(f888(f888(x44961,a879),a879),f888(f888(x44961,a879),a879)),f888(x44961,a879)),f18(f888(x44961,a879),a879,a879)),f335(f335(f8(f888(f888(x44961,a879),a879),f888(f888(x44961,a879),f888(a879,a879)),f888(x44961,a879)),f335(f8(a879,f888(a879,a879),f888(x44961,a879)),a333)),f243(f888(x44961,a879))))),f56(x44961)))),f309(x44961))
% 59.73/59.65 [4588]~P1(f335(f56(f882(x45881)),f252(f888(f882(x45881),a879))))
% 59.73/59.65 [4593]~P1(f335(f335(f86(a1),a91),f335(f335(f75(a1),x45931),x45931)))
% 59.73/59.65 [4603]~P1(f335(f335(f242(a1),f2(a1)),f335(f74(a1),f335(f94(a1),f335(a106,x46031)))))
% 59.73/59.65 [3380]E(f115(x33801,f113(f885(f883(f885(x33801))))),f113(f885(x33801)))
% 59.73/59.65 [3524]E(f335(f335(f23(a1),f335(f335(f75(a1),x35241),a91)),a91),x35241)
% 59.73/59.65 [3540]E(f335(f166(a881),f132(a881,f335(f304(a881,f2(a881)),x35401))),f335(f250(a881),x35401))
% 59.73/59.65 [3740]E(f335(f260(x37401,x37401),f310(x37401,f188(f888(f887(x37401,x37401),a879)))),f252(f888(x37401,a879)))
% 59.73/59.65 [3741]E(f335(f262(x37411,x37411),f310(x37411,f188(f888(f887(x37411,x37411),a879)))),f252(f888(x37411,a879)))
% 59.73/59.65 [3788]E(f335(f335(f75(a1),f335(f335(f75(a1),f73(a1)),x37881)),x37881),f335(f335(f23(a1),f335(f335(f75(a1),x37881),x37881)),a91))
% 59.73/59.65 [3838]E(f335(f289(x38381,x38381),f310(x38381,f188(f888(f887(x38381,x38381),a879)))),f310(x38381,f188(f888(f887(x38381,x38381),a879))))
% 59.73/59.65 [3885]P1(f335(f335(f242(a881),x38851),f335(f335(f76(a881),x38851),f335(f335(f76(a881),x38851),x38851))))
% 59.73/59.65 [3976]E(f335(f335(f291(x39761,x39761,x39761),f188(f888(f887(x39761,x39761),a879))),f310(x39761,f188(f888(f887(x39761,x39761),a879)))),f188(f888(f887(x39761,x39761),a879)))
% 59.73/59.65 [4167]P1(f335(f56(a881),f335(f249(a881),f335(f335(f7(a881,a881,a879),f242(a881)),x41671))))
% 59.73/59.65 [4168]P1(f335(f56(a881),f335(f249(a881),f335(f335(f7(a881,a881,a879),f243(a881)),x41681))))
% 59.73/59.65 [4461]E(f335(f249(f887(x44611,x44611)),f335(f335(f8(f888(x44611,a879),a879,f887(x44611,x44611)),f82(x44611)),f335(f335(f7(f887(x44611,x44611),f888(x44611,f887(x44611,x44611)),f888(x44611,a879)),f335(f335(f8(f888(f887(x44611,x44611),a879),f888(f888(x44611,f887(x44611,x44611)),f888(x44611,a879)),f887(x44611,x44611)),f8(f887(x44611,x44611),a879,x44611)),a332)),f335(f335(f18(x44611,x44611,f887(x44611,x44611)),f264(x44611,x44611)),f5(x44611))))),f310(x44611,f188(f888(f887(x44611,x44611),a879))))
% 59.73/59.65 [4589]~E(f335(f335(f23(a1),f335(f335(f75(a1),x45891),x45891)),a91),a78)
% 59.73/59.65 [4590]~E(f335(f335(f23(a1),f335(f335(f75(a1),x45901),x45901)),a91),a78)
% 59.73/59.65 [4592]~E(f335(f335(f75(a1),f335(f335(f75(a1),f73(a1)),x45921)),x45921),f2(a1))
% 59.73/59.65 [4600]~P1(f335(f335(f86(a1),f335(f335(f75(a1),x46001),x46001)),a91))
% 59.73/59.65 [3931]E(f335(f335(f75(a1),f335(f335(f23(a1),a91),x39311)),f335(f335(f23(a1),a91),x39311)),f335(f335(f23(a1),a91),f335(f335(f23(a1),f335(f335(f75(a1),x39311),x39311)),a91)))
% 59.73/59.65 [4054]E(f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),a91),x40541)),f335(f335(f23(a1),a91),x40541))),a91),f335(f335(f23(a1),a91),f335(f335(f75(a1),x40541),x40541)))
% 59.73/59.65 [4088]E(f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f75(a1),x40881),a91)),f335(f335(f75(a1),x40881),a91))),a91),f335(f335(f75(a1),f335(f335(f75(a1),x40881),x40881)),a91))
% 59.73/59.65 [4127]E(f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),a91),x41271)),f335(f335(f23(a1),a91),x41271))),a91),f335(f335(f23(a1),a78),f335(f335(f23(a1),f335(f335(f75(a1),x41271),x41271)),a91)))
% 59.73/59.65 [4232]E(f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),x42321),f2(a881))),f188(f888(f887(a881,a881),a879))))),f335(f94(a1),x42321))
% 59.73/59.65 [4242]E(f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),f340(x42421)),f414(x42421))),f188(f888(f887(a881,a881),a879))))),x42421)
% 59.73/59.65 [4278]E(f335(f249(a1),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f242(a1),f2(a1)))),x42781)),f335(f313(a881,a1,f94(a1)),f335(f249(a881),f335(f335(f8(a1,a879,a881),x42781),f94(a1)))))
% 59.73/59.65 [4324]P38(f335(f249(a1),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f242(a1),f2(a1)))),x43241)))
% 59.73/59.65 [4346]P1(f335(f335(f337(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879))),f335(f335(f264(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),x43461),f188(f888(f887(a881,a881),a879)))),a66))
% 59.73/59.65 [4352]E(f335(f313(a1,a881,a98),f335(f249(a1),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f242(a1),f2(a1)))),f335(f335(f8(a881,a879,a1),x43521),a98)))),f335(f249(a881),x43521))
% 59.73/59.65 [4510]E(f315(a881,f335(f335(f33(f887(a881,a881),f888(a881,a879)),f335(a101,x45101)),f335(f268(a881,a881,f888(a881,a879)),f335(f335(f7(a881,f888(a881,a879),f888(a881,f888(a881,a879))),f335(f335(f8(f888(a881,f888(f888(a881,a879),f888(a881,a879))),f888(f888(a881,a879),f888(a881,f888(a881,a879))),a881),f7(a881,f888(a881,a879),f888(a881,a879))),f335(f335(f8(f888(a881,a881),f888(a881,f888(f888(a881,a879),f888(a881,a879))),a881),f335(f8(a881,f888(f888(a881,a879),f888(a881,a879)),a881),f312(a881))),f23(a881)))),f188(f888(a881,a879)))))),f335(a98,x45101))
% 59.73/59.65 [4605]~P1(f335(f335(f86(a1),a78),f335(f335(f23(a1),f335(f335(f75(a1),x46051),x46051)),a91)))
% 59.73/59.65 [3977]E(f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),x39771),x39771)),a91)),a91),f335(f335(f75(a1),x39771),x39771))
% 59.73/59.65 [4030]E(f335(f335(f23(a1),f335(f335(f23(a1),f335(f335(f75(a1),x40301),x40301)),a91)),a91),f335(f335(f75(a1),f335(f335(f23(a1),x40301),a91)),f335(f335(f23(a1),x40301),a91)))
% 59.73/59.65 [4250]E(f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f75(a1),f335(f74(a1),x42501)),a91)),f335(f335(f75(a1),f335(f74(a1),x42501)),a91))),a91),f335(f74(a1),f335(f335(f23(a1),f335(f335(f75(a1),x42501),x42501)),a91)))
% 59.73/59.65 [4613]~P1(f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f75(a1),x46131),x46131)),a91)),a78))
% 59.73/59.65 [4296]E(f335(f335(f75(a881),x42961),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(a106,f335(a106,x42961)))
% 59.73/59.65 [4297]E(f335(f335(f76(a881),x42971),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(f335(f75(a881),x42971),x42971))
% 59.73/59.65 [4298]E(f335(f335(f30(a881),f335(f335(f75(a881),x42981),x42981)),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x42981)
% 59.73/59.65 [4381]E(f39(a881,f335(a106,f335(a106,x43811)),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f39(a881,x43811,f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))
% 59.73/59.65 [4524]E(f335(a84,f335(f335(f33(f887(a881,a881),f888(f887(a881,a881),a879)),f335(a101,x45241)),f335(f268(a881,a881,f888(f887(a881,a881),a879)),f335(f335(f8(f888(a881,f888(f887(a881,a881),a879)),f888(a881,f888(f887(a881,a881),a879)),a881),f335(f8(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879),a881),f288(f887(a881,a881),f887(a881,a881),a102))),f335(f335(f7(a881,f888(f887(a881,a881),a879),f888(a881,f888(f887(a881,a881),a879))),f335(f335(f8(f888(a881,f888(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879))),f888(f888(f887(a881,a881),a879),f888(a881,f888(f887(a881,a881),a879))),a881),f7(a881,f888(f887(a881,a881),a879),f888(f887(a881,a881),a879))),f335(f335(f8(f888(a881,f887(a881,a881)),f888(a881,f888(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879))),a881),f335(f8(f887(a881,a881),f888(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),a881),f312(f887(a881,a881)))),f335(f7(a881,a881,f887(a881,a881)),f264(a881,a881))))),f188(f888(f887(a881,a881),a879))))))),f335(f74(a1),x45241))
% 59.73/59.65 [4376]E(f335(f335(f75(a881),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x43761),f335(a106,f335(a106,x43761)))
% 59.73/59.65 [4377]E(f335(f335(f76(a881),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x43771),f335(f335(f75(a881),x43771),x43771))
% 59.73/59.65 [4413]E(f335(f335(f30(a881),f335(a106,f335(a106,x44131))),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(a106,f335(f335(f30(a881),x44131),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))))
% 59.73/59.65 [4467]E(f335(f335(f75(a881),f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),a91))),x44671),f335(a106,f335(a106,f335(a106,x44671))))
% 59.73/59.65 [4532]E(f335(f268(a1,a1,f887(a1,a1)),f335(f335(f18(a1,f888(a1,f887(a1,a1)),f888(a1,f887(a1,a1))),f335(f335(f8(f888(a1,f888(f887(a1,a1),f887(a1,a1))),f888(f888(a1,f887(a1,a1)),f888(a1,f887(a1,a1))),a1),f18(a1,f887(a1,a1),f887(a1,a1))),f335(f335(f8(f888(a1,f887(a1,a1)),f888(a1,f888(f887(a1,a1),f887(a1,a1))),a1),f335(f18(a1,f887(a1,a1),f888(f887(a1,a1),f887(a1,a1))),f335(f335(f8(a879,f888(f887(a1,a1),f888(f887(a1,a1),f887(a1,a1))),a1),f88(f887(a1,a1))),f335(f335(f8(a1,a879,a1),f335(f242(a1),f2(a1))),f335(f335(f7(a1,a1,a1),f23(a1)),x45321))))),f335(f335(f7(a1,f888(a1,a1),f888(a1,f887(a1,a1))),f335(f335(f8(f888(a1,f887(a1,a1)),f888(f888(a1,a1),f888(a1,f887(a1,a1))),a1),f8(a1,f887(a1,a1),a1)),f335(f335(f8(a1,f888(a1,f887(a1,a1)),a1),f264(a1,a1)),f335(f335(f7(a1,a1,a1),f335(f335(f8(a1,f888(a1,a1),a1),f75(a1)),f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))),f73(a1))))),f335(f335(f7(a1,a1,a1),f23(a1)),x45321))))),f335(f335(f8(a1,f888(a1,f887(a1,a1)),a1),f264(a1,a1)),f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))))),f37(x45321))
% 59.73/59.65 [3187]P96(f887(x31871,x31872))
% 59.73/59.65 [3188]P96(f889(x31881,x31882))
% 59.73/59.65 [3189]P96(f886(x31891,x31892))
% 59.73/59.65 [3190]P105(f887(x31901,x31902))
% 59.73/59.65 [3191]P105(f889(x31911,x31912))
% 59.73/59.65 [3192]P105(f886(x31921,x31922))
% 59.73/59.65 [3208]P15(a1,f172(x32081,x32082))
% 59.73/59.65 [3209]P36(x32091,f146(x32091,x32092))
% 59.73/59.65 [3279]P30(x32791,x32792,f107(x32791))
% 59.73/59.65 [3315]P46(x33151,x33152,f261(x33151,x33152))
% 59.73/59.65 [3316]P52(x33161,x33161,f261(x33161,x33162))
% 59.73/59.65 [3590]P26(x35901,x35901,f5(x35901),x35902)
% 59.73/59.65 [3591]P26(x35911,x35911,f25(x35911),x35912)
% 59.73/59.65 [3598]P31(x35981,x35982,f107(x35981),f107(x35981))
% 59.73/59.65 [3599]P31(x35991,x35992,f107(x35991),f107(x35991))
% 59.73/59.65 [3600]P26(x36001,f885(x36001),f235(x36001),x36002)
% 59.73/59.65 [3607]P26(f882(x36071),f882(x36071),f162(x36071),x36072)
% 59.73/59.65 [4559]~P32(x45591,x45592,f107(x45591))
% 59.73/59.65 [4560]~P34(x45601,x45602,f107(x45601))
% 59.73/59.65 [3173]E(f335(f249(x31731),x31732),x31732)
% 59.73/59.65 [3174]E(f335(f5(x31741),x31742),x31742)
% 59.73/59.65 [3175]E(f335(f25(x31751),x31752),x31752)
% 59.73/59.65 [3176]E(f335(f25(x31761),x31762),x31762)
% 59.73/59.65 [3186]E(f335(f191(x31861),x31862),f109(x31861))
% 59.73/59.65 [3206]E(f80(x32061,f335(a332,x32062)),x32062)
% 59.73/59.65 [3207]E(f85(x32071,f335(a332,x32072)),x32072)
% 59.73/59.65 [3226]E(f335(f119(x32261,x32262),f113(x32261)),f2(a881))
% 59.73/59.65 [3232]E(f335(f129(x32321,x32322),f107(x32321)),f107(x32321))
% 59.73/59.65 [3252]E(f310(x32521,f310(x32521,x32522)),f310(x32521,x32522))
% 59.73/59.65 [3253]E(f145(x32531,f145(x32531,x32532)),f145(x32531,x32532))
% 59.73/59.65 [3274]E(f335(f335(f127(x32741),x32742),f107(x32741)),x32742)
% 59.73/59.65 [3280]E(f167(x32801,x32802,f107(x32801)),x32802)
% 59.73/59.65 [3281]E(f110(x32811,f113(x32811),x32812),x32812)
% 59.73/59.65 [3282]E(f167(x32821,f107(x32821),x32822),x32822)
% 59.73/59.65 [3283]E(f163(x32831,f2(a881),x32832),f107(x32831))
% 59.73/59.65 [3289]E(f335(f335(f169(x32891),x32892),f107(x32891)),f107(x32891))
% 59.73/59.65 [3290]E(f335(f335(f131(x32901),x32902),f107(x32901)),f107(x32901))
% 59.73/59.65 [3292]E(f236(x32921,x32922,f200(x32921)),f2(a881))
% 59.73/59.65 [3293]E(f148(x32931,x32932,f107(x32931)),f2(a881))
% 59.73/59.65 [3295]E(f164(x32951,x32952,f107(x32951)),f107(x32951))
% 59.73/59.65 [3296]E(f171(x32961,x32962,f107(x32961)),f107(x32961))
% 59.73/59.65 [3297]E(f170(x32971,f107(x32971),x32972),f107(x32971))
% 59.73/59.65 [3301]E(f335(f166(x33011),f145(x33011,x33012)),f335(f166(x33011),x33012))
% 59.73/59.65 [3304]E(f335(f260(x33041,x33041),f261(x33041,x33042)),x33042)
% 59.73/59.65 [3305]E(f335(f262(x33051,x33051),f261(x33051,x33052)),x33052)
% 59.73/59.65 [3314]E(f335(f289(x33141,x33141),f261(x33141,x33142)),f261(x33141,x33142))
% 59.73/59.65 [3329]E(f310(f882(x33291),f150(x33291,x33292)),f151(x33291,f310(x33291,x33292)))
% 59.73/59.65 [3331]P1(f335(f130(a1),f172(x33311,x33312)))
% 59.73/59.65 [3339]E(f335(f260(x33391,x33391),f310(x33391,x33392)),f252(f888(x33391,a879)))
% 59.73/59.65 [3340]E(f335(f262(x33401,x33401),f310(x33401,x33402)),f252(f888(x33401,a879)))
% 59.73/59.65 [3344]P1(f335(f130(x33441),f145(x33441,x33442)))
% 59.73/59.65 [3345]P1(f335(f153(x33451,x33452),f107(x33451)))
% 59.73/59.65 [3346]P1(f335(f153(x33461,x33462),f107(x33461)))
% 59.73/59.65 [3351]E(f335(f166(a1),f172(x33511,x33512)),f305(a1,x33511,x33512))
% 59.73/59.65 [3352]E(f335(f166(a1),f172(x33521,x33522)),f305(a1,x33521,x33522))
% 59.73/59.65 [3367]P53(x33671,f188(f888(x33671,a879)),x33672)
% 59.73/59.65 [3372]E(f335(f267(a1,a1),f40(x33721,x33722)),f39(a1,x33721,x33722))
% 59.73/59.65 [3373]E(f335(f304(a881,x33731),f335(a106,x33732)),f305(a881,x33731,x33732))
% 59.73/59.65 [3389]E(f335(f335(f144(x33891),x33892),f107(x33891)),f133(x33891,x33892,f107(x33891)))
% 59.73/59.65 [3401]E(f305(a881,f335(a106,x34011),x34012),f307(a881,x34011,x34012))
% 59.73/59.65 [3404]P46(x34041,f252(f888(x34041,a879)),f310(x34041,x34042))
% 59.73/59.65 [3467]E(f335(f335(f23(a881),x34671),f335(a106,x34672)),f335(f29(a881),f308(a881,x34672,x34671)))
% 59.73/59.65 [3525]E(f160(x35251,x35252,f107(x35251)),f335(f335(f264(f882(x35251),f882(x35251)),f107(x35251)),f107(x35251)))
% 59.73/59.65 [3545]E(f335(f268(x35451,x35452,f887(x35451,x35452)),f264(x35451,x35452)),f25(f887(x35451,x35452)))
% 59.73/59.65 [3549]P1(f335(f335(f337(f882(x35491)),f107(x35491)),f154(x35491,x35492)))
% 59.73/59.65 [3550]E(f335(f189(f882(x35501)),f108(x35501,x35502)),f335(f335(f23(a881),f335(f189(f882(x35501)),x35502)),f73(a881)))
% 59.73/59.65 [3559]P1(f335(f56(a881),f308(a881,x35591,x35592)))
% 59.73/59.65 [3560]P1(f335(f56(a881),f307(a881,x35601,x35602)))
% 59.73/59.65 [3561]P1(f335(f56(a881),f305(a881,x35611,x35612)))
% 59.73/59.65 [3562]P1(f335(f56(a1),f308(a1,x35621,x35622)))
% 59.73/59.65 [3563]P1(f335(f56(a1),f307(a1,x35631,x35632)))
% 59.73/59.65 [3564]P1(f335(f56(a1),f305(a1,x35641,x35642)))
% 59.73/59.65 [3671]E(f335(f313(a881,a881,a106),f305(a881,x36711,x36712)),f305(a881,f335(a106,x36711),f335(a106,x36712)))
% 59.73/59.65 [3691]E(f335(f335(f291(x36911,x36911,x36911),f310(x36911,x36912)),f310(x36911,x36912)),f310(x36911,x36912))
% 59.73/59.65 [3724]E(f335(f335(f264(a1,a1),f335(f335(f30(a1),x37241),x37242)),f39(a1,x37241,x37242)),f40(x37241,x37242))
% 59.73/59.65 [3725]E(f335(f335(f264(a93,a93),f335(f335(f30(a93),x37251),x37252)),f39(a93,x37251,x37252)),f22(x37251,x37252))
% 59.73/59.65 [3753]E(f335(f335(f264(a881,a881),f335(f335(f30(a881),x37531),x37532)),f39(a881,x37531,x37532)),f80(f887(a881,a881),f42(x37531,x37532)))
% 59.73/59.65 [3805]P1(f335(f335(f243(a881),f335(f335(f23(a881),x38051),x38052)),f335(a106,x38051)))
% 59.73/59.65 [3896]E(f335(f335(f131(x38961),f335(f189(f882(x38961)),f171(x38961,x38962,f107(x38961)))),f107(x38961)),f107(x38961))
% 59.73/59.65 [3906]E(f335(f335(f75(a1),f335(f335(f76(a1),x39061),f335(f335(f30(a1),x39062),x39061))),f39(a1,x39062,x39061)),x39062)
% 59.73/59.65 [3910]E(f335(f335(f33(a881,f888(f887(f882(x39101),f882(x39101)),a879)),f252(f888(a881,a879))),f136(x39101,x39102)),f138(x39101,x39102))
% 59.73/59.65 [3994]E(f335(f129(x39941,f335(f335(f8(a879,a879,x39941),a330),f335(a332,x39942))),f107(x39941)),f107(x39941))
% 59.73/59.65 [4142]P1(f335(f335(f337(f887(f882(x41421),f882(x41421))),f335(f335(f264(f882(x41421),f882(x41421)),f107(x41421)),f107(x41421))),f151(x41421,x41422)))
% 59.73/59.65 [4262]E(f265(x42621,x42621,x42621,a332,f265(x42621,x42621,x42621,x42622,a332)),x42622)
% 59.73/59.65 [4308]E(f269(x43081,x43081,x43082,x43082,f25(x43081),f25(x43082)),f25(f887(x43081,x43082)))
% 59.73/59.65 [4309]E(f269(x43091,x43091,x43092,x43092,f5(x43091),f5(x43092)),f25(f887(x43091,x43092)))
% 59.73/59.65 [4310]E(f269(x43101,x43101,x43102,x43102,f25(x43101),f25(x43102)),f25(f887(x43101,x43102)))
% 59.73/59.65 [4311]E(f269(x43111,x43111,x43112,x43112,f25(x43111),f25(x43112)),f25(f887(x43111,x43112)))
% 59.73/59.65 [4545]~E(f335(f235(x45451),x45452),f200(x45451))
% 59.73/59.65 [4546]~E(f335(f235(x45461),x45462),f200(x45461))
% 59.73/59.65 [3272]E(f335(f239(x32721),f335(f235(x32721),x32722)),x32722)
% 59.73/59.65 [3273]E(f335(f162(x32731),f335(f162(x32731),x32732)),x32732)
% 59.73/59.65 [3275]E(f335(f335(f131(x32751),f2(a881)),x32752),x32752)
% 59.73/59.65 [3291]E(f335(f335(f169(x32911),f2(a881)),x32912),f107(x32911))
% 59.73/59.65 [3299]E(f335(f335(f127(x32991),f107(x32991)),x32992),x32992)
% 59.73/59.65 [3308]E(f335(f189(f885(x33081)),f335(f235(x33081),x33082)),f2(a881))
% 59.73/59.65 [3310]E(f31(f888(x33101,a879),f335(f311(x33101),x33102)),x33102)
% 59.73/59.65 [3312]E(f335(f166(x33121),f335(f161(x33121),x33122)),f335(f166(x33121),x33122))
% 59.73/59.65 [3313]E(f335(f166(x33131),f335(f162(x33131),x33132)),f335(f166(x33131),x33132))
% 59.73/59.65 [3318]E(f335(f335(f23(a93),x33181),x33182),f335(f335(a24,x33181),x33182))
% 59.73/59.65 [3333]E(f335(f335(f76(a881),x33331),x33332),f335(f335(f76(a881),x33332),x33331))
% 59.73/59.65 [3334]E(f335(f335(f76(a1),x33341),x33342),f335(f335(f76(a1),x33342),x33341))
% 59.73/59.65 [3335]E(f335(f335(f75(a881),x33351),x33352),f335(f335(f75(a881),x33352),x33351))
% 59.73/59.65 [3336]E(f335(f335(f75(a1),x33361),x33362),f335(f335(f75(a1),x33362),x33361))
% 59.73/59.65 [3359]E(f335(f335(f183(x33591,x33591),f2(a881)),x33592),f25(x33591))
% 59.73/59.65 [3360]E(f335(f189(f882(x33601)),f335(f161(x33601),x33602)),f335(f189(f882(x33601)),x33602))
% 59.73/59.65 [3361]E(f335(f189(f882(x33611)),f335(f162(x33611),x33612)),f335(f189(f882(x33611)),x33612))
% 59.73/59.65 [3362]E(f170(x33621,x33622,f188(f888(a881,a879))),f107(x33621))
% 59.73/59.65 [3363]E(f335(f335(f147(x33631,x33631),f5(x33631)),x33632),x33632)
% 59.73/59.65 [3365]E(f335(f263(a1,a1),f40(x33651,x33652)),f335(f335(f30(a1),x33651),x33652))
% 59.73/59.65 [3383]E(f335(f189(f882(x33831)),f145(x33831,x33832)),f335(f29(x33831),f335(f166(x33831),x33832)))
% 59.73/59.65 [3384]E(f335(f287(x33841),f335(f289(x33841,x33841),x33842)),f335(f287(x33841),x33842))
% 59.73/59.65 [3388]P1(f335(f56(x33881),f335(f166(x33881),x33882)))
% 59.73/59.65 [3395]E(f335(f335(f75(a1),x33951),f335(f74(a1),x33952)),f335(f335(f23(a1),x33951),x33952))
% 59.73/59.65 [3396]E(f335(f335(f75(a1),x33961),f335(f74(a1),x33962)),f335(f335(f23(a1),x33961),x33962))
% 59.73/59.65 [3402]P16(x34021,x34022,f188(f888(f880(x34021),a879)))
% 59.73/59.65 [3403]P16(x34031,x34032,f188(f888(f880(x34031),a879)))
% 59.73/59.65 [3405]E(f335(f313(x34051,x34051,f5(x34051)),x34052),x34052)
% 59.73/59.65 [3406]E(f335(f313(x34061,x34061,f25(x34061)),x34062),x34062)
% 59.73/59.65 [3407]E(f335(f314(x34071,x34071,f5(x34071)),x34072),x34072)
% 59.73/59.65 [3408]E(f335(f314(x34081,x34081,f25(x34081)),x34082),x34082)
% 59.73/59.65 [3409]P1(f335(f252(f888(x34091,a879)),x34092))
% 59.73/59.65 [3411]E(f335(f29(a881),f335(f304(a881,x34111),x34112)),f335(f335(f23(a881),x34112),x34111))
% 59.73/59.65 [3412]E(f335(f304(a881,f335(a106,x34121)),x34122),f308(a881,x34121,x34122))
% 59.73/59.65 [3425]E(f335(f335(f312(x34251),x34252),f188(f888(x34251,a879))),f335(f249(x34251),f335(a332,x34252)))
% 59.73/59.65 [3429]E(f335(f335(f312(x34291),x34292),f188(f888(x34291,a879))),f234(x34291,f335(f235(x34291),x34292)))
% 59.73/59.65 [3431]E(f310(x34311,f335(f289(x34311,x34311),x34312)),f335(f289(x34311,x34311),f310(x34311,x34312)))
% 59.73/59.65 [3436]E(f335(f335(f75(a881),f335(a106,x34361)),x34362),f335(f335(f75(a881),x34361),f335(a106,x34362)))
% 59.73/59.65 [3437]E(f335(f335(f23(a881),f335(a106,x34371)),f335(a106,x34372)),f335(f335(f23(a881),x34371),x34372))
% 59.73/59.65 [3443]E(f49(x34431,f2(a881),x34432),f335(f335(f144(f882(x34431)),f107(x34431)),f107(f882(x34431))))
% 59.73/59.65 [3444]E(f335(f29(a881),f307(a881,x34441,x34442)),f335(f335(f23(a881),x34442),x34441))
% 59.73/59.65 [3453]P36(x34531,f335(f335(f290(a881,x34531),a248),x34532))
% 59.73/59.65 [3455]P15(a881,f132(a881,f335(f304(a881,x34551),x34552)))
% 59.73/59.65 [3457]P1(f335(f56(a881),f335(f304(a881,x34571),x34572)))
% 59.73/59.65 [3458]P1(f335(f56(a1),f335(f304(a1,x34581),x34582)))
% 59.73/59.65 [3461]E(f335(f289(f882(x34611),f882(x34611)),f150(x34611,x34612)),f150(x34611,f335(f289(x34611,x34611),x34612)))
% 59.73/59.65 [3463]E(f335(f304(a1,x34631),f335(f335(f75(a1),x34632),f73(a1))),f305(a1,x34631,x34632))
% 59.73/59.65 [3466]E(f335(f335(f30(a1),f335(f74(a1),x34661)),f335(f74(a1),x34662)),f335(f335(f30(a1),x34661),x34662))
% 59.73/59.65 [3474]E(f177(x34741,x34742,f335(f16(f885(x34742),x34741),f200(x34742))),f188(f888(x34741,a879)))
% 59.73/59.65 [3475]E(f178(x34751,x34752,f335(f16(f885(x34752),x34751),f200(x34752))),f188(f888(x34752,a879)))
% 59.73/59.65 [3476]E(f335(f335(f183(f887(x34761,x34761),a879),f73(a881)),x34762),x34762)
% 59.73/59.65 [3478]E(f335(f335(f104(f888(x34781,a879)),x34782),f188(f888(x34781,a879))),x34782)
% 59.73/59.65 [3479]E(f335(f335(f23(f888(x34791,a879)),x34792),f188(f888(x34791,a879))),x34792)
% 59.73/59.65 [3480]E(f335(f335(f95(f888(x34801,a879)),x34802),f252(f888(x34801,a879))),x34802)
% 59.73/59.65 [3481]E(f335(f263(a881,a881),f80(f887(a881,a881),f42(x34811,x34812))),f335(f335(f30(a881),x34811),x34812))
% 59.73/59.65 [3487]E(f316(x34871,f335(a21,x34872),f335(f74(a1),f335(a21,x34872))),f335(f335(f319(a1),x34871),x34872))
% 59.73/59.65 [3488]E(f305(a1,f335(f335(f75(a1),x34881),f73(a1)),x34882),f307(a1,x34881,x34882))
% 59.73/59.65 [3493]E(f335(f267(a881,a881),f80(f887(a881,a881),f42(x34931,x34932))),f39(a881,x34931,x34932))
% 59.73/59.65 [3501]E(f317(x35011,f335(a21,x35012),f335(f74(a1),f335(a21,x35012))),f318(a1,x35011,x35012))
% 59.73/59.65 [3503]P1(f335(f335(f337(x35031),x35032),f252(f888(x35031,a879))))
% 59.73/59.65 [3504]P1(f335(f335(f337(x35041),x35042),f252(f888(x35041,a879))))
% 59.73/59.65 [3509]E(f335(f335(f23(a881),f335(a106,x35091)),x35092),f335(f29(a881),f305(a881,x35092,x35091)))
% 59.73/59.65 [3536]E(f335(f335(f104(f888(x35361,a879)),x35362),f252(f888(x35361,a879))),f252(f888(x35361,a879)))
% 59.73/59.65 [3537]E(f335(f335(f23(f888(x35371,a879)),x35372),f252(f888(x35371,a879))),f188(f888(x35371,a879)))
% 59.73/59.65 [3538]E(f335(f335(f95(f888(x35381,a879)),x35382),f188(f888(x35381,a879))),f188(f888(x35381,a879)))
% 59.73/59.65 [3553]E(f39(a1,f335(f94(a1),x35531),f335(f94(a1),x35532)),f335(f94(a1),f39(a881,x35531,x35532)))
% 59.73/59.65 [3554]E(f39(a1,f335(f74(a1),x35541),f335(f74(a1),x35542)),f335(f74(a1),f39(a1,x35541,x35542)))
% 59.73/59.65 [3555]E(f39(a1,f335(f94(a1),x35551),f335(f94(a1),x35552)),f335(f94(a1),f39(a881,x35551,x35552)))
% 59.73/59.65 [3566]E(f335(f189(f882(x35661)),f335(f165(x35661),x35662)),f335(f335(f23(a881),f335(f189(f882(x35661)),x35662)),f73(a881)))
% 59.73/59.65 [3592]E(f335(f335(f30(a1),f39(a1,x35921,x35922)),x35922),f2(a1))
% 59.73/59.65 [3602]E(f335(a3,f39(a881,f335(a20,x36021),f335(a20,x36022))),f39(a93,x36021,x36022))
% 59.73/59.65 [3636]E(f335(a3,f335(f335(f23(a881),f335(a20,x36361)),f335(a20,x36362))),f335(f335(f23(a93),x36361),x36362))
% 59.73/59.65 [3637]E(f335(a3,f335(f335(f76(a881),f335(a20,x36371)),f335(a20,x36372))),f335(f335(f76(a93),x36371),x36372))
% 59.73/59.65 [3638]E(f335(a3,f335(f335(f75(a881),f335(a20,x36381)),f335(a20,x36382))),f335(f335(f75(a93),x36381),x36382))
% 59.73/59.65 [3639]E(f335(a3,f335(f335(f30(a881),f335(a20,x36391)),f335(a20,x36392))),f335(f335(f30(a93),x36391),x36392))
% 59.73/59.65 [3647]E(f335(f313(a881,a881,a106),f335(f304(a881,x36471),x36472)),f335(f304(a881,f335(a106,x36471)),f335(a106,x36472)))
% 59.73/59.65 [3676]P1(f335(f42(x36761,x36762),f80(f887(a881,a881),f42(x36761,x36762))))
% 59.73/59.65 [3697]E(f39(a881,f335(a106,f39(a881,x36971,x36972)),x36972),f39(a881,f335(a106,x36971),x36972))
% 59.73/59.65 [3711]E(f335(f335(f34(f888(x37111,a879),f888(x37111,a879)),x37112),f5(f888(x37111,a879))),f32(f888(x37111,a879),x37112))
% 59.73/59.65 [3712]E(f335(f335(f33(f888(x37121,a879),f888(x37121,a879)),x37122),f5(f888(x37121,a879))),f31(f888(x37121,a879),x37122))
% 59.73/59.65 [3713]E(f335(f313(f882(x37131),f888(x37131,a879),f166(x37131)),f335(f166(f882(x37131)),f48(x37131,x37132))),f335(f311(x37131),f335(f166(x37131),x37132)))
% 59.73/59.65 [3717]P1(f335(f335(f337(f888(x37171,a879)),x37172),f335(f311(x37171),x37172)))
% 59.73/59.65 [3723]E(f39(a1,f335(f74(a1),f39(a1,x37231,x37232)),x37232),f39(a1,f335(f74(a1),x37231),x37232))
% 59.73/59.65 [3734]P1(f335(f335(f242(f888(x37341,a879)),x37342),f252(f888(x37341,a879))))
% 59.73/59.65 [3736]E(f335(f335(f291(x37361,x37361,x37361),f310(x37361,x37362)),f310(x37361,f310(x37361,x37362))),f310(x37361,x37362))
% 59.73/59.65 [3737]E(f335(f335(f104(f888(x37371,a879)),f335(f262(x37371,x37371),x37372)),f335(f260(x37371,x37371),x37372)),f335(f287(x37371),x37372))
% 59.73/59.65 [3759]E(f321(x37591,x37592,f252(f888(x37591,a879)),f252(f888(x37592,a879))),f252(f888(f889(x37591,x37592),a879)))
% 59.73/59.65 [3810]P1(f335(f335(f242(a881),f39(a881,x38101,x38102)),x38101))
% 59.73/59.65 [3836]P1(f335(f335(f242(a1),f335(f74(a1),f335(f94(a1),x38361))),f335(f94(a1),x38362)))
% 59.73/59.65 [3861]P1(f335(f335(f337(f888(x38611,a879)),f188(f888(x38611,a879))),f335(f311(x38611),x38612)))
% 59.73/59.65 [3866]E(f310(x38661,f335(f335(f291(x38661,x38661,x38661),x38662),f310(x38661,x38662))),f310(x38661,x38662))
% 59.73/59.65 [3868]E(f335(f335(f291(x38681,x38681,x38681),f310(x38681,x38682)),x38682),f335(f335(f291(x38681,x38681,x38681),x38682),f310(x38681,x38682)))
% 59.73/59.65 [3869]E(f335(f335(f291(x38691,x38691,x38691),f310(x38691,x38692)),x38692),f335(f335(f291(x38691,x38691,x38691),x38692),f310(x38691,x38692)))
% 59.73/59.65 [3871]E(f335(a98,f335(f335(f75(a1),f335(f335(f23(a1),x38711),x38712)),f73(a1))),f335(f29(a1),f305(a1,x38712,x38711)))
% 59.73/59.65 [3886]E(f335(f260(x38861,x38861),f335(f335(f291(x38861,x38861,x38861),x38862),f310(x38861,x38862))),f335(f260(x38861,x38861),x38862))
% 59.73/59.65 [3887]E(f335(f262(x38871,x38871),f335(f335(f291(x38871,x38871,x38871),x38872),f310(x38871,x38872))),f335(f262(x38871,x38871),x38872))
% 59.73/59.65 [3905]E(f335(f135(f882(x39051),f882(x39051),f127(x39051),f107(x39051)),f163(f882(x39051),x39052,f107(x39051))),f107(x39051))
% 59.73/59.65 [3914]P26(a881,a881,f335(f335(f7(a881,a881,a881),f75(a881)),x39141),x39142)
% 59.73/59.65 [3916]P15(a881,f335(f162(a881),f335(f335(f147(f882(x39161),a881),f189(f882(x39161))),f173(x39161,x39162))))
% 59.73/59.65 [3962]P1(f335(f335(f243(a1),f335(f74(a1),f335(f94(a1),f335(a106,x39621)))),f335(f94(a1),x39622)))
% 59.73/59.65 [4010]E(f335(f135(f882(x40101),x40101,f335(f7(x40101,f882(x40101),f882(x40101)),f144(x40101)),f107(x40101)),x40102),f335(f162(x40101),x40102))
% 59.73/59.65 [4061]P1(f335(f335(f242(f888(f887(f882(x40611),f882(x40611)),a879)),f151(x40611,x40612)),f310(f882(x40611),f150(x40611,x40612))))
% 59.73/59.65 [4092]P1(f335(f42(x40921,x40922),f335(f335(f264(a881,a881),f335(f335(f30(a881),x40921),x40922)),f39(a881,x40921,x40922))))
% 59.73/59.65 [4103]P1(f335(f335(f242(f888(f887(f882(x41031),f882(x41031)),a879)),f150(x41031,f310(x41031,x41032))),f310(f882(x41031),f150(x41031,x41032))))
% 59.73/59.65 [4336]E(f335(f335(f270(f887(a93,a93),a93,f887(a93,a93),f887(x43361,f887(a93,a93))),f275(f335(f159(a93),f335(f335(f147(f887(a93,x43361),a93),f263(a93,x43361)),x43362)))),f335(f335(f8(x43361,f888(f887(a93,a93),f887(x43361,f887(a93,a93))),a93),f264(x43361,f887(a93,a93))),f276(x43361,x43362))),f274(x43361,x43362))
% 59.73/59.65 [4449]E(f335(f237(a881,f887(x44491,f883(x44491)),f2(a881),f335(f268(x44491,f883(x44491),a881),f335(f16(f888(f883(x44491),a881),x44491),f335(f335(f7(f883(x44491),a881,a881),f335(f335(f8(a881,f888(a881,a881),f883(x44491)),f75(a881)),f189(f883(x44491)))),f73(a881))))),f335(f128(x44491),x44492)),f335(f189(f883(x44491)),x44492))
% 59.73/59.65 [4492]E(f39(a881,f335(f335(f75(a881),f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),a91))),x44921),f335(f97(a881),x44922)),f39(a881,f335(a106,f335(a106,f335(a106,x44921))),f335(f97(a881),x44922)))
% 59.73/59.65 [4506]E(f335(f335(f30(a881),f335(f335(f75(a881),f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),a91))),x45061)),f335(f97(a881),x45062)),f335(f335(f30(a881),f335(a106,f335(a106,f335(a106,x45061)))),f335(f97(a881),x45062)))
% 59.73/59.65 [4523]E(f335(f268(f888(f887(x45231,x45231),a879),f888(f887(x45231,x45231),a879),f888(f888(x45232,x45231),f887(f888(f887(x45232,x45232),a879),f888(f887(x45232,x45232),a879)))),f335(f335(f7(f888(f887(x45231,x45231),a879),f888(f888(f887(x45231,x45231),a879),f888(f888(x45232,x45231),f888(f887(x45232,x45232),a879))),f888(f888(f887(x45231,x45231),a879),f888(f888(x45232,x45231),f887(f888(f887(x45232,x45232),a879),f888(f887(x45232,x45232),a879))))),f335(f335(f8(f888(f888(f888(x45232,x45231),f888(f887(x45232,x45232),a879)),f888(f888(x45232,x45231),f887(f888(f887(x45232,x45232),a879),f888(f887(x45232,x45232),a879)))),f888(f888(f888(f887(x45231,x45231),a879),f888(f888(x45232,x45231),f888(f887(x45232,x45232),a879))),f888(f888(f887(x45231,x45231),a879),f888(f888(x45232,x45231),f887(f888(f887(x45232,x45232),a879),f888(f887(x45232,x45232),a879))))),f888(f887(x45231,x45231),a879)),f8(f888(f888(x45232,x45231),f888(f887(x45232,x45232),a879)),f888(f888(x45232,x45231),f887(f888(f887(x45232,x45232),a879),f888(f887(x45232,x45232),a879))),f888(f887(x45231,x45231),a879))),f335(f335(f8(f888(f888(x45232,x45231),f888(f888(f887(x45232,x45232),a879),f887(f888(f887(x45232,x45232),a879),f888(f887(x45232,x45232),a879)))),f888(f888(f888(x45232,x45231),f888(f887(x45232,x45232),a879)),f888(f888(x45232,x45231),f887(f888(f887(x45232,x45232),a879),f888(f887(x45232,x45232),a879)))),f888(f887(x45231,x45231),a879)),f18(f888(x45232,x45231),f888(f887(x45232,x45232),a879),f887(f888(f887(x45232,x45232),a879),f888(f887(x45232,x45232),a879)))),f335(f335(f8(f888(f888(x45232,x45231),f888(f887(x45232,x45232),a879)),f888(f888(x45232,x45231),f888(f888(f887(x45232,x45232),a879),f887(f888(f887(x45232,x45232),a879),f888(f887(x45232,x45232),a879)))),f888(f887(x45231,x45231),a879)),f335(f8(f888(f887(x45232,x45232),a879),f888(f888(f887(x45232,x45232),a879),f887(f888(f887(x45232,x45232),a879),f888(f887(x45232,x45232),a879))),f888(x45232,x45231)),f264(f888(f887(x45232,x45232),a879),f888(f887(x45232,x45232),a879)))),f290(x45231,x45232))))),f290(x45231,x45232))),f69(x45231,x45232))
% 59.73/59.65 [4573]~E(f335(f311(x45731),x45732),f188(f888(f888(x45731,a879),a879)))
% 59.73/59.65 [4582]~P1(f335(f335(f166(x45821),f107(x45821)),x45822))
% 59.73/59.65 [4586]~P1(f335(f335(f337(x45861),x45862),f188(f888(x45861,a879))))
% 59.73/59.65 [4587]~P1(f335(f335(f337(x45871),x45872),f188(f888(x45871,a879))))
% 59.73/59.65 [4597]~P1(f335(f335(f243(f888(x45971,a879)),x45972),f188(f888(x45971,a879))))
% 59.73/59.65 [3414]E(f335(f335(f23(a881),x34141),f335(f335(f75(a881),x34141),x34142)),f2(a881))
% 59.73/59.65 [3417]E(f335(f335(f104(f888(x34171,a879)),x34172),x34172),x34172)
% 59.73/59.65 [3418]E(f335(f335(f95(f888(x34181,a879)),x34182),x34182),x34182)
% 59.73/59.65 [3446]E(f335(f335(f23(f888(x34461,a879)),x34462),x34462),f188(f888(x34461,a879)))
% 59.73/59.65 [3449]E(f335(f136(x34491,x34492),f2(a881)),f188(f888(f887(f882(x34491),f882(x34491)),a879)))
% 59.73/59.65 [3450]E(f335(f335(f75(a881),x34501),f335(a106,x34502)),f335(a106,f335(f335(f75(a881),x34501),x34502)))
% 59.73/59.65 [3462]E(f194(f335(f94(a1),x34621),f335(f94(a1),x34622)),f335(f94(a1),f335(f335(f23(a881),x34621),x34622)))
% 59.73/59.65 [3465]E(f335(f335(f30(a1),f335(f74(a1),x34651)),x34652),f335(f335(f30(a1),x34651),f335(f74(a1),x34652)))
% 59.73/59.65 [3469]E(f335(f29(a1),f335(f304(a1,x34691),x34692)),f335(a98,f335(f335(f23(a1),x34692),x34691)))
% 59.73/59.65 [3472]E(f335(f335(f75(a881),f335(a106,x34721)),x34722),f335(a106,f335(f335(f75(a881),x34721),x34722)))
% 59.73/59.65 [3477]E(f335(f74(f888(x34771,a879)),f335(f74(f888(x34771,a879)),x34772)),x34772)
% 59.73/59.65 [3490]E(f173(x34901,f335(f335(f144(f882(x34901)),f107(x34901)),x34902)),f173(x34901,x34902))
% 59.73/59.65 [3494]E(f335(f335(f75(a881),x34941),f335(f335(f76(a881),x34941),x34942)),f335(f335(f76(a881),x34941),f335(a106,x34942)))
% 59.73/59.65 [3502]E(f335(f335(a24,f335(a3,x35021)),f335(a3,x35022)),f335(a3,f335(f335(f23(a881),x35021),x35022)))
% 59.73/59.65 [3515]E(f335(f335(f254(a1),f335(f94(a1),x35151)),x35152),f335(f94(a1),f335(f335(f254(a881),x35151),x35152)))
% 59.73/59.65 [3516]E(f335(f335(f76(a1),f335(f74(a1),x35161)),x35162),f335(f74(a1),f335(f335(f76(a1),x35161),x35162)))
% 59.73/59.65 [3517]E(f335(f335(f254(a1),f335(f94(a1),x35171)),x35172),f335(f94(a1),f335(f335(f254(a881),x35171),x35172)))
% 59.73/59.65 [3518]E(f335(f335(f254(a1),f335(f94(a1),x35181)),x35182),f335(f94(a1),f335(f335(f254(a881),x35181),x35182)))
% 59.73/59.65 [3519]E(f335(f335(f76(a93),f335(a3,x35191)),f335(a3,x35192)),f335(a3,f335(f335(f76(a881),x35191),x35192)))
% 59.73/59.65 [3520]E(f335(f335(f75(a93),f335(a3,x35201)),f335(a3,x35202)),f335(a3,f335(f335(f75(a881),x35201),x35202)))
% 59.73/59.65 [3521]E(f335(f335(f240(a881),f335(a106,x35211)),f335(a106,x35212)),f335(a106,f335(f335(f240(a881),x35211),x35212)))
% 59.73/59.65 [3522]E(f335(f335(f241(a881),f335(a106,x35221)),f335(a106,x35222)),f335(a106,f335(f335(f241(a881),x35221),x35222)))
% 59.73/59.65 [3527]E(f335(f166(a881),f132(a881,f335(f304(a881,x35271),x35272))),f335(f304(a881,x35271),x35272))
% 59.73/59.65 [3528]E(f335(f166(a881),f132(a881,f335(f304(a881,x35281),x35282))),f335(f304(a881,x35281),x35282))
% 59.73/59.65 [3529]E(f315(x35291,f335(f335(f312(x35291),x35292),f188(f888(x35291,a879)))),x35292)
% 59.73/59.65 [3534]E(f335(f260(x35341,x35342),f188(f888(f887(x35341,x35342),a879))),f188(f888(x35342,a879)))
% 59.73/59.65 [3535]E(f335(f262(x35351,x35352),f188(f888(f887(x35351,x35352),a879))),f188(f888(x35351,a879)))
% 59.73/59.65 [3539]E(f335(a98,f335(f335(f23(a1),x35391),x35392)),f335(f29(a1),f307(a1,x35392,x35391)))
% 59.73/59.65 [3544]E(f335(f335(f75(a881),x35441),f335(f335(f76(a881),x35442),x35441)),f335(f335(f76(a881),f335(a106,x35442)),x35441))
% 59.73/59.65 [3546]E(f335(f335(f55(x35461),f188(f888(x35461,a879))),x35462),f188(f888(f888(x35461,a879),a879)))
% 59.73/59.65 [3556]E(f335(f189(f882(a881)),f132(a881,f335(f304(a881,x35561),x35562))),f335(f335(f23(a881),x35562),x35561))
% 59.73/59.65 [3571]E(f335(f335(f104(f888(x35711,a879)),f188(f888(x35711,a879))),x35712),x35712)
% 59.73/59.65 [3572]E(f335(f335(f95(f888(x35721,a879)),f252(f888(x35721,a879))),x35722),x35722)
% 59.73/59.65 [3573]E(f335(f335(f75(a1),f335(f74(a1),x35731)),f335(f74(a1),x35732)),f335(f74(a1),f335(f335(f75(a1),x35731),x35732)))
% 59.73/59.65 [3575]E(f335(f335(f76(a1),f335(f94(a1),x35751)),f335(f94(a1),x35752)),f335(f94(a1),f335(f335(f76(a881),x35751),x35752)))
% 59.73/59.65 [3576]E(f335(f335(f30(a1),f335(f94(a1),x35761)),f335(f94(a1),x35762)),f335(f94(a1),f335(f335(f30(a881),x35761),x35762)))
% 59.73/59.65 [3577]E(f335(f335(f76(a1),f335(f97(a1),x35771)),f335(f97(a1),x35772)),f335(f97(a1),f335(f335(f76(a1),x35771),x35772)))
% 59.73/59.65 [3578]E(f335(f335(f76(a1),f335(f94(a1),x35781)),f335(f94(a1),x35782)),f335(f94(a1),f335(f335(f76(a881),x35781),x35782)))
% 59.73/59.65 [3579]E(f335(f335(f76(a1),f335(f94(a1),x35791)),f335(f94(a1),x35792)),f335(f94(a1),f335(f335(f76(a881),x35791),x35792)))
% 59.73/59.65 [3580]E(f335(f335(f75(a1),f335(f97(a1),x35801)),f335(f97(a1),x35802)),f335(f97(a1),f335(f335(f75(a1),x35801),x35802)))
% 59.73/59.65 [3581]E(f335(f335(f75(a1),f335(f94(a1),x35811)),f335(f94(a1),x35812)),f335(f94(a1),f335(f335(f75(a881),x35811),x35812)))
% 59.73/59.65 [3582]E(f335(f335(f75(a1),f335(f94(a1),x35821)),f335(f94(a1),x35822)),f335(f94(a1),f335(f335(f75(a881),x35821),x35822)))
% 59.73/59.65 [3583]E(f335(f335(f30(a1),f335(f94(a1),x35831)),f335(f94(a1),x35832)),f335(f94(a1),f335(f335(f30(a881),x35831),x35832)))
% 59.73/59.65 [3603]E(f335(f335(f6(x36031,a881),f335(f16(a881,x36031),f73(a881))),x36032),f335(f29(x36031),x36032))
% 59.73/59.65 [3608]E(f335(f74(a1),f39(a1,f335(f74(a1),x36081),x36082)),f39(a1,x36081,f335(f74(a1),x36082)))
% 59.73/59.65 [3610]E(f335(f166(a1),f172(x36101,f335(f335(f23(a1),x36102),f73(a1)))),f335(f304(a1,x36101),x36102))
% 59.73/59.65 [3615]P1(f335(f335(f242(a881),x36151),f335(f335(f75(a881),x36152),x36151)))
% 59.73/59.65 [3616]P1(f335(f335(f242(a881),x36161),f335(f335(f75(a881),x36161),x36162)))
% 59.73/59.65 [3618]E(f335(f335(f104(f888(x36181,a879)),f252(f888(x36181,a879))),x36182),f252(f888(x36181,a879)))
% 59.73/59.65 [3619]E(f335(f335(f23(f888(x36191,a879)),f188(f888(x36191,a879))),x36192),f188(f888(x36191,a879)))
% 59.73/59.65 [3620]E(f335(f335(f95(f888(x36201,a879)),f188(f888(x36201,a879))),x36202),f188(f888(x36201,a879)))
% 59.73/59.65 [3628]E(f335(f335(f264(a1,a1),x36281),f335(f74(a1),x36282)),f335(a45,f335(f335(f264(a1,a1),x36281),x36282)))
% 59.73/59.65 [3629]E(f335(f304(a1,f335(f335(f75(a1),x36291),f73(a1))),x36292),f308(a1,x36291,x36292))
% 59.73/59.65 [3640]E(f335(f335(f76(a881),x36401),f335(f335(f30(a881),x36402),x36401)),f335(f335(f23(a881),x36402),f39(a881,x36402,x36401)))
% 59.73/59.65 [3641]E(f335(f335(f76(a1),x36411),f335(f335(f30(a1),x36412),x36411)),f335(f335(f23(a1),x36412),f39(a1,x36412,x36411)))
% 59.73/59.65 [3644]E(f335(f166(a1),f172(f335(f335(f75(a1),x36441),f73(a1)),x36442)),f307(a1,x36441,x36442))
% 59.73/59.65 [3648]P1(f335(f335(f242(f888(x36481,a879)),x36482),x36482))
% 59.73/59.65 [3651]E(f335(f335(f104(f888(x36511,a879)),x36512),f335(f74(f888(x36511,a879)),x36512)),f252(f888(x36511,a879)))
% 59.73/59.65 [3652]E(f335(f335(f95(f888(x36521,a879)),x36522),f335(f74(f888(x36521,a879)),x36522)),f188(f888(x36521,a879)))
% 59.73/59.65 [3662]E(f335(f335(f23(a881),f335(f335(f23(a881),x36621),f73(a881))),x36622),f335(f335(f23(a881),x36621),f335(a106,x36622)))
% 59.73/59.65 [3668]E(f335(f335(f23(f888(x36681,a879)),f252(f888(x36681,a879))),x36682),f335(f74(f888(x36681,a879)),x36682))
% 59.73/59.65 [3669]E(f335(f335(f23(a1),f335(f97(a1),x36691)),f335(f97(a1),x36692)),f335(f97(a1),f335(f335(f75(a1),x36691),f335(f74(a1),x36692))))
% 59.73/59.65 [3682]E(f335(f166(a881),f132(a881,f335(f304(a881,x36821),f335(a106,x36822)))),f305(a881,x36821,x36822))
% 59.73/59.65 [3695]E(f335(f189(f882(f882(x36951))),f48(x36951,x36952)),f335(f335(f254(a881),f335(a106,f335(a106,f2(a881)))),f335(f189(f882(x36951)),x36952)))
% 59.73/59.65 [3715]E(f335(f335(f183(f887(x37151,x37151),a879),f2(a881)),x37152),f310(x37151,f188(f888(f887(x37151,x37151),a879))))
% 59.73/59.65 [3719]P1(f335(f130(a881),f132(a881,f335(f304(a881,x37191),x37192))))
% 59.73/59.65 [3735]E(f335(f313(a1,a881,a98),f305(a1,f335(f94(a1),x37351),f335(f94(a1),x37352))),f305(a881,x37351,x37352))
% 59.73/59.65 [3745]E(f185(a881,f2(a881),f5(a881),f335(f335(f23(a881),x37451),x37452)),f335(f335(f23(a881),x37451),f335(a106,x37452)))
% 59.73/59.65 [3746]E(f335(a98,f335(f335(f23(a1),x37461),f335(f335(f75(a1),x37462),f73(a1)))),f335(f29(a1),f308(a1,x37462,x37461)))
% 59.73/59.65 [3782]E(f335(f335(f147(a881,a881),a106),f132(a881,f335(f304(a881,x37821),x37822))),f132(a881,f335(f304(a881,f335(a106,x37821)),f335(a106,x37822))))
% 59.73/59.65 [3790]E(f335(f166(a1),f172(f335(f335(f75(a1),x37901),f73(a1)),f335(f335(f23(a1),x37902),f73(a1)))),f308(a1,x37901,x37902))
% 59.73/59.65 [3801]P1(f335(f335(f242(f888(x38011,a879)),f188(f888(x38011,a879))),x38012))
% 59.73/59.65 [3806]E(f80(x38061,f335(f335(f7(x38061,x38061,a879),a332),x38062)),x38062)
% 59.73/59.65 [3807]E(f85(x38071,f335(f335(f7(x38071,x38071,a879),a332),x38072)),x38072)
% 59.73/59.65 [3811]E(f335(f166(a881),f132(a881,f335(f304(a881,f335(a106,x38111)),f335(a106,x38112)))),f307(a881,x38111,x38112))
% 59.73/59.65 [3839]E(f335(f335(f266(x38391,x38392),f252(f888(x38391,a879))),f335(f16(f888(x38392,a879),x38391),f252(f888(x38392,a879)))),f252(f888(f887(x38391,x38392),a879)))
% 59.73/59.65 [3873]E(f335(f249(x38731),f335(f335(f8(a879,a879,x38731),a330),x38732)),f335(f74(f888(x38731,a879)),f335(f249(x38731),x38732)))
% 59.73/59.65 [3876]E(f335(f249(x38761),f335(f335(f7(x38761,x38761,a879),a332),x38762)),f335(f335(f312(x38761),x38762),f188(f888(x38761,a879))))
% 59.73/59.65 [3883]E(f335(f335(f75(a1),f335(f335(f23(a1),x38831),x38832)),f335(f335(f23(a1),x38831),x38832)),f335(f335(f23(a1),f335(f335(f75(a1),x38831),x38831)),f335(f335(f75(a1),x38832),x38832)))
% 59.73/59.65 [3884]E(f335(f335(f75(a1),f335(f335(f75(a1),x38841),x38841)),f335(f335(f75(a1),x38842),x38842)),f335(f335(f75(a1),f335(f335(f75(a1),x38841),x38842)),f335(f335(f75(a1),x38841),x38842)))
% 59.73/59.65 [3900]P1(f335(f335(f242(a881),f335(f29(x39001),f335(f166(x39001),x39002))),f335(f189(f882(x39001)),x39002)))
% 59.73/59.65 [3901]P1(f335(f335(f242(a881),f335(f189(f882(x39011)),f145(x39011,x39012))),f335(f189(f882(x39011)),x39012)))
% 59.73/59.65 [3911]E(f335(f249(x39111),f335(f335(f7(x39111,f888(x39111,a879),a879),f337(x39111)),x39112)),x39112)
% 59.73/59.65 [3927]E(f335(f335(f169(x39271),f335(f335(f23(a881),f335(f189(f882(x39271)),x39272)),f73(a881))),x39272),f108(x39271,x39272))
% 59.73/59.65 [3949]E(f185(a881,f2(a881),f335(f335(f8(a881,a881,a881),a106),f335(f240(a881),x39491)),x39492),f335(f335(f240(a881),f335(a106,x39491)),x39492))
% 59.73/59.65 [3953]E(f31(f888(x39531,a879),f335(f313(f888(f887(x39531,x39531),a879),f888(x39531,a879),f287(x39531)),x39532)),f335(f287(x39531),f31(f888(f887(x39531,x39531),a879),x39532)))
% 59.73/59.65 [3954]E(f185(a881,f335(a106,x39541),f335(f335(f8(a881,a881,a881),a106),f335(f241(a881),x39541)),x39542),f335(f335(f241(a881),f335(a106,x39541)),x39542))
% 59.73/59.65 [3956]E(f335(f335(f264(a1,a1),f335(f335(f30(a1),f335(f70(a1),x39561)),f335(f70(a1),x39562))),f39(a1,f335(f70(a1),x39561),f335(f70(a1),x39562))),f47(x39561,x39562))
% 59.73/59.65 [3980]P1(f335(f335(f242(f888(f888(x39801,a879),a879)),x39802),f335(f311(x39801),f31(f888(x39801,a879),x39802))))
% 59.73/59.65 [4015]E(f335(f335(f33(x40151,f888(x40151,a879)),x40152),f335(f335(f7(x40151,f888(x40151,a879),f888(x40151,a879)),f312(x40151)),f188(f888(x40151,a879)))),x40152)
% 59.73/59.65 [4016]E(f335(f335(f291(x40161,x40161,x40161),f335(f289(x40161,x40161),x40162)),f310(x40161,f335(f289(x40161,x40161),x40162))),f335(f289(x40161,x40161),f335(f335(f291(x40161,x40161,x40161),x40162),f310(x40161,x40162))))
% 59.73/59.65 [4083]E(f335(f166(x40831),f335(f135(f882(x40831),f882(x40831),f127(x40831),f107(x40831)),x40832)),f335(f335(f33(f882(x40831),f888(x40831,a879)),f335(f166(f882(x40831)),x40832)),f166(x40831)))
% 59.73/59.65 [4116]E(f335(f335(f104(f888(f887(x41161,x41161),a879)),f310(x41161,f188(f888(f887(x41161,x41161),a879)))),f335(f335(f291(x41161,x41161,x41161),f310(x41161,x41162)),x41162)),f310(x41161,x41162))
% 59.73/59.65 [4152]E(f335(f335(f175(x41521,x41521),x41522),x41522),f335(f335(f147(x41521,f887(x41521,x41521)),f335(f335(f18(x41521,x41521,f887(x41521,x41521)),f264(x41521,x41521)),f5(x41521))),x41522))
% 59.73/59.65 [4272]E(f335(f135(a881,f882(x42721),f335(f7(f882(x42721),a881,a881),f335(f335(f8(a881,f888(a881,a881),f882(x42721)),f241(a881)),f189(f882(x42721)))),f2(a881)),f335(f162(f882(x42721)),x42722)),f335(f189(f882(f882(x42721))),f173(x42721,x42722)))
% 59.73/59.65 [4351]E(f335(f335(f290(f887(a881,f882(x43511)),f882(x43511)),f328(a881,f882(x43511),a248,f138(x43511,x43512))),f335(f335(f18(f882(x43511),f882(x43511),f887(a881,f882(x43511))),f335(f335(f8(a881,f888(f882(x43511),f887(a881,f882(x43511))),f882(x43511)),f264(a881,f882(x43511))),f189(f882(x43511)))),f5(f882(x43511)))),f139(x43511,x43512))
% 59.73/59.65 [4483]E(f335(f249(x44831),f335(f335(f8(f888(f888(x44831,a879),a879),a879,x44831),f83(f888(x44831,a879))),f335(f335(f8(f888(f888(x44831,a879),a879),f888(f888(x44831,a879),a879),x44831),f335(f18(f888(x44831,a879),a879,a879),f335(f335(f8(a879,f888(a879,a879),f888(x44831,a879)),a338),f335(f335(f7(f888(x44831,a879),f888(f888(x44831,a879),a879),a879),f337(f888(x44831,a879))),x44832)))),f337(x44831)))),f32(f888(x44831,a879),x44832))
% 59.73/59.65 [4598]~P1(f335(f335(f243(a1),f335(f94(a1),x45981)),f335(f74(a1),f335(f94(a1),x45982))))
% 59.73/59.65 [4614]~P1(f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f75(a1),x46141),x46141)),a91)),f335(f335(f75(a1),x46142),x46142)))
% 59.73/59.65 [3542]E(f335(f335(f23(a881),f335(f335(f75(a881),x35421),x35422)),x35422),x35421)
% 59.73/59.65 [3543]E(f335(f335(f23(a881),f335(f335(f75(a881),x35431),x35432)),x35431),x35432)
% 59.73/59.65 [3609]E(f335(f335(f75(a881),f335(f335(f23(a881),x36091),x36092)),x36092),f335(f335(f241(a881),x36091),x36092))
% 59.73/59.65 [3722]E(f335(f335(f76(a881),f335(f335(f30(a881),x37221),x37222)),x37222),f335(f335(f23(a881),x37221),f39(a881,x37221,x37222)))
% 59.73/59.65 [3750]E(f335(f166(a881),f132(a881,f335(f304(a881,f335(a106,x37501)),x37502))),f308(a881,x37501,x37502))
% 59.73/59.65 [3758]E(f335(f94(a1),f219(f335(a98,f335(f70(a1),x37581)),f335(a98,f335(f70(a1),x37582)))),f335(f335(a220,x37581),x37582))
% 59.73/59.65 [3760]E(f335(f335(f104(f888(x37601,a879)),f335(f74(f888(x37601,a879)),x37602)),x37602),f252(f888(x37601,a879)))
% 59.73/59.65 [3761]E(f335(f335(f95(f888(x37611,a879)),f335(f74(f888(x37611,a879)),x37612)),x37612),f188(f888(x37611,a879)))
% 59.73/59.65 [3778]P1(f335(f335(f242(a881),f335(f335(f23(a881),x37781),x37782)),x37781))
% 59.73/59.65 [3779]P1(f335(f335(f242(a881),f335(f335(f30(a881),x37791),x37792)),x37791))
% 59.73/59.65 [3803]P1(f335(f335(f243(a881),x38031),f335(a106,f335(f335(f75(a881),x38032),x38031))))
% 59.73/59.65 [3804]P1(f335(f335(f243(a881),x38041),f335(a106,f335(f335(f75(a881),x38041),x38042))))
% 59.73/59.65 [3823]E(f335(f335(f76(a881),f335(a98,f335(f70(a1),x38231))),f335(a98,f335(f70(a1),x38232))),f335(a98,f335(f70(a1),f335(f335(f76(a1),x38231),x38232))))
% 59.73/59.65 [3833]E(f335(f335(f75(a1),f335(f335(f76(a1),x38331),x38332)),f335(f335(f76(a1),x38331),x38332)),f335(f335(f76(a1),f335(f335(f75(a1),x38331),x38331)),x38332))
% 59.73/59.65 [3835]P1(f335(f335(f242(a1),f2(a1)),f335(f335(f254(a1),f335(f70(a1),x38351)),x38352)))
% 59.73/59.65 [3904]E(f335(f288(f882(x39041),f882(x39041),f151(x39041,x39042)),f335(f335(f312(f882(x39041)),f107(x39041)),f188(f888(f882(x39041),a879)))),f335(f335(f312(f882(x39041)),f107(x39041)),f188(f888(f882(x39041),a879))))
% 59.73/59.65 [3925]E(f335(f335(f104(f888(f887(x39251,x39251),a879)),f310(x39251,x39252)),f310(x39251,f188(f888(f887(x39251,x39251),a879)))),f310(x39251,x39252))
% 59.73/59.65 [3939]E(f335(f335(f30(a1),f335(f97(a1),f335(f335(f75(a1),x39391),x39391))),f335(f97(a1),f335(f335(f75(a1),x39392),x39392))),f335(f335(f30(a1),f335(f97(a1),x39391)),f335(f97(a1),x39392)))
% 59.73/59.65 [4005]E(f335(f335(f254(a1),x40051),f335(f97(a881),f335(f335(f75(a1),x40052),x40052))),f335(f335(f81(a1,a1),f335(f335(f254(a1),x40051),f335(f97(a881),x40052))),f335(f335(f18(a1,a1,a1),f76(a1)),f5(a1))))
% 59.73/59.65 [4011]E(f335(f249(f888(x40111,a879)),f335(f335(f7(f888(x40111,a879),f888(x40111,a879),a879),f242(f888(x40111,a879))),x40112)),f335(f311(x40111),x40112))
% 59.73/59.65 [4027]E(f335(f335(f147(a1,a881),a98),f335(f335(f127(a1),f335(f335(f147(a881,a1),f94(a1)),x40271)),f335(f335(f147(a881,a1),f94(a1)),x40272))),f335(f335(f127(a881),x40271),x40272))
% 59.73/59.65 [4060]E(f335(f313(a1,a1,f335(f335(f7(a1,a1,a1),f75(a1)),x40601)),f335(f304(a1,f2(a1)),f335(f335(f23(a1),x40602),x40601))),f335(f304(a1,x40601),x40602))
% 59.73/59.65 [4062]P47(x40621,f335(f335(f23(f888(f887(x40621,x40621),a879)),x40622),f310(x40621,f188(f888(f887(x40621,x40621),a879)))))
% 59.73/59.65 [4081]E(f335(f189(f882(x40811)),f335(f135(f882(x40811),f882(x40811),f127(x40811),f107(x40811)),x40812)),f335(f159(a881),f335(f335(f147(f882(x40811),a881),f189(f882(x40811))),x40812)))
% 59.73/59.65 [4086]P46(x40861,f252(f888(x40861,a879)),f335(f335(f104(f888(f887(x40861,x40861),a879)),x40862),f310(x40861,f188(f888(f887(x40861,x40861),a879)))))
% 59.73/59.65 [4126]P1(f335(f335(f337(f887(x41261,x41261)),f335(f335(f264(x41261,x41261),x41262),x41262)),f310(x41261,f188(f888(f887(x41261,x41261),a879)))))
% 59.73/59.65 [4132]E(f185(a881,f2(a881),f335(f335(f8(a881,a881,a881),a106),f335(f335(f7(a881,a881,a881),f240(a881)),x41321)),x41322),f335(f335(f240(a881),x41322),f335(a106,x41321)))
% 59.73/59.65 [4135]E(f185(a881,f335(a106,x41351),f335(f335(f8(a881,a881,a881),a106),f335(f335(f7(a881,a881,a881),f241(a881)),x41351)),x41352),f335(f335(f241(a881),x41352),f335(a106,x41351)))
% 59.73/59.65 [4138]E(f335(f313(x41381,f882(x41381),f335(f335(f7(x41381,f882(x41381),f882(x41381)),f144(x41381)),f107(x41381))),x41382),f168(x41381,x41382,f335(f335(f312(f882(x41381)),f107(x41381)),f188(f888(f882(x41381),a879)))))
% 59.73/59.65 [4139]E(f335(f335(f104(f888(f887(x41391,x41391),a879)),f335(f335(f291(x41391,x41391,x41391),x41392),f310(x41391,x41392))),f310(x41391,f188(f888(f887(x41391,x41391),a879)))),f310(x41391,x41392))
% 59.73/59.65 [4147]P1(f335(f335(f242(f888(f887(x41471,x41471),a879)),f261(x41471,x41472)),f335(f335(f266(x41471,x41471),x41472),f335(f16(f888(x41471,a879),x41471),x41472))))
% 59.73/59.65 [4150]E(f335(f313(a1,a881,a98),f335(f335(f104(f888(a1,a879)),f335(f313(a881,a1,f94(a1)),x41501)),f335(f313(a881,a1,f94(a1)),x41502))),f335(f335(f104(f888(a881,a879)),x41501),x41502))
% 59.73/59.65 [4151]E(f335(f313(a1,a881,a98),f335(f335(f95(f888(a1,a879)),f335(f313(a881,a1,f94(a1)),x41511)),f335(f313(a881,a1,f94(a1)),x41512))),f335(f335(f95(f888(a881,a879)),x41511),x41512))
% 59.73/59.65 [4155]E(f335(f249(x41551),f335(f335(f8(a879,a879,x41551),a330),f335(f335(f7(x41551,f888(x41551,a879),a879),f337(x41551)),x41552))),f335(f74(f888(x41551,a879)),x41552))
% 59.73/59.65 [4182]E(f335(f135(f882(x41821),f882(x41821),f127(x41821),f107(x41821)),f335(f335(f147(f882(x41821),f882(x41821)),f162(x41821)),f335(f162(f882(x41821)),x41822))),f335(f162(x41821),f335(f135(f882(x41821),f882(x41821),f127(x41821),f107(x41821)),x41822)))
% 59.73/59.65 [4212]E(f335(f335(f33(a881,f888(f887(x42121,x42121),a879)),f252(f888(a881,a879))),f335(f335(f7(a881,f888(f887(x42121,x42121),a879),f888(f887(x42121,x42121),a879)),f183(f887(x42121,x42121),a879)),x42122)),f310(x42121,x42122))
% 59.73/59.65 [4233]E(f80(x42331,f335(f335(f8(f888(x42331,a879),a879,x42331),f335(a332,x42332)),f335(f335(f7(x42331,f888(x42331,a879),f888(x42331,a879)),f312(x42331)),f188(f888(x42331,a879))))),f315(x42331,x42332))
% 59.73/59.65 [4241]E(f335(f189(f882(x42411)),f145(x42411,f335(f135(f882(x42411),f882(x42411),f127(x42411),f107(x42411)),x42412))),f335(f29(x42411),f335(f335(f33(f882(x42411),f888(x42411,a879)),f335(f166(f882(x42411)),x42412)),f166(x42411))))
% 59.73/59.65 [4257]E(f335(f335(f104(f888(f887(x42571,x42571),a879)),x42572),f335(f335(f291(x42571,x42571,x42571),f335(f335(f291(x42571,x42571,x42571),x42572),f310(x42571,x42572))),x42572)),f335(f335(f291(x42571,x42571,x42571),x42572),f310(x42571,x42572)))
% 59.73/59.65 [4282]P1(f335(f335(f242(f888(f887(x42821,x42821),a879)),f335(f335(f291(x42821,x42821,x42821),x42822),f310(x42821,x42822))),f335(f335(f266(x42821,x42821),f335(f287(x42821),x42822)),f335(f16(f888(x42821,a879),x42821),f335(f287(x42821),x42822)))))
% 59.73/59.65 [4325]E(f335(f249(f882(x43251)),f335(f335(f7(f882(x43251),f888(x43251,a879),a879),f335(f335(f8(f888(x43251,a879),f888(f888(x43251,a879),a879),f882(x43251)),f242(f888(x43251,a879))),f166(x43251))),x43252)),f154(x43251,x43252))
% 59.73/59.65 [4338]E(f335(f149(f882(x43381),x43381,f107(x43381),f335(f335(f8(f882(x43381),f888(f882(x43381),f882(x43381)),x43381),f335(f7(f882(x43381),f882(x43381),f882(x43381)),f127(x43381))),f335(f335(f7(x43381,f882(x43381),f882(x43381)),f144(x43381)),f107(x43381)))),x43382),f335(f161(x43381),x43382))
% 59.73/59.65 [4380]P26(f888(x43801,x43802),f888(f887(x43801,x43802),a879),f335(f335(f8(f888(f887(x43801,x43802),a879),f888(f887(x43801,x43802),a879),f888(x43801,x43802)),f249(f887(x43801,x43802))),f335(f335(f8(f888(x43801,f888(x43802,a879)),f888(f887(x43801,x43802),a879),f888(x43801,x43802)),f268(x43801,x43802,a879)),f335(f8(x43802,f888(x43802,a879),x43801),f335(f7(x43802,x43802,a879),a332)))),f252(f888(f888(x43801,x43802),a879)))
% 59.73/59.65 [4385]E(f39(a1,f335(f97(a1),f335(f335(f75(a1),x43851),x43851)),f335(f97(a1),f335(f335(f75(a1),x43852),x43852))),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f39(a1,f335(f97(a1),x43851),f335(f97(a1),x43852))))
% 59.73/59.65 [4430]E(f335(f335(f33(x44301,f888(f887(x44301,x44301),a879)),x44302),f335(f335(f7(x44301,f888(f887(x44301,x44301),a879),f888(f887(x44301,x44301),a879)),f335(f335(f8(f887(x44301,x44301),f888(f888(f887(x44301,x44301),a879),f888(f887(x44301,x44301),a879)),x44301),f312(f887(x44301,x44301))),f335(f335(f18(x44301,x44301,f887(x44301,x44301)),f264(x44301,x44301)),f5(x44301)))),f188(f888(f887(x44301,x44301),a879)))),f261(x44301,x44302))
% 59.73/59.65 [4438]E(f205(x44381,f335(f335(f264(a1,a1),f335(f74(a1),f335(f335(f68(f887(a1,a1),a1,x44381,f263(a1,a1)),f215(x44381)),x44382))),f335(f335(f68(f887(a1,a1),a1,x44381,f267(a1,a1)),f215(x44381)),x44382))),f229(x44381,x44382))
% 59.73/59.65 [4519]E(f335(f249(f888(x45191,a879)),f335(f335(f8(f888(f888(x45191,a879),a879),a879,f888(x45191,a879)),f82(f888(x45191,a879))),f335(f335(f7(f888(x45191,a879),f888(f888(x45191,a879),a879),f888(f888(x45191,a879),a879)),f335(f335(f8(f888(f888(x45191,a879),f888(a879,a879)),f888(f888(f888(x45191,a879),a879),f888(f888(x45191,a879),a879)),f888(x45191,a879)),f18(f888(x45191,a879),a879,a879)),f335(f335(f8(f888(f888(x45191,a879),a879),f888(f888(x45191,a879),f888(a879,a879)),f888(x45191,a879)),f335(f8(a879,f888(a879,a879),f888(x45191,a879)),a333)),f335(f335(f7(f888(x45191,a879),f888(f888(x45191,a879),f888(x45191,a879)),f888(f888(x45191,a879),a879)),f335(f335(f8(f888(f888(x45191,a879),a879),f888(f888(f888(x45191,a879),f888(x45191,a879)),f888(f888(x45191,a879),a879)),f888(x45191,a879)),f8(f888(x45191,a879),a879,f888(x45191,a879))),a332)),f74(f888(x45191,a879)))))),f335(f335(f8(f888(f888(x45191,a879),a879),a879,f888(x45191,a879)),f335(f337(f888(x45191,a879)),x45192)),f311(x45191))))),f335(f311(x45191),f335(f74(f888(x45191,a879)),x45192)))
% 59.73/59.65 [4594]~E(f335(f335(f75(a1),x45941),x45941),f335(f335(f23(a1),f335(f335(f75(a1),x45942),x45942)),a91))
% 59.73/59.65 [4595]~E(f335(f335(f75(a1),x45951),x45951),f335(f335(f23(a1),f335(f335(f75(a1),x45952),x45952)),a91))
% 59.73/59.65 [4601]~P1(f335(f335(f243(a881),f335(f335(f75(a881),x46011),x46012)),x46012))
% 59.73/59.65 [4602]~P1(f335(f335(f243(a881),f335(f335(f75(a881),x46021),x46022)),x46021))
% 59.73/59.65 [3840]E(f335(f335(f23(a881),x38401),f335(f335(f76(a881),f335(f335(f30(a881),x38401),x38402)),x38402)),f39(a881,x38401,x38402))
% 59.73/59.65 [3841]E(f335(f335(f23(a1),x38411),f335(f335(f76(a1),f335(f335(f30(a1),x38411),x38412)),x38412)),f39(a1,x38411,x38412))
% 59.73/59.65 [3874]E(f335(f335(f147(a881,x38741),f335(f158(x38741),x38742)),f132(a881,f335(f304(a881,f2(a881)),f335(f189(f882(x38741)),x38742)))),x38742)
% 59.73/59.65 [3935]E(f335(f288(x39351,x39351,f310(x39351,f188(f888(f887(x39351,x39351),a879)))),x39352),x39352)
% 59.73/59.65 [4065]E(f310(x40651,f335(f335(f104(f888(f887(x40651,x40651),a879)),x40652),f310(x40651,f188(f888(f887(x40651,x40651),a879))))),f310(x40651,x40652))
% 59.73/59.65 [4066]E(f310(x40661,f335(f335(f23(f888(f887(x40661,x40661),a879)),x40662),f310(x40661,f188(f888(f887(x40661,x40661),a879))))),f310(x40661,x40662))
% 59.73/59.65 [4119]E(f335(f335(f23(a1),f335(f335(f23(a1),f335(f335(f75(a1),x41191),x41191)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),x41192),x41192)),a91)),f335(f335(f75(a1),f335(f335(f23(a1),x41191),x41192)),f335(f335(f23(a1),x41191),x41192)))
% 59.73/59.65 [4160]E(f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f75(a1),x41601),x41602)),f335(f335(f75(a1),x41601),x41602))),a91),f335(f335(f75(a1),f335(f335(f75(a1),x41601),x41601)),f335(f335(f23(a1),f335(f335(f75(a1),x41602),x41602)),a91)))
% 59.73/59.65 [4186]E(f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),x41861),x41861)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),x41862),x41862)),a91)),f335(f335(f75(a1),f335(f335(f75(a1),x41861),f335(f335(f23(a1),x41862),a91))),f335(f335(f75(a1),x41861),f335(f335(f23(a1),x41862),a91))))
% 59.73/59.65 [4197]E(f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),x41971),x41972)),f335(f335(f23(a1),x41971),x41972))),a91),f335(f335(f23(a1),f335(f335(f23(a1),f335(f335(f75(a1),x41971),x41971)),a91)),f335(f335(f75(a1),x41972),x41972)))
% 59.73/59.65 [4198]E(f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f75(a1),x41981),x41982)),f335(f335(f75(a1),x41981),x41982))),a91),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),x41981),x41981)),a91)),f335(f335(f75(a1),x41982),x41982)))
% 59.73/59.65 [4254]E(f335(f94(a1),f335(f335(f30(a881),f335(f335(f76(a881),f335(a98,f335(f70(a1),x42541))),f335(a98,f335(f70(a1),x42542)))),f219(f335(a98,f335(f70(a1),x42541)),f335(a98,f335(f70(a1),x42542))))),f221(x42541,x42542))
% 59.73/59.65 [4302]E(f335(f335(f270(f887(a93,a93),a93,f887(a93,a93),f887(x43021,f887(a93,a93))),f275(f335(a3,f335(f189(f882(x43021)),x43022)))),f335(f335(f8(x43021,f888(f887(a93,a93),f887(x43021,f887(a93,a93))),a93),f264(x43021,f887(a93,a93))),f335(f335(f8(a881,x43021,a93),f335(f158(x43021),x43022)),a20))),f281(x43021,x43022))
% 59.73/59.65 [4386]E(f335(f135(a881,f882(x43861),f335(f7(f882(x43861),a881,a881),f335(f335(f8(a881,f888(a881,a881),f882(x43861)),f241(a881)),f189(f882(x43861)))),f2(a881)),f335(f162(f882(x43861)),f173(x43861,x43862))),f335(f189(f882(f882(x43861))),f335(f129(f882(x43861),f335(f335(f8(a879,a879,f882(x43861)),a330),f335(f335(f7(f882(x43861),f882(x43861),a879),a332),f107(x43861)))),x43862)))
% 59.73/59.65 [4392]E(f335(f335(f33(a881,f888(x43921,a879)),f252(f888(a881,a879))),f335(f335(f7(a881,f888(a881,f888(x43921,a879)),f888(x43921,a879)),f335(f335(f8(f888(a881,a879),f888(f888(a881,f888(x43921,a879)),f888(x43921,a879)),a881),f33(a881,f888(x43921,a879))),f304(a881,f2(a881)))),x43922)),f335(f335(f33(a881,f888(x43921,a879)),f252(f888(a881,a879))),x43922))
% 59.73/59.65 [4414]P1(f335(f56(a881),f335(f249(a881),f335(f335(f18(a881,a879,a879),f335(f335(f8(a879,f888(a879,a879),a881),a333),x44141)),f335(f335(f7(a881,a881,a879),f243(a881)),x44142)))))
% 59.73/59.65 [4529]E(f335(f249(f887(f882(x45291),f882(x45291))),f335(f268(f882(x45291),f882(x45291),a879),f335(f335(f18(f882(x45291),f888(f882(x45291),a879),f888(f882(x45291),a879)),f335(f335(f8(f888(f882(x45291),f888(a879,a879)),f888(f888(f882(x45291),a879),f888(f882(x45291),a879)),f882(x45291)),f18(f882(x45291),a879,a879)),f335(f335(f8(f888(f882(x45291),a879),f888(f882(x45291),f888(a879,a879)),f882(x45291)),f335(f8(a879,f888(a879,a879),f882(x45291)),a334)),f335(f335(f7(f882(x45291),f888(f882(x45291),a881),f888(f882(x45291),a879)),f335(f335(f8(f888(a881,a879),f888(f888(f882(x45291),a881),f888(f882(x45291),a879)),f882(x45291)),f8(a881,a879,f882(x45291))),f335(f335(f8(a881,f888(a881,a879),f882(x45291)),f243(a881)),f189(f882(x45291))))),f189(f882(x45291)))))),f335(f335(f18(f882(x45291),f888(f882(x45291),a879),f888(f882(x45291),a879)),f335(f335(f8(f888(f882(x45291),f888(a879,a879)),f888(f888(f882(x45291),a879),f888(f882(x45291),a879)),f882(x45291)),f18(f882(x45291),a879,a879)),f335(f335(f8(f888(f882(x45291),a879),f888(f882(x45291),f888(a879,a879)),f882(x45291)),f335(f8(a879,f888(a879,a879),f882(x45291)),a333)),f335(f335(f7(f882(x45291),f888(f882(x45291),a881),f888(f882(x45291),a879)),f335(f335(f8(f888(a881,a879),f888(f888(f882(x45291),a881),f888(f882(x45291),a879)),f882(x45291)),f8(a881,a879,f882(x45291))),f335(f335(f8(a881,f888(a881,a879),f882(x45291)),a332),f189(f882(x45291))))),f189(f882(x45291)))))),f335(f335(f7(f882(x45291),f888(f887(f882(x45291),f882(x45291)),a879),f888(f882(x45291),a879)),f335(f335(f8(f888(f882(x45291),f888(f888(f887(f882(x45291),f882(x45291)),a879),a879)),f888(f888(f887(f882(x45291),f882(x45291)),a879),f888(f882(x45291),a879)),f882(x45291)),f7(f882(x45291),f888(f887(f882(x45291),f882(x45291)),a879),a879)),f335(f335(f8(f888(f882(x45291),f887(f882(x45291),f882(x45291))),f888(f882(x45291),f888(f888(f887(f882(x45291),f882(x45291)),a879),a879)),f882(x45291)),f335(f8(f887(f882(x45291),f882(x45291)),f888(f888(f887(f882(x45291),f882(x45291)),a879),a879),f882(x45291)),f337(f887(f882(x45291),f882(x45291))))),f264(f882(x45291),f882(x45291))))),f138(x45291,x45292)))))),f139(x45291,x45292))
% 59.73/59.65 [4607]~P1(f335(f335(f86(a1),f335(f335(f75(a1),x46071),x46071)),f335(f335(f23(a1),f335(f335(f75(a1),x46072),x46072)),a91)))
% 59.73/59.65 [4189]E(f335(f335(f75(a1),f335(f335(f75(a1),f335(f335(f76(a1),x41891),x41892)),f335(f335(f76(a1),x41891),x41892))),x41892),f335(f335(f76(a1),f335(f335(f23(a1),f335(f335(f75(a1),x41891),x41891)),a91)),x41892))
% 59.73/59.65 [4300]E(f335(a98,f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),x43001),x43002)),f188(f888(f887(a881,a881),a879)))))),f335(f335(f23(a881),x43001),x43002))
% 59.73/59.65 [4305]E(f335(f335(f291(x43051,x43051,x43051),f335(f335(f104(f888(f887(x43051,x43051),a879)),x43052),f310(x43051,f188(f888(f887(x43051,x43051),a879))))),f310(x43051,f335(f335(f104(f888(f887(x43051,x43051),a879)),x43052),f310(x43051,f188(f888(f887(x43051,x43051),a879)))))),f310(x43051,x43052))
% 59.73/59.65 [4344]E(f276(x43441,f335(f129(f887(a93,x43441),f335(f268(a93,x43441,a879),f335(f335(f8(a879,f888(x43441,a879),a93),f16(a879,x43441)),f335(f243(a93),f2(a93))))),x43442)),f276(x43441,x43442))
% 59.73/59.65 [4345]E(f274(x43451,f335(f129(f887(a93,x43451),f335(f268(a93,x43451,a879),f335(f335(f8(a879,f888(x43451,a879),a93),f16(a879,x43451)),f335(f243(a93),f2(a93))))),x43452)),f274(x43451,x43452))
% 59.73/59.65 [4347]E(f335(f74(a1),f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),x43471),x43472)),f188(f888(f887(a881,a881),a879)))))),f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),x43472),x43471)),f188(f888(f887(a881,a881),a879))))))
% 59.73/59.65 [4405]E(f335(f335(f290(f882(a881),x44051),f138(a881,a248)),f335(f335(f7(x44051,f882(f888(x44051,a881)),f882(a881)),f335(f335(f8(f888(f888(x44051,a881),a881),f888(f882(f888(x44051,a881)),f882(a881)),x44051),f147(f888(x44051,a881),a881)),f335(f7(f888(x44051,a881),x44051,a881),f5(f888(x44051,a881))))),x44052)),f146(x44051,x44052))
% 59.73/59.65 [4427]E(f335(f335(f81(a1,a881),f335(f97(a1),f335(f335(f75(a1),x44271),a91))),f335(f335(f18(a1,a881,a881),f335(f335(f7(a1,a881,f888(a881,a881)),f335(f335(f8(a879,f888(a881,f888(a881,a881)),a1),f88(a881)),a193)),f2(a881))),f335(f335(f8(a881,a881,a1),a106),f335(f335(f8(a881,a881,a1),f335(f240(a881),x44272)),a98)))),f335(f335(f240(a881),f335(a106,x44272)),f335(f97(a881),x44271)))
% 59.73/59.65 [4428]E(f335(f335(f81(a1,a881),f335(f97(a1),f335(f335(f75(a1),x44281),a91))),f335(f335(f18(a1,a881,a881),f335(f335(f7(a1,a881,f888(a881,a881)),f335(f335(f8(a879,f888(a881,f888(a881,a881)),a1),f88(a881)),a193)),f335(a106,x44282))),f335(f335(f8(a881,a881,a1),a106),f335(f335(f8(a881,a881,a1),f335(f241(a881),x44282)),a98)))),f335(f335(f241(a881),f335(a106,x44282)),f335(f97(a881),x44281)))
% 59.73/59.65 [4448]E(f335(f135(f882(x44481),f882(x44481),f127(x44481),f107(x44481)),f335(f335(f147(f882(x44481),f882(x44481)),f149(f882(x44481),x44481,f107(x44481),f335(f335(f8(f882(x44481),f888(f882(x44481),f882(x44481)),x44481),f16(f882(x44481),f882(x44481))),f335(f335(f7(x44481,f882(x44481),f882(x44481)),f144(x44481)),f107(x44481))))),x44482)),f335(f335(f147(f882(x44481),x44481),f134(x44481)),f335(f129(f882(x44481),f335(f335(f8(a879,a879,f882(x44481)),a330),f335(f335(f7(f882(x44481),f882(x44481),a879),a332),f107(x44481)))),x44482)))
% 59.73/59.65 [4511]E(f335(f268(a1,a1,a879),f335(f335(f7(a1,f888(a1,a879),f888(a1,a879)),f335(f335(f8(f888(a1,f888(a879,a879)),f888(f888(a1,a879),f888(a1,a879)),a1),f18(a1,a879,a879)),f335(f335(f8(f888(a1,a879),f888(a1,f888(a879,a879)),a1),f335(f8(a879,f888(a879,a879),a1),a333)),f335(f335(f8(f888(a1,a1),f888(a1,a879),a1),f335(f8(a1,a879,a1),f335(a332,x45111))),f335(f335(f8(a1,f888(a1,a1),a1),f75(a1)),f335(f76(a1),x45112)))))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f335(f8(a879,a879,a1),f335(a338,f335(f335(f243(a1),f2(a1)),x45112))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f242(a1),f2(a1)))),f335(f335(f7(a1,a1,a879),f243(a1)),x45112))))),f335(f335(f8(a879,a879,a1),f335(a338,f335(a330,f335(f335(f243(a1),f2(a1)),x45112)))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f243(a1),x45112))),f335(f335(f7(a1,a1,a879),f242(a1)),f2(a1))))))),f43(x45111,x45112))
% 59.73/59.65 [4513]E(f335(f249(x45131),f335(f335(f8(f888(a881,a879),a879,x45131),f82(a881)),f335(f335(f7(x45131,f888(a881,a879),f888(a881,a879)),f335(f335(f8(f888(a881,f888(a879,a879)),f888(f888(a881,a879),f888(a881,a879)),x45131),f18(a881,a879,a879)),f335(f335(f8(f888(a881,a879),f888(a881,f888(a879,a879)),x45131),f335(f8(a879,f888(a879,a879),a881),a333)),f335(f335(f7(x45131,f888(a881,x45131),f888(a881,a879)),f335(f335(f8(f888(x45131,a879),f888(f888(a881,x45131),f888(a881,a879)),x45131),f8(x45131,a879,a881)),a332)),f335(f158(x45131),x45132))))),f335(f335(f7(a881,a881,a879),f243(a881)),f335(f189(f882(x45131)),x45132))))),f335(f166(x45131),x45132))
% 59.73/59.65 [4315]E(f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),x43151),a91)),x43152)),f335(f335(f23(a1),f335(f335(f75(a1),x43151),a91)),x43152))),a91),f335(f335(f23(a1),f335(f335(f75(a1),x43151),x43151)),f335(f335(f23(a1),f335(f335(f75(a1),x43152),x43152)),a91)))
% 59.73/59.65 [4443]E(f335(f135(f882(f882(x44431)),f882(f882(x44431)),f127(f882(x44431)),f107(f882(x44431))),f335(f335(f147(f882(x44431),f882(f882(x44431))),f149(f882(f882(x44431)),x44431,f107(f882(x44431)),f335(f16(f888(f882(x44431),f882(f882(x44431))),x44431),f335(f335(f7(f882(x44431),f882(f882(x44431)),f882(f882(x44431))),f144(f882(x44431))),f107(f882(x44431)))))),x44432)),f335(f335(f147(f882(x44431),f882(x44431)),f165(x44431)),f335(f129(f882(x44431),f335(f335(f8(a879,a879,f882(x44431)),a330),f335(f335(f7(f882(x44431),f882(x44431),a879),a332),f107(x44431)))),x44432)))
% 59.73/59.65 [4454]E(f335(f335(f81(a1,a881),f335(f97(a1),f335(f335(f75(a1),x44541),a91))),f335(f335(f18(a1,a881,a881),f335(f335(f7(a1,a881,f888(a881,a881)),f335(f335(f8(a879,f888(a881,f888(a881,a881)),a1),f88(a881)),a193)),f2(a881))),f335(f335(f8(a881,a881,a1),a106),f335(f335(f7(a1,a881,a881),f335(f335(f8(a881,f888(a881,a881),a1),f240(a881)),a98)),x44542)))),f335(f335(f240(a881),f335(f97(a881),x44541)),f335(a106,x44542)))
% 59.73/59.65 [4455]E(f335(f335(f81(a1,a881),f335(f97(a1),f335(f335(f75(a1),x44551),a91))),f335(f335(f18(a1,a881,a881),f335(f335(f7(a1,a881,f888(a881,a881)),f335(f335(f8(a879,f888(a881,f888(a881,a881)),a1),f88(a881)),a193)),f335(a106,x44552))),f335(f335(f8(a881,a881,a1),a106),f335(f335(f7(a1,a881,a881),f335(f335(f8(a881,f888(a881,a881),a1),f241(a881)),a98)),x44552)))),f335(f335(f241(a881),f335(f97(a881),x44551)),f335(a106,x44552)))
% 59.73/59.65 [4442]E(f335(f268(x44421,x44421,a879),f335(f335(f18(x44421,a879,f888(x44421,a879)),f335(f335(f8(f888(x44421,f888(a879,a879)),f888(a879,f888(x44421,a879)),x44421),f7(x44421,a879,a879)),f335(f335(f8(f888(x44421,a879),f888(x44421,f888(a879,a879)),x44421),f335(f8(a879,f888(a879,a879),x44421),a333)),a332))),x44422)),f261(x44421,x44422))
% 59.73/59.65 [4489]E(f335(f335(f30(a881),x44891),f335(f335(f75(a881),f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),a91))),x44892)),f335(f335(f30(a881),x44891),f335(a106,f335(a106,f335(a106,x44892)))))
% 59.73/59.65 [4490]E(f39(a881,x44901,f335(f335(f75(a881),f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),a91))),x44902)),f39(a881,x44901,f335(a106,f335(a106,f335(a106,x44902)))))
% 59.73/59.65 [4491]E(f39(a881,f335(f335(f75(a881),f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),a91))),x44911),x44912),f39(a881,f335(a106,f335(a106,f335(a106,x44911))),x44912))
% 59.73/59.65 [4504]E(f117(f335(x45041,f335(f335(f76(a93),f335(f97(a93),f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),a91))),x45042))),f335(f203(x45041),x45042))
% 59.73/59.65 [4505]E(f335(f335(f30(a881),f335(f335(f75(a881),f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),a91))),x45051)),x45052),f335(f335(f30(a881),f335(a106,f335(a106,f335(a106,x45051)))),x45052))
% 59.73/59.65 [4557]~E(f120(x45571,x45572,x45573),f113(x45571))
% 59.73/59.65 [4558]~E(f120(x45581,x45582,x45583),f113(x45581))
% 59.73/59.65 [3254]E(f335(f192(x32541,x32542),x32543),f114(x32541,x32542))
% 59.73/59.65 [3276]E(f335(f202(x32761,x32762),x32763),f335(f123(x32761),x32762))
% 59.73/59.65 [3357]E(f335(f335(f147(x33571,x33572),x33573),f107(x33571)),f107(x33572))
% 59.73/59.65 [3358]E(f335(f335(f201(x33581,x33582),x33583),f200(x33581)),f200(x33582))
% 59.73/59.65 [3398]E(f335(f184(x33981,x33982,x33983),f2(a881)),x33982)
% 59.73/59.65 [3400]E(f335(f335(f175(x34001,x34002),x34003),f107(x34002)),f107(f887(x34001,x34002)))
% 59.73/59.65 [3415]E(f335(f189(f882(x34151)),f163(x34151,x34152,x34153)),x34152)
% 59.73/59.65 [3435]E(f80(x34351,f57(x34351,x34352,x34353)),f335(f58(x34351,x34352),x34353))
% 59.73/59.65 [3439]E(f253(x34391,x34392,f253(x34392,x34391,x34393)),x34393)
% 59.73/59.65 [3459]E(f335(f162(x34591),f163(x34591,x34592,x34593)),f163(x34591,x34592,x34593))
% 59.73/59.65 [3486]E(f133(x34861,x34862,f145(x34861,x34863)),f145(x34861,f133(x34861,x34862,x34863)))
% 59.73/59.65 [3505]E(f335(f263(f882(x35051),f882(x35051)),f160(x35051,x35052,x35053)),f335(f129(x35051,x35052),x35053))
% 59.73/59.65 [3552]E(f335(f335(f144(x35521),x35522),f163(x35521,x35523,x35522)),f163(x35521,f335(a106,x35523),x35522))
% 59.73/59.65 [3584]E(f185(x35841,x35842,x35843,f2(a881)),x35842)
% 59.73/59.65 [3585]E(f17(x35851,x35852,x35853,f2(a93)),x35852)
% 59.73/59.65 [3586]E(f19(x35861,x35862,x35863,f2(a93)),x35862)
% 59.73/59.65 [3593]E(f156(x35931,x35932,x35933,f107(x35931)),f107(x35932))
% 59.73/59.65 [3594]E(f157(x35941,x35942,x35943,f107(x35941)),f107(x35942))
% 59.73/59.65 [3601]E(f335(f335(f158(x36011),f335(f335(f144(x36011),x36012),x36013)),f2(a881)),x36012)
% 59.73/59.65 [3630]E(f54(x36301,x36302,f107(x36301),x36303),f107(f887(x36301,x36302)))
% 59.73/59.65 [3650]P26(x36501,x36502,x36503,f188(f888(x36501,a879)))
% 59.73/59.65 [3754]E(f273(x37541,x37542,x37543),f335(f264(f888(a93,f888(a879,f885(f883(x37541)))),f887(a93,a93)),f35(x37541)))
% 59.73/59.65 [3812]E(f335(f68(x38121,x38122,x38121,x38123),f25(x38121)),x38123)
% 59.73/59.65 [3995]P1(f335(f335(f337(f887(x39951,x39951)),f335(f335(f264(x39951,x39951),x39952),x39952)),f310(x39951,x39953)))
% 59.73/59.65 [4608]~P1(f335(f335(f337(f887(f882(x46081),f882(x46081))),f335(f335(f264(f882(x46081),f882(x46081)),x46082),f107(x46081))),f138(x46081,x46083)))
% 59.73/59.65 [4609]~P1(f335(f335(f337(f887(f882(x46091),f882(x46091))),f335(f335(f264(f882(x46091),f882(x46091)),x46092),f107(x46091))),f140(x46091,x46093)))
% 59.73/59.65 [4610]~P1(f335(f335(f337(f887(f882(x46101),f882(x46101))),f335(f335(f264(f882(x46101),f882(x46101)),x46102),f107(x46101))),f150(x46101,x46103)))
% 59.73/59.65 [4611]~P1(f335(f335(f337(f887(f882(x46111),f882(x46111))),f335(f335(f264(f882(x46111),f882(x46111)),f107(x46111)),x46112)),f138(x46111,x46113)))
% 59.73/59.65 [4612]~P1(f335(f335(f337(f887(f882(x46121),f882(x46121))),f335(f335(f264(f882(x46121),f882(x46121)),f107(x46121)),x46122)),f150(x46121,x46123)))
% 59.73/59.65 [3332]E(f335(f335(f204(x33321),x33322),x33323),f205(x33321,f218(x33322,x33323)))
% 59.73/59.65 [3387]E(f335(f289(x33871,x33872),f335(f289(x33872,x33871),x33873)),x33873)
% 59.73/59.65 [3410]E(f335(f335(f175(x34101,x34102),f107(x34101)),x34103),f107(f887(x34101,x34102)))
% 59.73/59.65 [3413]E(f170(x34131,x34132,f335(f250(a881),x34133)),f335(f335(f169(x34131),x34133),x34132))
% 59.73/59.65 [3430]E(f335(f262(x34301,x34302),f335(f289(x34302,x34301),x34303)),f335(f260(x34302,x34301),x34303))
% 59.73/59.65 [3432]E(f145(x34321,f335(f129(x34321,x34322),x34323)),f335(f129(x34321,x34322),f145(x34321,x34323)))
% 59.73/59.65 [3433]E(f335(f260(x34331,x34332),f335(f289(x34332,x34331),x34333)),f335(f262(x34332,x34331),x34333))
% 59.73/59.65 [3434]E(f335(f262(x34341,x34342),f335(f289(x34342,x34341),x34343)),f335(f260(x34342,x34341),x34343))
% 59.73/59.65 [3451]E(f335(f129(x34511,x34512),f335(f162(x34511),x34513)),f335(f162(x34511),f335(f129(x34511,x34512),x34513)))
% 59.73/59.65 [3464]E(f335(f335(f131(x34641),x34642),f335(f165(x34641),x34643)),f335(f335(f131(x34641),f335(a106,x34642)),x34643))
% 59.73/59.65 [3482]E(f335(f313(x34821,x34822,x34823),f188(f888(x34821,a879))),f188(f888(x34822,a879)))
% 59.73/59.65 [3483]E(f335(f288(x34831,x34832,x34833),f188(f888(x34831,a879))),f188(f888(x34832,a879)))
% 59.73/59.65 [3484]E(f335(f314(x34841,x34842,x34843),f188(f888(x34842,a879))),f188(f888(x34841,a879)))
% 59.73/59.65 [3485]E(f335(f314(x34851,x34852,x34853),f252(f888(x34852,a879))),f252(f888(x34851,a879)))
% 59.73/59.65 [3513]E(f167(x35131,f335(f335(f144(x35131),x35132),x35133),f107(x35131)),f335(f335(f144(x35131),x35132),x35133))
% 59.73/59.65 [3514]E(f335(f335(f312(x35141),x35142),f335(f166(x35141),x35143)),f335(f166(x35141),f133(x35141,x35142,x35143)))
% 59.73/59.65 [3526]E(f236(x35261,x35262,f335(f235(x35261),x35263)),f335(f335(f75(a881),f335(x35262,x35263)),f335(a106,f2(a881))))
% 59.73/59.65 [3605]E(f335(f313(f887(x36051,x36052),x36052,f267(x36051,x36052)),x36053),f335(f260(x36051,x36052),x36053))
% 59.73/59.65 [3606]E(f335(f313(f887(x36061,x36062),x36061,f263(x36061,x36062)),x36063),f335(f262(x36061,x36062),x36063))
% 59.73/59.65 [3621]E(f116(x36211,x36212,x36213,f113(f885(x36211))),f113(f885(x36212)))
% 59.73/59.65 [3622]E(f335(f166(x36221),f163(x36221,f335(a106,x36222),x36223)),f335(f335(f312(x36221),x36223),f188(f888(x36221,a879))))
% 59.73/59.65 [3680]E(f335(f335(f264(x36801,x36802),f335(f263(x36801,x36802),x36803)),f335(f267(x36801,x36802),x36803)),x36803)
% 59.73/59.65 [3681]E(f335(f335(f264(x36811,x36812),f335(f263(x36811,x36812),x36813)),f335(f267(x36811,x36812),x36813)),x36813)
% 59.73/59.65 [3689]E(f335(f189(f883(x36891)),f120(x36891,x36892,x36893)),f335(f335(f75(a881),f335(f189(f883(x36891)),x36893)),f335(a106,f2(a881))))
% 59.73/59.65 [3690]E(f335(f335(f268(x36901,x36902,x36901),f16(x36901,x36902)),x36903),f335(f263(x36901,x36902),x36903))
% 59.73/59.65 [3709]E(f180(x37091,x37092,x37093,f335(f16(f885(x37092),x37091),f200(x37092))),x37093)
% 59.73/59.65 [3710]E(f180(x37101,x37102,f335(f16(f885(x37102),x37101),f200(x37102)),x37103),x37103)
% 59.73/59.65 [3818]E(f335(f68(x38181,x38181,x38182,f25(x38181)),x38183),x38183)
% 59.73/59.65 [3826]E(f335(f335(f127(x38261),f163(x38261,x38262,x38263)),f335(f335(f144(x38261),x38263),f107(x38261))),f335(f335(f144(x38261),x38263),f163(x38261,x38262,x38263)))
% 59.73/59.65 [4006]P1(f335(f335(f242(f888(x40061,a879)),f335(f166(x40061),f335(f129(x40061,x40062),x40063))),f335(f166(x40061),x40063)))
% 59.73/59.65 [4050]P1(f335(f335(f242(f888(x40501,a879)),f335(f166(x40501),f335(f335(f169(x40501),x40502),x40503))),f335(f166(x40501),x40503)))
% 59.73/59.65 [4051]P1(f335(f335(f242(f888(x40511,a879)),f335(f166(x40511),f335(f335(f131(x40511),x40512),x40513))),f335(f166(x40511),x40513)))
% 59.73/59.65 [4056]P1(f335(f335(f242(f888(x40561,a879)),f335(f166(x40561),f170(x40561,x40562,x40563))),f335(f166(x40561),x40562)))
% 59.73/59.65 [4057]P1(f335(f335(f242(f888(x40571,a879)),f335(f166(x40571),f164(x40571,x40572,x40573))),f335(f166(x40571),x40573)))
% 59.73/59.65 [4079]P26(f887(x40791,x40792),f887(x40792,x40791),f335(f268(x40791,x40792,f887(x40792,x40791)),f335(f7(x40792,x40791,f887(x40792,x40791)),f264(x40792,x40791))),x40793)
% 59.73/59.65 [4091]E(f335(f335(f335(f183(f882(x40911),f882(x40911)),f39(a881,x40912,f335(f189(f882(x40911)),x40913))),f161(x40911)),x40913),f335(f335(f335(f183(f882(x40911),f882(x40911)),x40912),f161(x40911)),x40913))
% 59.73/59.65 [4133]E(f335(f68(f882(x41331),f882(x41331),f882(x41331),f335(f335(f183(f882(x41331),f882(x41331)),x41332),f161(x41331))),f335(f335(f183(f882(x41331),f882(x41331)),x41333),f161(x41331))),f335(f335(f183(f882(x41331),f882(x41331)),f335(f335(f75(a881),x41332),x41333)),f161(x41331)))
% 59.73/59.65 [4136]P1(f335(f335(f337(f887(f882(x41361),f882(x41361))),f335(f335(f264(f882(x41361),f882(x41361)),x41362),x41362)),f151(x41361,f310(x41361,x41363))))
% 59.73/59.65 [4285]E(f80(f887(x42851,x42852),f335(f335(f18(f887(x42851,x42852),x42852,a879),f335(f335(f8(x42851,f888(x42852,a879),f887(x42851,x42852)),x42853),f263(x42851,x42852))),f267(x42851,x42852))),f80(f887(x42851,x42852),f335(f268(x42851,x42852,a879),x42853)))
% 59.73/59.65 [4286]E(f85(f887(x42861,x42862),f335(f335(f18(f887(x42861,x42862),x42862,a879),f335(f335(f8(x42861,f888(x42862,a879),f887(x42861,x42862)),x42863),f263(x42861,x42862))),f267(x42861,x42862))),f85(f887(x42861,x42862),f335(f268(x42861,x42862,a879),x42863)))
% 59.73/59.65 [4322]E(f335(f335(f290(f887(a881,x43221),x43221),f328(a881,x43221,a248,x43222)),f335(f335(f18(x43221,x43221,f887(a881,x43221)),f335(f335(f8(a881,f888(x43221,f887(a881,x43221)),x43221),f264(a881,x43221)),x43223)),f5(x43221))),f329(x43221,x43223,x43222))
% 59.73/59.65 [4388]E(f335(f269(x43881,x43881,x43882,x43882,f5(x43881),f5(x43882)),x43883),x43883)
% 59.73/59.65 [4465]E(f335(f135(f882(f882(x44651)),f882(f882(x44651)),f127(f882(x44651)),f107(f882(x44651))),f335(f335(f147(f882(x44651),f882(f882(x44651))),f335(f335(f7(f882(x44651),f882(x44651),f882(f882(x44651))),f335(f335(f8(f888(x44651,f882(x44651)),f888(f882(x44651),f882(f882(x44651))),f882(x44651)),f147(x44651,f882(x44651))),f335(f7(x44651,f882(x44651),f882(x44651)),f144(x44651)))),x44652)),f49(x44651,x44653,x44652))),f49(x44651,f335(a106,x44653),x44652))
% 59.73/59.65 [4525]E(f335(f237(a881,f887(x45251,f883(x45251)),f2(a881),f335(f268(x45251,f883(x45251),a881),f335(f335(f7(x45251,a881,f888(f883(x45251),a881)),f335(f335(f8(f888(f883(x45251),f888(a881,a881)),f888(a881,f888(f883(x45251),a881)),x45251),f7(f883(x45251),a881,a881)),f335(f335(f8(f888(f883(x45251),a881),f888(f883(x45251),f888(a881,a881)),x45251),f335(f8(a881,f888(a881,a881),f883(x45251)),f75(a881))),f335(f335(f7(x45251,f888(f883(x45251),a881),f888(f883(x45251),a881)),f335(f335(f8(f888(a881,a881),f888(f888(f883(x45251),a881),f888(f883(x45251),a881)),x45251),f8(a881,a881,f883(x45251))),f335(f335(f8(a881,f888(a881,a881),x45251),f75(a881)),x45252))),f119(x45251,x45252))))),f73(a881)))),f335(f128(x45251),x45253)),f335(f119(x45251,x45252),x45253))
% 59.73/59.65 [4528]E(f335(f335(f81(a1,x45281),f221(f335(f335(f68(f887(a1,a1),a1,x45281,f267(a1,a1)),f215(x45281)),x45282),f335(f335(f68(f887(a1,a1),a1,x45281,f267(a1,a1)),f215(x45281)),x45283))),f335(f335(f18(a1,a1,x45281),f335(f335(f8(a1,f888(a1,x45281),a1),f204(x45281)),f335(f335(f18(a1,a1,a1),f335(f335(f8(a1,f888(a1,a1),a1),f75(a1)),f335(f335(f8(a1,a1,a1),f335(f76(a1),f335(f335(f68(f887(a1,a1),a1,x45281,f263(a1,a1)),f215(x45281)),x45282))),f335(f335(f7(a1,a1,a1),f30(a1)),f335(f335(f68(f887(a1,a1),a1,x45281,f267(a1,a1)),f215(x45281)),x45282))))),f335(f335(f8(a1,a1,a1),f335(f76(a1),f335(f335(f68(f887(a1,a1),a1,x45281,f263(a1,a1)),f215(x45281)),x45283))),f335(f335(f7(a1,a1,a1),f30(a1)),f335(f335(f68(f887(a1,a1),a1,x45281,f267(a1,a1)),f215(x45281)),x45283)))))),f5(a1))),f232(x45281,x45282,x45283))
% 59.73/59.65 [4552]~E(f335(f335(f144(x45521),x45522),x45523),x45523)
% 59.73/59.65 [4553]~E(f335(f335(f144(x45531),x45532),x45533),x45533)
% 59.73/59.65 [4555]~E(f335(f335(f144(x45551),x45552),x45553),f107(x45551))
% 59.73/59.65 [4556]~E(f335(f335(f144(x45561),x45562),x45563),f107(x45561))
% 59.73/59.65 [4561]~E(f335(f335(f312(x45611),x45612),x45613),f188(f888(x45611,a879)))
% 59.73/59.65 [4562]~E(f335(f335(f312(x45621),x45622),x45623),f188(f888(x45621,a879)))
% 59.73/59.65 [4585]~E(f335(f313(x45851,f888(x45851,a879),x45852),x45853),f335(f311(x45851),x45853))
% 59.73/59.65 [3391]E(f335(f335(f152(x33911,f107(x33911)),x33912),x33913),f107(x33911))
% 59.73/59.65 [3392]E(f335(f335(f152(x33921,f107(x33921)),x33922),x33923),f107(x33921))
% 59.73/59.65 [3393]E(f335(f134(x33931),f335(f335(f144(x33931),x33932),x33933)),x33932)
% 59.73/59.65 [3394]E(f335(f165(x33941),f335(f335(f144(x33941),x33942),x33943)),x33943)
% 59.73/59.65 [3438]E(f335(f335(f131(x34381),f73(a881)),f335(f335(f144(x34381),x34382),x34383)),x34383)
% 59.73/59.65 [3470]E(f108(x34701,f335(f335(f131(x34701),x34702),x34703)),f335(f335(f131(x34701),x34702),f108(x34701,x34703)))
% 59.73/59.65 [3471]E(f108(x34711,f335(f335(f131(x34711),x34712),x34713)),f335(f335(f131(x34711),x34712),f108(x34711,x34713)))
% 59.73/59.65 [3473]E(f335(f335(f152(x34731,x34732),x34733),f335(f335(f158(x34731),x34732),x34733)),x34732)
% 59.73/59.65 [3496]E(f335(f335(f312(x34961),x34962),f335(f335(f312(x34961),x34962),x34963)),f335(f335(f312(x34961),x34962),x34963))
% 59.73/59.65 [3506]E(f335(f335(f179(x35061,x35062),f107(f887(x35061,x35062))),x35063),f200(x35062))
% 59.73/59.65 [3507]E(f335(f335(f179(x35071,x35072),f107(f887(x35071,x35072))),x35073),f200(x35072))
% 59.73/59.65 [3510]E(f335(f335(f312(x35101),x35102),f335(f166(x35101),x35103)),f335(f166(x35101),f335(f335(f144(x35101),x35102),x35103)))
% 59.73/59.65 [3511]E(f335(f335(f131(x35111),x35112),f335(f165(x35111),x35113)),f335(f165(x35111),f335(f335(f131(x35111),x35112),x35113)))
% 59.73/59.65 [3512]E(f335(f335(f131(x35121),x35122),f335(f165(x35121),x35123)),f335(f165(x35121),f335(f335(f131(x35121),x35122),x35123)))
% 59.73/59.65 [3523]E(f335(f335(f169(x35231),f73(a881)),f335(f335(f144(x35231),x35232),x35233)),f335(f335(f144(x35231),x35232),f107(x35231)))
% 59.73/59.65 [3569]E(f335(f58(x35691,x35692),f335(f335(f312(x35691),x35693),f188(f888(x35691,a879)))),x35693)
% 59.73/59.65 [3611]E(f335(f335(f75(a881),x36111),f335(f335(f75(a881),x36112),x36113)),f335(f335(f75(a881),x36112),f335(f335(f75(a881),x36111),x36113)))
% 59.73/59.65 [3612]E(f335(f335(f75(a1),x36121),f335(f335(f75(a1),x36122),x36123)),f335(f335(f75(a1),x36122),f335(f335(f75(a1),x36121),x36123)))
% 59.73/59.65 [3617]E(f335(f335(f266(x36171,x36172),f188(f888(x36171,a879))),x36173),f188(f888(f887(x36171,x36172),a879)))
% 59.73/59.65 [3642]E(f335(f335(f104(f888(x36421,a879)),x36422),x36423),f335(f335(f104(f888(x36421,a879)),x36423),x36422))
% 59.73/59.65 [3643]E(f335(f335(f95(f888(x36431,a879)),x36432),x36433),f335(f335(f95(f888(x36431,a879)),x36433),x36432))
% 59.73/59.65 [3645]E(f335(f335(f127(x36451),x36452),f335(f335(f144(x36451),x36453),f107(x36451))),f335(f161(x36451),f335(f335(f144(x36451),x36453),x36452)))
% 59.73/59.65 [3646]E(f335(f335(f127(x36461),f335(f162(x36461),x36462)),f335(f162(x36461),x36463)),f335(f162(x36461),f335(f335(f127(x36461),x36463),x36462)))
% 59.73/59.65 [3658]E(f335(f165(x36581),f335(f335(f169(x36581),f335(a106,x36582)),x36583)),f335(f335(f169(x36581),x36582),f335(f165(x36581),x36583)))
% 59.73/59.65 [3666]P1(f335(f335(f337(x36661),x36662),f335(f335(f312(x36661),x36662),x36663)))
% 59.73/59.65 [3670]E(f335(f335(f34(x36701,f888(x36702,a879)),f188(f888(x36701,a879))),x36703),f252(f888(x36702,a879)))
% 59.73/59.65 [3673]E(f335(f288(x36731,x36731,f261(x36731,x36732)),x36733),f335(f335(f95(f888(x36731,a879)),x36732),x36733))
% 59.73/59.65 [3688]E(f335(f189(f882(x36881)),f335(f335(f144(x36881),x36882),x36883)),f335(f335(f75(a881),f335(f189(f882(x36881)),x36883)),f335(a106,f2(a881))))
% 59.73/59.65 [3692]E(f137(x36921,f335(f335(f127(x36921),x36922),f335(f335(f144(x36921),x36923),f107(x36921)))),x36923)
% 59.73/59.65 [3693]E(f108(x36931,f335(f335(f127(x36931),x36932),f335(f335(f144(x36931),x36933),f107(x36931)))),x36932)
% 59.73/59.65 [3698]E(f335(f335(f127(x36981),f335(f335(f169(x36981),x36982),x36983)),f335(f335(f131(x36981),x36982),x36983)),x36983)
% 59.73/59.65 [3707]E(f335(f335(f23(a881),f335(f335(f75(a881),x37071),x37072)),f335(f335(f75(a881),x37073),x37072)),f335(f335(f23(a881),x37071),x37073))
% 59.73/59.65 [3708]E(f335(f335(f23(a881),f335(f335(f75(a881),x37081),x37082)),f335(f335(f75(a881),x37081),x37083)),f335(f335(f23(a881),x37082),x37083))
% 59.73/59.65 [3716]E(f335(f335(f127(x37161),f335(f162(x37161),x37162)),f335(f335(f144(x37161),x37163),f107(x37161))),f335(f162(x37161),f335(f335(f144(x37161),x37163),x37162)))
% 59.73/59.65 [3718]E(f335(f335(f75(a881),f335(f189(f882(x37181)),x37182)),f335(f189(f882(x37181)),x37183)),f335(f189(f882(x37181)),f335(f335(f127(x37181),x37182),x37183)))
% 59.73/59.65 [3721]E(f335(f335(f75(a881),f335(f189(f882(x37211)),x37212)),f335(f189(f882(x37211)),x37213)),f335(f189(f882(x37211)),f167(x37211,x37212,x37213)))
% 59.73/59.65 [3728]E(f335(f335(f104(f888(x37281,a879)),f335(f166(x37281),x37282)),f335(f166(x37281),x37283)),f335(f166(x37281),f335(f335(f127(x37281),x37282),x37283)))
% 59.73/59.65 [3729]E(f39(a881,f335(f335(f76(a881),x37291),x37292),f335(f335(f76(a881),x37291),x37293)),f335(f335(f76(a881),x37291),f39(a881,x37292,x37293)))
% 59.73/59.65 [3742]E(f335(f335(f169(x37421),f335(f335(f23(a881),x37422),f73(a881))),f335(f165(x37421),x37423)),f335(f165(x37421),f335(f335(f169(x37421),x37422),x37423)))
% 59.73/59.65 [3747]E(f335(f335(f95(f888(x37471,a879)),x37472),f335(f74(f888(x37471,a879)),x37473)),f335(f335(f23(f888(x37471,a879)),x37472),x37473))
% 59.73/59.65 [3748]E(f335(f335(f23(f888(x37481,a879)),x37482),f335(f74(f888(x37481,a879)),x37483)),f335(f335(f95(f888(x37481,a879)),x37482),x37483))
% 59.73/59.65 [3770]E(f335(f335(f266(x37701,x37702),x37703),f335(f16(f888(x37702,a879),x37701),f188(f888(x37702,a879)))),f188(f888(f887(x37701,x37702),a879)))
% 59.73/59.65 [3772]E(f335(f335(f23(a881),f335(f335(f76(a881),x37721),x37722)),f335(f335(f76(a881),x37721),x37723)),f335(f335(f76(a881),x37721),f335(f335(f23(a881),x37722),x37723)))
% 59.73/59.65 [3773]E(f335(f335(f75(a881),f335(f335(f76(a881),x37731),x37732)),f335(f335(f76(a881),x37731),x37733)),f335(f335(f76(a881),x37731),f335(f335(f75(a881),x37732),x37733)))
% 59.73/59.65 [3774]E(f335(f335(f23(a1),f335(f335(f76(a1),x37741),x37742)),f335(f335(f76(a1),x37741),x37743)),f335(f335(f76(a1),x37741),f335(f335(f23(a1),x37742),x37743)))
% 59.73/59.65 [3775]E(f335(f335(f75(a1),f335(f335(f76(a1),x37751),x37752)),f335(f335(f76(a1),x37751),x37753)),f335(f335(f76(a1),x37751),f335(f335(f75(a1),x37752),x37753)))
% 59.73/59.65 [3776]E(f335(f335(f76(a1),f335(f335(f254(a1),x37761),x37762)),f335(f335(f254(a1),x37761),x37763)),f335(f335(f254(a1),x37761),f335(f335(f75(a881),x37762),x37763)))
% 59.73/59.65 [3791]E(f335(f335(f33(x37911,f888(x37912,a879)),x37913),f335(f16(f888(x37912,a879),x37911),f188(f888(x37912,a879)))),f188(f888(x37912,a879)))
% 59.73/59.65 [3793]E(f39(a881,f335(f335(f76(a881),x37931),x37932),f335(f335(f76(a881),x37933),x37932)),f335(f335(f76(a881),f39(a881,x37931,x37933)),x37932))
% 59.73/59.65 [3796]E(f39(a1,f335(f335(f76(a1),x37961),f39(a1,x37962,x37963)),x37963),f39(a1,f335(f335(f76(a1),x37961),x37962),x37963))
% 59.73/59.65 [3797]E(f39(a1,f335(f335(f23(a1),x37971),f39(a1,x37972,x37973)),x37973),f39(a1,f335(f335(f23(a1),x37971),x37972),x37973))
% 59.73/59.65 [3798]E(f39(a1,f335(f335(f76(a1),x37981),f39(a1,x37982,x37983)),x37983),f39(a1,f335(f335(f76(a1),x37981),x37982),x37983))
% 59.73/59.65 [3799]P1(f335(f335(f242(f888(x37991,a879)),x37992),f335(f335(f312(x37991),x37993),x37992)))
% 59.73/59.65 [3802]E(f335(f313(f887(x38021,x38022),x38021,f263(x38021,x38022)),f335(f166(f887(x38021,x38022)),x38023)),f177(x38021,x38022,f335(f179(x38021,x38022),x38023)))
% 59.73/59.65 [3855]P1(f335(f56(x38551),f177(x38551,x38552,f335(f179(x38551,x38552),x38553))))
% 59.73/59.65 [3878]E(f335(f335(f34(f888(x38781,a879),f888(x38781,a879)),x38782),f335(f104(f888(x38781,a879)),x38783)),f335(f335(f104(f888(x38781,a879)),x38783),f32(f888(x38781,a879),x38782)))
% 59.73/59.65 [3879]E(f335(f335(f33(f888(x38791,a879),f888(x38791,a879)),x38792),f335(f95(f888(x38791,a879)),x38793)),f335(f335(f95(f888(x38791,a879)),x38793),f31(f888(x38791,a879),x38792)))
% 59.73/59.65 [3890]E(f335(f166(x38901),f335(f335(f335(f183(f882(x38901),f882(x38901)),x38902),f161(x38901)),x38903)),f335(f166(x38901),x38903))
% 59.73/59.65 [3894]E(f335(f335(f169(x38941),f335(f189(f882(x38941)),f171(x38941,x38942,x38943))),x38943),f171(x38941,x38942,x38943))
% 59.73/59.65 [3895]E(f177(x38951,x38952,f335(f335(f8(x38952,f885(x38952),x38951),f235(x38952)),x38953)),f252(f888(x38951,a879)))
% 59.73/59.65 [3899]E(f335(f189(f882(x38991)),f335(f335(f335(f183(f882(x38991),f882(x38991)),x38992),f161(x38991)),x38993)),f335(f189(f882(x38991)),x38993))
% 59.73/59.65 [3902]E(f335(f335(f268(x39021,x39022,x39022),f335(f16(f888(x39022,x39022),x39021),f5(x39022))),x39023),f335(f267(x39021,x39022),x39023))
% 59.73/59.65 [3908]E(f39(a1,f335(f335(f23(a1),f39(a1,x39081,x39082)),x39083),x39082),f39(a1,f335(f335(f23(a1),x39081),x39083),x39082))
% 59.73/59.65 [3909]E(f39(a1,f335(f335(f254(a1),f39(a1,x39091,x39092)),x39093),x39092),f39(a1,f335(f335(f254(a1),x39091),x39093),x39092))
% 59.73/59.65 [3912]E(f335(f335(f33(f888(f887(x39121,x39122),a879),f888(x39122,a879)),x39123),f260(x39121,x39122)),f335(f260(x39121,x39122),f31(f888(f887(x39121,x39122),a879),x39123)))
% 59.73/59.65 [3913]E(f335(f335(f33(f888(f887(x39131,x39132),a879),f888(x39131,a879)),x39133),f262(x39131,x39132)),f335(f262(x39131,x39132),f31(f888(f887(x39131,x39132),a879),x39133)))
% 59.73/59.65 [3940]E(f335(f68(x39401,x39401,x39401,x39402),f335(f335(f183(x39401,x39401),x39403),x39402)),f335(f335(f183(x39401,x39401),f335(a106,x39403)),x39402))
% 59.73/59.65 [3950]E(f237(f885(x39501),x39502,f200(x39501),f335(f335(f8(x39501,f885(x39501),x39502),f235(x39501)),x39503)),f335(f201(x39502,x39501),x39503))
% 59.73/59.65 [3957]E(f335(f335(f131(x39571),f335(f335(f23(a881),f335(f189(f882(x39571)),x39572)),x39573)),f335(f162(x39571),x39572)),f335(f162(x39571),f335(f335(f169(x39571),x39573),x39572)))
% 59.73/59.65 [3958]E(f335(f335(f169(x39581),f335(f335(f23(a881),f335(f189(f882(x39581)),x39582)),x39583)),f335(f162(x39581),x39582)),f335(f162(x39581),f335(f335(f131(x39581),x39583),x39582)))
% 59.73/59.65 [3961]E(f335(f335(f75(a881),f335(f159(a881),f335(f335(f147(x39611,a881),x39612),x39613))),f335(f189(f882(x39611)),x39613)),f148(x39611,x39612,x39613))
% 59.73/59.65 [3973]E(f335(f335(f335(f183(f882(x39731),f882(x39731)),x39732),f161(x39731)),f335(f161(x39731),x39733)),f335(f161(x39731),f335(f335(f335(f183(f882(x39731),f882(x39731)),x39732),f161(x39731)),x39733)))
% 59.73/59.65 [3981]E(f335(f161(x39811),f335(f335(f335(f183(f882(x39811),f882(x39811)),x39812),f161(x39811)),x39813)),f335(f335(f335(f183(f882(x39811),f882(x39811)),f335(a106,x39812)),f161(x39811)),x39813))
% 59.73/59.65 [3996]P1(f335(f335(f242(a881),f335(f189(f882(x39961)),f335(f129(x39961,x39962),x39963))),f335(f189(f882(x39961)),x39963)))
% 59.73/59.65 [4014]E(f335(f335(f104(f888(f888(x40141,a879),a879)),f335(f311(x40141),x40142)),f335(f313(f888(x40141,a879),f888(x40141,a879),f335(f312(x40141),x40143)),f335(f311(x40141),x40142))),f335(f311(x40141),f335(f335(f312(x40141),x40143),x40142)))
% 59.73/59.65 [4047]P1(f335(f335(f242(a881),f335(f189(f882(x40471)),f171(x40471,x40472,x40473))),f335(f189(f882(x40471)),x40473)))
% 59.73/59.65 [4055]E(f335(f262(x40551,x40552),f335(f249(f887(x40551,x40552)),f335(f268(x40551,x40552,a879),x40553))),f335(f249(x40551),f335(f335(f8(f888(x40552,a879),a879,x40551),f82(x40552)),x40553)))
% 59.73/59.65 [4067]E(f335(f313(a881,a881,f335(f335(f7(a881,a881,a881),f75(a881)),x40671)),f305(a881,x40672,x40673)),f305(a881,f335(f335(f75(a881),x40672),x40671),f335(f335(f75(a881),x40673),x40671)))
% 59.73/59.65 [4069]P1(f335(f56(f885(x40691)),f335(f313(x40692,f885(x40691),f335(f179(x40692,x40691),x40693)),f252(f888(x40692,a879)))))
% 59.73/59.65 [4082]E(f335(f313(a881,a881,f335(f335(f7(a881,a881,a881),f75(a881)),x40821)),f335(f304(a881,x40822),x40823)),f335(f304(a881,f335(f335(f75(a881),x40822),x40821)),f335(f335(f75(a881),x40823),x40821)))
% 59.73/59.65 [4100]E(f335(f335(f175(x41001,x41002),f335(f335(f147(f887(x41001,x41002),x41001),f263(x41001,x41002)),x41003)),f335(f335(f147(f887(x41001,x41002),x41002),f267(x41001,x41002)),x41003)),x41003)
% 59.73/59.65 [4105]E(f335(f335(f75(a881),f335(f335(f76(a881),x41051),f39(a881,f335(f335(f30(a881),x41052),x41051),x41053))),f39(a881,x41052,x41051)),f39(a881,x41052,f335(f335(f76(a881),x41051),x41053)))
% 59.73/59.65 [4120]E(f335(f335(f127(x41201),x41202),f335(f135(f882(x41201),f882(x41201),f127(x41201),f107(x41201)),x41203)),f335(f135(f882(x41201),f882(x41201),f127(x41201),x41202),x41203))
% 59.73/59.65 [4140]P1(f335(f335(f337(f887(x41401,x41401)),f335(f335(f264(x41401,x41401),x41402),x41402)),f335(f335(f183(f887(x41401,x41401),a879),f2(a881)),x41403)))
% 59.73/59.65 [4146]E(f335(f249(x41461),f335(f335(f8(f888(x41462,a879),a879,x41461),f82(x41462)),f335(f7(x41462,x41461,a879),x41463))),f335(f260(x41462,x41461),f335(f249(f887(x41462,x41461)),f335(f268(x41462,x41461,a879),x41463))))
% 59.73/59.65 [4164]E(f335(f335(f104(f888(x41641,a879)),f335(f335(f33(a881,f888(x41641,a879)),f305(a881,f73(a881),x41642)),x41643)),f335(x41643,f2(a881))),f335(f335(f33(a881,f888(x41641,a879)),f335(f303(a881),x41642)),x41643))
% 59.73/59.65 [4179]E(f335(f135(f882(x41791),f882(x41791),f127(x41791),f107(x41791)),f335(f335(f147(f882(x41791),f882(x41791)),f129(x41791,x41792)),x41793)),f335(f129(x41791,x41792),f335(f135(f882(x41791),f882(x41791),f127(x41791),f107(x41791)),x41793)))
% 59.73/59.65 [4184]E(f335(f267(f882(x41841),f882(x41841)),f160(x41841,x41842,x41843)),f335(f129(x41841,f335(f68(a879,a879,x41841,a330),x41842)),x41843))
% 59.73/59.65 [4235]E(f335(f335(f75(a1),f335(f335(f75(a1),f335(f335(f76(a1),x42351),f335(f335(f30(a1),x42352),x42351))),f39(a1,x42352,x42351))),x42353),f335(f335(f75(a1),x42352),x42353))
% 59.73/59.65 [4274]E(f335(f335(f75(a1),f335(f335(f75(a1),f335(f335(f76(a1),f335(f335(f30(a1),x42741),x42742)),x42742)),f39(a1,x42741,x42742))),x42743),f335(f335(f75(a1),x42741),x42743))
% 59.73/59.65 [4303]E(f80(f887(x43031,x43032),f335(f268(x43031,x43032,a879),f335(f335(f8(f888(x43032,f887(x43031,x43032)),f888(x43032,a879),x43031),f335(f8(f887(x43031,x43032),a879,x43032),x43033)),f264(x43031,x43032)))),f80(f887(x43031,x43032),x43033))
% 59.73/59.65 [4304]E(f85(f887(x43041,x43042),f335(f268(x43041,x43042,a879),f335(f335(f8(f888(x43042,f887(x43041,x43042)),f888(x43042,a879),x43041),f335(f8(f887(x43041,x43042),a879,x43042),x43043)),f264(x43041,x43042)))),f85(f887(x43041,x43042),x43043))
% 59.73/59.65 [4333]P1(f335(f335(f242(f888(x43331,a879)),f31(f888(x43331,a879),f335(f335(f95(f888(f888(x43331,a879),a879)),x43332),x43333))),f335(f335(f95(f888(x43331,a879)),f31(f888(x43331,a879),x43332)),f31(f888(x43331,a879),x43333))))
% 59.73/59.65 [4334]E(f335(f162(x43341),f335(f335(f335(f183(f882(x43341),f882(x43341)),f335(f335(f23(a881),f335(f189(f882(x43341)),x43342)),f39(a881,x43343,f335(f189(f882(x43341)),x43342)))),f161(x43341)),x43342)),f335(f335(f335(f183(f882(x43341),f882(x43341)),x43343),f161(x43341)),f335(f162(x43341),x43342)))
% 59.73/59.65 [4348]E(f335(f249(x43481),f335(f335(f8(a879,a879,x43481),a330),f335(f335(f7(x43481,f885(x43482),a879),f335(f335(f8(f885(x43482),f888(f885(x43482),a879),x43481),a332),x43483)),f200(x43482)))),f177(x43481,x43482,x43483))
% 59.73/59.65 [4373]P1(f335(f335(f242(a881),f335(f189(f882(x43731)),f335(f335(f131(x43731),f335(f189(f882(x43731)),f171(x43731,x43732,x43733))),x43733))),f335(f189(f882(x43731)),x43733)))
% 59.73/59.65 [4416]E(f335(f249(x44161),f335(f335(f8(f888(x44162,a879),a879,x44161),f82(x44162)),f335(f335(f8(f885(x44161),f888(x44162,a879),x44161),f335(f7(x44162,f885(x44161),a879),f335(f335(f8(f885(x44161),f888(f885(x44161),a879),x44162),a332),x44163))),f235(x44161)))),f178(x44162,x44161,x44163))
% 59.73/59.65 [4599]~P1(f335(f57(x45991,x45992,f188(f888(x45991,a879))),x45993))
% 59.73/59.65 [4606]~P1(f335(f335(f337(f887(x46061,x46061)),f335(f335(f264(x46061,x46061),x46062),x46063)),f146(x46061,f107(f888(x46061,a881)))))
% 59.73/59.65 [3659]E(f335(f189(f882(x36591)),f335(f335(f169(x36591),x36592),x36593)),f335(f335(f240(a881),f335(f189(f882(x36591)),x36593)),x36592))
% 59.73/59.65 [3660]E(f335(f189(f882(x36601)),f335(f335(f131(x36601),x36602),x36603)),f335(f335(f23(a881),f335(f189(f882(x36601)),x36603)),x36602))
% 59.73/59.65 [3687]E(f335(f189(f882(f882(x36871))),f49(x36871,x36872,x36873)),f335(f335(f254(a881),f335(f189(f882(x36871)),x36873)),x36872))
% 59.73/59.65 [3700]E(f335(f335(f30(a881),f335(f335(f30(a881),x37001),x37002)),x37003),f335(f335(f30(a881),x37001),f335(f335(f76(a881),x37002),x37003)))
% 59.73/59.65 [3701]E(f335(f335(f23(a881),f335(f335(f23(a881),x37011),x37012)),x37013),f335(f335(f23(a881),x37011),f335(f335(f75(a881),x37012),x37013)))
% 59.73/59.65 [3702]E(f335(f335(f76(a881),f335(f335(f76(a881),x37021),x37022)),x37023),f335(f335(f76(a881),x37021),f335(f335(f76(a881),x37022),x37023)))
% 59.73/59.65 [3703]E(f335(f335(f76(a1),f335(f335(f76(a1),x37031),x37032)),x37033),f335(f335(f76(a1),x37031),f335(f335(f76(a1),x37032),x37033)))
% 59.73/59.65 [3704]E(f335(f335(f75(a881),f335(f335(f75(a881),x37041),x37042)),x37043),f335(f335(f75(a881),x37041),f335(f335(f75(a881),x37042),x37043)))
% 59.73/59.65 [3705]E(f335(f335(f75(a1),f335(f335(f75(a1),x37051),x37052)),x37053),f335(f335(f75(a1),x37051),f335(f335(f75(a1),x37052),x37053)))
% 59.73/59.65 [3706]E(f335(f335(f254(a1),f335(f335(f254(a1),x37061),x37062)),x37063),f335(f335(f254(a1),x37061),f335(f335(f76(a881),x37062),x37063)))
% 59.73/59.65 [3727]E(f155(x37271,f335(f335(f144(f888(x37271,a879)),x37272),x37273)),f168(x37271,x37272,f155(x37271,x37273)))
% 59.73/59.65 [3771]E(f335(f335(f23(a881),f335(f335(f23(a881),x37711),x37712)),x37713),f335(f335(f23(a881),f335(f335(f23(a881),x37711),x37713)),x37712))
% 59.73/59.65 [3777]E(f335(f235(f887(x37771,f883(x37771))),f335(f335(f264(x37771,f883(x37771)),x37772),x37773)),f335(f128(x37771),f120(x37771,x37772,x37773)))
% 59.73/59.65 [3780]E(f335(f335(f95(f888(x37801,a879)),x37802),f335(f335(f23(f888(x37801,a879)),x37803),x37802)),f188(f888(x37801,a879)))
% 59.73/59.65 [3784]E(f335(f335(f147(a881,x37841),f335(f16(x37841,a881),x37842)),f132(a881,f335(f304(a881,f2(a881)),x37843))),f163(x37841,x37843,x37842))
% 59.73/59.65 [3824]E(f32(f888(x38241,a879),f335(f335(f312(f888(x38241,a879)),x38242),x38243)),f335(f335(f95(f888(x38241,a879)),x38242),f32(f888(x38241,a879),x38243)))
% 59.73/59.65 [3825]E(f31(f888(x38251,a879),f335(f335(f312(f888(x38251,a879)),x38252),x38253)),f335(f335(f104(f888(x38251,a879)),x38252),f31(f888(x38251,a879),x38253)))
% 59.73/59.65 [3827]E(f163(x38271,f335(f189(f882(x38271)),f335(f129(x38271,f335(a332,x38272)),x38273)),x38272),f335(f129(x38271,f335(a332,x38272)),x38273))
% 59.73/59.65 [3829]E(f335(f335(f23(a881),f335(f335(f76(a881),x38291),x38292)),f335(f335(f76(a881),x38293),x38292)),f335(f335(f76(a881),f335(f335(f23(a881),x38291),x38293)),x38292))
% 59.73/59.65 [3830]E(f335(f335(f75(a881),f335(f335(f76(a881),x38301),x38302)),f335(f335(f76(a881),x38303),x38302)),f335(f335(f76(a881),f335(f335(f75(a881),x38301),x38303)),x38302))
% 59.73/59.65 [3831]E(f335(f335(f23(a1),f335(f335(f76(a1),x38311),x38312)),f335(f335(f76(a1),x38313),x38312)),f335(f335(f76(a1),f335(f335(f23(a1),x38311),x38313)),x38312))
% 59.73/59.65 [3832]E(f335(f335(f75(a1),f335(f335(f76(a1),x38321),x38322)),f335(f335(f76(a1),x38323),x38322)),f335(f335(f76(a1),f335(f335(f75(a1),x38321),x38323)),x38322))
% 59.73/59.65 [3834]E(f335(f335(f240(a881),f335(f335(f23(a881),x38341),x38342)),f335(f335(f23(a881),x38343),x38342)),f335(f335(f23(a881),f335(f335(f240(a881),x38341),x38343)),x38342))
% 59.73/59.65 [3856]E(f335(f335(f95(f888(f882(x38561),a879)),f153(x38561,x38562)),f153(x38561,x38563)),f153(x38561,f335(f335(f95(f888(x38561,a879)),x38562),x38563)))
% 59.73/59.65 [3858]E(f335(f335(f104(f888(x38581,a879)),x38582),f335(f335(f104(f888(x38581,a879)),x38582),x38583)),f335(f335(f104(f888(x38581,a879)),x38582),x38583))
% 59.73/59.65 [3859]E(f335(f335(f104(f888(x38591,a879)),x38592),f335(f335(f23(f888(x38591,a879)),x38593),x38592)),f335(f335(f104(f888(x38591,a879)),x38592),x38593))
% 59.73/59.65 [3860]E(f335(f335(f95(f888(x38601,a879)),x38602),f335(f335(f95(f888(x38601,a879)),x38602),x38603)),f335(f335(f95(f888(x38601,a879)),x38602),x38603))
% 59.73/59.65 [3872]E(f335(f335(f291(x38721,x38722,x38722),x38723),f310(x38722,f188(f888(f887(x38722,x38722),a879)))),x38723)
% 59.73/59.65 [3875]E(f335(f335(f104(f888(x38751,a879)),f335(f335(f312(x38751),x38752),f188(f888(x38751,a879)))),x38753),f335(f335(f312(x38751),x38752),x38753))
% 59.73/59.65 [3893]E(f335(f335(f23(a881),f335(f335(f23(a881),f335(a106,x38931)),x38932)),f335(a106,x38933)),f335(f335(f23(a881),f335(f335(f23(a881),x38931),x38932)),x38933))
% 59.73/59.65 [3922]E(f335(f335(f95(f888(f888(x39221,a879),a879)),f335(f311(x39221),x39222)),f335(f311(x39221),x39223)),f335(f311(x39221),f335(f335(f95(f888(x39221,a879)),x39222),x39223)))
% 59.73/59.65 [3926]E(f335(f335(f104(f888(x39261,a879)),f335(f74(f888(x39261,a879)),x39262)),x39263),f335(f74(f888(x39261,a879)),f335(f335(f23(f888(x39261,a879)),x39262),x39263)))
% 59.73/59.65 [3937]E(f335(f335(f312(x39371),x39372),f335(f335(f23(f888(x39371,a879)),x39373),f335(f335(f312(x39371),x39372),f188(f888(x39371,a879))))),f335(f335(f312(x39371),x39372),x39373))
% 59.73/59.65 [3947]P1(f335(f335(f242(f888(x39471,a879)),x39472),f335(f335(f104(f888(x39471,a879)),x39473),x39472)))
% 59.73/59.65 [3948]P1(f335(f335(f242(f888(x39481,a879)),x39482),f335(f335(f104(f888(x39481,a879)),x39482),x39483)))
% 59.73/59.65 [3951]E(f335(f335(f95(f888(x39511,a879)),f335(f74(f888(x39511,a879)),x39512)),f335(f74(f888(x39511,a879)),x39513)),f335(f74(f888(x39511,a879)),f335(f335(f104(f888(x39511,a879)),x39512),x39513)))
% 59.73/59.65 [3952]E(f335(f335(f104(f888(x39521,a879)),f335(f74(f888(x39521,a879)),x39522)),f335(f74(f888(x39521,a879)),x39523)),f335(f74(f888(x39521,a879)),f335(f335(f95(f888(x39521,a879)),x39522),x39523)))
% 59.73/59.65 [3966]P1(f335(f335(f242(f888(x39661,a879)),f335(f166(x39661),x39662)),f335(f166(x39661),f335(f335(f144(x39661),x39663),x39662))))
% 59.73/59.65 [3978]E(f335(f335(f104(f888(x39781,a879)),f335(f335(f23(f888(x39781,a879)),x39782),x39783)),f335(f335(f95(f888(x39781,a879)),x39782),x39783)),x39782)
% 59.73/59.65 [4034]E(f335(f335(f9(x40341,a1),f335(f335(f8(a881,a1,x40341),f94(a1)),x40342)),x40343),f335(f94(a1),f335(f335(f9(x40341,a881),x40342),x40343)))
% 59.73/59.65 [4035]E(f335(f335(f6(x40351,a1),f335(f335(f8(a881,a1,x40351),f94(a1)),x40352)),x40353),f335(f94(a1),f335(f335(f6(x40351,a881),x40352),x40353)))
% 59.73/59.65 [4084]E(f335(f335(f127(x40841),f171(x40841,x40842,x40843)),f335(f335(f131(x40841),f335(f189(f882(x40841)),f171(x40841,x40842,x40843))),x40843)),x40843)
% 59.73/59.65 [4089]E(f335(f74(f888(f887(x40891,x40892),a879)),f335(f335(f266(x40891,x40892),x40893),f335(f16(f888(x40892,a879),x40891),f252(f888(x40892,a879))))),f335(f335(f266(x40891,x40892),f335(f74(f888(x40891,a879)),x40893)),f335(f16(f888(x40892,a879),x40891),f252(f888(x40892,a879)))))
% 59.73/59.65 [4090]E(f335(f74(f888(f887(x40901,x40902),a879)),f335(f335(f266(x40901,x40902),f252(f888(x40901,a879))),f335(f16(f888(x40902,a879),x40901),x40903))),f335(f335(f266(x40901,x40902),f252(f888(x40901,a879))),f335(f16(f888(x40902,a879),x40901),f335(f74(f888(x40902,a879)),x40903))))
% 59.73/59.65 [4114]E(f110(f885(x41141),f335(f237(f883(f885(x41141)),f883(f885(x41141)),f118(x41141),f5(f883(f885(x41141)))),x41142),f115(x41141,x41143)),f115(x41141,f120(f885(f883(f885(x41141))),x41142,x41143)))
% 59.73/59.65 [4141]E(f335(f335(f33(f888(x41411,a879),f888(x41411,a879)),x41412),f335(f335(f7(f888(x41411,a879),f888(x41411,a879),f888(x41411,a879)),f95(f888(x41411,a879))),x41413)),f335(f335(f95(f888(x41411,a879)),f31(f888(x41411,a879),x41412)),x41413))
% 59.73/59.65 [4148]E(f335(f135(f882(x41481),f882(x41481),f127(x41481),f107(x41481)),f335(f335(f144(f882(x41481)),x41482),x41483)),f335(f335(f127(x41481),x41482),f335(f135(f882(x41481),f882(x41481),f127(x41481),f107(x41481)),x41483)))
% 59.73/59.65 [4170]E(f335(f335(f312(f888(x41701,a879)),f335(f288(x41701,x41701,x41702),f335(f335(f312(x41701),x41703),f188(f888(x41701,a879))))),f188(f888(f888(x41701,a879),a879))),f335(f335(f55(x41701),f335(f335(f312(x41701),x41703),f188(f888(x41701,a879)))),x41702))
% 59.73/59.65 [4180]E(f335(f335(f75(a881),f335(f335(f76(a881),x41801),f335(f335(f30(a881),x41802),x41803))),f335(f335(f30(a881),f335(f335(f76(a881),x41801),f39(a881,x41802,x41803))),x41803)),f335(f335(f30(a881),f335(f335(f76(a881),x41801),x41802)),x41803))
% 59.73/59.65 [4181]E(f335(f335(f75(a1),f335(f335(f76(a1),x41811),f335(f335(f30(a1),x41812),x41813))),f335(f335(f30(a1),f335(f335(f76(a1),x41811),f39(a1,x41812,x41813))),x41813)),f335(f335(f30(a1),f335(f335(f76(a1),x41811),x41812)),x41813))
% 59.73/59.65 [4219]E(f335(f335(f23(f888(x42191,a879)),f335(f166(x42191),x42192)),f335(f335(f312(x42191),x42193),f188(f888(x42191,a879)))),f335(f166(x42191),f335(f129(x42191,f335(f335(f8(a879,a879,x42191),a330),f335(a332,x42193))),x42192)))
% 59.73/59.65 [4271]E(f335(f335(f127(x42711),f335(f135(f882(x42711),f882(x42711),f127(x42711),f107(x42711)),x42712)),f335(f135(f882(x42711),f882(x42711),f127(x42711),f107(x42711)),x42713)),f335(f135(f882(x42711),f882(x42711),f127(x42711),f107(x42711)),f335(f335(f127(f882(x42711)),x42712),x42713)))
% 59.73/59.65 [4276]E(f335(f335(f264(f882(x42761),f882(x42761)),f335(f129(x42761,x42762),x42763)),f335(f129(x42761,f335(f68(a879,a879,x42761,a330),x42762)),x42763)),f160(x42761,x42762,x42763))
% 59.73/59.65 [4279]E(f335(f335(f75(a881),f335(f335(f75(a881),f335(f335(f30(a881),x42791),x42792)),f335(f335(f30(a881),x42793),x42792))),f335(f335(f30(a881),f335(f335(f75(a881),f39(a881,x42791,x42792)),f39(a881,x42793,x42792))),x42792)),f335(f335(f30(a881),f335(f335(f75(a881),x42791),x42793)),x42792))
% 59.73/59.65 [4280]E(f335(f335(f75(a1),f335(f335(f75(a1),f335(f335(f30(a1),x42801),x42802)),f335(f335(f30(a1),x42803),x42802))),f335(f335(f30(a1),f335(f335(f75(a1),f39(a1,x42801,x42802)),f39(a1,x42803,x42802))),x42802)),f335(f335(f30(a1),f335(f335(f75(a1),x42801),x42803)),x42802))
% 59.73/59.65 [4337]E(f335(f335(f95(f888(f882(x43371),a879)),f335(f335(f7(f882(x43371),f888(f882(x43371),a879),a879),f337(f882(x43371))),f154(x43371,x43372))),f335(f335(f7(f882(x43371),f888(f882(x43371),a879),a879),f337(f882(x43371))),f154(x43371,x43373))),f153(x43371,f335(f335(f95(f888(x43371,a879)),f335(f335(f7(x43371,f888(x43371,a879),a879),f337(x43371)),x43372)),f335(f335(f7(x43371,f888(x43371,a879),a879),f337(x43371)),x43373))))
% 59.73/59.65 [4349]E(f335(f249(x43491),f335(f335(f18(x43491,a879,a879),f335(f335(f8(a879,f888(a879,a879),x43491),a334),f335(f335(f7(x43491,x43491,a879),a332),x43492))),f335(f335(f7(x43491,f888(x43491,a879),a879),f337(x43491)),x43493))),f335(f335(f312(x43491),x43492),x43493))
% 59.73/59.65 [4350]E(f335(f249(x43501),f335(f335(f18(x43501,a879,a879),f335(f335(f8(a879,f888(a879,a879),x43501),a334),f335(f335(f7(x43501,x43501,a879),a332),x43502))),f335(f335(f7(x43501,f888(x43501,a879),a879),f337(x43501)),x43503))),f335(f335(f312(x43501),x43502),x43503))
% 59.73/59.65 [4370]E(f335(f335(f81(f882(f882(x43701)),f882(f882(x43701))),f48(x43701,x43702)),f335(f335(f18(f882(f882(x43701)),f882(f882(x43701)),f882(f882(x43701))),f335(f335(f8(f882(f882(x43701)),f888(f882(f882(x43701)),f882(f882(x43701))),f882(f882(x43701))),f127(f882(x43701))),f335(f147(f882(x43701),f882(x43701)),f335(f144(x43701),x43703)))),f5(f882(f882(x43701))))),f48(x43701,f335(f335(f144(x43701),x43703),x43702)))
% 59.73/59.65 [4374]E(f335(f249(x43741),f335(f335(f18(x43741,a879,a879),f335(f335(f8(a879,f888(a879,a879),x43741),a334),f335(f335(f7(x43741,f888(x43741,a879),a879),f337(x43741)),x43742))),f335(f335(f7(x43741,f888(x43741,a879),a879),f337(x43741)),x43743))),f335(f335(f104(f888(x43741,a879)),x43742),x43743))
% 59.73/59.65 [4375]E(f335(f249(x43751),f335(f335(f18(x43751,a879,a879),f335(f335(f8(a879,f888(a879,a879),x43751),a333),f335(f335(f7(x43751,f888(x43751,a879),a879),f337(x43751)),x43752))),f335(f335(f7(x43751,f888(x43751,a879),a879),f337(x43751)),x43753))),f335(f335(f95(f888(x43751,a879)),x43752),x43753))
% 59.73/59.65 [4468]E(f335(f335(f33(x44681,f888(f888(x44681,a879),a879)),x44682),f335(f335(f7(x44681,f888(f888(x44681,a879),a879),f888(f888(x44681,a879),a879)),f335(f335(f8(f888(x44681,a879),f888(f888(f888(x44681,a879),a879),f888(f888(x44681,a879),a879)),x44681),f312(f888(x44681,a879))),f335(f335(f8(f888(x44681,a879),f888(x44681,a879),x44681),f288(x44681,x44681,x44683)),f335(f335(f7(x44681,f888(x44681,a879),f888(x44681,a879)),f312(x44681)),f188(f888(x44681,a879)))))),f188(f888(f888(x44681,a879),a879)))),f335(f335(f55(x44681),x44682),x44683))
% 59.73/59.65 [4470]E(f335(f335(f204(x44701),f335(f335(f76(a1),f335(f335(f68(f887(a1,a1),a1,x44701,f263(a1,a1)),f215(x44701)),x44702)),f335(f335(f68(f887(a1,a1),a1,x44701,f263(a1,a1)),f215(x44701)),x44703))),f335(f335(f76(a1),f335(f335(f68(f887(a1,a1),a1,x44701,f267(a1,a1)),f215(x44701)),x44702)),f335(f335(f68(f887(a1,a1),a1,x44701,f267(a1,a1)),f215(x44701)),x44703))),f230(x44701,x44702,x44703))
% 59.73/59.65 [4473]E(f335(f249(f882(x44731)),f335(f335(f18(f882(x44731),a879,a879),f335(f335(f8(a879,f888(a879,a879),f882(x44731)),a333),f335(f335(f7(f882(x44731),a881,a879),f335(f335(f8(a881,f888(a881,a879),f882(x44731)),a332),f189(f882(x44731)))),x44732))),f335(f335(f7(f882(x44731),f888(x44731,a879),a879),f335(f335(f8(f888(x44731,a879),f888(f888(x44731,a879),a879),f882(x44731)),f242(f888(x44731,a879))),f166(x44731))),f335(f166(x44731),x44733)))),f335(f166(f882(x44731)),f49(x44731,x44732,x44733)))
% 59.73/59.65 [3847]E(f39(a881,f335(f335(f75(a881),f335(f335(f76(a881),x38471),x38472)),x38473),x38472),f39(a881,x38473,x38472))
% 59.73/59.65 [3892]E(f132(a881,f335(f304(a881,f335(f335(f75(a881),x38921),x38922)),x38923)),f335(f335(f131(a881),x38922),f132(a881,f335(f304(a881,x38921),x38923))))
% 59.73/59.65 [3936]E(f335(f335(f75(a1),f335(f94(a1),x39361)),f335(f335(f75(a1),f335(f94(a1),x39362)),x39363)),f335(f335(f75(a1),f335(f94(a1),f335(f335(f75(a881),x39361),x39362))),x39363))
% 59.73/59.65 [3943]E(f335(f335(f104(f888(x39431,a879)),f335(f335(f23(f888(x39431,a879)),x39432),x39433)),x39433),f335(f335(f104(f888(x39431,a879)),x39432),x39433))
% 59.73/59.65 [3944]E(f335(f335(f23(f888(x39441,a879)),f335(f335(f23(f888(x39441,a879)),x39442),x39443)),x39443),f335(f335(f23(f888(x39441,a879)),x39442),x39443))
% 59.73/59.65 [3967]E(f335(f335(f291(x39671,x39671,x39672),f310(x39671,f188(f888(f887(x39671,x39671),a879)))),x39673),x39673)
% 59.73/59.65 [3975]E(f335(f335(f104(f888(x39751,a879)),f335(f287(x39751),x39752)),f335(f287(x39751),x39753)),f335(f287(x39751),f335(f335(f104(f888(f887(x39751,x39751),a879)),x39752),x39753)))
% 59.73/59.65 [3986]E(f274(x39861,f335(f335(f144(f887(a93,x39861)),f335(f335(f264(a93,x39861),f2(a93)),x39862)),x39863)),f274(x39861,x39863))
% 59.73/59.65 [3989]E(f335(f335(f95(f888(x39891,a879)),f32(f888(x39891,a879),x39892)),f32(f888(x39891,a879),x39893)),f32(f888(x39891,a879),f335(f335(f104(f888(f888(x39891,a879),a879)),x39892),x39893)))
% 59.73/59.65 [3990]E(f335(f335(f104(f888(x39901,a879)),f31(f888(x39901,a879),x39902)),f31(f888(x39901,a879),x39903)),f31(f888(x39901,a879),f335(f335(f104(f888(f888(x39901,a879),a879)),x39902),x39903)))
% 59.73/59.65 [4028]E(f335(f335(f291(x40281,x40281,x40281),f335(f335(f183(f887(x40281,x40281),a879),x40282),x40283)),x40283),f335(f335(f183(f887(x40281,x40281),a879),f335(a106,x40282)),x40283))
% 59.73/59.65 [4075]P1(f335(f335(f242(f888(x40751,a879)),f335(f335(f23(f888(x40751,a879)),x40752),x40753)),x40752))
% 59.73/59.65 [4076]P1(f335(f335(f242(f888(x40761,a879)),f335(f335(f95(f888(x40761,a879)),x40762),x40763)),x40763))
% 59.73/59.65 [4077]P1(f335(f335(f242(f888(x40771,a879)),f335(f335(f95(f888(x40771,a879)),x40772),x40773)),x40772))
% 59.73/59.65 [4102]E(f310(x41021,f335(f335(f104(f888(f887(x41021,x41021),a879)),f310(x41021,x41022)),f310(x41021,x41023))),f310(x41021,f335(f335(f104(f888(f887(x41021,x41021),a879)),x41022),x41023)))
% 59.73/59.65 [4106]E(f31(f888(x41061,a879),f335(f335(f312(f888(x41061,a879)),x41062),f335(f335(f312(f888(x41061,a879)),x41063),f188(f888(f888(x41061,a879),a879))))),f335(f335(f104(f888(x41061,a879)),x41062),x41063))
% 59.73/59.65 [4107]E(f32(f888(x41071,a879),f335(f335(f312(f888(x41071,a879)),x41072),f335(f335(f312(f888(x41071,a879)),x41073),f188(f888(f888(x41071,a879),a879))))),f335(f335(f95(f888(x41071,a879)),x41072),x41073))
% 59.73/59.65 [4113]E(f335(f335(f291(x41131,x41131,x41131),f335(f335(f183(f887(x41131,x41131),a879),x41132),x41133)),x41133),f335(f335(f291(x41131,x41131,x41131),x41133),f335(f335(f183(f887(x41131,x41131),a879),x41132),x41133)))
% 59.73/59.65 [4185]E(f335(f335(f104(f888(x41851,a879)),f335(f249(x41851),f335(f335(f7(x41851,x41851,a879),a332),x41852))),x41853),f335(f335(f312(x41851),x41852),x41853))
% 59.73/59.65 [4187]E(f335(a98,f335(f335(f9(x41871,a1),f335(f335(f8(a881,a1,x41871),f94(a1)),x41872)),x41873)),f335(f335(f9(x41871,a881),x41872),x41873))
% 59.73/59.65 [4188]E(f335(a98,f335(f335(f6(x41881,a1),f335(f335(f8(a881,a1,x41881),f94(a1)),x41882)),x41883)),f335(f335(f6(x41881,a881),x41882),x41883))
% 59.73/59.65 [4268]E(f335(f149(f882(x42681),x42681,f335(f165(x42681),x42682),f335(f16(f888(f882(x42681),f882(x42681)),x42681),f335(f335(f7(f882(x42681),f882(x42681),f882(x42681)),f127(x42681)),x42682))),x42683),f335(f165(x42681),f335(f335(f127(x42681),x42683),x42682)))
% 59.73/59.65 [4299]P1(f335(f335(f242(f888(f888(x42991,a879),a879)),f335(f335(f104(f888(f888(x42991,a879),a879)),f335(f311(x42991),x42992)),f335(f311(x42991),x42993))),f335(f311(x42991),f335(f335(f104(f888(x42991,a879)),x42992),x42993))))
% 59.73/59.65 [4393]E(f335(f249(x43931),f335(f335(f18(x43931,a879,a879),f335(f335(f8(a879,f888(a879,a879),x43931),a333),f335(f335(f7(x43931,f888(x43931,a879),a879),f337(x43931)),x43932))),f335(f335(f8(a879,a879,x43931),a330),f335(f335(f7(x43931,f888(x43931,a879),a879),f337(x43931)),x43933)))),f335(f335(f23(f888(x43931,a879)),x43932),x43933))
% 59.73/59.65 [4417]E(f335(f29(a881),f335(f249(a881),f335(f335(f18(a881,a879,a879),f335(f335(f8(a879,f888(a879,a879),a881),a333),f335(f335(f7(a881,a881,a879),f243(a881)),f335(f189(f882(x44171)),x44172)))),f335(f335(f8(x44171,a879,a881),x44173),f335(f158(x44171),x44172))))),f335(f189(f882(x44171)),f335(f129(x44171,x44173),x44172)))
% 59.73/59.65 [4419]E(f335(f189(f882(x44191)),f170(x44191,x44192,x44193)),f335(f29(a881),f335(f249(a881),f335(f335(f18(a881,a879,a879),f335(f335(f8(a879,f888(a879,a879),a881),a333),f335(f335(f7(a881,a881,a879),f243(a881)),f335(f189(f882(x44191)),x44192)))),f335(f335(f7(a881,f888(a881,a879),a879),f337(a881)),x44193)))))
% 59.73/59.65 [4516]E(f335(f335(f95(f888(f887(f882(x45161),f882(x45161)),a879)),f335(f313(f887(f887(x45161,f882(x45161)),f887(x45161,f882(x45161))),f887(f882(x45161),f882(x45161)),f269(f887(x45161,f882(x45161)),f882(x45161),f887(x45161,f882(x45161)),f882(x45161),f335(f268(x45161,f882(x45161),f882(x45161)),f144(x45161)),f335(f268(x45161,f882(x45161),f882(x45161)),f144(x45161)))),f328(x45161,f882(x45161),x45162,f335(f136(x45161,x45162),x45163)))),f335(f249(f887(f882(x45161),f882(x45161))),f335(f268(f882(x45161),f882(x45161),a879),f335(f335(f7(f882(x45161),f888(f882(x45161),a879),f888(f882(x45161),a879)),f335(f335(f8(f888(a879,a879),f888(f888(f882(x45161),a879),f888(f882(x45161),a879)),f882(x45161)),f8(a879,a879,f882(x45161))),f335(f335(f8(a879,f888(a879,a879),f882(x45161)),a333),f335(f335(f7(f882(x45161),a881,a879),f335(f335(f8(a881,f888(a881,a879),f882(x45161)),a332),f189(f882(x45161)))),f335(a106,x45163))))),f335(f335(f7(f882(x45161),a881,a879),f335(f335(f8(a881,f888(a881,a879),f882(x45161)),a332),f189(f882(x45161)))),f335(a106,x45163)))))),f335(f136(x45161,x45162),f335(a106,x45163)))
% 59.73/59.65 [3991]E(f39(a881,f335(a106,f335(f335(f75(a881),f335(f335(f76(a881),x39911),x39912)),x39913)),x39912),f39(a881,f335(a106,x39913),x39912))
% 59.73/59.65 [4255]E(f335(f249(x42551),f335(f335(f18(x42551,a879,a879),f335(f335(f8(a879,f888(a879,a879),x42551),a333),x42552)),x42553)),f335(f335(f95(f888(x42551,a879)),f335(f249(x42551),x42552)),f335(f249(x42551),x42553)))
% 59.73/59.65 [4256]E(f335(f249(x42561),f335(f335(f18(x42561,a879,a879),f335(f335(f8(a879,f888(a879,a879),x42561),a334),x42562)),x42563)),f335(f335(f104(f888(x42561,a879)),f335(f249(x42561),x42562)),f335(f249(x42561),x42563)))
% 59.73/59.65 [4258]E(f335(f335(f127(x42581),f335(f335(f131(x42581),f39(a881,x42582,f335(f189(f882(x42581)),x42583))),x42583)),f335(f335(f169(x42581),f39(a881,x42582,f335(f189(f882(x42581)),x42583))),x42583)),f335(f335(f335(f183(f882(x42581),f882(x42581)),x42582),f161(x42581)),x42583))
% 59.73/59.65 [4264]E(f335(f249(x42641),f335(f335(f18(x42641,a879,a879),f335(f335(f8(a879,f888(a879,a879),x42641),a338),x42642)),x42643)),f335(f335(f104(f888(x42641,a879)),f335(f74(f888(x42641,a879)),f335(f249(x42641),x42642))),f335(f249(x42641),x42643)))
% 59.73/59.65 [4281]E(f335(f335(f75(a881),f335(f189(f882(x42811)),f335(f129(x42811,x42812),x42813))),f335(f189(f882(x42811)),f335(f129(x42811,f335(f335(f8(a879,a879,x42811),a330),x42812)),x42813))),f335(f189(f882(x42811)),x42813))
% 59.73/59.65 [4306]P1(f335(f335(f242(f888(x43061,a879)),f335(f335(f104(f888(x43061,a879)),f32(f888(x43061,a879),x43062)),f32(f888(x43061,a879),x43063))),f32(f888(x43061,a879),f335(f335(f95(f888(f888(x43061,a879),a879)),x43062),x43063))))
% 59.73/59.65 [4320]E(f335(f166(x43201),f335(f129(x43201,f335(f335(f8(a879,a879,x43201),a330),f335(f335(f7(x43201,x43201,a879),a332),x43202))),x43203)),f335(f335(f23(f888(x43201,a879)),f335(f166(x43201),x43203)),f335(f335(f312(x43201),x43202),f188(f888(x43201,a879)))))
% 59.73/59.65 [4329]P1(f335(f335(f242(f888(f887(x43291,x43291),a879)),f335(f335(f104(f888(f887(x43291,x43291),a879)),f310(x43291,x43292)),f310(x43291,x43293))),f310(x43291,f335(f335(f104(f888(f887(x43291,x43291),a879)),x43292),x43293))))
% 59.73/59.65 [4355]E(f335(f335(f76(a881),f335(a106,f335(a106,f2(a881)))),f335(f335(f6(a881,a881),f335(f335(f8(a881,a881,a881),f335(f75(a881),x43551)),f335(f335(f7(a881,a881,a881),f76(a881)),x43552))),f335(f250(a881),x43553))),f335(f335(f76(a881),x43553),f335(f335(f75(a881),x43551),f335(f335(f75(a881),x43551),f335(f335(f76(a881),f335(f335(f23(a881),x43553),f73(a881))),x43552)))))
% 59.73/59.65 [4365]E(f335(f249(x43651),f335(f335(f18(x43651,a879,a879),f335(f335(f8(a879,f888(a879,a879),x43651),a333),f335(f335(f7(x43651,f888(x43651,a879),a879),f337(x43651)),f335(f166(x43651),x43652)))),x43653)),f335(f166(x43651),f335(f129(x43651,x43653),x43652)))
% 59.73/59.65 [4515]E(f335(f249(x45151),f335(f335(f8(f888(a881,a879),a879,x45151),f82(a881)),f335(f335(f7(x45151,f888(a881,a879),f888(a881,a879)),f335(f335(f8(f888(a881,f888(a879,a879)),f888(f888(a881,a879),f888(a881,a879)),x45151),f18(a881,a879,a879)),f335(f335(f8(f888(a881,a879),f888(a881,f888(a879,a879)),x45151),f335(f8(a879,f888(a879,a879),a881),a333)),f335(f335(f7(x45151,f888(a881,x45151),f888(a881,a879)),f335(f335(f8(f888(x45151,a879),f888(f888(a881,x45151),f888(a881,a879)),x45151),f8(x45151,a879,a881)),a332)),f335(f158(x45151),x45152))))),f335(f335(f18(a881,a879,a879),f335(f335(f8(a879,f888(a879,a879),a881),a333),f335(f335(f7(a881,a881,a879),f243(a881)),f335(f189(f882(x45151)),x45152)))),f335(f335(f7(a881,f888(a881,a879),a879),f337(a881)),x45153))))),f335(f166(x45151),f170(x45151,x45152,x45153)))
% 59.73/59.65 [4406]E(f335(f249(x44061),f335(f335(f18(x44061,a879,a879),f335(f335(f8(a879,f888(a879,a879),x44061),a338),f335(f335(f8(a879,a879,x44061),a330),f335(f335(f7(x44061,x44061,a879),a332),x44062)))),x44063)),f335(f335(f312(x44061),x44062),f335(f249(x44061),x44063)))
% 59.73/59.65 [4439]E(f335(f335(f147(f887(x44391,a881),x44391),f263(x44391,a881)),f335(f129(f887(x44391,a881),f335(f335(f7(f887(x44391,a881),f888(a881,a879),a879),f335(f335(f8(a881,f888(f888(a881,a879),a879),f887(x44391,a881)),f337(a881)),f267(x44391,a881))),x44392)),f335(f335(f175(x44391,a881),x44393),f132(a881,f335(f304(a881,f2(a881)),f335(f189(f882(x44391)),x44393)))))),f170(x44391,x44393,x44392))
% 59.73/59.65 [4469]E(f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(f335(f6(a881,a1),f335(f335(f8(a1,a1,a881),f335(f75(a1),x44691)),f335(f335(f7(a881,a1,a1),f335(f335(f8(a1,f888(a1,a1),a881),f76(a1)),f94(a1))),x44692))),f335(f250(a881),x44693))),f335(f335(f76(a1),f335(f94(a1),x44693)),f335(f335(f75(a1),x44691),f335(f335(f75(a1),x44691),f335(f335(f76(a1),f335(f94(a1),f335(f335(f23(a881),x44693),f73(a881)))),x44692)))))
% 59.73/59.65 [4509]E(f335(f249(f887(x45091,x45092)),f335(f268(x45091,x45092,a879),f335(f335(f7(x45091,f888(f887(x45092,x45091),a879),f888(x45092,a879)),f335(f335(f8(f888(x45092,f888(f888(f887(x45092,x45091),a879),a879)),f888(f888(f887(x45092,x45091),a879),f888(x45092,a879)),x45091),f7(x45092,f888(f887(x45092,x45091),a879),a879)),f335(f335(f8(f888(x45092,f887(x45092,x45091)),f888(x45092,f888(f888(f887(x45092,x45091),a879),a879)),x45091),f335(f8(f887(x45092,x45091),f888(f888(f887(x45092,x45091),a879),a879),x45092),f337(f887(x45092,x45091)))),f335(f7(x45092,x45091,f887(x45092,x45091)),f264(x45092,x45091))))),x45093))),f335(f289(x45092,x45091),x45093))
% 59.73/59.65 [4530]E(f335(f249(f882(x45301)),f335(f335(f8(f888(x45301,a879),a879,f882(x45301)),f82(x45301)),f335(f335(f8(f888(x45301,f888(f882(x45301),a879)),f888(x45301,a879),f882(x45301)),f335(f8(f888(f882(x45301),a879),a879,x45301),f82(f882(x45301)))),f335(f335(f7(f882(x45301),f888(x45301,f888(f882(x45301),a879)),f888(x45301,f888(f882(x45301),a879))),f335(f335(f8(f888(x45301,f888(f888(f882(x45301),a879),f888(f882(x45301),a879))),f888(f888(x45301,f888(f882(x45301),a879)),f888(x45301,f888(f882(x45301),a879))),f882(x45301)),f18(x45301,f888(f882(x45301),a879),f888(f882(x45301),a879))),f335(f335(f8(f888(x45301,f888(f882(x45301),f888(a879,a879))),f888(x45301,f888(f888(f882(x45301),a879),f888(f882(x45301),a879))),f882(x45301)),f335(f8(f888(f882(x45301),f888(a879,a879)),f888(f888(f882(x45301),a879),f888(f882(x45301),a879)),x45301),f18(f882(x45301),a879,a879))),f335(f335(f8(f888(x45301,f888(f882(x45301),a879)),f888(x45301,f888(f882(x45301),f888(a879,a879))),f882(x45301)),f335(f8(f888(f882(x45301),a879),f888(f882(x45301),f888(a879,a879)),x45301),f335(f8(a879,f888(a879,a879),f882(x45301)),a333))),f335(f335(f7(f882(x45301),f888(x45301,f888(f882(x45301),f882(x45301))),f888(x45301,f888(f882(x45301),a879))),f335(f335(f8(f888(f888(f882(x45301),f882(x45301)),f888(f882(x45301),a879)),f888(f888(x45301,f888(f882(x45301),f882(x45301))),f888(x45301,f888(f882(x45301),a879))),f882(x45301)),f8(f888(f882(x45301),f882(x45301)),f888(f882(x45301),a879),x45301)),f335(f335(f8(f888(f882(x45301),a879),f888(f888(f882(x45301),f882(x45301)),f888(f882(x45301),a879)),f882(x45301)),f8(f882(x45301),a879,f882(x45301))),a332))),f144(x45301)))))),f335(f335(f7(x45301,f888(f882(x45301),a879),f888(f882(x45301),a879)),f335(f335(f8(f888(a879,a879),f888(f888(f882(x45301),a879),f888(f882(x45301),a879)),x45301),f8(a879,a879,f882(x45301))),f335(f335(f8(a879,f888(a879,a879),x45301),a333),f335(f335(f7(x45301,f888(x45301,a879),a879),f337(x45301)),x45302)))),f335(f335(f7(f882(x45301),f888(f882(x45301),a879),a879),f337(f882(x45301))),x45303)))))),f168(x45301,x45302,x45303))
% 59.73/59.65 [4527]E(f335(f335(f81(a1,f887(a1,a1)),f335(f335(f23(a1),x45271),x45272)),f335(f335(f7(a1,f887(a1,a1),f887(a1,a1)),f335(f335(f18(a1,f887(a1,a1),f888(f887(a1,a1),f887(a1,a1))),f335(f335(f8(a879,f888(f887(a1,a1),f888(f887(a1,a1),f887(a1,a1))),a1),f88(f887(a1,a1))),f335(f242(a1),f2(a1)))),f335(f264(a1,a1),f335(f335(f75(a1),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x45273)),f73(a1))))),f335(f335(f264(a1,a1),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x45273)),x45271))),f335(f37(x45272),f335(f335(f264(a1,a1),x45273),x45271)))
% 59.73/59.65 [3533]E(f335(f335(f335(f67(x35331,x35332),x35333),x35334),f335(x35333,x35334)),x35333)
% 59.73/59.65 [3541]E(f110(x35411,f335(x35412,x35413),f335(x35414,x35413)),f335(f206(x35411,x35412,x35414),x35413))
% 59.73/59.65 [3551]E(f110(f885(x35511),f335(x35512,x35513),f335(x35514,x35513)),f335(f197(x35511,x35512,x35514),x35513))
% 59.73/59.65 [3595]E(f335(f335(f255(x35951,x35952,x35953),x35954),f2(a881)),x35952)
% 59.73/59.65 [3635]E(f185(x36351,x36352,x36353,f335(a106,x36354)),f335(x36353,x36354))
% 59.73/59.65 [3678]E(f164(x36781,x36782,f164(x36781,x36783,x36784)),f164(x36781,x36783,f164(x36781,x36782,x36784)))
% 59.73/59.65 [3679]E(f120(x36791,x36792,f110(x36791,x36793,x36794)),f110(x36791,f120(x36791,x36792,x36793),x36794))
% 59.73/59.65 [3813]E(f335(f237(x38131,x38132,x38133,x38134),f200(x38132)),x38133)
% 59.73/59.65 [3814]E(f335(f149(x38141,x38142,x38143,x38144),f107(x38142)),x38143)
% 59.73/59.65 [3815]E(f335(f135(x38151,x38152,x38153,x38154),f107(x38152)),x38154)
% 59.73/59.65 [3854]E(f335(f189(f886(x38541,x38542)),f223(x38541,x38542,x38543,x38544)),f2(a881))
% 59.73/59.65 [3921]E(f335(f335(f127(x39211),f163(x39211,x39212,x39213)),f163(x39211,x39214,x39213)),f335(f335(f127(x39211),f163(x39211,x39214,x39213)),f163(x39211,x39212,x39213)))
% 59.73/59.65 [3933]E(f335(f237(f885(x39331),x39332,f200(x39331),f335(f16(f885(x39331),x39332),f200(x39331))),f335(x39333,x39334)),f200(x39331))
% 59.73/59.65 [3979]E(f335(f335(f104(f888(x39791,a879)),f177(x39791,x39792,x39793)),f177(x39791,x39792,x39794)),f177(x39791,x39792,f180(x39791,x39792,x39794,x39793)))
% 59.73/59.65 [4012]E(f335(f335(f270(x40121,x40122,x40123,f887(x40122,x40123)),x40124),f264(x40122,x40123)),x40124)
% 59.73/59.65 [4021]E(f238(x40211,x40212,x40213,x40214,f200(x40212)),x40213)
% 59.73/59.65 [4022]E(f181(x40221,x40222,x40223,x40224,f107(x40222)),x40223)
% 59.73/59.65 [4023]E(f121(x40231,x40232,x40233,x40234,f113(x40232)),x40233)
% 59.73/59.65 [4024]E(f181(x40241,x40242,x40243,f107(x40241),x40244),x40243)
% 59.73/59.65 [4312]P40(x43121,x43122,x43123,x43124,f188(f888(x43121,a879)),x43124)
% 59.73/59.65 [4313]P40(x43131,x43132,x43133,x43134,f188(f888(x43131,a879)),x43134)
% 59.73/59.65 [3338]E(f335(f335(f16(x33381,x33382),x33383),x33384),x33383)
% 59.73/59.65 [3452]E(f335(f335(f201(x34521,x34522),x34523),f335(f235(x34521),x34524)),f335(f235(x34522),f335(x34523,x34524)))
% 59.73/59.65 [3625]E(f164(x36251,x36252,f335(f129(x36251,x36253),x36254)),f335(f129(x36251,x36253),f164(x36251,x36252,x36254)))
% 59.73/59.65 [3661]E(f335(f335(f59(x36611,x36612,x36613),x36614),f188(f888(x36611,a879))),x36614)
% 59.73/59.65 [3686]E(f335(f335(f158(x36861),f335(f335(f144(x36861),x36862),x36863)),f335(a106,x36864)),f335(f335(f158(x36861),x36863),x36864))
% 59.73/59.65 [3752]E(f335(f335(x37521,x37522),f335(f184(x37523,x37524,x37521),x37522)),f335(f184(x37523,x37524,x37521),f335(a106,x37522)))
% 59.73/59.65 [3852]E(f335(f335(f152(x38521,f335(f335(f144(x38521),x38522),x38523)),f2(a881)),x38524),f335(f335(f144(x38521),x38524),x38523))
% 59.73/59.65 [3862]E(f335(f335(f33(f888(x38621,a879),f888(x38622,a879)),x38623),f313(x38621,x38622,x38624)),f335(f313(x38621,x38622,x38624),f31(f888(x38621,a879),x38623)))
% 59.73/59.65 [3863]E(f335(f335(f33(f888(x38631,a879),f888(x38632,a879)),x38633),f314(x38632,x38631,x38634)),f335(f314(x38632,x38631,x38634),f31(f888(x38631,a879),x38633)))
% 59.73/59.65 [3960]E(f177(x39601,x39602,f182(x39601,x39602,x39603,x39604)),f335(f335(f95(f888(x39601,a879)),f177(x39601,x39602,x39603)),x39604))
% 59.73/59.65 [3964]E(f335(f119(x39641,x39642),f120(x39641,x39643,x39644)),f335(f335(f75(a881),f335(f335(f75(a881),f335(x39642,x39643)),f335(f119(x39641,x39642),x39644))),f335(a106,f2(a881))))
% 59.73/59.65 [3985]E(f335(f135(x39851,x39852,f335(f7(x39852,x39851,x39851),x39853),x39854),f335(f162(x39852),f107(x39852))),x39854)
% 59.73/59.65 [4033]E(f71(x40331,x40332,x40333,x40334,f188(f888(x40331,a879))),x40333)
% 59.73/59.65 [4078]E(f335(f335(f335(f335(f67(x40781,f885(x40782)),f335(f16(f885(x40782),x40781),f200(x40782))),x40783),f200(x40782)),x40784),f200(x40782))
% 59.73/59.65 [4238]E(f335(f268(x42381,x42382,x42383),f335(f335(f8(f888(x42382,f887(x42381,x42382)),f888(x42382,x42383),x42381),f335(f8(f887(x42381,x42382),x42383,x42382),x42384)),f264(x42381,x42382))),x42384)
% 59.73/59.65 [3531]E(f335(f267(x35311,x35312),f335(f335(f264(x35311,x35312),x35313),x35314)),x35314)
% 59.73/59.65 [3532]E(f335(f263(x35321,x35322),f335(f335(f264(x35321,x35322),x35323),x35324)),x35323)
% 59.73/59.65 [3567]E(f335(f189(f882(x35671)),f335(f335(f147(x35672,x35671),x35673),x35674)),f335(f189(f882(x35672)),x35674))
% 59.73/59.65 [3568]E(f335(f189(f882(x35681)),f335(f335(f152(x35681,x35682),x35683),x35684)),f335(f189(f882(x35681)),x35682))
% 59.73/59.65 [3589]E(f335(f335(f131(x35891),f335(a106,x35892)),f335(f335(f144(x35891),x35893),x35894)),f335(f335(f131(x35891),x35892),x35894))
% 59.73/59.65 [3656]E(f335(f335(f169(x36561),x36562),f163(x36561,x36563,x36564)),f163(x36561,f335(f335(f240(a881),x36562),x36563),x36564))
% 59.73/59.65 [3657]E(f335(f335(f131(x36571),x36572),f163(x36571,x36573,x36574)),f163(x36571,f335(f335(f23(a881),x36573),x36572),x36574))
% 59.73/59.65 [3663]E(f335(f335(f312(x36631),x36632),f335(f335(f312(x36631),x36633),x36634)),f335(f335(f312(x36631),x36633),f335(f335(f312(x36631),x36632),x36634)))
% 59.73/59.65 [3667]E(f335(f335(f147(x36671,x36672),x36673),f108(x36671,x36674)),f108(x36672,f335(f335(f147(x36671,x36672),x36673),x36674)))
% 59.73/59.65 [3684]E(f335(f162(x36841),f335(f335(f147(x36842,x36841),x36843),x36844)),f335(f335(f147(x36842,x36841),x36843),f335(f162(x36842),x36844)))
% 59.73/59.65 [3685]E(f335(f335(f147(x36851,x36852),x36853),f335(f165(x36851),x36854)),f335(f165(x36852),f335(f335(f147(x36851,x36852),x36853),x36854)))
% 59.73/59.65 [3696]E(f335(f335(f169(x36961),f335(a106,x36962)),f335(f335(f144(x36961),x36963),x36964)),f335(f335(f144(x36961),x36963),f335(f335(f169(x36961),x36962),x36964)))
% 59.73/59.65 [3699]E(f335(f166(x36991),f335(f335(f147(x36992,x36991),x36993),x36994)),f335(f313(x36992,x36991,x36993),f335(f166(x36992),x36994)))
% 59.73/59.65 [3714]E(f335(f335(f147(x37141,x37142),f335(f16(x37142,x37141),x37143)),x37144),f163(x37142,f335(f189(f882(x37141)),x37144),x37143))
% 59.73/59.65 [3751]E(f17(x37511,x37512,x37513,f335(a3,f335(a106,f335(a20,x37514)))),f335(x37513,x37514))
% 59.73/59.65 [3755]E(f335(f335(f127(x37551),f335(f129(x37551,x37552),x37553)),f335(f129(x37551,x37552),x37554)),f335(f129(x37551,x37552),f335(f335(f127(x37551),x37553),x37554)))
% 59.73/59.65 [3767]E(f145(x37671,f335(f335(f147(x37672,x37671),x37673),f145(x37672,x37674))),f145(x37671,f335(f335(f147(x37672,x37671),x37673),x37674)))
% 59.73/59.65 [3783]E(f335(f289(x37831,x37831),f335(f335(f290(x37832,x37831),x37833),x37834)),f335(f335(f290(x37832,x37831),f335(f289(x37832,x37832),x37833)),x37834))
% 59.73/59.65 [3794]E(f335(f335(f291(x37941,x37942,x37943),x37944),f188(f888(f887(x37942,x37943),a879))),f188(f888(f887(x37941,x37943),a879)))
% 59.73/59.65 [3795]E(f335(f335(f169(x37951),f335(f335(f23(a881),x37952),x37953)),f335(f335(f131(x37951),x37953),x37954)),f335(f335(f131(x37951),x37953),f335(f335(f169(x37951),x37952),x37954)))
% 59.73/59.65 [3816]E(f335(f335(f127(x38161),f163(x38161,x38162,x38163)),f163(x38161,x38164,x38163)),f163(x38161,f335(f335(f75(a881),x38162),x38164),x38163))
% 59.73/59.65 [3817]E(f335(f335(f335(f284(x38171),x38172),x38173),x38174),f335(f264(f888(a93,f888(a879,f885(f883(x38171)))),f887(a93,a93)),f335(f36(x38171),x38172)))
% 59.73/59.65 [3842]E(f31(f888(x38421,a879),f335(f313(x38422,f888(x38421,a879),x38423),x38424)),f335(f335(f33(x38422,f888(x38421,a879)),x38424),x38423))
% 59.73/59.65 [3843]E(f32(f888(x38431,a879),f335(f313(x38432,f888(x38431,a879),x38433),x38434)),f335(f335(f34(x38432,f888(x38431,a879)),x38434),x38433))
% 59.73/59.65 [3844]E(f32(f888(x38441,a879),f335(f313(x38442,f888(x38441,a879),x38443),x38444)),f335(f335(f34(x38442,f888(x38441,a879)),x38444),x38443))
% 59.73/59.65 [3845]E(f31(f888(x38451,a879),f335(f313(x38452,f888(x38451,a879),x38453),x38454)),f335(f335(f33(x38452,f888(x38451,a879)),x38454),x38453))
% 59.73/59.65 [3846]E(f335(f189(f882(f887(x38461,x38462))),f335(f335(f175(x38461,x38462),x38463),x38464)),f335(f335(f240(a881),f335(f189(f882(x38461)),x38463)),f335(f189(f882(x38462)),x38464)))
% 59.73/59.65 [3848]E(f335(f314(x38481,x38482,x38483),f335(f74(f888(x38482,a879)),x38484)),f335(f74(f888(x38481,a879)),f335(f314(x38481,x38482,x38483),x38484)))
% 59.73/59.65 [3877]E(f335(f182(x38771,x38772,x38773,f188(f888(x38771,a879))),x38774),f200(x38772))
% 59.73/59.65 [3898]E(f335(f314(x38981,x38982,x38983),f335(f249(x38982),x38984)),f335(f249(x38981),f335(f335(f8(x38982,a879,x38981),x38984),x38983)))
% 59.73/59.65 [3915]E(f335(f335(f158(x39151),f335(f335(f127(x39151),x39152),f335(f335(f144(x39151),x39153),x39154))),f335(f189(f882(x39151)),x39152)),x39153)
% 59.73/59.65 [3920]E(f335(f182(x39201,x39202,f335(f16(f885(x39202),x39201),f200(x39202)),x39203),x39204),f200(x39202))
% 59.73/59.65 [3941]E(f335(f313(x39411,x39412,x39413),f335(f314(x39411,x39412,x39413),x39414)),f335(f335(f95(f888(x39412,a879)),x39414),f335(f313(x39411,x39412,x39413),f252(f888(x39411,a879)))))
% 59.73/59.65 [3959]P1(f335(f335(f337(x39591),f335(x39592,x39593)),f335(f313(x39594,x39591,x39592),f252(f888(x39594,a879)))))
% 59.73/59.65 [3968]E(f19(x39681,x39682,x39683,f335(a3,f335(a106,f335(a20,x39684)))),f335(f335(x39683,x39684),f19(x39681,x39682,x39683,x39684)))
% 59.73/59.65 [3972]E(f335(f335(f127(x39721),f163(x39721,x39722,x39723)),f335(f335(f144(x39721),x39723),x39724)),f335(f335(f144(x39721),x39723),f335(f335(f127(x39721),f163(x39721,x39722,x39723)),x39724)))
% 59.73/59.65 [3974]E(f335(f335(f266(x39741,x39742),f335(f166(x39741),x39743)),f335(f16(f888(x39742,a879),x39741),f335(f166(x39742),x39744))),f335(f166(f887(x39741,x39742)),f54(x39741,x39742,x39743,x39744)))
% 59.73/59.65 [3988]E(f148(x39881,x39882,f335(f335(f144(x39881),x39883),x39884)),f335(f335(f75(a881),f335(f335(f75(a881),f335(x39882,x39883)),f148(x39881,x39882,x39884))),f335(a106,f2(a881))))
% 59.73/59.65 [4003]E(f185(f882(x40031),f335(f335(f144(x40031),x40032),x40033),f335(f335(f7(a881,f882(x40031),f882(x40031)),f131(x40031)),x40033),x40034),f335(f335(f131(x40031),x40034),f335(f335(f144(x40031),x40032),x40033)))
% 59.73/59.65 [4004]P26(x40041,f887(x40042,x40041),f339(x40043,x40044,x40042,x40041),f335(f335(f33(x40042,f888(x40041,a879)),x40044),x40043))
% 59.73/59.65 [4013]E(f335(f335(f23(f888(x40131,a879)),f335(f335(f23(f888(x40131,a879)),x40132),x40133)),f335(f335(f312(x40131),x40134),f188(f888(x40131,a879)))),f335(f335(f23(f888(x40131,a879)),x40132),f335(f335(f312(x40131),x40134),x40133)))
% 59.73/59.65 [4026]E(f335(f335(f183(f888(x40261,x40262),f888(x40261,x40262)),x40263),f68(x40262,x40262,x40261,x40264)),f68(x40262,x40262,x40261,f335(f335(f183(x40262,x40262),x40263),x40264)))
% 59.73/59.65 [4101]E(f335(f335(f335(f183(f882(x41011),f882(x41011)),x41012),f161(x41011)),f335(f335(f335(f183(f882(x41011),f882(x41011)),x41013),f161(x41011)),x41014)),f335(f335(f335(f183(f882(x41011),f882(x41011)),f335(f335(f75(a881),x41012),x41013)),f161(x41011)),x41014))
% 59.73/59.65 [4190]P1(f335(f335(f242(f888(x41901,a879)),f335(f166(x41901),f335(f335(f152(x41901,x41902),x41903),x41904))),f335(f335(f312(x41901),x41904),f335(f166(x41901),x41902))))
% 59.73/59.65 [4227]E(f335(f335(f33(f888(x42271,a879),f888(f887(x42271,x42272),a879)),x42273),f335(f335(f7(f888(x42271,a879),f888(x42271,f888(x42272,a879)),f888(f887(x42271,x42272),a879)),f266(x42271,x42272)),x42274)),f335(f335(f266(x42271,x42272),f31(f888(x42271,a879),x42273)),x42274))
% 59.73/59.65 [4267]E(f212(x42671,x42672,x42673,f335(f68(x42672,f888(a93,f888(a93,f888(f887(a93,a93),f888(a93,f883(x42672))))),x42671,f207(x42672)),x42674)),f213(x42671,x42672,x42674,x42673))
% 59.73/59.65 [4284]E(f209(x42841,x42842,x42843,f335(f68(x42842,f888(a93,f888(a93,f888(f887(a93,a93),f888(a93,f883(f885(x42842)))))),x42841,f208(x42842)),x42844)),f210(x42841,x42842,x42844,x42843))
% 59.73/59.65 [4288]P1(f335(f61(x42881,x42882,x42883,x42884,f188(f888(x42881,a879))),x42884))
% 59.73/59.65 [4289]P1(f335(f61(x42891,x42892,x42893,x42894,f188(f888(x42891,a879))),x42894))
% 59.73/59.65 [4332]E(f335(f335(f33(x43321,f888(x43322,a879)),x43323),f335(f335(f7(x43321,f888(x43322,a879),f888(x43322,a879)),f335(f335(f8(x43322,f888(f888(x43322,a879),f888(x43322,a879)),x43321),f312(x43322)),x43324)),f188(f888(x43322,a879)))),f335(f313(x43321,x43322,x43324),x43323))
% 59.73/59.65 [4339]P1(f335(f335(f242(f888(x43391,a879)),f335(f260(x43392,x43391),f335(f335(f95(f888(f887(x43392,x43391),a879)),x43393),x43394))),f335(f335(f95(f888(x43391,a879)),f335(f260(x43392,x43391),x43393)),f335(f260(x43392,x43391),x43394))))
% 59.73/59.65 [4340]P1(f335(f335(f242(f888(x43401,a879)),f335(f262(x43401,x43402),f335(f335(f95(f888(f887(x43401,x43402),a879)),x43403),x43404))),f335(f335(f95(f888(x43401,a879)),f335(f262(x43401,x43402),x43403)),f335(f262(x43401,x43402),x43404))))
% 59.73/59.65 [4402]P1(f335(f335(f242(f888(f887(x44021,x44022),a879)),f335(f313(x44022,f887(x44021,x44022),f339(x44023,x44024,x44021,x44022)),f335(f335(f33(x44021,f888(x44022,a879)),x44024),x44023))),f335(f335(f266(x44021,x44022),x44024),x44023)))
% 59.73/59.65 [4403]E(f335(f112(x44031,f887(x44031,x44032),x44033),f335(f335(f8(f888(x44032,f883(f887(x44031,x44032))),f883(f887(x44031,x44032)),x44031),f112(x44032,f887(x44031,x44032),x44034)),f335(f335(f8(f888(x44032,f887(x44031,x44032)),f888(x44032,f883(f887(x44031,x44032))),x44031),f335(f8(f887(x44031,x44032),f883(f887(x44031,x44032)),x44032),f123(f887(x44031,x44032)))),f264(x44031,x44032)))),f124(x44031,x44032,x44033,x44034))
% 59.73/59.65 [4404]E(f282(x44041,x44042,x44043,f335(f68(x44042,f888(a93,f888(a93,f888(f887(a93,a93),f887(f888(a93,f888(a879,f885(f883(x44042)))),f887(a93,a93))))),x44041,f284(x44042)),x44044)),f285(x44041,x44042,x44044,x44043))
% 59.73/59.65 [4445]E(f80(f887(x44451,x44452),f335(f268(x44451,x44452,a879),f335(f335(f7(x44451,f888(x44452,a879),f888(x44452,a879)),f335(f335(f8(f888(a879,a879),f888(f888(x44452,a879),f888(x44452,a879)),x44451),f8(a879,a879,x44452)),f335(f335(f8(a879,f888(a879,a879),x44451),a333),f335(a332,x44453)))),f335(a332,x44454)))),f335(f335(f264(x44451,x44452),x44453),x44454))
% 59.73/59.65 [4446]E(f85(f887(x44461,x44462),f335(f268(x44461,x44462,a879),f335(f335(f7(x44461,f888(x44462,a879),f888(x44462,a879)),f335(f335(f8(f888(a879,a879),f888(f888(x44462,a879),f888(x44462,a879)),x44461),f8(a879,a879,x44462)),f335(f335(f8(a879,f888(a879,a879),x44461),a333),f335(a332,x44463)))),f335(a332,x44464)))),f335(f335(f264(x44461,x44462),x44463),x44464))
% 59.73/59.65 [4517]E(f335(f335(f268(f882(x45171),f882(x45171),f887(f882(x45171),f882(x45171))),f335(f335(f18(f882(x45171),f888(f882(x45171),f887(f882(x45171),f882(x45171))),f888(f882(x45171),f887(f882(x45171),f882(x45171)))),f335(f335(f8(f888(f882(x45171),f888(f887(f882(x45171),f882(x45171)),f887(f882(x45171),f882(x45171)))),f888(f888(f882(x45171),f887(f882(x45171),f882(x45171))),f888(f882(x45171),f887(f882(x45171),f882(x45171)))),f882(x45171)),f18(f882(x45171),f887(f882(x45171),f882(x45171)),f887(f882(x45171),f882(x45171)))),f335(f335(f8(f888(f882(x45171),f887(f882(x45171),f882(x45171))),f888(f882(x45171),f888(f887(f882(x45171),f882(x45171)),f887(f882(x45171),f882(x45171)))),f882(x45171)),f335(f8(f887(f882(x45171),f882(x45171)),f888(f887(f882(x45171),f882(x45171)),f887(f882(x45171),f882(x45171))),f882(x45171)),f335(f88(f887(f882(x45171),f882(x45171))),f335(x45172,x45173)))),f335(f335(f8(f882(x45171),f888(f882(x45171),f887(f882(x45171),f882(x45171))),f882(x45171)),f264(f882(x45171),f882(x45171))),f335(f144(x45171),x45173))))),f335(f335(f7(f882(x45171),f888(f882(x45171),f882(x45171)),f888(f882(x45171),f887(f882(x45171),f882(x45171)))),f335(f335(f8(f888(f882(x45171),f887(f882(x45171),f882(x45171))),f888(f888(f882(x45171),f882(x45171)),f888(f882(x45171),f887(f882(x45171),f882(x45171)))),f882(x45171)),f8(f882(x45171),f887(f882(x45171),f882(x45171)),f882(x45171))),f264(f882(x45171),f882(x45171)))),f335(f144(x45171),x45173)))),f160(x45171,x45172,x45174)),f160(x45171,x45172,f335(f335(f144(x45171),x45173),x45174)))
% 59.73/59.65 [4522]E(f335(f135(f888(x45221,f885(x45222)),f887(x45221,x45222),f335(f7(f887(x45221,x45222),f888(x45221,f885(x45222)),f888(x45221,f885(x45222))),f335(f268(x45221,x45222,f888(f888(x45221,f885(x45222)),f888(x45221,f885(x45222)))),f335(f335(f7(x45221,f888(x45222,f885(x45222)),f888(x45222,f888(f888(x45221,f885(x45222)),f888(x45221,f885(x45222))))),f335(f335(f8(f888(f885(x45222),f888(f888(x45221,f885(x45222)),f888(x45221,f885(x45222)))),f888(f888(x45222,f885(x45222)),f888(x45222,f888(f888(x45221,f885(x45222)),f888(x45221,f885(x45222))))),x45221),f8(f885(x45222),f888(f888(x45221,f885(x45222)),f888(x45221,f885(x45222))),x45222)),f335(f335(f8(f888(f888(x45221,f885(x45222)),f888(f885(x45222),f888(x45221,f885(x45222)))),f888(f885(x45222),f888(f888(x45221,f885(x45222)),f888(x45221,f885(x45222)))),x45221),f7(f888(x45221,f885(x45222)),f885(x45222),f888(x45221,f885(x45222)))),f335(f7(f888(x45221,f885(x45222)),x45221,f888(f885(x45222),f888(x45221,f885(x45222)))),f67(x45221,f885(x45222)))))),f235(x45222)))),x45223),f335(f162(f887(x45221,x45222)),x45224)),f180(x45221,x45222,x45223,f335(f179(x45221,x45222),x45224)))
% 59.73/59.65 [3730]E(f335(f335(f169(x37301),x37302),f335(f335(f169(x37301),x37303),x37304)),f335(f335(f169(x37301),f335(f335(f240(a881),x37302),x37303)),x37304))
% 59.73/59.65 [3731]E(f335(f335(f131(x37311),x37312),f335(f335(f131(x37311),x37313),x37314)),f335(f335(f131(x37311),f335(f335(f75(a881),x37312),x37313)),x37314))
% 59.73/59.65 [3743]E(f335(f335(f127(x37431),f335(f335(f144(x37431),x37432),x37433)),x37434),f335(f335(f144(x37431),x37432),f335(f335(f127(x37431),x37433),x37434)))
% 59.73/59.65 [3744]E(f335(f335(f127(x37441),f335(f335(f127(x37441),x37442),x37443)),x37444),f335(f335(f127(x37441),x37442),f335(f335(f127(x37441),x37443),x37444)))
% 59.73/59.65 [3828]E(f335(f335(f158(x38281),f335(f335(f144(x38281),x38282),x38283)),x38284),f185(x38281,x38282,f335(f158(x38281),x38283),x38284))
% 59.73/59.65 [3837]E(f335(f335(f183(x38371,x38371),x38372),f335(f335(f183(x38371,x38371),x38373),x38374)),f335(f335(f183(x38371,x38371),f335(f335(f76(a881),x38373),x38372)),x38374))
% 59.73/59.65 [3865]E(f335(f335(f104(f888(x38651,a879)),x38652),f335(f335(f312(x38651),x38653),x38654)),f335(f335(f312(x38651),x38653),f335(f335(f104(f888(x38651,a879)),x38652),x38654)))
% 59.73/59.65 [3880]E(f335(f335(f335(f183(x38801,x38801),x38802),x38803),f335(x38803,x38804)),f335(x38803,f335(f335(f335(f183(x38801,x38801),x38802),x38803),x38804)))
% 59.73/59.65 [3888]E(f335(f335(f291(x38881,x38882,x38883),f188(f888(f887(x38881,x38882),a879))),x38884),f188(f888(f887(x38881,x38883),a879)))
% 59.73/59.65 [3903]E(f335(f335(f104(f888(x39031,a879)),f335(f335(f312(x39031),x39032),x39033)),x39034),f335(f335(f312(x39031),x39032),f335(f335(f104(f888(x39031,a879)),x39033),x39034)))
% 59.73/59.65 [3923]E(f180(x39231,x39232,f335(f179(x39231,x39232),x39233),f335(f179(x39231,x39232),x39234)),f335(f179(x39231,x39232),f335(f335(f127(f887(x39231,x39232)),x39234),x39233)))
% 59.73/59.65 [3924]E(f335(f29(f887(x39241,x39242)),f335(f335(f266(x39241,x39242),x39243),f335(f16(f888(x39242,a879),x39241),x39244))),f335(f335(f76(a881),f335(f29(x39241),x39243)),f335(f29(x39242),x39244)))
% 59.73/59.65 [3930]E(f335(f335(f95(f888(x39301,a879)),f335(f335(f312(x39301),x39302),x39303)),f335(f335(f312(x39301),x39302),x39304)),f335(f335(f312(x39301),x39302),f335(f335(f95(f888(x39301,a879)),x39303),x39304)))
% 59.73/59.65 [3945]E(f335(f335(f104(f888(x39451,a879)),x39452),f335(f335(f104(f888(x39451,a879)),x39453),x39454)),f335(f335(f104(f888(x39451,a879)),x39453),f335(f335(f104(f888(x39451,a879)),x39452),x39454)))
% 59.73/59.65 [3946]E(f335(f335(f95(f888(x39461,a879)),x39462),f335(f335(f95(f888(x39461,a879)),x39463),x39464)),f335(f335(f95(f888(x39461,a879)),x39463),f335(f335(f95(f888(x39461,a879)),x39462),x39464)))
% 59.73/59.65 [3955]E(f59(x39551,x39552,f335(f335(f8(x39552,f888(x39552,x39552),x39551),x39553),x39554)),f335(f60(x39552,x39551,x39553),x39554))
% 59.73/59.65 [3965]E(f173(x39651,f335(f335(f147(f882(x39652),f882(x39651)),f335(f147(x39652,x39651),x39653)),x39654)),f335(f335(f147(f882(x39652),f882(x39651)),f335(f147(x39652,x39651),x39653)),f173(x39652,x39654)))
% 59.73/59.65 [3983]E(f335(f135(f882(x39831),f882(x39831),f127(x39831),f107(x39831)),f335(f335(f147(x39832,f882(x39831)),x39833),x39834)),f157(x39832,x39831,x39833,x39834))
% 59.73/59.65 [3984]E(f335(f135(f882(x39841),f882(x39841),f127(x39841),f107(x39841)),f335(f335(f147(x39842,f882(x39841)),x39843),x39844)),f157(x39842,x39841,x39843,x39844))
% 59.73/59.65 [3987]E(f182(x39871,x39872,x39873,f335(f74(f888(x39871,a879)),f335(f335(f312(x39871),x39874),f188(f888(x39871,a879))))),f335(f335(f335(f67(x39871,f885(x39872)),x39873),x39874),f200(x39872)))
% 59.73/59.65 [4031]E(f335(f335(f335(f67(x40311,f885(x40312)),f335(f179(x40311,x40312),x40313)),f335(f263(x40311,x40312),x40314)),f335(f235(x40312),f335(f267(x40311,x40312),x40314))),f335(f179(x40311,x40312),f335(f335(f144(f887(x40311,x40312)),x40314),x40313)))
% 59.73/59.65 [4046]E(f335(f68(x40461,x40461,x40461,f335(f335(f183(x40461,x40461),x40462),x40463)),f335(f335(f183(x40461,x40461),x40464),x40463)),f335(f335(f183(x40461,x40461),f335(f335(f75(a881),x40462),x40464)),x40463))
% 59.73/59.65 [4070]E(f335(f335(f95(f888(x40701,a879)),f335(f335(f104(f888(x40701,a879)),x40702),x40703)),f335(f335(f104(f888(x40701,a879)),x40702),x40704)),f335(f335(f104(f888(x40701,a879)),x40702),f335(f335(f95(f888(x40701,a879)),x40703),x40704)))
% 59.73/59.65 [4071]E(f335(f335(f95(f888(x40711,a879)),f335(f335(f23(f888(x40711,a879)),x40712),x40713)),f335(f335(f23(f888(x40711,a879)),x40712),x40714)),f335(f335(f23(f888(x40711,a879)),x40712),f335(f335(f104(f888(x40711,a879)),x40713),x40714)))
% 59.73/59.65 [4072]E(f335(f335(f104(f888(x40721,a879)),f335(f335(f23(f888(x40721,a879)),x40722),x40723)),f335(f335(f23(f888(x40721,a879)),x40722),x40724)),f335(f335(f23(f888(x40721,a879)),x40722),f335(f335(f95(f888(x40721,a879)),x40723),x40724)))
% 59.73/59.65 [4073]E(f335(f335(f104(f888(x40731,a879)),f335(f335(f95(f888(x40731,a879)),x40732),x40733)),f335(f335(f95(f888(x40731,a879)),x40732),x40734)),f335(f335(f95(f888(x40731,a879)),x40732),f335(f335(f104(f888(x40731,a879)),x40733),x40734)))
% 59.73/59.65 [4074]E(f335(f335(f23(f888(x40741,a879)),f335(f335(f95(f888(x40741,a879)),x40742),x40743)),f335(f335(f95(f888(x40741,a879)),x40742),x40744)),f335(f335(f95(f888(x40741,a879)),x40742),f335(f335(f23(f888(x40741,a879)),x40743),x40744)))
% 59.73/59.65 [4080]E(f335(f29(f887(x40801,x40802)),f335(f335(f266(x40801,x40802),f335(f335(f312(x40801),x40803),f188(f888(x40801,a879)))),f335(f16(f888(x40802,a879),x40801),x40804))),f335(f29(x40802),x40804))
% 59.73/59.65 [4117]E(f335(f335(f34(x41171,f888(x41172,a879)),x41173),f335(f335(f8(f888(x41172,a879),f888(x41172,a879),x41171),f74(f888(x41172,a879))),x41174)),f335(f74(f888(x41172,a879)),f335(f335(f33(x41171,f888(x41172,a879)),x41173),x41174)))
% 59.73/59.65 [4118]E(f335(f335(f33(x41181,f888(x41182,a879)),x41183),f335(f335(f8(f888(x41182,a879),f888(x41182,a879),x41181),f74(f888(x41182,a879))),x41184)),f335(f74(f888(x41182,a879)),f335(f335(f34(x41181,f888(x41182,a879)),x41183),x41184)))
% 59.73/59.65 [4134]E(f335(f335(f291(x41341,x41341,x41341),f335(f335(f183(f887(x41341,x41341),a879),x41342),x41343)),f335(f335(f183(f887(x41341,x41341),a879),x41344),x41343)),f335(f335(f183(f887(x41341,x41341),a879),f335(f335(f75(a881),x41342),x41344)),x41343))
% 59.73/59.65 [4165]E(f335(f335(f34(x41651,f888(f888(x41652,a879),a879)),x41653),f335(f335(f8(f888(x41652,a879),f888(f888(x41652,a879),a879),x41651),f311(x41652)),x41654)),f335(f311(x41652),f335(f335(f34(x41651,f888(x41652,a879)),x41653),x41654)))
% 59.73/59.65 [4193]E(f335(f335(f33(f888(x41931,a879),f888(x41932,a879)),x41933),f335(f335(f7(f888(x41931,a879),f888(x41931,f888(x41932,a879)),f888(x41932,a879)),f33(x41931,f888(x41932,a879))),x41934)),f335(f335(f33(x41931,f888(x41932,a879)),f31(f888(x41931,a879),x41933)),x41934))
% 59.73/59.65 [4194]E(f335(f335(f34(f888(x41941,a879),f888(x41942,a879)),x41943),f335(f335(f7(f888(x41941,a879),f888(x41941,f888(x41942,a879)),f888(x41942,a879)),f34(x41941,f888(x41942,a879))),x41944)),f335(f335(f34(x41941,f888(x41942,a879)),f31(f888(x41941,a879),x41943)),x41944))
% 59.73/59.65 [4195]E(f335(f335(f33(f888(x41951,a879),f888(x41952,a879)),x41953),f335(f335(f7(f888(x41951,a879),f888(x41951,f888(x41952,a879)),f888(x41952,a879)),f33(x41951,f888(x41952,a879))),x41954)),f335(f335(f33(x41951,f888(x41952,a879)),f31(f888(x41951,a879),x41953)),x41954))
% 59.73/59.65 [4196]E(f335(f335(f34(f888(x41961,a879),f888(x41962,a879)),x41963),f335(f335(f7(f888(x41961,a879),f888(x41961,f888(x41962,a879)),f888(x41962,a879)),f34(x41961,f888(x41962,a879))),x41964)),f335(f335(f34(x41961,f888(x41962,a879)),f31(f888(x41961,a879),x41963)),x41964))
% 59.73/59.65 [4201]E(f335(f335(f147(x42011,x42012),x42013),f335(f135(f882(x42011),f882(x42011),f127(x42011),f107(x42011)),x42014)),f335(f135(f882(x42012),f882(x42012),f127(x42012),f107(x42012)),f335(f335(f147(f882(x42011),f882(x42012)),f335(f147(x42011,x42012),x42013)),x42014)))
% 59.73/59.65 [4205]E(f185(f882(x42051),f107(x42051),f335(f335(f8(f882(x42051),f882(x42051),a881),f335(f144(x42051),x42052)),f335(f335(f7(a881,f882(x42051),f882(x42051)),f169(x42051)),x42053)),x42054),f335(f335(f169(x42051),x42054),f335(f335(f144(x42051),x42052),x42053)))
% 59.73/59.65 [4248]P1(f335(f335(f242(f888(x42481,a879)),f335(f313(x42482,x42481,x42483),f335(f314(x42482,x42481,x42483),x42484))),x42484))
% 59.73/59.65 [4251]E(f335(f313(f887(x42511,x42512),f887(x42512,x42511),f335(f268(x42511,x42512,f887(x42512,x42511)),f335(f7(x42512,x42511,f887(x42512,x42511)),f264(x42512,x42511)))),f335(f335(f266(x42511,x42512),x42513),f335(f16(f888(x42512,a879),x42511),x42514))),f335(f335(f266(x42512,x42511),x42514),f335(f16(f888(x42511,a879),x42512),x42513)))
% 59.73/59.65 [4260]E(f335(f335(f33(x42601,f888(x42602,a879)),x42603),f335(f335(f8(f888(x42601,a879),f888(x42602,a879),x42601),f288(x42601,x42602,x42604)),f335(f335(f7(x42601,f888(x42601,a879),f888(x42601,a879)),f312(x42601)),f188(f888(x42601,a879))))),f335(f288(x42601,x42602,x42604),x42603))
% 59.73/59.65 [4261]E(f335(f335(f33(x42611,f888(x42612,a879)),x42613),f335(f335(f8(f888(x42611,a879),f888(x42612,a879),x42611),f314(x42612,x42611,x42614)),f335(f335(f7(x42611,f888(x42611,a879),f888(x42611,a879)),f312(x42611)),f188(f888(x42611,a879))))),f335(f314(x42612,x42611,x42614),x42613))
% 59.73/59.65 [4341]E(f335(f335(f127(x43411),f335(f129(x43411,f335(f335(f8(a879,a879,x43411),a330),f335(a332,x43412))),x43413)),f335(f129(x43411,f335(f335(f8(a879,a879,x43411),a330),f335(a332,x43412))),x43414)),f335(f129(x43411,f335(f335(f8(a879,a879,x43411),a330),f335(a332,x43412))),f335(f335(f127(x43411),x43413),x43414)))
% 59.73/59.65 [4354]E(f335(f335(f104(f888(x43541,a879)),f335(f335(f104(f888(x43541,a879)),f335(f335(f95(f888(x43541,a879)),x43542),x43543)),f335(f335(f95(f888(x43541,a879)),x43543),x43544))),f335(f335(f95(f888(x43541,a879)),x43544),x43542)),f335(f335(f95(f888(x43541,a879)),f335(f335(f95(f888(x43541,a879)),f335(f335(f104(f888(x43541,a879)),x43542),x43543)),f335(f335(f104(f888(x43541,a879)),x43543),x43544))),f335(f335(f104(f888(x43541,a879)),x43544),x43542)))
% 59.73/59.65 [4418]E(f335(f135(f882(x44181),f882(x44181),f127(x44181),f107(x44181)),f335(f335(f147(x44182,f882(x44181)),f335(f335(f7(x44182,f882(x44181),f882(x44181)),f335(f335(f8(x44181,f888(f882(x44181),f882(x44181)),x44182),f144(x44181)),x44183)),f107(x44181))),x44184)),f335(f335(f147(x44182,x44181),x44183),x44184))
% 59.73/59.65 [4429]E(f335(f335(f81(a1,x44291),f335(f97(a1),f335(f335(f75(a1),x44292),a91))),f335(f335(f18(a1,x44291,x44291),f335(f335(f7(a1,x44291,f888(x44291,x44291)),f335(f335(f8(a879,f888(x44291,f888(x44291,x44291)),a1),f88(x44291)),a193)),x44293)),f335(f335(f8(a881,x44291,a1),x44294),a98))),f185(x44291,x44293,x44294,f335(f97(a881),x44292)))
% 59.73/59.65 [4604]~P1(f335(f335(f188(f888(x46041,f888(x46042,a879))),x46043),x46044))
% 59.73/59.65 [3891]E(f335(f335(f158(x38911),f335(f335(f127(x38911),x38912),x38913)),f335(f335(f75(a881),f335(f189(f882(x38911)),x38912)),x38914)),f335(f335(f158(x38911),x38913),x38914))
% 59.73/59.65 [3897]E(f335(f335(f131(x38971),x38972),f335(f335(f169(x38971),f335(f335(f75(a881),x38973),x38972)),x38974)),f335(f335(f169(x38971),x38973),f335(f335(f131(x38971),x38972),x38974)))
% 59.73/59.65 [4001]E(f335(f335(f104(f888(x40011,a879)),f335(f260(x40012,x40011),x40013)),f335(f260(x40012,x40011),x40014)),f335(f260(x40012,x40011),f335(f335(f104(f888(f887(x40012,x40011),a879)),x40013),x40014)))
% 59.73/59.65 [4002]E(f335(f335(f104(f888(x40021,a879)),f335(f262(x40021,x40022),x40023)),f335(f262(x40021,x40022),x40024)),f335(f262(x40021,x40022),f335(f335(f104(f888(f887(x40021,x40022),a879)),x40023),x40024)))
% 59.73/59.65 [4007]E(f335(f335(f104(f888(x40071,a879)),f335(f335(f104(f888(x40071,a879)),x40072),x40073)),x40074),f335(f335(f104(f888(x40071,a879)),x40072),f335(f335(f104(f888(x40071,a879)),x40073),x40074)))
% 59.73/59.65 [4008]E(f335(f335(f23(f888(x40081,a879)),f335(f335(f95(f888(x40081,a879)),x40082),x40083)),x40084),f335(f335(f95(f888(x40081,a879)),x40082),f335(f335(f23(f888(x40081,a879)),x40083),x40084)))
% 59.73/59.65 [4009]E(f335(f335(f95(f888(x40091,a879)),f335(f335(f95(f888(x40091,a879)),x40092),x40093)),x40094),f335(f335(f95(f888(x40091,a879)),x40092),f335(f335(f95(f888(x40091,a879)),x40093),x40094)))
% 59.73/59.65 [4048]E(f335(f335(f104(f888(f887(x40481,x40482),a879)),f335(f289(x40482,x40481),x40483)),f335(f289(x40482,x40481),x40484)),f335(f289(x40482,x40481),f335(f335(f104(f888(f887(x40482,x40481),a879)),x40483),x40484)))
% 59.73/59.65 [4049]E(f335(f335(f95(f888(f887(x40491,x40492),a879)),f335(f289(x40492,x40491),x40493)),f335(f289(x40492,x40491),x40494)),f335(f289(x40492,x40491),f335(f335(f95(f888(f887(x40492,x40491),a879)),x40493),x40494)))
% 59.73/59.65 [4063]E(f335(f335(f104(f888(x40631,f888(x40632,a879))),f253(x40632,x40631,x40633)),f253(x40632,x40631,x40634)),f253(x40632,x40631,f335(f335(f104(f888(x40632,f888(x40631,a879))),x40633),x40634)))
% 59.73/59.65 [4064]E(f335(f335(f95(f888(x40641,f888(x40642,a879))),f253(x40642,x40641,x40643)),f253(x40642,x40641,x40644)),f253(x40642,x40641,f335(f335(f95(f888(x40642,f888(x40641,a879))),x40643),x40644)))
% 59.73/59.65 [4121]E(f335(f335(f95(f888(x41211,a879)),f335(f335(f104(f888(x41211,a879)),x41212),x41213)),f335(f335(f104(f888(x41211,a879)),x41214),x41213)),f335(f335(f104(f888(x41211,a879)),f335(f335(f95(f888(x41211,a879)),x41212),x41214)),x41213))
% 59.73/59.65 [4122]E(f335(f335(f104(f888(x41221,a879)),f335(f335(f23(f888(x41221,a879)),x41222),x41223)),f335(f335(f23(f888(x41221,a879)),x41224),x41223)),f335(f335(f23(f888(x41221,a879)),f335(f335(f104(f888(x41221,a879)),x41222),x41224)),x41223))
% 59.73/59.65 [4123]E(f335(f335(f104(f888(x41231,a879)),f335(f335(f95(f888(x41231,a879)),x41232),x41233)),f335(f335(f95(f888(x41231,a879)),x41234),x41233)),f335(f335(f95(f888(x41231,a879)),f335(f335(f104(f888(x41231,a879)),x41232),x41234)),x41233))
% 59.73/59.65 [4124]E(f335(f335(f23(f888(x41241,a879)),f335(f335(f95(f888(x41241,a879)),x41242),x41243)),f335(f335(f95(f888(x41241,a879)),x41244),x41243)),f335(f335(f95(f888(x41241,a879)),f335(f335(f23(f888(x41241,a879)),x41242),x41244)),x41243))
% 59.73/59.65 [4125]E(f335(f335(f23(f888(x41251,a879)),f335(f335(f95(f888(x41251,a879)),x41252),x41253)),f335(f335(f95(f888(x41251,a879)),x41254),x41253)),f335(f335(f23(f888(x41251,a879)),f335(f335(f95(f888(x41251,a879)),x41252),x41253)),x41254))
% 59.73/59.65 [4137]E(f335(f335(f23(f888(x41371,a879)),f335(f335(f23(f888(x41371,a879)),x41372),f335(f335(f312(x41371),x41373),f188(f888(x41371,a879))))),x41374),f335(f335(f23(f888(x41371,a879)),x41372),f335(f335(f312(x41371),x41373),x41374)))
% 59.73/59.65 [4192]E(f335(f335(f104(f888(x41921,a879)),f335(f335(f312(x41921),x41922),f335(f335(f312(x41921),x41923),f188(f888(x41921,a879))))),f335(f287(x41921),x41924)),f335(f287(x41921),f335(f335(f312(f887(x41921,x41921)),f335(f335(f264(x41921,x41921),x41922),x41923)),x41924)))
% 59.73/59.65 [4222]E(f335(f335(f33(a881,f888(x42221,a879)),f335(f303(a881),x42222)),f335(f335(f8(a881,f888(x42221,a879),a881),x42223),f335(f335(f7(a881,a881,a881),f75(a881)),x42224))),f335(f335(f33(a881,f888(x42221,a879)),f305(a881,x42224,f335(f335(f75(a881),x42222),x42224))),x42223))
% 59.73/59.65 [4223]E(f168(x42231,f335(f288(x42231,x42231,x42232),f335(f335(f312(x42231),x42233),f188(f888(x42231,a879)))),f335(f288(f882(x42231),f882(x42231),f151(x42231,x42232)),f335(f335(f312(f882(x42231)),x42234),f188(f888(f882(x42231),a879))))),f335(f288(f882(x42231),f882(x42231),f151(x42231,x42232)),f335(f335(f312(f882(x42231)),f335(f335(f144(x42231),x42233),x42234)),f188(f888(f882(x42231),a879)))))
% 59.73/59.65 [4287]E(f335(f179(x42871,x42872),f335(f335(f147(x42871,f887(x42871,x42872)),f335(f335(f18(x42871,x42872,f887(x42871,x42872)),f264(x42871,x42872)),x42873)),x42874)),f182(x42871,x42872,f335(f68(x42872,f885(x42872),x42871,f235(x42872)),x42873),f335(f166(x42871),x42874)))
% 59.73/59.65 [4292]E(f335(f249(x42921),f335(f335(f7(x42921,f888(x42922,a879),a879),f335(f335(f8(x42922,f888(f888(x42922,a879),a879),x42921),f337(x42922)),x42923)),x42924)),f335(f314(x42921,x42922,x42923),x42924))
% 59.73/59.65 [4387]E(f335(f249(x43871),f335(f335(f7(x43871,f888(f887(x43872,x43871),a879),a879),f335(f335(f8(f887(x43872,x43871),f888(f888(f887(x43872,x43871),a879),a879),x43871),f337(f887(x43872,x43871))),f335(f264(x43872,x43871),x43873))),x43874)),f335(f288(x43872,x43871,x43874),f335(f335(f312(x43872),x43873),f188(f888(x43872,a879)))))
% 59.73/59.65 [4401]E(f335(f335(f147(f887(x44011,a881),x44011),f263(x44011,a881)),f335(f129(f887(x44011,a881),f335(f335(f8(a881,a879,f887(x44011,a881)),x44012),f335(f335(f8(a881,a881,f887(x44011,a881)),a106),f267(x44011,a881)))),f335(f335(f175(x44011,a881),x44013),x44014))),f335(f335(f147(f887(x44011,a881),x44011),f263(x44011,a881)),f335(f129(f887(x44011,a881),f335(f335(f8(a881,a879,f887(x44011,a881)),x44012),f267(x44011,a881))),f335(f335(f175(x44011,a881),x44013),f335(f335(f147(a881,a881),a106),x44014)))))
% 59.73/59.65 [4410]P1(f335(f335(f242(f888(f888(x44101,a879),a879)),f335(f335(f33(x44102,f888(f888(x44101,a879),a879)),x44103),f335(f335(f8(f888(x44101,a879),f888(f888(x44101,a879),a879),x44102),f311(x44101)),x44104))),f335(f311(x44101),f335(f335(f33(x44102,f888(x44101,a879)),x44103),x44104))))
% 59.73/59.65 [4453]E(f335(f335(f81(a1,x44531),f335(f97(a1),f335(f335(f75(a1),x44532),a91))),f335(f335(f18(a1,x44531,x44531),f335(f335(f7(a1,x44531,f888(x44531,x44531)),f335(f335(f8(a879,f888(x44531,f888(x44531,x44531)),a1),f88(x44531)),a193)),x44533)),f335(f335(f18(a1,x44531,x44531),f335(f335(f8(a881,f888(x44531,x44531),a1),x44534),a98)),f335(f335(f8(a881,x44531,a1),f184(x44531,x44533,x44534)),a98)))),f335(f184(x44531,x44533,x44534),f335(f97(a881),x44532)))
% 59.73/59.65 [4456]E(f335(f335(f147(x44561,x44562),f335(f68(f885(x44562),x44562,x44561,f239(x44562)),x44563)),f335(f129(x44561,f335(f335(f8(a879,a879,x44561),a330),f335(f335(f7(x44561,f885(x44562),a879),f335(f335(f8(f885(x44562),f888(f885(x44562),a879),x44561),a332),x44563)),f200(x44562)))),x44564)),f156(x44561,x44562,x44563,x44564))
% 59.73/59.65 [4479]E(f335(f249(f887(x44791,x44792)),f335(f268(x44791,x44792,a879),f335(f335(f7(x44791,f888(x44792,a879),f888(x44792,a879)),f335(f335(f8(f888(a879,a879),f888(f888(x44792,a879),f888(x44792,a879)),x44791),f8(a879,a879,x44792)),f335(f335(f8(a879,f888(a879,a879),x44791),a333),f335(f335(f7(x44791,f888(x44791,a879),a879),f337(x44791)),x44793)))),f335(f335(f7(x44792,f888(x44792,a879),a879),f337(x44792)),x44794)))),f231(x44791,x44792,x44793,x44794))
% 59.73/59.65 [4512]E(f335(f335(f33(x45121,f888(f887(x45121,x45122),a879)),x45123),f335(f335(f18(x45121,f888(x45122,f888(f887(x45121,x45122),a879)),f888(f887(x45121,x45122),a879)),f335(f335(f8(f888(x45122,a879),f888(f888(x45122,f888(f887(x45121,x45122),a879)),f888(f887(x45121,x45122),a879)),x45121),f33(x45122,f888(f887(x45121,x45122),a879))),x45124)),f335(f335(f7(x45121,f888(f887(x45121,x45122),a879),f888(x45122,f888(f887(x45121,x45122),a879))),f335(f335(f8(f888(x45122,f888(f888(f887(x45121,x45122),a879),f888(f887(x45121,x45122),a879))),f888(f888(f887(x45121,x45122),a879),f888(x45122,f888(f887(x45121,x45122),a879))),x45121),f7(x45122,f888(f887(x45121,x45122),a879),f888(f887(x45121,x45122),a879))),f335(f335(f8(f888(x45122,f887(x45121,x45122)),f888(x45122,f888(f888(f887(x45121,x45122),a879),f888(f887(x45121,x45122),a879))),x45121),f335(f8(f887(x45121,x45122),f888(f888(f887(x45121,x45122),a879),f888(f887(x45121,x45122),a879)),x45122),f312(f887(x45121,x45122)))),f264(x45121,x45122)))),f188(f888(f887(x45121,x45122),a879))))),f335(f335(f266(x45121,x45122),x45123),x45124))
% 59.73/59.65 [4058]E(f335(f335(f127(x40581),f335(f335(f169(x40581),x40582),x40583)),f335(f335(f169(x40581),f335(f335(f23(a881),x40582),f335(f189(f882(x40581)),x40583))),x40584)),f335(f335(f169(x40581),x40582),f335(f335(f127(x40581),x40583),x40584)))
% 59.73/59.65 [4059]E(f335(f335(f127(x40591),f335(f335(f131(x40591),x40592),x40593)),f335(f335(f131(x40591),f335(f335(f23(a881),x40592),f335(f189(f882(x40591)),x40593))),x40594)),f335(f335(f131(x40591),x40592),f335(f335(f127(x40591),x40593),x40594)))
% 59.73/59.65 [4110]E(f335(f335(f75(a881),f335(f335(f76(a881),x41101),x41102)),f335(f335(f75(a881),f335(f335(f76(a881),x41103),x41102)),x41104)),f335(f335(f75(a881),f335(f335(f76(a881),f335(f335(f75(a881),x41101),x41103)),x41102)),x41104))
% 59.73/59.65 [4265]E(f85(x42651,f335(f335(f7(x42651,x42652,a879),f335(f335(f8(x42652,f888(x42652,a879),x42651),a332),x42653)),x42654)),f335(f87(x42651,x42652,f252(f888(x42651,a879)),x42653),x42654))
% 59.73/59.65 [4317]P1(f335(f335(f242(f888(x43171,a879)),f335(f335(f23(f888(x43171,a879)),f335(f260(x43172,x43171),x43173)),f335(f260(x43172,x43171),x43174))),f335(f260(x43172,x43171),f335(f335(f23(f888(f887(x43172,x43171),a879)),x43173),x43174))))
% 59.73/59.65 [4318]P1(f335(f335(f242(f888(x43181,a879)),f335(f335(f23(f888(x43181,a879)),f335(f262(x43181,x43182),x43183)),f335(f262(x43181,x43182),x43184))),f335(f262(x43181,x43182),f335(f335(f23(f888(f887(x43181,x43182),a879)),x43183),x43184))))
% 59.73/59.65 [4431]E(f335(f335(f75(a1),f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),x44311),x44312)),f188(f888(f887(a881,a881),a879)))))),f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),x44313),x44314)),f188(f888(f887(a881,a881),a879)))))),f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),f335(f335(f75(a881),x44311),x44313)),f335(f335(f75(a881),x44312),x44314))),f188(f888(f887(a881,a881),a879))))))
% 59.73/59.65 [4474]E(f335(f335(f76(a1),f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),x44741),x44742)),f188(f888(f887(a881,a881),a879)))))),f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),x44743),x44744)),f188(f888(f887(a881,a881),a879)))))),f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),f335(f335(f75(a881),f335(f335(f76(a881),x44741),x44743)),f335(f335(f76(a881),x44742),x44744))),f335(f335(f75(a881),f335(f335(f76(a881),x44741),x44744)),f335(f335(f76(a881),x44742),x44743)))),f188(f888(f887(a881,a881),a879))))))
% 59.73/59.65 [4494]E(f335(f249(x44941),f335(f335(f8(f888(x44942,a879),a879,x44941),f83(x44942)),f335(f335(f8(f888(x44942,a879),f888(x44942,a879),x44941),f335(f18(x44942,a879,a879),f335(f335(f8(a879,f888(a879,a879),x44942),a338),f335(f335(f7(x44942,f888(x44942,a879),a879),f337(x44942)),x44943)))),f335(f335(f7(x44941,f888(x44942,f888(x44941,a879)),f888(x44942,a879)),f335(f335(f8(f888(f888(x44941,a879),a879),f888(f888(x44942,f888(x44941,a879)),f888(x44942,a879)),x44941),f8(f888(x44941,a879),a879,x44942)),f337(x44941))),x44944)))),f335(f335(f34(x44942,f888(x44941,a879)),x44943),x44944))
% 59.73/59.65 [4526]E(f335(f335(f291(x45261,x45261,x45261),f335(f335(f312(f887(x45261,x45261)),f335(f335(f264(x45261,x45261),x45262),x45263)),x45264)),f310(x45261,f335(f335(f312(f887(x45261,x45261)),f335(f335(f264(x45261,x45261),x45262),x45263)),x45264))),f335(f335(f104(f888(f887(x45261,x45261),a879)),f335(f335(f291(x45261,x45261,x45261),x45264),f310(x45261,x45264))),f335(f249(f887(x45261,x45261)),f335(f268(x45261,x45261,a879),f335(f335(f7(x45261,f888(x45261,a879),f888(x45261,a879)),f335(f335(f8(f888(a879,a879),f888(f888(x45261,a879),f888(x45261,a879)),x45261),f8(a879,a879,x45261)),f335(f335(f8(a879,f888(a879,a879),x45261),a333),f335(f335(f7(x45261,f888(f887(x45261,x45261),a879),a879),f335(f335(f8(f887(x45261,x45261),f888(f888(f887(x45261,x45261),a879),a879),x45261),f337(f887(x45261,x45261))),f335(f335(f7(x45261,x45261,f887(x45261,x45261)),f264(x45261,x45261)),x45262))),f310(x45261,x45264))))),f335(f335(f7(x45261,f888(f887(x45261,x45261),a879),a879),f335(f335(f8(f887(x45261,x45261),f888(f888(f887(x45261,x45261),a879),a879),x45261),f337(f887(x45261,x45261))),f335(f264(x45261,x45261),x45263))),f310(x45261,x45264)))))))
% 59.73/59.65 [4319]E(f335(f129(x43191,f335(f335(f18(x43191,a879,a879),f335(f335(f8(a879,f888(a879,a879),x43191),a333),x43192)),x43193)),x43194),f335(f129(x43191,x43193),f335(f129(x43191,x43192),x43194)))
% 59.73/59.65 [4425]E(f335(f335(f127(x44251),f335(f335(f335(f88(f882(x44251)),f335(f335(f337(a881),f2(a881)),x44252)),f335(f335(f144(x44251),x44253),f107(x44251))),f107(x44251))),f170(x44251,x44254,f335(f249(a881),f335(f335(f7(a881,f888(a881,a879),a879),f335(f335(f8(a881,f888(f888(a881,a879),a879),a881),f337(a881)),a106)),x44252)))),f170(x44251,f335(f335(f144(x44251),x44253),x44254),x44252))
% 59.73/59.65 [4520]E(f335(f249(f887(x45201,x45202)),f335(f335(f8(f888(a881,a879),a879,f887(x45201,x45202)),f82(a881)),f335(f335(f7(f887(x45201,x45202),f888(a881,a879),f888(a881,a879)),f335(f335(f8(f888(a881,f888(a879,a879)),f888(f888(a881,a879),f888(a881,a879)),f887(x45201,x45202)),f18(a881,a879,a879)),f335(f335(f8(f888(a881,a879),f888(a881,f888(a879,a879)),f887(x45201,x45202)),f335(f8(a879,f888(a879,a879),a881),a333)),f335(f335(f7(f887(x45201,x45202),f888(a881,f887(x45201,x45202)),f888(a881,a879)),f335(f335(f8(f888(f887(x45201,x45202),a879),f888(f888(a881,f887(x45201,x45202)),f888(a881,a879)),f887(x45201,x45202)),f8(f887(x45201,x45202),a879,a881)),a332)),f335(f335(f18(a881,x45202,f887(x45201,x45202)),f335(f335(f8(x45201,f888(x45202,f887(x45201,x45202)),a881),f264(x45201,x45202)),f335(f158(x45201),x45203))),f335(f158(x45202),x45204)))))),f335(f335(f7(a881,a881,a879),f243(a881)),f335(f335(f240(a881),f335(f189(f882(x45201)),x45203)),f335(f189(f882(x45202)),x45204)))))),f335(f166(f887(x45201,x45202)),f335(f335(f175(x45201,x45202),x45203),x45204)))
% 59.73/59.65 [4444]E(f335(f249(f887(x44441,x44442)),f335(f268(x44441,x44442,a879),f335(f335(f7(x44441,f888(x44442,a879),f888(x44442,a879)),f335(f335(f8(f888(a879,a879),f888(f888(x44442,a879),f888(x44442,a879)),x44441),f8(a879,a879,x44442)),f335(f335(f8(a879,f888(a879,a879),x44441),a333),x44443))),x44444))),f335(f335(f266(x44441,x44442),f335(f249(x44441),x44443)),f335(f16(f888(x44442,a879),x44441),f335(f249(x44442),x44444))))
% 59.73/59.65 [4447]E(f335(f249(f887(x44471,x44472)),f335(f268(x44471,x44472,a879),f335(f335(f18(x44471,f888(x44472,a879),f888(x44472,a879)),f335(f335(f8(f888(a879,a879),f888(f888(x44472,a879),f888(x44472,a879)),x44471),f8(a879,a879,x44472)),f335(f335(f8(a879,f888(a879,a879),x44471),a333),x44473))),x44474))),f335(f335(f266(x44471,x44472),f335(f249(x44471),x44473)),f335(f335(f8(f888(x44472,a879),f888(x44472,a879),x44471),f249(x44472)),x44474)))
% 59.73/59.65 [4463]E(f335(f249(x44631),f335(f335(f8(f888(x44632,a879),a879,x44631),f83(x44632)),f335(f335(f8(f888(x44632,a879),f888(x44632,a879),x44631),f335(f18(x44632,a879,a879),f335(f335(f8(a879,f888(a879,a879),x44632),a338),f335(f335(f7(x44632,f888(x44632,a879),a879),f337(x44632)),x44633)))),x44634))),f335(f335(f34(x44632,f888(x44631,a879)),x44633),f335(f335(f8(f888(x44631,a879),f888(x44631,a879),x44632),f249(x44631)),f335(f7(x44631,x44632,a879),x44634))))
% 59.73/59.65 [4507]E(f335(f335(f147(f887(x45071,a881),x45071),f263(x45071,a881)),f335(f129(f887(x45071,a881),f335(f335(f7(f887(x45071,a881),f888(a881,a879),a879),f335(f335(f8(a881,f888(f888(a881,a879),a879),f887(x45071,a881)),f337(a881)),f267(x45071,a881))),x45072)),f335(f335(f175(x45071,a881),x45073),f132(a881,f335(f304(a881,x45074),f335(f335(f75(a881),x45074),f335(f189(f882(x45071)),x45073))))))),f335(f335(f147(f887(x45071,a881),x45071),f263(x45071,a881)),f335(f129(f887(x45071,a881),f335(f335(f7(f887(x45071,a881),f888(a881,a879),a879),f335(f335(f8(a881,f888(f888(a881,a879),a879),f887(x45071,a881)),f337(a881)),f335(f335(f7(f887(x45071,a881),a881,a881),f335(f335(f8(a881,f888(a881,a881),f887(x45071,a881)),f75(a881)),f267(x45071,a881))),x45074))),x45072)),f335(f335(f175(x45071,a881),x45073),f132(a881,f335(f304(a881,f2(a881)),f335(f189(f882(x45071)),x45073)))))))
% 59.73/59.65 [4508]E(f335(a106,f335(f335(f241(a881),f335(f189(f882(x45081)),x45082)),f335(f135(a881,f882(x45083),f335(f7(f882(x45083),a881,a881),f335(f335(f8(a881,f888(a881,a881),f882(x45083)),f241(a881)),f335(f335(f7(f882(x45083),a881,a881),f335(f335(f8(a881,f888(a881,a881),f882(x45083)),f23(a881)),f189(f882(x45083)))),f335(a106,f2(a881))))),f2(a881)),f335(f162(f882(x45083)),f335(f129(f882(x45083),f335(f335(f8(a879,a879,f882(x45083)),a330),f335(f335(f7(f882(x45083),f882(x45083),a879),a332),f107(x45083)))),x45084))))),f335(f335(f241(a881),f335(a106,f335(f189(f882(x45081)),x45082))),f335(f135(a881,f882(x45083),f335(f7(f882(x45083),a881,a881),f335(f335(f8(a881,f888(a881,a881),f882(x45083)),f241(a881)),f189(f882(x45083)))),f2(a881)),f335(f162(f882(x45083)),x45084))))
% 59.73/59.65 [4462]E(f335(f335(f127(x44621),f170(x44621,x44622,x44623)),f170(x44621,x44624,f335(f249(a881),f335(f335(f7(a881,f888(a881,a879),a879),f335(f335(f8(a881,f888(f888(a881,a879),a879),a881),f337(a881)),f335(f335(f7(a881,a881,a881),f75(a881)),f335(f189(f882(x44621)),x44622)))),x44623)))),f170(x44621,f335(f335(f127(x44621),x44622),x44624),x44623))
% 59.73/59.65 [4514]E(f335(f335(f144(f882(x45141)),f335(f335(f144(x45141),x45142),f335(f135(f882(x45141),f882(x45141),f127(x45141),f107(x45141)),f335(f335(f147(f882(x45141),f882(x45141)),f149(f882(x45141),x45141,f107(x45141),f335(f335(f8(f882(x45141),f888(f882(x45141),f882(x45141)),x45141),f16(f882(x45141),f882(x45141))),f335(f335(f7(x45141,f882(x45141),f882(x45141)),f144(x45141)),f107(x45141))))),x45143)))),f173(x45141,f335(f335(f144(f882(x45141)),x45144),f335(f135(f882(f882(x45141)),f882(f882(x45141)),f127(f882(x45141)),f107(f882(x45141))),f335(f335(f147(f882(x45141),f882(f882(x45141))),f149(f882(f882(x45141)),x45141,f107(f882(x45141)),f335(f16(f888(f882(x45141),f882(f882(x45141))),x45141),f335(f335(f7(f882(x45141),f882(f882(x45141)),f882(f882(x45141))),f144(f882(x45141))),f107(f882(x45141)))))),x45143))))),f173(x45141,f335(f335(f144(f882(x45141)),f335(f335(f144(x45141),x45142),x45144)),x45143)))
% 59.73/59.65 [4521]E(f335(f249(f887(x45211,x45211)),f335(f268(x45211,x45211,a879),f335(f335(f7(x45211,f888(f887(x45212,x45212),a879),f888(x45211,a879)),f335(f335(f8(f888(x45211,f888(f888(f887(x45212,x45212),a879),a879)),f888(f888(f887(x45212,x45212),a879),f888(x45211,a879)),x45211),f7(x45211,f888(f887(x45212,x45212),a879),a879)),f335(f335(f8(f888(x45211,f887(x45212,x45212)),f888(x45211,f888(f888(f887(x45212,x45212),a879),a879)),x45211),f335(f8(f887(x45212,x45212),f888(f888(f887(x45212,x45212),a879),a879),x45211),f337(f887(x45212,x45212)))),f335(f335(f7(x45211,f888(x45211,x45212),f888(x45211,f887(x45212,x45212))),f335(f335(f8(f888(x45212,f887(x45212,x45212)),f888(f888(x45211,x45212),f888(x45211,f887(x45212,x45212))),x45211),f8(x45212,f887(x45212,x45212),x45211)),f335(f335(f8(x45212,f888(x45212,f887(x45212,x45212)),x45211),f264(x45212,x45212)),x45213))),x45213)))),x45214))),f335(f335(f290(x45212,x45211),x45214),x45213))
% 59.73/59.65 [3626]E(f335(f335(f147(x36261,x36262),x36263),f163(x36261,x36264,x36265)),f163(x36262,x36264,f335(x36263,x36265)))
% 59.73/59.65 [3999]E(f335(f180(x39991,x39992,x39993,x39994),x39995),f335(f237(f885(x39992),x39992,f335(x39993,x39995),f235(x39992)),f335(x39994,x39995)))
% 59.73/59.65 [4085]E(f180(x40851,x40852,f180(x40851,x40852,x40853,x40854),x40855),f180(x40851,x40852,x40853,f180(x40851,x40852,x40854,x40855)))
% 59.73/59.65 [4266]E(f265(x42661,x42662,x42663,f253(x42662,x42661,x42664),f253(x42663,x42662,x42665)),f253(x42663,x42661,f265(x42663,x42662,x42661,x42665,x42664)))
% 59.73/59.65 [4273]E(f335(f335(f104(f888(x42731,a879)),f335(f166(x42731),f335(f335(f169(x42731),f335(f189(f882(x42732)),x42733)),x42734))),f177(x42731,x42732,x42735)),f177(x42731,x42732,f181(x42731,x42732,x42735,x42734,x42733)))
% 59.73/59.65 [3820]E(f335(f335(f268(x38201,x38202,x38203),x38204),x38205),f335(f335(x38204,f335(f263(x38201,x38202),x38205)),f335(f267(x38201,x38202),x38205)))
% 59.73/59.65 [3821]E(f335(f335(f268(x38211,x38212,x38213),x38214),x38215),f335(f335(x38214,f335(f263(x38211,x38212),x38215)),f335(f267(x38211,x38212),x38215)))
% 59.73/59.65 [3822]E(f335(f335(f268(x38221,x38222,x38223),x38224),x38225),f335(f335(x38224,f335(f263(x38221,x38222),x38225)),f335(f267(x38221,x38222),x38225)))
% 59.73/59.65 [3849]E(f335(f237(x38491,x38492,x38493,x38494),f335(f235(x38492),x38495)),f335(x38494,x38495))
% 59.73/59.65 [3857]E(f335(f335(f335(f60(x38571,x38572,x38573),x38574),x38575),f188(f888(x38572,a879))),x38575)
% 59.73/59.65 [3998]E(f120(f885(x39981),f335(f335(f201(x39982,x39981),x39983),x39984),f116(x39982,x39981,x39983,x39985)),f116(x39982,x39981,x39983,f120(f885(x39982),x39984,x39985)))
% 59.73/59.65 [4032]E(f238(x40321,x40322,x40323,x40324,f335(f235(x40322),x40325)),f335(x40324,x40325))
% 59.73/59.65 [4143]E(f335(f68(f885(x41431),f885(x41432),f885(x41433),f335(f201(x41431,x41432),x41434)),f335(f201(x41433,x41431),x41435)),f335(f201(x41433,x41432),f335(f68(x41431,x41432,x41433,x41434),x41435)))
% 59.73/59.65 [4144]E(f335(f68(f882(x41441),f882(x41442),f882(x41443),f335(f147(x41441,x41442),x41444)),f335(f147(x41443,x41441),x41445)),f335(f147(x41443,x41442),f335(f68(x41441,x41442,x41443,x41444),x41445)))
% 59.73/59.65 [4145]E(f335(f68(f882(x41451),f882(x41452),f882(x41453),f335(f147(x41451,x41452),x41454)),f335(f147(x41453,x41451),x41455)),f335(f147(x41453,x41452),f335(f68(x41451,x41452,x41453,x41454),x41455)))
% 59.73/59.65 [4202]E(f335(f237(x42021,f887(x42022,f883(x42022)),x42023,f335(f268(x42022,f883(x42022),x42021),x42024)),f335(f128(x42022),x42025)),f121(x42021,x42022,x42023,x42024,x42025))
% 59.73/59.66 [4203]E(f115(x42031,f116(x42032,f883(f885(x42031)),f335(f335(f7(x42032,a93,f883(f885(x42031))),x42033),x42034),f335(x42035,x42034))),f335(f195(x42032,x42031,x42035,x42033),x42034))
% 59.73/59.66 [4226]E(f80(x42261,f61(x42262,x42261,x42263,x42264,x42265)),f335(f335(f59(x42262,x42261,x42263),x42264),x42265))
% 59.73/59.66 [4263]E(f335(f335(f75(a881),f335(f335(f75(a881),f335(x42631,f335(f263(x42632,x42633),x42634))),f335(x42635,f335(f267(x42632,x42633),x42634)))),f335(a106,f2(a881))),f272(x42632,x42633,x42631,x42635,x42634))
% 59.73/59.66 [4458]E(f156(x44581,x44582,f335(f335(f7(x44581,f885(x44582),f885(x44582)),f335(f335(f18(x44581,f885(x44582),f888(f885(x44582),f885(x44582))),f335(f335(f8(a879,f888(f885(x44582),f888(f885(x44582),f885(x44582))),x44581),f88(f885(x44582))),x44583)),f335(f335(f8(x44582,f885(x44582),x44581),f235(x44582)),x44584))),f200(x44582)),x44585),f335(f335(f147(x44581,x44582),x44584),f335(f129(x44581,x44583),x44585)))
% 59.73/59.66 [4596]~E(f335(f335(f335(f67(x45961,f885(x45962)),x45963),x45964),f335(f235(x45962),x45965)),f335(f16(f885(x45962),x45961),f200(x45962)))
% 59.73/59.66 [3756]E(f335(f335(f169(x37561),x37562),f335(f335(f147(x37563,x37561),x37564),x37565)),f335(f335(f147(x37563,x37561),x37564),f335(f335(f169(x37563),x37562),x37565)))
% 59.73/59.66 [3757]E(f335(f335(f131(x37571),x37572),f335(f335(f147(x37573,x37571),x37574),x37575)),f335(f335(f147(x37573,x37571),x37574),f335(f335(f131(x37573),x37572),x37575)))
% 59.73/59.66 [3789]E(f335(f335(f147(x37891,x37892),x37893),f335(f335(f144(x37891),x37894),x37895)),f335(f335(f144(x37892),f335(x37893,x37894)),f335(f335(f147(x37891,x37892),x37893),x37895)))
% 59.73/59.66 [3853]E(f335(f313(x38531,x38532,x38533),f335(f335(f312(x38531),x38534),x38535)),f335(f335(f312(x38532),f335(x38533,x38534)),f335(f313(x38531,x38532,x38533),x38535)))
% 59.73/59.66 [3881]E(f167(x38811,f335(f335(f144(x38811),x38812),x38813),f335(f335(f144(x38811),x38814),x38815)),f335(f335(f144(x38811),x38812),f335(f335(f144(x38811),x38814),f167(x38811,x38813,x38815))))
% 59.73/59.66 [3917]E(f335(f335(f175(x39171,x39172),f335(f335(f169(x39171),x39173),x39174)),f335(f335(f169(x39172),x39173),x39175)),f335(f335(f169(f887(x39171,x39172)),x39173),f335(f335(f175(x39171,x39172),x39174),x39175)))
% 59.73/59.66 [3918]E(f335(f335(f175(x39181,x39182),f335(f335(f131(x39181),x39183),x39184)),f335(f335(f131(x39182),x39183),x39185)),f335(f335(f131(f887(x39181,x39182)),x39183),f335(f335(f175(x39181,x39182),x39184),x39185)))
% 59.73/59.66 [3929]E(f335(f335(f152(x39291,f335(f335(f144(x39291),x39292),x39293)),f335(a106,x39294)),x39295),f335(f335(f144(x39291),x39292),f335(f335(f152(x39291,x39293),x39294),x39295)))
% 59.73/59.66 [3932]E(f335(f237(f885(x39321),x39322,f200(x39321),x39323),f335(f335(f16(f885(x39322),x39324),f200(x39322)),x39325)),f200(x39321))
% 59.73/59.66 [3934]E(f335(f335(f127(x39341),f335(f335(f147(x39342,x39341),x39343),x39344)),f335(f335(f147(x39342,x39341),x39343),x39345)),f335(f335(f147(x39342,x39341),x39343),f335(f335(f127(x39342),x39344),x39345)))
% 59.73/59.66 [3938]E(f335(f335(x39381,x39382),f335(f335(f255(x39383,x39384,x39381),x39382),x39385)),f335(f335(f255(x39383,x39384,x39381),x39382),f335(a106,x39385)))
% 59.73/59.66 [3969]E(f157(x39691,x39692,x39693,f335(f335(f144(x39691),x39694),x39695)),f335(f335(f127(x39692),f335(x39693,x39694)),f157(x39691,x39692,x39693,x39695)))
% 59.73/59.66 [3982]E(f335(f335(f291(x39821,x39822,x39823),f335(f289(x39822,x39821),x39824)),f335(f289(x39823,x39822),x39825)),f335(f289(x39823,x39821),f335(f335(f291(x39823,x39822,x39821),x39825),x39824)))
% 59.73/59.66 [4017]E(f335(f335(f335(f183(f882(x40171),f882(x40171)),x40172),f161(x40171)),f335(f335(f147(x40173,x40171),x40174),x40175)),f335(f335(f147(x40173,x40171),x40174),f335(f335(f335(f183(f882(x40173),f882(x40173)),x40172),f161(x40173)),x40175)))
% 59.73/59.66 [4018]E(f335(f335(f270(x40181,x40182,x40181,x40183),f335(f264(x40182,x40181),x40184)),x40185),f335(x40185,x40184))
% 59.73/59.66 [4044]E(f148(x40441,x40442,f335(f335(f147(x40443,x40441),x40444),x40445)),f148(x40443,f335(f68(x40441,a881,x40443,x40442),x40444),x40445))
% 59.73/59.66 [4108]E(f335(f335(f68(f885(x41081),f885(x41082),x41083,f335(f201(x41081,x41082),x41084)),f335(f16(f885(x41081),x41083),f200(x41081))),x41085),f200(x41082))
% 59.73/59.66 [4109]E(f171(f887(x41091,x41092),f335(f68(x41092,a879,f887(x41091,x41092),x41093),f267(x41091,x41092)),f335(f335(f175(x41091,x41092),x41094),x41095)),f335(f335(f175(x41091,x41092),x41094),f171(x41092,x41093,x41095)))
% 59.73/59.66 [4115]E(f335(f313(x41151,x41152,f335(f335(f8(x41153,x41152,x41151),x41154),x41155)),f252(f888(x41151,a879))),f335(f313(x41153,x41152,x41154),f335(f313(x41151,x41153,x41155),f252(f888(x41151,a879)))))
% 59.73/59.66 [4128]E(f171(f887(x41281,x41282),f335(f68(x41281,a879,f887(x41281,x41282),x41283),f263(x41281,x41282)),f335(f335(f175(x41281,x41282),x41284),x41285)),f335(f335(f175(x41281,x41282),f171(x41281,x41283,x41284)),x41285))
% 59.73/59.66 [4149]E(f335(f335(f104(f888(x41491,a879)),f335(f314(x41491,x41492,x41493),f335(f335(f312(x41492),x41494),f188(f888(x41492,a879))))),f335(f314(x41491,x41492,x41493),x41495)),f335(f314(x41491,x41492,x41493),f335(f335(f312(x41492),x41494),x41495)))
% 59.73/59.66 [4210]E(f335(f335(f127(f887(x42101,x42102)),f335(f335(f147(x42102,f887(x42101,x42102)),f335(f264(x42101,x42102),x42103)),x42104)),f54(x42101,x42102,x42105,x42104)),f54(x42101,x42102,f335(f335(f144(x42101),x42103),x42105),x42104))
% 59.73/59.66 [4211]E(f335(f335(f147(x42111,x42112),x42113),f171(x42111,f335(f68(x42112,a879,x42111,x42114),x42113),x42115)),f171(x42112,x42114,f335(f335(f147(x42111,x42112),x42113),x42115)))
% 59.73/59.66 [4217]E(f335(f135(x42171,x42172,f335(f7(x42172,x42171,x42171),f335(f7(x42171,x42172,x42171),x42173)),x42174),f335(f162(x42172),f335(f162(x42172),x42175))),f335(f135(x42171,x42172,x42173,x42174),x42175))
% 59.73/59.66 [4218]E(f335(f335(f335(f67(x42181,f885(x42182)),f182(x42181,x42182,x42183,x42184)),x42185),f335(x42183,x42185)),f182(x42181,x42182,x42183,f335(f335(f312(x42181),x42185),x42184)))
% 59.73/59.66 [4228]E(f335(f322(x42281,x42282,x42283,f335(f16(x42282,x42281),x42284),f335(f16(x42282,x42283),x42284)),x42285),x42284)
% 59.73/59.66 [4290]E(f335(f237(f882(x42901),x42901,f156(x42902,x42901,x42903,x42904),f335(f335(f7(x42901,f882(x42901),f882(x42901)),f144(x42901)),f156(x42902,x42901,x42903,x42904))),f335(x42903,x42905)),f156(x42902,x42901,x42903,f335(f335(f144(x42902),x42905),x42904)))
% 59.73/59.66 [4327]P1(f335(f335(f242(f888(x43271,a879)),f335(f313(x43272,x43271,x43273),f335(f335(f95(f888(x43272,a879)),x43274),x43275))),f335(f335(f95(f888(x43271,a879)),f335(f313(x43272,x43271,x43273),x43274)),f335(f313(x43272,x43271,x43273),x43275))))
% 59.73/59.66 [4328]P1(f335(f335(f242(f888(x43281,a879)),f335(f288(x43282,x43281,x43283),f335(f335(f95(f888(x43282,a879)),x43284),x43285))),f335(f335(f95(f888(x43281,a879)),f335(f288(x43282,x43281,x43283),x43284)),f335(f288(x43282,x43281,x43283),x43285))))
% 59.73/59.66 [4432]E(f335(f267(x44321,x44322),f335(f269(x44323,x44321,x44322,x44322,x44324,f25(x44322)),x44325)),f335(f267(x44323,x44322),x44325))
% 59.73/59.66 [4433]E(f335(f263(x44331,x44332),f335(f269(x44331,x44331,x44333,x44332,f25(x44331),x44334),x44335)),f335(f263(x44331,x44333),x44335))
% 59.73/59.66 [4436]E(f335(f263(x44361,x44362),f335(f269(x44363,x44361,x44362,x44362,x44364,f25(x44362)),x44365)),f335(x44364,f335(f263(x44363,x44362),x44365)))
% 59.73/59.66 [4437]E(f335(f267(x44371,x44372),f335(f269(x44371,x44371,x44373,x44372,f25(x44371),x44374),x44375)),f335(x44374,f335(f267(x44371,x44373),x44375)))
% 59.73/59.66 [4518]E(f335(f135(f888(x45181,f885(x45182)),f887(x45181,x45182),f335(f335(f8(f888(x45181,f888(x45182,f888(x45181,f885(x45182)))),f888(f887(x45181,x45182),f888(x45181,f885(x45182))),f888(x45181,f885(x45182))),f268(x45181,x45182,f888(x45181,f885(x45182)))),f335(f335(f7(f888(x45181,f885(x45182)),f888(x45182,f885(x45182)),f888(x45181,f888(x45182,f888(x45181,f885(x45182))))),f335(f335(f8(f888(x45181,f888(f888(x45182,f885(x45182)),f888(x45182,f888(x45181,f885(x45182))))),f888(f888(x45182,f885(x45182)),f888(x45181,f888(x45182,f888(x45181,f885(x45182))))),f888(x45181,f885(x45182))),f7(x45181,f888(x45182,f885(x45182)),f888(x45182,f888(x45181,f885(x45182))))),f335(f335(f8(f888(x45181,f888(f885(x45182),f888(x45181,f885(x45182)))),f888(x45181,f888(f888(x45182,f885(x45182)),f888(x45182,f888(x45181,f885(x45182))))),f888(x45181,f885(x45182))),f335(f8(f888(f885(x45182),f888(x45181,f885(x45182))),f888(f888(x45182,f885(x45182)),f888(x45182,f888(x45181,f885(x45182)))),x45181),f8(f885(x45182),f888(x45181,f885(x45182)),x45182))),f67(x45181,f885(x45182))))),f235(x45182))),x45183),f335(f335(f175(x45181,x45182),x45184),x45185)),f181(x45181,x45182,x45183,x45184,x45185))
% 59.73/59.66 [3596]E(f335(f335(f335(f335(f207(x35961),x35962),x35963),x35964),x35965),f202(x35961,x35962))
% 59.73/59.66 [3597]E(f335(f335(f335(f335(f208(x35971),x35972),x35973),x35974),x35975),f192(x35971,x35972))
% 59.73/59.66 [3739]E(f335(f335(f335(f335(f67(x37391,x37392),x37393),x37394),x37395),x37394),x37395)
% 59.73/59.66 [3970]E(f335(f335(f33(x39701,f888(x39702,a879)),f335(f335(f312(x39701),x39703),x39704)),x39705),f335(f335(f104(f888(x39702,a879)),f335(x39705,x39703)),f335(f335(f33(x39701,f888(x39702,a879)),x39704),x39705)))
% 59.73/59.66 [3971]E(f335(f335(f34(x39711,f888(x39712,a879)),f335(f335(f312(x39711),x39713),x39714)),x39715),f335(f335(f95(f888(x39712,a879)),f335(x39715,x39713)),f335(f335(f34(x39711,f888(x39712,a879)),x39714),x39715)))
% 59.73/59.66 [4025]E(f335(f112(x40251,x40252,f335(x40253,x40254)),f335(f335(f7(x40251,a93,f883(x40252)),x40255),x40254)),f335(f198(x40251,x40252,x40253,x40255),x40254))
% 59.73/59.66 [4037]E(f335(f335(f104(f888(x40371,a879)),f335(f313(x40372,x40371,x40373),x40374)),f335(f313(x40372,x40371,x40373),x40375)),f335(f313(x40372,x40371,x40373),f335(f335(f104(f888(x40372,a879)),x40374),x40375)))
% 59.73/59.66 [4038]E(f335(f335(f104(f888(x40381,a879)),f335(f288(x40382,x40381,x40383),x40384)),f335(f288(x40382,x40381,x40383),x40385)),f335(f288(x40382,x40381,x40383),f335(f335(f104(f888(x40382,a879)),x40384),x40385)))
% 59.73/59.66 [4039]E(f335(f335(f104(f888(x40391,a879)),f335(f314(x40391,x40392,x40393),x40394)),f335(f314(x40391,x40392,x40393),x40395)),f335(f314(x40391,x40392,x40393),f335(f335(f104(f888(x40392,a879)),x40394),x40395)))
% 59.73/59.66 [4040]E(f335(f335(f23(f888(x40401,a879)),f335(f314(x40401,x40402,x40403),x40404)),f335(f314(x40401,x40402,x40403),x40405)),f335(f314(x40401,x40402,x40403),f335(f335(f23(f888(x40402,a879)),x40404),x40405)))
% 59.73/59.66 [4041]E(f335(f335(f95(f888(x40411,a879)),f335(f314(x40411,x40412,x40413),x40414)),f335(f314(x40411,x40412,x40413),x40415)),f335(f314(x40411,x40412,x40413),f335(f335(f95(f888(x40412,a879)),x40414),x40415)))
% 59.73/59.66 [4043]E(f182(x40431,x40432,f182(x40431,x40432,x40433,x40434),x40435),f182(x40431,x40432,x40433,f335(f335(f95(f888(x40431,a879)),x40434),x40435)))
% 59.73/59.66 [4104]E(f335(f335(f152(x41041,f335(f335(f127(x41041),x41042),f335(f335(f144(x41041),x41043),x41044))),f335(f189(f882(x41041)),x41042)),x41045),f335(f335(f127(x41041),x41042),f335(f335(f144(x41041),x41045),x41044)))
% 59.73/59.66 [4111]E(f335(f335(f34(x41111,f888(x41112,a879)),x41113),f335(f335(f8(f888(x41112,a879),f888(x41112,a879),x41111),f335(f312(x41112),x41114)),x41115)),f335(f335(f312(x41112),x41114),f335(f335(f34(x41111,f888(x41112,a879)),x41113),x41115)))
% 59.73/59.66 [4112]E(f335(f335(f34(x41121,f888(x41122,a879)),x41123),f335(f335(f8(f888(x41122,a879),f888(x41122,a879),x41121),f335(f312(x41122),x41124)),x41125)),f335(f335(f312(x41122),x41124),f335(f335(f34(x41121,f888(x41122,a879)),x41123),x41125)))
% 59.73/59.66 [4183]E(f182(x41831,x41832,f335(f335(f335(f67(x41831,f885(x41832)),x41833),x41834),f335(f235(x41832),x41835)),f335(f74(f888(x41831,a879)),f335(f335(f312(x41831),x41834),f188(f888(x41831,a879))))),f182(x41831,x41832,x41833,f335(f74(f888(x41831,a879)),f335(f335(f312(x41831),x41834),f188(f888(x41831,a879))))))
% 59.73/59.66 [4229]E(f335(f335(f104(f888(f887(x42291,x42292),a879)),f335(f335(f266(x42291,x42292),x42293),f335(f16(f888(x42292,a879),x42291),x42294))),f335(f335(f266(x42291,x42292),x42295),f335(f16(f888(x42292,a879),x42291),x42294))),f335(f335(f266(x42291,x42292),f335(f335(f104(f888(x42291,a879)),x42293),x42295)),f335(f16(f888(x42292,a879),x42291),x42294)))
% 59.73/59.66 [4230]E(f335(f335(f23(f888(f887(x42301,x42302),a879)),f335(f335(f266(x42301,x42302),x42303),f335(f16(f888(x42302,a879),x42301),x42304))),f335(f335(f266(x42301,x42302),x42305),f335(f16(f888(x42302,a879),x42301),x42304))),f335(f335(f266(x42301,x42302),f335(f335(f23(f888(x42301,a879)),x42303),x42305)),f335(f16(f888(x42302,a879),x42301),x42304)))
% 59.73/59.66 [4231]E(f335(f335(f95(f888(f887(x42311,x42312),a879)),f335(f335(f266(x42311,x42312),x42313),f335(f16(f888(x42312,a879),x42311),x42314))),f335(f335(f266(x42311,x42312),x42315),f335(f16(f888(x42312,a879),x42311),x42314))),f335(f335(f266(x42311,x42312),f335(f335(f95(f888(x42311,a879)),x42313),x42315)),f335(f16(f888(x42312,a879),x42311),x42314)))
% 59.73/59.66 [4277]E(f335(f335(f147(x42771,x42772),x42773),f335(f129(x42771,f335(f68(x42772,a879,x42771,x42774),x42773)),x42775)),f335(f129(x42772,x42774),f335(f335(f147(x42771,x42772),x42773),x42775)))
% 59.73/59.66 [4283]E(f335(f189(f882(x42831)),f335(f129(x42831,x42832),f335(f335(f147(x42833,x42831),x42834),x42835))),f335(f189(f882(x42833)),f335(f129(x42833,f335(f68(x42831,a879,x42833,x42832),x42834)),x42835)))
% 59.73/59.66 [4424]E(f335(f335(f104(f888(x44241,a879)),f335(f335(f23(f888(x44241,a879)),f177(x44241,x44242,x44243)),f335(f249(x44241),f335(f335(f7(x44241,f888(x44241,a879),a879),f337(x44241)),f335(f335(f23(f888(x44241,a879)),x44244),f177(x44241,x44242,x44245)))))),f335(f249(x44241),f335(f335(f7(x44241,f888(x44241,a879),a879),f337(x44241)),f335(f335(f95(f888(x44241,a879)),x44244),f177(x44241,x44242,x44245))))),f177(x44241,x44242,f71(x44241,f885(x44242),x44243,x44245,x44244)))
% 59.73/59.66 [4499]E(f335(f149(f882(f887(x44991,x44992)),x44992,f107(f887(x44991,x44992)),f335(f335(f7(x44992,f888(f882(x44992),f882(f887(x44991,x44992))),f888(f882(x44992),f882(f887(x44991,x44992)))),f335(f335(f8(f888(f882(f887(x44991,x44992)),f882(f887(x44991,x44992))),f888(f888(f882(x44992),f882(f887(x44991,x44992))),f888(f882(x44992),f882(f887(x44991,x44992)))),x44992),f8(f882(f887(x44991,x44992)),f882(f887(x44991,x44992)),f882(x44992))),f335(f335(f8(f887(x44991,x44992),f888(f882(f887(x44991,x44992)),f882(f887(x44991,x44992))),x44992),f144(f887(x44991,x44992))),f335(f264(x44991,x44992),x44993)))),f335(f175(x44991,x44992),x44994))),x44995),f335(f335(f175(x44991,x44992),f335(f335(f144(x44991),x44993),x44994)),x44995))
% 59.73/59.66 [3963]E(f335(f335(f152(x39631,f335(f335(f152(x39631,x39632),x39633),x39634)),x39633),x39635),f335(f335(f152(x39631,x39632),x39633),x39635))
% 59.73/59.66 [4019]E(f335(f260(x40191,x40192),f335(f335(f312(f887(x40191,x40192)),f335(f335(f264(x40191,x40192),x40193),x40194)),x40195)),f335(f335(f312(x40192),x40194),f335(f260(x40191,x40192),x40195)))
% 59.73/59.66 [4020]E(f335(f262(x40201,x40202),f335(f335(f312(f887(x40201,x40202)),f335(f335(f264(x40201,x40202),x40203),x40204)),x40205)),f335(f335(f312(x40201),x40203),f335(f262(x40201,x40202),x40205)))
% 59.73/59.66 [4097]E(f335(f335(f104(f888(f887(x40971,x40972),a879)),f335(f335(f266(x40971,x40972),x40973),x40974)),f335(f335(f266(x40971,x40972),x40975),x40974)),f335(f335(f266(x40971,x40972),f335(f335(f104(f888(x40971,a879)),x40973),x40975)),x40974))
% 59.73/59.66 [4098]E(f335(f335(f23(f888(f887(x40981,x40982),a879)),f335(f335(f266(x40981,x40982),x40983),x40984)),f335(f335(f266(x40981,x40982),x40985),x40984)),f335(f335(f266(x40981,x40982),f335(f335(f23(f888(x40981,a879)),x40983),x40985)),x40984))
% 59.73/59.66 [4099]E(f335(f335(f95(f888(f887(x40991,x40992),a879)),f335(f335(f266(x40991,x40992),x40993),x40994)),f335(f335(f266(x40991,x40992),x40995),x40994)),f335(f335(f266(x40991,x40992),f335(f335(f95(f888(x40991,a879)),x40993),x40995)),x40994))
% 59.73/59.66 [4161]E(f335(f335(f104(f888(x41611,a879)),f335(f335(f33(x41612,f888(x41611,a879)),x41613),x41614)),f335(f335(f33(x41612,f888(x41611,a879)),x41615),x41614)),f335(f335(f33(x41612,f888(x41611,a879)),f335(f335(f104(f888(x41612,a879)),x41613),x41615)),x41614))
% 59.73/59.66 [4162]E(f335(f335(f95(f888(x41621,a879)),f335(f335(f34(x41622,f888(x41621,a879)),x41623),x41624)),f335(f335(f34(x41622,f888(x41621,a879)),x41625),x41624)),f335(f335(f34(x41622,f888(x41621,a879)),f335(f335(f104(f888(x41622,a879)),x41623),x41625)),x41624))
% 59.73/59.66 [4171]E(f335(f335(f34(x41711,f888(x41712,a879)),x41713),f335(f335(f8(f888(x41712,a879),f888(x41712,a879),x41711),f335(f104(f888(x41712,a879)),x41714)),x41715)),f335(f335(f104(f888(x41712,a879)),x41714),f335(f335(f34(x41711,f888(x41712,a879)),x41713),x41715)))
% 59.73/59.66 [4172]E(f335(f335(f34(x41721,f888(x41722,a879)),x41723),f335(f335(f8(f888(x41722,a879),f888(x41722,a879),x41721),f335(f104(f888(x41722,a879)),x41724)),x41725)),f335(f335(f104(f888(x41722,a879)),x41724),f335(f335(f34(x41721,f888(x41722,a879)),x41723),x41725)))
% 59.73/59.66 [4173]E(f335(f335(f33(x41731,f888(x41732,a879)),x41733),f335(f335(f8(f888(x41732,a879),f888(x41732,a879),x41731),f335(f23(f888(x41732,a879)),x41734)),x41735)),f335(f335(f23(f888(x41732,a879)),x41734),f335(f335(f34(x41731,f888(x41732,a879)),x41733),x41735)))
% 59.73/59.66 [4174]E(f335(f335(f33(x41741,f888(x41742,a879)),x41743),f335(f335(f8(f888(x41742,a879),f888(x41742,a879),x41741),f335(f95(f888(x41742,a879)),x41744)),x41745)),f335(f335(f95(f888(x41742,a879)),x41744),f335(f335(f33(x41741,f888(x41742,a879)),x41743),x41745)))
% 59.73/59.66 [4175]E(f335(f335(f33(x41751,f888(x41752,a879)),x41753),f335(f335(f8(f888(x41752,a879),f888(x41752,a879),x41751),f335(f95(f888(x41752,a879)),x41754)),x41755)),f335(f335(f95(f888(x41752,a879)),x41754),f335(f335(f33(x41751,f888(x41752,a879)),x41753),x41755)))
% 59.73/59.66 [4176]E(f335(f335(f33(x41761,f888(x41762,a879)),x41763),f335(f335(f8(f888(x41762,a879),f888(x41762,a879),x41761),f335(f23(f888(x41762,a879)),x41764)),x41765)),f335(f335(f23(f888(x41762,a879)),x41764),f335(f335(f34(x41761,f888(x41762,a879)),x41763),x41765)))
% 59.73/59.66 [4177]E(f335(f335(f33(x41771,f888(x41772,a879)),x41773),f335(f335(f8(f888(x41772,a879),f888(x41772,a879),x41771),f335(f95(f888(x41772,a879)),x41774)),x41775)),f335(f335(f95(f888(x41772,a879)),x41774),f335(f335(f33(x41771,f888(x41772,a879)),x41773),x41775)))
% 59.73/59.66 [4178]E(f335(f335(f34(x41781,f888(x41782,a879)),x41783),f335(f335(f8(f888(x41782,a879),f888(x41782,a879),x41781),f335(f104(f888(x41782,a879)),x41784)),x41785)),f335(f335(f104(f888(x41782,a879)),x41784),f335(f335(f34(x41781,f888(x41782,a879)),x41783),x41785)))
% 59.73/59.66 [4216]E(f180(x42161,x42162,x42163,f335(f179(x42161,x42162),f335(f162(f887(x42161,x42162)),f335(f335(f175(x42161,x42162),x42164),x42165)))),f181(x42161,x42162,x42163,x42164,x42165))
% 59.73/59.66 [4239]E(f185(f882(x42391),f335(f335(f144(x42391),x42392),x42393),f335(f335(f8(f882(x42391),f882(x42391),a881),f335(f144(x42391),x42394)),f335(f335(f7(a881,x42391,f882(x42391)),f152(x42391,x42393)),x42392)),x42395),f335(f335(f152(x42391,f335(f335(f144(x42391),x42394),x42393)),x42395),x42392))
% 59.73/59.66 [4243]E(f335(f335(f33(x42431,f888(f887(x42432,x42433),a879)),x42434),f335(f335(f8(f888(f887(x42433,x42432),a879),f888(f887(x42432,x42433),a879),x42431),f289(x42433,x42432)),x42435)),f335(f289(x42433,x42432),f335(f335(f33(x42431,f888(f887(x42433,x42432),a879)),x42434),x42435)))
% 59.73/59.66 [4244]E(f335(f335(f34(x42441,f888(f887(x42442,x42443),a879)),x42444),f335(f335(f8(f888(f887(x42443,x42442),a879),f888(f887(x42442,x42443),a879),x42441),f289(x42443,x42442)),x42445)),f335(f289(x42443,x42442),f335(f335(f34(x42441,f888(f887(x42443,x42442),a879)),x42444),x42445)))
% 59.73/59.66 [4301]E(f177(x43011,x43012,f335(f335(f18(x43011,f885(x43013),f885(x43012)),f335(f335(f8(f888(x43013,x43012),f888(f885(x43013),f885(x43012)),x43011),f201(x43013,x43012)),x43014)),x43015)),f177(x43011,x43013,x43015))
% 59.73/59.66 [4353]P1(f335(f335(f242(f888(x43531,a879)),f335(f335(f23(f888(x43531,a879)),f335(f313(x43532,x43531,x43533),x43534)),f335(f313(x43532,x43531,x43533),x43535))),f335(f313(x43532,x43531,x43533),f335(f335(f23(f888(x43532,a879)),x43534),x43535))))
% 59.73/59.66 [4503]E(f335(f149(f882(f887(x45031,x45032)),x45031,f107(f887(x45031,x45032)),f335(f335(f7(x45031,f888(f882(x45031),f882(f887(x45031,x45032))),f888(f882(x45031),f882(f887(x45031,x45032)))),f335(f335(f8(f888(f882(f887(x45031,x45032)),f882(f887(x45031,x45032))),f888(f888(f882(x45031),f882(f887(x45031,x45032))),f888(f882(x45031),f882(f887(x45031,x45032)))),x45031),f8(f882(f887(x45031,x45032)),f882(f887(x45031,x45032)),f882(x45031))),f335(f335(f8(f887(x45031,x45032),f888(f882(f887(x45031,x45032)),f882(f887(x45031,x45032))),x45031),f144(f887(x45031,x45032))),f335(f335(f7(x45031,x45032,f887(x45031,x45032)),f264(x45031,x45032)),x45033)))),f335(f335(f7(f882(x45031),f882(x45032),f882(f887(x45031,x45032))),f175(x45031,x45032)),x45034))),x45035),f335(f335(f175(x45031,x45032),x45035),f335(f335(f144(x45032),x45033),x45034)))
% 59.73/59.66 [4204]E(f335(f335(f104(f888(x42041,a879)),f335(f288(x42042,x42041,x42043),x42044)),f335(f288(x42042,x42041,x42045),x42044)),f335(f288(x42042,x42041,f335(f335(f104(f888(f887(x42042,x42041),a879)),x42043),x42045)),x42044))
% 59.73/59.66 [4246]E(f335(f335(f127(f887(x42461,x42462)),f335(f335(f175(x42461,x42462),x42463),f335(f335(f169(x42462),f335(f189(f882(x42461)),x42463)),x42464))),f335(f335(f175(x42461,x42462),x42465),f335(f335(f131(x42462),f335(f189(f882(x42461)),x42463)),x42464))),f335(f335(f175(x42461,x42462),f335(f335(f127(x42461),x42463),x42465)),x42464))
% 59.73/59.66 [4356]E(f335(f335(f266(x43561,x43562),x43563),f335(f335(f18(x43561,f888(x43562,a879),f888(x43562,a879)),f335(f335(f8(f888(x43562,a879),f888(f888(x43562,a879),f888(x43562,a879)),x43561),f104(f888(x43562,a879))),x43564)),x43565)),f335(f335(f104(f888(f887(x43561,x43562),a879)),f335(f335(f266(x43561,x43562),x43563),x43564)),f335(f335(f266(x43561,x43562),x43563),x43565)))
% 59.73/59.66 [4357]E(f335(f335(f266(x43571,x43572),x43573),f335(f335(f18(x43571,f888(x43572,a879),f888(x43572,a879)),f335(f335(f8(f888(x43572,a879),f888(f888(x43572,a879),f888(x43572,a879)),x43571),f23(f888(x43572,a879))),x43574)),x43575)),f335(f335(f23(f888(f887(x43571,x43572),a879)),f335(f335(f266(x43571,x43572),x43573),x43574)),f335(f335(f266(x43571,x43572),x43573),x43575)))
% 59.73/59.66 [4358]E(f335(f335(f266(x43581,x43582),x43583),f335(f335(f18(x43581,f888(x43582,a879),f888(x43582,a879)),f335(f335(f8(f888(x43582,a879),f888(f888(x43582,a879),f888(x43582,a879)),x43581),f95(f888(x43582,a879))),x43584)),x43585)),f335(f335(f95(f888(f887(x43581,x43582),a879)),f335(f335(f266(x43581,x43582),x43583),x43584)),f335(f335(f266(x43581,x43582),x43583),x43585)))
% 59.73/59.66 [4359]E(f335(f335(f34(x43591,f888(x43592,a879)),x43593),f335(f335(f7(x43591,f888(x43592,a879),f888(x43592,a879)),f335(f335(f8(f888(x43592,a879),f888(f888(x43592,a879),f888(x43592,a879)),x43591),f104(f888(x43592,a879))),x43594)),x43595)),f335(f335(f104(f888(x43592,a879)),f335(f335(f34(x43591,f888(x43592,a879)),x43593),x43594)),x43595))
% 59.73/59.66 [4360]E(f335(f335(f33(x43601,f888(x43602,a879)),x43603),f335(f335(f7(x43601,f888(x43602,a879),f888(x43602,a879)),f335(f335(f8(f888(x43602,a879),f888(f888(x43602,a879),f888(x43602,a879)),x43601),f23(f888(x43602,a879))),x43604)),x43605)),f335(f335(f23(f888(x43602,a879)),f335(f335(f33(x43601,f888(x43602,a879)),x43603),x43604)),x43605))
% 59.73/59.66 [4361]E(f335(f335(f33(x43611,f888(x43612,a879)),x43613),f335(f335(f7(x43611,f888(x43612,a879),f888(x43612,a879)),f335(f335(f8(f888(x43612,a879),f888(f888(x43612,a879),f888(x43612,a879)),x43611),f95(f888(x43612,a879))),x43614)),x43615)),f335(f335(f95(f888(x43612,a879)),f335(f335(f33(x43611,f888(x43612,a879)),x43613),x43614)),x43615))
% 59.73/59.66 [4362]E(f335(f335(f33(x43621,f888(x43622,a879)),x43623),f335(f335(f7(x43621,f888(x43622,a879),f888(x43622,a879)),f335(f335(f8(f888(x43622,a879),f888(f888(x43622,a879),f888(x43622,a879)),x43621),f23(f888(x43622,a879))),x43624)),x43625)),f335(f335(f23(f888(x43622,a879)),f335(f335(f33(x43621,f888(x43622,a879)),x43623),x43624)),x43625))
% 59.73/59.66 [4363]E(f335(f335(f33(x43631,f888(x43632,a879)),x43633),f335(f335(f7(x43631,f888(x43632,a879),f888(x43632,a879)),f335(f335(f8(f888(x43632,a879),f888(f888(x43632,a879),f888(x43632,a879)),x43631),f95(f888(x43632,a879))),x43634)),x43635)),f335(f335(f95(f888(x43632,a879)),f335(f335(f33(x43631,f888(x43632,a879)),x43633),x43634)),x43635))
% 59.73/59.66 [4364]E(f335(f335(f34(x43641,f888(x43642,a879)),x43643),f335(f335(f7(x43641,f888(x43642,a879),f888(x43642,a879)),f335(f335(f8(f888(x43642,a879),f888(f888(x43642,a879),f888(x43642,a879)),x43641),f104(f888(x43642,a879))),x43644)),x43645)),f335(f335(f104(f888(x43642,a879)),f335(f335(f34(x43641,f888(x43642,a879)),x43643),x43644)),x43645))
% 59.73/59.66 [4368]E(f335(f335(f33(x43681,f888(x43682,a879)),x43683),f335(f335(f18(x43681,f888(x43682,a879),f888(x43682,a879)),f335(f335(f8(f888(x43682,a879),f888(f888(x43682,a879),f888(x43682,a879)),x43681),f104(f888(x43682,a879))),x43684)),x43685)),f335(f335(f104(f888(x43682,a879)),f335(f335(f33(x43681,f888(x43682,a879)),x43683),x43684)),f335(f335(f33(x43681,f888(x43682,a879)),x43683),x43685)))
% 59.73/59.66 [4369]E(f335(f335(f34(x43691,f888(x43692,a879)),x43693),f335(f335(f18(x43691,f888(x43692,a879),f888(x43692,a879)),f335(f335(f8(f888(x43692,a879),f888(f888(x43692,a879),f888(x43692,a879)),x43691),f95(f888(x43692,a879))),x43694)),x43695)),f335(f335(f95(f888(x43692,a879)),f335(f335(f34(x43691,f888(x43692,a879)),x43693),x43694)),f335(f335(f34(x43691,f888(x43692,a879)),x43693),x43695)))
% 59.73/59.66 [4383]E(f335(f335(f33(x43831,f888(x43832,a879)),x43833),f335(f335(f18(x43831,f888(x43832,a879),f888(x43832,a879)),f335(f335(f8(f888(x43832,a879),f888(f888(x43832,a879),f888(x43832,a879)),x43831),f104(f888(x43832,a879))),x43834)),x43835)),f335(f335(f104(f888(x43832,a879)),f31(f888(x43832,a879),f335(f313(x43831,f888(x43832,a879),x43834),x43833))),f31(f888(x43832,a879),f335(f313(x43831,f888(x43832,a879),x43835),x43833))))
% 59.73/59.66 [4384]E(f335(f335(f34(x43841,f888(x43842,a879)),x43843),f335(f335(f18(x43841,f888(x43842,a879),f888(x43842,a879)),f335(f335(f8(f888(x43842,a879),f888(f888(x43842,a879),f888(x43842,a879)),x43841),f95(f888(x43842,a879))),x43844)),x43845)),f335(f335(f95(f888(x43842,a879)),f32(f888(x43842,a879),f335(f313(x43841,f888(x43842,a879),x43844),x43843))),f32(f888(x43842,a879),f335(f313(x43841,f888(x43842,a879),x43845),x43843))))
% 59.73/59.66 [4420]E(f335(f335(f131(x44201),f335(f189(f882(x44201)),f171(x44201,x44202,f335(f335(f147(x44203,x44201),x44204),x44205)))),f335(f335(f147(x44203,x44201),x44204),x44205)),f335(f335(f147(x44203,x44201),x44204),f335(f335(f131(x44203),f335(f189(f882(x44203)),f171(x44203,f335(f68(x44201,a879,x44203,x44202),x44204),x44205))),x44205)))
% 59.73/59.66 [4291]E(f335(f335(f127(f887(x42911,x42912)),f335(f335(f175(x42911,x42912),f335(f335(f169(x42911),f335(f189(f882(x42912)),x42913)),x42914)),x42913)),f335(f335(f175(x42911,x42912),f335(f335(f131(x42911),f335(f189(f882(x42912)),x42913)),x42914)),x42915)),f335(f335(f175(x42911,x42912),x42914),f335(f335(f127(x42912),x42913),x42915)))
% 59.73/59.66 [4411]E(f80(x44111,f335(f335(f18(x44111,a879,a879),f335(f335(f8(a879,f888(a879,a879),x44111),a333),f335(f335(f7(x44111,f888(x44111,a879),a879),f337(x44111)),x44112))),f335(f335(f7(x44111,x44113,a879),f335(f335(f8(x44113,f888(x44113,a879),x44111),a332),x44114)),x44115))),f335(f72(x44111,x44113,x44112,x44114),x44115))
% 59.73/59.66 [4412]E(f85(x44121,f335(f335(f18(x44121,a879,a879),f335(f335(f8(a879,f888(a879,a879),x44121),a333),f335(f335(f7(x44121,f888(x44121,a879),a879),f337(x44121)),x44122))),f335(f335(f7(x44121,x44123,a879),f335(f335(f8(x44123,f888(x44123,a879),x44121),a332),x44124)),x44125))),f335(f87(x44121,x44123,x44122,x44124),x44125))
% 59.73/59.66 [4464]E(f335(f335(f81(a1,x44641),f335(f97(a1),f335(f335(f75(a1),x44642),a91))),f335(f335(f18(a1,x44641,x44641),f335(f335(f7(a1,x44641,f888(x44641,x44641)),f335(f335(f8(a879,f888(x44641,f888(x44641,x44641)),a1),f88(x44641)),a193)),f185(x44641,x44643,x44644,x44645))),f335(f335(f8(a881,x44641,a1),x44644),f335(f335(f7(a1,a881,a881),f335(f335(f8(a881,f888(a881,a881),a1),f75(a881)),a98)),x44645)))),f185(x44641,x44643,x44644,f335(f335(f75(a881),f335(f97(a881),x44642)),x44645)))
% 59.73/59.66 [4500]E(f335(f179(x45001,x45002),f335(f335(f147(f887(x45001,x45003),f887(x45001,x45002)),f335(f268(x45001,x45003,f887(x45001,x45002)),f335(f335(f7(x45001,f888(x45003,x45002),f888(x45003,f887(x45001,x45002))),f335(f335(f8(f888(x45002,f887(x45001,x45002)),f888(f888(x45003,x45002),f888(x45003,f887(x45001,x45002))),x45001),f8(x45002,f887(x45001,x45002),x45003)),f264(x45001,x45002))),x45004))),x45005)),f335(f68(f885(x45003),f885(x45002),x45001,f335(f201(x45003,x45002),x45004)),f335(f179(x45001,x45003),x45005)))
% 59.73/59.66 [4457]E(f177(x44571,x44572,f335(f335(f18(x44571,f885(x44572),f885(x44572)),f335(f335(f18(x44571,f885(x44572),f888(f885(x44572),f885(x44572))),f335(f335(f8(a879,f888(f885(x44572),f888(f885(x44572),f885(x44572))),x44571),f88(f885(x44572))),x44573)),x44574)),x44575)),f335(f335(f104(f888(x44571,a879)),f335(f335(f95(f888(x44571,a879)),f177(x44571,x44572,x44574)),f335(f249(x44571),x44573))),f335(f335(f95(f888(x44571,a879)),f177(x44571,x44572,x44575)),f335(f249(x44571),f335(f335(f8(a879,a879,x44571),a330),x44573)))))
% 59.73/59.66 [4498]E(f335(f335(f81(a1,x44981),f335(f97(a1),f335(f335(f75(a1),x44982),a91))),f335(f335(f18(a1,x44981,x44981),f335(f335(f7(a1,x44981,f888(x44981,x44981)),f335(f335(f8(a879,f888(x44981,f888(x44981,x44981)),a1),f88(x44981)),a193)),f335(f184(x44981,x44983,x44984),x44985))),f335(f335(f18(a1,x44981,x44981),f335(f335(f8(a881,f888(x44981,x44981),a1),x44984),f335(f335(f7(a1,a881,a881),f335(f335(f8(a881,f888(a881,a881),a1),f75(a881)),a98)),x44985))),f335(f335(f8(a881,x44981,a1),f184(x44981,x44983,x44984)),f335(f335(f7(a1,a881,a881),f335(f335(f8(a881,f888(a881,a881),a1),f75(a881)),a98)),x44985))))),f335(f184(x44981,x44983,x44984),f335(f335(f75(a881),f335(f97(a881),x44982)),x44985)))
% 59.73/59.66 [4531]E(f335(f249(f887(x45311,x45312)),f335(f268(x45311,x45312,a879),f335(f335(f8(f888(x45312,f888(x45313,a879)),f888(x45312,a879),x45311),f335(f8(f888(x45313,a879),a879,x45312),f82(x45313))),f335(f335(f7(x45311,f888(x45312,f888(x45313,a879)),f888(x45312,f888(x45313,a879))),f335(f335(f8(f888(f888(x45313,a879),f888(x45313,a879)),f888(f888(x45312,f888(x45313,a879)),f888(x45312,f888(x45313,a879))),x45311),f8(f888(x45313,a879),f888(x45313,a879),x45312)),f335(f335(f8(f888(x45313,f888(a879,a879)),f888(f888(x45313,a879),f888(x45313,a879)),x45311),f18(x45313,a879,a879)),f335(f335(f8(f888(x45313,a879),f888(x45313,f888(a879,a879)),x45311),f335(f8(a879,f888(a879,a879),x45313),a333)),f335(f335(f7(x45311,f888(f887(x45311,x45313),a879),f888(x45313,a879)),f335(f335(f8(f888(x45313,f888(f888(f887(x45311,x45313),a879),a879)),f888(f888(f887(x45311,x45313),a879),f888(x45313,a879)),x45311),f7(x45313,f888(f887(x45311,x45313),a879),a879)),f335(f335(f8(f888(x45313,f887(x45311,x45313)),f888(x45313,f888(f888(f887(x45311,x45313),a879),a879)),x45311),f335(f8(f887(x45311,x45313),f888(f888(f887(x45311,x45313),a879),a879),x45313),f337(f887(x45311,x45313)))),f264(x45311,x45313)))),x45314))))),f335(f335(f7(x45312,f888(f887(x45313,x45312),a879),f888(x45313,a879)),f335(f335(f8(f888(x45313,f888(f888(f887(x45313,x45312),a879),a879)),f888(f888(f887(x45313,x45312),a879),f888(x45313,a879)),x45312),f7(x45313,f888(f887(x45313,x45312),a879),a879)),f335(f335(f8(f888(x45313,f887(x45313,x45312)),f888(x45313,f888(f888(f887(x45313,x45312),a879),a879)),x45312),f335(f8(f887(x45313,x45312),f888(f888(f887(x45313,x45312),a879),a879),x45313),f337(f887(x45313,x45312)))),f335(f7(x45313,x45312,f887(x45313,x45312)),f264(x45313,x45312))))),x45315))))),f335(f335(f291(x45311,x45313,x45312),x45314),x45315))
% 59.73/59.66 [4053]E(f121(x40531,x40532,x40533,x40534,f120(x40532,x40535,x40536)),f335(f335(x40534,x40535),x40536))
% 59.73/59.66 [4129]E(f226(x41291,x41292,x41293,x41294,f223(x41291,x41292,x41295,x41296)),f335(f335(x41294,x41295),x41296))
% 59.73/59.66 [4130]E(f227(x41301,x41302,x41303,x41304,f223(x41301,x41302,x41305,x41306)),f335(f335(x41304,x41305),x41306))
% 59.73/59.66 [4275]E(f181(x42751,x42752,f180(x42751,x42752,x42753,x42754),x42755,x42756),f180(x42751,x42752,x42753,f181(x42751,x42752,x42754,x42755,x42756)))
% 59.73/59.66 [4399]E(f335(f68(f887(x43991,x43992),x43992,f887(x43993,x43994),f267(x43991,x43992)),f269(x43993,x43991,x43994,x43992,x43995,x43996)),f335(f68(x43994,x43992,f887(x43993,x43994),x43996),f267(x43993,x43994)))
% 59.73/59.66 [4400]E(f335(f68(f887(x44001,x44002),x44001,f887(x44003,x44004),f263(x44001,x44002)),f269(x44003,x44001,x44004,x44002,x44005,x44006)),f335(f68(x44003,x44001,f887(x44003,x44004),x44005),f263(x44003,x44004)))
% 59.73/59.66 [3992]E(f335(f335(f68(x39921,x39922,x39923,x39924),x39925),x39926),f335(x39924,f335(x39925,x39926)))
% 59.73/59.66 [3993]E(f335(f335(f68(x39931,x39932,x39933,x39934),x39935),x39936),f335(x39934,f335(x39935,x39936)))
% 59.73/59.66 [4191]E(f228(x41911,x41912,x41913,x41914,f223(x41911,x41912,x41915,x41916)),f335(f335(f75(a881),f335(f335(f75(a881),f335(x41913,x41915)),f335(x41914,x41916))),f335(a106,f2(a881))))
% 59.73/59.66 [3785]E(f335(f335(f268(x37851,x37852,x37853),x37854),f335(f335(f264(x37851,x37852),x37855),x37856)),f335(f335(x37854,x37855),x37856))
% 59.73/59.66 [3786]E(f335(f335(f268(x37861,x37862,x37863),x37864),f335(f335(f264(x37861,x37862),x37865),x37866)),f335(f335(x37864,x37865),x37866))
% 59.73/59.66 [3787]E(f335(f335(f268(x37871,x37872,x37873),x37874),f335(f335(f264(x37871,x37872),x37875),x37876)),f335(f335(x37874,x37875),x37876))
% 59.73/59.66 [3850]E(f335(f335(f335(f8(x38501,x38502,x38503),x38504),x38505),x38506),f335(x38504,f335(x38505,x38506)))
% 59.73/59.66 [3851]E(f335(f335(f335(f7(x38511,x38512,x38513),x38514),x38515),x38516),f335(f335(x38514,x38516),x38515))
% 59.73/59.66 [3867]E(f335(f335(f335(f18(x38671,x38672,x38673),x38674),x38675),x38676),f335(f335(x38674,x38676),f335(x38675,x38676)))
% 59.73/59.66 [3889]E(f335(f149(x38891,x38892,x38893,x38894),f335(f335(f144(x38892),x38895),x38896)),f335(f335(x38894,x38895),x38896))
% 59.73/59.66 [3928]E(f163(f887(x39281,x39282),f335(f335(f240(a881),x39283),x39284),f335(f335(f264(x39281,x39282),x39285),x39286)),f335(f335(f175(x39281,x39282),f163(x39281,x39283,x39285)),f163(x39282,x39284,x39286)))
% 59.73/59.66 [3997]E(f335(f335(f144(f887(x39971,x39972)),f335(f335(f264(x39971,x39972),x39973),x39974)),f335(f335(f175(x39971,x39972),x39975),x39976)),f335(f335(f175(x39971,x39972),f335(f335(f144(x39971),x39973),x39975)),f335(f335(f144(x39972),x39974),x39976)))
% 59.73/59.66 [4000]E(f335(f335(f147(x40001,x40002),x40003),f335(f335(f152(x40001,x40004),x40005),x40006)),f335(f335(f152(x40002,f335(f335(f147(x40001,x40002),x40003),x40004)),x40005),f335(x40003,x40006)))
% 59.73/59.66 [4042]E(f335(f135(x40421,x40422,x40423,x40424),f335(f335(f144(x40422),x40425),x40426)),f335(f135(x40421,x40422,x40423,f335(f335(x40423,x40424),x40425)),x40426))
% 59.73/59.66 [4068]E(f271(x40681,x40682,x40683,x40684,f335(f335(f264(x40681,x40682),x40685),x40686)),f335(f335(x40684,x40685),x40686))
% 59.73/59.66 [4154]E(f335(f335(f33(x41541,f888(x41542,a879)),x41543),f335(f68(x41544,f888(x41542,a879),x41541,x41545),x41546)),f335(f335(f33(x41544,f888(x41542,a879)),f335(f313(x41541,x41544,x41546),x41543)),x41545))
% 59.73/59.66 [4206]E(f335(f335(f147(x42061,x42062),x42063),f335(f335(f147(x42064,x42061),x42065),x42066)),f335(f335(f147(x42064,x42062),f335(f68(x42061,x42062,x42064,x42063),x42065)),x42066))
% 59.73/59.66 [4207]E(f335(f335(f147(x42071,x42072),x42073),f335(f335(f147(x42074,x42071),x42075),x42076)),f335(f335(f147(x42074,x42072),f335(f68(x42071,x42072,x42074,x42073),x42075)),x42076))
% 59.73/59.66 [4208]E(f335(f335(f201(x42081,x42082),x42083),f335(f335(f201(x42084,x42081),x42085),x42086)),f335(f335(f201(x42084,x42082),f335(f68(x42081,x42082,x42084,x42083),x42085)),x42086))
% 59.73/59.66 [4209]E(f335(f335(f201(x42091,x42092),x42093),f335(f335(f201(x42094,x42091),x42095),x42096)),f335(f335(f201(x42094,x42092),f335(f68(x42091,x42092,x42094,x42093),x42095)),x42096))
% 59.73/59.66 [4214]E(f335(f313(x42141,x42142,f335(f68(x42143,x42142,x42141,x42144),x42145)),x42146),f335(f313(x42143,x42142,x42144),f335(f313(x42141,x42143,x42145),x42146)))
% 59.73/59.66 [4215]E(f335(f314(x42151,x42152,f335(f68(x42153,x42152,x42151,x42154),x42155)),x42156),f335(f314(x42151,x42153,x42155),f335(f314(x42153,x42152,x42154),x42156)))
% 59.73/59.66 [4245]E(f180(x42451,x42452,x42453,f335(f335(f335(f67(x42451,f885(x42452)),x42454),x42455),f335(f235(x42452),x42456))),f335(f335(f335(f67(x42451,f885(x42452)),f180(x42451,x42452,x42453,x42454)),x42455),f335(f235(x42452),x42456)))
% 59.73/59.66 [4247]E(f335(f135(x42471,x42472,x42473,f335(f135(x42471,x42472,x42473,x42474),x42475)),x42476),f335(f135(x42471,x42472,x42473,x42474),f335(f335(f127(x42472),x42475),x42476)))
% 59.73/59.66 [4389]E(f335(f269(x43891,x43891,x43892,x43893,f25(x43891),x43894),f335(f335(f264(x43891,x43892),x43895),x43896)),f335(f335(f264(x43891,x43893),x43895),f335(x43894,x43896)))
% 59.73/59.66 [4390]E(f335(f269(x43901,x43902,x43903,x43903,x43904,f25(x43903)),f335(f335(f264(x43901,x43903),x43905),x43906)),f335(f335(f264(x43902,x43903),f335(x43904,x43905)),x43906))
% 59.73/59.66 [4482]E(f335(f335(f147(f887(x44821,x44822),f887(x44821,x44823)),f335(f268(x44821,x44822,f887(x44821,x44823)),f335(f335(f7(x44821,f888(x44822,x44823),f888(x44822,f887(x44821,x44823))),f335(f335(f8(f888(x44823,f887(x44821,x44823)),f888(f888(x44822,x44823),f888(x44822,f887(x44821,x44823))),x44821),f8(x44823,f887(x44821,x44823),x44822)),f264(x44821,x44823))),x44824))),f335(f335(f175(x44821,x44822),x44825),x44826)),f335(f335(f175(x44821,x44823),x44825),f335(f335(f147(x44822,x44823),x44824),x44826)))
% 59.73/59.66 [4052]E(f335(f335(f68(x40521,x40522,x40523,f335(f16(x40522,x40521),x40524)),x40525),x40526),x40524)
% 59.73/59.66 [4087]E(f335(f313(x40871,x40872,x40873),f335(f313(x40874,x40871,x40875),x40876)),f335(f313(x40874,x40872,f335(f335(f8(x40871,x40872,x40874),x40873),x40875)),x40876))
% 59.73/59.66 [4093]E(f335(f335(f33(x40931,f888(x40932,a879)),f335(f313(x40933,x40931,x40934),x40935)),x40936),f335(f335(f33(x40933,f888(x40932,a879)),x40935),f335(f335(f8(x40931,f888(x40932,a879),x40933),x40936),x40934)))
% 59.73/59.66 [4094]E(f335(f335(f34(x40941,f888(x40942,a879)),f335(f313(x40943,x40941,x40944),x40945)),x40946),f335(f335(f34(x40943,f888(x40942,a879)),x40945),f335(f335(f8(x40941,f888(x40942,a879),x40943),x40946),x40944)))
% 59.73/59.66 [4095]E(f335(f335(f33(x40951,f888(x40952,a879)),x40953),f335(f335(f8(x40954,f888(x40952,a879),x40951),x40955),x40956)),f335(f335(f33(x40954,f888(x40952,a879)),f335(f313(x40951,x40954,x40956),x40953)),x40955))
% 59.73/59.66 [4096]E(f335(f335(f34(x40961,f888(x40962,a879)),x40963),f335(f335(f8(x40964,f888(x40962,a879),x40961),x40965),x40966)),f335(f335(f34(x40964,f888(x40962,a879)),f335(f313(x40961,x40964,x40966),x40963)),x40965))
% 59.73/59.66 [4156]E(f335(f335(f33(x41561,f888(x41562,a879)),x41563),f335(f335(f8(f888(x41564,a879),f888(x41562,a879),x41561),f313(x41564,x41562,x41565)),x41566)),f335(f313(x41564,x41562,x41565),f335(f335(f33(x41561,f888(x41564,a879)),x41563),x41566)))
% 59.73/59.66 [4157]E(f335(f335(f33(x41571,f888(x41572,a879)),x41573),f335(f335(f8(f888(x41574,a879),f888(x41572,a879),x41571),f288(x41574,x41572,x41575)),x41576)),f335(f288(x41574,x41572,x41575),f335(f335(f33(x41571,f888(x41574,a879)),x41573),x41576)))
% 59.73/59.66 [4158]E(f335(f335(f33(x41581,f888(x41582,a879)),x41583),f335(f335(f8(f888(x41584,a879),f888(x41582,a879),x41581),f314(x41582,x41584,x41585)),x41586)),f335(f314(x41582,x41584,x41585),f335(f335(f33(x41581,f888(x41584,a879)),x41583),x41586)))
% 59.73/59.66 [4159]E(f335(f335(f34(x41591,f888(x41592,a879)),x41593),f335(f335(f8(f888(x41594,a879),f888(x41592,a879),x41591),f314(x41592,x41594,x41595)),x41596)),f335(f314(x41592,x41594,x41595),f335(f335(f34(x41591,f888(x41594,a879)),x41593),x41596)))
% 59.73/59.66 [4253]E(f335(f135(x42531,x42532,f335(f7(x42532,x42531,x42531),x42533),x42534),f335(f162(x42532),f335(f335(f144(x42532),x42535),x42536))),f335(f335(x42533,x42535),f335(f135(x42531,x42532,f335(f7(x42532,x42531,x42531),x42533),x42534),f335(f162(x42532),x42536))))
% 59.73/59.66 [4314]E(f335(f335(f18(f887(x43141,x43142),x43142,x43143),f335(f335(f8(x43144,f888(x43142,x43143),f887(x43141,x43142)),x43145),f335(f335(f8(x43141,x43144,f887(x43141,x43142)),x43146),f263(x43141,x43142)))),f267(x43141,x43142)),f335(f268(x43141,x43142,x43143),f335(f335(f8(x43144,f888(x43142,x43143),x43141),x43145),x43146)))
% 59.73/59.66 [4321]E(f335(f135(x43211,x43212,f335(f7(x43212,x43211,x43211),x43213),f335(f135(x43211,x43212,f335(f7(x43212,x43211,x43211),x43213),x43214),f335(f162(x43212),x43215))),f335(f162(x43212),x43216)),f335(f135(x43211,x43212,f335(f7(x43212,x43211,x43211),x43213),x43214),f335(f162(x43212),f335(f335(f127(x43212),x43216),x43215))))
% 59.73/59.66 [4323]E(f335(f335(f147(f887(x43231,x43232),f887(x43233,x43232)),f335(f268(x43231,x43232,f887(x43233,x43232)),f335(f335(f8(x43233,f888(x43232,f887(x43233,x43232)),x43231),f264(x43233,x43232)),x43234))),f335(f335(f175(x43231,x43232),x43235),x43236)),f335(f335(f175(x43233,x43232),f335(f335(f147(x43231,x43233),x43234),x43235)),x43236))
% 59.73/59.66 [4372]P1(f335(f335(f242(f888(x43721,a879)),f335(f288(x43722,x43721,x43723),f335(f335(f34(x43724,f888(x43722,a879)),x43725),x43726))),f335(f335(f34(x43724,f888(x43721,a879)),x43725),f335(f335(f8(f888(x43722,a879),f888(x43721,a879),x43724),f288(x43722,x43721,x43723)),x43726))))
% 59.73/59.66 [4169]E(f335(f335(f175(x41691,x41692),f335(f335(f152(x41691,x41693),x41694),f335(f263(x41691,x41692),x41695))),f335(f335(f152(x41692,x41696),x41694),f335(f267(x41691,x41692),x41695))),f335(f335(f152(f887(x41691,x41692),f335(f335(f175(x41691,x41692),x41693),x41696)),x41694),x41695))
% 59.73/59.66 [4234]E(f335(f335(f104(f888(f887(x42341,x42342),a879)),f335(f335(f291(x42341,x42343,x42342),x42344),x42345)),f335(f335(f291(x42341,x42343,x42342),x42344),x42346)),f335(f335(f291(x42341,x42343,x42342),x42344),f335(f335(f104(f888(f887(x42343,x42342),a879)),x42345),x42346)))
% 59.73/59.66 [4335]E(f335(f335(f312(f887(x43351,x43352)),f335(f335(f264(x43351,x43352),x43353),x43354)),f335(f335(f104(f888(f887(x43351,x43352),a879)),f335(f335(f266(x43351,x43352),x43355),f335(f16(f888(x43352,a879),x43351),f335(f335(f312(x43352),x43354),x43356)))),f335(f335(f266(x43351,x43352),f335(f335(f312(x43351),x43353),x43355)),f335(f16(f888(x43352,a879),x43351),x43356)))),f335(f335(f266(x43351,x43352),f335(f335(f312(x43351),x43353),x43355)),f335(f16(f888(x43352,a879),x43351),f335(f335(f312(x43352),x43354),x43356))))
% 59.73/59.66 [4415]E(f335(f335(f95(f888(x44151,a879)),f335(f314(x44151,x44152,f335(f68(f887(x44152,x44153),x44152,x44151,f263(x44152,x44153)),x44154)),x44155)),f335(f314(x44151,x44153,f335(f68(f887(x44152,x44153),x44153,x44151,f267(x44152,x44153)),x44154)),x44156)),f335(f314(x44151,f887(x44152,x44153),x44154),f335(f335(f266(x44152,x44153),x44155),f335(f16(f888(x44153,a879),x44152),x44156))))
% 59.73/59.66 [4153]E(f335(f335(f335(f67(x41531,x41532),f335(f335(f335(f67(x41531,x41532),x41533),x41534),x41535)),x41534),x41536),f335(f335(f335(f67(x41531,x41532),x41533),x41534),x41536))
% 59.73/59.66 [4259]E(f335(f335(f104(f888(f887(x42591,x42592),a879)),f335(f335(f291(x42591,x42593,x42592),x42594),x42595)),f335(f335(f291(x42591,x42593,x42592),x42596),x42595)),f335(f335(f291(x42591,x42593,x42592),f335(f335(f104(f888(f887(x42591,x42593),a879)),x42594),x42596)),x42595))
% 59.73/59.66 [4394]E(f335(f335(f33(x43941,f888(x43942,a879)),x43943),f335(f335(f7(x43941,f888(x43944,f888(x43942,a879)),f888(x43942,a879)),f335(f335(f8(f888(x43944,a879),f888(f888(x43944,f888(x43942,a879)),f888(x43942,a879)),x43941),f33(x43944,f888(x43942,a879))),x43945)),x43946)),f335(f335(f33(x43944,f888(x43942,a879)),f335(f335(f33(x43941,f888(x43944,a879)),x43943),x43945)),x43946))
% 59.73/59.66 [4395]E(f335(f335(f33(x43951,f888(x43952,a879)),x43953),f335(f335(f7(x43951,f888(x43954,f888(x43952,a879)),f888(x43952,a879)),f335(f335(f8(f888(x43954,a879),f888(f888(x43954,f888(x43952,a879)),f888(x43952,a879)),x43951),f33(x43954,f888(x43952,a879))),x43955)),x43956)),f335(f335(f33(x43954,f888(x43952,a879)),f335(f335(f33(x43951,f888(x43954,a879)),x43953),x43955)),x43956))
% 59.73/59.66 [4396]E(f335(f335(f34(x43961,f888(x43962,a879)),x43963),f335(f335(f7(x43961,f888(x43964,f888(x43962,a879)),f888(x43962,a879)),f335(f335(f8(f888(x43964,a879),f888(f888(x43964,f888(x43962,a879)),f888(x43962,a879)),x43961),f34(x43964,f888(x43962,a879))),x43965)),x43966)),f335(f335(f34(x43964,f888(x43962,a879)),f335(f335(f33(x43961,f888(x43964,a879)),x43963),x43965)),x43966))
% 59.73/59.66 [4397]E(f335(f335(f33(x43971,f888(x43972,a879)),x43973),f335(f335(f7(x43971,f888(x43974,f888(x43972,a879)),f888(x43972,a879)),f335(f335(f8(f888(x43974,a879),f888(f888(x43974,f888(x43972,a879)),f888(x43972,a879)),x43971),f33(x43974,f888(x43972,a879))),x43975)),x43976)),f335(f335(f33(x43974,f888(x43972,a879)),f335(f335(f33(x43971,f888(x43974,a879)),x43973),x43975)),x43976))
% 59.73/59.66 [4398]E(f335(f335(f34(x43981,f888(x43982,a879)),x43983),f335(f335(f7(x43981,f888(x43984,f888(x43982,a879)),f888(x43982,a879)),f335(f335(f8(f888(x43984,a879),f888(f888(x43984,f888(x43982,a879)),f888(x43982,a879)),x43981),f34(x43984,f888(x43982,a879))),x43985)),x43986)),f335(f335(f34(x43984,f888(x43982,a879)),f335(f335(f33(x43981,f888(x43984,a879)),x43983),x43985)),x43986))
% 59.73/59.66 [4452]E(f335(f268(x44521,x44522,f887(x44523,x44524)),f335(f335(f7(x44521,f888(x44522,x44524),f888(x44522,f887(x44523,x44524))),f335(f335(f8(f888(x44524,f887(x44523,x44524)),f888(f888(x44522,x44524),f888(x44522,f887(x44523,x44524))),x44521),f8(x44524,f887(x44523,x44524),x44522)),f335(f335(f8(x44523,f888(x44524,f887(x44523,x44524)),x44521),f264(x44523,x44524)),x44525))),x44526)),f269(x44521,x44523,x44522,x44524,x44525,x44526))
% 59.73/59.66 [4371]E(f335(f335(f335(f67(x43711,f885(x43712)),f182(x43711,x43712,x43713,f335(f335(f23(f888(x43711,a879)),x43714),f335(f335(f312(x43711),x43715),f188(f888(x43711,a879)))))),x43715),x43716),f335(f335(f335(f67(x43711,f885(x43712)),f182(x43711,x43712,x43713,x43714)),x43715),x43716))
% 59.73/59.66 [4477]E(f335(f313(x44771,x44772,f335(f335(f18(x44771,x44772,x44772),f335(f335(f18(x44771,x44772,f888(x44772,x44772)),f335(f335(f8(a879,f888(x44772,f888(x44772,x44772)),x44771),f88(x44772)),x44773)),x44774)),x44775)),x44776),f335(f335(f104(f888(x44772,a879)),f335(f313(x44771,x44772,x44774),f335(f335(f95(f888(x44771,a879)),x44776),f335(f249(x44771),x44773)))),f335(f313(x44771,x44772,x44775),f335(f335(f95(f888(x44771,a879)),x44776),f335(f249(x44771),f335(f335(f8(a879,a879,x44771),a330),x44773))))))
% 59.73/59.66 [4488]E(f335(f313(x44881,f887(x44882,x44883),f335(f335(f18(x44881,x44883,f887(x44882,x44883)),f335(f335(f8(x44882,f888(x44883,f887(x44882,x44883)),x44881),f264(x44882,x44883)),x44884)),x44885)),x44886),f335(f335(f266(x44882,x44883),f335(f313(x44881,x44882,x44884),x44886)),f335(f335(f8(f888(x44881,a879),f888(x44883,a879),x44882),f313(x44881,x44883,x44885)),f335(f335(f7(x44882,f888(x44881,a879),f888(x44881,a879)),f335(f335(f8(f888(x44881,a879),f888(f888(x44881,a879),f888(x44881,a879)),x44882),f95(f888(x44881,a879))),f335(f335(f8(f888(x44882,a879),f888(x44881,a879),x44882),f314(x44881,x44882,x44884)),f335(f335(f7(x44882,f888(x44882,a879),f888(x44882,a879)),f312(x44882)),f188(f888(x44882,a879)))))),x44886))))
% 59.73/59.66 [4434]E(f335(f267(x44341,x44342),f335(f269(x44343,x44341,x44344,x44342,x44345,x44346),x44347)),f335(x44346,f335(f267(x44343,x44344),x44347)))
% 59.73/59.66 [4435]E(f335(f263(x44351,x44352),f335(f269(x44353,x44351,x44354,x44352,x44355,x44356),x44357)),f335(x44355,f335(f263(x44353,x44354),x44357)))
% 59.73/59.66 [4131]E(f335(f335(f175(x41311,x41312),f335(f335(f152(x41311,x41313),x41314),x41315)),f335(f335(f152(x41312,x41316),x41314),x41317)),f335(f335(f152(f887(x41311,x41312),f335(f335(f175(x41311,x41312),x41313),x41316)),x41314),f335(f335(f264(x41311,x41312),x41315),x41317)))
% 59.73/59.66 [4199]E(f335(f335(f335(f270(x41991,x41992,x41993,x41994),x41995),x41996),x41997),f335(f335(f268(x41992,x41993,x41994),x41996),f335(x41995,x41997)))
% 59.73/59.66 [4200]E(f335(f335(f335(f270(x42001,x42002,x42003,x42004),x42005),x42006),x42007),f335(f335(f268(x42002,x42003,x42004),x42006),f335(x42005,x42007)))
% 59.73/59.66 [4213]E(f335(f335(f335(f270(x42131,x42132,x42133,x42134),x42135),x42136),x42137),f335(f335(x42136,f335(f263(x42132,x42133),f335(x42135,x42137))),f335(f267(x42132,x42133),f335(x42135,x42137))))
% 59.73/59.66 [4249]E(f181(x42491,x42492,f335(f335(f335(f67(x42491,f885(x42492)),x42493),x42494),f335(f235(x42492),x42495)),x42496,x42497),f181(x42491,x42492,x42493,f335(f335(f144(x42491),x42494),x42496),f335(f335(f144(x42492),x42495),x42497)))
% 59.73/59.66 [4269]E(f335(f68(x42691,x42692,x42693,x42694),f335(f68(x42695,x42691,x42693,x42696),x42697)),f335(f68(x42695,x42692,x42693,f335(f68(x42691,x42692,x42695,x42694),x42696)),x42697))
% 59.73/59.66 [4330]E(f335(f68(f885(x43301),f885(x43302),x43303,f335(f201(x43301,x43302),x43304)),f335(f335(f335(f67(x43303,f885(x43301)),x43305),x43306),f335(f235(x43301),x43307))),f335(f335(f335(f67(x43303,f885(x43302)),f335(f68(f885(x43301),f885(x43302),x43303,f335(f201(x43301,x43302),x43304)),x43305)),x43306),f335(f235(x43302),f335(x43304,x43307))))
% 59.73/59.66 [4459]E(f335(f269(x44591,x44592,x44593,x44593,x44594,f25(x44593)),f335(f269(x44591,x44591,x44595,x44593,f25(x44591),x44596),x44597)),f335(f335(f264(x44592,x44593),f335(x44594,f335(f263(x44591,x44595),x44597))),f335(x44596,f335(f267(x44591,x44595),x44597))))
% 59.73/59.66 [4460]E(f335(f269(x44601,x44601,x44602,x44603,f25(x44601),x44604),f335(f269(x44605,x44601,x44602,x44602,x44606,f25(x44602)),x44607)),f335(f335(f264(x44601,x44603),f335(x44606,f335(f263(x44605,x44602),x44607))),f335(x44604,f335(f267(x44605,x44602),x44607))))
% 59.73/59.66 [4475]E(f335(f269(x44751,x44752,x44753,x44753,x44754,f25(x44753)),f335(f269(x44755,x44751,x44753,x44753,x44756,f25(x44753)),x44757)),f335(f269(x44755,x44752,x44753,x44753,f335(f68(x44751,x44752,x44755,x44754),x44756),f25(x44753)),x44757))
% 59.73/59.66 [4476]E(f335(f269(x44761,x44761,x44762,x44763,f25(x44761),x44764),f335(f269(x44761,x44761,x44765,x44762,f25(x44761),x44766),x44767)),f335(f269(x44761,x44761,x44765,x44763,f25(x44761),f335(f68(x44762,x44763,x44765,x44764),x44766)),x44767))
% 59.73/59.66 [4485]E(f335(f269(x44851,x44852,x44853,x44853,x44854,f25(x44853)),f335(f269(x44851,x44851,x44855,x44853,f25(x44851),x44856),x44857)),f335(f269(x44852,x44852,x44855,x44853,f25(x44852),x44856),f335(f269(x44851,x44852,x44855,x44855,x44854,f25(x44855)),x44857)))
% 59.73/59.66 [4166]E(f335(f335(f291(x41661,x41662,x41663),f335(f335(f291(x41661,x41664,x41662),x41665),x41666)),x41667),f335(f335(f291(x41661,x41664,x41663),x41665),f335(f335(f291(x41664,x41662,x41663),x41666),x41667)))
% 59.73/59.66 [4240]E(f335(f335(f268(x42401,x42402,x42403),f335(f68(x42404,f888(x42402,x42403),x42401,x42405),x42406)),x42407),f335(f335(x42405,f335(x42406,f335(f263(x42401,x42402),x42407))),f335(f267(x42401,x42402),x42407)))
% 59.73/59.66 [4294]E(f335(f68(x42941,x42942,x42943,x42944),f335(f335(f335(f67(x42943,x42941),x42945),x42946),x42947)),f335(f335(f335(f67(x42943,x42942),f335(f68(x42941,x42942,x42943,x42944),x42945)),x42946),f335(x42944,x42947)))
% 59.73/59.66 [4326]E(f335(f135(x43261,x43262,f335(f7(x43262,x43261,x43261),x43263),x43264),f335(f162(x43262),f335(f335(f147(x43265,x43262),x43266),x43267))),f335(f135(x43261,x43265,f335(f7(x43265,x43261,x43261),f335(f68(x43262,f888(x43261,x43261),x43265,x43263),x43266)),x43264),f335(f162(x43265),x43267)))
% 59.73/59.66 [4331]E(f322(x43311,f885(x43312),x43313,f335(f68(f885(x43314),f885(x43312),x43311,f335(f201(x43314,x43312),x43315)),x43316),f335(f68(f885(x43314),f885(x43312),x43313,f335(f201(x43314,x43312),x43315)),x43317)),f335(f68(f885(x43314),f885(x43312),f889(x43311,x43313),f335(f201(x43314,x43312),x43315)),f322(x43311,f885(x43314),x43313,x43316,x43317)))
% 59.73/59.66 [4270]E(f335(f335(f33(x42701,f888(f887(x42702,x42703),a879)),x42704),f335(f335(f8(f888(f887(x42705,x42703),a879),f888(f887(x42702,x42703),a879),x42701),f335(f291(x42702,x42705,x42703),x42706)),x42707)),f335(f335(f291(x42702,x42705,x42703),x42706),f335(f335(f33(x42701,f888(f887(x42705,x42703),a879)),x42704),x42707)))
% 59.73/59.66 [4421]E(f335(f335(f33(x44211,f888(f887(x44212,x44213),a879)),x44214),f335(f335(f7(x44211,f888(f887(x44215,x44213),a879),f888(f887(x44212,x44213),a879)),f335(f335(f8(f888(f887(x44212,x44215),a879),f888(f888(f887(x44215,x44213),a879),f888(f887(x44212,x44213),a879)),x44211),f291(x44212,x44215,x44213)),x44216)),x44217)),f335(f335(f291(x44212,x44215,x44213),f335(f335(f33(x44211,f888(f887(x44212,x44215),a879)),x44214),x44216)),x44217))
% 59.73/59.66 [4422]E(f335(f135(x44221,x44222,f335(f335(f7(x44221,f888(x44222,x44223),f888(x44222,x44221)),f335(f335(f8(f888(x44223,x44221),f888(f888(x44222,x44223),f888(x44222,x44221)),x44221),f8(x44223,x44221,x44222)),x44224)),x44225),x44226),x44227),f335(f135(x44221,x44223,x44224,x44226),f335(f335(f147(x44222,x44223),x44225),x44227)))
% 59.73/59.66 [4486]E(f335(f335(f34(x44861,f888(x44862,a879)),x44863),f335(f335(f8(f888(x44864,f888(x44862,a879)),f888(x44862,a879),x44861),f335(f34(x44864,f888(x44862,a879)),x44865)),f335(f335(f7(x44861,f888(x44864,f888(x44862,a879)),f888(x44864,f888(x44862,a879))),f335(f335(f8(f888(f888(x44862,a879),f888(x44862,a879)),f888(f888(x44864,f888(x44862,a879)),f888(x44864,f888(x44862,a879))),x44861),f8(f888(x44862,a879),f888(x44862,a879),x44864)),f335(f335(f8(f888(x44862,a879),f888(f888(x44862,a879),f888(x44862,a879)),x44861),f104(f888(x44862,a879))),x44866))),x44867))),f335(f335(f104(f888(x44862,a879)),f335(f335(f34(x44861,f888(x44862,a879)),x44863),x44866)),f335(f335(f34(x44864,f888(x44862,a879)),x44865),x44867)))
% 59.73/59.66 [4487]E(f335(f335(f33(x44871,f888(x44872,a879)),x44873),f335(f335(f8(f888(x44874,f888(x44872,a879)),f888(x44872,a879),x44871),f335(f33(x44874,f888(x44872,a879)),x44875)),f335(f335(f7(x44871,f888(x44874,f888(x44872,a879)),f888(x44874,f888(x44872,a879))),f335(f335(f8(f888(f888(x44872,a879),f888(x44872,a879)),f888(f888(x44874,f888(x44872,a879)),f888(x44874,f888(x44872,a879))),x44871),f8(f888(x44872,a879),f888(x44872,a879),x44874)),f335(f335(f8(f888(x44872,a879),f888(f888(x44872,a879),f888(x44872,a879)),x44871),f95(f888(x44872,a879))),x44876))),x44877))),f335(f335(f95(f888(x44872,a879)),f335(f335(f33(x44871,f888(x44872,a879)),x44873),x44876)),f335(f335(f33(x44874,f888(x44872,a879)),x44875),x44877)))
% 59.73/59.66 [4480]E(f198(x44801,x44802,f335(f335(f335(x44803,x44804),x44805),x44806),f335(f335(f7(x44801,f887(a93,a93),f888(a93,f883(x44802))),f335(f335(f7(x44801,a93,f888(f887(a93,a93),f888(a93,f883(x44802)))),f335(f335(f7(x44801,a93,f888(a93,f888(f887(a93,a93),f888(a93,f883(x44802))))),x44807),x44804)),x44805)),x44806)),f335(f335(f335(f212(x44801,x44802,x44803,x44807),x44804),x44805),x44806))
% 59.73/59.66 [4493]E(f199(x44931,x44932,f335(f335(f335(x44933,x44934),x44935),x44936),f335(f335(f7(x44931,f887(a93,a93),f888(a93,f883(x44932))),f335(f335(f7(x44931,a93,f888(f887(a93,a93),f888(a93,f883(x44932)))),f335(f335(f7(x44931,a93,f888(a93,f888(f887(a93,a93),f888(a93,f883(x44932))))),x44937),x44934)),x44935)),x44936)),f214(x44931,x44932,x44933,x44937,x44934,x44935,x44936))
% 59.73/59.66 [4484]E(f195(x44841,x44842,f335(f335(f335(x44843,x44844),x44845),x44846),f335(f335(f7(x44841,f887(a93,a93),f888(a93,f883(f885(x44842)))),f335(f335(f7(x44841,a93,f888(f887(a93,a93),f888(a93,f883(f885(x44842))))),f335(f335(f7(x44841,a93,f888(a93,f888(f887(a93,a93),f888(a93,f883(f885(x44842)))))),x44847),x44844)),x44845)),x44846)),f335(f335(f335(f209(x44841,x44842,x44843,x44847),x44844),x44845),x44846))
% 59.73/59.66 [4495]E(f196(x44951,x44952,f335(f335(f335(x44953,x44954),x44955),x44956),f335(f335(f7(x44951,f887(a93,a93),f888(a93,f883(f885(x44952)))),f335(f335(f7(x44951,a93,f888(f887(a93,a93),f888(a93,f883(f885(x44952))))),f335(f335(f7(x44951,a93,f888(a93,f888(f887(a93,a93),f888(a93,f883(f885(x44952)))))),x44957),x44954)),x44955)),x44956)),f211(x44951,x44952,x44953,x44957,x44954,x44955,x44956))
% 59.73/59.66 [4391]E(f335(f269(x43911,x43912,x43913,x43914,x43915,x43916),f335(f335(f264(x43911,x43913),x43917),x43918)),f335(f335(f264(x43912,x43914),f335(x43915,x43917)),f335(x43916,x43918)))
% 59.73/59.66 [4497]E(f335(f335(f147(f887(x44971,x44972),f887(x44973,x44974)),f335(f268(x44971,x44972,f887(x44973,x44974)),f335(f335(f7(x44971,f888(x44972,x44974),f888(x44972,f887(x44973,x44974))),f335(f335(f8(f888(x44974,f887(x44973,x44974)),f888(f888(x44972,x44974),f888(x44972,f887(x44973,x44974))),x44971),f8(x44974,f887(x44973,x44974),x44972)),f335(f335(f8(x44973,f888(x44974,f887(x44973,x44974)),x44971),f264(x44973,x44974)),x44975))),x44976))),f335(f335(f175(x44971,x44972),x44977),x44978)),f335(f335(f175(x44973,x44974),f335(f335(f147(x44971,x44973),x44975),x44977)),f335(f335(f147(x44972,x44974),x44976),x44978)))
% 59.73/59.66 [4501]E(f335(f335(f147(f887(x45011,x45012),x45013),f335(f268(x45011,x45012,x45013),f335(f335(f8(f888(x45012,f887(x45011,x45014)),f888(x45012,x45013),x45011),f335(f8(f887(x45011,x45014),x45013,x45012),x45015)),f335(f335(f7(x45011,f888(x45012,x45014),f888(x45012,f887(x45011,x45014))),f335(f335(f8(f888(x45014,f887(x45011,x45014)),f888(f888(x45012,x45014),f888(x45012,f887(x45011,x45014))),x45011),f8(x45014,f887(x45011,x45014),x45012)),f264(x45011,x45014))),x45016)))),f335(f335(f175(x45011,x45012),x45017),x45018)),f335(f335(f147(f887(x45011,x45014),x45013),x45015),f335(f335(f175(x45011,x45014),x45017),f335(f335(f147(x45012,x45014),x45016),x45018))))
% 59.73/59.66 [4426]E(f335(f335(f147(f887(x44261,x44262),x44263),f335(f268(x44261,x44262,x44263),f335(f335(f8(f888(x44262,f887(x44264,x44262)),f888(x44262,x44263),x44261),f335(f8(f887(x44264,x44262),x44263,x44262),x44265)),f335(f335(f8(x44264,f888(x44262,f887(x44264,x44262)),x44261),f264(x44264,x44262)),x44266)))),f335(f335(f175(x44261,x44262),x44267),x44268)),f335(f335(f147(f887(x44264,x44262),x44263),x44265),f335(f335(f175(x44264,x44262),f335(f335(f147(x44261,x44264),x44266),x44267)),x44268)))
% 59.73/59.66 [4382]E(f335(f335(f268(x43821,x43822,x43823),f335(f335(f8(f888(x43822,f887(x43824,x43825)),f888(x43822,x43823),x43821),f335(f8(f887(x43824,x43825),x43823,x43822),f335(f268(x43824,x43825,x43823),x43826))),x43827)),x43828),f335(f335(f268(x43824,x43825,x43823),x43826),f335(f335(f268(x43821,x43822,f887(x43824,x43825)),x43827),x43828)))
% 59.73/59.66 [4502]E(f335(f335(f33(f887(x45021,x45022),f888(f887(x45023,x45024),a879)),f335(f335(f266(x45021,x45022),x45025),f335(f16(f888(x45022,a879),x45021),x45026))),f335(f268(x45021,x45022,f888(f887(x45023,x45024),a879)),f335(f335(f7(x45021,f888(x45022,f888(x45023,f888(x45024,a879))),f888(x45022,f888(f887(x45023,x45024),a879))),f335(f335(f8(f888(f888(x45023,f888(x45024,a879)),f888(f887(x45023,x45024),a879)),f888(f888(x45022,f888(x45023,f888(x45024,a879))),f888(x45022,f888(f887(x45023,x45024),a879))),x45021),f8(f888(x45023,f888(x45024,a879)),f888(f887(x45023,x45024),a879),x45022)),f335(f335(f8(f888(x45023,a879),f888(f888(x45023,f888(x45024,a879)),f888(f887(x45023,x45024),a879)),x45021),f266(x45023,x45024)),x45027))),f335(f335(f8(f888(x45024,a879),f888(x45023,f888(x45024,a879)),x45022),f16(f888(x45024,a879),x45023)),x45028)))),f335(f335(f266(x45023,x45024),f335(f335(f33(x45021,f888(x45023,a879)),x45025),x45027)),f335(f16(f888(x45024,a879),x45023),f335(f335(f33(x45022,f888(x45024,a879)),x45026),x45028))))
% 59.73/59.66 [4440]E(f335(f335(f270(x44401,x44402,x44403,x44404),f335(f335(f270(x44401,x44405,x44406,f887(x44402,x44403)),x44407),x44408)),x44409),f335(f335(f270(x44401,x44405,x44406,x44404),x44407),f335(f335(f7(x44405,f888(x44402,f888(x44403,x44404)),f888(x44406,x44404)),f335(f335(f8(f888(x44406,f887(x44402,x44403)),f888(f888(x44402,f888(x44403,x44404)),f888(x44406,x44404)),x44405),f270(x44406,x44402,x44403,x44404)),x44408)),x44409)))
% 59.73/59.66 [4471]E(f335(f68(f887(x44711,x44712),f887(x44713,x44714),f887(x44715,x44716),f269(x44711,x44713,x44712,x44714,x44717,x44718)),f269(x44715,x44711,x44716,x44712,x44719,x447110)),f269(x44715,x44713,x44716,x44714,f335(f68(x44711,x44713,x44715,x44717),x44719),f335(f68(x44712,x44714,x44716,x44718),x447110)))
% 59.73/59.66 [4472]E(f335(f68(f887(x44721,x44722),f887(x44723,x44724),f887(x44725,x44726),f269(x44721,x44723,x44722,x44724,x44727,x44728)),f269(x44725,x44721,x44726,x44722,x44729,x447210)),f269(x44725,x44723,x44726,x44724,f335(f68(x44721,x44723,x44725,x44727),x44729),f335(f68(x44722,x44724,x44726,x44728),x447210)))
% 59.73/59.66 [4478]E(f335(f269(x44781,x44782,x44783,x44784,x44785,x44786),f335(f269(x44787,x44781,x44788,x44783,x44789,x447810),x447811)),f335(f269(x44787,x44782,x44788,x44784,f335(f68(x44781,x44782,x44787,x44785),x44789),f335(f68(x44783,x44784,x44788,x44786),x447810)),x447811))
% 59.73/59.66 [4615]~P96(x46151)+E(f86(x46151),a332)
% 59.73/59.66 [4616]~P96(x46161)+E(f86(x46161),a332)
% 59.73/59.66 [4617]~P4(x46171)+P4(f885(x46171))
% 59.73/59.66 [4618]~P65(x46181)+P65(f885(x46181))
% 59.73/59.66 [4619]~P104(x46191)+P104(f882(x46191))
% 59.73/59.66 [4621]~P141(x46211)+~E(f73(x46211),f2(x46211))
% 59.73/59.66 [4622]~P141(x46221)+~E(f73(x46221),f2(x46221))
% 59.73/59.66 [4624]~E(x46241,f2(a93))+E(f335(a21,x46241),f2(a1))
% 59.73/59.66 [4625]~E(x46251,f2(a1))+E(f77(a1,x46251),f2(a1))
% 59.73/59.66 [4631]~P143(x46311)+P28(x46311,f2(x46311))
% 59.73/59.66 [4632]~P106(x46321)+P15(x46321,f107(x46321))
% 59.73/59.66 [4633]~P106(x46331)+P15(x46331,f107(x46331))
% 59.73/59.66 [4642]P1(x46421)+P1(f335(a330,x46421))
% 59.73/59.66 [4685]~P143(x46851)+~P28(x46851,f73(x46851))
% 59.73/59.66 [4727]~P1(x47271)+~P1(f335(a330,x47271))
% 59.73/59.66 [4750]E(f335(a98,x47501),f2(a881))+~P1(f335(a193,x47501))
% 59.73/59.66 [4816]~P60(x48161)+P17(x48161,x48161,f104(x48161))
% 59.73/59.66 [4817]~P102(x48171)+P17(x48171,x48171,f95(x48171))
% 59.73/59.66 [4818]~P98(x48181)+P17(x48181,x48181,f76(x48181))
% 59.73/59.66 [4819]~P106(x48191)+P17(x48191,x48191,f240(x48191))
% 59.73/59.66 [4820]~P106(x48201)+P17(x48201,x48201,f241(x48201))
% 59.73/59.66 [4821]~P70(x48211)+P18(x48211,x48211,f76(x48211))
% 59.73/59.66 [4628]~E(x46281,f2(a881))+E(f335(f94(a1),x46281),f2(a1))
% 59.73/59.66 [4634]~P97(x46341)+E(f335(f97(x46341),a78),f2(x46341))
% 59.73/59.66 [4635]~P97(x46351)+E(f335(f97(x46351),a78),f2(x46351))
% 59.73/59.66 [4638]~E(f556(x46381),f2(a881))+E(f335(f159(a881),x46381),f2(a881))
% 59.73/59.66 [4639]~P108(x46391)+E(f244(x46391,f242(x46391)),f240(x46391))
% 59.73/59.66 [4640]~P108(x46401)+E(f245(x46401,f242(x46401)),f241(x46401))
% 59.73/59.66 [4641]~P91(x46411)+E(f77(x46411,f2(x46411)),f2(x46411))
% 59.73/59.66 [4650]~P137(x46501)+E(f335(f96(x46501),f73(a1)),f73(x46501))
% 59.73/59.66 [4651]~P137(x46511)+E(f335(f96(x46511),f2(a1)),f2(x46511))
% 59.73/59.66 [4652]~P143(x46521)+E(f335(f94(x46521),f73(a881)),f73(x46521))
% 59.73/59.66 [4653]~P143(x46531)+E(f335(f94(x46531),f2(a881)),f2(x46531))
% 59.73/59.66 [4654]E(x46541,f2(a881))+~E(f335(f94(a1),x46541),f2(a1))
% 59.73/59.66 [4679]~P84(x46791)+E(f335(f74(x46791),f188(x46791)),f252(x46791))
% 59.73/59.66 [4680]~P84(x46801)+E(f335(f74(x46801),f252(x46801)),f188(x46801))
% 59.73/59.66 [4681]~P72(x46811)+E(f335(f74(x46811),f2(x46811)),f2(x46811))
% 59.73/59.66 [4682]~P119(x46821)+E(f335(f70(x46821),f73(x46821)),f73(x46821))
% 59.73/59.66 [4683]~P88(x46831)+E(f335(f70(x46831),f2(x46831)),f2(x46831))
% 59.73/59.66 [4684]~P83(x46841)+E(f335(f159(x46841),f107(x46841)),f2(x46841))
% 59.73/59.66 [4704]~P35(x47041)+P38(f335(f166(a1),x47041))
% 59.73/59.66 [4731]~P97(x47311)+E(f335(f74(x47311),f73(x47311)),f335(f97(x47311),a91))
% 59.73/59.66 [4732]~P97(x47321)+E(f335(f74(x47321),f73(x47321)),f335(f97(x47321),a91))
% 59.73/59.66 [4749]~P97(x47491)+P28(x47491,f335(f97(x47491),a78))
% 59.73/59.66 [4765]~P4(x47651)+E(f335(f166(x47651),f50(x47651)),f252(f888(x47651,a879)))
% 59.73/59.66 [4766]~P4(x47661)+E(f335(f166(x47661),f50(x47661)),f252(f888(x47661,a879)))
% 59.73/59.66 [4776]P35(x47761)+~P38(f335(f166(a1),x47761))
% 59.73/59.66 [4777]~P4(x47771)+P1(f335(f130(x47771),f50(x47771)))
% 59.73/59.66 [4822]E(f335(f94(a1),f335(a98,x48221)),x48221)+P1(f335(a193,x48221))
% 59.73/59.66 [4890]~P113(x48901)+E(f255(x48901,f73(x48901),f76(x48901)),f254(x48901))
% 59.73/59.66 [4920]~P97(x49201)+~P28(x49201,f335(f97(x49201),a91))
% 59.73/59.66 [5009]~E(x50091,f2(a881))+P1(f335(f335(f242(a881),x50091),f2(a881)))
% 59.73/59.66 [5063]E(f335(f70(a1),x50631),x50631)+P1(f335(f335(f243(a1),x50631),f2(a1)))
% 59.73/59.66 [5081]~E(f335(a98,x50811),f2(a881))+P1(f335(f335(f242(a1),x50811),f2(a1)))
% 59.73/59.66 [5146]~P1(f335(a193,x51461))+P1(f335(f335(f243(a1),x51461),f2(a1)))
% 59.73/59.66 [5189]~P122(x51891)+P1(f335(f335(f242(x51891),f2(x51891)),f73(x51891)))
% 59.73/59.66 [5190]~P137(x51901)+P1(f335(f335(f337(x51901),f73(x51901)),f103(x51901)))
% 59.73/59.66 [5191]~P143(x51911)+P1(f335(f335(f337(x51911),f73(x51911)),f186(x51911)))
% 59.73/59.66 [5192]~P137(x51921)+P1(f335(f335(f337(x51921),f2(x51921)),f103(x51921)))
% 59.73/59.66 [5193]~P143(x51931)+P1(f335(f335(f337(x51931),f2(x51931)),f186(x51931)))
% 59.73/59.66 [5194]~P122(x51941)+P1(f335(f335(f243(x51941),f2(x51941)),f73(x51941)))
% 59.73/59.66 [5246]E(x52461,f2(a881))+~P1(f335(f335(f242(a881),x52461),f2(a881)))
% 59.73/59.66 [5289]E(f335(a98,x52891),f2(a881))+~P1(f335(f335(f242(a1),x52891),f2(a1)))
% 59.73/59.66 [5290]E(f335(a98,x52901),f2(a881))+~P1(f335(f335(f242(a1),x52901),f2(a1)))
% 59.73/59.66 [5347]P1(f335(a193,x53471))+~P1(f335(f335(f243(a1),x53471),f2(a1)))
% 59.73/59.66 [5352]~P106(x53521)+P18(x53521,f882(x53521),f141(x53521,x53521,f5(x53521)))
% 59.73/59.66 [5369]P38(x53691)+~P1(f335(f335(f242(a1),f2(a1)),f341(x53691)))
% 59.73/59.66 [5375]E(f335(f70(a1),x53751),f335(f74(a1),x53751))+~P1(f335(f335(f243(a1),x53751),f2(a1)))
% 59.73/59.66 [5547]~P122(x55471)+~P1(f335(f335(f242(x55471),f73(x55471)),f2(x55471)))
% 59.73/59.66 [5548]~P122(x55481)+~P1(f335(f335(f243(x55481),f73(x55481)),f2(x55481)))
% 59.73/59.66 [5558]~E(x55581,f2(a881))+P1(f335(f335(f242(a1),f335(f94(a1),x55581)),f2(a1)))
% 59.73/59.66 [5559]~E(x55591,f2(a1))+P1(f335(f335(f243(a1),f335(f70(a1),x55591)),f73(a1)))
% 59.73/59.66 [5681]~P83(x56811)+E(f135(x56811,x56811,f75(x56811),f2(x56811)),f159(x56811))
% 59.73/59.66 [5853]~P103(x58531)+P26(a881,x58531,f94(x58531),f252(f888(a881,a879)))
% 59.73/59.66 [6050]E(x60501,f2(a881))+~P1(f335(f335(f242(a1),f335(f94(a1),x60501)),f2(a1)))
% 59.73/59.66 [6051]E(x60511,f2(a1))+~P1(f335(f335(f243(a1),f335(f70(a1),x60511)),f73(a1)))
% 59.73/59.66 [6854]~P1(f335(f335(f243(a1),x68541),f2(a1)))+P1(f335(f335(f243(a1),f335(f335(f75(a1),x68541),x68541)),f2(a1)))
% 59.73/59.66 [7404]P1(f335(f335(f243(a1),x74041),f2(a1)))+~P1(f335(f335(f243(a1),f335(f335(f75(a1),x74041),x74041)),f2(a1)))
% 59.73/59.66 [7962]E(x79621,f335(a3,f2(a881)))+P1(f335(f335(f243(a881),f335(f335(f23(a881),f335(a20,x79621)),f335(a106,f2(a881)))),f335(a20,x79621)))
% 59.73/59.66 [8725]~P1(f335(f335(f243(a1),x87251),f2(a1)))+P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f75(a1),x87251),x87251)),a91)),f2(a1)))
% 59.73/59.66 [8815]~P1(f335(f335(f243(a1),x88151),f2(a1)))+P1(f335(f335(f243(a1),f335(f335(f75(a1),f335(f335(f75(a1),f73(a1)),x88151)),x88151)),f2(a1)))
% 59.73/59.66 [9135]P1(f335(f335(f243(a1),x91351),f2(a1)))+~P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f75(a1),x91351),x91351)),a91)),f2(a1)))
% 59.73/59.66 [9199]P1(f335(f335(f243(a1),x91991),f2(a1)))+~P1(f335(f335(f243(a1),f335(f335(f75(a1),f335(f335(f75(a1),f73(a1)),x91991)),x91991)),f2(a1)))
% 59.73/59.66 [4720]~E(a78,x47201)+E(f335(f335(f75(a1),x47201),x47201),a78)
% 59.73/59.66 [4721]~E(x47211,a78)+E(f335(f335(f75(a1),x47211),x47211),a78)
% 59.73/59.66 [4735]E(x47351,f2(a1))+E(f335(f335(f30(a1),x47351),x47351),f73(a1))
% 59.73/59.66 [4867]E(x48671,a78)+~E(f335(f335(f75(a1),x48671),x48671),a78)
% 59.73/59.66 [4868]E(a78,x48681)+~E(f335(f335(f75(a1),x48681),x48681),a78)
% 59.73/59.66 [4870]~P97(x48701)+E(f335(f96(x48701),f335(f97(a1),a91)),f335(f97(x48701),a91))
% 59.73/59.66 [4880]~P5(x48801)+E(f32(x48801,f188(f888(x48801,a879))),f252(x48801))
% 59.73/59.66 [4881]~P5(x48811)+E(f32(x48811,f252(f888(x48811,a879))),f188(x48811))
% 59.73/59.66 [4882]~P5(x48821)+E(f31(x48821,f188(f888(x48821,a879))),f188(x48821))
% 59.73/59.66 [4883]~P5(x48831)+E(f31(x48831,f252(f888(x48831,a879))),f252(x48831))
% 59.73/59.66 [4884]~P106(x48841)+E(f132(x48841,f188(f888(x48841,a879))),f107(x48841))
% 59.73/59.66 [5020]E(x50201,f2(a881))+P1(f335(f335(f243(a881),f2(a881)),x50201))
% 59.73/59.66 [5021]E(x50211,f2(a881))+P1(f335(f335(f243(a881),f2(a881)),x50211))
% 59.73/59.66 [5040]~P6(x50401)+P1(f335(f335(f242(a1),f2(a1)),x50401))
% 59.73/59.66 [5071]~E(f335(f97(a881),x50711),f2(a881))+P1(f335(f335(f242(a1),x50711),a78))
% 59.73/59.66 [5072]~E(f335(f97(a881),x50721),f2(a881))+P1(f335(f335(f242(a1),x50721),a78))
% 59.73/59.66 [5077]P38(x50771)+P1(f335(f335(f337(a1),f341(x50771)),x50771))
% 59.73/59.66 [5078]E(x50781,f335(a3,f2(a881)))+P1(f335(f335(f242(a93),f73(a93)),x50781))
% 59.73/59.66 [5119]P1(f335(a193,x51191))+P1(f335(f335(f242(a1),f2(a1)),x51191))
% 59.73/59.66 [5171]E(f335(f94(a1),f335(a98,x51711)),f2(a1))+P1(f335(f335(f242(a1),f2(a1)),x51711))
% 59.73/59.66 [5214]~P65(x52141)+P1(f335(f56(x52141),f252(f888(x52141,a879))))
% 59.73/59.66 [5231]E(f335(f94(a1),f335(f97(a881),x52311)),f335(f97(a1),x52311))+P1(f335(a193,f335(f97(a1),x52311)))
% 59.73/59.66 [5234]~E(x52341,f2(a881))+P1(f335(f335(f243(a881),x52341),f335(a106,f2(a881))))
% 59.73/59.66 [5251]E(f335(f97(a881),x52511),f2(a881))+~P1(f335(f335(f242(a1),x52511),a78))
% 59.73/59.66 [5252]E(f335(f97(a881),x52521),f2(a881))+~P1(f335(a193,f335(f97(a1),x52521)))
% 59.73/59.66 [5253]E(f335(f97(a881),x52531),f2(a881))+~P1(f335(f335(f242(a1),x52531),a78))
% 59.73/59.66 [5287]P6(x52871)+~P1(f335(f335(f242(a1),f2(a1)),x52871))
% 59.73/59.66 [5300]~E(x53001,f2(a881))+~P1(f335(f335(f243(a881),f2(a881)),x53001))
% 59.73/59.66 [5355]E(f335(a106,f343(x53551)),x53551)+~P1(f335(f335(f243(a881),f2(a881)),x53551))
% 59.73/59.66 [5363]E(f335(a106,f335(f97(a881),x53631)),f73(a881))+~P1(f335(a193,f335(f97(a1),x53631)))
% 59.73/59.66 [5371]E(f335(f94(a1),f416(x53711)),x53711)+~P1(f335(f335(f243(a1),f2(a1)),x53711))
% 59.73/59.66 [5378]~E(x53781,f335(a3,f2(a881)))+~P1(f335(f335(f242(a93),f73(a93)),x53781))
% 59.73/59.66 [5385]E(f335(f94(a1),f335(f97(a881),x53851)),f2(a1))+~P1(f335(a193,f335(f97(a1),x53851)))
% 59.73/59.66 [5411]E(f335(f159(a881),x54111),f2(a881))+P1(f335(f335(f337(a881),f556(x54111)),f335(f166(a881),x54111)))
% 59.73/59.66 [5431]E(f335(f94(a1),f335(a98,x54311)),x54311)+~P1(f335(f335(f242(a1),f2(a1)),x54311))
% 59.73/59.66 [5432]E(f335(f94(a1),f335(a98,x54321)),x54321)+~P1(f335(f335(f242(a1),f2(a1)),x54321))
% 59.73/59.66 [5441]~P1(f335(a193,x54411))+~P1(f335(f335(f242(a1),f2(a1)),x54411))
% 59.73/59.66 [5540]E(f335(f335(f75(a881),f73(a881)),f335(f97(a881),x55401)),f73(a881))+~P1(f335(f335(f243(a1),x55401),a78))
% 59.73/59.66 [5600]E(x56001,f2(a881))+~P1(f335(f335(f243(a881),x56001),f335(a106,f2(a881))))
% 59.73/59.66 [5639]E(f335(f335(f23(a881),f335(f97(a881),x56391)),f73(a881)),f2(a881))+~P1(f335(f335(f242(a1),x56391),a78))
% 59.73/59.66 [5640]E(f335(f335(f75(a881),f335(f97(a881),x56401)),f73(a881)),f73(a881))+~P1(f335(f335(f243(a1),x56401),a78))
% 59.73/59.66 [5650]~P38(x56501)+E(f335(f29(a881),f335(f313(a1,a881,a98),x56501)),f335(f29(a1),x56501))
% 59.73/59.66 [5682]~P106(x56821)+E(f245(x56821,f335(f7(x56821,x56821,a879),f242(x56821))),f240(x56821))
% 59.73/59.66 [5683]~P106(x56831)+E(f244(x56831,f335(f7(x56831,x56831,a879),f242(x56831))),f241(x56831))
% 59.73/59.66 [5693]E(f39(a881,f335(a106,f2(a881)),f335(f97(a881),x56931)),f335(a106,f2(a881)))+~P1(f335(a193,f335(f97(a1),x56931)))
% 59.73/59.66 [5702]~P1(f335(f335(f243(a1),f2(a1)),x57021))+P1(f335(f335(f242(a1),f73(a1)),x57021))
% 59.73/59.66 [5703]P1(f335(f335(f243(a1),f2(a1)),x57031))+~P1(f335(f335(f242(a1),f73(a1)),x57031))
% 59.73/59.66 [5713]E(f335(a106,f335(f335(f23(a881),x57131),f73(a881))),x57131)+~P1(f335(f335(f243(a881),f2(a881)),x57131))
% 59.73/59.66 [5714]E(f335(a106,f335(f335(f23(a881),x57141),f73(a881))),x57141)+~P1(f335(f335(f243(a881),f2(a881)),x57141))
% 59.73/59.66 [5770]P1(f335(f335(f243(a881),f2(a881)),f416(x57701)))+~P1(f335(f335(f243(a1),f2(a1)),x57701))
% 59.73/59.66 [5829]E(f39(a1,f335(f97(a1),a91),x58291),f335(f335(f23(a1),x58291),f73(a1)))+~P1(f335(f335(f243(a1),f2(a1)),x58291))
% 59.73/59.66 [5865]~P1(f335(f335(f243(a1),a78),x58651))+P1(f335(f335(f243(a881),f2(a881)),f335(f97(a881),x58651)))
% 59.73/59.66 [5916]P1(f335(f335(f243(a881),f2(a881)),f335(a98,x59161)))+~P1(f335(f335(f243(a1),f2(a1)),x59161))
% 59.73/59.66 [5936]E(f335(a20,f335(a3,x59361)),x59361)+~P1(f335(f335(f337(a881),x59361),f252(f888(a881,a879))))
% 59.73/59.66 [5966]~P1(f335(f335(f243(a881),f2(a881)),x59661))+P1(f335(f335(f243(a1),f2(a1)),f335(f94(a1),x59661)))
% 59.73/59.66 [6001]~P1(f335(f335(f243(a881),f2(a881)),f335(a98,x60011)))+P1(f335(f335(f243(a1),f2(a1)),x60011))
% 59.73/59.66 [6018]~P38(x60181)+E(f335(f313(a881,a1,f94(a1)),f335(f313(a1,a881,a98),x60181)),x60181)
% 59.73/59.66 [6031]P1(f335(f335(f243(a1),a78),x60311))+~P1(f335(f335(f243(a881),f2(a881)),f335(f97(a881),x60311)))
% 59.73/59.66 [6076]~P4(x60761)+E(f335(f335(f144(f885(x60761)),f200(x60761)),f335(f335(f147(x60761,f885(x60761)),f235(x60761)),f50(x60761))),f50(f885(x60761)))
% 59.73/59.66 [6087]P1(f335(f335(f243(a881),f2(a881)),x60871))+~P1(f335(f335(f243(a1),f2(a1)),f335(f94(a1),x60871)))
% 59.73/59.66 [6119]E(f173(x61191,f107(f882(x61191))),f107(f882(x61191)))+~P1(f335(f323(f882(f882(x61191)),f174(x61191)),f107(f882(x61191))))
% 59.73/59.66 [6197]E(f335(f313(a881,a1,f94(a1)),f335(f250(a881),f335(a98,x61971))),f335(f304(a1,f2(a1)),x61971))+~P1(f335(f335(f242(a1),f2(a1)),x61971))
% 59.73/59.66 [6214]~P122(x62141)+P1(f335(f335(f243(x62141),f2(x62141)),f335(f335(f75(x62141),f73(x62141)),f73(x62141))))
% 59.73/59.66 [6265]P1(f335(f335(f243(a881),f335(a106,f2(a881))),f335(a98,x62651)))+~P1(f335(f335(f243(a1),f73(a1)),x62651))
% 59.73/59.66 [6361]E(x63611,f2(a1))+P1(f335(f43(f2(a1),x63611),f335(f335(f264(a1,a1),f2(a1)),f2(a1))))
% 59.73/59.66 [6529]~P1(f335(f335(f243(a881),f335(a106,f2(a881))),f335(a98,x65291)))+P1(f335(f335(f243(a1),f73(a1)),x65291))
% 59.73/59.66 [6578]E(f335(a106,f335(f335(f23(a881),f335(f97(a881),x65781)),f73(a881))),f335(f97(a881),x65781))+~P1(f335(f335(f243(a881),f2(a881)),f335(f97(a881),x65781)))
% 59.73/59.66 [6965]~P109(x69651)+P36(x69651,f335(f249(f887(x69651,x69651)),f335(f268(x69651,x69651,a879),f243(x69651))))
% 59.73/59.66 [5587]E(f335(f97(a881),f335(f335(f23(a1),x55871),a91)),f335(a106,f335(f97(a881),x55871)))+P1(f335(a193,f335(f97(a1),x55871)))
% 59.73/59.66 [5603]~P35(x56031)+E(f335(f335(f147(a881,a1),f94(a1)),f335(f335(f147(a1,a881),a98),x56031)),x56031)
% 59.73/59.66 [5720]E(f335(f74(a1),f335(f94(a1),f335(a106,f417(x57201)))),x57201)+~P1(f335(f335(f243(a1),x57201),f2(a1)))
% 59.73/59.66 [5730]E(f335(f335(f75(a881),f73(a881)),f335(f97(a881),x57301)),f335(f97(a881),f335(f335(f23(a1),x57301),a91)))+P1(f335(f335(f243(a1),x57301),a78))
% 59.73/59.66 [5772]E(f335(f335(f30(a1),f335(f97(a1),a91)),x57721),f335(f97(a1),a91))+~P1(f335(f335(f243(a1),f2(a1)),x57721))
% 59.73/59.66 [5861]E(f335(f335(f23(a881),f335(f97(a881),x58611)),f73(a881)),f335(f97(a881),f335(f335(f75(a1),x58611),a91)))+P1(f335(f335(f242(a1),x58611),a78))
% 59.73/59.66 [5862]E(f335(f335(f75(a881),f335(f97(a881),x58621)),f73(a881)),f335(f97(a881),f335(f335(f23(a1),x58621),a91)))+P1(f335(f335(f243(a1),x58621),a78))
% 59.73/59.66 [5904]E(f335(a98,f335(f335(f75(a1),f73(a1)),x59041)),f335(a106,f335(a98,x59041)))+~P1(f335(f335(f242(a1),f2(a1)),x59041))
% 59.73/59.66 [5938]E(f335(a106,f335(f335(f23(a881),x59381),f335(a106,f2(a881)))),x59381)+~P1(f335(f335(f243(a881),f2(a881)),x59381))
% 59.73/59.66 [6146]E(f39(a881,f335(a106,f2(a881)),f335(f97(a881),x61461)),f335(a98,f39(a1,f73(a1),f335(f97(a1),x61461))))+P1(f335(a193,f335(f97(a1),x61461)))
% 59.73/59.66 [6187]~P1(f335(f335(f242(a1),a78),x61871))+P1(f335(f335(f242(a1),a78),f335(f335(f75(a1),x61871),x61871)))
% 59.73/59.66 [6188]~P1(f335(f335(f243(a1),a91),x61881))+P1(f335(f335(f242(a1),a91),f335(f335(f75(a1),x61881),x61881)))
% 59.73/59.66 [6189]~P1(f335(f335(f243(a1),a78),x61891))+P1(f335(f335(f243(a1),a78),f335(f335(f75(a1),x61891),x61891)))
% 59.73/59.66 [6190]~P1(f335(f335(f243(a1),a91),x61901))+P1(f335(f335(f243(a1),a91),f335(f335(f75(a1),x61901),x61901)))
% 59.73/59.66 [6191]~P1(f335(f335(f86(a1),a78),x61911))+P1(f335(f335(f86(a1),a78),f335(f335(f75(a1),x61911),x61911)))
% 59.73/59.66 [6374]~P1(f335(f56(x63741),f252(f888(x63741,a879))))+P1(f335(f56(f885(x63741)),f252(f888(f885(x63741),a879))))
% 59.73/59.66 [6462]~P1(f335(f335(f242(a1),f2(a1)),x64621))+P1(f335(f335(f243(a1),f2(a1)),f335(f335(f75(a1),f73(a1)),x64621)))
% 59.73/59.66 [6469]E(f335(f263(a1,a1),f41(f73(a1),f335(f97(a1),x64691))),f335(f335(f30(a1),f73(a1)),f335(f97(a1),x64691)))+~P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),x64691)))
% 59.73/59.66 [6489]E(f335(f267(a1,a1),f41(f73(a1),f335(f97(a1),x64891))),f39(a1,f73(a1),f335(f97(a1),x64891)))+~P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),x64891)))
% 59.73/59.66 [6500]P1(f335(f56(x65001),f252(f888(x65001,a879))))+~P1(f335(f56(f885(x65001)),f252(f888(f885(x65001),a879))))
% 59.73/59.66 [6530]P1(f335(f335(f242(a1),a78),x65301))+~P1(f335(f335(f242(a1),a78),f335(f335(f75(a1),x65301),x65301)))
% 59.73/59.66 [6531]P1(f335(f335(f243(a1),a78),x65311))+~P1(f335(f335(f243(a1),a78),f335(f335(f75(a1),x65311),x65311)))
% 59.73/59.66 [6532]P1(f335(f335(f243(a1),a91),x65321))+~P1(f335(f335(f242(a1),a91),f335(f335(f75(a1),x65321),x65321)))
% 59.73/59.66 [6533]P1(f335(f335(f243(a1),a91),x65331))+~P1(f335(f335(f243(a1),a91),f335(f335(f75(a1),x65331),x65331)))
% 59.73/59.66 [6534]P1(f335(f335(f86(a1),a78),x65341))+~P1(f335(f335(f86(a1),a78),f335(f335(f75(a1),x65341),x65341)))
% 59.73/59.66 [6729]~P1(f335(f56(a881),x67291))+P1(f335(f56(a1),f335(f313(a881,a1,f94(a1)),x67291)))
% 59.73/59.66 [6860]~P1(f335(f56(x68601),f252(f888(x68601,a879))))+P1(f335(f335(f243(a881),f2(a881)),f335(f29(x68601),f252(f888(x68601,a879)))))
% 59.73/59.66 [7445]P1(f335(f56(a881),x74451))+~P1(f335(f56(a1),f335(f313(a881,a1,f94(a1)),x74451)))
% 59.73/59.66 [5515]~E(a91,x55151)+E(f335(f335(f23(a1),f335(f335(f75(a1),x55151),x55151)),a91),a91)
% 59.73/59.66 [5516]~E(x55161,a91)+E(f335(f335(f23(a1),f335(f335(f75(a1),x55161),x55161)),a91),a91)
% 59.73/59.66 [6026]E(x60261,a91)+~E(f335(f335(f23(a1),f335(f335(f75(a1),x60261),x60261)),a91),a91)
% 59.73/59.66 [6027]E(a91,x60271)+~E(f335(f335(f23(a1),f335(f335(f75(a1),x60271),x60271)),a91),a91)
% 59.73/59.66 [6430]~E(f335(f97(a881),x64301),f2(a881))+P1(f335(a193,f335(f97(a1),f335(f335(f75(a1),x64301),a91))))
% 59.73/59.66 [6784]~P1(f335(a193,f335(f97(a1),x67841)))+P1(f335(a193,f335(f97(a1),f335(f335(f75(a1),x67841),x67841))))
% 59.73/59.66 [6785]~P1(f335(f335(f242(a1),x67851),a78))+P1(f335(f335(f242(a1),f335(f335(f75(a1),x67851),x67851)),a78))
% 59.73/59.66 [6786]~P1(f335(f335(f242(a1),x67861),a91))+P1(f335(f335(f242(a1),f335(f335(f75(a1),x67861),x67861)),a91))
% 59.73/59.66 [6787]~P1(f335(f335(f243(a1),x67871),a78))+P1(f335(f335(f243(a1),f335(f335(f75(a1),x67871),x67871)),a78))
% 59.73/59.66 [6788]~P1(f335(f335(f242(a1),x67881),a91))+P1(f335(f335(f243(a1),f335(f335(f75(a1),x67881),x67881)),a91))
% 59.73/59.66 [6789]~P1(f335(f335(f86(a1),x67891),a78))+P1(f335(f335(f86(a1),f335(f335(f75(a1),x67891),x67891)),a78))
% 59.73/59.66 [7110]E(f335(f97(a881),x71101),f2(a881))+~P1(f335(a193,f335(f97(a1),f335(f335(f75(a1),x71101),a91))))
% 59.73/59.66 [7355]~P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),x73551)))+P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),f335(f335(f75(a1),x73551),x73551))))
% 59.73/59.66 [7356]P1(f335(a193,f335(f97(a1),x73561)))+~P1(f335(a193,f335(f97(a1),f335(f335(f75(a1),x73561),x73561))))
% 59.73/59.66 [7357]P1(f335(f335(f242(a1),x73571),a78))+~P1(f335(f335(f242(a1),f335(f335(f75(a1),x73571),x73571)),a78))
% 59.73/59.66 [7358]P1(f335(f335(f242(a1),x73581),a91))+~P1(f335(f335(f242(a1),f335(f335(f75(a1),x73581),x73581)),a91))
% 59.73/59.66 [7359]P1(f335(f335(f242(a1),x73591),a91))+~P1(f335(f335(f243(a1),f335(f335(f75(a1),x73591),x73591)),a91))
% 59.73/59.66 [7360]P1(f335(f335(f243(a1),x73601),a78))+~P1(f335(f335(f243(a1),f335(f335(f75(a1),x73601),x73601)),a78))
% 59.73/59.66 [7361]P1(f335(f335(f86(a1),x73611),a78))+~P1(f335(f335(f86(a1),f335(f335(f75(a1),x73611),x73611)),a78))
% 59.73/59.66 [7728]E(f335(a101,f549(x77281)),x77281)+~P1(f335(f335(f337(f888(f887(a881,a881),a879)),x77281),a92))
% 59.73/59.66 [6345]~P97(x63451)+E(f335(f97(x63451),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f73(x63451))
% 59.73/59.66 [6346]~P97(x63461)+E(f335(f97(x63461),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f73(x63461))
% 59.73/59.66 [6836]~P1(f335(a193,f335(f97(a1),x68361)))+E(f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),x68361),x68361)),a91)),f2(a881))
% 59.73/59.66 [7905]~P1(f335(f335(f243(a1),f335(f97(a1),x79051)),f2(a1)))+E(f335(f263(a1,a1),f335(a45,f44(f335(f74(a1),f73(a1)),f335(f74(a1),f335(f97(a1),x79051))))),f335(f335(f30(a1),f73(a1)),f335(f97(a1),x79051)))
% 59.73/59.66 [7919]~P1(f335(f335(f243(a1),f335(f97(a1),x79191)),f2(a1)))+E(f335(f267(a1,a1),f335(a45,f44(f335(f74(a1),f73(a1)),f335(f74(a1),f335(f97(a1),x79191))))),f39(a1,f73(a1),f335(f97(a1),x79191)))
% 59.73/59.66 [7970]~P1(f335(f335(f242(a1),a78),x79701))+P1(f335(f335(f242(a1),a78),f335(f335(f23(a1),f335(f335(f75(a1),x79701),x79701)),a91)))
% 59.73/59.66 [7971]~P1(f335(f335(f242(a1),a91),x79711))+P1(f335(f335(f242(a1),a91),f335(f335(f23(a1),f335(f335(f75(a1),x79711),x79711)),a91)))
% 59.73/59.66 [7972]~P1(f335(f335(f242(a1),a78),x79721))+P1(f335(f335(f243(a1),a78),f335(f335(f23(a1),f335(f335(f75(a1),x79721),x79721)),a91)))
% 59.73/59.66 [7973]~P1(f335(f335(f243(a1),a91),x79731))+P1(f335(f335(f243(a1),a91),f335(f335(f23(a1),f335(f335(f75(a1),x79731),x79731)),a91)))
% 59.73/59.66 [7974]~P1(f335(f335(f86(a1),a91),x79741))+P1(f335(f335(f86(a1),a91),f335(f335(f23(a1),f335(f335(f75(a1),x79741),x79741)),a91)))
% 59.73/59.66 [8274]~P97(x82741)+~P28(x82741,f335(f97(x82741),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))
% 59.73/59.66 [8456]P1(f335(f335(f242(a1),a78),x84561))+~P1(f335(f335(f242(a1),a78),f335(f335(f23(a1),f335(f335(f75(a1),x84561),x84561)),a91)))
% 59.73/59.66 [8457]P1(f335(f335(f242(a1),a78),x84571))+~P1(f335(f335(f243(a1),a78),f335(f335(f23(a1),f335(f335(f75(a1),x84571),x84571)),a91)))
% 59.73/59.66 [8458]P1(f335(f335(f242(a1),a91),x84581))+~P1(f335(f335(f242(a1),a91),f335(f335(f23(a1),f335(f335(f75(a1),x84581),x84581)),a91)))
% 59.73/59.66 [8459]P1(f335(f335(f243(a1),a91),x84591))+~P1(f335(f335(f243(a1),a91),f335(f335(f23(a1),f335(f335(f75(a1),x84591),x84591)),a91)))
% 59.73/59.66 [8460]P1(f335(f335(f86(a1),a91),x84601))+~P1(f335(f335(f86(a1),a91),f335(f335(f23(a1),f335(f335(f75(a1),x84601),x84601)),a91)))
% 59.73/59.66 [8769]E(f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),x87691),x87691)),a91)),f335(f335(f81(a881,a881),f335(f97(a881),x87691)),f335(f335(f8(a881,a881,a881),a106),f335(f335(f18(a881,a881,a881),f75(a881)),f5(a881)))))+P1(f335(a193,f335(f97(a1),x87691)))
% 59.73/59.66 [9615]E(x96151,f188(f888(f887(a881,a881),a879)))+P1(f335(f335(f337(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879))),f335(f335(f264(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),x96151),f188(f888(f887(a881,a881),a879)))),a27))
% 59.73/59.66 [8698]~P1(f335(a193,f335(f97(a1),x86981)))+P1(f335(a193,f335(f97(a1),f335(f335(f23(a1),f335(f335(f75(a1),x86981),x86981)),a91))))
% 59.73/59.66 [8699]~P1(f335(f335(f243(a1),x86991),a78))+P1(f335(f335(f242(a1),f335(f335(f23(a1),f335(f335(f75(a1),x86991),x86991)),a91)),a78))
% 59.73/59.66 [8700]~P1(f335(f335(f242(a1),x87001),a91))+P1(f335(f335(f242(a1),f335(f335(f23(a1),f335(f335(f75(a1),x87001),x87001)),a91)),a91))
% 59.73/59.66 [8701]~P1(f335(f335(f243(a1),x87011),a78))+P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f75(a1),x87011),x87011)),a91)),a78))
% 59.73/59.66 [8702]~P1(f335(f335(f243(a1),x87021),a91))+P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f75(a1),x87021),x87021)),a91)),a91))
% 59.73/59.66 [8703]~P1(f335(f335(f86(a1),x87031),a91))+P1(f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f75(a1),x87031),x87031)),a91)),a91))
% 59.73/59.66 [8808]~P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),x88081)))+P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),f335(f335(f23(a1),f335(f335(f75(a1),x88081),x88081)),a91))))
% 59.73/59.66 [8966]~P97(x89661)+E(f335(f335(f75(x89661),f73(x89661)),f73(x89661)),f335(f97(x89661),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))
% 59.73/59.66 [9118]P1(f335(a193,f335(f97(a1),x91181)))+~P1(f335(a193,f335(f97(a1),f335(f335(f23(a1),f335(f335(f75(a1),x91181),x91181)),a91))))
% 59.73/59.66 [9119]P1(f335(f335(f242(a1),x91191),a91))+~P1(f335(f335(f242(a1),f335(f335(f23(a1),f335(f335(f75(a1),x91191),x91191)),a91)),a91))
% 59.73/59.66 [9120]P1(f335(f335(f243(a1),x91201),a78))+~P1(f335(f335(f242(a1),f335(f335(f23(a1),f335(f335(f75(a1),x91201),x91201)),a91)),a78))
% 59.73/59.66 [9121]P1(f335(f335(f243(a1),x91211),a78))+~P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f75(a1),x91211),x91211)),a91)),a78))
% 59.73/59.66 [9122]P1(f335(f335(f243(a1),x91221),a91))+~P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f75(a1),x91221),x91221)),a91)),a91))
% 59.73/59.66 [9123]P1(f335(f335(f86(a1),x91231),a91))+~P1(f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f75(a1),x91231),x91231)),a91)),a91))
% 59.73/59.66 [9661]~P1(f335(f56(f887(a881,a881)),x96611))+P1(f335(f335(f337(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879))),f335(f335(f264(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),f188(f888(f887(a881,a881),a879))),x96611)),a64))
% 59.73/59.66 [9445]~P143(x94451)+E(f335(f335(f254(x94451),f73(x94451)),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f73(x94451))
% 59.73/59.66 [9446]~P143(x94461)+E(f335(f335(f254(x94461),f2(x94461)),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f2(x94461))
% 59.73/59.66 [9900]~P1(f335(f335(f243(a881),f73(a881)),x99001))+P1(f335(f335(f243(a881),f2(a881)),f335(f335(f30(a881),x99001),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))))
% 59.73/59.66 [9910]~P1(f335(f335(f243(a881),f2(a881)),x99101))+P1(f335(f335(f243(a881),f2(a881)),f335(f335(f30(a881),f335(f335(f75(a881),x99101),f73(a881))),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))))
% 59.73/59.66 [9950]~E(f39(a881,x99501,f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f73(a881))+P1(f335(f335(f243(a881),f2(a881)),f39(a881,x99501,f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))))
% 59.73/59.66 [9970]E(f39(a881,x99701,f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f73(a881))+~P1(f335(f335(f243(a881),f2(a881)),f39(a881,x99701,f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))))
% 59.73/59.66 [4658]~P36(x46581,x46582)+P55(x46581,x46582)
% 59.73/59.66 [4659]~P41(x46591,x46592)+P55(x46591,x46592)
% 59.73/59.66 [4620]~E(x46201,x46202)+E(f277(x46201,x46202),f73(a93))
% 59.73/59.66 [4623]E(f219(x46231,x46232),x46231)+~E(x46232,f2(a881))
% 59.73/59.66 [4629]~E(x46292,f107(x46291))+E(f145(x46291,x46292),f107(x46291))
% 59.73/59.66 [4630]~E(x46302,f107(x46301))+E(f145(x46301,x46302),f107(x46301))
% 59.73/59.66 [4648]~E(f145(x46482,x46481),f107(x46482))+E(x46481,f107(x46482))
% 59.73/59.66 [4649]~E(f145(x46492,x46491),f107(x46492))+E(x46491,f107(x46492))
% 59.73/59.66 [4663]~P2(x46632)+P2(f888(x46631,x46632))
% 59.73/59.66 [4664]~P3(x46642)+P3(f888(x46641,x46642))
% 59.73/59.66 [4665]~P107(x46652)+P107(f888(x46651,x46652))
% 59.73/59.66 [4666]~P108(x46662)+P108(f888(x46661,x46662))
% 59.73/59.66 [4667]~P61(x46672)+P60(f888(x46671,x46672))
% 59.73/59.66 [4668]~P61(x46682)+P61(f888(x46681,x46682))
% 59.73/59.66 [4669]~P99(x46692)+P62(f888(x46691,x46692))
% 59.73/59.66 [4670]~P63(x46702)+P63(f888(x46701,x46702))
% 59.73/59.66 [4671]~P61(x46712)+P102(f888(x46711,x46712))
% 59.73/59.66 [4672]~P5(x46722)+P5(f888(x46721,x46722))
% 59.73/59.66 [4673]~P100(x46732)+P100(f888(x46731,x46732))
% 59.73/59.66 [4674]~P110(x46742)+P110(f888(x46741,x46742))
% 59.73/59.66 [4675]~P99(x46752)+P101(f888(x46751,x46752))
% 59.73/59.66 [4676]~P84(x46762)+P84(f888(x46761,x46762))
% 59.73/59.66 [4677]~P85(x46772)+P85(f888(x46771,x46772))
% 59.73/59.66 [4678]~P99(x46782)+P99(f888(x46781,x46782))
% 59.73/59.66 [4690]E(x46901,x46902)+~E(f335(a106,x46901),f335(a106,x46902))
% 59.73/59.66 [4691]E(x46911,x46912)+~E(f335(a106,x46911),f335(a106,x46912))
% 59.73/59.66 [4692]E(x46921,x46922)+~E(f335(a101,x46921),f335(a101,x46922))
% 59.73/59.66 [4693]E(x46931,x46932)+~E(f335(a3,x46931),f335(a3,x46932))
% 59.73/59.66 [4694]E(x46941,x46942)+~E(f335(a20,x46941),f335(a20,x46942))
% 59.73/59.66 [4695]E(x46951,x46952)+~E(f335(a20,x46951),f335(a20,x46952))
% 59.73/59.66 [4795]~P58(x47951)+E(f39(x47951,x47952,x47952),f2(x47951))
% 59.73/59.66 [4829]~P36(x48291,x48292)+P36(f882(x48291),f139(x48291,x48292))
% 59.73/59.66 [4830]~P36(x48301,x48302)+P36(f882(x48301),f138(x48301,x48302))
% 59.73/59.66 [4925]~P36(x49251,x49252)+P36(f888(x49251,a879),f327(x49251,x49252))
% 59.73/59.66 [4926]~P36(x49261,x49262)+P36(f888(x49261,a879),f326(x49261,x49262))
% 59.73/59.66 [5046]~P6(x50461)+P38(f305(a1,x50461,x50462))
% 59.73/59.66 [5149]~P36(x51491,x51492)+P57(x51491,f62(x51491,x51491,x51492))
% 59.73/59.66 [5644]~P80(x56441)+P26(x56441,x56441,f74(x56441),x56442)
% 59.73/59.66 [4643]~E(x46432,f107(x46431))+E(f335(f162(x46431),x46432),f107(x46431))
% 59.73/59.66 [4644]~E(x46442,f107(x46441))+E(f335(f161(x46441),x46442),f107(x46441))
% 59.73/59.66 [4645]~E(x46452,f107(x46451))+E(f335(f162(x46451),x46452),f107(x46451))
% 59.73/59.66 [4699]E(x46991,f335(a98,x46992))+~E(f335(f94(a1),x46991),x46992)
% 59.73/59.66 [4701]E(x47011,f107(x47012))+~E(f335(f162(x47012),x47011),f107(x47012))
% 59.73/59.66 [4702]E(x47021,f107(x47022))+~E(f335(f161(x47022),x47021),f107(x47022))
% 59.73/59.66 [4703]E(x47031,f107(x47032))+~E(f335(f162(x47032),x47031),f107(x47032))
% 59.73/59.66 [4717]~P97(x47171)+E(f335(f97(x47171),x47172),f335(f96(x47171),x47172))
% 59.73/59.66 [4724]~E(x47242,f200(x47241))+E(f234(x47241,x47242),f188(f888(x47241,a879)))
% 59.73/59.66 [4725]~P65(x47251)+P1(f335(f56(x47251),x47252))
% 59.73/59.66 [4726]~P65(x47261)+P1(f335(f56(x47261),x47262))
% 59.73/59.66 [4733]E(x47331,f200(x47332))+E(f335(f235(x47332),f672(x47332,x47331)),x47331)
% 59.73/59.66 [4734]E(x47341,f200(x47342))+E(f335(f235(x47342),f842(x47342,x47341)),x47341)
% 59.73/59.66 [4736]~E(f673(x47362,x47361),f107(x47361))+E(f173(x47361,x47362),f107(f882(x47361)))
% 59.73/59.66 [4745]~E(x47452,f107(x47451))+E(f335(f166(x47451),x47452),f188(f888(x47451,a879)))
% 59.73/59.66 [4746]~E(x47462,f107(x47461))+E(f188(f888(x47461,a879)),f335(f166(x47461),x47462))
% 59.73/59.66 [4747]E(x47471,x47472)+~E(f335(f94(a1),x47471),f335(f94(a1),x47472))
% 59.73/59.66 [4748]E(x47481,x47482)+~E(f335(f94(a1),x47481),f335(f94(a1),x47482))
% 59.73/59.66 [4751]E(f217(x47511,x47512),f2(a881))+P1(f335(f56(x47511),x47512))
% 59.73/59.66 [4771]~P119(x47711)+E(f77(x47711,f77(x47711,x47712)),f77(x47711,x47712))
% 59.73/59.66 [4784]~P82(x47841)+E(f335(f335(f254(x47841),x47842),f73(a881)),x47842)
% 59.73/59.66 [4785]~P114(x47851)+E(f335(f335(f254(x47851),x47852),f73(a881)),x47852)
% 59.73/59.66 [4789]E(x47891,x47892)+E(f277(x47891,x47892),f335(f335(f75(a93),x47892),f73(a93)))
% 59.73/59.66 [4790]E(f335(f29(x47901),x47902),f2(a881))+P1(f335(f56(x47901),x47902))
% 59.73/59.66 [4791]E(f335(f29(x47911),x47912),f2(a881))+P1(f335(f56(x47911),x47912))
% 59.73/59.66 [4792]E(f335(f29(x47921),x47922),f2(a881))+P1(f335(f56(x47921),x47922))
% 59.73/59.66 [4796]~E(f145(x47961,x47962),x47962)+P1(f335(f130(x47961),x47962))
% 59.73/59.66 [4799]~P62(x47991)+E(f335(f335(f104(x47991),x47992),f188(x47991)),x47992)
% 59.73/59.66 [4800]~P72(x48001)+E(f335(f335(f23(x48001),x48002),f2(x48001)),x48002)
% 59.73/59.66 [4801]~P101(x48011)+E(f335(f335(f95(x48011),x48012),f252(x48011)),x48012)
% 59.73/59.66 [4802]~P73(x48021)+E(f335(f335(f76(x48021),x48022),f73(x48021)),x48022)
% 59.73/59.66 [4803]~P82(x48031)+E(f335(f335(f76(x48031),x48032),f73(x48031)),x48032)
% 59.73/59.66 [4804]~P114(x48041)+E(f335(f335(f76(x48041),x48042),f73(x48041)),x48042)
% 59.73/59.66 [4805]~P114(x48051)+E(f335(f335(f75(x48051),x48052),f2(x48051)),x48052)
% 59.73/59.66 [4806]~P83(x48061)+E(f335(f335(f75(x48061),x48062),f2(x48061)),x48062)
% 59.73/59.66 [4807]~P77(x48071)+E(f335(f335(f75(x48071),x48072),f2(x48071)),x48072)
% 59.73/59.66 [4808]~P58(x48081)+E(f335(f335(f30(x48081),x48082),f73(x48081)),x48082)
% 59.73/59.66 [4809]~P116(x48091)+E(f335(f335(f292(x48091),x48092),f73(x48091)),x48092)
% 59.73/59.66 [4810]~P114(x48101)+E(f335(f335(f254(x48101),x48102),f2(a881)),f73(x48101))
% 59.73/59.66 [4811]~P113(x48111)+E(f335(f335(f254(x48111),x48112),f2(a881)),f73(x48111))
% 59.73/59.66 [4812]~E(x48122,f188(f888(x48121,a879)))+E(f335(f29(x48121),x48122),f2(a881))
% 59.73/59.66 [4823]~P58(x48231)+E(f39(x48231,x48232,f2(x48231)),x48232)
% 59.73/59.66 [4831]~P101(x48311)+E(f335(f335(f104(x48311),x48312),f252(x48311)),f252(x48311))
% 59.73/59.66 [4832]~P62(x48321)+E(f335(f335(f95(x48321),x48322),f188(x48321)),f188(x48321))
% 59.73/59.66 [4833]~P114(x48331)+E(f335(f335(f76(x48331),x48332),f2(x48331)),f2(x48331))
% 59.73/59.66 [4834]~P126(x48341)+E(f335(f335(f76(x48341),x48342),f2(x48341)),f2(x48341))
% 59.73/59.66 [4835]~P58(x48351)+E(f335(f335(f30(x48351),x48352),f2(x48351)),f2(x48351))
% 59.73/59.66 [4836]~P117(x48361)+E(f335(f335(f292(x48361),x48362),f2(x48361)),f2(x48361))
% 59.73/59.66 [4837]E(x48371,f200(x48372))+~E(f234(x48372,x48371),f188(f888(x48372,a879)))
% 59.73/59.66 [4839]~P58(x48391)+E(f39(x48391,x48392,f73(x48391)),f2(x48391))
% 59.73/59.66 [4840]~P58(x48401)+E(f39(x48401,f2(x48401),x48402),f2(x48401))
% 59.73/59.66 [4869]E(x48691,f2(a881))+E(f49(x48692,x48691,f107(x48692)),f107(f882(x48692)))
% 59.73/59.66 [4892]P36(x48921,x48922)+~E(f557(x48922,x48921),f188(f888(x48921,a879)))
% 59.73/59.66 [4893]E(x48931,f107(x48932))+~E(f335(f166(x48932),x48931),f188(f888(x48932,a879)))
% 59.73/59.66 [4894]E(x48941,f107(x48942))+~E(f188(f888(x48942,a879)),f335(f166(x48942),x48941))
% 59.73/59.66 [4897]~E(x48971,x48972)+P1(f335(f335(a332,x48971),x48972))
% 59.73/59.66 [4907]P1(x49071)+P1(f335(f335(a338,x49071),x49072))
% 59.73/59.66 [4908]E(x49081,f107(x49082))+E(f335(f335(f158(x49082),x49081),f2(a881)),f335(f134(x49082),x49081))
% 59.73/59.66 [4910]E(f145(x49101,x49102),x49102)+~P1(f335(f130(x49101),x49102))
% 59.73/59.66 [4911]E(f145(x49111,x49112),x49112)+~P1(f335(f130(x49111),x49112))
% 59.73/59.66 [4916]~P1(x49162)+P1(f335(f335(a338,x49161),x49162))
% 59.73/59.66 [4917]~P1(x49172)+P1(f335(f335(a334,x49171),x49172))
% 59.73/59.66 [4918]~P1(x49181)+P1(f335(f335(a334,x49181),x49182))
% 59.73/59.66 [4928]~E(f674(x49282,x49281),f688(x49282,x49281))+P1(f335(f130(x49281),x49282))
% 59.73/59.66 [4935]E(f335(f249(x49351),x49352),f188(f888(x49351,a879)))+P1(f335(x49352,f843(x49352)))
% 59.73/59.66 [4936]E(f188(f888(x49361,a879)),f335(f249(x49361),x49362))+P1(f335(x49362,f844(x49362)))
% 59.73/59.66 [5003]~P119(x50031)+E(f335(f335(f76(x50031),x50032),f77(x50031,x50032)),f335(f70(x50031),x50032))
% 59.73/59.66 [5013]~E(x50131,f2(a1))+E(f40(x50131,x50132),f335(f335(f264(a1,a1),f2(a1)),f2(a1)))
% 59.73/59.66 [5014]~E(x50141,f2(a1))+E(f40(x50141,x50142),f335(f335(f264(a1,a1),f2(a1)),f2(a1)))
% 59.73/59.66 [5045]~P55(x50451,x50452)+P55(x50451,f335(f289(x50451,x50451),x50452))
% 59.73/59.66 [5068]E(x50681,x50682)+~P1(f335(f335(a332,x50681),x50682))
% 59.73/59.66 [5079]P1(x50791)+~P1(f335(f335(a333,x50792),x50791))
% 59.73/59.66 [5080]P1(x50801)+~P1(f335(f335(a333,x50801),x50802))
% 59.73/59.66 [5085]~P110(x50851)+P1(f335(f335(f242(x50851),x50852),f252(x50851)))
% 59.73/59.66 [5089]E(x50891,x50892)+~E(f335(x50891,f415(x50892,x50891)),f335(x50892,f415(x50892,x50891)))
% 59.73/59.66 [5121]E(x51211,f2(a881))+E(f219(x51211,f39(a881,x51212,x51211)),f219(x51212,x51211))
% 59.73/59.66 [5126]~P106(x51261)+P15(x51261,f335(f335(f144(x51261),x51262),f107(x51261)))
% 59.73/59.66 [5130]E(x51301,f2(a1))+P1(f335(f43(x51302,x51301),f40(x51302,x51301)))
% 59.73/59.66 [5147]~E(x51471,x51472)+P1(f335(f335(f243(a881),x51471),f335(a106,x51472)))
% 59.73/59.66 [5157]~E(x51571,f2(a881))+P1(f335(f335(f243(a881),x51571),f335(a106,x51572)))
% 59.73/59.66 [5170]P1(f335(x51701,x51702))+P1(f335(f335(f242(a1),f2(a1)),f361(x51701)))
% 59.73/59.66 [5236]P55(x52361,x52362)+~P55(x52361,f335(f289(x52361,x52361),x52362))
% 59.73/59.66 [5239]~E(f39(a881,x52392,x52391),f2(a881))+E(f335(f335(f76(a881),x52391),f362(x52391,x52392)),x52392)
% 59.73/59.66 [5240]~E(f39(a1,x52402,x52401),f2(a1))+E(f335(f335(f76(a1),x52401),f363(x52401,x52402)),x52402)
% 59.73/59.66 [5245]~E(x52451,f335(a106,x52452))+P1(f335(f335(f242(a881),x52451),f335(a106,x52452)))
% 59.73/59.66 [5266]~P1(f335(x52661,x52662))+P1(f335(f335(f242(a1),f2(a1)),f360(x52661)))
% 59.73/59.66 [5278]E(f335(f335(f23(a881),f335(a98,x52781)),f335(a98,x52782)),f335(a98,x52781))+~P1(f335(a193,x52782))
% 59.73/59.66 [5302]E(f278(x53021,x53022),f73(a93))+~P1(f335(f335(f242(a93),x53021),f73(a93)))
% 59.73/59.66 [5397]E(f335(f335(f158(x53971),x53972),f674(x53972,x53971)),f335(f335(f158(x53971),x53972),f688(x53972,x53971)))+P1(f335(f130(x53971),x53972))
% 59.73/59.66 [5442]~P1(f335(x54421,f85(x54422,x54421)))+P1(f335(x54421,f558(x54422,x54421)))
% 59.73/59.66 [5505]P57(x55051,x55052)+~P1(f335(f323(x55051,x55052),f529(x55052,x55051)))
% 59.73/59.66 [5651]~E(f335(a106,f39(a881,x56511,x56512)),x56512)+E(f39(a881,f335(a106,x56511),x56512),f2(a881))
% 59.73/59.66 [5709]P36(x57091,x57092)+P1(f335(f335(f337(x57091),f627(x57092,x57091)),f628(x57092,x57091)))
% 59.73/59.66 [5716]~P97(x57161)+P1(f335(f335(f337(x57161),f335(f97(x57161),x57162)),f103(x57161)))
% 59.73/59.66 [5717]~P137(x57171)+P1(f335(f335(f337(x57171),f335(f96(x57171),x57172)),f103(x57171)))
% 59.73/59.66 [5718]~P137(x57181)+P1(f335(f335(f337(x57181),f335(f94(x57181),x57182)),f103(x57181)))
% 59.73/59.66 [5719]~P143(x57191)+P1(f335(f335(f337(x57191),f335(f94(x57191),x57192)),f186(x57191)))
% 59.73/59.66 [5864]E(f335(a106,f39(a881,x58641,x58642)),x58642)+E(f39(a881,f335(a106,x58641),x58642),f335(a106,f39(a881,x58641,x58642)))
% 59.73/59.66 [6277]P36(x62771,x62772)+~P1(f335(f335(f337(x62771),f506(x62772,x62771)),f324(x62771,x62772)))
% 59.73/59.66 [6311]~P122(x63111)+~P1(f335(f335(f243(x63111),f335(f94(x63111),x63112)),f2(x63111)))
% 59.73/59.66 [6312]~P88(x63121)+~P1(f335(f335(f243(x63121),f335(f70(x63121),x63122)),f2(x63121)))
% 59.73/59.66 [6403]P1(f335(f335(f243(a1),x64031),f39(a1,x64032,x64031)))+~P1(f335(f335(f243(a1),x64031),f2(a1)))
% 59.73/59.66 [6404]P1(f335(f335(f243(a1),x64041),f39(a1,x64042,x64041)))+~P1(f335(f335(f243(a1),x64041),f2(a1)))
% 59.73/59.66 [6502]E(f335(f335(f312(a881),f335(a106,x65021)),f305(a881,x65022,x65021)),f305(a881,x65022,f335(a106,x65021)))+~P1(f335(f335(f242(a881),x65022),f335(a106,x65021)))
% 59.73/59.66 [6592]~P106(x65921)+P15(x65921,f143(x65921,x65921,f5(x65921),x65922))
% 59.73/59.66 [6727]E(f335(f161(x67271),x67272),x67272)+~P1(f335(f335(f242(a881),f335(f189(f882(x67271)),x67272)),f73(a881)))
% 59.73/59.66 [6748]~P88(x67481)+P1(f335(f335(f242(x67481),f335(f74(x67481),f335(f70(x67481),x67482))),f2(x67481)))
% 59.73/59.66 [6781]~P36(x67811,x67812)+P36(x67811,f335(f335(f291(x67811,x67811,x67811),x67812),f310(x67811,x67812)))
% 59.73/59.66 [7002]~P1(f335(f335(f243(a1),x70022),f2(a1)))+P1(f335(f335(f242(a1),f39(a1,x70021,x70022)),f2(a1)))
% 59.73/59.66 [7003]~P1(f335(f335(f243(a1),x70032),f2(a1)))+P1(f335(f335(f242(a1),f39(a1,x70031,x70032)),f2(a1)))
% 59.73/59.66 [7400]~P143(x74001)+E(f190(x74001,f335(f335(f7(x74001,x74001,x74001),f75(x74001)),f73(x74001)),x74002,f2(x74001)),f335(f94(x74001),x74002))
% 59.73/59.66 [7428]~P124(x74281)+~P1(f335(f335(f243(x74281),f335(f335(f76(x74281),x74282),x74282)),f2(x74281)))
% 59.73/59.66 [10060]~P119(x100601)+~P1(f335(f335(f243(x100601),f335(f335(f254(x100601),x100602),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f2(x100601)))
% 59.73/59.66 [4700]~E(x47002,f107(x47001))+E(f335(f189(f882(x47001)),x47002),f2(a881))
% 59.73/59.66 [4737]~E(x47371,f2(a881))+E(f335(f335(f75(a881),x47371),x47372),x47372)
% 59.73/59.66 [4738]~E(x47382,f2(a881))+E(f335(f335(f76(a881),x47381),x47382),f2(a881))
% 59.73/59.66 [4739]~E(x47391,f2(a881))+E(f335(f335(f76(a881),x47391),x47392),f2(a881))
% 59.73/59.66 [4740]~E(x47401,f2(a881))+E(f335(f335(f76(a881),x47401),x47402),f2(a881))
% 59.73/59.66 [4741]~E(x47412,f2(a881))+E(f335(f335(f254(a881),x47411),x47412),f73(a881))
% 59.73/59.66 [4742]~E(x47422,f2(a1))+E(f335(f335(f30(a1),x47421),x47422),f2(a1))
% 59.73/59.66 [4752]E(x47521,f107(x47522))+~E(f335(f189(f882(x47522)),x47521),f2(a881))
% 59.73/59.66 [4753]~P60(x47531)+E(f335(f335(f104(x47531),x47532),x47532),x47532)
% 59.73/59.66 [4754]~P60(x47541)+E(f335(f335(f104(x47541),x47542),x47542),x47542)
% 59.73/59.66 [4755]~P61(x47551)+E(f335(f335(f104(x47551),x47552),x47552),x47552)
% 59.73/59.66 [4756]~P61(x47561)+E(f335(f335(f95(x47561),x47562),x47562),x47562)
% 59.73/59.66 [4757]~P102(x47571)+E(f335(f335(f95(x47571),x47572),x47572),x47572)
% 59.73/59.66 [4758]~P102(x47581)+E(f335(f335(f95(x47581),x47582),x47582),x47582)
% 59.73/59.66 [4759]~P98(x47591)+E(f335(f335(f76(x47591),x47592),x47592),x47592)
% 59.73/59.66 [4760]~P98(x47601)+E(f335(f335(f76(x47601),x47602),x47602),x47602)
% 59.73/59.66 [4761]~P106(x47611)+E(f335(f335(f240(x47611),x47612),x47612),x47612)
% 59.73/59.66 [4762]~P106(x47621)+E(f335(f335(f240(x47621),x47622),x47622),x47622)
% 59.73/59.66 [4763]~P106(x47631)+E(f335(f335(f241(x47631),x47632),x47632),x47632)
% 59.73/59.66 [4764]~P106(x47641)+E(f335(f335(f241(x47641),x47642),x47642),x47642)
% 59.73/59.66 [4783]~P72(x47831)+E(f335(f335(f23(x47831),x47832),x47832),f2(x47831))
% 59.73/59.66 [4797]~P72(x47971)+E(f335(f74(x47971),f335(f74(x47971),x47972)),x47972)
% 59.73/59.66 [4798]~P84(x47981)+E(f335(f74(x47981),f335(f74(x47981),x47982)),x47982)
% 59.73/59.66 [4815]~E(x48152,f2(a881))+E(f335(f335(f254(a881),x48151),x48152),f335(a106,f2(a881)))
% 59.73/59.66 [4848]~P62(x48481)+E(f335(f335(f104(x48481),f188(x48481)),x48482),x48482)
% 59.73/59.66 [4849]~P101(x48491)+E(f335(f335(f95(x48491),f252(x48491)),x48492),x48492)
% 59.73/59.66 [4850]~P73(x48501)+E(f335(f335(f76(x48501),f73(x48501)),x48502),x48502)
% 59.73/59.66 [4851]~P82(x48511)+E(f335(f335(f76(x48511),f73(x48511)),x48512),x48512)
% 59.73/59.66 [4852]~P114(x48521)+E(f335(f335(f76(x48521),f73(x48521)),x48522),x48522)
% 59.73/59.66 [4853]~P114(x48531)+E(f335(f335(f75(x48531),f2(x48531)),x48532),x48532)
% 59.73/59.66 [4854]~P83(x48541)+E(f335(f335(f75(x48541),f2(x48541)),x48542),x48542)
% 59.73/59.66 [4855]~P77(x48551)+E(f335(f335(f75(x48551),f2(x48551)),x48552),x48552)
% 59.73/59.66 [4873]~P101(x48731)+E(f335(f335(f104(x48731),f252(x48731)),x48732),f252(x48731))
% 59.73/59.66 [4874]~P62(x48741)+E(f335(f335(f95(x48741),f188(x48741)),x48742),f188(x48741))
% 59.73/59.66 [4875]~P114(x48751)+E(f335(f335(f76(x48751),f2(x48751)),x48752),f2(x48751))
% 59.73/59.66 [4876]~P126(x48761)+E(f335(f335(f76(x48761),f2(x48761)),x48762),f2(x48761))
% 59.73/59.66 [4877]~P82(x48771)+E(f335(f335(f254(x48771),f73(x48771)),x48772),f73(x48771))
% 59.73/59.66 [4878]~P58(x48781)+E(f335(f335(f30(x48781),f2(x48781)),x48782),f2(x48781))
% 59.73/59.66 [4879]~P116(x48791)+E(f335(f335(f292(x48791),f2(x48791)),x48792),f2(x48791))
% 59.73/59.66 [4887]E(x48871,f107(x48872))+E(f137(x48872,f335(f162(x48872),x48871)),f335(f134(x48872),x48871))
% 59.73/59.66 [4888]E(x48881,f107(x48882))+E(f335(f134(x48882),f335(f162(x48882),x48881)),f137(x48882,x48881))
% 59.73/59.66 [4889]E(x48891,f2(a881))+~E(f335(f335(f75(a881),x48892),x48891),x48892)
% 59.73/59.66 [4895]~P97(x48951)+E(f335(f96(x48951),f335(f97(a1),x48952)),f335(f97(x48951),x48952))
% 59.73/59.66 [4896]~P137(x48961)+E(f335(f96(x48961),f335(f94(a1),x48962)),f335(f94(x48961),x48962))
% 59.73/59.66 [4901]E(x49011,f73(a881))+~E(f335(f335(f76(a881),x49012),x49011),f73(a881))
% 59.73/59.66 [4902]E(x49021,f73(a881))+~E(f335(f335(f76(a881),x49021),x49022),f73(a881))
% 59.73/59.66 [4903]E(x49031,f73(a881))+~E(f335(f335(f76(a881),x49032),x49031),f73(a881))
% 59.73/59.66 [4904]E(x49041,f73(a881))+~E(f335(f335(f76(a881),x49041),x49042),f73(a881))
% 59.73/59.66 [4905]E(x49051,f2(a881))+~E(f335(f335(f75(a881),x49052),x49051),f2(a881))
% 59.73/59.66 [4906]E(x49061,f2(a881))+~E(f335(f335(f75(a881),x49061),x49062),f2(a881))
% 59.73/59.66 [4921]~P88(x49211)+E(f335(f70(x49211),f335(f74(x49211),x49212)),f335(f70(x49211),x49212))
% 59.73/59.66 [4922]~P119(x49221)+E(f335(f70(x49221),f335(f94(x49221),x49222)),f335(f94(x49221),x49222))
% 59.73/59.66 [4923]~P88(x49231)+E(f335(f70(x49231),f335(f70(x49231),x49232)),f335(f70(x49231),x49232))
% 59.73/59.66 [4924]~P77(x49241)+E(f335(f159(x49241),f335(f162(x49241),x49242)),f335(f159(x49241),x49242))
% 59.73/59.66 [4929]~E(x49291,f335(a106,f2(a881)))+E(f335(f335(f254(a881),x49291),x49292),f335(a106,f2(a881)))
% 59.73/59.66 [4938]~P72(x49381)+E(f335(f335(f23(x49381),f2(x49381)),x49382),f335(f74(x49381),x49382))
% 59.73/59.66 [4939]~E(x49392,f2(a881))+E(f132(a881,f335(f304(a881,x49391),x49392)),f107(a881))
% 59.73/59.66 [4948]~P97(x49481)+E(f335(f335(f75(x49481),x49482),f335(f97(x49481),a78)),x49482)
% 59.73/59.66 [4949]E(x49491,f2(a1))+E(f41(f335(f70(a1),x49492),f335(f70(a1),x49491)),f47(x49492,x49491))
% 59.73/59.66 [4963]~E(x49631,x49632)+P1(f335(f335(f242(a881),x49631),x49632))
% 59.73/59.66 [4964]~E(x49641,x49642)+P1(f335(f335(f242(a881),x49641),x49642))
% 59.73/59.66 [4965]~E(x49651,x49652)+P1(f335(f335(f242(a881),x49651),x49652))
% 59.73/59.66 [4972]~E(x49721,f2(a93))+E(f335(f335(f75(a881),f335(a20,x49721)),x49722),x49722)
% 59.73/59.66 [4973]~E(f335(f94(a1),x49731),f335(f97(a1),x49732))+E(x49731,f335(a98,f335(f97(a1),x49732)))
% 59.73/59.66 [4974]~P5(x49741)+E(f89(x49741,f335(f16(x49741,x49741),x49742)),x49742)
% 59.73/59.66 [4983]~P6(x49831)+P6(f335(f335(f254(a1),x49831),x49832))
% 59.73/59.66 [4984]~P84(x49841)+E(f335(f335(f104(x49841),x49842),f335(f74(x49841),x49842)),f252(x49841))
% 59.73/59.66 [4985]~P84(x49851)+E(f335(f335(f95(x49851),x49852),f335(f74(x49851),x49852)),f188(x49851))
% 59.73/59.66 [4986]~P72(x49861)+E(f335(f335(f75(x49861),x49862),f335(f74(x49861),x49862)),f2(x49861))
% 59.73/59.66 [5011]E(x50111,f2(a881))+~E(f335(f74(a1),f335(f94(a1),x50112)),f335(f94(a1),x50111))
% 59.73/59.66 [5012]E(x50121,f2(a881))+~E(f335(f74(a1),f335(f94(a1),x50121)),f335(f94(a1),x50122))
% 59.73/59.66 [5022]E(f194(x50221,x50222),f2(a1))+P1(f335(f335(f242(a1),x50222),x50221))
% 59.73/59.66 [5023]E(f172(x50231,x50232),f107(a1))+P1(f335(f335(f242(a1),x50231),x50232))
% 59.73/59.66 [5036]E(x50361,f335(a106,f2(a881)))+~E(f335(f335(f76(a881),x50362),x50361),f335(a106,f2(a881)))
% 59.73/59.66 [5037]E(x50371,f335(a106,f2(a881)))+~E(f335(f335(f76(a881),x50371),x50372),f335(a106,f2(a881)))
% 59.73/59.66 [5038]~P2(x50381)+P1(f335(f335(f242(x50381),x50382),x50382))
% 59.73/59.66 [5039]~P96(x50391)+P1(f335(f335(f86(x50391),x50392),x50392))
% 59.73/59.66 [5042]~P97(x50421)+E(f335(f335(f76(x50421),x50422),f335(f97(x50421),a91)),f335(f74(x50421),x50422))
% 59.73/59.66 [5059]~P97(x50591)+E(f335(f74(x50591),f335(f97(x50591),x50592)),f335(f97(x50591),f335(f74(a1),x50592)))
% 59.73/59.66 [5060]~P97(x50601)+E(f335(f74(x50601),f335(f97(x50601),x50602)),f335(f97(x50601),f335(f74(a1),x50602)))
% 59.73/59.66 [5061]~P137(x50611)+E(f335(f74(x50611),f335(f96(x50611),x50612)),f335(f96(x50611),f335(f74(a1),x50612)))
% 59.73/59.66 [5090]~E(x50901,f335(a106,x50902))+P1(f335(f335(f243(a881),f2(a881)),x50901))
% 59.73/59.66 [5107]~P106(x51071)+E(f335(f74(f888(x51071,a879)),f335(f250(x51071),x51072)),f335(f251(x51071),x51072))
% 59.73/59.66 [5108]~P106(x51081)+E(f335(f74(f888(x51081,a879)),f335(f303(x51081),x51082)),f335(f306(x51081),x51082))
% 59.73/59.66 [5109]~P106(x51091)+E(f335(f74(f888(x51091,a879)),f335(f306(x51091),x51092)),f335(f303(x51091),x51092))
% 59.73/59.66 [5110]~P106(x51101)+E(f335(f74(f888(x51101,a879)),f335(f251(x51101),x51102)),f335(f250(x51101),x51102))
% 59.73/59.66 [5120]~E(f335(f94(a1),x51202),x51201)+P1(f335(f335(f242(a1),f2(a1)),x51201))
% 59.73/59.66 [5129]~E(x51292,f2(a1))+E(f47(x51291,x51292),f335(f335(f264(a1,a1),f2(a1)),f335(f70(a1),x51291)))
% 59.73/59.66 [5131]~P3(x51311)+P1(f335(f335(f242(x51311),f188(x51311)),x51312))
% 59.73/59.66 [5162]E(x51621,x51622)+~E(f335(f335(f75(a1),x51621),x51621),f335(f335(f75(a1),x51622),x51622))
% 59.73/59.66 [5169]~P1(f335(x51691,x51692))+P1(f335(x51691,f335(a98,f360(x51691))))
% 59.73/59.66 [5195]~P119(x51951)+E(f335(f335(f76(x51951),f77(x51951,x51952)),f335(f70(x51951),x51952)),x51952)
% 59.73/59.66 [5202]~E(x52022,f2(a881))+E(f80(f887(a881,a881),f42(x52021,x52022)),f335(f335(f264(a881,a881),f2(a881)),x52021))
% 59.73/59.66 [5203]~E(x52031,x52032)+~P1(f335(f335(f243(a881),x52031),x52032))
% 59.73/59.66 [5204]~E(x52041,x52042)+~P1(f335(f335(f243(a881),x52041),x52042))
% 59.73/59.66 [5205]~E(x52051,x52052)+~P1(f335(f335(f243(a881),x52051),x52052))
% 59.73/59.66 [5206]~E(x52061,x52062)+~P1(f335(f335(f243(a881),x52061),x52062))
% 59.73/59.66 [5207]~E(x52071,x52072)+~P1(f335(f335(f243(a881),x52071),x52072))
% 59.73/59.66 [5208]~E(x52081,x52082)+~P1(f335(f335(f243(a1),x52081),x52082))
% 59.73/59.66 [5211]~P143(x52111)+E(f335(f335(f75(x52111),f73(x52111)),f335(f94(x52111),x52112)),f335(f94(x52111),f335(a106,x52112)))
% 59.73/59.66 [5215]~E(x52151,f2(a881))+~P1(f335(f335(f243(a881),x52152),x52151))
% 59.73/59.66 [5232]E(f145(x52321,x52322),x52322)+~E(f335(f189(f882(x52321)),f145(x52321,x52322)),f335(f189(f882(x52321)),x52322))
% 59.73/59.66 [5233]E(f335(f29(x52331),f335(f166(x52331),x52332)),f335(f189(f882(x52331)),x52332))+~P1(f335(f130(x52331),x52332))
% 59.73/59.66 [5244]~P1(f335(x52441,f393(x52441)))+P1(f335(x52441,f335(f94(a1),x52442)))
% 59.73/59.66 [5255]E(f278(x52551,x52552),f73(a93))+~P1(f335(f335(f243(a93),x52552),x52551))
% 59.73/59.66 [5256]E(f172(x52561,x52562),f107(a1))+~P1(f335(f335(f243(a1),x52562),x52561))
% 59.73/59.66 [5257]E(f122(x52571,x52572),f109(a1))+~P1(f335(f335(f243(a1),x52571),x52572))
% 59.73/59.66 [5259]~P107(x52591)+E(f305(x52591,x52592,x52592),f335(f335(f312(x52591),x52592),f188(f888(x52591,a879))))
% 59.73/59.66 [5281]~E(f335(f335(f23(a881),x52811),x52812),f2(a881))+P1(f335(f335(f242(a881),x52811),x52812))
% 59.73/59.66 [5282]~E(f335(f335(f23(a1),x52821),x52822),f2(a1))+P1(f335(f335(f86(a1),x52821),x52822))
% 59.73/59.66 [5299]~E(x52992,f2(a881))+E(f49(x52991,x52992,f107(x52991)),f335(f335(f144(f882(x52991)),f107(x52991)),f107(f882(x52991))))
% 59.73/59.66 [5303]~P2(x53031)+~P1(f335(f335(f243(x53031),x53032),x53032))
% 59.73/59.66 [5305]~E(f39(a1,x53051,x53052),f2(a1))+E(f39(a1,x53051,f335(f74(a1),x53052)),f2(a1))
% 59.73/59.66 [5306]~E(f39(a1,x53061,x53062),f2(a1))+E(f39(a1,x53061,f335(f74(a1),x53062)),f2(a1))
% 59.73/59.66 [5307]~E(f39(a1,x53071,x53072),f2(a1))+E(f39(a1,f335(f74(a1),x53071),x53072),f2(a1))
% 59.73/59.66 [5308]~E(f39(a1,x53081,x53082),f2(a1))+E(f39(a1,f335(f74(a1),x53081),x53082),f2(a1))
% 59.73/59.66 [5316]E(f335(f304(a881,x53161),f335(a106,x53162)),f188(f888(a881,a879)))+P1(f335(f335(f242(a881),x53161),x53162))
% 59.73/59.66 [5338]E(f132(a881,f335(f304(a881,x53381),x53382)),f107(a881))+P1(f335(f335(f243(a881),x53381),x53382))
% 59.73/59.66 [5343]~E(f335(f29(x53431),f335(f166(x53431),x53432)),f335(f189(f882(x53431)),x53432))+P1(f335(f130(x53431),x53432))
% 59.73/59.66 [5348]~P1(f335(f130(x53481),x53482))+P1(f335(f130(x53481),f335(f161(x53481),x53482)))
% 59.73/59.66 [5349]~P1(f335(f130(x53491),x53492))+P1(f335(f130(x53491),f335(f165(x53491),x53492)))
% 59.73/59.66 [5350]~P1(f335(f130(x53501),x53502))+P1(f335(f130(x53501),f335(f162(x53501),x53502)))
% 59.73/59.66 [5357]P1(f335(x53571,x53572))+~P1(f335(x53571,f335(a98,f361(x53571))))
% 59.73/59.66 [5358]P1(f335(f335(f242(a881),x53582),x53581))+P1(f335(f335(f242(a881),x53581),x53582))
% 59.73/59.66 [5359]P1(f335(f335(f242(a1),x53592),x53591))+P1(f335(f335(f242(a1),x53591),x53592))
% 59.73/59.66 [5361]~P88(x53611)+P1(f335(f335(f242(x53611),x53612),f335(f70(x53611),x53612)))
% 59.73/59.66 [5364]P1(f335(x53641,f399(x53641)))+~P1(f335(x53641,f335(f94(a1),x53642)))
% 59.73/59.66 [5388]E(f335(f335(f23(a881),x53881),x53882),f2(a881))+~P1(f335(f335(f242(a881),x53881),x53882))
% 59.73/59.66 [5389]E(f335(f335(f23(a881),x53891),x53892),f2(a881))+~P1(f335(f335(f242(a881),x53891),x53892))
% 59.73/59.66 [5390]E(f335(f335(f23(a1),x53901),x53902),f2(a1))+~P1(f335(f335(f86(a1),x53901),x53902))
% 59.73/59.66 [5391]E(f335(f335(f30(a881),x53911),x53912),f2(a881))+~P1(f335(f335(f243(a881),x53911),x53912))
% 59.73/59.66 [5408]E(f39(a881,x54081,x54082),x54081)+~P1(f335(f335(f243(a881),x54081),x54082))
% 59.73/59.66 [5409]E(f39(a881,x54091,x54092),x54091)+~P1(f335(f335(f243(a881),x54091),x54092))
% 59.73/59.66 [5418]E(f39(a1,x54181,f335(f74(a1),x54182)),f293(x54181,x54182))+P1(f335(f335(f242(a1),f2(a1)),x54182))
% 59.73/59.66 [5429]E(f335(f335(f23(a1),x54291),x54292),f194(x54291,x54292))+~P1(f335(f335(f242(a1),x54292),x54291))
% 59.73/59.66 [5430]E(f335(f335(f23(a1),x54301),x54302),f194(x54301,x54302))+~P1(f335(f335(f242(a1),x54302),x54301))
% 59.73/59.66 [5449]P1(f335(f335(f242(a1),f2(a1)),f393(x54491)))+P1(f335(x54491,f335(f94(a1),x54492)))
% 59.73/59.66 [5461]~P4(x54611)+P1(f335(f335(f337(x54611),x54612),f335(f166(x54611),f50(x54611))))
% 59.73/59.66 [5462]~P122(x54621)+P1(f335(f335(f242(x54621),f2(x54621)),f335(f94(x54621),x54622)))
% 59.73/59.66 [5463]~P122(x54631)+P1(f335(f335(f242(x54631),f2(x54631)),f335(f94(x54631),x54632)))
% 59.73/59.66 [5464]~P88(x54641)+P1(f335(f335(f242(x54641),f2(x54641)),f335(f70(x54641),x54642)))
% 59.73/59.66 [5491]E(f335(f335(f75(a881),x54911),f344(x54912,x54911)),x54912)+~P1(f335(f335(f242(a881),x54911),x54912))
% 59.73/59.66 [5503]~E(f335(f94(a1),x55032),f335(f97(a1),x55031))+P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),x55031)))
% 59.73/59.66 [5506]E(f305(a1,x55061,x55062),f188(f888(a1,a879)))+~P1(f335(f335(f243(a1),x55062),x55061))
% 59.73/59.66 [5509]~P119(x55091)+E(f335(f335(f76(x55091),f335(f70(x55091),x55092)),f335(f70(x55091),x55092)),f335(f335(f76(x55091),x55092),x55092))
% 59.73/59.66 [5514]E(f132(a881,f335(f304(a881,x55141),f335(a106,x55142))),f107(a881))+P1(f335(f335(f242(a881),x55141),x55142))
% 59.73/59.66 [5518]E(f335(f335(f30(a1),x55181),x55182),f294(x55181,x55182))+~P1(f335(f335(f242(a1),f2(a1)),x55182))
% 59.73/59.66 [5538]P1(f335(f130(x55381),x55382))+~P1(f335(f130(x55381),f335(f161(x55381),x55382)))
% 59.73/59.66 [5539]P1(f335(f130(x55391),x55392))+~P1(f335(f130(x55391),f335(f162(x55391),x55392)))
% 59.73/59.66 [5560]P1(f335(f56(a881),x55601))+P1(f335(f335(f337(a881),f850(x55601,x55602)),x55601))
% 59.73/59.66 [5561]P1(f335(f56(a881),x55611))+P1(f335(f335(f337(a881),f854(x55611,x55612)),x55611))
% 59.73/59.66 [5564]P1(f335(f335(f243(a881),x55642),f335(a106,x55641)))+P1(f335(f335(f243(a881),x55641),x55642))
% 59.73/59.66 [5565]E(f39(a1,x55651,x55652),f293(x55651,x55652))+~P1(f335(f335(f242(a1),f2(a1)),x55652))
% 59.73/59.66 [5567]E(f132(a881,f335(f304(a881,x55671),x55672)),f107(a881))+~P1(f335(f335(f242(a881),x55672),x55671))
% 59.73/59.66 [5568]E(f132(a881,f335(f304(a881,x55681),x55682)),f107(a881))+~P1(f335(f335(f242(a881),x55682),x55681))
% 59.73/59.66 [5569]~P80(x55691)+E(f335(f313(x55691,x55691,f74(x55691)),f335(f250(x55691),x55692)),f335(f306(x55691),f335(f74(x55691),x55692)))
% 59.73/59.66 [5570]~P80(x55701)+E(f335(f313(x55701,x55701,f74(x55701)),f335(f303(x55701),x55702)),f335(f251(x55701),f335(f74(x55701),x55702)))
% 59.73/59.66 [5571]~P80(x55711)+E(f335(f313(x55711,x55711,f74(x55711)),f335(f306(x55711),x55712)),f335(f250(x55711),f335(f74(x55711),x55712)))
% 59.73/59.66 [5572]~P80(x55721)+E(f335(f313(x55721,x55721,f74(x55721)),f335(f251(x55721),x55722)),f335(f303(x55721),f335(f74(x55721),x55722)))
% 59.73/59.66 [5583]E(x55831,f188(f888(x55832,a879)))+P1(f335(f335(f337(x55832),f451(x55831,x55832)),x55831))
% 59.73/59.66 [5584]E(x55841,f188(f888(x55842,a879)))+P1(f335(f335(f337(x55842),f439(x55841,x55842)),x55841))
% 59.73/59.66 [5591]~P1(f335(f335(f243(a881),x55911),x55912))+P1(f335(f335(f242(a881),x55911),x55912))
% 59.73/59.66 [5592]~P1(f335(f335(f243(a881),x55921),x55922))+P1(f335(f335(f242(a881),x55921),x55922))
% 59.73/59.66 [5593]~P1(f335(f335(f243(a881),x55931),x55932))+P1(f335(f335(f242(a881),x55931),x55932))
% 59.73/59.66 [5594]~P1(f335(f335(f243(a881),x55941),x55942))+P1(f335(f335(f242(a881),x55941),x55942))
% 59.73/59.66 [5595]~P1(f335(f335(f243(a881),x55951),x55952))+P1(f335(f335(f242(a881),x55951),x55952))
% 59.73/59.66 [5596]~P1(f335(f335(f243(a1),x55961),x55962))+P1(f335(f335(f242(a1),x55961),x55962))
% 59.73/59.66 [5612]E(f41(x56121,x56122),f335(f335(f264(a1,a1),f2(a1)),x56121))+~P1(f335(f335(f243(a1),x56121),x56122))
% 59.73/59.66 [5614]E(f218(f335(f74(a1),x56141),f335(f74(a1),x56142)),f218(x56141,x56142))+~P1(f335(f335(f243(a1),x56142),f2(a1)))
% 59.73/59.66 [5625]E(x56251,x56252)+~E(f335(a3,f335(a106,f335(a20,x56251))),f335(a3,f335(a106,f335(a20,x56252))))
% 59.73/59.66 [5630]E(f41(x56301,x56302),f335(f335(f264(a1,a1),f2(a1)),x56301))+~P1(f335(f335(f242(a1),x56302),f2(a1)))
% 59.73/59.66 [5657]E(f39(a881,f335(f97(a881),x56571),f335(f97(a881),x56572)),f2(a881))+~P1(f335(a193,f335(f97(a1),x56571)))
% 59.73/59.66 [5673]P1(f335(f335(f242(a1),f2(a1)),f399(x56731)))+~P1(f335(x56731,f335(f94(a1),x56732)))
% 59.73/59.66 [5707]P38(f305(a1,x57071,x57072))+~P1(f335(f335(f242(a1),f2(a1)),x57071))
% 59.73/59.66 [5712]~P1(f335(f56(x57121),x57122))+P1(f335(f56(f888(x57121,a879)),f335(f311(x57121),x57122)))
% 59.73/59.66 [5725]E(f335(f335(f75(a1),x57251),f335(f94(a1),f402(x57252,x57251))),x57252)+~P1(f335(f335(f242(a1),x57251),x57252))
% 59.73/59.66 [5733]P1(f335(f335(f242(a881),x57331),x57332))+P1(f335(f335(f242(a881),f335(a106,x57332)),x57331))
% 59.73/59.66 [5776]E(f335(f335(f30(a881),f335(f97(a881),x57761)),f335(f97(a881),x57762)),f2(a881))+~P1(f335(a193,f335(f97(a1),x57761)))
% 59.73/59.66 [5777]E(f335(f335(f76(a881),f335(f97(a881),x57771)),f335(f97(a881),x57772)),f2(a881))+~P1(f335(f335(f243(a1),x57771),a78))
% 59.73/59.66 [5778]P1(f335(f335(f242(a881),x57781),f335(a106,x57782)))+~P1(f335(f335(f242(a881),x57781),x57782))
% 59.73/59.66 [5779]P1(f335(f335(f242(a881),x57791),f335(a106,x57792)))+~P1(f335(f335(f242(a881),x57791),x57792))
% 59.73/59.66 [5780]P1(f335(f335(f243(a881),x57801),f335(a106,x57802)))+~P1(f335(f335(f242(a881),x57801),x57802))
% 59.73/59.66 [5781]P1(f335(f335(f243(a881),x57811),f335(a106,x57812)))+~P1(f335(f335(f242(a881),x57811),x57812))
% 59.73/59.66 [5782]P1(f335(f335(f243(a881),x57821),f335(a106,x57822)))+~P1(f335(f335(f243(a881),x57821),x57822))
% 59.73/59.66 [5783]P1(f335(f335(f243(a881),x57831),f335(a106,x57832)))+~P1(f335(f335(f243(a881),x57831),x57832))
% 59.73/59.66 [5786]~E(x57861,x57862)+P1(f335(f335(f243(a1),x57861),f335(f335(f75(a1),x57862),f73(a1))))
% 59.73/59.66 [5789]E(f39(a1,x57891,x57892),f2(a1))+E(f335(f335(f23(a1),x57892),f39(a1,x57891,x57892)),f39(a1,f335(f74(a1),x57891),x57892))
% 59.73/59.66 [5798]E(x57981,f107(x57982))+P1(f335(f335(f337(x57982),f137(x57982,x57981)),f335(f166(x57982),x57981)))
% 59.73/59.66 [5809]E(f80(f887(a881,a881),f42(x58091,x58092)),f335(f335(f264(a881,a881),f2(a881)),x58091))+~P1(f335(f335(f243(a881),x58091),x58092))
% 59.73/59.66 [5810]E(f80(f887(a881,a881),f42(x58101,x58102)),f335(f335(f264(a881,a881),f2(a881)),x58101))+~P1(f335(f335(f243(a881),x58101),x58102))
% 59.73/59.66 [5844]E(f335(f335(f23(a881),f335(f97(a881),x58441)),f335(f97(a881),x58442)),f335(f97(a881),x58441))+~P1(f335(f335(f243(a1),x58442),a78))
% 59.73/59.66 [5845]E(f335(f335(f75(a881),f335(f97(a881),x58451)),f335(f97(a881),x58452)),f335(f97(a881),x58452))+~P1(f335(f335(f243(a1),x58451),a78))
% 59.73/59.66 [5850]E(f335(a106,f335(f335(f75(a881),x58501),f345(x58502,x58501))),x58502)+~P1(f335(f335(f243(a881),x58501),x58502))
% 59.73/59.66 [5874]P1(f335(x58741,x58742))+~P1(f335(x58741,f335(a84,f548(x58742,x58741))))
% 59.73/59.66 [5883]~P1(f335(f335(f243(a881),x58831),f335(a106,x58832)))+P1(f335(f335(f242(a881),x58831),x58832))
% 59.73/59.66 [5929]E(f335(f335(f312(a881),x59291),f335(f304(a881,x59292),x59291)),f335(f304(a881,x59292),f335(a106,x59291)))+~P1(f335(f335(f242(a881),x59292),x59291))
% 59.73/59.66 [5931]E(x59311,f107(x59312))+E(f335(f335(f127(x59312),f108(x59312,x59311)),f335(f335(f144(x59312),f137(x59312,x59311)),f107(x59312))),x59311)
% 59.73/59.66 [5945]P1(f335(f56(x59451),x59452))+~P1(f335(f335(f243(a881),f2(a881)),f335(f29(x59451),x59452)))
% 59.73/59.66 [5946]P1(f335(f56(x59461),x59462))+~P1(f335(f335(f243(a881),f2(a881)),f335(f29(x59461),x59462)))
% 59.73/59.66 [5948]~E(x59481,f188(f888(x59482,a879)))+~P1(f335(f335(f243(a881),f2(a881)),f335(f29(x59482),x59481)))
% 59.73/59.66 [5958]~P1(f335(f335(f243(a881),x59581),x59582))+P1(f335(f335(f242(a881),f335(a106,x59581)),x59582))
% 59.73/59.66 [5959]~P1(f335(f335(f243(a881),x59591),x59592))+P1(f335(f335(f242(a881),f335(a106,x59591)),x59592))
% 59.73/59.66 [5960]~P1(f335(f335(f243(a881),x59601),x59602))+P1(f335(f335(f242(a881),f335(a106,x59601)),x59602))
% 59.73/59.66 [5967]~P106(x59671)+E(f143(x59671,x59671,f5(x59671),f145(x59671,x59672)),f132(x59671,f335(f166(x59671),x59672)))
% 59.73/59.66 [5970]E(x59701,f107(x59702))+P1(f335(f335(f337(x59702),f335(f134(x59702),x59701)),f335(f166(x59702),x59701)))
% 59.73/59.66 [5976]~P122(x59761)+P1(f335(f335(f243(x59761),x59762),f335(f335(f75(x59761),x59762),f73(x59761))))
% 59.73/59.66 [5978]~P88(x59781)+P1(f335(f335(f242(x59781),f335(f74(x59781),x59782)),f335(f70(x59781),x59782)))
% 59.73/59.66 [6010]P1(f335(f56(a881),x60101))+~P1(f335(f335(f242(a881),f850(x60101,x60102)),x60102))
% 59.73/59.66 [6011]P1(f335(f56(a881),x60111))+~P1(f335(f335(f243(a881),f854(x60111,x60112)),x60112))
% 59.73/59.66 [6015]~P1(f335(f56(f887(x60151,x60151)),x60152))+P1(f335(f56(x60151),f335(f287(x60151),x60152)))
% 59.73/59.66 [6066]E(f172(f335(f97(a1),x60661),f335(f97(a1),x60662)),f107(a1))+P1(f335(f335(f242(a1),f335(f97(a1),x60661)),f335(f97(a1),x60662)))
% 59.73/59.66 [6068]~P1(f335(f335(f243(a881),x60682),f335(a106,x60681)))+~P1(f335(f335(f243(a881),x60681),x60682))
% 59.73/59.66 [6069]~P107(x60691)+E(f335(f335(f95(f888(x60691,a879)),f335(f303(x60691),x60692)),f335(f251(x60691),x60692)),f335(f335(f312(x60691),x60692),f188(f888(x60691,a879))))
% 59.73/59.66 [6071]E(f335(f335(f254(a881),f335(f97(a881),x60711)),f335(f97(a881),x60712)),f335(f335(f254(a881),f2(a881)),f335(f97(a881),x60712)))+~P1(f335(a193,f335(f97(a1),x60711)))
% 59.73/59.66 [6082]P1(f335(f56(x60821),x60822))+~P1(f335(f56(f888(x60821,a879)),f335(f311(x60821),x60822)))
% 59.73/59.66 [6105]P1(f335(f335(f242(a881),f335(a106,x61051)),f335(a106,x61052)))+~P1(f335(f335(f242(a881),x61051),x61052))
% 59.73/59.66 [6106]P1(f335(f335(f242(a881),f335(a20,x61061)),f335(a20,x61062)))+~P1(f335(f335(f242(a93),x61061),x61062))
% 59.73/59.66 [6107]P1(f335(f335(f242(a93),f335(a3,x61071)),f335(a3,x61072)))+~P1(f335(f335(f242(a881),x61071),x61072))
% 59.73/59.66 [6108]P1(f335(f335(f243(a881),f335(a106,x61081)),f335(a106,x61082)))+~P1(f335(f335(f243(a881),x61081),x61082))
% 59.73/59.66 [6109]P1(f335(f335(f243(a881),f335(a106,x61091)),f335(a106,x61092)))+~P1(f335(f335(f243(a881),x61091),x61092))
% 59.73/59.66 [6110]P1(f335(f335(f243(a881),f335(a20,x61101)),f335(a20,x61102)))+~P1(f335(f335(f243(a93),x61101),x61102))
% 59.73/59.66 [6111]P1(f335(f335(f243(a93),f335(a3,x61111)),f335(a3,x61112)))+~P1(f335(f335(f243(a881),x61111),x61112))
% 59.73/59.66 [6114]E(x61141,x61142)+~E(f335(f313(a881,a1,f94(a1)),x61141),f335(f313(a881,a1,f94(a1)),x61142))
% 59.73/59.66 [6130]P1(f335(f335(f242(a881),x61301),x61302))+~P1(f335(f335(f242(a881),f335(a106,x61301)),x61302))
% 59.73/59.66 [6131]P1(f335(f335(f243(a881),x61311),x61312))+~P1(f335(f335(f242(a881),f335(a106,x61311)),x61312))
% 59.73/59.66 [6132]P1(f335(f335(f243(a881),x61321),x61322))+~P1(f335(f335(f242(a881),f335(a106,x61321)),x61322))
% 59.73/59.66 [6133]P1(f335(f335(f243(a881),x61331),x61332))+~P1(f335(f335(f242(a881),f335(a106,x61331)),x61332))
% 59.73/59.66 [6134]P1(f335(f335(f243(a881),x61341),x61342))+~P1(f335(f335(f243(a881),f335(a106,x61341)),x61342))
% 59.73/59.66 [6149]E(f39(a1,x61491,x61492),f2(a1))+E(f335(f335(f23(a1),f39(a1,x61491,x61492)),x61492),f39(a1,x61491,f335(f74(a1),x61492)))
% 59.73/59.66 [6217]E(f335(f29(f888(x62171,a879)),f335(f311(x62171),x62172)),f335(f335(f254(a881),f335(a106,f335(a106,f2(a881)))),f335(f29(x62171),x62172)))+~P1(f335(f56(x62171),x62172))
% 59.73/59.66 [6220]E(x62201,f107(x62202))+E(f335(f335(f158(x62202),x62201),f335(f335(f23(a881),f335(f189(f882(x62202)),x62201)),f73(a881))),f137(x62202,x62201))
% 59.73/59.66 [6245]E(x62451,f107(x62452))+E(f335(f335(f127(x62452),f335(f165(x62452),x62451)),f335(f335(f144(x62452),f335(f134(x62452),x62451)),f107(x62452))),f335(f161(x62452),x62451))
% 59.73/59.66 [6246]~P1(f335(f188(f888(x62461,a879)),x62462))+P1(f335(f335(f337(x62461),x62462),f188(f888(x62461,a879))))
% 59.73/59.66 [6274]~P1(f335(f56(x62741),f31(f888(x62741,a879),x62742)))+P1(f335(f56(f888(x62741,a879)),x62742))
% 59.73/59.66 [6296]P1(f335(f335(f242(a881),f335(f97(a881),x62961)),f335(f97(a881),x62962)))+~P1(f335(f335(f242(a1),x62961),a78))
% 59.73/59.66 [6313]~P1(f335(f335(f243(a1),x63131),x63132))+P1(f335(f335(f242(a1),x63131),f335(f335(f23(a1),x63132),f73(a1))))
% 59.73/59.66 [6314]~P1(f335(f335(f242(a1),x63141),x63142))+P1(f335(f335(f243(a1),x63141),f335(f335(f75(a1),x63142),f73(a1))))
% 59.73/59.66 [6315]~P1(f335(f335(f243(a1),x63151),x63152))+P1(f335(f335(f243(a1),x63151),f335(f335(f75(a1),x63152),f73(a1))))
% 59.73/59.66 [6317]~P1(f335(f335(f242(a1),x63171),x63172))+P1(f335(f335(f242(a881),f335(f97(a881),x63171)),f335(f97(a881),x63172)))
% 59.73/59.66 [6318]~P1(f335(f335(f242(a1),x63181),x63182))+P1(f335(f335(f242(a1),f335(f97(a1),x63181)),f335(f97(a1),x63182)))
% 59.73/59.66 [6319]~P1(f335(f335(f242(a881),x63191),x63192))+P1(f335(f335(f242(a1),f335(f94(a1),x63191)),f335(f94(a1),x63192)))
% 59.73/59.66 [6320]~P1(f335(f335(f242(a881),x63201),x63202))+P1(f335(f335(f242(a1),f335(f94(a1),x63201)),f335(f94(a1),x63202)))
% 59.73/59.66 [6321]~P1(f335(f335(f243(a1),x63211),x63212))+P1(f335(f335(f243(a1),f335(f97(a1),x63211)),f335(f97(a1),x63212)))
% 59.73/59.66 [6322]~P1(f335(f335(f243(a881),x63221),x63222))+P1(f335(f335(f243(a1),f335(f94(a1),x63221)),f335(f94(a1),x63222)))
% 59.73/59.66 [6323]~P1(f335(f335(f243(a881),x63231),x63232))+P1(f335(f335(f243(a1),f335(f94(a1),x63231)),f335(f94(a1),x63232)))
% 59.73/59.66 [6324]~P1(f335(f335(f86(a1),x63241),x63242))+P1(f335(f335(f86(a1),f335(f97(a1),x63241)),f335(f97(a1),x63242)))
% 59.73/59.66 [6331]~E(x63312,f188(f888(x63311,a879)))+P1(f335(f335(f242(f888(x63311,a879)),x63312),f188(f888(x63311,a879))))
% 59.73/59.66 [6343]~P1(f335(f335(f242(a881),x63431),x63432))+~P1(f335(f335(f242(a881),f335(a106,x63432)),x63431))
% 59.73/59.66 [6387]~P1(f335(f335(f242(a881),f335(a106,x63871)),f335(a106,x63872)))+P1(f335(f335(f242(a881),x63871),x63872))
% 59.73/59.66 [6388]~P1(f335(f335(f242(a93),f335(a3,x63881)),f335(a3,x63882)))+P1(f335(f335(f242(a881),x63881),x63882))
% 59.73/59.66 [6389]~P1(f335(f335(f242(a881),f335(a20,x63891)),f335(a20,x63892)))+P1(f335(f335(f242(a93),x63891),x63892))
% 59.73/59.66 [6390]~P1(f335(f335(f243(a881),f335(a106,x63901)),f335(a106,x63902)))+P1(f335(f335(f243(a881),x63901),x63902))
% 59.73/59.66 [6391]~P1(f335(f335(f243(a881),f335(a106,x63911)),f335(a106,x63912)))+P1(f335(f335(f243(a881),x63911),x63912))
% 59.73/59.66 [6392]~P1(f335(f335(f243(a93),f335(a3,x63921)),f335(a3,x63922)))+P1(f335(f335(f243(a881),x63921),x63922))
% 59.73/59.66 [6393]~P1(f335(f335(f243(a881),f335(a98,x63931)),f335(a98,x63932)))+P1(f335(f335(f243(a1),x63931),x63932))
% 59.73/59.66 [6394]~P1(f335(f335(f243(a881),f335(a20,x63941)),f335(a20,x63942)))+P1(f335(f335(f243(a93),x63941),x63942))
% 59.73/59.66 [6416]~P1(f335(f335(f337(x64161),x64162),f188(f888(x64161,a879))))+P1(f335(f188(f888(x64161,a879)),x64162))
% 59.73/59.66 [6436]~P1(f335(f335(f243(a881),f335(a98,x64362)),f335(a98,x64361)))+P1(f335(f335(f243(a1),f2(a1)),x64361))
% 59.73/59.66 [6467]P1(f335(f335(f242(a1),f2(a1)),f39(a1,x64671,x64672)))+~P1(f335(f335(f243(a1),f2(a1)),x64672))
% 59.73/59.66 [6468]P1(f335(f335(f242(a1),f2(a1)),f39(a1,x64681,x64682)))+~P1(f335(f335(f243(a1),f2(a1)),x64682))
% 59.73/59.66 [6631]P36(x66311,x66312)+~E(f335(f335(f291(x66311,x66311,x66311),x66312),x66312),f188(f888(f887(x66311,x66311),a879)))
% 59.73/59.66 [6643]~P36(x66431,x66432)+P36(x66431,f335(f335(f291(x66431,x66431,x66431),x66432),x66432))
% 59.73/59.66 [6654]P1(f335(f335(f242(a1),x66541),x66542))+~P1(f335(f335(f243(a1),x66541),f335(f335(f75(a1),x66542),f73(a1))))
% 59.73/59.66 [6655]P1(f335(f335(f243(a1),x66551),x66552))+~P1(f335(f335(f242(a1),x66551),f335(f335(f23(a1),x66552),f73(a1))))
% 59.73/59.66 [6657]P1(f335(f335(f242(a881),x66571),x66572))+~P1(f335(f335(f242(a1),f335(f94(a1),x66571)),f335(f94(a1),x66572)))
% 59.73/59.66 [6658]P1(f335(f335(f242(a881),x66581),x66582))+~P1(f335(f335(f242(a1),f335(f94(a1),x66581)),f335(f94(a1),x66582)))
% 59.73/59.66 [6659]P1(f335(f335(f242(a1),x66591),x66592))+~P1(f335(f335(f242(a1),f335(f97(a1),x66591)),f335(f97(a1),x66592)))
% 59.73/59.66 [6660]P1(f335(f335(f243(a881),x66601),x66602))+~P1(f335(f335(f243(a1),f335(f94(a1),x66601)),f335(f94(a1),x66602)))
% 59.73/59.66 [6661]P1(f335(f335(f243(a881),x66611),x66612))+~P1(f335(f335(f243(a1),f335(f94(a1),x66611)),f335(f94(a1),x66612)))
% 59.73/59.66 [6662]P1(f335(f335(f243(a1),x66621),x66622))+~P1(f335(f335(f243(a881),f335(f97(a881),x66621)),f335(f97(a881),x66622)))
% 59.73/59.66 [6663]P1(f335(f335(f243(a1),x66631),x66632))+~P1(f335(f335(f243(a1),f335(f97(a1),x66631)),f335(f97(a1),x66632)))
% 59.73/59.66 [6664]P1(f335(f335(f86(a1),x66641),x66642))+~P1(f335(f335(f86(a1),f335(f97(a1),x66641)),f335(f97(a1),x66642)))
% 59.73/59.66 [6761]~E(f727(x67612,x67611),f107(x67611))+E(f335(f135(f882(x67611),f882(x67611),f127(x67611),f107(x67611)),x67612),f107(x67611))
% 59.73/59.66 [6762]~E(f728(x67622,x67621),f107(x67621))+E(f335(f135(f882(x67621),f882(x67621),f127(x67621),f107(x67621)),x67622),f107(x67621))
% 59.73/59.66 [6768]~P5(x67681)+E(f335(f135(x67681,x67681,f95(x67681),f252(x67681)),x67682),f32(x67681,f335(f166(x67681),x67682)))
% 59.73/59.66 [6769]~P5(x67691)+E(f335(f135(x67691,x67691,f104(x67691),f188(x67691)),x67692),f31(x67691,f335(f166(x67691),x67692)))
% 59.73/59.66 [6782]E(x67821,f2(a93))+E(f335(f335(f75(a881),f335(a20,f335(f335(f23(a93),x67821),f73(a93)))),f335(a106,x67822)),f335(f335(f75(a881),f335(a20,x67821)),x67822))
% 59.73/59.66 [6832]P1(f335(f335(f243(a1),f335(f335(f23(a1),x68321),x68322)),f2(a1)))+~P1(f335(f335(f243(a1),x68321),x68322))
% 59.73/59.66 [6862]~P106(x68621)+E(f335(f335(f104(f888(x68621,a879)),f335(f335(f312(x68621),x68622),f188(f888(x68621,a879)))),f335(f306(x68621),x68622)),f335(f251(x68621),x68622))
% 59.73/59.66 [6936]~P57(x69361,x69362)+P36(x69361,f335(f249(f887(x69361,x69361)),f335(f268(x69361,x69361,a879),x69362)))
% 59.73/59.66 [6937]~P57(x69371,x69372)+P55(x69371,f335(f249(f887(x69371,x69371)),f335(f268(x69371,x69371,a879),x69372)))
% 59.73/59.66 [6938]E(x69381,f188(f888(x69382,a879)))+~P1(f335(f335(f242(f888(x69382,a879)),x69381),f188(f888(x69382,a879))))
% 59.73/59.66 [7019]~P1(f335(f335(f243(a881),f2(a881)),x70192))+P1(f335(f335(f242(a881),f39(a881,x70191,x70192)),x70192))
% 59.73/59.66 [7020]~P1(f335(f335(f242(a1),f2(a1)),x70201))+P1(f335(f335(f242(a1),f39(a1,x70201,x70202)),x70201))
% 59.73/59.66 [7021]~P1(f335(f335(f243(a881),f2(a881)),x70212))+P1(f335(f335(f243(a881),f39(a881,x70211,x70212)),x70212))
% 59.73/59.66 [7022]~P1(f335(f335(f243(a1),f2(a1)),x70222))+P1(f335(f335(f243(a1),f39(a1,x70221,x70222)),x70222))
% 59.73/59.66 [7023]~P1(f335(f335(f243(a1),f2(a1)),x70232))+P1(f335(f335(f243(a1),f39(a1,x70231,x70232)),x70232))
% 59.73/59.66 [7099]~P107(x70991)+E(f335(f335(f23(f888(x70991,a879)),f335(f335(f312(x70991),x70992),f188(f888(x70991,a879)))),f335(f250(x70991),x70992)),f335(f335(f312(x70991),x70992),f188(f888(x70991,a879))))
% 59.73/59.66 [7172]~P48(x71721,x71722)+P46(x71721,f252(f888(x71721,a879)),f335(f249(f887(x71721,x71721)),f335(f268(x71721,x71721,a879),x71722)))
% 59.73/59.66 [7173]P1(f335(x71731,x71732))+P1(f335(f335(f337(f888(f887(a881,a881),a879)),f548(x71732,x71731)),a92))
% 59.73/59.66 [7217]E(f335(f335(f127(a881),f132(a881,f335(f304(a881,x72171),x72172))),f335(f335(f144(a881),x72172),f107(a881))),f132(a881,f335(f304(a881,x72171),f335(a106,x72172))))+~P1(f335(f335(f242(a881),x72171),x72172))
% 59.73/59.66 [7218]E(f335(f335(f127(a881),f132(a881,f335(f304(a881,x72181),x72182))),f335(f335(f144(a881),x72182),f107(a881))),f132(a881,f335(f304(a881,x72181),f335(a106,x72182))))+~P1(f335(f335(f242(a881),x72181),x72182))
% 59.73/59.66 [7365]E(x73651,f2(a881))+~E(f335(f135(a881,a881,f75(a881),x73651),x73652),f2(a881))
% 59.73/59.66 [7390]~P1(f335(f335(f243(a1),f335(f335(f23(a1),x73901),x73902)),f2(a1)))+P1(f335(f335(f243(a1),x73901),x73902))
% 59.73/59.66 [7420]P36(x74201,x74202)+~P36(x74201,f335(f335(f291(x74201,x74201,x74201),x74202),x74202))
% 59.73/59.66 [7448]~P1(f335(f335(f242(a881),f335(a106,x74481)),x74482))+P1(f185(a879,a247,f335(f242(a881),x74481),x74482))
% 59.73/59.66 [7606]P26(a881,a881,f335(f335(f7(a881,a881,a881),f23(a881)),x76061),x76062)+P1(f335(f335(f337(a881),f560(x76061,x76062)),x76062))
% 59.73/59.66 [7661]E(f335(f335(f335(f60(a881,x76611,f75(a881)),f335(f16(a881,x76611),f73(a881))),f2(a881)),x76612),f335(f29(x76611),x76612))+~P1(f335(f56(x76611),x76612))
% 59.73/59.66 [7662]E(f335(f335(f335(f60(a881,x76621,f75(a881)),f335(f16(a881,x76621),f73(a881))),f2(a881)),x76622),f335(f29(x76621),x76622))+~P1(f335(f56(x76621),x76622))
% 59.73/59.66 [7705]P26(a881,a881,f335(f335(f7(a881,a881,a881),f23(a881)),x77051),x77052)+~P1(f335(f335(f242(a881),x77051),f560(x77051,x77052)))
% 59.73/59.66 [7763]P36(x77631,x77632)+P1(f335(f335(f242(f888(x77631,a879)),f557(x77632,x77631)),f335(f288(x77631,x77631,x77632),f557(x77632,x77631))))
% 59.73/59.66 [7768]P57(x77681,x77682)+~P36(x77681,f335(f249(f887(x77681,x77681)),f335(f268(x77681,x77681,a879),x77682)))
% 59.73/59.66 [7836]P1(f335(f335(f242(a881),f335(a106,x78361)),x78362))+~P1(f185(a879,a247,f335(f242(a881),x78361),x78362))
% 59.73/59.66 [7892]P1(f335(f335(f337(f887(a881,a881)),f335(f335(f264(a881,a881),x78921),x78922)),f310(a881,a325)))+~P1(f335(f335(f242(a881),x78921),x78922))
% 59.73/59.66 [7996]P48(x79961,x79962)+~P46(x79961,f252(f888(x79961,a879)),f335(f249(f887(x79961,x79961)),f335(f268(x79961,x79961,a879),x79962)))
% 59.73/59.66 [8051]~P1(f335(f130(x80511),x80512))+P1(f335(f130(f888(x80511,a879)),f335(f335(f147(f882(x80511),f888(x80511,a879)),f166(x80511)),f48(x80511,x80512))))
% 59.73/59.66 [8251]~P36(x82511,f335(f289(x82511,x82511),x82512))+P36(x82511,f335(f289(x82511,x82511),f335(f335(f291(x82511,x82511,x82511),x82512),f310(x82511,x82512))))
% 59.73/59.66 [8374]P1(f335(f56(f887(x83741,x83741)),f335(f335(f291(x83741,x83741,x83741),x83742),f310(x83741,x83742))))+~P1(f335(f56(f887(x83741,x83741)),x83742))
% 59.73/59.66 [8405]E(x84051,f2(a1))+P1(f335(f43(x84052,x84051),f335(f335(f264(a1,a1),f335(f335(f30(a1),x84052),x84051)),f39(a1,x84052,x84051))))
% 59.73/59.66 [8419]~P1(f335(f335(f337(f887(a881,a881)),f335(f335(f264(a881,a881),x84191),x84192)),f310(a881,a325)))+P1(f335(f335(f242(a881),x84191),x84192))
% 59.73/59.66 [8434]~P83(x84341)+E(f335(f135(x84341,x84341,f335(f7(x84341,x84341,x84341),f75(x84341)),f2(x84341)),f335(f162(x84341),x84342)),f335(f135(x84341,x84341,f75(x84341),f2(x84341)),x84342))
% 59.73/59.66 [8604]~P106(x86041)+E(f335(f135(f882(x86041),x86041,f335(f7(x86041,f882(x86041),f882(x86041)),f141(x86041,x86041,f5(x86041))),f107(x86041)),x86042),f143(x86041,x86041,f5(x86041),x86042))
% 59.73/59.66 [8710]~P55(x87101,f335(f249(f887(x87101,x87101)),f335(f268(x87101,x87101,a879),x87102)))+P55(x87101,f335(f249(f887(x87101,x87101)),f335(f268(x87101,x87101,a879),f253(x87101,x87101,x87102))))
% 59.73/59.66 [8724]P1(f335(f335(f337(f887(a881,a881)),f335(f335(f264(a881,a881),x87241),x87242)),f335(f335(f291(a881,a881,a881),a325),f310(a881,a325))))+~P1(f335(f335(f243(a881),x87241),x87242))
% 59.73/59.66 [8767]~P1(f335(f56(f887(x87671,x87671)),f335(f335(f291(x87671,x87671,x87671),x87672),f310(x87671,x87672))))+P1(f335(f56(f887(x87671,x87671)),x87672))
% 59.73/59.66 [8822]~P55(x88221,f335(f249(f887(x88221,x88221)),f335(f268(x88221,x88221,a879),f253(x88221,x88221,x88222))))+P55(x88221,f335(f249(f887(x88221,x88221)),f335(f268(x88221,x88221,a879),x88222)))
% 59.73/59.66 [9018]P55(x90181,x90182)+P1(f335(f335(f337(f887(x90181,x90181)),f335(f335(f264(x90181,x90181),f589(x90182,x90181)),f589(x90182,x90181))),f335(f335(f291(x90181,x90181,x90181),x90182),f310(x90181,x90182))))
% 59.73/59.66 [9019]P55(x90191,x90192)+P1(f335(f335(f337(f887(x90191,x90191)),f335(f335(f264(x90191,x90191),f598(x90192,x90191)),f598(x90192,x90191))),f335(f335(f291(x90191,x90191,x90191),x90192),f310(x90191,x90192))))
% 59.73/59.66 [9138]~P1(f335(f335(f337(f887(a881,a881)),f335(f335(f264(a881,a881),x91381),x91382)),f335(f335(f291(a881,a881,a881),a325),f310(a881,a325))))+P1(f335(f335(f243(a881),x91381),x91382))
% 59.73/59.66 [5103]~P97(x51031)+E(f335(f335(f75(x51031),f335(f97(x51031),a78)),x51032),x51032)
% 59.73/59.66 [5136]~P84(x51361)+E(f335(f335(f104(x51361),f335(f74(x51361),x51362)),x51362),f252(x51361))
% 59.73/59.66 [5137]~P84(x51371)+E(f335(f335(f95(x51371),f335(f74(x51371),x51372)),x51372),f188(x51371))
% 59.73/59.66 [5138]~P64(x51381)+E(f335(f335(f75(x51381),f335(f74(x51381),x51382)),x51382),f2(x51381))
% 59.73/59.66 [5139]~P72(x51391)+E(f335(f335(f75(x51391),f335(f74(x51391),x51392)),x51392),f2(x51391))
% 59.73/59.66 [5173]~P97(x51731)+E(f335(f335(f76(x51731),f335(f97(x51731),a91)),x51732),f335(f74(x51731),x51732))
% 59.73/59.66 [5331]~P112(x53311)+E(f335(f335(f76(x53311),f335(f74(x53311),f73(x53311))),x53312),f335(f74(x53311),x53312))
% 59.73/59.66 [5374]E(f335(f70(a1),x53741),f73(a1))+~E(f335(f70(a1),f335(f335(f76(a1),x53741),x53742)),f73(a1))
% 59.73/59.66 [5466]~P97(x54661)+E(f335(f335(f75(x54661),f73(x54661)),f335(f97(x54661),x54662)),f335(f97(x54661),f335(f335(f23(a1),x54662),a91)))
% 59.73/59.66 [5519]~P61(x55191)+E(f10(x55191,f335(f335(f312(x55191),x55192),f188(f888(x55191,a879)))),x55192)
% 59.73/59.66 [5520]~P61(x55201)+E(f13(x55201,f335(f335(f312(x55201),x55202),f188(f888(x55201,a879)))),x55202)
% 59.73/59.66 [5521]~P106(x55211)+E(f14(x55211,f335(f335(f312(x55211),x55212),f188(f888(x55211,a879)))),x55212)
% 59.73/59.66 [5522]~P106(x55221)+E(f15(x55221,f335(f335(f312(x55221),x55222),f188(f888(x55221,a879)))),x55222)
% 59.73/59.66 [5523]~P5(x55231)+E(f32(x55231,f335(f335(f312(x55231),x55232),f188(f888(x55231,a879)))),x55232)
% 59.73/59.66 [5524]~P5(x55241)+E(f31(x55241,f335(f335(f312(x55241),x55242),f188(f888(x55241,a879)))),x55242)
% 59.73/59.66 [5546]E(f335(f335(f75(a881),x55461),f335(f335(f23(a881),x55462),x55461)),x55462)+P1(f335(f335(f243(a881),x55462),x55461))
% 59.73/59.66 [5578]E(x55781,f107(x55782))+P1(f335(f335(f243(a881),f2(a881)),f335(f189(f882(x55782)),x55781)))
% 59.73/59.66 [5704]~P106(x57041)+E(f11(x57041,f240(x57041),f335(f335(f312(x57041),x57042),f188(f888(x57041,a879)))),x57042)
% 59.73/59.66 [5705]~P106(x57051)+E(f12(x57051,f241(x57051),f335(f335(f312(x57051),x57052),f188(f888(x57051,a879)))),x57052)
% 59.73/59.66 [5766]E(f335(f335(f23(a881),x57661),f335(f335(f23(a881),x57661),x57662)),x57662)+~P1(f335(f335(f242(a881),x57662),x57661))
% 59.73/59.66 [5767]E(f335(f335(f75(a881),x57671),f335(f335(f23(a881),x57672),x57671)),x57672)+~P1(f335(f335(f242(a881),x57671),x57672))
% 59.73/59.66 [5787]E(f39(a881,f335(f335(f23(a881),x57871),x57872),x57872),f39(a881,x57871,x57872))+P1(f335(f335(f243(a881),x57871),x57872))
% 59.73/59.66 [5788]E(f39(a881,f335(f335(f23(a881),x57881),x57882),x57882),f39(a881,x57881,x57882))+P1(f335(f335(f243(a881),x57881),x57882))
% 59.73/59.66 [5799]E(f335(f74(a1),f335(f335(f30(a1),x57991),f335(f74(a1),x57992))),f294(x57991,x57992))+P1(f335(f335(f242(a1),f2(a1)),x57992))
% 59.73/59.66 [5801]~E(x58012,f2(a881))+P1(f335(f335(f243(a881),f2(a881)),f335(f335(f254(a881),x58011),x58012)))
% 59.73/59.66 [5854]~P97(x58541)+E(f335(f335(f75(x58541),f335(f74(x58541),f73(x58541))),f335(f97(x58541),x58542)),f335(f97(x58541),f335(f335(f75(a1),x58542),a91)))
% 59.73/59.66 [5855]E(f335(f335(f254(a881),f335(f97(a881),x58551)),x58552),f335(f335(f254(a881),f2(a881)),x58552))+~P1(f335(a193,f335(f97(a1),x58551)))
% 59.73/59.66 [5952]E(f335(f134(a881),f132(a881,f335(f304(a881,x59521),x59522))),x59521)+~P1(f335(f335(f243(a881),x59521),x59522))
% 59.73/59.66 [5971]E(f335(f335(f76(a881),f335(f97(a881),x59711)),f335(f97(a881),x59712)),f335(f97(a881),f335(f335(f76(a1),x59711),x59712)))+P1(f335(f335(f243(a1),x59711),a78))
% 59.73/59.66 [5977]~P124(x59771)+P1(f335(f335(f242(x59771),f2(x59771)),f335(f335(f76(x59771),x59772),x59772)))
% 59.73/59.66 [5989]E(f335(f335(f23(a881),f335(a106,x59891)),x59892),f335(a106,f335(f335(f23(a881),x59891),x59892)))+~P1(f335(f335(f242(a881),x59892),x59891))
% 59.73/59.66 [5992]E(f39(a881,f335(f335(f23(a881),x59921),x59922),x59922),f39(a881,x59921,x59922))+~P1(f335(f335(f242(a881),x59922),x59921))
% 59.73/59.66 [6045]E(f335(f335(f254(a881),f335(a98,x60451)),x60452),f335(a98,f335(f335(f254(a1),x60451),x60452)))+~P1(f335(f335(f242(a1),f2(a1)),x60451))
% 59.73/59.66 [6046]E(f335(f335(f254(a881),f335(a98,x60461)),x60462),f335(a98,f335(f335(f254(a1),x60461),x60462)))+~P1(f335(f335(f242(a1),f2(a1)),x60461))
% 59.73/59.66 [6062]P1(f335(f130(x60621),x60622))+P1(f335(f335(f243(a881),f674(x60622,x60621)),f335(f189(f882(x60621)),x60622)))
% 59.73/59.66 [6063]P1(f335(f130(x60631),x60632))+P1(f335(f335(f243(a881),f688(x60632,x60631)),f335(f189(f882(x60631)),x60632)))
% 59.73/59.66 [6075]~E(x60751,f107(x60752))+~P1(f335(f335(f243(a881),f2(a881)),f335(f189(f882(x60752)),x60751)))
% 59.73/59.66 [6089]E(f137(a881,f132(a881,f335(f304(a881,x60891),x60892))),f335(f335(f23(a881),x60892),f73(a881)))+~P1(f335(f335(f243(a881),x60891),x60892))
% 59.73/59.66 [6092]E(f335(f335(f75(a1),x60921),f335(f94(a1),f335(a106,f403(x60922,x60921)))),x60922)+~P1(f335(f335(f243(a1),x60921),x60922))
% 59.73/59.66 [6099]E(x60991,f2(a881))+E(f335(f335(f76(a881),x60992),f335(f335(f254(a881),x60992),f335(f335(f23(a881),x60991),f73(a881)))),f335(f335(f254(a881),x60992),x60991))
% 59.73/59.66 [6124]E(f335(f335(f76(a881),f335(a98,x61241)),f335(a98,x61242)),f335(a98,f335(f335(f76(a1),x61241),x61242)))+~P1(f335(f335(f242(a1),f2(a1)),x61241))
% 59.73/59.66 [6125]E(f335(f335(f30(a881),f335(a98,x61251)),f335(a98,x61252)),f335(a98,f335(f335(f30(a1),x61251),x61252)))+~P1(f335(f335(f242(a1),f2(a1)),x61251))
% 59.73/59.66 [6139]~P114(x61391)+E(f335(f335(f75(x61391),x61392),x61392),f335(f335(f76(x61391),f335(f335(f75(x61391),f73(x61391)),f73(x61391))),x61392))
% 59.73/59.66 [6158]E(f335(f335(f23(a1),f335(f94(a1),x61581)),f335(f94(a1),x61582)),f335(f94(a1),f335(f335(f23(a881),x61581),x61582)))+~P1(f335(f335(f242(a881),x61582),x61581))
% 59.73/59.66 [6160]E(f335(f335(f264(a1,a1),f335(f97(a1),a91)),f335(f335(f75(a1),x61601),x61602)),f44(x61601,x61602))+~P1(f335(f335(f242(a1),x61602),f2(a1)))
% 59.73/59.66 [6194]E(f173(x61941,x61942),f107(f882(x61941)))+P1(f335(f335(f337(f882(x61941)),f673(x61942,x61941)),f335(f166(f882(x61941)),x61942)))
% 59.73/59.66 [6203]E(f110(a1,f335(f123(a1),x62031),f122(x62032,f335(f335(f75(a1),x62031),f73(a1)))),f122(x62032,x62031))+P1(f335(f335(f243(a1),x62032),x62031))
% 59.73/59.66 [6280]E(f335(f335(f144(a1),x62801),f172(f335(f335(f75(a1),x62801),f73(a1)),x62802)),f172(x62801,x62802))+~P1(f335(f335(f242(a1),x62801),x62802))
% 59.73/59.66 [6316]~P1(f335(f335(f243(a881),x63162),x63161))+P1(f335(f335(f243(a881),f2(a881)),f335(f335(f23(a881),x63161),x63162)))
% 59.73/59.66 [6348]~P1(f335(f335(f243(a881),x63481),f335(a98,x63482)))+P1(f335(f335(f243(a1),f335(f94(a1),x63481)),x63482))
% 59.73/59.66 [6378]~P106(x63781)+E(f335(f335(f104(f888(x63781,a879)),f335(f250(x63781),x63782)),f335(f335(f312(x63781),x63782),f188(f888(x63781,a879)))),f335(f303(x63781),x63782))
% 59.73/59.66 [6379]~P1(f335(f335(f242(a1),f2(a1)),x63791))+P1(f335(f335(f242(a1),f2(a1)),f335(f335(f254(a1),x63791),x63792)))
% 59.73/59.66 [6380]~P1(f335(f335(f243(a881),f2(a881)),x63802))+P1(f335(f335(f243(a881),f2(a881)),f335(f335(f75(a881),x63801),x63802)))
% 59.73/59.66 [6381]~P1(f335(f335(f243(a881),f2(a881)),x63811))+P1(f335(f335(f243(a881),f2(a881)),f335(f335(f75(a881),x63811),x63812)))
% 59.73/59.66 [6382]~P1(f335(f335(f243(a881),f2(a881)),x63821))+P1(f335(f335(f243(a881),f2(a881)),f335(f335(f254(a881),x63821),x63822)))
% 59.73/59.66 [6412]~E(f335(x64121,f2(a881)),f2(a881))+E(f335(f335(f6(a881,a881),x64121),f305(a881,f335(a106,f2(a881)),x64122)),f335(f335(f6(a881,a881),x64121),f305(a881,f2(a881),x64122)))
% 59.73/59.66 [6476]~P97(x64761)+E(f335(f335(f76(x64761),f335(f335(f75(x64761),f73(x64761)),f73(x64761))),f335(f97(x64761),x64762)),f335(f97(x64761),f335(f335(f75(a1),x64762),x64762)))
% 59.73/59.66 [6491]E(f335(f335(f312(a1),x64911),f305(a1,f335(f335(f75(a1),x64911),f73(a1)),x64912)),f305(a1,x64911,x64912))+P1(f335(f335(f243(a1),x64912),x64911))
% 59.73/59.66 [6492]P1(f335(f335(f243(a881),x64921),f335(a98,x64922)))+~P1(f335(f335(f243(a1),f335(f94(a1),x64921)),x64922))
% 59.73/59.66 [6594]E(f335(a98,f335(f335(f254(a1),f335(f97(a1),x65941)),f335(f97(a881),x65942))),f335(f335(f254(a881),f335(f97(a881),x65941)),f335(f97(a881),x65942)))+P1(f335(a193,f335(f97(a1),x65941)))
% 59.73/59.66 [6595]E(f335(a98,f335(f335(f30(a1),f335(f97(a1),x65951)),f335(f97(a1),x65952))),f335(f335(f30(a881),f335(f97(a881),x65951)),f335(f97(a881),x65952)))+P1(f335(a193,f335(f97(a1),x65951)))
% 59.73/59.66 [6656]P1(f335(f335(f243(a881),x66561),x66562))+~P1(f335(f335(f243(a881),f2(a881)),f335(f335(f23(a881),x66562),x66561)))
% 59.73/59.66 [6701]P1(f335(f335(f243(a881),f2(a881)),x67011))+~P1(f335(f335(f243(a881),f2(a881)),f335(f335(f76(a881),x67012),x67011)))
% 59.73/59.66 [6702]P1(f335(f335(f243(a881),f2(a881)),x67021))+~P1(f335(f335(f243(a881),f2(a881)),f335(f335(f76(a881),x67021),x67022)))
% 59.73/59.66 [6719]E(f132(a881,f335(f304(a881,f335(f97(a881),x67191)),f335(f97(a881),x67192))),f107(a881))+P1(f335(f335(f243(a881),f335(f97(a881),x67191)),f335(f97(a881),x67192)))
% 59.73/59.66 [6721]~P1(f335(f335(f242(a1),x67211),f2(a1)))+E(f335(f335(f76(a881),f335(a98,f335(f74(a1),x67211))),f335(a98,f335(f74(a1),x67212))),f335(a98,f335(f335(f76(a1),x67211),x67212)))
% 59.73/59.66 [6780]~E(x67802,f188(f888(x67801,a879)))+P1(f335(f335(f242(f888(x67801,a879)),x67802),f335(f74(f888(x67801,a879)),x67802)))
% 59.73/59.66 [6843]~P97(x68431)+E(f335(f335(f75(x68431),f335(f335(f75(x68431),f2(x68431)),f335(f97(x68431),x68432))),f335(f97(x68431),x68432)),f335(f97(x68431),f335(f335(f75(a1),x68432),x68432)))
% 59.73/59.66 [6901]~P1(f335(f335(f243(a1),x69011),x69012))+P1(f335(f335(f242(a1),f335(f335(f75(a1),x69011),f73(a1))),x69012))
% 59.73/59.66 [6902]~P1(f335(f335(f243(a1),x69021),x69022))+P1(f335(f335(f242(a1),f335(f335(f75(a1),x69021),f73(a1))),x69022))
% 59.73/59.66 [6966]E(x69661,f2(a881))+~P1(f335(f335(f242(a1),f335(f94(a1),x69662)),f335(f74(a1),f335(f94(a1),x69661))))
% 59.73/59.66 [6967]E(x69671,f2(a881))+~P1(f335(f335(f242(a1),f335(f94(a1),x69671)),f335(f74(a1),f335(f94(a1),x69672))))
% 59.73/59.66 [7069]E(f335(f335(f264(a1,a1),f335(f97(a1),a91)),f335(f335(f75(a1),x70691),x70692)),f44(x70691,x70692))+~P1(f335(f335(f242(a1),f2(a1)),f335(f335(f75(a1),x70691),x70692)))
% 59.73/59.66 [7112]~P27(x71121,x71122)+P36(x71121,f335(f263(f888(f887(x71121,x71121),a879),f888(f887(x71121,x71121),a879)),x71122))
% 59.73/59.66 [7130]~P1(f335(f335(f242(a881),f335(a106,f2(a881))),x71301))+P1(f335(f335(f242(a881),f335(a106,f2(a881))),f335(f335(f254(a881),x71301),x71302)))
% 59.73/59.66 [7304]~P1(f335(f335(f242(a1),x73041),x73042))+P1(f335(f335(f242(a1),f335(f335(f75(a1),x73041),x73041)),f335(f335(f75(a1),x73042),x73042)))
% 59.73/59.66 [7305]~P1(f335(f335(f242(a1),x73051),x73052))+P1(f335(f335(f242(a1),f335(f335(f75(a1),x73051),x73051)),f335(f335(f75(a1),x73052),x73052)))
% 59.73/59.66 [7309]~P1(f335(f335(f243(a1),x73091),x73092))+P1(f335(f335(f243(a1),f335(f335(f75(a1),x73091),x73091)),f335(f335(f75(a1),x73092),x73092)))
% 59.73/59.66 [7310]~P1(f335(f335(f243(a1),x73101),x73102))+P1(f335(f335(f243(a1),f335(f335(f75(a1),x73101),x73101)),f335(f335(f75(a1),x73102),x73102)))
% 59.73/59.66 [7311]~P1(f335(f335(f86(a1),x73111),x73112))+P1(f335(f335(f86(a1),f335(f335(f75(a1),x73111),x73111)),f335(f335(f75(a1),x73112),x73112)))
% 59.73/59.66 [7367]~P1(f335(f335(f243(a881),f2(a881)),x73671))+P1(f335(f335(f243(a881),f335(f335(f23(a881),x73671),f335(a106,x73672))),x73671))
% 59.73/59.66 [7402]P1(f335(f335(f242(a881),f335(a106,f2(a881))),x74021))+~P1(f335(f335(f242(a881),f335(a106,f2(a881))),f335(f335(f76(a881),x74022),x74021)))
% 59.73/59.66 [7403]P1(f335(f335(f242(a881),f335(a106,f2(a881))),x74031))+~P1(f335(f335(f242(a881),f335(a106,f2(a881))),f335(f335(f76(a881),x74031),x74032)))
% 59.73/59.66 [7407]P1(f335(f335(f242(a881),f335(f335(f158(a881),x74071),x74072)),f335(f159(a881),x74071)))+~P1(f335(f335(f243(a881),x74072),f335(f189(f882(a881)),x74071)))
% 59.73/59.66 [7447]P1(f335(f335(f243(a1),x74471),x74472))+~P1(f335(f335(f242(a1),f335(f335(f75(a1),x74471),f73(a1))),x74472))
% 59.73/59.66 [7456]~P1(f335(f335(f337(a881),x74561),x74562))+P1(f335(f335(f337(a1),f335(f94(a1),x74561)),f335(f313(a881,a1,f94(a1)),x74562)))
% 59.73/59.66 [7491]P1(f335(f56(x74911),f252(f888(x74911,a879))))+~P1(f335(f56(f888(x74912,x74911)),f252(f888(f888(x74912,x74911),a879))))
% 59.73/59.66 [7492]P1(f335(f56(x74921),f252(f888(x74921,a879))))+~P1(f335(f56(f889(x74922,x74921)),f252(f888(f889(x74922,x74921),a879))))
% 59.73/59.66 [7493]P1(f335(f56(x74931),f252(f888(x74931,a879))))+~P1(f335(f56(f889(x74931,x74932)),f252(f888(f889(x74931,x74932),a879))))
% 59.73/59.66 [7533]E(x75331,f188(f888(x75332,a879)))+~P1(f335(f335(f242(f888(x75332,a879)),x75331),f335(f74(f888(x75332,a879)),x75331)))
% 59.73/59.66 [7672]E(f335(f135(f882(x76721),f882(x76721),f127(x76721),f107(x76721)),x76722),f107(x76721))+P1(f335(f335(f337(f882(x76721)),f727(x76722,x76721)),f335(f166(f882(x76721)),x76722)))
% 59.73/59.66 [7673]E(f335(f135(f882(x76731),f882(x76731),f127(x76731),f107(x76731)),x76732),f107(x76731))+P1(f335(f335(f337(f882(x76731)),f728(x76732,x76731)),f335(f166(f882(x76731)),x76732)))
% 59.73/59.66 [7814]E(f173(x78141,f335(f335(f144(f882(x78141)),f107(x78141)),x78142)),f173(x78141,x78142))+~P1(f335(f323(f882(f882(x78141)),f174(x78141)),f335(f335(f144(f882(x78141)),f107(x78141)),x78142)))
% 59.73/59.66 [7910]P1(f335(f335(f242(a1),x79101),x79102))+~P1(f335(f335(f242(a1),f335(f335(f75(a1),x79101),x79101)),f335(f335(f75(a1),x79102),x79102)))
% 59.73/59.66 [7911]P1(f335(f335(f242(a1),x79111),x79112))+~P1(f335(f335(f242(a1),f335(f335(f75(a1),x79111),x79111)),f335(f335(f75(a1),x79112),x79112)))
% 59.73/59.66 [7915]P1(f335(f335(f243(a1),x79151),x79152))+~P1(f335(f335(f243(a1),f335(f335(f75(a1),x79151),x79151)),f335(f335(f75(a1),x79152),x79152)))
% 59.73/59.66 [7916]P1(f335(f335(f243(a1),x79161),x79162))+~P1(f335(f335(f243(a1),f335(f335(f75(a1),x79161),x79161)),f335(f335(f75(a1),x79162),x79162)))
% 59.73/59.66 [7917]P1(f335(f335(f86(a1),x79171),x79172))+~P1(f335(f335(f86(a1),f335(f335(f75(a1),x79171),x79171)),f335(f335(f75(a1),x79172),x79172)))
% 59.73/59.66 [8016]~P114(x80161)+E(f335(f335(f76(x80161),f335(f335(f75(x80161),f73(x80161)),f73(x80161))),f335(f335(f6(a881,x80161),f94(x80161)),f305(a881,f73(a881),x80162))),f335(f335(f76(x80161),f335(f94(x80161),x80162)),f335(f335(f75(x80161),f335(f94(x80161),x80162)),f73(x80161))))
% 59.73/59.66 [8050]E(f335(f335(f144(a1),f335(f97(a1),x80501)),f172(f335(f335(f75(a1),f335(f97(a1),x80501)),f73(a1)),f335(f97(a1),x80502))),f172(f335(f97(a1),x80501),f335(f97(a1),x80502)))+~P1(f335(f335(f242(a1),f335(f97(a1),x80501)),f335(f97(a1),x80502)))
% 59.73/59.66 [8065]P1(f335(f335(f337(a881),x80651),x80652))+~P1(f335(f335(f337(a1),f335(f94(a1),x80651)),f335(f313(a881,a1,f94(a1)),x80652)))
% 59.73/59.66 [8223]~P1(f335(f56(x82231),x82232))+E(f335(f313(a881,x82231,f871(x82232,x82231)),f335(f249(a881),f335(f335(f7(a881,a881,a879),f243(a881)),f872(x82232,x82231)))),x82232)
% 59.73/59.66 [8506]P47(x85061,x85062)+P1(f335(f335(f337(f887(x85061,x85061)),f335(f335(f264(x85061,x85061),f835(x85062,x85061)),f835(x85062,x85061))),x85062))
% 59.73/59.66 [8646]~P97(x86461)+E(f335(f335(f23(x86461),f73(x86461)),f335(f97(x86461),x86462)),f335(f97(x86461),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f74(a1),x86462))))
% 59.73/59.66 [8763]~P1(f335(f335(f242(f888(a881,a879)),x87631),x87632))+P1(f335(f335(f242(f888(a1,a879)),f335(f313(a881,a1,f94(a1)),x87631)),f335(f313(a881,a1,f94(a1)),x87632)))
% 59.73/59.66 [8764]~P1(f335(f335(f243(f888(a881,a879)),x87641),x87642))+P1(f335(f335(f243(f888(a1,a879)),f335(f313(a881,a1,f94(a1)),x87641)),f335(f313(a881,a1,f94(a1)),x87642)))
% 59.73/59.66 [8795]~P1(f335(f335(f243(a1),x87951),x87952))+P1(f335(f335(f242(a1),f335(f335(f23(a1),f335(f335(f75(a1),x87951),x87951)),a91)),f335(f335(f75(a1),x87952),x87952)))
% 59.73/59.66 [8796]~P1(f335(f335(f243(a1),x87961),x87962))+P1(f335(f335(f242(a1),f335(f335(f23(a1),f335(f335(f75(a1),x87961),x87961)),a91)),f335(f335(f75(a1),x87962),x87962)))
% 59.73/59.66 [8797]~P1(f335(f335(f243(a1),x87971),x87972))+P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f75(a1),x87971),x87971)),a91)),f335(f335(f75(a1),x87972),x87972)))
% 59.73/59.66 [8798]~P1(f335(f335(f243(a1),x87981),x87982))+P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f75(a1),x87981),x87981)),a91)),f335(f335(f75(a1),x87982),x87982)))
% 59.73/59.66 [8868]~P1(f335(f335(f337(a881),x88681),f335(f166(a881),x88682)))+P1(f335(f335(f242(a881),x88681),f335(f135(a881,a881,f75(a881),f2(a881)),x88682)))
% 59.73/59.66 [8962]P43(x89621,x89622)+~P1(f335(f335(f337(f887(x89621,x89621)),f335(f335(f264(x89621,x89621),f838(x89622,x89621)),f838(x89622,x89621))),x89622))
% 59.73/59.66 [9100]~P1(f335(f335(f242(f888(a1,a879)),f335(f313(a881,a1,f94(a1)),x91001)),f335(f313(a881,a1,f94(a1)),x91002)))+P1(f335(f335(f242(f888(a881,a879)),x91001),x91002))
% 59.73/59.66 [9101]~P1(f335(f335(f243(f888(a1,a879)),f335(f313(a881,a1,f94(a1)),x91011)),f335(f313(a881,a1,f94(a1)),x91012)))+P1(f335(f335(f243(f888(a881,a879)),x91011),x91012))
% 59.73/59.66 [9187]P1(f335(f335(f243(a1),x91871),x91872))+~P1(f335(f335(f242(a1),f335(f335(f23(a1),f335(f335(f75(a1),x91871),x91871)),a91)),f335(f335(f75(a1),x91872),x91872)))
% 59.73/59.66 [9188]P1(f335(f335(f243(a1),x91881),x91882))+~P1(f335(f335(f242(a1),f335(f335(f23(a1),f335(f335(f75(a1),x91881),x91881)),a91)),f335(f335(f75(a1),x91882),x91882)))
% 59.73/59.66 [9189]P1(f335(f335(f243(a1),x91891),x91892))+~P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f75(a1),x91891),x91891)),a91)),f335(f335(f75(a1),x91892),x91892)))
% 59.73/59.66 [9190]P1(f335(f335(f243(a1),x91901),x91902))+~P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f75(a1),x91901),x91901)),a91)),f335(f335(f75(a1),x91902),x91902)))
% 59.73/59.66 [10079]~P104(x100791)+E(f110(f882(x100791),f335(f123(f882(x100791)),f107(x100791)),f335(f335(f335(f88(f883(f882(x100791))),f335(f335(f243(a1),f2(a1)),x100792)),f335(f112(f887(x100791,f882(x100791)),f882(x100791),f124(x100791,f882(x100791),f125(x100791,f335(f335(f23(a1),x100792),f73(a1))),f125(f882(x100791),f335(f335(f23(a1),x100792),f73(a1))))),f335(f268(x100791,f882(x100791),f883(f882(x100791))),f335(f335(f8(f888(f882(x100791),f882(x100791)),f888(f882(x100791),f883(f882(x100791))),x100791),f335(f8(f882(x100791),f883(f882(x100791)),f882(x100791)),f123(f882(x100791)))),f144(x100791))))),f109(f882(x100791)))),f125(f882(x100791),x100792))
% 59.73/59.66 [10100]~P1(f335(f56(x101001),x101002))+E(f335(f189(f882(x101001)),f85(f882(x101001),f335(f335(f18(f882(x101001),a879,a879),f335(f335(f8(a879,f888(a879,a879),f882(x101001)),a333),f335(f335(f7(f882(x101001),f888(x101001,a879),a879),f335(f335(f8(f888(x101001,a879),f888(f888(x101001,a879),a879),f882(x101001)),a332),f166(x101001))),x101002))),f130(x101001)))),f217(x101001,x101002))
% 59.73/59.66 [6088]E(f335(f335(f75(a881),f335(f335(f23(a881),x60881),x60882)),x60882),x60881)+~P1(f335(f335(f242(a881),x60882),x60881))
% 59.73/59.66 [6154]E(f335(f335(f30(a881),f335(f335(f76(a881),x61541),x61542)),x61542),x61541)+~P1(f335(f335(f243(a881),f2(a881)),x61542))
% 59.73/59.66 [6155]E(f335(f335(f30(a881),f335(f335(f76(a881),x61551),x61552)),x61551),x61552)+~P1(f335(f335(f243(a881),f2(a881)),x61551))
% 59.73/59.66 [6159]~P77(x61591)+E(f335(f335(f6(a881,x61591),f335(f158(x61591),x61592)),f335(f304(a881,f2(a881)),f335(f189(f882(x61591)),x61592))),f335(f159(x61591),x61592))
% 59.73/59.66 [6272]E(f39(a881,f335(a106,f335(f335(f76(a881),x62721),x62722)),x62721),f73(a881))+~P1(f335(f335(f243(a881),f73(a881)),x62721))
% 59.73/59.66 [6278]E(f335(a106,f335(f335(f75(a881),f335(f97(a881),x62781)),x62782)),f335(f335(f75(a881),f73(a881)),x62782))+~P1(f335(a193,f335(f97(a1),x62781)))
% 59.73/59.66 [6305]E(f335(a98,f335(f335(f254(a1),f335(f97(a1),x63051)),x63052)),f335(f335(f254(a881),f335(f97(a881),x63051)),x63052))+P1(f335(a193,f335(f97(a1),x63051)))
% 59.73/59.66 [6546]E(f335(f335(f23(a881),x65461),f335(f97(a881),f335(f335(f75(a1),x65462),a91))),f335(f335(f23(a881),f335(a106,x65461)),f335(f97(a881),x65462)))+~P1(f335(f335(f243(a1),a78),x65462))
% 59.73/59.66 [6630]E(x66301,f2(a881))+E(f335(a106,f335(f335(f75(a881),f335(f335(f23(a881),x66301),f73(a881))),x66302)),f335(f335(f75(a881),x66301),x66302))
% 59.73/59.66 [6670]E(x66701,f2(a1))+P1(f335(f335(f243(a1),f2(a1)),f335(f335(f254(a1),f335(f70(a1),x66701)),x66702)))
% 59.73/59.66 [6686]~E(x66862,f2(a881))+P1(f335(f335(f243(a1),f2(a1)),f335(f335(f254(a1),f335(f70(a1),x66861)),x66862)))
% 59.73/59.66 [6725]E(x67251,f2(a881))+E(f335(f335(f75(a881),x67252),f335(f335(f76(a881),f335(f335(f23(a881),x67251),f73(a881))),x67252)),f335(f335(f76(a881),x67251),x67252))
% 59.73/59.66 [6773]~P1(f335(f335(f242(a1),x67731),x67732))+P1(f335(f335(f243(a1),f335(f335(f75(a1),x67731),a91)),x67732))
% 59.73/59.66 [6904]E(f335(f335(f144(a881),x69041),f132(a881,f335(f304(a881,f335(a106,x69041)),x69042))),f132(a881,f335(f304(a881,x69041),x69042)))+~P1(f335(f335(f243(a881),x69041),x69042))
% 59.73/59.66 [6905]E(f335(f335(f144(a881),x69051),f132(a881,f335(f304(a881,f335(a106,x69051)),x69052))),f132(a881,f335(f304(a881,x69051),x69052)))+~P1(f335(f335(f243(a881),x69051),x69052))
% 59.73/59.66 [7103]E(x71031,x71032)+~E(f335(f335(f23(a1),f335(f335(f75(a1),x71031),x71031)),a91),f335(f335(f23(a1),f335(f335(f75(a1),x71032),x71032)),a91))
% 59.73/59.66 [7106]E(x71061,f107(x71062))+E(f274(x71062,f335(f335(f147(x71062,f887(a93,x71062)),f335(f264(a93,x71062),f73(a93))),x71061)),f281(x71062,x71061))
% 59.73/59.66 [7336]P1(f335(f335(f242(a1),x73361),x73362))+~P1(f335(f335(f243(a1),f335(f335(f75(a1),x73361),a91)),x73362))
% 59.73/59.66 [7816]~P1(f335(f335(f243(a881),x78161),x78162))+P1(f335(f335(f337(f887(a881,a881)),f335(f335(f264(a881,a881),x78161),x78162)),a248))
% 59.73/59.66 [8042]~P1(f335(f335(f243(a93),f2(a93)),x80421))+P1(f335(f335(f243(a93),f335(f263(a93,f887(a93,a93)),f335(f275(x80421),x80422))),x80421))
% 59.73/59.66 [8352]~P88(x83521)+P1(f335(f335(f242(x83521),f335(f70(x83521),f335(f159(x83521),x83522))),f335(f159(x83521),f335(f335(f147(x83521,x83521),f70(x83521)),x83522))))
% 59.73/59.66 [8376]P1(f335(f335(f243(a881),x83761),x83762))+~P1(f335(f335(f337(f887(a881,a881)),f335(f335(f264(a881,a881),x83761),x83762)),a248))
% 59.73/59.66 [8528]E(f335(f335(f264(x85281,x85281),f606(x85282,x85281)),f606(x85282,x85281)),x85282)+~P1(f335(f335(f337(f887(x85281,x85281)),x85282),f310(x85281,f188(f888(f887(x85281,x85281),a879)))))
% 59.73/59.66 [8570]E(f335(f304(a881,x85701),f335(f335(f75(a881),x85701),f335(f29(a881),x85702))),x85702)+~P1(f335(f335(f242(f888(a881,a879)),x85702),f335(f304(a881,x85701),f335(f335(f75(a881),x85701),f335(f29(a881),x85702)))))
% 59.73/59.66 [8591]E(f335(f335(f144(a881),f335(f97(a881),x85911)),f132(a881,f335(f304(a881,f335(a106,f335(f97(a881),x85911))),f335(f97(a881),x85912)))),f132(a881,f335(f304(a881,f335(f97(a881),x85911)),f335(f97(a881),x85912))))+~P1(f335(f335(f243(a881),f335(f97(a881),x85911)),f335(f97(a881),x85912)))
% 59.73/59.66 [8907]E(f335(f335(f30(a1),f335(f97(a1),f335(f335(f23(a1),f335(f335(f75(a1),x89071),x89071)),a91))),f335(f97(a1),f335(f335(f75(a1),x89072),x89072))),f335(f335(f30(a1),f335(f97(a1),x89071)),f335(f97(a1),x89072)))+~P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),x89072)))
% 59.73/59.66 [9029]E(f171(f882(x90291),f335(f335(f8(a879,a879,f882(x90291)),a330),f335(f335(f7(f882(x90291),f882(x90291),a879),a332),f107(x90291))),x90292),f173(x90291,f173(x90291,x90292)))+~P15(a881,f335(f162(a881),f335(f335(f147(f882(x90291),a881),f189(f882(x90291))),x90292)))
% 59.73/59.66 [9032]E(f335(f335(f30(a1),f335(f97(a1),f335(f335(f23(a1),f335(f335(f75(a1),x90321),x90321)),a91))),f335(f97(a1),f335(f335(f75(a1),x90322),x90322))),f335(f335(f30(a1),f335(f335(f75(a1),f335(f97(a1),x90321)),f73(a1))),f335(f97(a1),x90322)))+P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),x90322)))
% 59.73/59.66 [9880]P1(f335(a193,x98802))+E(f335(f335(f81(a1,a881),f335(f335(f23(a1),x98801),x98802)),f335(f335(f18(a1,a881,a881),f335(f335(f7(a1,a881,f888(a881,a881)),f335(f335(f8(a879,f888(a881,f888(a881,a881)),a1),f88(a881)),a193)),f2(a881))),a98)),f335(f335(f23(a881),f335(a98,x98801)),f335(a98,x98802)))
% 59.73/59.66 [9889]E(f335(f335(f81(a1,a881),f335(f97(a1),f335(f335(f75(a1),x98891),f335(f74(a1),x98892)))),f335(f335(f18(a1,a881,a881),f335(f335(f7(a1,a881,f888(a881,a881)),f335(f335(f8(a879,f888(a881,f888(a881,a881)),a1),f88(a881)),a193)),f2(a881))),a98)),f335(f335(f23(a881),f335(f97(a881),x98891)),f335(f97(a881),x98892)))+P1(f335(f335(f243(a1),x98892),a78))
% 59.73/59.66 [9890]~P27(x98901,x98902)+P1(f335(f335(f242(f888(f887(x98901,x98901),a879)),f335(f335(f291(x98901,x98901,x98901),f335(f263(f888(f887(x98901,x98901),a879),f888(f887(x98901,x98901),a879)),x98902)),f335(f267(f888(f887(x98901,x98901),a879),f888(f887(x98901,x98901),a879)),x98902))),f335(f263(f888(f887(x98901,x98901),a879),f888(f887(x98901,x98901),a879)),x98902)))
% 59.73/59.66 [9951]~E(f335(f29(a881),f335(f249(a881),f335(f335(f18(a881,a879,a879),f335(f335(f8(a879,f888(a879,a879),a881),a333),f335(f335(f7(a881,f888(a881,a879),a879),f337(a881)),x99511))),f335(f335(f7(a881,a881,a879),f243(a881)),f335(a106,x99512))))),f2(a881))+~P1(f335(f335(f337(a881),f2(a881)),x99511))
% 59.73/59.66 [10008]E(f39(a1,f335(f97(a1),f335(f335(f23(a1),f335(f335(f75(a1),x100081),x100081)),a91)),f335(f97(a1),f335(f335(f75(a1),x100082),x100082))),f335(f335(f75(a1),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f39(a1,f335(f97(a1),x100081),f335(f97(a1),x100082)))),f73(a1)))+~P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),x100082)))
% 59.73/59.66 [10017]E(f39(a1,f335(f97(a1),f335(f335(f23(a1),f335(f335(f75(a1),x100171),x100171)),a91)),f335(f97(a1),f335(f335(f75(a1),x100172),x100172))),f335(f335(f23(a1),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f39(a1,f335(f335(f75(a1),f335(f97(a1),x100171)),f73(a1)),f335(f97(a1),x100172)))),f73(a1)))+P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),x100172)))
% 59.73/59.66 [10069]~P5(x100691)+E(f31(x100691,f335(f249(x100691),f335(f335(f8(f888(x100691,a879),a879,x100691),f83(x100691)),f335(f335(f8(f888(x100691,a879),f888(x100691,a879),x100691),f335(f18(x100691,a879,a879),f335(f335(f8(a879,f888(a879,a879),x100691),a338),f335(f335(f7(x100691,f888(x100691,a879),a879),f337(x100691)),x100692)))),f242(x100691))))),f32(x100691,x100692))
% 59.73/59.66 [10093]~P36(x100931,x100932)+P57(x100931,f335(f335(f7(x100931,f888(f887(x100931,x100931),a879),f888(x100931,a879)),f335(f335(f8(f888(x100931,f888(f888(f887(x100931,x100931),a879),a879)),f888(f888(f887(x100931,x100931),a879),f888(x100931,a879)),x100931),f7(x100931,f888(f887(x100931,x100931),a879),a879)),f335(f335(f8(f888(x100931,f887(x100931,x100931)),f888(x100931,f888(f888(f887(x100931,x100931),a879),a879)),x100931),f335(f8(f887(x100931,x100931),f888(f888(f887(x100931,x100931),a879),a879),x100931),f337(f887(x100931,x100931)))),f264(x100931,x100931)))),x100932))
% 59.73/59.66 [10094]~P8(x100941,f252(f888(x100941,a879)),x100942)+P7(x100941,f335(f335(f7(x100941,f888(f887(x100941,x100941),a879),f888(x100941,a879)),f335(f335(f8(f888(x100941,f888(f888(f887(x100941,x100941),a879),a879)),f888(f888(f887(x100941,x100941),a879),f888(x100941,a879)),x100941),f7(x100941,f888(f887(x100941,x100941),a879),a879)),f335(f335(f8(f888(x100941,f887(x100941,x100941)),f888(x100941,f888(f888(f887(x100941,x100941),a879),a879)),x100941),f335(f8(f887(x100941,x100941),f888(f888(f887(x100941,x100941),a879),a879),x100941),f337(f887(x100941,x100941)))),f264(x100941,x100941)))),x100942))
% 59.73/59.66 [10129]P36(x101291,x101292)+~P57(x101291,f335(f335(f7(x101291,f888(f887(x101291,x101291),a879),f888(x101291,a879)),f335(f335(f8(f888(x101291,f888(f888(f887(x101291,x101291),a879),a879)),f888(f888(f887(x101291,x101291),a879),f888(x101291,a879)),x101291),f7(x101291,f888(f887(x101291,x101291),a879),a879)),f335(f335(f8(f888(x101291,f887(x101291,x101291)),f888(x101291,f888(f888(f887(x101291,x101291),a879),a879)),x101291),f335(f8(f887(x101291,x101291),f888(f888(f887(x101291,x101291),a879),a879),x101291),f337(f887(x101291,x101291)))),f264(x101291,x101291)))),x101292))
% 59.73/59.66 [10130]P8(x101301,f252(f888(x101301,a879)),x101302)+~P7(x101301,f335(f335(f7(x101301,f888(f887(x101301,x101301),a879),f888(x101301,a879)),f335(f335(f8(f888(x101301,f888(f888(f887(x101301,x101301),a879),a879)),f888(f888(f887(x101301,x101301),a879),f888(x101301,a879)),x101301),f7(x101301,f888(f887(x101301,x101301),a879),a879)),f335(f335(f8(f888(x101301,f887(x101301,x101301)),f888(x101301,f888(f888(f887(x101301,x101301),a879),a879)),x101301),f335(f8(f887(x101301,x101301),f888(f888(f887(x101301,x101301),a879),a879),x101301),f337(f887(x101301,x101301)))),f264(x101301,x101301)))),x101302))
% 59.73/59.66 [7285]E(f335(f335(f75(a881),f335(f97(a881),f335(f335(f23(a1),x72851),a91))),x72852),f335(a106,f335(f335(f75(a881),f335(f97(a881),x72851)),x72852)))+P1(f335(a193,f335(f97(a1),x72851)))
% 59.73/59.66 [7732]~P97(x77321)+E(f335(f335(f75(x77321),f335(f335(f75(x77321),f73(x77321)),f335(f97(x77321),x77322))),f335(f97(x77321),x77322)),f335(f97(x77321),f335(f335(f23(a1),f335(f335(f75(a1),x77322),x77322)),a91)))
% 59.73/59.66 [8377]~P1(f335(f335(f242(a1),x83771),x83772))+P1(f335(f335(f242(a1),f335(f335(f75(a1),x83771),x83771)),f335(f335(f23(a1),f335(f335(f75(a1),x83772),x83772)),a91)))
% 59.73/59.66 [8378]~P1(f335(f335(f242(a1),x83781),x83782))+P1(f335(f335(f242(a1),f335(f335(f75(a1),x83781),x83781)),f335(f335(f23(a1),f335(f335(f75(a1),x83782),x83782)),a91)))
% 59.73/59.66 [8379]~P1(f335(f335(f242(a1),x83791),x83792))+P1(f335(f335(f243(a1),f335(f335(f75(a1),x83791),x83791)),f335(f335(f23(a1),f335(f335(f75(a1),x83792),x83792)),a91)))
% 59.73/59.66 [8380]~P1(f335(f335(f242(a1),x83801),x83802))+P1(f335(f335(f243(a1),f335(f335(f75(a1),x83801),x83801)),f335(f335(f23(a1),f335(f335(f75(a1),x83802),x83802)),a91)))
% 59.73/59.66 [8799]P1(f335(f335(f242(a1),x87991),x87992))+~P1(f335(f335(f242(a1),f335(f335(f75(a1),x87991),x87991)),f335(f335(f23(a1),f335(f335(f75(a1),x87992),x87992)),a91)))
% 59.73/59.66 [8800]P1(f335(f335(f242(a1),x88001),x88002))+~P1(f335(f335(f242(a1),f335(f335(f75(a1),x88001),x88001)),f335(f335(f23(a1),f335(f335(f75(a1),x88002),x88002)),a91)))
% 59.73/59.66 [8801]P1(f335(f335(f242(a1),x88011),x88012))+~P1(f335(f335(f243(a1),f335(f335(f75(a1),x88011),x88011)),f335(f335(f23(a1),f335(f335(f75(a1),x88012),x88012)),a91)))
% 59.73/59.66 [8802]P1(f335(f335(f242(a1),x88021),x88022))+~P1(f335(f335(f243(a1),f335(f335(f75(a1),x88021),x88021)),f335(f335(f23(a1),f335(f335(f75(a1),x88022),x88022)),a91)))
% 59.73/59.66 [9087]~P1(f335(f335(f242(a1),x90871),x90872))+P1(f335(f335(f242(a1),f335(f335(f23(a1),f335(f335(f75(a1),x90871),x90871)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),x90872),x90872)),a91)))
% 59.73/59.66 [9088]~P1(f335(f335(f242(a1),x90881),x90882))+P1(f335(f335(f242(a1),f335(f335(f23(a1),f335(f335(f75(a1),x90881),x90881)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),x90882),x90882)),a91)))
% 59.73/59.66 [9089]~P1(f335(f335(f243(a1),x90891),x90892))+P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f75(a1),x90891),x90891)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),x90892),x90892)),a91)))
% 59.73/59.66 [9090]~P1(f335(f335(f243(a1),x90901),x90902))+P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f75(a1),x90901),x90901)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),x90902),x90902)),a91)))
% 59.73/59.66 [9091]~P1(f335(f335(f86(a1),x90911),x90912))+P1(f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f75(a1),x90911),x90911)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),x90912),x90912)),a91)))
% 59.73/59.66 [9356]P1(f335(f335(f242(a1),x93561),x93562))+~P1(f335(f335(f242(a1),f335(f335(f23(a1),f335(f335(f75(a1),x93561),x93561)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),x93562),x93562)),a91)))
% 59.73/59.66 [9357]P1(f335(f335(f242(a1),x93571),x93572))+~P1(f335(f335(f242(a1),f335(f335(f23(a1),f335(f335(f75(a1),x93571),x93571)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),x93572),x93572)),a91)))
% 59.73/59.66 [9358]P1(f335(f335(f243(a1),x93581),x93582))+~P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f75(a1),x93581),x93581)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),x93582),x93582)),a91)))
% 59.73/59.66 [9359]P1(f335(f335(f243(a1),x93591),x93592))+~P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f75(a1),x93591),x93591)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),x93592),x93592)),a91)))
% 59.73/59.66 [9360]P1(f335(f335(f86(a1),x93601),x93602))+~P1(f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f75(a1),x93601),x93601)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),x93602),x93602)),a91)))
% 59.73/59.66 [9394]~P1(f335(f56(x93941),x93942))+P1(f335(f56(f888(x93941,a879)),f335(f249(f888(x93941,a879)),f335(f335(f7(f888(x93941,a879),f888(x93941,a879),a879),f242(f888(x93941,a879))),x93942))))
% 59.73/59.66 [9440]~E(f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),x94401),f188(f888(f887(a881,a881),a879)))),f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),x94402),f188(f888(f887(a881,a881),a879)))))+P1(f335(f335(f337(f887(f887(a881,a881),f887(a881,a881))),f335(f335(f264(f887(a881,a881),f887(a881,a881)),x94401),x94402)),a102))
% 59.73/59.66 [9528]E(f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),x95281),f188(f888(f887(a881,a881),a879)))),f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),x95282),f188(f888(f887(a881,a881),a879)))))+~P1(f335(f335(f337(f887(f887(a881,a881),f887(a881,a881))),f335(f335(f264(f887(a881,a881),f887(a881,a881)),x95281),x95282)),a102))
% 59.73/59.66 [9563]P1(f335(f335(f242(a1),f2(a1)),f656(x95631,x95632)))+E(f335(f249(a1),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f242(a1),f2(a1)))),x95631)),f335(f249(a1),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f242(a1),f2(a1)))),x95632)))
% 59.73/59.66 [10078]~P5(x100781)+E(f32(x100781,f335(f249(x100781),f335(f335(f8(f888(x100781,a879),a879,x100781),f83(x100781)),f335(f335(f8(f888(x100781,a879),f888(x100781,a879),x100781),f335(f18(x100781,a879,a879),f335(f335(f8(a879,f888(a879,a879),x100781),a338),f335(f335(f7(x100781,f888(x100781,a879),a879),f337(x100781)),x100782)))),f335(f7(x100781,x100781,a879),f242(x100781)))))),f31(x100781,x100782))
% 59.73/59.66 [10099]P1(f335(f335(f337(a881),f2(a881)),x100991))+E(f335(f29(a881),f335(f249(a881),f335(f335(f18(a881,a879,a879),f335(f335(f8(a879,f888(a879,a879),a881),a333),f335(f335(f7(a881,f888(a881,a879),a879),f335(f335(f8(a881,f888(f888(a881,a879),a879),a881),f337(a881)),a106)),x100991))),f335(f335(f7(a881,a881,a879),f243(a881)),x100992)))),f335(f29(a881),f335(f249(a881),f335(f335(f18(a881,a879,a879),f335(f335(f8(a879,f888(a879,a879),a881),a333),f335(f335(f7(a881,f888(a881,a879),a879),f337(a881)),x100991))),f335(f335(f7(a881,a881,a879),f243(a881)),f335(a106,x100992))))))
% 59.73/59.66 [7600]~P97(x76001)+E(f335(f335(f76(x76001),x76002),f335(f97(x76001),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),x76002)
% 59.73/59.66 [7862]~P97(x78621)+E(f335(f335(f75(x78621),f335(f97(x78621),x78622)),f73(x78621)),f335(f97(x78621),f335(f335(f75(a1),x78622),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))
% 59.73/59.66 [8014]P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),x80142)))+E(f335(f335(f254(a1),x80141),f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),x80142),x80142)),a91))),f73(a1))
% 59.73/59.66 [9418]~P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),x94182)))+E(f335(f335(f254(a1),x94181),f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),x94182),x94182)),a91))),f335(f335(f81(a1,a1),f335(f335(f254(a1),x94181),f335(f97(a881),x94182))),f335(f335(f18(a1,a1,a1),f335(f335(f8(a1,f888(a1,a1),a1),f76(a1)),f335(f76(a1),x94181))),f5(a1))))
% 59.73/59.66 [9793]~P1(f335(f335(f242(a881),f800(x97932,x97931)),f335(x97931,f800(x97932,x97931))))+P1(f335(f56(a881),f335(f249(a881),f335(f335(f7(a881,a881,a879),f335(f335(f8(a881,f888(a881,a879),a881),f242(a881)),x97931)),x97932))))
% 59.73/59.66 [9941]~P1(f335(f335(f242(a881),f335(f97(a881),x99411)),f335(a106,x99412)))+P1(f335(f335(f81(a1,a879),f335(f97(a1),f335(f335(f75(a1),x99411),a91))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a338),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f7(a1,a881,a879),f335(f335(f8(a881,f888(a881,a879),a1),f242(a881)),a98)),x99412))))
% 59.73/59.66 [9942]~P1(f335(f335(f243(a881),f335(f97(a881),x99421)),f335(a106,x99422)))+P1(f335(f335(f81(a1,a879),f335(f97(a1),f335(f335(f75(a1),x99421),a91))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a338),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f7(a1,a881,a879),f335(f335(f8(a881,f888(a881,a879),a1),f243(a881)),a98)),x99422))))
% 59.73/59.66 [9992]P1(f335(f335(f242(a881),f335(f97(a881),x99921)),f335(a106,x99922)))+~P1(f335(f335(f81(a1,a879),f335(f97(a1),f335(f335(f75(a1),x99921),a91))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a338),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f7(a1,a881,a879),f335(f335(f8(a881,f888(a881,a879),a1),f242(a881)),a98)),x99922))))
% 59.73/59.66 [9993]P1(f335(f335(f243(a881),f335(f97(a881),x99931)),f335(a106,x99932)))+~P1(f335(f335(f81(a1,a879),f335(f97(a1),f335(f335(f75(a1),x99931),a91))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a338),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f7(a1,a881,a879),f335(f335(f8(a881,f888(a881,a879),a1),f243(a881)),a98)),x99932))))
% 59.73/59.66 [10023]~P1(f335(f335(f242(a881),f335(a106,x100232)),f335(f97(a881),x100231)))+P1(f335(f335(f81(a1,a879),f335(f97(a1),f335(f335(f75(a1),x100231),a91))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a338),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f8(a881,a879,a1),f335(f242(a881),x100232)),a98)))))
% 59.73/59.66 [10024]~P1(f335(f335(f243(a881),f335(a106,x100242)),f335(f97(a881),x100241)))+P1(f335(f335(f81(a1,a879),f335(f97(a1),f335(f335(f75(a1),x100241),a91))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a338),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f8(a881,a879,a1),f335(f243(a881),x100242)),a98)))))
% 59.73/59.66 [10067]P1(f335(f335(f242(a881),f335(a106,x100671)),f335(f97(a881),x100672)))+~P1(f335(f335(f81(a1,a879),f335(f97(a1),f335(f335(f75(a1),x100672),a91))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a338),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f8(a881,a879,a1),f335(f242(a881),x100671)),a98)))))
% 59.73/59.66 [10068]P1(f335(f335(f243(a881),f335(a106,x100681)),f335(f97(a881),x100682)))+~P1(f335(f335(f81(a1,a879),f335(f97(a1),f335(f335(f75(a1),x100682),a91))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a338),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f8(a881,a879,a1),f335(f243(a881),x100681)),a98)))))
% 59.73/59.66 [10137]~P1(f335(f335(f337(a881),f2(a881)),x101371))+E(f335(a106,f335(f29(a881),f335(f249(a881),f335(f335(f18(a881,a879,a879),f335(f335(f8(a879,f888(a879,a879),a881),a333),f335(f335(f7(a881,f888(a881,a879),a879),f335(f335(f8(a881,f888(f888(a881,a879),a879),a881),f337(a881)),a106)),x101371))),f335(f335(f7(a881,a881,a879),f243(a881)),x101372))))),f335(f29(a881),f335(f249(a881),f335(f335(f18(a881,a879,a879),f335(f335(f8(a879,f888(a879,a879),a881),a333),f335(f335(f7(a881,f888(a881,a879),a879),f337(a881)),x101371))),f335(f335(f7(a881,a881,a879),f243(a881)),f335(a106,x101372))))))
% 59.73/59.66 [8554]~P97(x85541)+E(f335(f335(f76(x85541),f335(f97(x85541),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),x85542),x85542)
% 59.73/59.66 [8613]~P97(x86131)+E(f335(f335(f75(x86131),f73(x86131)),f335(f97(x86131),x86132)),f335(f97(x86131),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),x86132)))
% 59.73/59.66 [8674]~P97(x86741)+E(f335(f335(f23(x86741),f335(f97(x86741),x86742)),f73(x86741)),f335(f97(x86741),f335(f335(f75(a1),x86742),f335(f74(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))
% 59.73/59.66 [8818]~P1(f335(f335(f243(a881),f335(f97(a881),a78)),x88182))+E(f335(f335(f23(a881),x88181),f335(f335(f23(a881),x88182),f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(f335(f23(a881),f335(a106,x88181)),x88182))
% 59.73/59.66 [9458]~P114(x94581)+E(f335(f335(f76(x94581),x94582),x94582),f335(f335(f254(x94581),x94582),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))
% 59.73/59.66 [9459]~P82(x94591)+E(f335(f335(f254(x94591),x94592),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(f335(f76(x94591),x94592),x94592))
% 59.73/59.66 [9461]~P97(x94611)+E(f335(f335(f76(x94611),x94612),f335(f97(x94611),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(f335(f75(x94611),x94612),x94612))
% 59.73/59.66 [9705]~P137(x97051)+E(f335(f335(f254(x97051),f335(f74(x97051),x97052)),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(f335(f254(x97051),x97052),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))
% 59.73/59.66 [9706]~P119(x97061)+E(f335(f335(f254(x97061),f335(f70(x97061),x97062)),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(f335(f254(x97061),x97062),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))
% 59.73/59.66 [9702]~P97(x97021)+E(f335(f335(f76(x97021),f335(f97(x97021),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x97022),f335(f335(f75(x97021),x97022),x97022))
% 59.73/59.66 [9835]~P119(x98351)+E(f335(f70(x98351),f335(f335(f254(x98351),x98352),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f335(f335(f254(x98351),x98352),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))
% 59.73/59.66 [9897]~P119(x98971)+P1(f335(f335(f242(x98971),f2(x98971)),f335(f335(f254(x98971),x98972),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))))
% 59.73/59.66 [10058]~E(f335(a106,x100582),f335(f97(a881),x100581))+P1(f335(f335(f81(a1,a879),f335(f97(a1),f335(f335(f75(a1),x100581),a91))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a338),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f7(a1,a881,a879),f335(f335(f8(a881,f888(a881,a879),a1),a332),a98)),x100582)))))
% 59.73/59.66 [10059]~E(f335(f97(a881),x100591),f335(a106,x100592))+P1(f335(f335(f81(a1,a879),f335(f97(a1),f335(f335(f75(a1),x100591),a91))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a338),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f7(a1,a881,a879),f335(f335(f8(a881,f888(a881,a879),a1),a332),a98)),x100592)))))
% 59.73/59.66 [10102]E(f335(a106,x101021),f335(f97(a881),x101022))+~P1(f335(f335(f81(a1,a879),f335(f97(a1),f335(f335(f75(a1),x101022),a91))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a338),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f7(a1,a881,a879),f335(f335(f8(a881,f888(a881,a879),a1),a332),a98)),x101021)))))
% 59.73/59.66 [10103]E(f335(f97(a881),x101031),f335(a106,x101032))+~P1(f335(f335(f81(a1,a879),f335(f97(a1),f335(f335(f75(a1),x101031),a91))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a338),f335(f335(f8(a879,a879,a1),a330),a193))),f335(f335(f7(a1,a881,a879),f335(f335(f8(a881,f888(a881,a879),a1),a332),a98)),x101032)))))
% 59.73/59.66 [9895]~P97(x98951)+E(f335(f335(f254(x98951),f335(f97(x98951),a91)),f335(f335(f76(a881),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x98952)),f73(x98951))
% 59.73/59.66 [9896]~P137(x98961)+E(f335(f335(f254(x98961),f335(f74(x98961),f73(x98961))),f335(f335(f76(a881),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x98962)),f73(x98961))
% 59.73/59.66 [9899]~P82(x98991)+E(f335(f335(f254(x98991),x98992),f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),a91))),f335(f335(f76(x98991),f335(f335(f76(x98991),x98992),x98992)),x98992))
% 59.73/59.66 [10082]~P1(f335(f335(f242(a1),f2(a1)),x100822))+E(f39(a1,f335(f335(f75(a1),f73(a1)),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x100821)),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x100822)),f335(f335(f75(a1),f73(a1)),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f39(a1,x100821,x100822))))
% 59.73/59.66 [10105]~P1(f335(f335(f242(a1),f2(a1)),x101052))+E(f335(f335(f30(a1),f335(f335(f75(a1),f73(a1)),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x101051))),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x101052)),f335(f335(f30(a1),x101051),x101052))
% 59.73/59.66 [10107]~P1(f335(f335(f242(a1),x101072),f2(a1)))+E(f335(f335(f30(a1),f335(f335(f75(a1),f73(a1)),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x101071))),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x101072)),f335(f335(f30(a1),f335(f335(f75(a1),x101071),f73(a1))),x101072))
% 59.73/59.66 [10108]~P1(f335(f335(f242(a1),x101082),f2(a1)))+E(f39(a1,f335(f335(f75(a1),f73(a1)),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x101081)),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x101082)),f335(f335(f23(a1),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f39(a1,f335(f335(f75(a1),x101081),f73(a1)),x101082))),f73(a1)))
% 59.73/59.66 [9983]~P97(x99831)+E(f335(f335(f254(x99831),f335(f97(x99831),a91)),f335(a106,f335(f335(f76(a881),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x99832))),f335(f97(x99831),a91))
% 59.73/59.66 [9985]~P137(x99851)+E(f335(f335(f254(x99851),f335(f74(x99851),f73(x99851))),f335(a106,f335(f335(f76(a881),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x99852))),f335(f74(x99851),f73(x99851)))
% 59.73/59.66 [8080]~E(x80802,x80803)+P33(x80801,x80801,a332,x80802,x80803)
% 59.73/59.66 [8627]E(x86271,x86272)+~P33(x86273,x86273,a332,x86271,x86272)
% 59.73/59.66 [4786]E(f163(x47861,x47862,x47863),f107(x47861))+~E(x47862,f2(a881))
% 59.73/59.66 [4787]E(f163(x47871,x47872,x47873),f107(x47871))+~E(x47872,f2(a881))
% 59.73/59.66 [4950]~E(f163(x49502,x49501,x49503),f107(x49502))+E(x49501,f2(a881))
% 59.73/59.66 [4951]~E(f163(x49512,x49511,x49513),f107(x49512))+E(x49511,f2(a881))
% 59.73/59.66 [5148]~P36(x51481,x51483)+P36(x51481,f329(x51481,x51482,x51483))
% 59.73/59.66 [5258]~P29(x52581,x52582,x52583)+P30(a1,x52581,f172(x52582,x52583))
% 59.73/59.66 [5329]P29(x53291,x53292,x53293)+~P30(a1,x53291,f172(x53292,x53293))
% 59.73/59.66 [5398]~P8(x53981,x53982,x53983)+P8(f882(x53981),f154(x53981,x53982),f151(x53981,x53983))
% 59.73/59.66 [5399]~P46(x53991,x53992,x53993)+P46(f882(x53991),f154(x53991,x53992),f151(x53991,x53993))
% 59.73/59.66 [5511]P53(x55111,x55112,x55113)+~E(f575(x55113,x55112,x55111),f576(x55113,x55112,x55111))
% 59.73/59.66 [5512]P52(x55121,x55122,x55123)+~E(f594(x55123,x55122,x55121),f595(x55123,x55122,x55121))
% 59.73/59.66 [4696]~E(x46961,f200(x46962))+~E(x46961,f335(f235(x46962),x46963))
% 59.73/59.66 [4697]~E(x46971,f200(x46972))+~E(x46971,f335(f235(x46972),x46973))
% 59.73/59.66 [4743]~E(f335(f162(x47432),x47431),x47433)+E(x47431,f335(f162(x47432),x47433))
% 59.73/59.66 [4744]~E(x47442,f335(f162(x47441),x47443))+E(f335(f162(x47441),x47442),x47443)
% 59.73/59.66 [4793]E(x47931,x47932)+~E(f335(f235(x47933),x47931),f335(f235(x47933),x47932))
% 59.73/59.66 [4794]E(x47941,x47942)+~E(f335(f162(x47943),x47941),f335(f162(x47943),x47942))
% 59.73/59.66 [4999]~P7(x49993,x49991)+P1(f335(f335(x49991,x49992),x49992))
% 59.73/59.66 [5000]~P48(x50003,x50001)+P1(f335(f335(x50001,x50002),x50002))
% 59.73/59.66 [5001]~P57(x50011,x50012)+P1(f335(f323(x50011,x50012),x50013))
% 59.73/59.66 [5002]~P57(x50021,x50022)+P1(f335(f323(x50021,x50022),x50023))
% 59.73/59.66 [5064]~P36(x50641,x50642)+P36(f882(x50641),f335(f136(x50641,x50642),x50643))
% 59.73/59.66 [5069]~P1(f335(x50692,x50693))+~E(f335(f249(x50691),x50692),f188(f888(x50691,a879)))
% 59.73/59.66 [5070]~P1(f335(x50702,x50703))+~E(f188(f888(x50701,a879)),f335(f249(x50701),x50702))
% 59.73/59.66 [5082]E(x50821,f2(a881))+E(f137(x50822,f163(x50822,x50821,x50823)),x50823)
% 59.73/59.66 [5097]~P1(f335(x50971,x50973))+P1(f335(x50971,f85(x50972,x50971)))
% 59.73/59.66 [5098]~P1(f335(x50981,x50983))+P1(f335(x50981,f85(x50982,x50981)))
% 59.73/59.66 [5099]~P1(f335(x50991,x50993))+P1(f335(x50991,f85(x50992,x50991)))
% 59.73/59.66 [5100]~P1(f335(x51001,x51003))+P1(f335(x51001,f85(x51002,x51001)))
% 59.73/59.66 [5112]E(x51121,f2(a881))+E(f335(f134(x51122),f163(x51122,x51121,x51123)),x51123)
% 59.73/59.66 [5224]~E(x52242,x52243)+P1(f335(f335(f337(x52241),x52242),f335(a332,x52243)))
% 59.73/59.66 [5237]~E(x52372,f2(a881))+E(f335(f166(x52371),f163(x52371,x52372,x52373)),f188(f888(x52371,a879)))
% 59.73/59.66 [5283]E(f335(f162(x52831),x52832),f335(f335(f144(x52831),x52833),f107(x52831)))+~E(x52832,f335(f335(f144(x52831),x52833),f107(x52831)))
% 59.73/59.66 [5284]~E(x52843,f335(f335(f144(x52841),x52842),f107(x52841)))+E(f335(f335(f144(x52841),x52842),f107(x52841)),f335(f162(x52841),x52843))
% 59.73/59.66 [5304]~E(x53043,f335(f16(f885(x53042),x53041),f200(x53042)))+E(f177(x53041,x53042,x53043),f188(f888(x53041,a879)))
% 59.73/59.66 [5325]~P32(x53251,x53252,x53253)+P32(x53251,x53252,f335(f162(x53251),x53253))
% 59.73/59.66 [5326]~P30(x53261,x53262,x53263)+P30(x53261,x53262,f335(f162(x53261),x53263))
% 59.73/59.66 [5330]E(f335(f29(x53301),f342(x53302,x53303,x53301)),x53302)+~E(f335(f29(x53301),x53303),f335(a106,x53302))
% 59.73/59.66 [5335]~P36(x53351,x53353)+P1(f335(f335(f337(x53351),x53352),f324(x53351,x53353)))
% 59.73/59.66 [5336]~P36(x53361,x53363)+P1(f335(f335(f337(x53361),x53362),f324(x53361,x53363)))
% 59.73/59.66 [5340]~E(f335(f162(x53402),x53401),f335(f335(f144(x53402),x53403),f107(x53402)))+E(x53401,f335(f335(f144(x53402),x53403),f107(x53402)))
% 59.73/59.66 [5341]~E(f335(f335(f144(x53412),x53413),f107(x53412)),f335(f162(x53412),x53411))+E(x53411,f335(f335(f144(x53412),x53413),f107(x53412)))
% 59.73/59.66 [5356]E(x53561,f335(f16(f885(x53562),x53563),f200(x53562)))+~E(f177(x53563,x53562,x53561),f188(f888(x53563,a879)))
% 59.73/59.66 [5362]E(f80(f887(a881,a881),f42(x53621,x53622)),x53623)+~P1(f335(f42(x53621,x53622),x53623))
% 59.73/59.66 [5370]~E(x53703,f335(f235(x53701),x53702))+P1(f335(f335(f337(x53701),x53702),f234(x53701,x53703)))
% 59.73/59.66 [5402]P32(x54021,x54022,x54023)+~P32(x54021,x54022,f335(f162(x54021),x54023))
% 59.73/59.66 [5403]P30(x54031,x54032,x54033)+~P30(x54031,x54032,f335(f162(x54031),x54033))
% 59.73/59.66 [5465]~E(x54652,f107(x54651))+P1(f335(f335(f337(f882(x54651)),x54652),f154(x54651,x54653)))
% 59.73/59.66 [5472]~P46(x54721,x54722,x54723)+P46(x54721,x54722,f335(f289(x54721,x54721),x54723))
% 59.73/59.66 [5473]~P53(x54731,x54732,x54733)+P53(x54731,x54732,f335(f289(x54731,x54731),x54733))
% 59.73/59.66 [5492]~P58(x54921)+E(f39(x54921,f39(x54921,x54922,x54923),x54923),f39(x54921,x54922,x54923))
% 59.73/59.66 [5589]E(x55891,x55892)+~P1(f335(f335(f337(x55893),x55891),f335(a332,x55892)))
% 59.73/59.66 [5635]~P143(x56351)+E(f190(x56351,x56352,f2(a881),x56353),x56353)
% 59.73/59.66 [5655]P46(x56551,x56552,x56553)+~P46(x56551,x56552,f335(f289(x56551,x56551),x56553))
% 59.73/59.66 [5656]P53(x56561,x56562,x56563)+~P53(x56561,x56562,f335(f289(x56561,x56561),x56563))
% 59.73/59.66 [5660]~P106(x56602)+E(f143(x56601,x56602,x56603,f107(x56601)),f107(x56601))
% 59.73/59.66 [5674]E(f164(x56741,x56742,f145(x56741,x56743)),f145(x56741,f164(x56741,x56742,x56743)))+~P1(f335(f130(x56741),x56743))
% 59.73/59.66 [5680]E(x56801,f335(f235(x56802),x56803))+~P1(f335(f335(f337(x56802),x56803),f234(x56802,x56801)))
% 59.73/59.66 [5775]E(f335(f129(x57751,x57752),x57753),f107(x57751))+P1(f335(x57752,f725(x57753,x57752,x57751)))
% 59.73/59.66 [5833]E(f63(x58331,x58332,x58333),x58332)+P1(f335(x58333,f763(x58332,x58331,x58333)))
% 59.73/59.66 [5921]~P1(f335(f130(x59211),x59212))+P1(f335(f130(x59211),f170(x59211,x59212,x59213)))
% 59.73/59.66 [5922]~P1(f335(f130(x59221),x59223))+P1(f335(f130(x59221),f164(x59221,x59222,x59223)))
% 59.73/59.66 [5923]~P1(f335(f130(x59231),x59233))+P1(f335(f130(x59231),f171(x59231,x59232,x59233)))
% 59.73/59.66 [5924]~P1(f335(f130(x59241),x59243))+P1(f335(f130(x59241),f133(x59241,x59242,x59243)))
% 59.73/59.66 [5925]~P145(x59251,x59253,x59252)+P1(f335(x59251,f39(a1,x59252,x59253)))
% 59.73/59.66 [5942]~P32(x59423,x59421,x59422)+P1(f335(x59421,f766(x59422,x59421,x59423)))
% 59.73/59.66 [5943]~P34(x59433,x59431,x59432)+P1(f335(x59431,f792(x59432,x59431,x59433)))
% 59.73/59.66 [5944]~P34(x59443,x59441,x59442)+P1(f335(x59441,f793(x59442,x59441,x59443)))
% 59.73/59.66 [5965]E(f335(f129(x59651,x59652),x59653),f171(x59651,x59652,x59653))+P1(f335(x59652,f741(x59653,x59652,x59651)))
% 59.73/59.66 [6006]~P1(f335(f130(x60061),x60063))+P1(f335(f130(f882(x60061)),f49(x60061,x60062,x60063)))
% 59.73/59.66 [6041]~P107(x60411)+E(f335(f335(f95(f888(x60411,a879)),f335(f250(x60411),x60412)),f305(x60411,x60412,x60413)),f188(f888(x60411,a879)))
% 59.73/59.66 [6042]~P107(x60421)+E(f335(f335(f95(f888(x60421,a879)),f335(f303(x60421),x60422)),f308(x60421,x60422,x60423)),f188(f888(x60421,a879)))
% 59.73/59.66 [6043]~P107(x60431)+E(f335(f335(f95(f888(x60431,a879)),f335(f303(x60431),x60432)),f307(x60431,x60432,x60433)),f188(f888(x60431,a879)))
% 59.73/59.66 [6268]E(f335(f129(x62681,x62682),x62683),x62683)+~P1(f335(x62682,f726(x62683,x62682,x62681)))
% 59.73/59.66 [6270]E(f335(f335(f312(x62701),f358(x62702,x62703,x62701)),f342(x62702,x62703,x62701)),x62703)+~E(f335(f29(x62701),x62703),f335(a106,x62702))
% 59.73/59.66 [6285]P145(x62851,x62852,x62853)+~P1(f335(x62851,f39(a1,x62853,x62852)))
% 59.73/59.66 [6332]P30(x63321,x63322,x63323)+~P1(f335(x63322,f786(x63323,x63322,x63321)))
% 59.73/59.66 [6333]P30(x63331,x63332,x63333)+~P1(f335(x63332,f790(x63332,x63333,x63331)))
% 59.73/59.66 [6334]P30(x63341,x63342,x63343)+~P1(f335(x63342,f791(x63343,x63342,x63341)))
% 59.73/59.66 [6335]P29(x63351,x63352,x63353)+~P1(f335(x63351,f811(x63353,x63352,x63351)))
% 59.73/59.66 [6337]E(f171(x63371,x63372,x63373),x63373)+~P1(f335(x63372,f742(x63373,x63372,x63371)))
% 59.73/59.66 [6419]~P1(f335(x64192,f554(x64193,x64192,x64191)))+P1(f335(f257(x64191,x64192),x64193))
% 59.73/59.66 [6420]~P1(f335(x64202,f744(x64203,x64202,x64201)))+P1(f335(f153(x64201,x64202),x64203))
% 59.73/59.66 [6671]~P1(f335(f323(x66711,x66712),f371(x66713,x66712,x66711)))+P1(f335(f323(x66711,x66712),x66713))
% 59.73/59.66 [6672]~P1(f335(f323(x66721,x66722),f380(x66723,x66722,x66721)))+P1(f335(f323(x66721,x66722),x66723))
% 59.73/59.66 [7286]~P58(x72861)+E(f335(f335(f75(x72861),f335(f335(f76(x72861),x72862),f335(f335(f30(x72861),x72863),x72862))),f39(x72861,x72863,x72862)),x72863)
% 59.73/59.66 [7316]P29(x73161,x73162,x73163)+P1(f335(f335(f337(a1),f811(x73163,x73162,x73161)),f305(a1,x73162,x73163)))
% 59.73/59.66 [7755]E(f335(f335(f264(x77551,x77551),f852(x77552,x77553,x77551)),f852(x77552,x77553,x77551)),x77553)+~P1(f335(f335(f337(f887(x77551,x77551)),x77553),f261(x77551,x77552)))
% 59.73/59.66 [7870]~P1(f335(f335(f337(x78701),f508(x78703,x78702,x78701)),f324(x78701,x78703)))+P1(f335(f335(f337(x78701),x78702),f324(x78701,x78703)))
% 59.73/59.66 [7871]~P1(f335(f335(f337(x78711),f578(x78713,x78712,x78711)),f324(x78711,x78713)))+P1(f335(f335(f337(x78711),x78712),f324(x78711,x78713)))
% 59.73/59.66 [7872]~P1(f335(f335(f337(x78721),f580(x78723,x78722,x78721)),f324(x78721,x78723)))+P1(f335(f335(f337(x78721),x78722),f324(x78721,x78723)))
% 59.73/59.66 [7969]P32(a1,x79691,f172(x79692,x79693))+P29(f335(f68(a879,a879,a1,a330),x79691),x79692,x79693)
% 59.73/59.66 [8060]~P58(x80601)+E(f335(f335(f75(x80601),f335(f335(f76(x80601),f335(f335(f30(x80601),x80602),x80603)),x80603)),f39(x80601,x80602,x80603)),x80602)
% 59.73/59.66 [8061]~P58(x80611)+E(f335(f335(f75(x80611),f335(f335(f76(x80611),f335(f335(f30(x80611),x80612),x80613)),x80613)),f39(x80611,x80612,x80613)),x80612)
% 59.73/59.66 [8106]~E(f335(f29(x81061),x81062),f335(a106,x81063))+~P1(f335(f335(f337(x81061),f358(x81063,x81062,x81061)),f342(x81063,x81062,x81061)))
% 59.73/59.66 [8546]~P32(a1,x85461,f172(x85462,x85463))+~P29(f335(f68(a879,a879,a1,a330),x85461),x85462,x85463)
% 59.73/59.66 [8726]P1(f335(f335(f242(f888(f887(x87261,x87261),a879)),f310(x87261,x87262)),f310(x87261,x87263)))+~P1(f335(f335(f242(f888(f887(x87261,x87261),a879)),x87262),f310(x87261,x87263)))
% 59.73/59.66 [8998]E(x89981,f107(x89982))+~P1(f335(f335(f337(f887(f882(x89982),f882(x89982))),f335(f335(f264(f882(x89982),f882(x89982)),x89981),f107(x89982))),f151(x89982,x89983)))
% 59.73/59.66 [9023]E(x90231,f107(x90232))+~P1(f335(f335(f337(f887(f882(x90232),f882(x90232))),f335(f335(f264(f882(x90232),f882(x90232)),f107(x90232)),x90231)),f151(x90232,x90233)))
% 59.73/59.66 [9152]E(f335(f335(f144(x91521),f712(x91522,x91523,x91521)),f713(x91522,x91523,x91521)),x91523)+~P1(f335(f335(f337(f887(f882(x91521),f882(x91521))),f335(f335(f264(f882(x91521),f882(x91521)),f107(x91521)),x91523)),f140(x91521,x91522)))
% 59.73/59.66 [9387]~P124(x93871)+~P1(f335(f335(f243(x93871),f335(f335(f75(x93871),f335(f335(f76(x93871),x93872),x93872)),f335(f335(f76(x93871),x93873),x93873))),f2(x93871)))
% 59.73/59.66 [9435]P1(f335(f56(x94351),x94352))+~P1(f335(f335(f337(f887(f888(x94351,a879),f888(x94351,a879))),f335(f335(f264(f888(x94351,a879),f888(x94351,a879)),x94353),x94352)),f309(x94351)))
% 59.73/59.66 [9730]~P44(x97301,x97302,x97303)+P1(f335(f335(f242(a1),f335(f335(f68(f887(a1,a1),a1,x97301,f263(a1,a1)),f215(x97301)),f232(x97301,x97302,f229(x97301,x97303)))),f2(a1)))
% 59.73/59.66 [9731]~P45(x97311,x97312,x97313)+P1(f335(f335(f243(a1),f335(f335(f68(f887(a1,a1),a1,x97311,f263(a1,a1)),f215(x97311)),f232(x97311,x97312,f229(x97311,x97313)))),f2(a1)))
% 59.73/59.66 [9864]P45(x98641,x98642,x98643)+~P1(f335(f335(f243(a1),f335(f335(f68(f887(a1,a1),a1,x98641,f263(a1,a1)),f215(x98641)),f232(x98641,x98642,f229(x98641,x98643)))),f2(a1)))
% 59.73/59.66 [9865]P44(x98651,x98652,x98653)+~P1(f335(f335(f242(a1),f335(f335(f68(f887(a1,a1),a1,x98651,f263(a1,a1)),f215(x98651)),f232(x98651,x98652,f229(x98651,x98653)))),f2(a1)))
% 59.73/59.66 [10183]~P119(x101831)+~P1(f335(f335(f243(x101831),f335(f335(f75(x101831),f335(f335(f254(x101831),x101832),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f335(f335(f254(x101831),x101833),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))),f2(x101831)))
% 59.73/59.66 [4772]~E(x47723,f107(x47721))+E(f335(f335(f127(x47721),x47722),x47723),x47722)
% 59.73/59.66 [4773]~E(x47732,f107(x47731))+E(f335(f335(f127(x47731),x47732),x47733),x47733)
% 59.73/59.66 [4774]~E(x47743,f107(x47741))+E(f335(f335(f127(x47741),x47742),x47743),x47742)
% 59.73/59.66 [4775]~E(x47752,f107(x47751))+E(f335(f335(f127(x47751),x47752),x47753),x47753)
% 59.73/59.66 [4782]~E(x47822,f2(a881))+E(f335(f335(f169(x47821),x47822),x47823),f107(x47821))
% 59.73/59.66 [4788]~E(x47883,f107(x47881))+E(f335(f335(f169(x47881),x47882),x47883),f107(x47881))
% 59.73/59.66 [4828]~E(x48281,x48283)+E(x48281,f335(f335(f127(x48282),f107(x48282)),x48283))
% 59.73/59.66 [4913]~P3(x49132)+E(f335(f188(f888(x49131,x49132)),x49133),f188(x49132))
% 59.73/59.66 [4914]~P3(x49142)+E(f335(f188(f888(x49141,x49142)),x49143),f188(x49142))
% 59.73/59.66 [4915]~P110(x49152)+E(f335(f252(f888(x49151,x49152)),x49153),f252(x49152))
% 59.73/59.66 [4931]E(x49311,f107(x49312))+~E(f335(f335(f127(x49312),x49311),x49313),x49313)
% 59.73/59.66 [4932]E(x49321,f107(x49322))+~E(f335(f335(f127(x49322),x49323),x49321),x49323)
% 59.73/59.66 [4933]E(x49331,f107(x49332))+~E(f335(f335(f127(x49332),x49333),x49331),x49333)
% 59.73/59.66 [4934]E(x49341,f107(x49342))+~E(f335(f335(f127(x49342),x49341),x49343),x49343)
% 59.73/59.66 [4940]E(x49401,f107(x49402))+~E(f335(f335(f127(x49402),x49403),x49401),f107(x49402))
% 59.73/59.66 [4941]E(x49411,f107(x49412))+~E(f335(f335(f127(x49412),x49411),x49413),f107(x49412))
% 59.73/59.66 [4942]E(x49421,f107(x49422))+~E(f335(f335(f127(x49422),x49423),x49421),f107(x49422))
% 59.73/59.66 [4943]E(x49431,f107(x49432))+~E(f335(f335(f127(x49432),x49431),x49433),f107(x49432))
% 59.73/59.66 [4968]~E(x49682,f2(a881))+E(f335(f335(f76(a881),x49681),x49682),f335(f335(f76(a881),x49683),x49682))
% 59.73/59.66 [4969]~E(x49691,f2(a881))+E(f335(f335(f76(a881),x49691),x49692),f335(f335(f76(a881),x49691),x49693))
% 59.73/59.66 [4970]~E(x49701,f2(a881))+E(f335(f335(f76(a881),x49701),x49702),f335(f335(f76(a881),x49701),x49703))
% 59.73/59.66 [5024]~P60(x50241)+E(f335(f335(f104(x50241),x50242),x50243),f335(f335(f104(x50241),x50243),x50242))
% 59.73/59.66 [5025]~P60(x50251)+E(f335(f335(f104(x50251),x50252),x50253),f335(f335(f104(x50251),x50253),x50252))
% 59.73/59.66 [5026]~P61(x50261)+E(f335(f335(f104(x50261),x50262),x50263),f335(f335(f104(x50261),x50263),x50262))
% 59.73/59.66 [5027]~P61(x50271)+E(f335(f335(f95(x50271),x50272),x50273),f335(f335(f95(x50271),x50273),x50272))
% 59.73/59.66 [5028]~P102(x50281)+E(f335(f335(f95(x50281),x50282),x50283),f335(f335(f95(x50281),x50283),x50282))
% 59.73/59.66 [5029]~P102(x50291)+E(f335(f335(f95(x50291),x50292),x50293),f335(f335(f95(x50291),x50293),x50292))
% 59.73/59.66 [5030]~P114(x50301)+E(f335(f335(f76(x50301),x50302),x50303),f335(f335(f76(x50301),x50303),x50302))
% 59.73/59.66 [5031]~P114(x50311)+E(f335(f335(f75(x50311),x50312),x50313),f335(f335(f75(x50311),x50313),x50312))
% 59.73/59.66 [5032]~P106(x50321)+E(f335(f335(f240(x50321),x50322),x50323),f335(f335(f240(x50321),x50323),x50322))
% 59.73/59.66 [5033]~P106(x50331)+E(f335(f335(f240(x50331),x50332),x50333),f335(f335(f240(x50331),x50333),x50332))
% 59.73/59.66 [5034]~P106(x50341)+E(f335(f335(f241(x50341),x50342),x50343),f335(f335(f241(x50341),x50343),x50342))
% 59.73/59.66 [5035]~P106(x50351)+E(f335(f335(f241(x50351),x50352),x50353),f335(f335(f241(x50351),x50353),x50352))
% 59.73/59.66 [5095]E(f39(a881,x50951,x50952),f2(a881))+~E(x50951,f335(f335(f76(a881),x50952),x50953))
% 59.73/59.66 [5096]E(f39(a1,x50961,x50962),f2(a1))+~E(x50961,f335(f335(f76(a1),x50962),x50963))
% 59.73/59.66 [5160]E(x51601,x51602)+~E(f335(f335(f75(a881),x51603),x51601),f335(f335(f75(a881),x51603),x51602))
% 59.73/59.66 [5161]E(x51611,x51612)+~E(f335(f335(f75(a881),x51611),x51613),f335(f335(f75(a881),x51612),x51613))
% 59.73/59.66 [5174]~P84(x51741)+E(f335(f335(f95(x51741),x51742),f335(f74(x51741),x51743)),f335(f335(f23(x51741),x51742),x51743))
% 59.73/59.66 [5175]~P64(x51751)+E(f335(f335(f75(x51751),x51752),f335(f74(x51751),x51753)),f335(f335(f23(x51751),x51752),x51753))
% 59.73/59.66 [5176]~P72(x51761)+E(f335(f335(f75(x51761),x51762),f335(f74(x51761),x51763)),f335(f335(f23(x51761),x51762),x51763))
% 59.73/59.66 [5177]~P112(x51771)+E(f335(f335(f75(x51771),x51772),f335(f74(x51771),x51773)),f335(f335(f23(x51771),x51772),x51773))
% 59.73/59.66 [5178]~P72(x51781)+E(f335(f335(f23(x51781),x51782),f335(f74(x51781),x51783)),f335(f335(f75(x51781),x51782),x51783))
% 59.73/59.66 [5216]~P1(f335(x52163,x52162))+P1(f335(f335(f337(x52161),x52162),x52163))
% 59.73/59.66 [5217]~P73(x52172)+E(f335(f335(f9(x52171,x52172),x52173),f188(f888(x52171,a879))),f73(x52172))
% 59.73/59.66 [5218]~P73(x52182)+E(f335(f335(f9(x52181,x52182),x52183),f188(f888(x52181,a879))),f73(x52182))
% 59.73/59.66 [5219]~P77(x52192)+E(f335(f335(f6(x52191,x52192),x52193),f188(f888(x52191,a879))),f2(x52192))
% 59.73/59.66 [5220]~P77(x52202)+E(f335(f335(f6(x52201,x52202),x52203),f188(f888(x52201,a879))),f2(x52202))
% 59.73/59.66 [5271]~E(x52712,f335(f335(f75(a881),x52711),x52713))+P1(f335(f335(f242(a881),x52711),x52712))
% 59.73/59.66 [5274]~E(x52742,f188(f888(x52741,a879)))+E(f335(f335(f55(x52741),x52742),x52743),f188(f888(f888(x52741,a879),a879)))
% 59.73/59.66 [5275]~E(x52752,f188(f888(x52751,a879)))+E(f188(f888(f888(x52751,a879),a879)),f335(f335(f55(x52751),x52752),x52753))
% 59.73/59.66 [5345]~E(f335(f260(x53452,x53453),x53451),f188(f888(x53453,a879)))+E(x53451,f188(f888(f887(x53452,x53453),a879)))
% 59.73/59.66 [5346]~E(f335(f262(x53462,x53463),x53461),f188(f888(x53462,a879)))+E(x53461,f188(f888(f887(x53462,x53463),a879)))
% 59.73/59.66 [5376]E(f335(f260(x53761,x53762),x53763),f188(f888(x53762,a879)))+~E(x53763,f188(f888(f887(x53761,x53762),a879)))
% 59.73/59.66 [5377]E(f335(f262(x53771,x53772),x53773),f188(f888(x53771,a879)))+~E(x53773,f188(f888(f887(x53771,x53772),a879)))
% 59.73/59.66 [5380]E(f280(x53801,x53802,x53803),f335(f335(f23(a93),x53802),x53803))+P1(f335(f335(f243(a93),x53802),x53803))
% 59.73/59.66 [5396]P1(f335(x53961,x53962))+~P1(f335(f335(f337(x53963),x53962),x53961))
% 59.73/59.66 [5435]E(x54351,x54352)+~E(f335(f74(f888(x54353,a879)),x54351),f335(f74(f888(x54353,a879)),x54352))
% 59.73/59.66 [5440]E(f316(x54401,x54402,x54403),f200(f882(a331)))+~P1(f335(f335(f243(a1),x54402),x54403))
% 59.73/59.66 [5443]~E(x54431,f188(f888(x54432,a879)))+~P1(f335(f335(f337(x54432),x54433),x54431))
% 59.73/59.66 [5444]~E(x54441,f188(f888(x54442,a879)))+~P1(f335(f335(f337(x54442),x54443),x54441))
% 59.73/59.66 [5445]~E(x54451,f188(f888(x54452,a879)))+~P1(f335(f335(f337(x54452),x54453),x54451))
% 59.73/59.66 [5474]~E(x54742,f335(f335(f75(a1),x54741),f335(f94(a1),x54743)))+P1(f335(f335(f242(a1),x54741),x54742))
% 59.73/59.66 [5490]E(f335(f335(f312(x54901),x54902),x54903),x54903)+~P1(f335(f335(f337(x54901),x54902),x54903))
% 59.73/59.66 [5501]E(x55011,f188(f888(x55012,a879)))+~E(f335(f335(f55(x55012),x55011),x55013),f188(f888(f888(x55012,a879),a879)))
% 59.73/59.66 [5502]E(x55021,f188(f888(x55022,a879)))+~E(f188(f888(f888(x55022,a879),a879)),f335(f335(f55(x55022),x55021),x55023))
% 59.73/59.66 [5508]~P118(x55081)+E(f335(f335(f76(x55081),f335(f74(x55081),x55082)),f335(f74(x55081),x55083)),f335(f335(f76(x55081),x55082),x55083))
% 59.73/59.66 [5510]~P66(x55101)+E(f335(f335(f292(x55101),f335(f74(x55101),x55102)),f335(f74(x55101),x55103)),f335(f335(f292(x55101),x55102),x55103))
% 59.73/59.66 [5541]~P1(f335(x55413,x55412))+P1(f335(f335(f337(x55411),x55412),f335(f249(x55411),x55413)))
% 59.73/59.66 [5542]~P1(f335(x55423,x55422))+P1(f335(f335(f337(x55421),x55422),f335(f249(x55421),x55423)))
% 59.73/59.66 [5562]E(x55621,f2(a881))+E(f335(f166(x55622),f163(x55622,x55621,x55623)),f335(f335(f312(x55622),x55623),f188(f888(x55622,a879))))
% 59.73/59.66 [5563]E(x55631,f2(a881))+E(f335(f166(x55632),f163(x55632,x55631,x55633)),f335(f335(f312(x55632),x55633),f188(f888(x55632,a879))))
% 59.73/59.66 [5582]E(f164(x55821,x55822,x55823),x55823)+P1(f335(f335(f337(x55821),x55822),f335(f166(x55821),x55823)))
% 59.73/59.66 [5664]~P1(f335(f130(x56641),x56643))+P1(f335(f130(x56641),f335(f129(x56641,x56642),x56643)))
% 59.73/59.66 [5710]~P58(x57101)+E(f335(f335(f30(x57101),f39(x57101,x57102,x57103)),x57103),f2(x57101))
% 59.73/59.66 [5729]E(f170(x57291,f335(f335(f144(x57291),x57292),f107(x57291)),x57293),f107(x57291))+P1(f335(f335(f337(a881),f2(a881)),x57293))
% 59.73/59.66 [5735]E(x57351,f2(a881))+E(f335(f165(x57352),f163(x57352,x57351,x57353)),f163(x57352,f335(f335(f23(a881),x57351),f73(a881)),x57353))
% 59.73/59.66 [5784]E(f335(f335(f144(x57841),x57842),x57843),f133(x57841,x57842,x57843))+P1(f335(f335(f337(x57841),x57842),f335(f166(x57841),x57843)))
% 59.73/59.66 [5785]E(f335(f335(f144(x57851),x57852),x57853),f133(x57851,x57852,x57853))+P1(f335(f335(f337(x57851),x57852),f335(f166(x57851),x57853)))
% 59.73/59.66 [5794]E(x57941,x57942)+~E(f335(f335(f76(a881),f335(a106,x57943)),x57941),f335(f335(f76(a881),f335(a106,x57943)),x57942))
% 59.73/59.66 [5795]~E(x57952,f335(f335(f75(a1),x57951),f335(f94(a1),f335(a106,x57953))))+P1(f335(f335(f243(a1),x57951),x57952))
% 59.73/59.66 [5903]~E(x59033,f107(x59031))+E(f335(f335(f335(f183(f882(x59031),f882(x59031)),x59032),f161(x59031)),x59033),f107(x59031))
% 59.73/59.66 [5905]P1(f335(x59051,x59052))+~P1(f335(f335(f337(x59053),x59052),f335(f249(x59053),x59051)))
% 59.73/59.66 [5906]P1(f335(x59061,x59062))+~P1(f335(f335(f337(x59063),x59062),f335(f249(x59063),x59061)))
% 59.73/59.66 [5907]P1(f335(x59071,x59072))+~P1(f335(f335(f337(x59073),x59072),f335(f249(x59073),x59071)))
% 59.73/59.66 [5937]E(x59371,x59372)+~E(f335(f335(f312(x59373),x59371),f188(f888(x59373,a879))),f335(f335(f312(x59373),x59372),f188(f888(x59373,a879))))
% 59.73/59.66 [5949]~P107(x59491)+E(f335(f335(f95(f888(x59491,a879)),f335(f250(x59491),x59492)),f335(f304(x59491,x59492),x59493)),f188(f888(x59491,a879)))
% 59.73/59.66 [5990]E(f133(x59901,x59902,x59903),x59903)+~P1(f335(f335(f337(x59901),x59902),f335(f166(x59901),x59903)))
% 59.73/59.66 [5991]E(f133(x59911,x59912,x59913),x59913)+~P1(f335(f335(f337(x59911),x59912),f335(f166(x59911),x59913)))
% 59.73/59.66 [6014]~P80(x60141)+E(f335(f313(x60141,x60141,f74(x60141)),f335(f304(x60141,x60142),x60143)),f307(x60141,f335(f74(x60141),x60143),f335(f74(x60141),x60142)))
% 59.73/59.66 [6019]P1(f335(f335(f337(x60191),x60192),f335(f166(x60191),x60193)))+~P1(f335(f335(f166(x60191),x60193),x60192))
% 59.73/59.66 [6020]P1(f335(f335(f337(x60201),x60202),f335(f166(x60201),x60203)))+~P1(f335(f335(f166(x60201),x60203),x60202))
% 59.73/59.66 [6025]E(f335(f189(f882(x60251)),f164(x60251,x60252,x60253)),f335(f189(f882(x60251)),x60253))+P1(f335(f335(f337(x60251),x60252),f335(f166(x60251),x60253)))
% 59.73/59.66 [6044]P1(f335(x60441,x60442))+~P1(f335(f335(f337(x60443),x60442),f188(f888(x60443,a879))))
% 59.73/59.66 [6074]~P107(x60741)+E(f335(f335(f95(f888(x60741,a879)),f335(f304(x60741,x60742),x60743)),f335(f251(x60741),x60743)),f188(f888(x60741,a879)))
% 59.73/59.66 [6097]~P80(x60971)+E(f335(f313(x60971,x60971,f74(x60971)),f308(x60971,x60972,x60973)),f308(x60971,f335(f74(x60971),x60973),f335(f74(x60971),x60972)))
% 59.73/59.66 [6098]~P80(x60981)+E(f335(f313(x60981,x60981,f74(x60981)),f305(x60981,x60982,x60983)),f305(x60981,f335(f74(x60981),x60983),f335(f74(x60981),x60982)))
% 59.73/59.66 [6151]~P1(f335(f335(f337(x61511),x61513),f335(f166(x61511),x61512)))+P1(f335(f335(f166(x61511),x61512),x61513))
% 59.73/59.66 [6152]~P1(f335(f335(f337(x61521),x61523),f335(f166(x61521),x61522)))+P1(f335(f335(f166(x61521),x61522),x61523))
% 59.73/59.66 [6156]E(f170(x61561,f335(f335(f144(x61561),x61562),f107(x61561)),x61563),f335(f335(f144(x61561),x61562),f107(x61561)))+~P1(f335(f335(f337(a881),f2(a881)),x61563))
% 59.73/59.66 [6163]~P80(x61631)+E(f335(f313(x61631,x61631,f74(x61631)),f307(x61631,x61632,x61633)),f335(f304(x61631,f335(f74(x61631),x61633)),f335(f74(x61631),x61632)))
% 59.73/59.66 [6183]~P59(x61831)+E(f39(x61831,f335(f74(x61831),f39(x61831,x61832,x61833)),x61833),f39(x61831,f335(f74(x61831),x61832),x61833))
% 59.73/59.66 [6283]~P1(f335(f56(f887(x62832,x62831)),x62833))+P1(f335(f56(x62831),f335(f260(x62832,x62831),x62833)))
% 59.73/59.66 [6284]~P1(f335(f56(f887(x62841,x62842)),x62843))+P1(f335(f56(x62841),f335(f262(x62841,x62842),x62843)))
% 59.73/59.66 [6289]~P107(x62891)+E(f335(f335(f95(f888(x62891,a879)),f308(x62891,x62892,x62893)),f335(f251(x62891),x62893)),f188(f888(x62891,a879)))
% 59.73/59.66 [6290]~P107(x62901)+E(f335(f335(f95(f888(x62901,a879)),f307(x62901,x62902,x62903)),f335(f306(x62901),x62903)),f188(f888(x62901,a879)))
% 59.73/59.66 [6291]~P107(x62911)+E(f335(f335(f95(f888(x62911,a879)),f305(x62911,x62912,x62913)),f335(f306(x62911),x62913)),f188(f888(x62911,a879)))
% 59.73/59.66 [6359]E(f335(f335(f158(x63591),x63592),f689(x63592,x63593,x63591)),x63593)+~P1(f335(f335(f337(x63591),x63593),f335(f166(x63591),x63592)))
% 59.73/59.66 [6501]E(x65011,f107(x65012))+~E(f335(f335(f335(f183(f882(x65012),f882(x65012)),x65013),f161(x65012)),x65011),f107(x65012))
% 59.73/59.66 [6609]~P1(f335(f56(f887(x66092,x66091)),x66093))+P1(f335(f56(f887(x66091,x66092)),f335(f289(x66092,x66091),x66093)))
% 59.73/59.66 [6763]P53(x67631,x67632,x67633)+P1(f335(f335(f337(x67631),f576(x67633,x67632,x67631)),x67632))
% 59.73/59.66 [6764]P53(x67641,x67642,x67643)+P1(f335(f335(f337(x67641),f575(x67643,x67642,x67641)),x67642))
% 59.73/59.66 [6776]P1(f335(f323(x67761,x67762),x67763))+P1(f335(f335(x67762,f371(x67763,x67762,x67761)),x67763))
% 59.73/59.66 [6777]P1(f335(f323(x67771,x67772),x67773))+P1(f335(f335(x67772,f380(x67773,x67772,x67771)),x67773))
% 59.73/59.66 [6808]E(f335(f189(f882(x68081)),f164(x68081,x68082,x68083)),f335(f335(f23(a881),f335(f189(f882(x68081)),x68083)),f73(a881)))+~P1(f335(f335(f337(x68081),x68082),f335(f166(x68081),x68083)))
% 59.73/59.66 [6848]P1(f335(f257(x68481,x68482),x68483))+P1(f335(f335(f337(x68481),f554(x68483,x68482,x68481)),x68483))
% 59.73/59.66 [6861]~P1(f335(f56(f887(x68612,x68611)),f335(f289(x68611,x68612),x68613)))+P1(f335(f56(f887(x68611,x68612)),x68613))
% 59.73/59.66 [6917]~P1(f335(f335(f337(x69171),x69172),f335(f166(x69171),f108(x69171,x69173))))+P1(f335(f335(f337(x69171),x69172),f335(f166(x69171),x69173)))
% 59.73/59.66 [6949]E(f335(f129(x69491,x69492),x69493),x69493)+P1(f335(f335(f337(x69491),f726(x69493,x69492,x69491)),f335(f166(x69491),x69493)))
% 59.73/59.66 [6964]E(f335(f129(x69641,x69642),x69643),f107(x69641))+P1(f335(f335(f337(x69641),f725(x69643,x69642,x69641)),f335(f166(x69641),x69643)))
% 59.73/59.66 [6987]P30(x69871,x69872,x69873)+P1(f335(f335(f337(x69871),f786(x69873,x69872,x69871)),f335(f166(x69871),x69873)))
% 59.73/59.66 [6988]P30(x69881,x69882,x69883)+P1(f335(f335(f337(x69881),f791(x69883,x69882,x69881)),f335(f166(x69881),x69883)))
% 59.73/59.66 [6989]P30(x69891,x69892,x69893)+P1(f335(f335(f337(x69891),f790(x69892,x69893,x69891)),f335(f166(x69891),x69893)))
% 59.73/59.66 [6992]E(f171(x69921,x69922,x69923),x69923)+P1(f335(f335(f337(x69921),f742(x69923,x69922,x69921)),f335(f166(x69921),x69923)))
% 59.73/59.66 [7070]P1(f335(f153(x70701,x70702),x70703))+P1(f335(f335(f337(x70701),f744(x70703,x70702,x70701)),f335(f166(x70701),x70703)))
% 59.73/59.66 [7079]~P32(x70791,x70793,x70792)+P1(f335(f335(f337(x70791),f766(x70792,x70793,x70791)),f335(f166(x70791),x70792)))
% 59.73/59.66 [7080]~P34(x70801,x70803,x70802)+P1(f335(f335(f337(x70801),f792(x70802,x70803,x70801)),f335(f166(x70801),x70802)))
% 59.73/59.66 [7081]~P34(x70811,x70813,x70812)+P1(f335(f335(f337(x70811),f793(x70812,x70813,x70811)),f335(f166(x70811),x70812)))
% 59.73/59.66 [7116]P1(f335(f335(f337(x71161),x71162),f654(x71163,x71162,x71161)))+~P1(f335(f335(f337(x71161),x71162),f31(f888(x71161,a879),x71163)))
% 59.73/59.66 [7117]~P77(x71171)+E(f335(f335(f75(x71171),f335(f335(f6(a881,x71171),x71172),f335(f250(a881),x71173))),f335(x71172,x71173)),f335(f335(f6(a881,x71171),x71172),f335(f250(a881),f335(a106,x71173))))
% 59.73/59.66 [7207]~P32(x72072,x72071,x72073)+P1(f335(x72071,f335(f335(f158(x72072),x72073),f778(x72073,x72071,x72072))))
% 59.73/59.66 [7219]~P1(f335(f335(f337(x72191),x72192),f644(x72192,x72193,x72191)))+P1(f335(f335(f337(x72191),x72192),f32(f888(x72191,a879),x72193)))
% 59.73/59.66 [7249]~P77(x72491)+E(f335(f335(f75(x72491),f335(f335(f6(a881,x72491),x72492),f335(f303(a881),x72493))),f335(x72492,f335(a106,x72493))),f335(f335(f6(a881,x72491),x72492),f335(f303(a881),f335(a106,x72493))))
% 59.73/59.66 [7255]P1(f335(x72551,f870(x72552,x72553,x72551)))+P1(f335(f335(f242(f888(x72552,a879)),f335(f249(x72552),x72551)),f335(f249(x72552),x72553)))
% 59.73/59.66 [7388]P1(f335(f335(f337(f882(x73881)),x73882),f154(x73881,x73883)))+P1(f335(f335(f337(x73881),f691(x73883,x73882,x73881)),f335(f166(x73881),x73882)))
% 59.73/59.66 [7405]~P1(f335(f335(f337(f882(x74051)),x74052),f154(x74051,f324(x74051,x74053))))+P1(f335(f335(f337(f882(x74051)),x74052),f324(f882(x74051),f150(x74051,x74053))))
% 59.73/59.66 [7429]~P1(f335(f335(f337(f882(x74291)),x74292),f324(f882(x74291),f150(x74291,x74293))))+P1(f335(f335(f337(f882(x74291)),x74292),f154(x74291,f324(x74291,x74293))))
% 59.73/59.66 [7465]E(f335(f335(f335(f183(f882(x74651),f882(x74651)),x74652),f161(x74651)),x74653),x74653)+~P1(f335(f335(f242(a881),f335(f189(f882(x74651)),x74653)),f73(a881)))
% 59.73/59.66 [7500]E(f335(f335(f127(x75001),f779(x75002,x75003,x75001)),f335(f335(f144(x75001),x75003),f788(x75002,x75003,x75001))),x75002)+~P1(f335(f335(f337(x75001),x75003),f335(f166(x75001),x75002)))
% 59.73/59.66 [7501]E(f335(f335(f127(x75011),f780(x75012,x75013,x75011)),f335(f335(f144(x75011),x75013),f781(x75012,x75013,x75011))),x75012)+~P1(f335(f335(f337(x75011),x75013),f335(f166(x75011),x75012)))
% 59.73/59.66 [7502]E(f335(f335(f127(x75021),f782(x75022,x75023,x75021)),f335(f335(f144(x75021),x75023),f783(x75022,x75023,x75021))),x75022)+~P1(f335(f335(f337(x75021),x75023),f335(f166(x75021),x75022)))
% 59.73/59.66 [7523]~P26(x75231,x75232,x75233,f252(f888(x75231,a879)))+P26(f882(x75231),f882(x75232),f335(f147(x75231,x75232),x75233),f252(f888(f882(x75231),a879)))
% 59.73/59.66 [7524]~P26(x75241,x75242,x75243,f252(f888(x75241,a879)))+P26(f882(x75241),f882(x75242),f335(f147(x75241,x75242),x75243),f252(f888(f882(x75241),a879)))
% 59.73/59.66 [7562]~P1(f335(x75623,f870(x75621,x75623,x75622)))+P1(f335(f335(f242(f888(x75621,a879)),f335(f249(x75621),x75622)),f335(f249(x75621),x75623)))
% 59.73/59.66 [7675]E(x76751,f335(f335(f75(a881),f335(f335(f76(a881),f335(f263(a881,a881),x76752)),x76753)),f335(f267(a881,a881),x76752)))+~P1(f335(f42(x76751,x76753),x76752))
% 59.73/59.66 [7682]P26(x76821,x76822,x76823,f252(f888(x76821,a879)))+~P26(f882(x76821),f882(x76822),f335(f147(x76821,x76822),x76823),f252(f888(f882(x76821),a879)))
% 59.73/59.66 [7683]P26(x76831,x76832,x76833,f252(f888(x76831,a879)))+~P26(f882(x76831),f882(x76832),f335(f147(x76831,x76832),x76833),f252(f888(f882(x76831),a879)))
% 59.73/59.66 [7727]P1(f335(f335(f337(f888(x77271,a879)),f644(x77272,x77273,x77271)),x77273))+P1(f335(f335(f337(x77271),x77272),f32(f888(x77271,a879),x77273)))
% 59.73/59.66 [7819]P1(f335(f335(f337(f882(x78191)),x78192),f154(x78191,x78193)))+~P1(f335(f335(f337(x78191),f691(x78193,x78192,x78191)),x78193))
% 59.73/59.66 [7921]P30(x79211,x79212,x79213)+~P1(f335(x79212,f335(f335(f158(x79211),x79213),f787(x79213,x79212,x79211))))
% 59.73/59.66 [7945]E(x79451,x79452)+~E(f335(f335(f7(x79453,f888(x79453,a879),a879),f337(x79453)),x79451),f335(f335(f7(x79453,f888(x79453,a879),a879),f337(x79453)),x79452))
% 59.73/59.66 [7953]~P1(f335(f335(f337(f887(x79531,x79531)),x79533),f261(x79531,x79532)))+P1(f335(f335(f337(x79531),f852(x79532,x79533,x79531)),x79532))
% 59.73/59.66 [7955]~P1(f335(f335(f337(x79551),x79553),f31(f888(x79551,a879),x79552)))+P1(f335(f335(f337(f888(x79551,a879)),f654(x79552,x79553,x79551)),x79552))
% 59.73/59.66 [8081]P26(x80811,x80812,f87(x80812,x80811,f252(f888(x80812,a879)),x80813),f252(f888(x80811,a879)))+~E(f335(f313(x80812,x80811,x80813),f252(f888(x80812,a879))),f252(f888(x80811,a879)))
% 59.73/59.66 [8132]~P1(f335(f335(f337(x81321),x81322),f335(f166(x81321),f780(x81323,x81322,x81321))))+~P1(f335(f335(f337(x81321),x81322),f335(f166(x81321),x81323)))
% 59.73/59.66 [8133]~P1(f335(f335(f337(x81331),x81332),f335(f166(x81331),f783(x81333,x81332,x81331))))+~P1(f335(f335(f337(x81331),x81332),f335(f166(x81331),x81333)))
% 59.73/59.66 [8222]E(f335(f237(f885(f882(a331)),f882(a331),f316(x82221,x82222,f335(f335(f75(a1),x82223),f73(a1))),f235(f882(a331))),f335(x82221,x82223)),f316(x82221,x82222,x82223))+P1(f335(f335(f243(a1),x82222),x82223))
% 59.73/59.66 [8324]E(x83241,f107(x83242))+P1(f335(f335(f337(x83242),f335(f263(x83242,f887(a93,a93)),f335(f281(x83242,x83241),x83243))),f335(f166(x83242),x83241)))
% 59.73/59.66 [8424]~P71(x84241)+E(f335(f135(x84241,x84241,f335(f7(x84241,x84241,x84241),f75(x84241)),x84242),f335(f162(x84241),x84243)),f335(f135(x84241,x84241,f75(x84241),x84242),x84243))
% 59.73/59.66 [8614]~P26(x86142,x86141,x86143,f252(f888(x86142,a879)))+E(f335(f313(x86141,x86142,f87(x86142,x86141,f252(f888(x86142,a879)),x86143)),f252(f888(x86141,a879))),f252(f888(x86142,a879)))
% 59.73/59.66 [8913]~P106(x89131)+E(f335(f166(x89131),f142(x89131,x89131,f5(x89131),x89132,x89133)),f335(f335(f312(x89131),x89132),f335(f166(x89131),x89133)))
% 59.73/59.66 [8924]~E(f335(x89243,f335(f87(x89241,x89242,f252(f888(x89241,a879)),x89243),f660(x89243,x89242,x89241))),f660(x89243,x89242,x89241))+E(f335(f313(x89241,x89242,x89243),f252(f888(x89241,a879))),f252(f888(x89242,a879)))
% 59.73/59.66 [8926]P1(f335(f335(f243(a881),f2(a881)),f601(x89261,x89262,x89263)))+~P1(f335(f335(f337(f887(x89263,x89263)),x89262),f335(f335(f291(x89263,x89263,x89263),x89261),f310(x89263,x89261))))
% 59.73/59.66 [9211]~P55(x92111,x92112)+~P1(f335(f335(f337(f887(x92111,x92111)),f335(f335(f264(x92111,x92111),x92113),x92113)),f335(f335(f291(x92111,x92111,x92111),x92112),f310(x92111,x92112))))
% 59.73/59.66 [9340]~E(f335(f335(f95(f888(f887(x93401,x93401),a879)),f335(f289(x93401,x93401),x93402)),f310(x93401,x93402)),f188(f888(f887(x93401,x93401),a879)))+~P1(f335(f335(f337(f887(x93401,x93401)),f335(f335(f264(x93401,x93401),x93403),x93403)),f335(f335(f291(x93401,x93401,x93401),x93402),f310(x93401,x93402))))
% 59.73/59.66 [9522]~P1(f335(f56(x95221),x95222))+P1(f335(f335(f242(a881),f335(f29(x95221),f335(f335(f23(f888(x95221,a879)),x95222),f335(f335(f312(x95221),x95223),f188(f888(x95221,a879)))))),f335(f29(x95221),x95222)))
% 59.73/59.66 [5083]~E(x50833,f107(x50831))+E(f137(x50831,f335(f335(f144(x50831),x50832),x50833)),x50832)
% 59.73/59.66 [5084]~E(x50843,f107(x50841))+E(f137(x50841,f335(f335(f144(x50841),x50842),x50843)),x50842)
% 59.73/59.66 [5092]~E(x50923,f107(x50921))+E(f108(x50921,f335(f335(f144(x50921),x50922),x50923)),f107(x50921))
% 59.73/59.66 [5122]E(x51221,f107(x51222))+E(f137(x51222,f335(f335(f144(x51222),x51223),x51221)),f137(x51222,x51221))
% 59.73/59.66 [5123]E(x51231,f107(x51232))+E(f137(x51232,f335(f335(f144(x51232),x51233),x51231)),f137(x51232,x51231))
% 59.73/59.66 [5124]E(x51241,f107(x51242))+E(f137(x51242,f335(f335(f127(x51242),x51243),x51241)),f137(x51242,x51241))
% 59.73/59.66 [5125]E(x51251,f107(x51252))+E(f137(x51252,f335(f335(f127(x51252),x51253),x51251)),f137(x51252,x51251))
% 59.73/59.66 [5132]~E(x51323,f107(x51321))+E(f137(x51321,f335(f335(f127(x51321),x51322),x51323)),f137(x51321,x51322))
% 59.73/59.66 [5133]~E(x51333,f107(x51331))+E(f137(x51331,f335(f335(f127(x51331),x51332),x51333)),f137(x51331,x51332))
% 59.73/59.66 [5134]~E(x51343,f107(x51341))+E(f108(x51341,f335(f335(f127(x51341),x51342),x51343)),f108(x51341,x51342))
% 59.73/59.66 [5167]E(x51671,f107(x51672))+E(f335(f134(x51672),f335(f335(f127(x51672),x51671),x51673)),f335(f134(x51672),x51671))
% 59.73/59.66 [5168]E(x51681,f107(x51682))+E(f335(f134(x51682),f335(f335(f127(x51682),x51681),x51683)),f335(f134(x51682),x51681))
% 59.73/59.66 [5196]~E(x51962,f107(x51961))+E(f335(f134(x51961),f335(f335(f127(x51961),x51962),x51963)),f335(f134(x51961),x51963))
% 59.73/59.66 [5247]~P61(x52471)+E(f335(f335(f104(x52471),x52472),f335(f335(f95(x52471),x52472),x52473)),x52472)
% 59.73/59.66 [5248]~P61(x52481)+E(f335(f335(f95(x52481),x52482),f335(f335(f104(x52481),x52482),x52483)),x52482)
% 59.73/59.66 [5249]~P106(x52491)+E(f335(f335(f240(x52491),x52492),f335(f335(f241(x52491),x52492),x52493)),x52492)
% 59.73/59.66 [5250]~P106(x52501)+E(f335(f335(f241(x52501),x52502),f335(f335(f240(x52501),x52502),x52503)),x52502)
% 59.73/59.66 [5269]~P58(x52691)+E(f39(x52691,f335(f335(f76(x52691),x52692),x52693),x52693),f2(x52691))
% 59.73/59.66 [5270]~P58(x52701)+E(f39(x52701,f335(f335(f76(x52701),x52702),x52703),x52702),f2(x52701))
% 59.73/59.66 [5339]~P64(x53391)+E(f335(f74(x53391),f335(f335(f23(x53391),x53392),x53393)),f335(f335(f23(x53391),x53393),x53392))
% 59.73/59.66 [5400]E(x54001,f107(x54002))+E(f108(x54002,f335(f335(f144(x54002),x54003),x54001)),f335(f335(f144(x54002),x54003),f108(x54002,x54001)))
% 59.73/59.66 [5401]E(x54011,f107(x54012))+E(f108(x54012,f335(f335(f127(x54012),x54013),x54011)),f335(f335(f127(x54012),x54013),f108(x54012,x54011)))
% 59.73/59.66 [5404]~P5(x54041)+E(f32(x54041,f335(f335(f312(x54041),x54042),x54043)),f335(f335(f95(x54041),x54042),f32(x54041,x54043)))
% 59.73/59.66 [5405]~P5(x54051)+E(f31(x54051,f335(f335(f312(x54051),x54052),x54053)),f335(f335(f104(x54051),x54052),f31(x54051,x54053)))
% 59.73/59.66 [5450]~P60(x54501)+E(f335(f335(f104(x54501),x54502),f335(f335(f104(x54501),x54502),x54503)),f335(f335(f104(x54501),x54502),x54503))
% 59.73/59.66 [5451]~P60(x54511)+E(f335(f335(f104(x54511),x54512),f335(f335(f104(x54511),x54512),x54513)),f335(f335(f104(x54511),x54512),x54513))
% 59.73/59.66 [5452]~P61(x54521)+E(f335(f335(f104(x54521),x54522),f335(f335(f104(x54521),x54522),x54523)),f335(f335(f104(x54521),x54522),x54523))
% 59.73/59.66 [5453]~P61(x54531)+E(f335(f335(f95(x54531),x54532),f335(f335(f95(x54531),x54532),x54533)),f335(f335(f95(x54531),x54532),x54533))
% 59.73/59.66 [5454]~P102(x54541)+E(f335(f335(f95(x54541),x54542),f335(f335(f95(x54541),x54542),x54543)),f335(f335(f95(x54541),x54542),x54543))
% 59.73/59.66 [5455]~P102(x54551)+E(f335(f335(f95(x54551),x54552),f335(f335(f95(x54551),x54552),x54553)),f335(f335(f95(x54551),x54552),x54553))
% 59.73/59.66 [5456]~P98(x54561)+E(f335(f335(f76(x54561),x54562),f335(f335(f76(x54561),x54562),x54563)),f335(f335(f76(x54561),x54562),x54563))
% 59.73/59.66 [5457]~P106(x54571)+E(f335(f335(f240(x54571),x54572),f335(f335(f240(x54571),x54572),x54573)),f335(f335(f240(x54571),x54572),x54573))
% 59.73/59.66 [5458]~P106(x54581)+E(f335(f335(f240(x54581),x54582),f335(f335(f240(x54581),x54582),x54583)),f335(f335(f240(x54581),x54582),x54583))
% 59.73/59.66 [5459]~P106(x54591)+E(f335(f335(f241(x54591),x54592),f335(f335(f241(x54591),x54592),x54593)),f335(f335(f241(x54591),x54592),x54593))
% 59.73/59.66 [5460]~P106(x54601)+E(f335(f335(f241(x54601),x54602),f335(f335(f241(x54601),x54602),x54603)),f335(f335(f241(x54601),x54602),x54603))
% 59.73/59.66 [5468]~P58(x54681)+E(f39(x54681,f335(f335(f75(x54681),x54682),x54683),x54683),f39(x54681,x54682,x54683))
% 59.73/59.66 [5469]~P58(x54691)+E(f39(x54691,f335(f335(f75(x54691),x54692),x54693),x54692),f39(x54691,x54693,x54692))
% 59.73/59.66 [5475]~P118(x54751)+E(f335(f335(f76(x54751),x54752),f335(f74(x54751),x54753)),f335(f74(x54751),f335(f335(f76(x54751),x54752),x54753)))
% 59.73/59.66 [5476]~P66(x54761)+E(f335(f335(f292(x54761),x54762),f335(f74(x54761),x54763)),f335(f74(x54761),f335(f335(f292(x54761),x54762),x54763)))
% 59.73/59.66 [5477]~P83(x54771)+E(f335(f335(f75(x54771),x54772),f335(f159(x54771),x54773)),f335(f159(x54771),f335(f335(f144(x54771),x54772),x54773)))
% 59.73/59.66 [5507]~P118(x55071)+E(f335(f335(f76(x55071),f335(f74(x55071),x55072)),x55073),f335(f335(f76(x55071),x55072),f335(f74(x55071),x55073)))
% 59.73/59.66 [5513]~P8(x55131,x55132,x55133)+E(f31(f888(x55131,a879),f335(f335(f55(x55131),x55132),x55133)),x55132)
% 59.73/59.66 [5573]~P114(x55731)+E(f335(f335(f76(x55731),x55732),f335(f335(f254(x55731),x55732),x55733)),f335(f335(f254(x55731),x55732),f335(a106,x55733)))
% 59.73/59.66 [5574]~P113(x55741)+E(f335(f335(f76(x55741),x55742),f335(f335(f254(x55741),x55742),x55743)),f335(f335(f254(x55741),x55742),f335(a106,x55743)))
% 59.73/59.66 [5575]~P114(x55751)+E(f335(f335(f76(x55751),x55752),f335(f335(f254(x55751),x55752),x55753)),f335(f335(f254(x55751),x55752),f335(a106,x55753)))
% 59.73/59.66 [5585]~P72(x55851)+E(f335(f335(f75(x55851),f335(f74(x55851),x55852)),f335(f335(f75(x55851),x55852),x55853)),x55853)
% 59.73/59.66 [5608]~P137(x56081)+E(f335(f335(f254(x56081),f335(f96(x56081),x56082)),x56083),f335(f96(x56081),f335(f335(f254(a1),x56082),x56083)))
% 59.73/59.66 [5609]~P143(x56091)+E(f335(f335(f254(x56091),f335(f94(x56091),x56092)),x56093),f335(f94(x56091),f335(f335(f254(a881),x56092),x56093)))
% 59.73/59.66 [5615]~P88(x56151)+E(f335(f70(x56151),f335(f335(f23(x56151),x56152),x56153)),f335(f70(x56151),f335(f335(f23(x56151),x56153),x56152)))
% 59.73/59.66 [5617]~P119(x56171)+E(f335(f335(f76(x56171),f77(x56171,x56172)),f77(x56171,x56173)),f77(x56171,f335(f335(f76(x56171),x56172),x56173)))
% 59.73/59.66 [5621]E(x56211,f107(x56212))+E(f335(f335(f127(x56212),f335(f165(x56212),x56211)),x56213),f335(f165(x56212),f335(f335(f127(x56212),x56211),x56213)))
% 59.73/59.66 [5626]~E(x56262,f335(a106,f335(f335(f75(a881),x56261),x56263)))+P1(f335(f335(f243(a881),x56261),x56262))
% 59.73/59.66 [5627]~P118(x56271)+E(f335(f335(f76(x56271),f335(f74(x56271),x56272)),x56273),f335(f74(x56271),f335(f335(f76(x56271),x56272),x56273)))
% 59.73/59.66 [5628]~P116(x56281)+E(f335(f335(f292(x56281),f335(f74(x56281),x56282)),x56283),f335(f74(x56281),f335(f335(f292(x56281),x56282),x56283)))
% 59.73/59.66 [5629]~P119(x56291)+E(f335(f335(f254(x56291),f335(f70(x56291),x56292)),x56293),f335(f70(x56291),f335(f335(f254(x56291),x56292),x56293)))
% 59.73/59.66 [5728]E(f462(x57281,x57282,x57283),f495(x57281,x57282,x57283))+E(f335(f335(f95(f888(x57283,a879)),x57282),x57281),f188(f888(x57283,a879)))
% 59.73/59.66 [5743]~P73(x57432)+E(f335(f335(f9(x57431,x57432),f335(f16(x57432,x57431),f73(x57432))),x57433),f73(x57432))
% 59.73/59.66 [5744]~P77(x57442)+E(f335(f335(f6(x57441,x57442),f335(f16(x57442,x57441),f2(x57442))),x57443),f2(x57442))
% 59.73/59.66 [5746]~P97(x57461)+E(f335(f335(f23(x57461),f335(f97(x57461),x57462)),f335(f97(x57461),x57463)),f335(f97(x57461),f335(f335(f23(a1),x57462),x57463)))
% 59.73/59.66 [5747]~P97(x57471)+E(f335(f335(f76(x57471),f335(f97(x57471),x57472)),f335(f97(x57471),x57473)),f335(f97(x57471),f335(f335(f76(a1),x57472),x57473)))
% 59.73/59.66 [5748]~P97(x57481)+E(f335(f335(f75(x57481),f335(f97(x57481),x57482)),f335(f97(x57481),x57483)),f335(f97(x57481),f335(f335(f75(a1),x57482),x57483)))
% 59.73/59.66 [5749]~P137(x57491)+E(f335(f335(f23(x57491),f335(f96(x57491),x57492)),f335(f96(x57491),x57493)),f335(f96(x57491),f335(f335(f23(a1),x57492),x57493)))
% 59.73/59.66 [5750]~P137(x57501)+E(f335(f335(f76(x57501),f335(f96(x57501),x57502)),f335(f96(x57501),x57503)),f335(f96(x57501),f335(f335(f76(a1),x57502),x57503)))
% 59.73/59.66 [5751]~P137(x57511)+E(f335(f335(f75(x57511),f335(f96(x57511),x57512)),f335(f96(x57511),x57513)),f335(f96(x57511),f335(f335(f75(a1),x57512),x57513)))
% 59.73/59.66 [5752]~P143(x57521)+E(f335(f335(f76(x57521),f335(f94(x57521),x57522)),f335(f94(x57521),x57523)),f335(f94(x57521),f335(f335(f76(a881),x57522),x57523)))
% 59.73/59.66 [5753]~P143(x57531)+E(f335(f335(f75(x57531),f335(f94(x57531),x57532)),f335(f94(x57531),x57533)),f335(f94(x57531),f335(f335(f75(a881),x57532),x57533)))
% 59.73/59.66 [5754]~P97(x57541)+E(f335(f335(f76(x57541),f335(f97(x57541),x57542)),f335(f97(x57541),x57543)),f335(f97(x57541),f335(f335(f76(a1),x57542),x57543)))
% 59.73/59.66 [5755]~P97(x57551)+E(f335(f335(f75(x57551),f335(f97(x57551),x57552)),f335(f97(x57551),x57553)),f335(f97(x57551),f335(f335(f75(a1),x57552),x57553)))
% 59.73/59.66 [5802]~E(x58023,x58022)+P1(f335(f335(f242(f888(x58021,a879)),x58022),x58023))
% 59.73/59.66 [5803]~E(x58032,x58033)+P1(f335(f335(f242(f888(x58031,a879)),x58032),x58033))
% 59.73/59.66 [5804]~E(x58042,x58043)+P1(f335(f335(f242(f888(x58041,a879)),x58042),x58043))
% 59.73/59.66 [5805]~E(x58052,x58053)+P1(f335(f335(f242(f888(x58051,a879)),x58052),x58053))
% 59.73/59.66 [5806]~E(x58062,x58063)+P1(f335(f335(f242(f888(x58061,a879)),x58062),x58063))
% 59.73/59.66 [5807]~E(x58072,x58073)+P1(f335(f335(f242(f888(x58071,a879)),x58072),x58073))
% 59.73/59.66 [5808]~E(x58082,x58083)+P1(f335(f335(f242(f888(x58081,a879)),x58082),x58083))
% 59.73/59.66 [5813]~P84(x58131)+E(f335(f335(f95(x58131),f335(f74(x58131),x58132)),f335(f74(x58131),x58133)),f335(f74(x58131),f335(f335(f104(x58131),x58132),x58133)))
% 59.73/59.66 [5814]~P84(x58141)+E(f335(f335(f104(x58141),f335(f74(x58141),x58142)),f335(f74(x58141),x58143)),f335(f74(x58141),f335(f335(f95(x58141),x58142),x58143)))
% 59.73/59.66 [5815]~P72(x58151)+E(f335(f335(f75(x58151),f335(f74(x58151),x58152)),f335(f74(x58151),x58153)),f335(f74(x58151),f335(f335(f75(x58151),x58153),x58152)))
% 59.73/59.66 [5816]~P64(x58161)+E(f335(f335(f75(x58161),f335(f74(x58161),x58162)),f335(f74(x58161),x58163)),f335(f74(x58161),f335(f335(f75(x58161),x58162),x58163)))
% 59.73/59.66 [5817]~P79(x58171)+E(f335(f335(f241(x58171),f335(f74(x58171),x58172)),f335(f74(x58171),x58173)),f335(f74(x58171),f335(f335(f240(x58171),x58172),x58173)))
% 59.73/59.66 [5818]~P79(x58181)+E(f335(f335(f240(x58181),f335(f74(x58181),x58182)),f335(f74(x58181),x58183)),f335(f74(x58181),f335(f335(f241(x58181),x58182),x58183)))
% 59.73/59.66 [5819]~P119(x58191)+E(f335(f335(f76(x58191),f335(f70(x58191),x58192)),f335(f70(x58191),x58193)),f335(f70(x58191),f335(f335(f76(x58191),x58192),x58193)))
% 59.73/59.66 [5820]~P68(x58201)+E(f335(f335(f292(x58201),f335(f70(x58201),x58202)),f335(f70(x58201),x58203)),f335(f70(x58201),f335(f335(f292(x58201),x58202),x58203)))
% 59.73/59.66 [5821]~P83(x58211)+E(f335(f335(f75(x58211),f335(f159(x58211),x58212)),f335(f159(x58211),x58213)),f335(f159(x58211),f335(f335(f127(x58211),x58212),x58213)))
% 59.73/59.66 [5822]E(x58221,f188(f888(x58222,a879)))+~E(f335(f335(f104(f888(x58222,a879)),x58223),x58221),f188(f888(x58222,a879)))
% 59.73/59.66 [5823]E(x58231,f188(f888(x58232,a879)))+~E(f335(f335(f104(f888(x58232,a879)),x58231),x58233),f188(f888(x58232,a879)))
% 59.73/59.66 [5824]~P146(x58241,x58243,x58242)+P1(f335(x58241,f335(f335(f30(a1),x58242),x58243)))
% 59.73/59.66 [5875]~P1(f335(f56(x58751),x58753))+P1(f335(f56(x58751),f335(f335(f312(x58751),x58752),x58753)))
% 59.73/59.66 [5876]~P1(f335(f56(x58761),x58763))+P1(f335(f56(x58761),f335(f335(f312(x58761),x58762),x58763)))
% 59.73/59.66 [5877]~P1(f335(f130(x58771),x58773))+P1(f335(f130(x58771),f335(f335(f169(x58771),x58772),x58773)))
% 59.73/59.66 [5878]~P1(f335(f130(x58781),x58783))+P1(f335(f130(x58781),f335(f335(f131(x58781),x58782),x58783)))
% 59.73/59.66 [5908]~P60(x59081)+P1(f335(f335(f242(x59081),x59082),f335(f335(f104(x59081),x59083),x59082)))
% 59.73/59.66 [5909]~P61(x59091)+P1(f335(f335(f242(x59091),x59092),f335(f335(f104(x59091),x59093),x59092)))
% 59.73/59.66 [5910]~P60(x59101)+P1(f335(f335(f242(x59101),x59102),f335(f335(f104(x59101),x59102),x59103)))
% 59.73/59.66 [5911]~P61(x59111)+P1(f335(f335(f242(x59111),x59112),f335(f335(f104(x59111),x59112),x59113)))
% 59.73/59.66 [5912]~P106(x59121)+P1(f335(f335(f242(x59121),x59122),f335(f335(f241(x59121),x59123),x59122)))
% 59.73/59.66 [5913]~P106(x59131)+P1(f335(f335(f242(x59131),x59132),f335(f335(f241(x59131),x59132),x59133)))
% 59.73/59.66 [5927]~E(x59271,f2(a881))+E(f335(f335(f30(a881),f335(f335(f76(a881),x59271),x59272)),f335(f335(f76(a881),x59271),x59273)),f2(a881))
% 59.73/59.66 [6008]~P97(x60081)+E(f335(f335(f23(x60081),f335(f97(x60081),x60082)),f335(f97(x60081),x60083)),f335(f97(x60081),f335(f335(f75(a1),x60082),f335(f74(a1),x60083))))
% 59.73/59.66 [6064]E(x60641,f2(a881))+E(f335(f335(f30(a881),f335(f335(f76(a881),x60641),x60642)),f335(f335(f76(a881),x60641),x60643)),f335(f335(f30(a881),x60642),x60643))
% 59.73/59.66 [6095]E(f145(x60951,f335(f335(f144(x60951),x60952),x60953)),f335(f335(f144(x60951),x60952),f145(x60951,x60953)))+P1(f335(f335(f337(x60951),x60952),f335(f166(x60951),x60953)))
% 59.73/59.66 [6128]P146(x61281,x61282,x61283)+~P1(f335(x61281,f335(f335(f30(a1),x61283),x61282)))
% 59.73/59.66 [6199]E(x61991,f107(x61992))+E(f335(f335(f144(x61992),f335(f134(x61992),x61991)),f335(f335(f169(x61992),x61993),f335(f165(x61992),x61991))),f335(f335(f169(x61992),f335(a106,x61993)),x61991))
% 59.73/59.66 [6206]E(f335(f335(f23(f888(x62061,a879)),x62062),x62063),x62062)+~E(f335(f335(f95(f888(x62061,a879)),x62062),x62063),f188(f888(x62061,a879)))
% 59.73/59.66 [6221]E(f145(x62211,f335(f335(f144(x62211),x62212),x62213)),f145(x62211,x62213))+~P1(f335(f335(f337(x62211),x62212),f335(f166(x62211),x62213)))
% 59.73/59.66 [6252]~P1(f335(f335(f242(a881),x62521),x62523))+P1(f335(f335(f242(a881),x62521),f335(f335(f75(a881),x62522),x62523)))
% 59.73/59.66 [6253]~P1(f335(f335(f242(a881),x62531),x62533))+P1(f335(f335(f242(a881),x62531),f335(f335(f75(a881),x62532),x62533)))
% 59.73/59.66 [6254]~P1(f335(f335(f242(a881),x62541),x62542))+P1(f335(f335(f242(a881),x62541),f335(f335(f75(a881),x62542),x62543)))
% 59.73/59.66 [6255]~P1(f335(f335(f242(a881),x62551),x62552))+P1(f335(f335(f242(a881),x62551),f335(f335(f75(a881),x62552),x62553)))
% 59.73/59.66 [6256]~P1(f335(f335(f243(a881),x62561),x62563))+P1(f335(f335(f243(a881),x62561),f335(f335(f75(a881),x62562),x62563)))
% 59.73/59.66 [6257]~P1(f335(f335(f243(a881),x62571),x62573))+P1(f335(f335(f243(a881),x62571),f335(f335(f75(a881),x62572),x62573)))
% 59.73/59.66 [6258]~P1(f335(f335(f243(a881),x62581),x62582))+P1(f335(f335(f243(a881),x62581),f335(f335(f75(a881),x62582),x62583)))
% 59.73/59.66 [6259]~P1(f335(f335(f243(a881),x62591),x62592))+P1(f335(f335(f243(a881),x62591),f335(f335(f75(a881),x62592),x62593)))
% 59.73/59.66 [6297]P1(f335(f56(x62971),x62972))+~P1(f335(f56(x62971),f335(f335(f312(x62971),x62973),x62972)))
% 59.73/59.66 [6298]P1(f335(f130(x62981),x62982))+~P1(f335(f130(x62981),f335(f335(f144(x62981),x62983),x62982)))
% 59.73/59.66 [6299]P1(f335(f130(x62991),x62992))+~P1(f335(f130(x62991),f335(f335(f127(x62991),x62993),x62992)))
% 59.73/59.66 [6300]P1(f335(f130(x63001),x63002))+~P1(f335(f130(x63001),f335(f335(f127(x63001),x63002),x63003)))
% 59.73/59.66 [6347]~P114(x63471)+E(f335(f335(f75(x63471),x63472),f335(f335(f76(x63471),x63473),x63472)),f335(f335(f76(x63471),f335(f335(f75(x63471),x63473),f73(x63471))),x63472))
% 59.73/59.66 [6395]~E(x63951,x63952)+~P1(f335(f335(f243(f888(x63953,a879)),x63951),x63952))
% 59.73/59.66 [6441]P1(f335(f335(f337(x64411),x64412),x64413))+P1(f335(f335(f337(x64411),x64412),f335(f74(f888(x64411,a879)),x64413)))
% 59.73/59.66 [6442]P1(f335(f335(f337(x64421),x64422),x64423))+P1(f335(f335(f337(x64421),x64422),f335(f74(f888(x64421,a879)),x64423)))
% 59.73/59.66 [6448]E(f137(x64481,f335(f335(f131(x64481),x64482),x64483)),f137(x64481,x64483))+~P1(f335(f335(f243(a881),x64482),f335(f189(f882(x64481)),x64483)))
% 59.73/59.66 [6449]E(f335(f335(f169(x64491),x64492),f108(x64491,x64493)),f335(f335(f169(x64491),x64492),x64493))+~P1(f335(f335(f243(a881),x64492),f335(f189(f882(x64491)),x64493)))
% 59.73/59.66 [6503]E(f335(f335(f335(f183(f882(x65031),f882(x65031)),x65032),f161(x65031)),x65033),x65033)+~E(f39(a881,x65032,f335(f189(f882(x65031)),x65033)),f2(a881))
% 59.73/59.66 [6510]~P8(x65101,x65103,x65102)+E(f335(f335(f291(x65101,x65101,x65101),f335(f289(x65101,x65101),x65102)),x65102),x65102)
% 59.73/59.66 [6553]~E(f335(f335(f104(f888(x65531,a879)),x65532),x65533),x65533)+P1(f335(f335(f242(f888(x65531,a879)),x65532),x65533))
% 59.73/59.66 [6558]~P52(x65581,x65581,x65583)+P52(x65581,x65581,f335(f335(f183(f887(x65581,x65581),a879),x65582),x65583))
% 59.73/59.66 [6562]~P1(f335(f335(f337(x65621),x65623),f335(f166(x65621),x65622)))+P1(f335(f335(f243(a881),f2(a881)),f335(f189(f882(x65621)),x65622)))
% 59.73/59.66 [6577]~E(x65772,x65773)+P1(f335(f335(f337(x65771),x65772),f335(f335(f312(x65771),x65773),f188(f888(x65771,a879)))))
% 59.73/59.66 [6588]~P88(x65881)+E(f335(f70(x65881),f335(f335(f75(x65881),f335(f70(x65881),x65882)),f335(f70(x65881),x65883))),f335(f335(f75(x65881),f335(f70(x65881),x65882)),f335(f70(x65881),x65883)))
% 59.73/59.66 [6598]E(f335(f335(f30(a881),f335(f335(f76(a881),x65981),x65982)),f335(f335(f76(a881),x65981),x65983)),f335(f335(f30(a881),x65982),x65983))+~P1(f335(f335(f243(a881),f2(a881)),x65981))
% 59.73/59.66 [6742]~P1(f335(f56(x67421),x67423))+E(f335(f335(f59(x67421,f888(x67421,a879),f312(x67421)),x67422),x67423),f335(f335(f104(f888(x67421,a879)),x67423),x67422))
% 59.73/59.66 [6801]E(f335(f335(f104(f888(x68011,a879)),x68012),x68013),x68012)+~P1(f335(f335(f242(f888(x68011,a879)),x68013),x68012))
% 59.73/59.66 [6802]E(f335(f335(f104(f888(x68021,a879)),x68022),x68023),x68023)+~P1(f335(f335(f242(f888(x68021,a879)),x68022),x68023))
% 59.73/59.66 [6803]E(f335(f335(f104(f888(x68031,a879)),x68032),x68033),x68033)+~P1(f335(f335(f242(f888(x68031,a879)),x68032),x68033))
% 59.73/59.66 [6804]E(f335(f335(f95(f888(x68041,a879)),x68042),x68043),x68043)+~P1(f335(f335(f242(f888(x68041,a879)),x68043),x68042))
% 59.73/59.66 [6805]E(f335(f335(f95(f888(x68051,a879)),x68052),x68053),x68052)+~P1(f335(f335(f242(f888(x68051,a879)),x68052),x68053))
% 59.73/59.66 [6859]~P1(f335(f130(x68591),x68592))+E(f335(f335(f23(f888(x68591,a879)),f335(f166(x68591),x68592)),f335(f335(f312(x68591),x68593),f188(f888(x68591,a879)))),f335(f166(x68591),f164(x68591,x68593,x68592)))
% 59.73/59.66 [6912]P36(x69121,x69122)+~P36(x69121,f335(f335(f183(f887(x69121,x69121),a879),x69123),x69122))
% 59.73/59.66 [6975]P1(f335(f43(x69751,x69752),f335(a45,x69753)))+~P1(f335(f43(f335(f74(a1),x69751),f335(f74(a1),x69752)),x69753))
% 59.73/59.66 [6980]E(f335(f335(f23(f888(x69801,a879)),f335(f335(f312(x69801),x69802),x69803)),f335(f335(f312(x69801),x69802),f188(f888(x69801,a879)))),x69803)+P1(f335(f335(f337(x69801),x69802),x69803))
% 59.73/59.66 [7001]E(f335(f335(f95(f888(x70011,a879)),f335(f166(x70011),x70012)),f335(f166(x70011),x70013)),f188(f888(x70011,a879)))+~P1(f335(f130(x70011),f335(f335(f127(x70011),x70012),x70013)))
% 59.73/59.66 [7017]~P1(f335(f335(f337(x70171),x70172),f335(f166(x70171),x70173)))+~P1(f335(f130(x70171),f335(f335(f144(x70171),x70172),x70173)))
% 59.73/59.66 [7087]P30(x70871,x70872,x70873)+P1(f335(f335(f243(a881),f787(x70873,x70872,x70871)),f335(f189(f882(x70871)),x70873)))
% 59.73/59.66 [7097]E(f335(f335(f95(f888(x70971,a879)),x70972),x70973),f188(f888(x70971,a879)))+P1(f335(f335(f337(x70971),f462(x70973,x70972,x70971)),x70972))
% 59.73/59.66 [7098]E(f335(f335(f95(f888(x70981,a879)),x70982),x70983),f188(f888(x70981,a879)))+P1(f335(f335(f337(x70981),f495(x70983,x70982,x70981)),x70983))
% 59.73/59.66 [7102]E(f108(x71021,f335(f335(f169(x71021),x71022),x71023)),f335(f335(f169(x71021),f335(f335(f23(a881),x71022),f73(a881))),x71023))+~P1(f335(f335(f242(a881),x71022),f335(f189(f882(x71021)),x71023)))
% 59.73/59.66 [7161]~P32(x71613,x71612,x71611)+P1(f335(f335(f243(a881),f778(x71611,x71612,x71613)),f335(f189(f882(x71613)),x71611)))
% 59.73/59.66 [7179]P1(f335(f335(f243(a881),f2(a881)),x71791))+P1(f335(f335(f242(a881),f335(f335(f76(a881),x71792),x71791)),f335(f335(f76(a881),x71793),x71791)))
% 59.73/59.66 [7180]P1(f335(f335(f243(a881),f2(a881)),x71801))+P1(f335(f335(f242(a881),f335(f335(f76(a881),x71801),x71802)),f335(f335(f76(a881),x71801),x71803)))
% 59.73/59.66 [7181]~P1(f335(f335(f337(x71811),x71812),x71813))+~P1(f335(f335(f337(x71811),x71812),f335(f74(f888(x71811,a879)),x71813)))
% 59.73/59.66 [7182]~P1(f335(f335(f337(x71821),x71822),x71823))+~P1(f335(f335(f337(x71821),x71822),f335(f74(f888(x71821,a879)),x71823)))
% 59.73/59.66 [7183]~P1(f335(f335(f337(x71831),x71832),x71833))+~P1(f335(f335(f337(x71831),x71832),f335(f74(f888(x71831,a879)),x71833)))
% 59.73/59.66 [7188]~P1(f335(f335(f243(f888(x71881,a879)),x71882),x71883))+P1(f335(f335(f242(f888(x71881,a879)),x71882),x71883))
% 59.73/59.66 [7189]~P1(f335(f335(f243(f888(x71891,a879)),x71892),x71893))+P1(f335(f335(f242(f888(x71891,a879)),x71892),x71893))
% 59.73/59.66 [7190]~P1(f335(f335(f243(f888(x71901,a879)),x71902),x71903))+P1(f335(f335(f242(f888(x71901,a879)),x71902),x71903))
% 59.73/59.66 [7294]~P1(f335(f335(f242(a881),x72943),x72942))+P1(f335(f335(f242(a881),f335(f335(f23(a881),x72941),x72942)),f335(f335(f23(a881),x72941),x72943)))
% 59.73/59.66 [7295]~P1(f335(f335(f242(a881),x72951),x72953))+P1(f335(f335(f242(a881),f335(f335(f23(a881),x72951),x72952)),f335(f335(f23(a881),x72953),x72952)))
% 59.73/59.66 [7296]~P1(f335(f335(f242(a881),x72962),x72963))+P1(f335(f335(f242(a881),f335(f335(f76(a881),x72961),x72962)),f335(f335(f76(a881),x72961),x72963)))
% 59.73/59.66 [7297]~P1(f335(f335(f242(a881),x72972),x72973))+P1(f335(f335(f242(a881),f335(f335(f76(a881),x72971),x72972)),f335(f335(f76(a881),x72971),x72973)))
% 59.73/59.66 [7298]~P1(f335(f335(f242(a881),x72981),x72983))+P1(f335(f335(f242(a881),f335(f335(f76(a881),x72981),x72982)),f335(f335(f76(a881),x72983),x72982)))
% 59.73/59.66 [7299]~P1(f335(f335(f242(a881),x72991),x72993))+P1(f335(f335(f242(a881),f335(f335(f76(a881),x72991),x72992)),f335(f335(f76(a881),x72993),x72992)))
% 59.73/59.66 [7300]~P1(f335(f335(f242(a881),x73002),x73003))+P1(f335(f335(f242(a881),f335(f335(f75(a881),x73001),x73002)),f335(f335(f75(a881),x73001),x73003)))
% 59.73/59.66 [7301]~P1(f335(f335(f242(a881),x73011),x73013))+P1(f335(f335(f242(a881),f335(f335(f75(a881),x73011),x73012)),f335(f335(f75(a881),x73013),x73012)))
% 59.73/59.66 [7302]~P1(f335(f335(f242(a881),x73021),x73023))+P1(f335(f335(f242(a881),f335(f335(f30(a881),x73021),x73022)),f335(f335(f30(a881),x73023),x73022)))
% 59.73/59.66 [7303]~P1(f335(f335(f242(a1),x73032),x73033))+P1(f335(f335(f242(a1),f335(f335(f75(a1),x73031),x73032)),f335(f335(f75(a1),x73031),x73033)))
% 59.73/59.66 [7306]~P1(f335(f335(f243(a881),x73062),x73063))+P1(f335(f335(f243(a881),f335(f335(f75(a881),x73061),x73062)),f335(f335(f75(a881),x73061),x73063)))
% 59.73/59.66 [7307]~P1(f335(f335(f243(a881),x73071),x73073))+P1(f335(f335(f243(a881),f335(f335(f75(a881),x73071),x73072)),f335(f335(f75(a881),x73073),x73072)))
% 59.73/59.66 [7308]~P1(f335(f335(f243(a1),x73081),x73083))+P1(f335(f335(f243(a1),f335(f335(f75(a1),x73081),x73082)),f335(f335(f75(a1),x73083),x73082)))
% 59.73/59.66 [7386]E(x73861,x73862)+~P1(f335(f335(f337(x73863),x73861),f335(f335(f312(x73863),x73862),f188(f888(x73863,a879)))))
% 59.73/59.66 [7387]E(x73871,x73872)+~P1(f335(f335(f337(x73873),x73871),f335(f335(f312(x73873),x73872),f188(f888(x73873,a879)))))
% 59.73/59.66 [7389]~E(f335(f335(f95(f888(x73891,a879)),x73892),x73893),f188(f888(x73891,a879)))+P1(f335(f335(f242(f888(x73891,a879)),x73892),f335(f74(f888(x73891,a879)),x73893)))
% 59.73/59.66 [7395]P1(f335(f335(f337(f888(x73951,a879)),x73952),f335(f311(x73951),x73953)))+~P1(f335(f335(f242(f888(x73951,a879)),x73952),x73953))
% 59.73/59.66 [7396]P1(f335(f335(f337(f888(x73961,a879)),x73962),f335(f311(x73961),x73963)))+~P1(f335(f335(f242(f888(x73961,a879)),x73962),x73963))
% 59.73/59.66 [7401]P1(f335(f335(f337(x74011),f657(x74012,x74013,x74011)),x74013))+P1(f335(f335(f242(f888(x74011,a879)),x74013),x74012))
% 59.73/59.66 [7449]E(f335(f335(f144(x74491),f335(f335(f158(x74491),x74492),x74493)),f335(f335(f131(x74491),f335(a106,x74493)),x74492)),f335(f335(f131(x74491),x74493),x74492))+~P1(f335(f335(f243(a881),x74493),f335(f189(f882(x74491)),x74492)))
% 59.73/59.66 [7476]P1(f335(f335(f337(f887(x74761,x74761)),x74762),f310(x74761,x74763)))+~P1(f335(f335(f337(f887(x74761,x74761)),x74762),x74763))
% 59.73/59.66 [7485]~P1(f335(f335(f337(f888(x74851,a879)),x74852),f335(f311(x74851),x74853)))+P1(f335(f335(f242(f888(x74851,a879)),x74852),x74853))
% 59.73/59.66 [7486]~P1(f335(f335(f337(f888(x74861,a879)),x74862),f335(f311(x74861),x74863)))+P1(f335(f335(f242(f888(x74861,a879)),x74862),x74863))
% 59.73/59.66 [7530]P1(f335(f335(f242(f888(x75301,a879)),x75302),f31(f888(x75301,a879),x75303)))+~P1(f335(f335(f337(f888(x75301,a879)),x75302),x75303))
% 59.73/59.66 [7555]~P137(x75551)+E(f335(f335(f76(x75551),f335(f335(f254(x75551),f335(f74(x75551),f73(x75551))),x75552)),f335(f335(f254(x75551),x75553),x75552)),f335(f335(f254(x75551),f335(f74(x75551),x75553)),x75552))
% 59.73/59.66 [7578]E(f335(f335(f158(x75781),x75782),f335(f335(f23(a881),f335(f189(f882(x75781)),x75782)),f335(a106,x75783))),f335(f335(f158(x75781),f335(f162(x75781),x75782)),x75783))+~P1(f335(f335(f243(a881),x75783),f335(f189(f882(x75781)),x75782)))
% 59.73/59.66 [7595]~E(f335(f335(f95(f888(x75951,a879)),f635(x75953,x75952,x75951)),x75953),f188(f888(x75951,a879)))+E(f335(f335(f95(f888(x75951,a879)),f31(f888(x75951,a879),x75952)),x75953),f188(f888(x75951,a879)))
% 59.73/59.66 [7657]~P1(f335(f335(f337(x76573),x76572),f335(f166(x76573),x76571)))+P1(f335(f335(f243(a881),f689(x76571,x76572,x76573)),f335(f189(f882(x76573)),x76571)))
% 59.73/59.66 [7665]P1(f335(f335(f337(x76651),f335(f335(f158(x76651),x76652),x76653)),f335(f166(x76651),x76652)))+~P1(f335(f335(f243(a881),x76653),f335(f189(f882(x76651)),x76652)))
% 59.73/59.66 [7766]~P1(f335(x77662,f743(x77663,x77662,x77661)))+E(f335(f335(f131(x77661),f335(f189(f882(x77661)),f171(x77661,x77662,x77663))),x77663),f107(x77661))
% 59.73/59.66 [7777]P1(f335(f335(f242(f888(f882(x77771),a879)),f154(x77771,x77772)),f154(x77771,x77773)))+~P1(f335(f335(f242(f888(x77771,a879)),x77772),x77773))
% 59.73/59.66 [7778]P1(f335(f335(f242(f888(f882(x77781),a879)),f153(x77781,x77782)),f153(x77781,x77783)))+~P1(f335(f335(f242(f888(x77781,a879)),x77782),x77783))
% 59.73/59.66 [7805]E(f335(f335(f95(f888(x78051,a879)),f31(f888(x78051,a879),x78052)),x78053),f188(f888(x78051,a879)))+P1(f335(f335(f337(f888(x78051,a879)),f635(x78053,x78052,x78051)),x78052))
% 59.73/59.66 [7808]~P1(f335(f335(f337(f888(x78081,a879)),x78083),x78082))+P1(f335(f335(f242(f888(x78081,a879)),f32(f888(x78081,a879),x78082)),x78083))
% 59.73/59.66 [7810]E(f335(f335(f95(f888(x78101,a879)),x78102),x78103),f188(f888(x78101,a879)))+~P1(f335(f335(f242(f888(x78101,a879)),x78102),f335(f74(f888(x78101,a879)),x78103)))
% 59.73/59.66 [7857]E(f335(f335(f23(a881),f335(f335(f75(a881),f335(f159(a881),x78571)),x78572)),f335(f335(f158(a881),x78571),x78573)),f335(f159(a881),f335(f335(f152(a881,x78571),x78573),x78572)))+~P1(f335(f335(f243(a881),x78573),f335(f189(f882(a881)),x78571)))
% 59.73/59.66 [7909]P1(f335(f335(f242(a881),x79091),x79092))+~P1(f335(f335(f242(a881),f335(f335(f75(a881),x79093),x79091)),f335(f335(f75(a881),x79093),x79092)))
% 59.73/59.66 [7912]P1(f335(f335(f243(a881),x79121),x79122))+~P1(f335(f335(f243(a881),f335(f335(f75(a881),x79123),x79121)),f335(f335(f75(a881),x79123),x79122)))
% 59.73/59.66 [7913]P1(f335(f335(f243(a881),x79131),x79132))+~P1(f335(f335(f243(a881),f335(f335(f76(a881),x79133),x79131)),f335(f335(f76(a881),x79133),x79132)))
% 59.73/59.66 [7914]P1(f335(f335(f243(a881),x79141),x79142))+~P1(f335(f335(f243(a881),f335(f335(f76(a881),x79141),x79143)),f335(f335(f76(a881),x79142),x79143)))
% 59.73/59.66 [7943]P1(f335(f335(f243(a881),f2(a881)),x79431))+~P1(f335(f335(f243(a881),f335(f335(f76(a881),x79432),x79431)),f335(f335(f76(a881),x79433),x79431)))
% 59.73/59.66 [7944]P1(f335(f335(f243(a881),f2(a881)),x79441))+~P1(f335(f335(f243(a881),f335(f335(f76(a881),x79441),x79442)),f335(f335(f76(a881),x79441),x79443)))
% 59.73/59.66 [7987]~P1(f335(f335(f337(x79871),f657(x79873,x79872,x79871)),x79873))+P1(f335(f335(f242(f888(x79871,a879)),x79872),x79873))
% 59.73/59.66 [8024]E(f256(x80241,x80242,x80243),x80242)+~P1(f335(f335(f242(f888(x80241,a879)),x80243),f335(f335(f312(x80241),x80242),f188(f888(x80241,a879)))))
% 59.73/59.66 [8074]~P1(f335(f130(x80741),x80743))+E(f335(f129(x80741,f335(f335(f8(a879,a879,x80741),a330),f335(a332,x80742))),x80743),f164(x80741,x80742,x80743))
% 59.73/59.66 [8098]E(f335(f335(f131(x80981),f335(f189(f882(x80981)),f171(x80981,x80982,x80983))),x80983),f107(x80981))+P1(f335(f335(f337(x80981),f743(x80983,x80982,x80981)),f335(f166(x80981),x80983)))
% 59.73/59.66 [8102]E(f335(f335(f127(x81021),f335(f335(f169(x81021),x81022),x81023)),f335(f335(f144(x81021),f335(f335(f158(x81021),x81023),x81022)),f107(x81021))),f335(f335(f169(x81021),f335(a106,x81022)),x81023))+~P1(f335(f335(f243(a881),x81022),f335(f189(f882(x81021)),x81023)))
% 59.73/59.66 [8161]E(f335(f129(x81611,f335(f335(f8(a879,a879,x81611),a330),f335(a332,x81612))),x81613),x81613)+P1(f335(f335(f337(x81611),x81612),f335(f166(x81611),x81613)))
% 59.73/59.66 [8168]P1(f335(f335(f242(f888(f888(x81681,a879),a879)),f257(x81681,x81682)),f257(x81681,x81683)))+~P1(f335(f335(f242(f888(x81681,a879)),x81682),x81683))
% 59.73/59.66 [8213]~P1(f335(f130(x82131),x82133))+P1(f335(f130(x82131),f335(f335(f335(f183(f882(x82131),f882(x82131)),x82132),f161(x82131)),x82133)))
% 59.73/59.66 [8218]~P1(f335(f335(f242(a881),x82182),x82183))+P1(f335(f335(f242(a881),f335(f335(f76(a881),f335(a106,x82181)),x82182)),f335(f335(f76(a881),f335(a106,x82181)),x82183)))
% 59.73/59.66 [8219]~P1(f335(f335(f243(a881),x82192),x82193))+P1(f335(f335(f243(a881),f335(f335(f76(a881),f335(a106,x82191)),x82192)),f335(f335(f76(a881),f335(a106,x82191)),x82193)))
% 59.73/59.66 [8240]P1(f335(f335(f242(f888(f888(x82401,a879),a879)),f335(f311(x82401),x82402)),f335(f311(x82401),x82403)))+~P1(f335(f335(f242(f888(x82401,a879)),x82402),x82403))
% 59.73/59.66 [8309]~E(f335(f313(x83091,x83092,x83093),f252(f888(x83091,a879))),f252(f888(x83092,a879)))+E(f335(f68(x83091,x83092,x83092,x83093),f87(x83091,x83092,f252(f888(x83091,a879)),x83093)),f25(x83092))
% 59.73/59.66 [8403]~P1(f335(f335(f242(f888(x84031,a879)),x84033),x84032))+P1(f335(f335(f242(f888(x84031,a879)),f335(f74(f888(x84031,a879)),x84032)),f335(f74(f888(x84031,a879)),x84033)))
% 59.73/59.66 [8404]~P1(f335(f335(f242(f888(x84041,a879)),x84043),x84042))+P1(f335(f335(f242(f888(x84041,a879)),f335(f74(f888(x84041,a879)),x84042)),f335(f74(f888(x84041,a879)),x84043)))
% 59.73/59.66 [8437]E(f335(f313(a881,a881,f335(f335(f7(a881,a881,a881),f23(a881)),x84371)),f335(f304(a881,x84372),x84373)),f335(f304(a881,f335(f335(f23(a881),x84372),x84371)),f335(f335(f23(a881),x84373),x84371)))+~P1(f335(f335(f243(a881),x84371),x84373))
% 59.73/59.66 [8464]~P83(x84641)+E(f335(f335(f75(x84641),x84642),f335(f135(x84641,x84641,f75(x84641),f2(x84641)),x84643)),f335(f135(x84641,x84641,f75(x84641),x84642),x84643))
% 59.73/59.66 [8540]~P88(x85401)+P1(f335(f335(f242(x85401),f335(f70(x85401),f335(f335(f23(x85401),x85402),x85403))),f335(f335(f75(x85401),f335(f70(x85401),x85402)),f335(f70(x85401),x85403))))
% 59.73/59.66 [8541]~P88(x85411)+P1(f335(f335(f242(x85411),f335(f70(x85411),f335(f335(f75(x85411),x85412),x85413))),f335(f335(f75(x85411),f335(f70(x85411),x85412)),f335(f70(x85411),x85413))))
% 59.73/59.66 [8552]E(f335(f335(f75(a1),f335(f335(f76(a1),x85521),f39(a1,f335(f335(f30(a1),x85522),x85521),x85523))),f39(a1,x85522,x85521)),f39(a1,x85522,f335(f335(f76(a1),x85521),x85523)))+~P1(f335(f335(f243(a1),f2(a1)),x85523))
% 59.73/59.66 [8558]E(f335(f335(f127(x85581),f335(f335(f169(x85581),x85582),x85583)),f335(f335(f144(x85581),f335(f134(x85581),f335(f335(f131(x85581),x85582),x85583))),f107(x85581))),f335(f335(f169(x85581),f335(a106,x85582)),x85583))+~P1(f335(f335(f243(a881),x85582),f335(f189(f882(x85581)),x85583)))
% 59.73/59.66 [8577]E(f335(f276(x85771,f335(f335(f147(x85771,f887(a93,x85771)),f335(f264(a93,x85771),f73(a93))),x85772)),f335(a3,x85773)),f335(f335(f158(x85771),x85772),x85773))+~P1(f335(f335(f243(a881),x85773),f335(f189(f882(x85771)),x85772)))
% 59.73/59.66 [8643]P1(f335(f335(f337(f887(x86431,x86431)),x86432),f335(f335(f291(x86431,x86431,x86431),x86433),f310(x86431,x86433))))+~P1(f335(f335(f337(f887(x86431,x86431)),x86432),x86433))
% 59.73/59.66 [8653]E(f335(f313(x86531,x86532,x86533),f252(f888(x86531,a879))),f252(f888(x86532,a879)))+~E(f335(f68(x86531,x86532,x86532,x86533),f87(x86531,x86532,f252(f888(x86531,a879)),x86533)),f25(x86532))
% 59.73/59.66 [8663]P1(f335(f335(f242(a881),x86631),x86632))+~P1(f335(f335(f242(a881),f335(f335(f76(a881),f335(a106,x86633)),x86631)),f335(f335(f76(a881),f335(a106,x86633)),x86632)))
% 59.73/59.66 [8664]P1(f335(f335(f243(a881),x86641),x86642))+~P1(f335(f335(f243(a881),f335(f335(f76(a881),f335(a106,x86643)),x86641)),f335(f335(f76(a881),f335(a106,x86643)),x86642)))
% 59.73/59.66 [8679]P1(f335(f335(f242(f888(x86791,a879)),x86792),x86793))+~P1(f335(f335(f242(f888(x86791,a879)),f335(f74(f888(x86791,a879)),x86793)),f335(f74(f888(x86791,a879)),x86792)))
% 59.73/59.66 [8697]P1(f335(f130(x86971),x86972))+~P1(f335(f130(x86971),f335(f335(f335(f183(f882(x86971),f882(x86971)),x86973),f161(x86971)),x86972)))
% 59.73/59.66 [8759]E(f335(f313(f887(x87591,x87592),x87592,f267(x87591,x87592)),f335(f166(f887(x87591,x87592)),x87593)),f178(x87591,x87592,f335(f179(x87591,x87592),x87593)))+~P1(f335(f130(x87591),f335(f335(f147(f887(x87591,x87592),x87591),f263(x87591,x87592)),x87593)))
% 59.73/59.66 [8768]E(f335(f288(x87681,x87681,f310(x87681,x87682)),x87683),x87683)+~P1(f335(f335(f242(f888(x87681,a879)),f335(f288(x87681,x87681,x87682),x87683)),x87683))
% 59.73/59.66 [8814]~P106(x88141)+P15(x88141,f335(f129(x88141,f335(f335(f7(x88141,x88141,a879),a332),f335(x88142,x88143))),x88143))
% 59.73/59.66 [8820]~P1(f335(f335(f242(a881),x88201),x88202))+P1(f335(f335(f242(a881),x88201),f335(f135(a881,a881,f75(a881),x88202),x88203)))
% 59.73/59.66 [8898]~P1(f335(f335(f337(f887(x88981,x88981)),x88982),f310(x88981,x88983)))+P1(f335(f335(f337(f887(x88981,x88981)),x88982),f335(f335(f183(f887(x88981,x88981),a879),f597(x88983,x88982,x88981)),x88983)))
% 59.73/59.66 [8986]~P83(x89861)+E(f335(f335(f75(x89861),x89862),f335(f135(x89861,x89861,f335(f7(x89861,x89861,x89861),f75(x89861)),f2(x89861)),f335(f162(x89861),x89863))),f335(f135(x89861,x89861,f75(x89861),x89862),x89863))
% 59.73/59.66 [9258]P52(x92581,x92582,x92583)+P1(f335(f335(f337(f887(x92581,x92582)),f335(f335(f264(x92581,x92582),f599(x92583,x92582,x92581)),f595(x92583,x92582,x92581))),x92583))
% 59.73/59.66 [9259]P52(x92591,x92592,x92593)+P1(f335(f335(f337(f887(x92591,x92592)),f335(f335(f264(x92591,x92592),f599(x92593,x92592,x92591)),f594(x92593,x92592,x92591))),x92593))
% 59.73/59.66 [9327]~P1(f335(f335(f337(f887(x93271,x93271)),x93272),f335(f335(f291(x93271,x93271,x93271),x93273),f310(x93271,x93273))))+P1(f335(f335(f337(f887(x93271,x93271)),x93272),f335(f335(f183(f887(x93271,x93271),a879),f601(x93273,x93272,x93271)),x93273)))
% 59.73/59.66 [9328]~P1(f335(x93281,f335(f335(f158(x93282),x93283),f335(f189(f882(x93282)),f171(x93282,x93281,x93283)))))+~P1(f335(f335(f243(a881),f335(f189(f882(x93282)),f171(x93282,x93281,x93283))),f335(f189(f882(x93282)),x93283)))
% 59.73/59.66 [9416]~P1(f335(f335(f242(f888(x94161,a879)),x94162),x94163))+P1(f335(f335(f242(f888(x94161,a879)),f335(f335(f7(x94161,f888(x94161,a879),a879),f337(x94161)),x94162)),f335(f335(f7(x94161,f888(x94161,a879),a879),f337(x94161)),x94163)))
% 59.73/59.66 [9472]~P1(f335(f335(f337(f887(f888(x94721,a879),f888(x94721,a879))),f335(f335(f264(f888(x94721,a879),f888(x94721,a879)),x94722),x94723)),f309(x94721)))+P1(f335(f335(f243(f888(x94721,a879)),x94722),x94723))
% 59.73/59.66 [9497]P53(x94971,x94972,x94973)+~P1(f335(f335(f337(f887(x94971,x94971)),f335(f335(f264(x94971,x94971),f576(x94973,x94972,x94971)),f575(x94973,x94972,x94971))),x94973))
% 59.73/59.66 [9498]P53(x94981,x94982,x94983)+~P1(f335(f335(f337(f887(x94981,x94981)),f335(f335(f264(x94981,x94981),f575(x94983,x94982,x94981)),f576(x94983,x94982,x94981))),x94983))
% 59.73/59.66 [9534]~P1(f335(f335(f337(f887(f882(x95341),f882(x95341))),f335(f335(f264(f882(x95341),f882(x95341)),x95342),x95342)),f140(x95341,x95343)))+P1(f335(f335(f337(f887(x95341,x95341)),f335(f335(f264(x95341,x95341),f715(x95342,x95343,x95341)),f715(x95342,x95343,x95341))),x95343))
% 59.73/59.66 [9584]P1(f335(f335(f242(f888(x95841,a879)),x95842),x95843))+~P1(f335(f335(f242(f888(x95841,a879)),f335(f335(f7(x95841,f888(x95841,a879),a879),f337(x95841)),x95842)),f335(f335(f7(x95841,f888(x95841,a879),a879),f337(x95841)),x95843)))
% 59.73/59.66 [9665]E(f335(f335(f23(a881),f335(f335(f6(a881,a881),x96651),f335(f250(a881),x96652))),f335(f335(f6(a881,a881),x96653),f335(f250(a881),x96652))),f335(f335(f6(a881,a881),f335(f335(f18(a881,a881,a881),f335(f335(f8(a881,f888(a881,a881),a881),f23(a881)),x96651)),x96653)),f335(f250(a881),x96652)))+~P1(f335(f335(f242(a881),f335(x96653,f497(x96652,x96651,x96653))),f335(x96651,f497(x96652,x96651,x96653))))
% 59.73/59.66 [9977]E(f335(f249(f887(x99771,x99772)),f335(f268(x99771,x99772,a879),f335(f335(f7(x99771,f888(x99772,f885(x99772)),f888(x99772,a879)),f335(f335(f8(f888(f885(x99772),a879),f888(f888(x99772,f885(x99772)),f888(x99772,a879)),x99771),f8(f885(x99772),a879,x99772)),f335(f335(f8(f885(x99772),f888(f885(x99772),a879),x99771),a332),f335(f179(x99771,x99772),x99773)))),f235(x99772)))),f335(f166(f887(x99771,x99772)),x99773))+~P1(f335(f130(x99771),f335(f335(f147(f887(x99771,x99772),x99771),f263(x99771,x99772)),x99773)))
% 59.73/59.66 [5661]~P72(x56611)+E(f335(f335(f23(x56611),f335(f335(f75(x56611),x56612),x56613)),x56613),x56612)
% 59.73/59.66 [5662]~P72(x56621)+E(f335(f335(f75(x56621),f335(f335(f23(x56621),x56622),x56623)),x56623),x56622)
% 59.73/59.66 [5885]~P72(x58851)+E(f335(f335(f75(x58851),x58852),f335(f335(f75(x58851),f335(f74(x58851),x58852)),x58853)),x58853)
% 59.73/59.66 [5968]~P82(x59681)+E(f335(f335(f76(x59681),f335(f335(f254(x59681),x59682),x59683)),x59682),f335(f335(f254(x59681),x59682),f335(a106,x59683)))
% 59.73/59.66 [5969]~P114(x59691)+E(f335(f335(f76(x59691),f335(f335(f254(x59691),x59692),x59693)),x59692),f335(f335(f254(x59691),x59692),f335(a106,x59693)))
% 59.73/59.66 [6180]~P119(x61801)+E(f335(f70(x61801),f335(f335(f254(x61801),f335(f74(x61801),x61802)),x61803)),f335(f70(x61801),f335(f335(f254(x61801),x61802),x61803)))
% 59.73/59.66 [6233]~P82(x62331)+E(f335(f335(f76(x62331),f335(f335(f254(x62331),x62332),x62333)),x62332),f335(f335(f76(x62331),x62332),f335(f335(f254(x62331),x62332),x62333)))
% 59.73/59.66 [6288]E(f335(f335(f23(a93),f335(f335(f75(a93),x62881),x62882)),x62883),f280(x62881,x62882,x62883))+~P1(f335(f335(f243(a93),x62882),x62883))
% 59.73/59.66 [6309]~E(f335(f335(f131(x63091),x63093),x63092),f107(x63091))+P1(f335(f335(f242(a881),f335(f189(f882(x63091)),x63092)),x63093))
% 59.73/59.66 [6447]E(f335(f335(f76(a881),f335(f97(a881),x64471)),f335(f335(f76(a881),f335(f97(a881),x64472)),x64473)),f2(a881))+~P1(f335(f335(f243(a1),x64471),a78))
% 59.73/59.66 [6463]~P66(x64631)+E(f335(f335(f254(x64631),f335(f335(f292(x64631),f73(x64631)),x64632)),x64633),f335(f335(f292(x64631),f73(x64631)),f335(f335(f254(x64631),x64632),x64633)))
% 59.73/59.66 [6540]E(f335(f335(f23(a881),f335(f335(f75(a881),x65401),x65402)),x65403),f335(f335(f23(a881),x65401),f335(f335(f23(a881),x65403),x65402)))+~P1(f335(f335(f242(a881),x65402),x65403))
% 59.73/59.66 [6541]E(f335(f335(f23(a881),f335(f335(f75(a881),x65411),x65412)),x65413),f335(f335(f75(a881),x65411),f335(f335(f23(a881),x65412),x65413)))+~P1(f335(f335(f242(a881),x65413),x65412))
% 59.73/59.66 [6542]E(f335(f335(f23(a881),f335(f335(f75(a881),x65421),x65422)),x65423),f335(f335(f75(a881),x65421),f335(f335(f23(a881),x65422),x65423)))+~P1(f335(f335(f242(a881),x65423),x65422))
% 59.73/59.66 [6579]~P61(x65791)+P1(f335(f335(f242(x65791),f335(f335(f95(x65791),x65792),x65793)),x65793))
% 59.73/59.66 [6580]~P102(x65801)+P1(f335(f335(f242(x65801),f335(f335(f95(x65801),x65802),x65803)),x65803))
% 59.73/59.66 [6581]~P61(x65811)+P1(f335(f335(f242(x65811),f335(f335(f95(x65811),x65812),x65813)),x65812))
% 59.73/59.66 [6582]~P102(x65821)+P1(f335(f335(f242(x65821),f335(f335(f95(x65821),x65822),x65823)),x65822))
% 59.73/59.66 [6583]~P106(x65831)+P1(f335(f335(f242(x65831),f335(f335(f240(x65831),x65832),x65833)),x65833))
% 59.73/59.66 [6584]~P106(x65841)+P1(f335(f335(f242(x65841),f335(f335(f240(x65841),x65842),x65843)),x65842))
% 59.73/59.66 [6597]E(f335(f335(f30(a1),f335(f335(f30(a1),x65971),x65972)),x65973),f335(f335(f30(a1),x65971),f335(f335(f76(a1),x65972),x65973)))+~P1(f335(f335(f243(a1),f2(a1)),x65973))
% 59.73/59.66 [6652]~P114(x66521)+E(f335(f335(f75(x66521),f335(f335(f76(x66521),x66522),x66523)),x66523),f335(f335(f76(x66521),f335(f335(f75(x66521),x66522),f73(x66521))),x66523))
% 59.73/59.66 [6653]~P97(x66531)+E(f335(f335(f76(x66531),f335(f74(x66531),f335(f97(x66531),x66532))),x66533),f335(f335(f76(x66531),f335(f97(x66531),f335(f74(a1),x66532))),x66533))
% 59.73/59.66 [6728]~P83(x67281)+E(f335(f159(x67281),f335(f335(f147(x67282,x67281),f335(f16(x67281,x67282),f2(x67281))),x67283)),f2(x67281))
% 59.73/59.66 [6745]E(f335(f335(f75(a881),f335(f97(a881),x67451)),f335(f335(f75(a881),f335(f97(a881),x67452)),x67453)),f335(f335(f75(a881),f335(f97(a881),x67452)),x67453))+~P1(f335(a193,f335(f97(a1),x67451)))
% 59.73/59.66 [6759]~P5(x67591)+E(f32(x67591,f335(f335(f312(x67591),x67592),f335(f335(f312(x67591),x67593),f188(f888(x67591,a879))))),f335(f335(f95(x67591),x67592),x67593))
% 59.73/59.66 [6760]~P5(x67601)+E(f31(x67601,f335(f335(f312(x67601),x67602),f335(f335(f312(x67601),x67603),f188(f888(x67601,a879))))),f335(f335(f104(x67601),x67602),x67603))
% 59.73/59.66 [6783]E(f335(f335(f169(x67831),x67832),x67833),x67833)+~P1(f335(f335(f242(a881),f335(f189(f882(x67831)),x67833)),x67832))
% 59.73/59.66 [6795]E(f335(f335(f131(x67951),x67952),x67953),f107(x67951))+~P1(f335(f335(f242(a881),f335(f189(f882(x67951)),x67953)),x67952))
% 59.73/59.66 [6796]E(f335(f335(f131(x67961),x67962),x67963),f107(x67961))+~P1(f335(f335(f242(a881),f335(f189(f882(x67961)),x67963)),x67962))
% 59.73/59.66 [6806]E(f335(f335(f75(a881),f335(f335(f23(a881),x68061),x68062)),x68063),f335(f335(f23(a881),f335(f335(f75(a881),x68061),x68063)),x68062))+~P1(f335(f335(f242(a881),x68062),x68061))
% 59.73/59.66 [6807]E(f335(f335(f75(a881),f335(f335(f23(a881),x68071),x68072)),x68073),f335(f335(f23(a881),f335(f335(f75(a881),x68071),x68073)),x68072))+~P1(f335(f335(f242(a881),x68072),x68071))
% 59.73/59.66 [6821]~P1(f335(f335(f243(a881),x68211),x68213))+P1(f335(f335(f243(a881),f335(f335(f23(a881),x68211),x68212)),x68213))
% 59.73/59.66 [6849]~P106(x68491)+E(f164(x68491,x68492,f335(f335(f141(x68491,x68491,f5(x68491)),x68492),x68493)),x68493)
% 59.73/59.66 [6939]E(f335(f335(f23(a881),f335(f335(f75(a881),x69391),x69392)),f335(a106,x69393)),f335(f335(f23(a881),x69391),f335(a106,f335(f335(f23(a881),x69393),x69392))))+~P1(f335(f335(f242(a881),x69392),x69393))
% 59.73/59.66 [6940]~P119(x69401)+P1(f335(f335(f242(x69401),f2(x69401)),f335(f335(f254(x69401),f335(f70(x69401),x69402)),x69403)))
% 59.73/59.66 [6985]P16(x69851,x69852,x69853)+~P1(f335(f335(f242(f888(f880(x69851),a879)),x69853),x69852))
% 59.73/59.66 [7028]~P1(f335(f56(x70281),x70282))+P1(f335(f56(x70281),f335(f335(f23(f888(x70281,a879)),x70282),x70283)))
% 59.73/59.66 [7029]~P1(f335(f56(x70291),x70293))+P1(f335(f56(x70291),f335(f335(f95(f888(x70291,a879)),x70292),x70293)))
% 59.73/59.66 [7030]~P1(f335(f56(x70301),x70302))+P1(f335(f56(x70301),f335(f335(f95(f888(x70301,a879)),x70302),x70303)))
% 59.73/59.66 [7169]~P36(x71691,x71693)+P36(x71691,f335(f335(f95(f888(f887(x71691,x71691),a879)),x71692),x71693))
% 59.73/59.66 [7170]~P36(x71701,x71702)+P36(x71701,f335(f335(f95(f888(f887(x71701,x71701),a879)),x71702),x71703))
% 59.73/59.66 [7290]~P61(x72901)+E(f10(x72901,f335(f166(x72901),f335(f335(f144(x72901),x72902),x72903))),f335(f135(x72901,x72901,f95(x72901),x72902),x72903))
% 59.73/59.66 [7291]~P61(x72911)+E(f13(x72911,f335(f166(x72911),f335(f335(f144(x72911),x72912),x72913))),f335(f135(x72911,x72911,f104(x72911),x72912),x72913))
% 59.73/59.66 [7292]~P106(x72921)+E(f14(x72921,f335(f166(x72921),f335(f335(f144(x72921),x72922),x72923))),f335(f135(x72921,x72921,f241(x72921),x72922),x72923))
% 59.73/59.66 [7293]~P106(x72931)+E(f15(x72931,f335(f166(x72931),f335(f335(f144(x72931),x72932),x72933))),f335(f135(x72931,x72931,f240(x72931),x72932),x72933))
% 59.73/59.66 [7354]~P1(f335(f56(x73541),x73542))+P1(f335(f335(f242(a881),f335(f29(x73541),x73542)),f335(f29(x73541),f335(f335(f312(x73541),x73543),x73542))))
% 59.73/59.66 [7362]E(f335(f335(f104(f888(a881,a879)),f335(f304(a881,x73621),x73622)),f335(f304(a881,x73622),f335(f335(f75(a881),x73622),x73623))),f335(f304(a881,x73621),f335(f335(f75(a881),x73622),x73623)))+~P1(f335(f335(f242(a881),x73621),x73622))
% 59.73/59.66 [7370]P1(f335(f335(f242(a881),x73701),x73702))+~P1(f335(f335(f242(a881),f335(f335(f75(a881),x73703),x73701)),x73702))
% 59.73/59.66 [7371]P1(f335(f335(f242(a881),x73711),x73712))+~P1(f335(f335(f242(a881),f335(f335(f75(a881),x73711),x73713)),x73712))
% 59.73/59.66 [7372]P1(f335(f335(f242(a881),x73721),x73722))+~P1(f335(f335(f242(a881),f335(f335(f75(a881),x73723),x73721)),x73722))
% 59.73/59.66 [7373]P1(f335(f335(f242(a881),x73731),x73732))+~P1(f335(f335(f242(a881),f335(f335(f75(a881),x73731),x73733)),x73732))
% 59.73/59.66 [7374]P1(f335(f335(f243(a881),x73741),x73742))+~P1(f335(f335(f243(a881),f335(f335(f75(a881),x73741),x73743)),x73742))
% 59.73/59.66 [7414]~P106(x74141)+E(f11(x74141,f240(x74141),f335(f166(x74141),f335(f335(f144(x74141),x74142),x74143))),f335(f135(x74141,x74141,f240(x74141),x74142),x74143))
% 59.73/59.66 [7415]~P106(x74151)+E(f12(x74151,f241(x74151),f335(f166(x74151),f335(f335(f144(x74151),x74152),x74153))),f335(f135(x74151,x74151,f241(x74151),x74152),x74153))
% 59.73/59.66 [7419]~E(x74192,f188(f888(f887(x74191,x74191),a879)))+P1(f335(f335(f242(f888(f887(x74191,x74191),a879)),x74192),x74193))
% 59.73/59.66 [7525]E(f335(f335(f104(f888(x75251,a879)),x75252),f335(f335(f23(f888(x75251,a879)),x75253),x75252)),x75253)+~P1(f335(f335(f242(f888(x75251,a879)),x75252),x75253))
% 59.73/59.66 [7526]~P1(f335(f335(f242(a881),x75261),f335(f335(f75(a881),x75263),x75262)))+P1(f335(f335(f242(a881),f335(f335(f23(a881),x75261),x75262)),x75263))
% 59.73/59.66 [7527]~P1(f335(f335(f243(a881),x75271),f335(f335(f23(a881),x75273),x75272)))+P1(f335(f335(f243(a881),f335(f335(f75(a881),x75271),x75272)),x75273))
% 59.73/59.66 [7585]E(x75851,f107(x75852))+E(f335(f134(x75852),f335(f335(f335(f183(f882(x75852),f882(x75852)),x75853),f161(x75852)),x75851)),f335(f335(f158(x75852),x75851),f39(a881,x75853,f335(f189(f882(x75852)),x75851))))
% 59.73/59.66 [7594]E(f335(f335(f312(x75941),x75942),f335(f335(f23(f888(x75941,a879)),x75943),f335(f335(f312(x75941),x75942),f188(f888(x75941,a879))))),x75943)+~P1(f335(f335(f337(x75941),x75942),x75943))
% 59.73/59.66 [7757]P1(f335(f335(f242(a881),x77571),f335(f335(f75(a881),x77572),x77573)))+~P1(f335(f335(f242(a881),f335(f335(f23(a881),x77571),x77573)),x77572))
% 59.73/59.66 [7758]P1(f335(f335(f243(a881),x77581),f335(f335(f23(a881),x77582),x77583)))+~P1(f335(f335(f243(a881),f335(f335(f75(a881),x77581),x77583)),x77582))
% 59.73/59.66 [7781]P1(f335(f56(x77811),x77812))+~P1(f335(f56(x77811),f335(f335(f104(f888(x77811,a879)),x77813),x77812)))
% 59.73/59.66 [7782]P1(f335(f56(x77821),x77822))+~P1(f335(f56(x77821),f335(f335(f104(f888(x77821,a879)),x77822),x77823)))
% 59.73/59.66 [7855]~P43(x78551,x78553)+P1(f335(f335(f337(f887(x78551,x78551)),f335(f335(f264(x78551,x78551),x78552),x78552)),x78553))
% 59.73/59.66 [7997]E(f335(f335(f158(a881),f132(a881,f335(f304(a881,x79971),x79972))),x79973),f335(f335(f75(a881),x79971),x79973))+~P1(f335(f335(f243(a881),f335(f335(f75(a881),x79971),x79973)),x79972))
% 59.73/59.66 [8063]E(f335(f335(f169(a881),x80631),f132(a881,f335(f304(a881,x80632),x80633))),f132(a881,f335(f304(a881,x80632),f335(f335(f75(a881),x80632),x80631))))+~P1(f335(f335(f242(a881),f335(f335(f75(a881),x80632),x80631)),x80633))
% 59.73/59.66 [8116]~P97(x81161)+E(f335(f335(f254(x81161),x81162),f335(f97(a881),f335(f335(f75(a1),x81163),x81163))),f335(f335(f81(x81161,x81161),f335(f335(f254(x81161),x81162),f335(f97(a881),x81163))),f335(f335(f18(x81161,x81161,x81161),f76(x81161)),f5(x81161))))
% 59.73/59.66 [8384]E(f335(f335(f127(x83841),f335(f335(f169(x83841),x83842),x83843)),f335(f335(f144(x83841),f335(f335(f158(x83841),x83843),x83842)),f335(f335(f131(x83841),f335(a106,x83842)),x83843))),x83843)+~P1(f335(f335(f243(a881),x83842),f335(f189(f882(x83841)),x83843)))
% 59.73/59.66 [8391]P1(f335(f335(f242(f888(x83911,a879)),f323(x83911,x83912)),f323(x83911,x83913)))+~P1(f335(f335(f242(f888(x83911,f888(x83911,a879))),x83913),x83912))
% 59.73/59.66 [8393]~P53(x83931,x83932,x83933)+P53(x83931,x83932,f335(f335(f23(f888(f887(x83931,x83931),a879)),x83933),f310(x83931,f188(f888(f887(x83931,x83931),a879)))))
% 59.73/59.66 [8412]P1(f335(f335(f242(f888(x84121,a879)),f324(x84121,x84122)),f324(x84121,x84123)))+~P1(f335(f335(f242(f888(f887(x84121,x84121),a879)),x84123),x84122))
% 59.73/59.66 [8418]~P1(f335(f335(f243(f888(x84181,a879)),x84183),x84182))+P1(f335(f335(f337(x84181),f586(x84182,x84183,x84181)),f335(f335(f23(f888(x84181,a879)),x84182),x84183)))
% 59.73/59.66 [8420]~P124(x84201)+P1(f335(f335(f242(x84201),f2(x84201)),f335(f335(f75(x84201),f335(f335(f76(x84201),x84202),x84202)),f335(f335(f76(x84201),x84203),x84203))))
% 59.73/59.66 [8447]~P97(x84471)+E(f335(f335(f254(x84471),f335(f97(x84471),x84472)),f335(f97(a881),f335(f335(f75(a1),x84473),x84473))),f335(f335(f81(x84471,x84471),f335(f335(f254(x84471),f335(f97(x84471),x84472)),f335(f97(a881),x84473))),f335(f335(f18(x84471,x84471,x84471),f76(x84471)),f5(x84471))))
% 59.73/59.66 [8452]P1(f335(f335(f242(f888(x84521,a879)),f335(f287(x84521),x84522)),f335(f287(x84521),x84523)))+~P1(f335(f335(f242(f888(f887(x84521,x84521),a879)),x84522),x84523))
% 59.73/59.66 [8484]~P47(x84841,x84842)+~P1(f335(f335(f337(f887(x84841,x84841)),f335(f335(f264(x84841,x84841),x84843),x84843)),x84842))
% 59.73/59.66 [8485]~P36(x84851,x84852)+~P1(f335(f335(f337(f887(x84851,x84851)),f335(f335(f264(x84851,x84851),x84853),x84853)),x84852))
% 59.73/59.66 [8486]~P36(x84861,x84862)+~P1(f335(f335(f337(f887(x84861,x84861)),f335(f335(f264(x84861,x84861),x84863),x84863)),x84862))
% 59.73/59.66 [8525]~E(x85252,x85253)+P1(f335(f335(f337(f887(x85251,x85251)),f335(f335(f264(x85251,x85251),x85252),x85253)),f310(x85251,f188(f888(f887(x85251,x85251),a879)))))
% 59.73/59.66 [8542]P1(f335(f335(f242(f888(x85421,a879)),f32(f888(x85421,a879),x85422)),f32(f888(x85421,a879),x85423)))+~P1(f335(f335(f242(f888(f888(x85421,a879),a879)),x85423),x85422))
% 59.73/59.66 [8543]P1(f335(f335(f242(f888(x85431,a879)),f31(f888(x85431,a879),x85432)),f31(f888(x85431,a879),x85433)))+~P1(f335(f335(f242(f888(f888(x85431,a879),a879)),x85432),x85433))
% 59.73/59.66 [8596]~P8(x85961,x85963,x85962)+P1(f335(f335(f242(f888(f887(x85961,x85961),a879)),x85962),f335(f335(f266(x85961,x85961),x85963),f335(f16(f888(x85961,a879),x85961),x85963))))
% 59.73/59.66 [8597]~P46(x85971,x85973,x85972)+P1(f335(f335(f242(f888(f887(x85971,x85971),a879)),x85972),f335(f335(f266(x85971,x85971),x85973),f335(f16(f888(x85971,a879),x85971),x85973))))
% 59.73/59.66 [8644]~P88(x86441)+P1(f335(f335(f242(x86441),f335(f335(f23(x86441),f335(f70(x86441),x86442)),f335(f70(x86441),x86443))),f335(f70(x86441),f335(f335(f23(x86441),x86443),x86442))))
% 59.73/59.66 [8645]~P88(x86451)+P1(f335(f335(f242(x86451),f335(f335(f23(x86451),f335(f70(x86451),x86452)),f335(f70(x86451),x86453))),f335(f70(x86451),f335(f335(f23(x86451),x86452),x86453))))
% 59.73/59.66 [8677]P1(f335(f335(f242(f888(f887(x86771,x86771),a879)),f310(x86771,x86772)),f310(x86771,x86773)))+~P1(f335(f335(f242(f888(f887(x86771,x86771),a879)),x86772),x86773))
% 59.73/59.66 [8777]~P26(x87772,x87771,x87773,f252(f888(x87772,a879)))+E(f335(f68(x87771,x87772,x87772,f87(x87772,x87771,f252(f888(x87772,a879)),x87773)),x87773),f25(x87772))
% 59.73/59.66 [8778]~P26(x87782,x87781,x87783,f252(f888(x87782,a879)))+E(f335(f68(x87781,x87782,x87782,f87(x87782,x87781,f252(f888(x87782,a879)),x87783)),x87783),f25(x87782))
% 59.73/59.66 [8838]P53(x88381,x88382,x88383)+~P53(x88381,x88382,f335(f335(f23(f888(f887(x88381,x88381),a879)),x88383),f310(x88381,f188(f888(f887(x88381,x88381),a879)))))
% 59.73/59.66 [8856]P1(f335(f335(f242(f888(f887(f882(x88561),f882(x88561)),a879)),f150(x88561,x88562)),f150(x88561,x88563)))+~P1(f335(f335(f242(f888(f887(x88561,x88561),a879)),x88562),x88563))
% 59.73/59.66 [8857]P1(f335(f335(f242(f888(f887(f882(x88571),f882(x88571)),a879)),f151(x88571,x88572)),f151(x88571,x88573)))+~P1(f335(f335(f242(f888(f887(x88571,x88571),a879)),x88572),x88573))
% 59.73/59.66 [8876]~P46(x88761,x88763,x88762)+P1(f335(f335(f242(f888(f887(x88761,x88761),a879)),x88762),f335(f335(f291(x88761,x88761,x88761),f335(f289(x88761,x88761),x88762)),x88762)))
% 59.73/59.66 [8908]~P1(f335(f130(x89081),x89083))+P1(f335(f130(x89081),f335(f335(f131(x89081),f335(f189(f882(x89081)),f171(x89081,x89082,x89083))),x89083)))
% 59.73/59.66 [8927]~P1(f335(f130(x89271),x89272))+E(f335(f129(x89271,f335(f335(f7(x89271,f888(x89271,a879),a879),f337(x89271)),f335(f166(x89271),f170(x89271,x89272,x89273)))),x89272),f170(x89271,x89272,x89273))
% 59.73/59.66 [8984]E(x89841,x89842)+~P1(f335(f335(f337(f887(x89843,x89843)),f335(f335(f264(x89843,x89843),x89841),x89842)),f310(x89843,f188(f888(f887(x89843,x89843),a879)))))
% 59.73/59.66 [9067]P1(f335(f335(f337(x90671),x90672),f324(x90671,x90673)))+P1(f335(f335(f337(f887(x90671,x90671)),f335(f335(f264(x90671,x90671),f508(x90673,x90672,x90671)),x90672)),x90673))
% 59.73/59.66 [9068]P1(f335(f335(f337(x90681),x90682),f324(x90681,x90683)))+P1(f335(f335(f337(f887(x90681,x90681)),f335(f335(f264(x90681,x90681),f578(x90683,x90682,x90681)),x90682)),x90683))
% 59.73/59.66 [9069]P1(f335(f335(f337(x90691),x90692),f324(x90691,x90693)))+P1(f335(f335(f337(f887(x90691,x90691)),f335(f335(f264(x90691,x90691),f580(x90693,x90692,x90691)),x90692)),x90693))
% 59.73/59.66 [9104]P26(x91041,x91042,x91043,f252(f888(x91041,a879)))+~E(f335(f68(x91042,x91041,x91041,f87(x91041,x91042,f252(f888(x91041,a879)),x91043)),x91043),f25(x91041))
% 59.73/59.66 [9161]~P1(f335(f335(f337(f882(x91611)),x91613),f154(x91611,x91612)))+P1(f335(f153(x91611,f335(f335(f7(x91611,f888(x91611,a879),a879),f337(x91611)),x91612)),x91613))
% 59.73/59.66 [9183]P1(f335(x91833,x91832))+E(f335(f249(x91831),f335(f335(f18(x91831,a879,a879),f335(f335(f8(a879,f888(a879,a879),x91831),a333),f335(a332,x91832))),x91833)),f188(f888(x91831,a879)))
% 59.73/59.66 [9201]~P88(x92011)+P1(f335(f335(f242(x92011),f335(f70(x92011),f335(f335(f23(x92011),f335(f70(x92011),x92012)),f335(f70(x92011),x92013)))),f335(f70(x92011),f335(f335(f23(x92011),x92012),x92013))))
% 59.73/59.66 [9216]~P1(f335(x92163,x92162))+E(f335(f249(x92161),f335(f335(f18(x92161,a879,a879),f335(f335(f8(a879,f888(a879,a879),x92161),a333),f335(a332,x92162))),x92163)),f335(f335(f312(x92161),x92162),f188(f888(x92161,a879))))
% 59.73/59.66 [9224]~P1(f335(f335(f337(f888(x92241,a879)),x92243),f335(f311(x92241),x92242)))+P1(f335(f257(x92241,f335(f335(f7(x92241,f888(x92241,a879),a879),f337(x92241)),x92242)),x92243))
% 59.73/59.66 [9257]P36(x92571,x92572)+P1(f335(f335(f337(f887(x92571,x92571)),f335(f335(f264(x92571,x92571),f335(f519(x92572,x92571),f335(a106,x92573))),f335(f519(x92572,x92571),x92573))),x92572))
% 59.73/59.66 [9350]~P1(f335(f130(x93501),x93503))+P1(f335(f130(x93501),f335(f129(x93501,f335(f335(f8(a879,a879,x93501),a330),f335(a332,x93502))),x93503)))
% 59.73/59.66 [9396]P1(f335(f335(f337(f882(x93961)),x93962),f154(x93961,x93963)))+~P1(f335(f153(x93961,f335(f335(f7(x93961,f888(x93961,a879),a879),f337(x93961)),x93963)),x93962))
% 59.73/59.66 [9408]P1(f335(f335(f337(f888(x94081,a879)),x94082),f335(f311(x94081),x94083)))+~P1(f335(f257(x94081,f335(f335(f7(x94081,f888(x94081,a879),a879),f337(x94081)),x94083)),x94082))
% 59.73/59.66 [9467]P1(f335(f335(f337(x94671),f335(f276(x94671,x94672),x94673)),f335(f166(x94671),f335(f335(f147(f887(a93,x94671),x94671),f267(a93,x94671)),x94672))))+~P1(f335(f335(f243(a93),x94673),f335(f159(a93),f335(f335(f147(f887(a93,x94671),a93),f263(a93,x94671)),x94672))))
% 59.73/59.66 [9515]P1(f335(f335(f242(f888(f887(f882(x95151),f882(x95151)),a879)),f151(x95151,x95152)),f335(f335(f266(f882(x95151),f882(x95151)),f154(x95151,x95153)),f335(f16(f888(f882(x95151),a879),f882(x95151)),f154(x95151,x95153)))))+~P1(f335(f335(f242(f888(f887(x95151,x95151),a879)),x95152),f335(f335(f266(x95151,x95151),x95153),f335(f16(f888(x95151,a879),x95151),x95153))))
% 59.73/59.66 [9537]P1(f335(f335(f337(x95371),f335(f263(x95371,f887(a93,a93)),f335(f274(x95371,x95372),x95373))),f335(f166(x95371),f335(f335(f147(f887(a93,x95371),x95371),f267(a93,x95371)),x95372))))+~P1(f335(f335(f243(a93),f2(a93)),f335(f159(a93),f335(f335(f147(f887(a93,x95371),a93),f263(a93,x95371)),x95372))))
% 59.73/59.66 [9553]~P1(f335(f335(f242(f888(f887(x95531,x95531),a879)),x95532),f335(f335(f266(x95531,x95531),x95533),f335(f16(f888(x95531,a879),x95531),x95533))))+P1(f335(f335(f242(f888(f887(x95531,x95531),a879)),f335(f335(f291(x95531,x95531,x95531),x95532),f310(x95531,x95532))),f335(f335(f266(x95531,x95531),x95533),f335(f16(f888(x95531,a879),x95531),x95533))))
% 59.73/59.66 [9867]~P36(x98671,x98672)+~P1(f335(f335(f337(f887(x98671,x98671)),f335(f335(f264(x98671,x98671),f335(x98673,f335(a106,f521(x98672,x98671,x98673)))),f335(x98673,f521(x98672,x98671,x98673)))),x98672))
% 59.73/59.66 [9868]~P36(x98681,x98682)+~P1(f335(f335(f337(f887(x98681,x98681)),f335(f335(f264(x98681,x98681),f335(x98683,f335(a106,f590(x98683,x98682,x98681)))),f335(x98683,f590(x98683,x98682,x98681)))),x98682))
% 59.73/59.66 [10114]P1(f335(f335(f242(f888(f887(f888(x101141,a879),f888(x101141,a879)),a879)),f335(f335(f291(f888(x101141,a879),f888(x101141,a879),f888(x101141,a879)),f327(x101141,x101142)),f335(f335(f104(f888(f887(f888(x101141,a879),f888(x101141,a879)),a879)),f327(x101141,x101143)),f335(f335(f312(f887(f888(x101141,a879),f888(x101141,a879))),f335(f335(f264(f888(x101141,a879),f888(x101141,a879)),f188(f888(x101141,a879))),f188(f888(x101141,a879)))),f188(f888(f887(f888(x101141,a879),f888(x101141,a879)),a879)))))),f327(x101141,x101142)))+~P1(f335(f335(f242(f888(f887(x101141,x101141),a879)),f335(f335(f291(x101141,x101141,x101141),x101142),x101143)),x101142))
% 59.73/59.66 [10115]P1(f335(f335(f242(f888(f887(f888(x101151,a879),f888(x101151,a879)),a879)),f335(f335(f291(f888(x101151,a879),f888(x101151,a879),f888(x101151,a879)),f326(x101151,x101152)),f335(f335(f104(f888(f887(f888(x101151,a879),f888(x101151,a879)),a879)),f326(x101151,x101153)),f335(f335(f312(f887(f888(x101151,a879),f888(x101151,a879))),f335(f335(f264(f888(x101151,a879),f888(x101151,a879)),f188(f888(x101151,a879))),f188(f888(x101151,a879)))),f188(f888(f887(f888(x101151,a879),f888(x101151,a879)),a879)))))),f326(x101151,x101152)))+~P1(f335(f335(f242(f888(f887(x101151,x101151),a879)),f335(f335(f291(x101151,x101151,x101151),x101152),x101153)),x101152))
% 59.73/59.66 [7289]~P1(f335(f335(f242(a881),x72892),x72891))+E(f335(f335(f23(a881),f335(a106,f335(f335(f23(a881),x72891),x72892))),x72893),f335(f335(f23(a881),f335(a106,x72891)),f335(f335(f75(a881),x72892),x72893)))
% 59.73/59.66 [7329]~P58(x73291)+E(f335(f335(f75(x73291),f39(x73291,x73292,x73293)),f335(f335(f76(x73291),f335(f335(f30(x73291),x73292),x73293)),x73293)),x73292)
% 59.73/59.66 [7531]E(f335(f335(f76(a881),f335(f97(a881),x75311)),f335(f335(f76(a881),f335(f97(a881),x75312)),x75313)),f335(f335(f76(a881),f335(f97(a881),f335(f335(f76(a1),x75311),x75312))),x75313))+P1(f335(f335(f243(a1),x75311),a78))
% 59.73/59.66 [8006]~P1(f335(f335(f242(a881),x80063),x80062))+P1(f335(f335(f242(a881),x80061),f335(f335(f23(a881),f335(f335(f75(a881),x80062),x80061)),x80063)))
% 59.73/59.66 [8203]~P1(f335(f335(f242(a881),x82031),x82032))+E(f335(f335(f127(a881),f132(a881,f335(f304(a881,x82031),x82032))),f132(a881,f335(f304(a881,x82032),f335(f335(f75(a881),x82032),x82033)))),f132(a881,f335(f304(a881,x82031),f335(f335(f75(a881),x82032),x82033))))
% 59.73/59.66 [8461]~P1(f335(f56(x84611),x84612))+E(f335(a106,f335(f29(x84611),f335(f335(f23(f888(x84611,a879)),x84612),f335(f335(f312(x84611),x84613),f188(f888(x84611,a879)))))),f335(f29(x84611),f335(f335(f312(x84611),x84613),x84612)))
% 59.73/59.66 [8503]~P1(f335(f56(x85031),x85032))+E(f335(f335(f75(a881),f73(a881)),f335(f29(x85031),f335(f335(f23(f888(x85031,a879)),x85032),f335(f335(f312(x85031),x85033),f188(f888(x85031,a879)))))),f335(f29(x85031),f335(f335(f312(x85031),x85033),x85032)))
% 59.73/59.66 [8686]E(f335(f335(f23(a881),f335(f29(x86861),x86862)),f335(f29(x86861),f335(f335(f95(f888(x86861,a879)),x86862),x86863))),f335(f29(x86861),f335(f335(f23(f888(x86861,a879)),x86862),x86863)))+~P1(f335(f56(x86861),f335(f335(f95(f888(x86861,a879)),x86862),x86863)))
% 59.73/59.66 [8922]~P6(f335(x89222,f411(x89222,x89223,x89221)))+E(f335(f94(a1),f335(f335(f9(x89221,a881),f335(f335(f8(a1,a881,x89221),a98),x89222)),x89223)),f335(f335(f9(x89221,a1),x89222),x89223))
% 59.73/59.66 [8923]~P6(f335(x89232,f492(x89232,x89233,x89231)))+E(f335(f94(a1),f335(f335(f6(x89231,a881),f335(f335(f8(a1,a881,x89231),a98),x89232)),x89233)),f335(f335(f6(x89231,a1),x89232),x89233))
% 59.73/59.66 [8969]~P1(f335(f56(x89691),x89693))+P1(f335(f335(f242(a881),f335(f335(f23(a881),f335(f29(x89691),x89692)),f335(f29(x89691),x89693))),f335(f29(x89691),f335(f335(f23(f888(x89691,a879)),x89692),x89693))))
% 59.73/59.66 [8993]P1(f335(f335(f337(x89931),f411(x89932,x89933,x89931)),x89933))+E(f335(f94(a1),f335(f335(f9(x89931,a881),f335(f335(f8(a1,a881,x89931),a98),x89932)),x89933)),f335(f335(f9(x89931,a1),x89932),x89933))
% 59.73/59.66 [8994]P1(f335(f335(f337(x89941),f492(x89942,x89943,x89941)),x89943))+E(f335(f94(a1),f335(f335(f6(x89941,a881),f335(f335(f8(a1,a881,x89941),a98),x89942)),x89943)),f335(f335(f6(x89941,a1),x89942),x89943))
% 59.73/59.66 [9059]E(f80(x90591,f335(f335(f7(x90591,f888(x90591,a879),a879),f337(x90591)),f335(f335(f23(f888(x90591,a879)),x90592),f335(f335(f312(x90591),x90593),f188(f888(x90591,a879)))))),f256(x90591,x90593,x90592))+P1(f335(f335(f242(f888(x90591,a879)),x90592),f335(f335(f312(x90591),x90593),f188(f888(x90591,a879)))))
% 59.73/59.66 [9409]E(f335(f335(f147(f882(x94091),x94091),f335(f335(f7(f882(x94091),a881,x94091),f158(x94091)),x94092)),f335(f129(f882(x94091),f335(f335(f8(a881,a879,f882(x94091)),f335(f243(a881),x94092)),f189(f882(x94091)))),x94093)),f335(f335(f158(f882(x94091)),f173(x94091,x94093)),x94092))+~P1(f335(f335(f243(a881),x94092),f335(f189(f882(f882(x94091))),f173(x94091,x94093))))
% 59.73/59.66 [9487]E(f335(f129(x94871,x94872),x94873),f171(x94871,x94872,x94873))+P1(f335(f335(f337(x94871),f741(x94873,x94872,x94871)),f335(f166(x94871),f335(f335(f131(x94871),f335(f189(f882(x94871)),f171(x94871,x94872,x94873))),x94873))))
% 59.73/59.66 [9624]E(f335(f335(f131(x96241),f335(f189(f882(x96241)),f171(x96241,x96242,x96243))),x96243),f107(x96241))+~P1(f335(x96242,f335(f134(x96241),f335(f335(f131(x96241),f335(f189(f882(x96241)),f171(x96241,x96242,x96243))),x96243))))
% 59.73/59.66 [9721]~P1(f335(f335(f337(f887(x97211,x97211)),x97212),f310(x97211,x97213)))+P1(f335(f335(f337(f887(x97211,x97211)),x97212),f335(f335(f33(a881,f888(f887(x97211,x97211),a879)),f252(f888(a881,a879))),f335(f335(f7(a881,f888(f887(x97211,x97211),a879),f888(f887(x97211,x97211),a879)),f183(f887(x97211,x97211),a879)),x97213))))
% 59.73/59.66 [9782]~P1(f335(f335(f242(f888(x97821,a879)),f335(f335(f33(a881,f888(x97821,a879)),f335(f304(a881,f2(a881)),f486(x97823,x97822,x97821))),x97822)),x97823))+P1(f335(f335(f242(f888(x97821,a879)),f335(f335(f33(a881,f888(x97821,a879)),f252(f888(a881,a879))),x97822)),x97823))
% 59.73/59.66 [9842]~P1(f335(f335(f243(a1),f2(a1)),x98423))+P1(f335(f335(f243(a1),x98421),f335(f335(f75(a1),x98422),f335(f335(f76(a1),f335(f335(f75(a1),f335(f70(a1),f335(f335(f23(a1),x98422),x98421))),f73(a1))),x98423))))
% 59.73/59.66 [9854]~P36(x98541,f335(f335(f104(f888(f887(x98541,x98541),a879)),x98542),x98543))+P36(x98541,f335(f335(f104(f888(f887(x98541,x98541),a879)),f335(f335(f104(f888(f887(x98541,x98541),a879)),f335(f335(f291(x98541,x98541,x98541),x98542),x98542)),f335(f335(f291(x98541,x98541,x98541),x98543),x98542))),x98543))
% 59.73/59.66 [9934]P36(x99341,f335(f335(f104(f888(f887(x99341,x99341),a879)),x99342),x99343))+~P36(x99341,f335(f335(f104(f888(f887(x99341,x99341),a879)),f335(f335(f104(f888(f887(x99341,x99341),a879)),f335(f335(f291(x99341,x99341,x99341),x99342),x99342)),f335(f335(f291(x99341,x99341,x99341),x99343),x99342))),x99343))
% 59.73/59.66 [9490]~P137(x94901)+E(f335(f96(x94901),f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),x94902),x94903)),f188(f888(f887(a881,a881),a879)))))),f335(f335(f23(x94901),f335(f94(x94901),x94902)),f335(f94(x94901),x94903)))
% 59.73/59.66 [9571]P1(f335(x95713,x95712))+E(f335(f249(x95711),f335(f335(f18(x95711,a879,a879),f335(f335(f8(a879,f888(a879,a879),x95711),a333),f335(f335(f7(x95711,x95711,a879),a332),x95712))),x95713)),f188(f888(x95711,a879)))
% 59.73/59.66 [9573]~P1(f335(x95733,x95732))+E(f335(f249(x95731),f335(f335(f18(x95731,a879,a879),f335(f335(f8(a879,f888(a879,a879),x95731),a333),f335(f335(f7(x95731,x95731,a879),a332),x95732))),x95733)),f335(f335(f312(x95731),x95732),f188(f888(x95731,a879))))
% 59.73/59.66 [9821]E(x98211,x98212)+P1(f335(f335(f253(x98213,x98213,f335(f335(f8(f888(x98213,a879),f888(x98213,a879),x98213),f335(f8(a879,a879,x98213),a330)),a332)),x98211),x98212))
% 59.73/59.66 [9912]~E(x99121,x99122)+~P1(f335(f335(f253(x99123,x99123,f335(f335(f8(f888(x99123,a879),f888(x99123,a879),x99123),f335(f8(a879,a879,x99123),a330)),a332)),x99121),x99122))
% 59.73/59.66 [9926]~P1(f335(f56(x99261),x99263))+E(f335(f335(f59(x99261,f888(x99261,a879),f335(f335(f8(f888(x99261,a879),f888(f888(x99261,a879),f888(x99261,a879)),x99261),f335(f7(f888(x99261,a879),f888(x99261,a879),f888(x99261,a879)),f23(f888(x99261,a879)))),f335(f335(f7(x99261,f888(x99261,a879),f888(x99261,a879)),f312(x99261)),f188(f888(x99261,a879))))),x99262),x99263),f335(f335(f23(f888(x99261,a879)),x99262),x99263))
% 59.73/59.66 [9956]~P1(f335(f335(f243(a1),f2(a1)),x99563))+P1(f335(f335(f243(a1),f335(f335(f23(a1),x99561),f335(f335(f76(a1),f335(f335(f75(a1),f335(f70(a1),f335(f335(f23(a1),x99561),x99562))),f73(a1))),x99563))),x99562))
% 59.73/59.66 [10179]~P1(f335(f335(f337(x101791),x101793),f324(x101791,x101792)))+P1(f335(f323(x101791,f335(f335(f7(x101791,f888(f887(x101791,x101791),a879),f888(x101791,a879)),f335(f335(f8(f888(x101791,f888(f888(f887(x101791,x101791),a879),a879)),f888(f888(f887(x101791,x101791),a879),f888(x101791,a879)),x101791),f7(x101791,f888(f887(x101791,x101791),a879),a879)),f335(f335(f8(f888(x101791,f887(x101791,x101791)),f888(x101791,f888(f888(f887(x101791,x101791),a879),a879)),x101791),f335(f8(f887(x101791,x101791),f888(f888(f887(x101791,x101791),a879),a879),x101791),f337(f887(x101791,x101791)))),f264(x101791,x101791)))),x101792)),x101793))
% 59.73/59.66 [10192]P1(f335(f335(f337(x101921),x101922),f324(x101921,x101923)))+~P1(f335(f323(x101921,f335(f335(f7(x101921,f888(f887(x101921,x101921),a879),f888(x101921,a879)),f335(f335(f8(f888(x101921,f888(f888(f887(x101921,x101921),a879),a879)),f888(f888(f887(x101921,x101921),a879),f888(x101921,a879)),x101921),f7(x101921,f888(f887(x101921,x101921),a879),a879)),f335(f335(f8(f888(x101921,f887(x101921,x101921)),f888(x101921,f888(f888(f887(x101921,x101921),a879),a879)),x101921),f335(f8(f887(x101921,x101921),f888(f888(f887(x101921,x101921),a879),a879),x101921),f337(f887(x101921,x101921)))),f264(x101921,x101921)))),x101923)),x101922))
% 59.73/59.66 [9780]~P1(f335(f56(x97801),f335(f249(x97801),x97803)))+P1(f335(f56(x97801),f335(f249(x97801),f335(f335(f18(x97801,a879,a879),f335(f335(f8(a879,f888(a879,a879),x97801),a333),x97802)),x97803))))
% 59.73/59.66 [9781]~P1(f335(f56(x97811),f335(f249(x97811),x97812)))+P1(f335(f56(x97811),f335(f249(x97811),f335(f335(f18(x97811,a879,a879),f335(f335(f8(a879,f888(a879,a879),x97811),a333),x97812)),x97813))))
% 59.73/59.66 [9887]P1(f335(f56(x98871),f335(f249(x98871),x98872)))+~P1(f335(f56(x98871),f335(f249(x98871),f335(f335(f18(x98871,a879,a879),f335(f335(f8(a879,f888(a879,a879),x98871),a334),x98873)),x98872))))
% 59.73/59.66 [9888]P1(f335(f56(x98881),f335(f249(x98881),x98882)))+~P1(f335(f56(x98881),f335(f249(x98881),f335(f335(f18(x98881,a879,a879),f335(f335(f8(a879,f888(a879,a879),x98881),a334),x98882)),x98883))))
% 59.73/59.66 [10165]~P1(f335(f56(x101651),x101652))+P1(f335(f56(f882(x101651)),f335(f249(f882(x101651)),f335(f335(f18(f882(x101651),a879,a879),f335(f335(f8(a879,f888(a879,a879),f882(x101651)),a333),f335(f335(f7(f882(x101651),f888(x101651,a879),a879),f335(f335(f8(f888(x101651,a879),f888(f888(x101651,a879),a879),f882(x101651)),f242(f888(x101651,a879))),f166(x101651))),x101652))),f335(f335(f7(f882(x101651),a881,a879),f335(f335(f8(a881,f888(a881,a879),f882(x101651)),a332),f189(f882(x101651)))),x101653)))))
% 59.73/59.66 [10166]~P1(f335(f56(x101661),x101662))+P1(f335(f56(f882(x101661)),f335(f249(f882(x101661)),f335(f335(f18(f882(x101661),a879,a879),f335(f335(f8(a879,f888(a879,a879),f882(x101661)),a333),f335(f335(f7(f882(x101661),f888(x101661,a879),a879),f335(f335(f8(f888(x101661,a879),f888(f888(x101661,a879),a879),f882(x101661)),f242(f888(x101661,a879))),f166(x101661))),x101662))),f335(f335(f7(f882(x101661),a881,a879),f335(f335(f8(a881,f888(a881,a879),f882(x101661)),f242(a881)),f189(f882(x101661)))),x101663)))))
% 59.73/59.66 [9901]~P114(x99011)+E(f335(f335(f254(x99011),x99012),f335(f335(f76(a881),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x99013)),f335(f335(f76(x99011),f335(f335(f254(x99011),x99012),x99013)),f335(f335(f254(x99011),x99012),x99013)))
% 59.73/59.66 [9937]~P82(x99371)+E(f335(f335(f254(x99371),f335(f335(f254(x99371),x99372),x99373)),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(f335(f254(x99371),x99372),f335(f335(f76(a881),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x99373)))
% 59.73/59.66 [9984]~P137(x99841)+E(f335(f335(f254(x99841),f335(f74(x99841),x99842)),f335(f335(f76(a881),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x99843)),f335(f335(f254(x99841),x99842),f335(f335(f76(a881),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x99843)))
% 59.73/59.66 [10121]~P119(x101211)+P1(f335(f335(f242(x101211),f2(x101211)),f335(f335(f75(x101211),f335(f335(f254(x101211),x101212),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f335(f335(f254(x101211),x101213),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))))
% 59.73/59.66 [9994]~P114(x99941)+E(f335(f335(f254(x99941),x99942),f335(a106,f335(f335(f76(a881),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x99943))),f335(f335(f76(x99941),x99942),f335(f335(f76(x99941),f335(f335(f254(x99941),x99942),x99943)),f335(f335(f254(x99941),x99942),x99943))))
% 59.73/59.66 [10043]~P82(x100431)+E(f335(f335(f76(x100431),x100432),f335(f335(f254(x100431),f335(f335(f254(x100431),x100432),x100433)),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f335(f335(f254(x100431),x100432),f335(a106,f335(f335(f76(a881),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x100433))))
% 59.73/59.66 [10081]~P119(x100811)+P1(f335(f335(f242(x100811),f2(x100811)),f335(f335(f254(x100811),x100812),f335(f335(f76(a881),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x100813))))
% 59.73/59.66 [10144]~P97(x101441)+E(f335(f335(f23(x101441),f335(f335(f75(x101441),f335(f335(f254(x101441),x101442),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f335(f335(f254(x101441),x101443),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))),f335(f335(f76(x101441),f335(f335(f76(x101441),f335(f97(x101441),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x101442)),x101443)),f335(f335(f254(x101441),f335(f335(f23(x101441),x101442),x101443)),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))
% 59.73/59.66 [10145]~P97(x101451)+E(f335(f335(f75(x101451),f335(f335(f75(x101451),f335(f335(f254(x101451),x101452),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f335(f335(f254(x101451),x101453),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))),f335(f335(f76(x101451),f335(f335(f76(x101451),f335(f97(x101451),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x101452)),x101453)),f335(f335(f254(x101451),f335(f335(f75(x101451),x101452),x101453)),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))
% 59.73/59.66 [7799]P26(x77991,x77992,x77993,x77994)+~E(f596(x77994,x77993,x77992,x77991),f600(x77994,x77993,x77992,x77991))
% 59.73/59.66 [8096]P33(x80961,x80962,x80963,x80964,f107(x80962))+~E(x80964,f107(x80961))
% 59.73/59.66 [8097]P33(x80971,x80972,x80973,f107(x80971),x80974)+~E(x80974,f107(x80972))
% 59.73/59.66 [8308]~P26(x83081,f885(x83082),x83084,f177(x83081,x83082,x83084))+P26(x83081,f885(x83082),f180(x83081,x83082,x83083,x83084),f177(x83081,x83082,x83084))
% 59.73/59.66 [8519]~P26(x85191,f885(x85192),f180(x85191,x85192,x85194,x85193),f177(x85191,x85192,x85193))+P26(x85191,f885(x85192),x85193,f177(x85191,x85192,x85193))
% 59.73/59.66 [8634]~P33(x86342,x86343,x86344,x86341,f107(x86343))+E(x86341,f107(x86342))
% 59.73/59.66 [8635]~P33(x86353,x86352,x86354,f107(x86353),x86351)+E(x86351,f107(x86352))
% 59.73/59.66 [5088]~P19(x50883,x50881,x50884)+E(f335(f335(x50881,x50882),x50882),x50882)
% 59.73/59.66 [5337]P1(f335(x53372,x53374))+E(f335(f129(x53371,x53372),f163(x53371,x53373,x53374)),f107(x53371))
% 59.73/59.66 [5372]~E(x53724,f188(f888(x53721,a879)))+E(f335(f313(x53721,x53722,x53723),x53724),f188(f888(x53722,a879)))
% 59.73/59.66 [5373]~E(x53734,f188(f888(x53731,a879)))+E(f335(f313(x53731,x53732,x53733),x53734),f188(f888(x53732,a879)))
% 59.73/59.66 [5613]~P1(f335(x56132,x56134))+E(f335(f129(x56131,x56132),f163(x56131,x56133,x56134)),f163(x56131,x56133,x56134))
% 59.73/59.66 [5641]~E(f335(f313(x56412,x56413,x56414),x56411),f188(f888(x56413,a879)))+E(x56411,f188(f888(x56412,a879)))
% 59.73/59.66 [5642]~E(f335(f313(x56422,x56423,x56424),x56421),f188(f888(x56423,a879)))+E(x56421,f188(f888(x56422,a879)))
% 59.73/59.66 [5928]~P106(x59282)+E(f335(f335(f141(x59281,x59282,x59283),x59284),f107(x59281)),f335(f335(f144(x59281),x59284),f107(x59281)))
% 59.73/59.66 [5964]E(f335(x59641,x59642),f200(x59643))+P1(f335(f335(f337(x59644),x59642),f177(x59644,x59643,x59641)))
% 59.73/59.66 [6282]~E(x62821,f188(f888(x62822,a879)))+~P1(f335(f57(x62822,x62823,x62821),x62824))
% 59.73/59.66 [6303]~P56(x63031,x63033,x63034,x63032)+P1(f335(f56(x63031),x63032))
% 59.73/59.66 [6304]~P56(x63041,x63043,x63042,x63044)+P1(f335(f56(x63041),x63042))
% 59.73/59.66 [6310]~P56(x63102,x63103,x63104,x63101)+~E(x63101,f188(f888(x63102,a879)))
% 59.73/59.66 [6342]~P107(x63421)+E(f335(f335(f95(f888(x63421,a879)),f335(f304(x63421,x63422),x63423)),f305(x63421,x63423,x63424)),f188(f888(x63421,a879)))
% 59.73/59.66 [6370]~P1(f335(f335(x63703,x63704),x63702))+P1(f335(f335(f337(x63701),x63702),f295(x63701,x63703,x63704)))
% 59.73/59.66 [6371]~P1(f335(f335(x63713,x63714),x63712))+P1(f335(f335(f337(x63711),x63712),f296(x63711,x63713,x63714)))
% 59.73/59.66 [6372]~P1(f335(f335(x63723,x63722),x63724))+P1(f335(f335(f337(x63721),x63722),f297(x63721,x63723,x63724)))
% 59.73/59.66 [6373]~P1(f335(f335(x63733,x63732),x63734))+P1(f335(f335(f337(x63731),x63732),f300(x63731,x63733,x63734)))
% 59.73/59.66 [6438]~P50(x64384,x64381,x64382,x64383)+P1(f335(f335(x64381,x64382),x64383))
% 59.73/59.66 [6514]~P107(x65141)+E(f335(f335(f95(f888(x65141,a879)),f308(x65141,x65142,x65143)),f305(x65141,x65143,x65144)),f188(f888(x65141,a879)))
% 59.73/59.66 [6515]~P107(x65151)+E(f335(f335(f95(f888(x65151,a879)),f307(x65151,x65152,x65153)),f308(x65151,x65153,x65154)),f188(f888(x65151,a879)))
% 59.73/59.66 [6516]~P107(x65161)+E(f335(f335(f95(f888(x65161,a879)),f307(x65161,x65162,x65163)),f307(x65161,x65163,x65164)),f188(f888(x65161,a879)))
% 59.73/59.66 [6517]~P107(x65171)+E(f335(f335(f95(f888(x65171,a879)),f305(x65171,x65172,x65173)),f308(x65171,x65173,x65174)),f188(f888(x65171,a879)))
% 59.73/59.66 [6518]~P107(x65181)+E(f335(f335(f95(f888(x65181,a879)),f305(x65181,x65182,x65183)),f307(x65181,x65183,x65184)),f188(f888(x65181,a879)))
% 59.73/59.66 [6556]P1(f335(f335(x65561,x65562),f516(x65562,x65561)))+~P1(f335(f258(x65563,x65564,x65561),x65562))
% 59.73/59.66 [6560]~P50(x65601,x65602,x65603,x65604)+~P1(f335(f335(x65602,x65604),x65603))
% 59.73/59.66 [6610]~E(f335(x66101,x66102),f200(x66103))+~P1(f335(f335(f337(x66104),x66102),f177(x66104,x66103,x66101)))
% 59.73/59.66 [6639]~P106(x66392)+E(f335(f166(x66391),f143(x66391,x66392,x66393,x66394)),f335(f166(x66391),x66394))
% 59.73/59.66 [6691]~P143(x66911)+E(f190(x66911,x66912,f335(a106,x66913),x66914),f190(x66911,x66912,x66913,f335(x66912,x66914)))
% 59.73/59.66 [6754]~P1(f335(f335(f337(x67544),x67543),f295(x67544,x67541,x67542)))+P1(f335(f335(x67541,x67542),x67543))
% 59.73/59.66 [6755]~P1(f335(f335(f337(x67554),x67553),f296(x67554,x67551,x67552)))+P1(f335(f335(x67551,x67552),x67553))
% 59.73/59.66 [6756]~P1(f335(f335(f337(x67564),x67562),f297(x67564,x67561,x67563)))+P1(f335(f335(x67561,x67562),x67563))
% 59.73/59.66 [6757]~P1(f335(f335(f337(x67574),x67572),f300(x67574,x67571,x67573)))+P1(f335(f335(x67571,x67572),x67573))
% 59.73/59.66 [6834]E(f335(f29(f889(x68341,x68342)),f321(x68341,x68342,x68343,x68344)),f2(a881))+P1(f335(f56(x68342),x68344))
% 59.73/59.66 [6835]E(f335(f29(f889(x68351,x68352)),f321(x68351,x68352,x68353,x68354)),f2(a881))+P1(f335(f56(x68351),x68353))
% 59.73/59.66 [7037]~P17(x70374,x70371,x70372)+E(f335(f68(x70371,x70371,x70371,f335(x70372,x70373)),f335(x70372,x70373)),f335(x70372,x70373))
% 59.73/59.66 [7274]E(f283(x72741,x72742,x72743,x72744),f335(f264(f888(a93,f888(a879,f885(f883(x72741)))),f887(a93,a93)),f35(x72741)))+~P1(f335(f335(f242(a93),x72743),f2(a93)))
% 59.73/59.66 [7922]~E(x79222,x79223)+P1(f335(f335(f337(f887(x79221,x79221)),f335(f335(f264(x79221,x79221),x79222),x79223)),f310(x79221,x79224)))
% 59.73/59.66 [7951]~P26(x79511,x79512,x79513,f252(f888(x79511,a879)))+E(f335(f72(x79511,x79512,f252(f888(x79511,a879)),x79513),f335(x79513,x79514)),x79514)
% 59.73/59.66 [7952]~P26(x79521,x79522,x79523,f252(f888(x79521,a879)))+E(f335(f87(x79521,x79522,f252(f888(x79521,a879)),x79523),f335(x79523,x79524)),x79524)
% 59.73/59.66 [8046]~P1(f335(f335(f337(f882(x80461)),f335(f335(f144(x80461),x80464),x80462)),f154(x80461,x80463)))+P1(f335(f335(f337(f882(x80461)),x80462),f154(x80461,x80463)))
% 59.73/59.66 [8047]~P1(f335(f335(f337(f882(x80471)),f335(f335(f127(x80471),x80474),x80472)),f154(x80471,x80473)))+P1(f335(f335(f337(f882(x80471)),x80472),f154(x80471,x80473)))
% 59.73/59.66 [8048]~P1(f335(f335(f337(f882(x80481)),f335(f335(f127(x80481),x80482),x80484)),f154(x80481,x80483)))+P1(f335(f335(f337(f882(x80481)),x80482),f154(x80481,x80483)))
% 59.73/59.66 [8059]~P106(x80591)+P15(x80591,f335(f335(f147(x80592,x80591),x80593),f143(x80592,x80591,x80593,x80594)))
% 59.73/59.66 [8155]P26(x81554,x81553,x81551,x81552)+E(f335(x81551,f596(x81552,x81551,x81553,x81554)),f335(x81551,f600(x81552,x81551,x81553,x81554)))
% 59.73/59.66 [8167]E(f180(x81671,x81672,x81673,x81674),f180(x81671,x81672,x81674,x81673))+~E(f335(f335(f95(f888(x81671,a879)),f177(x81671,x81672,x81673)),f177(x81671,x81672,x81674)),f188(f888(x81671,a879)))
% 59.73/59.66 [8270]~P26(x82702,x82701,x82704,x82703)+P26(x82701,x82702,f72(x82702,x82701,x82703,x82704),f335(f313(x82702,x82701,x82704),x82703))
% 59.73/59.66 [8410]P36(f887(x84102,x84104),f286(x84102,x84104,x84101,x84103))+P1(f335(x84101,f518(x84102,x84103,x84104,x84101)))
% 59.73/59.66 [8526]E(x85261,x85262)+~P1(f335(f335(f337(f887(x85263,x85263)),f335(f335(f264(x85263,x85263),x85261),x85262)),f261(x85263,x85264)))
% 59.73/59.66 [8586]~P1(f335(f56(f889(x85863,x85861)),f321(x85863,x85861,x85864,x85862)))+P1(f335(f56(x85861),x85862))
% 59.73/59.66 [8587]~P1(f335(f56(f889(x85871,x85873)),f321(x85871,x85873,x85872,x85874)))+P1(f335(f56(x85871),x85872))
% 59.73/59.66 [8588]~P1(f335(f56(f889(x85883,x85881)),f321(x85883,x85881,x85884,x85882)))+P1(f335(f56(x85881),x85882))
% 59.73/59.66 [8589]~P1(f335(f56(f889(x85891,x85893)),f321(x85891,x85893,x85892,x85894)))+P1(f335(f56(x85891),x85892))
% 59.73/59.66 [8771]P36(f887(x87711,x87712),f286(x87711,x87712,x87713,x87714))+~P36(x87712,f335(x87714,f518(x87711,x87714,x87712,x87713)))
% 59.73/59.66 [9332]E(f335(f335(f152(x93321,x93322),f697(x93323,x93324,x93322,x93321)),f695(x93323,x93324,x93322,x93321)),x93324)+~P1(f335(f335(f337(f887(f882(x93321),f882(x93321))),f335(f335(f264(f882(x93321),f882(x93321)),x93322),x93324)),f150(x93321,x93323)))
% 59.73/59.66 [9337]~P1(f335(f335(f337(f887(f882(x93371),f882(x93371))),f335(f335(f264(f882(x93371),f882(x93371)),x93372),x93373)),f138(x93371,x93374)))+P1(f335(f335(f337(f887(f882(x93371),f882(x93371))),f335(f335(f264(f882(x93371),f882(x93371)),x93372),x93373)),f140(x93371,x93374)))
% 59.73/59.66 [9443]P1(f335(f56(x94431),x94432))+~P1(f335(f335(f337(f887(f888(x94431,a879),f888(x94431,a879))),f335(f335(f264(f888(x94431,a879),f888(x94431,a879)),x94433),x94432)),f327(x94431,x94434)))
% 59.73/59.66 [9444]P1(f335(f56(x94441),x94442))+~P1(f335(f335(f337(f887(f888(x94441,a879),f888(x94441,a879))),f335(f335(f264(f888(x94441,a879),f888(x94441,a879)),x94442),x94443)),f327(x94441,x94444)))
% 59.73/59.66 [9447]~E(x94471,f188(f888(x94472,a879)))+~P1(f335(f335(f337(f887(f888(x94472,a879),f888(x94472,a879))),f335(f335(f264(f888(x94472,a879),f888(x94472,a879)),x94473),x94471)),f327(x94472,x94474)))
% 59.73/59.66 [10092]P13(x100921,x100922,x100923,x100924)+~P1(f335(f335(f268(x100921,x100921,a879),f335(f335(f7(x100921,f888(x100921,x100922),f888(x100921,a879)),f335(f335(f8(f888(x100922,a879),f888(f888(x100921,x100922),f888(x100921,a879)),x100921),f8(x100922,a879,x100921)),f335(f335(f8(x100922,f888(x100922,a879),x100921),a332),x100924))),x100924)),f555(x100924,x100923,x100922,x100921)))
% 59.73/59.66 [4989]~E(x49894,f107(x49891))+E(f335(f335(f147(x49891,x49892),x49893),x49894),f107(x49892))
% 59.73/59.66 [4990]~E(x49904,f107(x49901))+E(f335(f335(f147(x49901,x49902),x49903),x49904),f107(x49902))
% 59.73/59.66 [4991]~E(x49914,f200(x49911))+E(f335(f335(f201(x49911,x49912),x49913),x49914),f200(x49912))
% 59.73/59.66 [4992]~E(x49922,f107(x49921))+E(f335(f335(f152(x49921,x49922),x49923),x49924),f107(x49921))
% 59.73/59.66 [5225]E(x52251,f107(x52252))+~E(f335(f335(f147(x52252,x52253),x52254),x52251),f107(x52253))
% 59.73/59.66 [5226]E(x52261,f200(x52262))+~E(f335(f335(f201(x52262,x52263),x52264),x52261),f200(x52263))
% 59.73/59.66 [5227]E(x52271,f107(x52272))+~E(f335(f335(f147(x52272,x52273),x52274),x52271),f107(x52273))
% 59.73/59.66 [5228]E(x52281,f107(x52282))+~E(f335(f335(f152(x52282,x52281),x52283),x52284),f107(x52282))
% 59.73/59.66 [5261]E(x52611,x52612)+~E(f335(f335(f127(x52613),x52614),x52611),f335(f335(f127(x52613),x52614),x52612))
% 59.73/59.66 [5262]E(x52621,x52622)+~E(f335(f335(f127(x52623),x52621),x52624),f335(f335(f127(x52623),x52622),x52624))
% 59.73/59.66 [5410]P1(f335(x54103,x54102))+E(f164(x54101,x54102,f335(f129(x54101,x54103),x54104)),f335(f129(x54101,x54103),x54104))
% 59.73/59.66 [5413]~P1(f335(x54132,x54133))+P32(x54131,x54132,f335(f335(f144(x54131),x54133),x54134))
% 59.73/59.66 [5422]E(x54221,x54222)+~E(f132(a881,f335(f304(a881,x54221),x54223)),f335(f335(f144(a881),x54222),x54224))
% 59.73/59.66 [5470]~P27(x54702,x54703)+P27(x54701,f335(f335(f69(x54702,x54701),x54703),x54704))
% 59.73/59.66 [5471]~P36(x54712,x54713)+P36(x54711,f335(f335(f290(x54712,x54711),x54713),x54714))
% 59.73/59.66 [5597]~P32(x55971,x55972,x55974)+P32(x55971,x55972,f335(f335(f144(x55971),x55973),x55974))
% 59.73/59.66 [5598]~P32(x55981,x55982,x55984)+P32(x55981,x55982,f335(f335(f127(x55981),x55983),x55984))
% 59.73/59.66 [5599]~P32(x55991,x55992,x55993)+P32(x55991,x55992,f335(f335(f127(x55991),x55993),x55994))
% 59.73/59.66 [5686]~E(x56861,f107(x56862))+~E(f335(f335(f127(x56862),x56863),f335(f335(f144(x56862),x56864),f107(x56862))),x56861)
% 59.73/59.66 [5711]~P30(x57113,x57111,f335(f335(f144(x57113),x57112),x57114))+P1(f335(x57111,x57112))
% 59.73/59.66 [5721]E(f137(x57211,x57212),x57213)+~E(f335(f335(f127(x57211),x57214),f335(f335(f144(x57211),x57213),f107(x57211))),x57212)
% 59.73/59.66 [5722]E(f108(x57221,x57222),x57223)+~E(f335(f335(f127(x57221),x57223),f335(f335(f144(x57221),x57224),f107(x57221))),x57222)
% 59.73/59.66 [5830]~E(f132(a881,f335(f304(a881,x58301),x58302)),f335(f335(f144(a881),x58303),x58304))+P1(f335(f335(f243(a881),x58301),x58302))
% 59.73/59.66 [5839]P30(x58391,x58392,x58393)+~P30(x58391,x58392,f335(f335(f144(x58391),x58394),x58393))
% 59.73/59.66 [5840]P30(x58401,x58402,x58403)+~P30(x58401,x58402,f335(f335(f127(x58401),x58404),x58403))
% 59.73/59.66 [5841]P30(x58411,x58412,x58413)+~P30(x58411,x58412,f335(f335(f127(x58411),x58413),x58414))
% 59.73/59.66 [5917]~E(f335(f97(a881),x59174),f2(a881))+E(f335(f335(f158(x59171),f335(f335(f144(x59171),x59172),x59173)),f335(f97(a881),x59174)),x59172)
% 59.73/59.66 [6032]E(x60321,f335(f335(f127(x60322),f335(f162(x60322),x60323)),f335(f335(f144(x60322),x60324),f107(x60322))))+~E(f335(f162(x60322),x60321),f335(f335(f144(x60322),x60324),x60323))
% 59.73/59.66 [6201]~P107(x62011)+E(f335(f335(f95(f888(x62011,a879)),f335(f304(x62011,x62012),x62013)),f335(f304(x62011,x62013),x62014)),f188(f888(x62011,a879)))
% 59.73/59.66 [6213]E(f335(f335(f158(x62131),f163(x62131,x62132,x62133)),x62134),x62133)+~P1(f335(f335(f243(a881),x62134),x62132))
% 59.73/59.66 [6240]~P77(x62401)+E(f335(f159(x62401),f335(f335(f147(a1,x62401),x62402),f172(x62403,x62404))),f335(f335(f6(a1,x62401),x62402),f335(f166(a1),f172(x62403,x62404))))
% 59.73/59.66 [6241]~P77(x62411)+E(f335(f335(f6(a1,x62411),x62412),f335(f166(a1),f172(x62413,x62414))),f335(f159(x62411),f335(f335(f147(a1,x62411),x62412),f172(x62413,x62414))))
% 59.73/59.66 [6383]~E(x63832,f335(f335(f127(x63831),f335(f162(x63831),x63834)),f335(f335(f144(x63831),x63833),f107(x63831))))+E(f335(f162(x63831),x63832),f335(f335(f144(x63831),x63833),x63834))
% 59.73/59.66 [6401]~P21(x64012,x64013,x64014,x64011)+E(f335(x64011,f188(f888(x64012,a879))),f25(x64013))
% 59.73/59.66 [6427]~P107(x64271)+E(f335(f335(f95(f888(x64271,a879)),f308(x64271,x64272,x64273)),f335(f304(x64271,x64273),x64274)),f188(f888(x64271,a879)))
% 59.73/59.66 [6640]E(x66401,f188(f888(x66402,a879)))+~E(f321(x66403,x66402,x66404,x66401),f188(f888(f889(x66403,x66402),a879)))
% 59.73/59.66 [6641]E(x66411,f188(f888(x66412,a879)))+~E(f321(x66412,x66413,x66411,x66414),f188(f888(f889(x66412,x66413),a879)))
% 59.73/59.66 [6712]~P106(x67122)+E(f335(f189(f882(x67121)),f143(x67121,x67122,x67123,x67124)),f335(f189(f882(x67121)),x67124))
% 59.73/59.66 [6724]~P1(f335(f259(x67243,x67244,x67241),x67242))+P1(f335(f335(x67241,f517(x67242,x67241)),x67242))
% 59.73/59.66 [6750]E(f335(f97(a881),x67501),f2(a881))+E(f335(f335(f158(x67502),f335(f335(f144(x67502),x67503),x67504)),f335(f97(a881),x67501)),f335(f335(f158(x67502),x67504),f335(f335(f23(a881),f335(f97(a881),x67501)),f73(a881))))
% 59.73/59.66 [6765]~P1(f335(f56(x67652),x67654))+P1(f335(f56(x67651),f335(f313(x67652,x67651,x67653),x67654)))
% 59.73/59.66 [6997]~P26(x69972,x69971,x69973,x69974)+E(f335(f29(x69971),f335(f313(x69972,x69971,x69973),x69974)),f335(f29(x69972),x69974))
% 59.73/59.66 [7016]E(f335(f313(x70161,x70162,x70163),f335(f314(x70161,x70162,x70163),x70164)),x70164)+~E(f335(f313(x70161,x70162,x70163),f252(f888(x70161,a879))),f252(f888(x70162,a879)))
% 59.73/59.66 [7427]~P26(x74271,x74272,x74273,f252(f888(x74271,a879)))+E(f335(f314(x74271,x74272,x74273),f335(f313(x74271,x74272,x74273),x74274)),x74274)
% 59.73/59.66 [7715]E(x77151,x77152)+~P1(f335(f335(f337(x77153),x77151),f335(f166(x77153),f163(x77153,x77154,x77152))))
% 59.73/59.66 [7724]~E(x77241,f2(a881))+~P1(f335(f335(f337(x77242),x77243),f335(f166(x77242),f163(x77242,x77241,x77244))))
% 59.73/59.66 [7760]P1(f335(x77601,x77602))+~P1(f335(f335(f337(x77603),x77602),f335(f166(x77603),f171(x77603,x77601,x77604))))
% 59.73/59.66 [7867]~P1(f335(f335(f337(f882(x78671)),f335(f335(f144(x78671),x78672),x78674)),f154(x78671,x78673)))+P1(f335(f335(f337(x78671),x78672),x78673))
% 59.73/59.66 [8002]~P1(f335(f335(f337(x80021),x80022),f335(f166(x80021),f170(x80021,x80023,x80024))))+P1(f335(f335(f337(x80021),x80022),f335(f166(x80021),x80023)))
% 59.73/59.66 [8003]~P1(f335(f335(f337(x80031),x80032),f335(f166(x80031),f170(x80031,x80033,x80034))))+P1(f335(f335(f337(x80031),x80032),f335(f166(x80031),x80033)))
% 59.73/59.66 [8004]~P1(f335(f335(f337(x80041),x80042),f335(f166(x80041),f164(x80041,x80044,x80043))))+P1(f335(f335(f337(x80041),x80042),f335(f166(x80041),x80043)))
% 59.73/59.66 [8005]~P1(f335(f335(f337(x80051),x80052),f335(f166(x80051),f171(x80051,x80054,x80053))))+P1(f335(f335(f337(x80051),x80052),f335(f166(x80051),x80053)))
% 59.73/59.66 [8015]E(f335(f189(f882(x80151)),x80152),x80153)+~P1(f335(f335(f337(f882(x80151)),x80152),f335(f166(f882(x80151)),f49(x80151,x80153,x80154))))
% 59.73/59.66 [8107]P1(f335(x81073,x81072))+E(f335(f129(x81071,f335(f335(f8(a879,a879,x81071),a330),f335(a332,x81072))),f335(f129(x81071,x81073),x81074)),f335(f129(x81071,x81073),x81074))
% 59.73/59.66 [8220]E(f335(f335(f158(x82201),f171(x82201,x82202,x82203)),x82204),f335(f335(f158(x82201),x82203),x82204))+~P1(f335(f335(f243(a881),x82204),f335(f189(f882(x82201)),f171(x82201,x82202,x82203))))
% 59.73/59.66 [8306]~P77(x83061)+E(f335(f335(f6(a881,x83061),f335(f335(f8(a881,x83061,a881),x83062),a106)),f335(f304(a881,x83063),x83064)),f335(f335(f6(a881,x83061),x83062),f335(f304(a881,f335(a106,x83063)),f335(a106,x83064))))
% 59.73/59.66 [8317]~P77(x83171)+E(f335(f335(f6(a881,x83171),f335(f335(f8(a881,x83171,a881),x83172),a106)),f305(a881,x83173,x83174)),f335(f335(f6(a881,x83171),x83172),f305(a881,f335(a106,x83173),f335(a106,x83174))))
% 59.73/59.66 [8446]~P26(x84461,x84463,x84464,f252(f888(x84461,a879)))+P26(x84461,f888(x84462,x84463),f335(f335(f8(x84463,f888(x84462,x84463),x84461),f16(x84463,x84462)),x84464),f252(f888(x84461,a879)))
% 59.73/59.66 [8531]~P26(x85312,x85311,x85314,x85313)+E(f335(f313(x85311,x85312,f72(x85312,x85311,x85313,x85314)),f335(f313(x85312,x85311,x85314),x85313)),x85313)
% 59.73/59.66 [8590]~P1(f335(f335(f337(f887(x85901,x85901)),f335(f335(f264(x85901,x85901),x85902),x85904)),f261(x85901,x85903)))+P1(f335(f335(f337(x85901),x85902),x85903))
% 59.73/59.66 [8682]E(f335(f335(f335(f67(x86821,f885(x86822)),f335(f16(f885(x86822),x86821),f200(x86822))),x86823),f335(f235(x86822),f836(x86823,x86824,x86822,x86821))),x86824)+~E(f177(x86821,x86822,x86824),f335(f335(f312(x86821),x86823),f188(f888(x86821,a879))))
% 59.73/59.66 [8706]~P26(x87062,x87061,x87063,f252(f888(x87062,a879)))+E(f335(f313(x87061,x87062,f87(x87062,x87061,f252(f888(x87062,a879)),x87063)),f335(f313(x87062,x87061,x87063),x87064)),x87064)
% 59.73/59.66 [8707]~P26(x87072,x87071,x87073,f252(f888(x87072,a879)))+E(f335(f313(x87071,x87072,f87(x87072,x87071,f252(f888(x87072,a879)),x87073)),f335(f313(x87072,x87071,x87073),x87074)),x87074)
% 59.73/59.66 [8810]~E(f335(f335(f6(x88101,a881),x88104),x88103),f335(a106,x88102))+P1(f335(f335(f337(x88101),f567(x88102,x88103,x88104,x88101)),x88103))
% 59.73/59.66 [8830]~E(f335(f335(f6(x88304,a881),x88301),x88303),f335(a106,x88302))+P1(f335(f335(f243(a881),f2(a881)),f335(x88301,f567(x88302,x88303,x88301,x88304))))
% 59.73/59.66 [8841]~P1(f335(f56(x88412),x88414))+P1(f335(f335(f242(a881),f335(f29(x88411),f335(f313(x88412,x88411,x88413),x88414))),f335(f29(x88412),x88414)))
% 59.73/59.66 [8842]E(f335(f335(f264(x88421,x88422),f658(x88423,x88424,x88422,x88421)),f659(x88423,x88424,x88422,x88421)),x88424)+~P1(f335(f335(f337(f887(x88421,x88422)),x88424),f335(f289(x88422,x88421),x88423)))
% 59.73/59.66 [8850]P26(x88501,x88502,x88503,x88504)+P1(f335(f335(f337(x88501),f596(x88504,x88503,x88502,x88501)),x88504))
% 59.73/59.66 [8851]P26(x88511,x88512,x88513,x88514)+P1(f335(f335(f337(x88511),f600(x88514,x88513,x88512,x88511)),x88514))
% 59.73/59.66 [8912]P13(x89121,x89122,x89123,x89124)+P1(f335(f335(f337(f887(x89121,x89121)),f555(x89124,x89123,x89122,x89121)),x89123))
% 59.73/59.66 [8973]P1(f335(x89731,x89732))+~P1(f335(x89731,f335(f335(f264(x89733,x89734),f387(x89734,x89733,x89731)),f388(x89734,x89733,x89731))))
% 59.73/59.66 [8987]E(f335(f189(f882(x89871)),x89872),f335(f189(f882(x89871)),x89873))+~P1(f335(f335(f337(f887(f882(x89871),f882(x89871))),f335(f335(f264(f882(x89871),f882(x89871)),x89872),x89873)),f138(x89871,x89874)))
% 59.73/59.66 [8988]E(f335(f189(f882(x89881)),x89882),f335(f189(f882(x89881)),x89883))+~P1(f335(f335(f337(f887(f882(x89881),f882(x89881))),f335(f335(f264(f882(x89881),f882(x89881)),x89882),x89883)),f150(x89881,x89884)))
% 59.73/59.66 [8989]E(f335(f189(f882(x89891)),x89892),f335(f189(f882(x89891)),x89893))+~P1(f335(f335(f337(f887(f882(x89891),f882(x89891))),f335(f335(f264(f882(x89891),f882(x89891)),x89892),x89893)),f151(x89891,x89894)))
% 59.73/59.66 [8990]E(f335(f189(f882(x89901)),x89902),f335(f189(f882(x89901)),x89903))+~P1(f335(f335(f337(f887(f882(x89901),f882(x89901))),f335(f335(f264(f882(x89901),f882(x89901)),x89902),x89903)),f151(x89901,x89904)))
% 59.73/59.66 [8991]E(f335(f189(f882(x89911)),x89912),f335(f189(f882(x89911)),x89913))+~P1(f335(f335(f337(f887(f882(x89911),f882(x89911))),f335(f335(f264(f882(x89911),f882(x89911)),x89912),x89913)),f151(x89911,x89914)))
% 59.73/59.66 [9063]P1(f335(f335(f242(a881),f148(x90631,x90632,x90633)),f148(x90631,x90634,x90633)))+P1(f335(f335(f337(x90631),f720(x90634,x90632,x90633,x90631)),f335(f166(x90631),x90633)))
% 59.73/59.66 [9066]E(f335(f189(f882(x90661)),x90662),f335(f189(f882(x90661)),x90663))+~P1(f335(f335(f337(f887(f882(x90661),f882(x90661))),f335(f335(f264(f882(x90661),f882(x90661)),x90662),x90663)),f310(f882(x90661),f150(x90661,x90664))))
% 59.73/59.66 [9306]~P26(x93061,x93062,x93063,x93064)+~P1(f335(f335(f243(a881),f335(f29(x93062),f335(f313(x93061,x93062,x93063),x93064))),f335(f29(x93061),x93064)))
% 59.73/59.66 [9348]~P1(f335(f335(f337(f887(f882(x93481),f882(x93481))),f335(f335(f264(f882(x93481),f882(x93481)),x93482),x93483)),f150(x93481,x93484)))+P1(f335(f335(f337(f887(f882(x93481),f882(x93481))),f335(f335(f264(f882(x93481),f882(x93481)),x93482),x93483)),f151(x93481,f310(x93481,x93484))))
% 59.73/59.66 [9352]~P1(f335(f335(f337(f887(f882(x93521),f882(x93521))),f335(f335(f264(f882(x93521),f882(x93521)),x93522),x93523)),f151(x93521,x93524)))+P1(f335(f335(f337(f887(f882(x93521),f882(x93521))),f335(f335(f264(f882(x93521),f882(x93521)),x93522),x93523)),f310(f882(x93521),f150(x93521,x93524))))
% 59.73/59.66 [9369]P1(f335(f335(f337(f887(x93691,x93691)),f335(f335(f264(x93691,x93691),x93692),x93693)),f310(x93691,x93694)))+~P1(f335(f335(f337(f887(x93691,x93691)),f335(f335(f264(x93691,x93691),x93692),x93693)),f335(f335(f291(x93691,x93691,x93691),x93694),f310(x93691,x93694))))
% 59.73/59.66 [9554]E(f335(f335(f127(x95541),f707(x95542,x95543,x95544,x95541)),f335(f335(f144(x95541),f705(x95542,x95543,x95544,x95541)),f708(x95542,x95543,x95544,x95541))),x95544)+~P1(f335(f335(f337(f887(f882(x95541),f882(x95541))),f335(f335(f264(f882(x95541),f882(x95541)),x95544),x95543)),f150(x95541,x95542)))
% 59.73/59.66 [9555]E(f335(f335(f127(x95551),f707(x95552,x95553,x95554,x95551)),f335(f335(f144(x95551),f706(x95552,x95553,x95554,x95551)),f708(x95552,x95553,x95554,x95551))),x95553)+~P1(f335(f335(f337(f887(f882(x95551),f882(x95551))),f335(f335(f264(f882(x95551),f882(x95551)),x95554),x95553)),f150(x95551,x95552)))
% 59.73/59.66 [9631]P1(f335(f335(f337(f887(x96311,x96311)),f335(f335(f264(x96311,x96311),x96312),f615(x96313,x96314,x96312,x96311))),f310(x96311,x96313)))+~P1(f335(f335(f337(f887(x96311,x96311)),f335(f335(f264(x96311,x96311),x96312),x96314)),f335(f335(f291(x96311,x96311,x96311),x96313),f310(x96311,x96313))))
% 59.73/59.66 [9703]P1(f335(f335(f242(a881),f148(x97031,x97032,x97033)),f148(x97031,x97034,x97033)))+~P1(f335(f335(f243(a881),f335(x97032,f720(x97034,x97032,x97033,x97031))),f335(x97034,f720(x97034,x97032,x97033,x97031))))
% 59.73/59.66 [9776]P1(f335(f335(f337(f887(x97761,x97761)),f335(f335(f264(x97761,x97761),f607(x97762,x97763,x97764,x97761)),x97763)),f310(x97761,x97762)))+~P1(f335(f335(f337(f887(x97761,x97761)),f335(f335(f264(x97761,x97761),x97764),x97763)),f335(f335(f291(x97761,x97761,x97761),x97762),f310(x97761,x97762))))
% 59.73/59.66 [5243]~E(x52432,x52433)+E(f164(x52431,x52432,f335(f335(f144(x52431),x52433),x52434)),x52434)
% 59.73/59.66 [5254]~E(x52542,f2(a881))+E(f335(f335(f169(x52541),x52542),f335(f335(f144(x52541),x52543),x52544)),f107(x52541))
% 59.73/59.66 [5365]P1(f335(x53652,x53653))+E(f171(x53651,x53652,f335(f335(f144(x53651),x53653),x53654)),f107(x53651))
% 59.73/59.66 [5433]~P85(x54332)+E(f335(f335(f74(f888(x54331,x54332)),x54333),x54334),f335(f74(x54332),f335(x54333,x54334)))
% 59.73/59.66 [5434]~P85(x54342)+E(f335(f335(f74(f888(x54341,x54342)),x54343),x54344),f335(f74(x54342),f335(x54343,x54344)))
% 59.73/59.66 [5446]~E(x54462,f2(a881))+E(f335(f335(f131(x54461),x54462),f335(f335(f144(x54461),x54463),x54464)),f335(f335(f144(x54461),x54463),x54464))
% 59.73/59.66 [5447]P1(f335(x54472,x54473))+E(f335(f129(x54471,x54472),f335(f335(f144(x54471),x54473),x54474)),f335(f129(x54471,x54472),x54474))
% 59.73/59.66 [5580]~E(x55802,x55804)+P1(f335(f335(f335(f312(x55801),x55802),x55803),x55804))
% 59.73/59.66 [5588]E(x55881,f107(x55882))+E(f137(x55883,f335(f335(f147(x55882,x55883),x55884),x55881)),f335(x55884,f137(x55882,x55881)))
% 59.73/59.66 [5602]~E(x56021,f58(x56022,x56024))+E(f335(x56021,f335(f335(f312(x56022),x56023),f188(f888(x56022,a879)))),x56023)
% 59.73/59.66 [5618]~E(f335(f97(a881),x56182),f2(a881))+E(f335(f335(f169(x56181),f335(f97(a881),x56182)),f335(f335(f144(x56181),x56183),x56184)),f107(x56181))
% 59.73/59.66 [5637]E(x56371,f107(x56372))+E(f335(f134(x56373),f335(f335(f147(x56372,x56373),x56374),x56371)),f335(x56374,f335(f134(x56372),x56371)))
% 59.73/59.66 [5741]~P1(f335(x57413,x57414))+P1(f335(f335(f335(f312(x57411),x57412),x57413),x57414))
% 59.73/59.66 [5842]~E(f335(f97(a881),x58422),f2(a881))+E(f335(f335(f131(x58421),f335(f97(a881),x58422)),f335(f335(f144(x58421),x58423),x58424)),f335(f335(f144(x58421),x58423),x58424))
% 59.73/59.66 [5857]~P20(x58572,x58574,x58571)+E(f335(x58571,f335(f335(f312(x58572),x58573),f188(f888(x58572,a879)))),x58573)
% 59.73/59.66 [5881]~E(x58812,x58813)+P1(f335(f335(f337(x58811),x58812),f335(f335(f312(x58811),x58813),x58814)))
% 59.73/59.66 [5882]~E(x58822,x58823)+P1(f335(f335(f337(x58821),x58822),f335(f335(f312(x58821),x58823),x58824)))
% 59.73/59.66 [5886]~P60(x58861)+E(f335(f335(f104(x58861),x58862),f335(f335(f104(x58861),x58863),x58864)),f335(f335(f104(x58861),x58863),f335(f335(f104(x58861),x58862),x58864)))
% 59.73/59.66 [5887]~P60(x58871)+E(f335(f335(f104(x58871),x58872),f335(f335(f104(x58871),x58873),x58874)),f335(f335(f104(x58871),x58873),f335(f335(f104(x58871),x58872),x58874)))
% 59.73/59.66 [5888]~P61(x58881)+E(f335(f335(f104(x58881),x58882),f335(f335(f104(x58881),x58883),x58884)),f335(f335(f104(x58881),x58883),f335(f335(f104(x58881),x58882),x58884)))
% 59.73/59.66 [5889]~P61(x58891)+E(f335(f335(f95(x58891),x58892),f335(f335(f95(x58891),x58893),x58894)),f335(f335(f95(x58891),x58893),f335(f335(f95(x58891),x58892),x58894)))
% 59.73/59.66 [5890]~P102(x58901)+E(f335(f335(f95(x58901),x58902),f335(f335(f95(x58901),x58903),x58904)),f335(f335(f95(x58901),x58903),f335(f335(f95(x58901),x58902),x58904)))
% 59.73/59.66 [5891]~P102(x58911)+E(f335(f335(f95(x58911),x58912),f335(f335(f95(x58911),x58913),x58914)),f335(f335(f95(x58911),x58913),f335(f335(f95(x58911),x58912),x58914)))
% 59.73/59.66 [5892]~P114(x58921)+E(f335(f335(f76(x58921),x58922),f335(f335(f76(x58921),x58923),x58924)),f335(f335(f76(x58921),x58923),f335(f335(f76(x58921),x58922),x58924)))
% 59.73/59.66 [5893]~P114(x58931)+E(f335(f335(f75(x58931),x58932),f335(f335(f75(x58931),x58933),x58934)),f335(f335(f75(x58931),x58933),f335(f335(f75(x58931),x58932),x58934)))
% 59.73/59.66 [5894]~P106(x58941)+E(f335(f335(f240(x58941),x58942),f335(f335(f240(x58941),x58943),x58944)),f335(f335(f240(x58941),x58943),f335(f335(f240(x58941),x58942),x58944)))
% 59.73/59.66 [5895]~P106(x58951)+E(f335(f335(f240(x58951),x58952),f335(f335(f240(x58951),x58953),x58954)),f335(f335(f240(x58951),x58953),f335(f335(f240(x58951),x58952),x58954)))
% 59.73/59.66 [5896]~P106(x58961)+E(f335(f335(f241(x58961),x58962),f335(f335(f241(x58961),x58963),x58964)),f335(f335(f241(x58961),x58963),f335(f335(f241(x58961),x58962),x58964)))
% 59.73/59.66 [5897]~P106(x58971)+E(f335(f335(f241(x58971),x58972),f335(f335(f241(x58971),x58973),x58974)),f335(f335(f241(x58971),x58973),f335(f335(f241(x58971),x58972),x58974)))
% 59.73/59.66 [5902]E(x59021,x59022)+E(f164(x59023,x59021,f335(f335(f144(x59023),x59022),x59024)),f335(f335(f144(x59023),x59022),f164(x59023,x59021,x59024)))
% 59.73/59.66 [5915]~P1(f335(x59152,x59153))+E(f335(f129(x59151,x59152),f335(f335(f144(x59151),x59153),x59154)),f335(f335(f144(x59151),x59153),f335(f129(x59151,x59152),x59154)))
% 59.73/59.66 [6007]~E(x60074,f188(f888(x60071,a879)))+E(f335(f313(x60071,x60072,f335(f16(x60072,x60071),x60073)),x60074),f188(f888(x60072,a879)))
% 59.73/59.66 [6052]~P1(f335(x60522,x60523))+E(f171(x60521,x60522,f335(f335(f144(x60521),x60523),x60524)),f335(f335(f144(x60521),x60523),f171(x60521,x60522,x60524)))
% 59.73/59.66 [6112]E(x61121,f188(f888(x61122,a879)))+E(f335(f335(f33(x61122,f888(x61123,a879)),x61121),f335(f16(f888(x61123,a879),x61122),x61124)),x61124)
% 59.73/59.66 [6113]E(x61131,f188(f888(x61132,a879)))+E(f335(f335(f34(x61132,f888(x61133,a879)),x61131),f335(f16(f888(x61133,a879),x61132),x61134)),x61134)
% 59.73/59.66 [6122]~E(x61224,f188(f888(x61222,a879)))+E(f335(f335(f266(x61221,x61222),x61223),f335(f16(f888(x61222,a879),x61221),x61224)),f188(f888(f887(x61221,x61222),a879)))
% 59.73/59.66 [6123]~E(x61233,f188(f888(x61231,a879)))+E(f335(f335(f266(x61231,x61232),x61233),f335(f16(f888(x61232,a879),x61231),x61234)),f188(f888(f887(x61231,x61232),a879)))
% 59.73/59.66 [6171]E(x61711,f2(a881))+E(f335(f335(f131(x61712),x61711),f335(f335(f144(x61712),x61713),x61714)),f335(f335(f131(x61712),f335(f335(f23(a881),x61711),f73(a881))),x61714))
% 59.73/59.66 [6195]E(x61951,f188(f888(x61952,a879)))+E(f335(f313(x61952,x61953,f335(f16(x61953,x61952),x61954)),x61951),f335(f335(f312(x61953),x61954),f188(f888(x61953,a879))))
% 59.73/59.66 [6198]E(f335(f314(x61981,x61982,f335(f16(x61982,x61981),x61983)),x61984),f188(f888(x61981,a879)))+P1(f335(f335(f337(x61982),x61983),x61984))
% 59.73/59.66 [6266]~E(x62663,f188(f888(x62661,a879)))+E(f335(f335(f33(x62661,f888(x62662,a879)),x62663),f335(f16(f888(x62662,a879),x62661),x62664)),f188(f888(x62662,a879)))
% 59.73/59.66 [6267]~E(x62673,f188(f888(x62671,a879)))+E(f335(f335(f34(x62671,f888(x62672,a879)),x62673),f335(f16(f888(x62672,a879),x62671),x62674)),f252(f888(x62672,a879)))
% 59.73/59.66 [6269]~P58(x62691)+E(f39(x62691,f335(f335(f76(x62691),x62692),x62693),f335(f335(f76(x62691),x62692),x62694)),f335(f335(f76(x62691),x62692),f39(x62691,x62693,x62694)))
% 59.73/59.66 [6437]E(f335(f314(x64371,x64372,f335(f16(x64372,x64371),x64373)),x64374),f252(f888(x64371,a879)))+~P1(f335(f335(f337(x64372),x64373),x64374))
% 59.73/59.66 [6459]~P1(f335(f335(f337(x64591),x64592),x64594))+P1(f335(f335(f337(x64591),x64592),f335(f335(f312(x64591),x64593),x64594)))
% 59.73/59.66 [6460]~P1(f335(f335(f337(x64601),x64602),x64604))+P1(f335(f335(f337(x64601),x64602),f335(f335(f312(x64601),x64603),x64604)))
% 59.73/59.66 [6461]~P1(f335(f335(f337(x64611),x64612),x64614))+P1(f335(f335(f337(x64611),x64612),f335(f335(f312(x64611),x64613),x64614)))
% 59.73/59.66 [6466]P1(f335(x64661,x64662))+~P1(f335(f153(x64663,x64661),f335(f335(f144(x64663),x64662),x64664)))
% 59.73/59.66 [6475]~E(x64753,f335(f335(f23(a881),f335(f189(f882(x64751)),x64752)),f73(a881)))+E(f108(x64751,f335(f335(f152(x64751,x64752),x64753),x64754)),f108(x64751,x64752))
% 59.73/59.66 [6493]~P106(x64931)+E(f335(f335(f95(f888(x64931,a879)),f335(f303(x64931),x64932)),f305(x64931,x64933,x64934)),f305(x64931,x64933,f335(f335(f240(x64931),x64932),x64934)))
% 59.73/59.66 [6494]~P106(x64941)+E(f335(f335(f95(f888(x64941,a879)),f335(f251(x64941),x64942)),f305(x64941,x64943,x64944)),f305(x64941,f335(f335(f241(x64941),x64942),x64943),x64944))
% 59.73/59.66 [6508]E(f335(f335(f95(f888(x65081,a879)),x65082),f335(f335(f312(x65081),x65083),x65084)),f335(f335(f95(f888(x65081,a879)),x65082),x65084))+P1(f335(f335(f337(x65081),x65083),x65082))
% 59.73/59.66 [6509]E(f335(f335(f95(f888(x65091,a879)),x65092),f335(f335(f312(x65091),x65093),x65094)),f335(f335(f95(f888(x65091,a879)),x65092),x65094))+P1(f335(f335(f337(x65091),x65093),x65092))
% 59.73/59.66 [6521]E(f164(x65211,x65212,f335(f335(f127(x65211),x65213),x65214)),f335(f335(f127(x65211),x65213),f164(x65211,x65212,x65214)))+P1(f335(f335(f337(x65211),x65212),f335(f166(x65211),x65213)))
% 59.73/59.66 [6526]~P82(x65261)+E(f335(f335(f76(x65261),f335(f335(f254(x65261),x65262),x65263)),f335(f335(f254(x65261),x65262),x65264)),f335(f335(f254(x65261),x65262),f335(f335(f75(a881),x65263),x65264)))
% 59.73/59.66 [6527]~P114(x65271)+E(f335(f335(f76(x65271),f335(f335(f254(x65271),x65272),x65273)),f335(f335(f254(x65271),x65272),x65274)),f335(f335(f254(x65271),x65272),f335(f335(f75(a881),x65273),x65274)))
% 59.73/59.66 [6565]~P100(x65651)+E(f335(f335(f95(x65651),f335(f335(f104(x65651),x65652),x65653)),f335(f335(f104(x65651),x65652),x65654)),f335(f335(f104(x65651),x65652),f335(f335(f95(x65651),x65653),x65654)))
% 59.73/59.66 [6566]~P100(x65661)+E(f335(f335(f104(x65661),f335(f335(f95(x65661),x65662),x65663)),f335(f335(f95(x65661),x65662),x65664)),f335(f335(f95(x65661),x65662),f335(f335(f104(x65661),x65663),x65664)))
% 59.73/59.66 [6567]~P114(x65671)+E(f335(f335(f75(x65671),f335(f335(f76(x65671),x65672),x65673)),f335(f335(f76(x65671),x65672),x65674)),f335(f335(f76(x65671),x65672),f335(f335(f75(x65671),x65673),x65674)))
% 59.73/59.66 [6568]~P106(x65681)+E(f335(f335(f241(x65681),f335(f335(f240(x65681),x65682),x65683)),f335(f335(f240(x65681),x65682),x65684)),f335(f335(f240(x65681),x65682),f335(f335(f241(x65681),x65683),x65684)))
% 59.73/59.66 [6569]~P106(x65691)+E(f335(f335(f240(x65691),f335(f335(f241(x65691),x65692),x65693)),f335(f335(f241(x65691),x65692),x65694)),f335(f335(f241(x65691),x65692),f335(f335(f240(x65691),x65693),x65694)))
% 59.73/59.66 [6604]~P58(x66041)+E(f39(x66041,f335(f335(f76(x66041),x66042),x66043),f335(f335(f76(x66041),x66044),x66043)),f335(f335(f76(x66041),f39(x66041,x66042,x66044)),x66043))
% 59.73/59.66 [6607]~E(f335(f189(f882(x66071)),x66073),f335(f189(f882(x66072)),x66074))+E(f335(f335(f147(f887(x66071,x66072),x66072),f267(x66071,x66072)),f335(f335(f175(x66071,x66072),x66073),x66074)),x66074)
% 59.73/59.66 [6608]~E(f335(f189(f882(x66081)),x66083),f335(f189(f882(x66082)),x66084))+E(f335(f335(f147(f887(x66081,x66082),x66081),f263(x66081,x66082)),f335(f335(f175(x66081,x66082),x66083),x66084)),x66083)
% 59.73/59.66 [6614]P1(f335(f153(x66141,x66142),x66143))+~P1(f335(f153(x66141,x66142),f335(f335(f144(x66141),x66144),x66143)))
% 59.73/59.66 [6615]P1(f335(f153(x66151,x66152),x66153))+~P1(f335(f153(x66151,x66152),f335(f335(f127(x66151),x66154),x66153)))
% 59.73/59.66 [6616]P1(f335(f153(x66161,x66162),x66163))+~P1(f335(f153(x66161,x66162),f335(f335(f127(x66161),x66163),x66164)))
% 59.73/59.66 [6621]~P59(x66211)+E(f39(x66211,f335(f335(f23(x66211),x66212),f39(x66211,x66213,x66214)),x66214),f39(x66211,f335(f335(f23(x66211),x66212),x66213),x66214))
% 59.73/59.66 [6622]~P58(x66221)+E(f39(x66221,f335(f335(f76(x66221),x66222),f39(x66221,x66223,x66224)),x66224),f39(x66221,f335(f335(f76(x66221),x66222),x66223),x66224))
% 59.73/59.66 [6623]~P58(x66231)+E(f39(x66231,f335(f335(f75(x66231),x66232),f39(x66231,x66233,x66234)),x66234),f39(x66231,f335(f335(f75(x66231),x66232),x66233),x66234))
% 59.73/59.66 [6624]~P58(x66241)+E(f39(x66241,f335(f335(f75(x66241),x66242),f39(x66241,x66243,x66244)),x66244),f39(x66241,f335(f335(f75(x66241),x66242),x66243),x66244))
% 59.73/59.66 [6704]~P106(x67041)+E(f335(f335(f95(f888(x67041,a879)),f305(x67041,x67042,x67043)),f335(f303(x67041),x67044)),f305(x67041,x67042,f335(f335(f240(x67041),x67043),x67044)))
% 59.73/59.66 [6705]~P106(x67051)+E(f335(f335(f95(f888(x67051,a879)),f305(x67051,x67052,x67053)),f335(f251(x67051),x67054)),f305(x67051,f335(f335(f241(x67051),x67052),x67054),x67053))
% 59.73/59.66 [6708]~E(f335(f189(f882(x67081)),x67083),f335(f189(f882(x67082)),x67084))+E(f335(f335(f175(x67081,x67082),f335(f162(x67081),x67083)),f335(f162(x67082),x67084)),f335(f162(f887(x67081,x67082)),f335(f335(f175(x67081,x67082),x67083),x67084)))
% 59.73/59.66 [6720]E(x67201,f335(f335(f23(a881),f335(f189(f882(x67202)),x67203)),f73(a881)))+E(f108(x67202,f335(f335(f152(x67202,x67203),x67201),x67204)),f335(f335(f152(x67202,f108(x67202,x67203)),x67201),x67204))
% 59.73/59.66 [6736]~P1(f335(f130(x67362),x67364))+P1(f335(f130(f887(x67361,x67362)),f335(f335(f175(x67361,x67362),x67363),x67364)))
% 59.73/59.66 [6737]~P1(f335(f130(x67371),x67373))+P1(f335(f130(f887(x67371,x67372)),f335(f335(f175(x67371,x67372),x67373),x67374)))
% 59.73/59.66 [7000]E(f335(f335(f30(a881),x70001),x70002),x70003)+~P1(f335(f42(x70001,x70002),f335(f335(f264(a881,a881),x70003),x70004)))
% 59.73/59.66 [7024]E(f39(a881,x70241,x70242),x70243)+~P1(f335(f42(x70241,x70242),f335(f335(f264(a881,a881),x70244),x70243)))
% 59.73/59.66 [7027]P1(f335(f130(x70271),x70272))+~P1(f335(f130(x70273),f335(f335(f147(x70271,x70273),x70274),x70272)))
% 59.73/59.66 [7111]E(f164(x71111,x71112,f335(f335(f127(x71111),x71113),x71114)),f335(f335(f127(x71111),f164(x71111,x71112,x71113)),x71114))+~P1(f335(f335(f337(x71111),x71112),f335(f166(x71111),x71113)))
% 59.73/59.66 [7174]E(f335(f97(a881),x71741),f2(a881))+E(f335(f335(f131(x71742),f335(f97(a881),x71741)),f335(f335(f144(x71742),x71743),x71744)),f335(f335(f131(x71742),f335(f335(f23(a881),f335(f97(a881),x71741)),f73(a881))),x71744))
% 59.73/59.66 [7202]~P59(x72021)+E(f39(x72021,f335(f335(f23(x72021),f39(x72021,x72022,x72023)),x72024),x72023),f39(x72021,f335(f335(f23(x72021),x72022),x72024),x72023))
% 59.73/59.66 [7203]~P58(x72031)+E(f39(x72031,f335(f335(f76(x72031),f39(x72031,x72032,x72033)),x72034),x72033),f39(x72031,f335(f335(f76(x72031),x72032),x72034),x72033))
% 59.73/59.66 [7204]~P58(x72041)+E(f39(x72041,f335(f335(f75(x72041),f39(x72041,x72042,x72043)),x72044),x72043),f39(x72041,f335(f335(f75(x72041),x72042),x72044),x72043))
% 59.73/59.66 [7205]~P58(x72051)+E(f39(x72051,f335(f335(f76(x72051),f39(x72051,x72052,x72053)),x72054),x72053),f39(x72051,f335(f335(f76(x72051),x72052),x72054),x72053))
% 59.73/59.66 [7206]~P58(x72061)+E(f39(x72061,f335(f335(f75(x72061),f39(x72061,x72062,x72063)),x72064),x72063),f39(x72061,f335(f335(f75(x72061),x72062),x72064),x72063))
% 59.73/59.66 [7398]~E(x73981,f335(f335(f144(x73982),x73983),x73984))+~P1(f335(f335(f242(a881),f335(f189(f882(x73982)),x73981)),f335(f189(f882(x73982)),x73984)))
% 59.73/59.66 [7473]~E(f335(f179(x74731,x74732),x74733),f335(f179(x74731,x74732),x74734))+E(f335(f313(f887(x74731,x74732),x74731,f263(x74731,x74732)),f335(f166(f887(x74731,x74732)),x74733)),f335(f313(f887(x74731,x74732),x74731,f263(x74731,x74732)),f335(f166(f887(x74731,x74732)),x74734)))
% 59.73/59.66 [7607]P26(x76071,x76072,x76073,f335(f166(x76071),x76074))+~P1(f335(f130(x76072),f335(f335(f147(x76071,x76072),x76073),x76074)))
% 59.73/59.66 [7681]~P1(f335(f335(f242(f888(x76811,a879)),x76812),x76814))+P1(f335(f335(f242(f888(x76811,a879)),x76812),f335(f335(f312(x76811),x76813),x76814)))
% 59.73/59.66 [7716]~P59(x77161)+E(f39(x77161,f335(f335(f23(x77161),f39(x77161,x77162,x77163)),f39(x77161,x77164,x77163)),x77163),f39(x77161,f335(f335(f23(x77161),x77162),x77164),x77163))
% 59.73/59.66 [7717]~P58(x77171)+E(f39(x77171,f335(f335(f76(x77171),f39(x77171,x77172,x77173)),f39(x77171,x77174,x77173)),x77173),f39(x77171,f335(f335(f76(x77171),x77172),x77174),x77173))
% 59.73/59.66 [7718]~P58(x77181)+E(f39(x77181,f335(f335(f75(x77181),f39(x77181,x77182,x77183)),f39(x77181,x77184,x77183)),x77183),f39(x77181,f335(f335(f75(x77181),x77182),x77184),x77183))
% 59.73/59.66 [7823]~E(f335(x78234,f813(x78234,x78233,x78231,x78232)),f188(f888(x78232,a879)))+E(f335(f335(f33(x78231,f888(x78232,a879)),x78233),x78234),f188(f888(x78232,a879)))
% 59.73/59.66 [7824]~E(f335(x78244,f617(x78244,x78243,x78241,x78242)),f252(f888(x78242,a879)))+E(f335(f335(f34(x78241,f888(x78242,a879)),x78243),x78244),f252(f888(x78242,a879)))
% 59.73/59.66 [7825]~E(f335(x78254,f806(x78254,x78253,x78252,x78251)),f188(f888(x78252,a879)))+E(f335(f335(f33(x78251,f888(x78252,a879)),x78253),x78254),f188(f888(x78252,a879)))
% 59.73/59.66 [7826]~E(f335(x78264,f622(x78264,x78263,x78262,x78261)),f252(f888(x78262,a879)))+E(f335(f335(f34(x78261,f888(x78262,a879)),x78263),x78264),f252(f888(x78262,a879)))
% 59.73/59.66 [8221]P1(f335(x82211,x82212))+~P1(f335(f335(f337(x82213),x82212),f335(f335(f95(f888(x82213,a879)),x82214),f335(f249(x82213),x82211))))
% 59.73/59.66 [8259]~P1(f335(f335(f242(f888(x82591,a879)),x82593),x82594))+P1(f335(f335(f242(f888(x82591,a879)),f335(f335(f312(x82591),x82592),x82593)),f335(f335(f312(x82591),x82592),x82594)))
% 59.73/59.66 [8304]P1(f335(f335(f337(x83041),x83042),x83043))+~P1(f335(f335(f337(x83041),x83042),f335(f335(f95(f888(x83041,a879)),x83043),f335(f249(x83041),x83044))))
% 59.73/59.66 [8438]P1(f335(x84382,x84383))+E(f335(f335(f131(x84381),f335(f189(f882(x84381)),f171(x84381,x84382,f335(f335(f144(x84381),x84383),x84384)))),f335(f335(f144(x84381),x84383),x84384)),f335(f335(f144(x84381),x84383),x84384))
% 59.73/59.66 [8545]~P1(f335(f335(f243(a881),f335(x85454,x85452)),f335(x85454,x85453)))+P1(f335(f335(f337(f887(x85451,x85451)),f335(f335(f264(x85451,x85451),x85452),x85453)),f335(f335(f290(a881,x85451),a248),x85454)))
% 59.73/59.66 [8637]~P1(f335(x86372,f768(x86374,x86372,x86373,x86371)))+E(f171(x86371,x86372,f335(f335(f127(x86371),x86373),x86374)),f335(f335(f127(x86371),x86373),f171(x86371,x86372,x86374)))
% 59.73/59.66 [8711]P26(f882(x87111),f882(x87112),f335(f147(x87111,x87112),x87113),x87114)+~P26(x87111,x87112,x87113,f31(f888(x87111,a879),f335(f313(f882(x87111),f888(x87111,a879),f166(x87111)),x87114)))
% 59.73/59.66 [8780]~P1(f335(x87802,x87803))+E(f335(f335(f131(x87801),f335(f189(f882(x87801)),f171(x87801,x87802,f335(f335(f144(x87801),x87803),x87804)))),f335(f335(f144(x87801),x87803),x87804)),f335(f335(f131(x87801),f335(f189(f882(x87801)),f171(x87801,x87802,x87804))),x87804))
% 59.73/59.66 [8821]~E(x88212,x88213)+E(f335(f129(x88211,f335(f335(f8(a879,a879,x88211),a330),f335(a332,x88212))),f335(f335(f144(x88211),x88213),x88214)),f335(f129(x88211,f335(f335(f8(a879,a879,x88211),a330),f335(a332,x88212))),x88214))
% 59.73/59.66 [8831]E(f335(f335(f33(x88311,f888(x88312,a879)),x88313),x88314),f188(f888(x88312,a879)))+P1(f335(f335(f337(x88311),f813(x88314,x88313,x88311,x88312)),x88313))
% 59.73/59.66 [8832]E(f335(f335(f34(x88321,f888(x88322,a879)),x88323),x88324),f252(f888(x88322,a879)))+P1(f335(f335(f337(x88321),f617(x88324,x88323,x88321,x88322)),x88323))
% 59.73/59.66 [8833]E(f335(f335(f33(x88331,f888(x88332,a879)),x88333),x88334),f188(f888(x88332,a879)))+P1(f335(f335(f337(x88331),f806(x88334,x88333,x88332,x88331)),x88333))
% 59.73/59.66 [8834]E(f335(f335(f34(x88341,f888(x88342,a879)),x88343),x88344),f252(f888(x88342,a879)))+P1(f335(f335(f337(x88341),f622(x88344,x88343,x88342,x88341)),x88343))
% 59.73/59.66 [8870]P1(f335(f335(f243(a881),f335(x88701,x88702)),f335(x88701,x88703)))+~P1(f335(f335(f337(f887(x88704,x88704)),f335(f335(f264(x88704,x88704),x88702),x88703)),f335(f335(f290(a881,x88704),a248),x88701)))
% 59.73/59.66 [8892]E(f171(x88921,x88922,f335(f335(f127(x88921),x88923),x88924)),f335(f335(f127(x88921),x88923),f171(x88921,x88922,x88924)))+P1(f335(f335(f337(x88921),f768(x88924,x88922,x88923,x88921)),f335(f166(x88921),x88923)))
% 59.73/59.66 [9052]P1(f335(f335(f337(x90521),f702(x90522,x90523,x90524,x90521)),x90523))+~P1(f335(f335(f337(f888(x90521,a879)),x90524),f335(f335(f55(x90521),x90523),x90522)))
% 59.73/59.66 [9055]E(x90551,x90552)+~P1(f335(f335(f337(f887(x90553,x90553)),f335(f335(f264(x90553,x90553),x90551),x90552)),f335(f335(f183(f887(x90553,x90553),a879),f2(a881)),x90554)))
% 59.73/59.66 [9137]E(f335(f288(x91371,x91371,x91372),f335(f335(f312(x91371),f702(x91372,x91373,x91374,x91371)),f188(f888(x91371,a879)))),x91374)+~P1(f335(f335(f337(f888(x91371,a879)),x91374),f335(f335(f55(x91371),x91373),x91372)))
% 59.73/59.66 [9144]~P1(f335(f335(f337(f887(x91441,x91441)),f335(f335(f264(x91441,x91441),x91443),x91442)),f310(x91441,x91444)))+P1(f335(f335(f337(f887(x91441,x91441)),f335(f335(f264(x91441,x91441),x91442),x91443)),f310(x91441,f335(f289(x91441,x91441),x91444))))
% 59.73/59.66 [9157]~P58(x91571)+E(f335(f335(f75(x91571),f335(f335(f75(x91571),f335(f335(f76(x91571),x91572),f335(f335(f30(x91571),x91573),x91572))),f39(x91571,x91573,x91572))),x91574),f335(f335(f75(x91571),x91573),x91574))
% 59.73/59.66 [9168]~P1(f335(f335(f337(x91681),x91683),x91684))+P1(f335(f335(f337(f888(x91681,a879)),f335(f288(x91681,x91681,x91682),f335(f335(f312(x91681),x91683),f188(f888(x91681,a879))))),f335(f335(f55(x91681),x91684),x91682)))
% 59.73/59.66 [9179]P1(f335(f335(f337(f887(x91791,x91791)),f335(f335(f264(x91791,x91791),x91792),x91793)),f310(x91791,x91794)))+~P1(f335(f335(f337(f887(x91791,x91791)),f335(f335(f264(x91791,x91791),x91793),x91792)),f310(x91791,f335(f289(x91791,x91791),x91794))))
% 59.73/59.66 [9264]E(f335(f335(f152(x92641,f335(f162(x92641),x92642)),f335(f335(f23(a881),f335(f335(f23(a881),f335(f189(f882(x92641)),x92642)),x92643)),f73(a881))),x92644),f335(f162(x92641),f335(f335(f152(x92641,x92642),x92643),x92644)))+~P1(f335(f335(f243(a881),x92643),f335(f189(f882(x92641)),x92642)))
% 59.73/59.66 [9268]~P1(f335(x92682,f760(x92684,x92682,x92683,x92681)))+E(f335(f335(f131(x92681),f335(f189(f882(x92681)),f171(x92681,x92682,f335(f335(f127(x92681),x92683),x92684)))),f335(f335(f127(x92681),x92683),x92684)),f335(f335(f131(x92681),f335(f189(f882(x92681)),f171(x92681,x92682,x92684))),x92684))
% 59.73/59.66 [9312]~P26(x93122,x93121,x93123,f252(f888(x93122,a879)))+P1(f335(f335(f242(f888(x93121,a879)),f335(f313(x93122,x93121,x93123),f335(f74(f888(x93122,a879)),x93124))),f335(f74(f888(x93121,a879)),f335(f313(x93122,x93121,x93123),x93124))))
% 59.73/59.66 [9323]~P5(x93231)+E(f335(f135(x93231,x93232,f335(f7(x93232,x93231,x93231),f335(f335(f8(x93231,f888(x93231,x93231),x93232),f104(x93231)),x93233)),f188(x93231)),x93234),f335(f335(f33(x93232,x93231),f335(f166(x93232),x93234)),x93233))
% 59.73/59.66 [9324]~P5(x93241)+E(f335(f135(x93241,x93242,f335(f7(x93242,x93241,x93241),f335(f335(f8(x93241,f888(x93241,x93241),x93242),f95(x93241)),x93243)),f252(x93241)),x93244),f335(f335(f34(x93242,x93241),f335(f166(x93242),x93244)),x93243))
% 59.73/59.66 [9334]E(f335(f335(f131(x93341),f335(f189(f882(x93341)),f171(x93341,x93342,f335(f335(f127(x93341),x93343),x93344)))),f335(f335(f127(x93341),x93343),x93344)),f335(f335(f131(x93341),f335(f189(f882(x93341)),f171(x93341,x93342,x93344))),x93344))+P1(f335(f335(f337(x93341),f760(x93344,x93342,x93343,x93341)),f335(f166(x93341),x93343)))
% 59.73/59.66 [9403]~P1(f335(f335(f337(f887(f882(x94034),f882(x94034))),f335(f335(f264(f882(x94034),f882(x94034)),x94033),x94032)),f150(x94034,x94031)))+P1(f335(f335(f243(a881),f697(x94031,x94032,x94033,x94034)),f335(f189(f882(x94034)),x94033)))
% 59.73/59.66 [9404]~P58(x94041)+E(f335(f335(f75(x94041),f335(f335(f75(x94041),f335(f335(f76(x94041),f335(f335(f30(x94041),x94042),x94043)),x94043)),f39(x94041,x94042,x94043))),x94044),f335(f335(f75(x94041),x94042),x94044))
% 59.73/59.66 [9431]~P1(f335(f335(f337(f887(f882(x94311),f882(x94311))),f335(f335(f264(f882(x94311),f882(x94311)),x94312),x94313)),f335(f289(f882(x94311),f882(x94311)),f150(x94311,x94314))))+P1(f335(f335(f337(f887(f882(x94311),f882(x94311))),f335(f335(f264(f882(x94311),f882(x94311)),x94312),x94313)),f150(x94311,f335(f289(x94311,x94311),x94314))))
% 59.73/59.66 [9432]P1(f335(f335(f337(f887(f882(x94321),f882(x94321))),f335(f335(f264(f882(x94321),f882(x94321)),x94322),x94323)),f335(f289(f882(x94321),f882(x94321)),f150(x94321,x94324))))+~P1(f335(f335(f337(f887(f882(x94321),f882(x94321))),f335(f335(f264(f882(x94321),f882(x94321)),x94322),x94323)),f150(x94321,f335(f289(x94321,x94321),x94324))))
% 59.73/59.66 [9470]~P1(f335(f335(f337(x94701),x94703),f335(f262(x94701,x94702),x94704)))+P1(f335(f335(f337(f887(x94701,x94702)),f335(f335(f264(x94701,x94702),x94703),f525(x94704,x94702,x94703,x94701))),x94704))
% 59.73/59.66 [9471]~P1(f335(f335(f337(x94711),x94713),f335(f262(x94711,x94712),x94714)))+P1(f335(f335(f337(f887(x94711,x94712)),f335(f335(f264(x94711,x94712),x94713),f527(x94714,x94712,x94713,x94711))),x94714))
% 59.73/59.66 [9579]~P1(f335(f56(f885(x95791)),f335(f313(x95792,f885(x95791),x95793),f252(f888(x95792,a879)))))+P1(f335(f56(f885(x95791)),f335(f313(x95792,f885(x95791),f180(x95792,x95791,x95793,f335(f179(x95792,x95791),x95794))),f252(f888(x95792,a879)))))
% 59.73/59.66 [9626]~P1(f335(f335(f337(f887(x96261,x96261)),f335(f335(f264(x96261,x96261),x96262),x96264)),f335(f335(f291(x96261,x96261,x96261),x96263),f310(x96261,x96263))))+P1(f335(f335(f337(f887(x96261,x96261)),f335(f335(f264(x96261,x96261),x96262),f607(x96263,x96264,x96262,x96261))),x96263))
% 59.73/59.66 [9805]~P1(f335(f335(f337(f887(x98052,x98051)),x98054),f335(f289(x98051,x98052),x98053)))+P1(f335(f335(f337(f887(x98051,x98052)),f335(f335(f264(x98051,x98052),f659(x98053,x98054,x98051,x98052)),f658(x98053,x98054,x98051,x98052))),x98053))
% 59.73/59.66 [9834]~P1(f335(f335(f337(f887(f882(x98341),f882(x98341))),f335(f335(f264(f882(x98341),f882(x98341)),x98344),x98343)),f150(x98341,x98342)))+P1(f335(f335(f337(f887(x98341,x98341)),f335(f335(f264(x98341,x98341),f705(x98342,x98343,x98344,x98341)),f706(x98342,x98343,x98344,x98341))),x98342))
% 59.73/59.66 [9928]~P1(f335(f335(f337(f887(f882(x99281),f882(x99281))),f335(f335(f264(f882(x99281),f882(x99281)),x99282),x99284)),f150(x99281,x99283)))+P1(f335(f335(f337(f887(x99281,x99281)),f335(f335(f264(x99281,x99281),f335(f335(f158(x99281),x99282),f697(x99283,x99284,x99282,x99281))),f695(x99283,x99284,x99282,x99281))),x99283))
% 59.73/59.66 [9948]~P1(f335(f56(x99482),x99484))+E(f335(f335(f335(f60(f888(x99481,a879),x99482,f104(f888(x99481,a879))),f335(f335(f7(x99482,f888(x99481,a879),f888(x99481,a879)),f335(f335(f8(x99481,f888(f888(x99481,a879),f888(x99481,a879)),x99482),f312(x99481)),x99483)),f188(f888(x99481,a879)))),f188(f888(x99481,a879))),x99484),f335(f313(x99482,x99481,x99483),x99484))
% 59.73/59.66 [10044]~P26(x100441,x100442,x100443,f252(f888(x100441,a879)))+P1(f335(f335(f242(f888(x100441,a879)),f335(f314(x100441,x100442,x100443),f335(f335(f312(x100442),x100444),f188(f888(x100442,a879))))),f335(f335(f312(x100441),f80(x100441,f335(f335(f7(x100441,x100442,a879),f335(f335(f8(x100442,f888(x100442,a879),x100441),a332),x100443)),x100444))),f188(f888(x100441,a879)))))
% 59.73/59.66 [5646]~E(f335(f335(f127(x56461),x56462),x56464),x56463)+E(f335(f335(f169(x56461),f335(f189(f882(x56461)),x56462)),x56463),x56462)
% 59.73/59.66 [5647]~E(f335(f335(f127(x56472),x56473),x56471),x56474)+E(x56471,f335(f335(f131(x56472),f335(f189(f882(x56472)),x56473)),x56474))
% 59.73/59.66 [5658]~E(x56584,f2(a881))+E(f335(f335(f158(x56581),f335(f335(f144(x56581),x56582),x56583)),x56584),x56582)
% 59.73/59.66 [6184]~P114(x61841)+E(f335(f335(f254(x61841),f335(f335(f254(x61841),x61842),x61843)),x61844),f335(f335(f254(x61841),x61842),f335(f335(f76(a881),x61843),x61844)))
% 59.73/59.66 [6185]~P82(x61851)+E(f335(f335(f254(x61851),f335(f335(f254(x61851),x61852),x61853)),x61854),f335(f335(f254(x61851),x61852),f335(f335(f76(a881),x61853),x61854)))
% 59.73/59.66 [6196]E(x61961,f2(a881))+E(f335(f335(f158(x61962),f335(f335(f144(x61962),x61963),x61964)),x61961),f335(f335(f158(x61962),x61964),f335(f335(f23(a881),x61961),f73(a881))))
% 59.73/59.66 [6222]~P114(x62221)+E(f335(f335(f76(x62221),f335(f335(f76(x62221),x62222),x62223)),x62224),f335(f335(f76(x62221),x62222),f335(f335(f76(x62221),x62223),x62224)))
% 59.73/59.66 [6223]~P116(x62231)+E(f335(f335(f292(x62231),f335(f335(f76(x62231),x62232),x62233)),x62234),f335(f335(f76(x62231),x62232),f335(f335(f292(x62231),x62233),x62234)))
% 59.73/59.66 [6224]~P114(x62241)+E(f335(f335(f75(x62241),f335(f335(f75(x62241),x62242),x62243)),x62244),f335(f335(f75(x62241),x62242),f335(f335(f75(x62241),x62243),x62244)))
% 59.73/59.66 [6225]~P60(x62251)+E(f335(f335(f104(x62251),f335(f335(f104(x62251),x62252),x62253)),x62254),f335(f335(f104(x62251),x62252),f335(f335(f104(x62251),x62253),x62254)))
% 59.73/59.66 [6226]~P60(x62261)+E(f335(f335(f104(x62261),f335(f335(f104(x62261),x62262),x62263)),x62264),f335(f335(f104(x62261),x62262),f335(f335(f104(x62261),x62263),x62264)))
% 59.73/59.66 [6227]~P61(x62271)+E(f335(f335(f104(x62271),f335(f335(f104(x62271),x62272),x62273)),x62274),f335(f335(f104(x62271),x62272),f335(f335(f104(x62271),x62273),x62274)))
% 59.73/59.66 [6228]~P61(x62281)+E(f335(f335(f95(x62281),f335(f335(f95(x62281),x62282),x62283)),x62284),f335(f335(f95(x62281),x62282),f335(f335(f95(x62281),x62283),x62284)))
% 59.73/59.66 [6229]~P102(x62291)+E(f335(f335(f95(x62291),f335(f335(f95(x62291),x62292),x62293)),x62294),f335(f335(f95(x62291),x62292),f335(f335(f95(x62291),x62293),x62294)))
% 59.73/59.66 [6230]~P102(x62301)+E(f335(f335(f95(x62301),f335(f335(f95(x62301),x62302),x62303)),x62304),f335(f335(f95(x62301),x62302),f335(f335(f95(x62301),x62303),x62304)))
% 59.73/59.66 [6231]~P70(x62311)+E(f335(f335(f76(x62311),f335(f335(f76(x62311),x62312),x62313)),x62314),f335(f335(f76(x62311),x62312),f335(f335(f76(x62311),x62313),x62314)))
% 59.73/59.66 [6232]~P114(x62321)+E(f335(f335(f76(x62321),f335(f335(f76(x62321),x62322),x62323)),x62324),f335(f335(f76(x62321),x62322),f335(f335(f76(x62321),x62323),x62324)))
% 59.73/59.66 [6234]~P114(x62341)+E(f335(f335(f75(x62341),f335(f335(f75(x62341),x62342),x62343)),x62344),f335(f335(f75(x62341),x62342),f335(f335(f75(x62341),x62343),x62344)))
% 59.73/59.66 [6235]~P71(x62351)+E(f335(f335(f75(x62351),f335(f335(f75(x62351),x62352),x62353)),x62354),f335(f335(f75(x62351),x62352),f335(f335(f75(x62351),x62353),x62354)))
% 59.73/59.66 [6236]~P106(x62361)+E(f335(f335(f240(x62361),f335(f335(f240(x62361),x62362),x62363)),x62364),f335(f335(f240(x62361),x62362),f335(f335(f240(x62361),x62363),x62364)))
% 59.73/59.66 [6237]~P106(x62371)+E(f335(f335(f240(x62371),f335(f335(f240(x62371),x62372),x62373)),x62374),f335(f335(f240(x62371),x62372),f335(f335(f240(x62371),x62373),x62374)))
% 59.73/59.66 [6238]~P106(x62381)+E(f335(f335(f241(x62381),f335(f335(f241(x62381),x62382),x62383)),x62384),f335(f335(f241(x62381),x62382),f335(f335(f241(x62381),x62383),x62384)))
% 59.73/59.66 [6239]~P106(x62391)+E(f335(f335(f241(x62391),f335(f335(f241(x62391),x62392),x62393)),x62394),f335(f335(f241(x62391),x62392),f335(f335(f241(x62391),x62393),x62394)))
% 59.73/59.66 [6250]~P58(x62501)+E(f39(x62501,f335(f335(f75(x62501),x62502),f335(f335(f76(x62501),x62503),x62504)),x62504),f39(x62501,x62502,x62504))
% 59.73/59.66 [6251]~P58(x62511)+E(f39(x62511,f335(f335(f75(x62511),x62512),f335(f335(f76(x62511),x62513),x62514)),x62513),f39(x62511,x62512,x62513))
% 59.73/59.66 [6384]E(f335(f335(f158(x63841),f335(f335(f169(x63841),x63842),x63843)),x63844),f335(f335(f158(x63841),x63843),x63844))+~P1(f335(f335(f243(a881),x63844),x63842))
% 59.73/59.66 [6561]~E(x65612,x65614)+P1(f335(f335(f166(x65611),f335(f335(f144(x65611),x65612),x65613)),x65614))
% 59.73/59.66 [6563]~P114(x65631)+E(f335(f335(f76(x65631),f335(f335(f76(x65631),x65632),x65633)),x65634),f335(f335(f76(x65631),f335(f335(f76(x65631),x65632),x65634)),x65633))
% 59.73/59.66 [6564]~P114(x65641)+E(f335(f335(f75(x65641),f335(f335(f75(x65641),x65642),x65643)),x65644),f335(f335(f75(x65641),f335(f335(f75(x65641),x65642),x65644)),x65643))
% 59.73/59.66 [6627]~P143(x66272)+E(f335(f335(f6(x66271,x66272),f335(f16(x66272,x66271),x66273)),x66274),f335(f335(f76(x66272),f335(f94(x66272),f335(f29(x66271),x66274))),x66273))
% 59.73/59.66 [6798]E(f335(f335(f95(f888(x67981,a879)),f335(f335(f312(x67981),x67982),x67983)),x67984),f335(f335(f95(f888(x67981,a879)),x67983),x67984))+P1(f335(f335(f337(x67981),x67982),x67984))
% 59.73/59.66 [6799]E(f335(f335(f95(f888(x67991,a879)),f335(f335(f312(x67991),x67992),x67993)),x67994),f335(f335(f95(f888(x67991,a879)),x67993),x67994))+P1(f335(f335(f337(x67991),x67992),x67994))
% 59.73/59.66 [6871]~P100(x68711)+E(f335(f335(f95(x68711),f335(f335(f104(x68711),x68712),x68713)),f335(f335(f104(x68711),x68714),x68713)),f335(f335(f104(x68711),f335(f335(f95(x68711),x68712),x68714)),x68713))
% 59.73/59.66 [6872]~P80(x68721)+E(f335(f335(f240(x68721),f335(f335(f23(x68721),x68722),x68723)),f335(f335(f23(x68721),x68724),x68723)),f335(f335(f23(x68721),f335(f335(f240(x68721),x68722),x68724)),x68723))
% 59.73/59.66 [6873]~P80(x68731)+E(f335(f335(f241(x68731),f335(f335(f23(x68731),x68732),x68733)),f335(f335(f23(x68731),x68734),x68733)),f335(f335(f23(x68731),f335(f335(f241(x68731),x68732),x68734)),x68733))
% 59.73/59.66 [6874]~P100(x68741)+E(f335(f335(f104(x68741),f335(f335(f95(x68741),x68742),x68743)),f335(f335(f95(x68741),x68744),x68743)),f335(f335(f95(x68741),f335(f335(f104(x68741),x68742),x68744)),x68743))
% 59.73/59.66 [6875]~P114(x68751)+E(f335(f335(f75(x68751),f335(f335(f76(x68751),x68752),x68753)),f335(f335(f76(x68751),x68754),x68753)),f335(f335(f76(x68751),f335(f335(f75(x68751),x68752),x68754)),x68753))
% 59.73/59.66 [6876]~P115(x68761)+E(f335(f335(f75(x68761),f335(f335(f76(x68761),x68762),x68763)),f335(f335(f76(x68761),x68764),x68763)),f335(f335(f76(x68761),f335(f335(f75(x68761),x68762),x68764)),x68763))
% 59.73/59.66 [6877]~P86(x68771)+E(f335(f335(f240(x68771),f335(f335(f75(x68771),x68772),x68773)),f335(f335(f75(x68771),x68774),x68773)),f335(f335(f75(x68771),f335(f335(f240(x68771),x68772),x68774)),x68773))
% 59.73/59.66 [6878]~P86(x68781)+E(f335(f335(f241(x68781),f335(f335(f75(x68781),x68782),x68783)),f335(f335(f75(x68781),x68784),x68783)),f335(f335(f75(x68781),f335(f335(f241(x68781),x68782),x68784)),x68783))
% 59.73/59.66 [6879]~P73(x68791)+E(f335(f335(f76(x68791),f335(f335(f254(x68791),x68792),x68793)),f335(f335(f254(x68791),x68794),x68793)),f335(f335(f254(x68791),f335(f335(f76(x68791),x68792),x68794)),x68793))
% 59.73/59.66 [6880]~P114(x68801)+E(f335(f335(f76(x68801),f335(f335(f254(x68801),x68802),x68803)),f335(f335(f254(x68801),x68804),x68803)),f335(f335(f254(x68801),f335(f335(f76(x68801),x68802),x68804)),x68803))
% 59.73/59.66 [6881]~P66(x68811)+E(f335(f335(f292(x68811),f335(f335(f254(x68811),x68812),x68813)),f335(f335(f254(x68811),x68814),x68813)),f335(f335(f254(x68811),f335(f335(f292(x68811),x68812),x68814)),x68813))
% 59.73/59.66 [6882]~P116(x68821)+E(f335(f335(f23(x68821),f335(f335(f292(x68821),x68822),x68823)),f335(f335(f292(x68821),x68824),x68823)),f335(f335(f292(x68821),f335(f335(f23(x68821),x68822),x68824)),x68823))
% 59.73/59.66 [6883]~P116(x68831)+E(f335(f335(f75(x68831),f335(f335(f292(x68831),x68832),x68833)),f335(f335(f292(x68831),x68834),x68833)),f335(f335(f292(x68831),f335(f335(f75(x68831),x68832),x68834)),x68833))
% 59.73/59.66 [6884]~P106(x68841)+E(f335(f335(f241(x68841),f335(f335(f240(x68841),x68842),x68843)),f335(f335(f240(x68841),x68844),x68843)),f335(f335(f240(x68841),f335(f335(f241(x68841),x68842),x68844)),x68843))
% 59.73/59.66 [6885]~P106(x68851)+E(f335(f335(f240(x68851),f335(f335(f241(x68851),x68852),x68853)),f335(f335(f241(x68851),x68854),x68853)),f335(f335(f241(x68851),f335(f335(f240(x68851),x68852),x68854)),x68853))
% 59.73/59.66 [6886]~P114(x68861)+E(f335(f335(f75(x68861),f335(f335(f76(x68861),x68862),x68863)),f335(f335(f76(x68861),x68864),x68863)),f335(f335(f76(x68861),f335(f335(f75(x68861),x68862),x68864)),x68863))
% 59.73/59.66 [6918]E(f335(f335(f152(x69181,x69182),x69183),x69184),x69182)+~P1(f335(f335(f242(a881),f335(f189(f882(x69181)),x69182)),x69183))
% 59.73/59.66 [6941]~P1(f335(x69413,x69414))+P1(f335(f335(f335(f104(f888(x69411,a879)),x69412),x69413),x69414))
% 59.73/59.66 [6942]~P1(f335(x69423,x69424))+P1(f335(f335(f335(f104(f888(x69421,a879)),x69422),x69423),x69424))
% 59.73/59.66 [6943]~P1(f335(x69432,x69434))+P1(f335(f335(f335(f104(f888(x69431,a879)),x69432),x69433),x69434))
% 59.73/59.66 [6944]~P1(f335(x69442,x69444))+P1(f335(f335(f335(f104(f888(x69441,a879)),x69442),x69443),x69444))
% 59.73/59.66 [6963]E(f335(f335(f158(x69631),f335(f335(f127(x69631),x69632),x69633)),x69634),f335(f335(f158(x69631),x69632),x69634))+~P1(f335(f335(f243(a881),x69634),f335(f189(f882(x69631)),x69632)))
% 59.73/59.66 [6972]E(f335(f335(f23(f888(x69721,a879)),f335(f335(f312(x69721),x69722),x69723)),x69724),f335(f335(f23(f888(x69721,a879)),x69723),x69724))+~P1(f335(f335(f337(x69721),x69722),x69724))
% 59.73/59.66 [6973]E(f335(f335(f23(f888(x69731,a879)),f335(f335(f312(x69731),x69732),x69733)),x69734),f335(f335(f23(f888(x69731,a879)),x69733),x69734))+~P1(f335(f335(f337(x69731),x69732),x69734))
% 59.73/59.66 [7014]~E(f132(a881,f335(f304(a881,x70141),x70142)),f335(f335(f144(a881),x70144),x70143))+E(f132(a881,f335(f304(a881,f335(f335(f75(a881),x70141),f73(a881))),x70142)),x70143)
% 59.73/59.66 [7035]~P1(f335(f335(f166(x70351),x70353),x70354))+P1(f335(f335(f166(x70351),f335(f335(f144(x70351),x70352),x70353)),x70354))
% 59.73/59.66 [7085]E(x70851,f2(a881))+E(f335(f335(f144(x70852),x70853),f335(f335(f169(x70852),f335(f335(f23(a881),x70851),f73(a881))),x70854)),f335(f335(f169(x70852),x70851),f335(f335(f144(x70852),x70853),x70854)))
% 59.73/59.66 [7185]E(f335(f335(f158(x71851),x71852),f335(f335(f23(a881),x71853),f335(f189(f882(x71851)),x71854))),f335(f335(f158(x71851),f335(f335(f127(x71851),x71854),x71852)),x71853))+P1(f335(f335(f243(a881),x71853),f335(f189(f882(x71851)),x71854)))
% 59.73/59.66 [7214]E(f335(f335(f95(f888(x72141,a879)),x72142),f335(f335(f312(x72141),x72143),x72144)),f335(f335(f312(x72141),x72143),f335(f335(f95(f888(x72141,a879)),x72142),x72144)))+~P1(f335(f335(f337(x72141),x72143),x72142))
% 59.73/59.66 [7215]E(f335(f335(f95(f888(x72151,a879)),x72152),f335(f335(f312(x72151),x72153),x72154)),f335(f335(f312(x72151),x72153),f335(f335(f95(f888(x72151,a879)),x72152),x72154)))+~P1(f335(f335(f337(x72151),x72153),x72152))
% 59.73/59.66 [7250]E(f335(f335(f158(x72501),f335(f335(f152(x72501,x72502),x72503),x72504)),x72503),x72504)+~P1(f335(f335(f243(a881),x72503),f335(f189(f882(x72501)),x72502)))
% 59.73/59.66 [7272]E(x72721,f188(f888(x72722,a879)))+E(f335(f313(f887(x72723,x72722),x72723,f263(x72723,x72722)),f335(f335(f266(x72723,x72722),x72724),f335(f16(f888(x72722,a879),x72723),x72721))),x72724)
% 59.73/59.66 [7273]E(x72731,f188(f888(x72732,a879)))+E(f335(f313(f887(x72732,x72733),x72733,f267(x72732,x72733)),f335(f335(f266(x72732,x72733),x72731),f335(f16(f888(x72733,a879),x72732),x72734))),x72734)
% 59.73/59.66 [7345]E(f335(f335(f23(f888(x73451,a879)),f335(f335(f312(x73451),x73452),x73453)),x73454),f335(f335(f312(x73451),x73452),f335(f335(f23(f888(x73451,a879)),x73453),x73454)))+P1(f335(f335(f337(x73451),x73452),x73454))
% 59.73/59.66 [7382]~E(x73824,f188(f888(x73822,a879)))+E(f335(f313(f887(x73821,x73822),x73821,f263(x73821,x73822)),f335(f335(f266(x73821,x73822),x73823),f335(f16(f888(x73822,a879),x73821),x73824))),f188(f888(x73821,a879)))
% 59.73/59.66 [7383]~E(x73833,f188(f888(x73831,a879)))+E(f335(f313(f887(x73831,x73832),x73832,f267(x73831,x73832)),f335(f335(f266(x73831,x73832),x73833),f335(f16(f888(x73832,a879),x73831),x73834))),f188(f888(x73832,a879)))
% 59.73/59.66 [7436]~P1(f335(f335(f337(x74361),x74362),x74364))+P1(f335(f335(f337(x74361),x74362),f335(f335(f104(f888(x74361,a879)),x74363),x74364)))
% 59.73/59.66 [7437]~P1(f335(f335(f337(x74371),x74372),x74374))+P1(f335(f335(f337(x74371),x74372),f335(f335(f104(f888(x74371,a879)),x74373),x74374)))
% 59.73/59.66 [7438]~P1(f335(f335(f337(x74381),x74382),x74384))+P1(f335(f335(f337(x74381),x74382),f335(f335(f104(f888(x74381,a879)),x74383),x74384)))
% 59.73/59.66 [7439]~P1(f335(f335(f337(x74391),x74392),x74393))+P1(f335(f335(f337(x74391),x74392),f335(f335(f104(f888(x74391,a879)),x74393),x74394)))
% 59.73/59.66 [7440]~P1(f335(f335(f337(x74401),x74402),x74403))+P1(f335(f335(f337(x74401),x74402),f335(f335(f104(f888(x74401,a879)),x74403),x74404)))
% 59.73/59.66 [7441]~P1(f335(f335(f337(x74411),x74412),x74413))+P1(f335(f335(f337(x74411),x74412),f335(f335(f104(f888(x74411,a879)),x74413),x74414)))
% 59.73/59.66 [7459]E(f335(f335(f95(f888(x74591,a879)),f335(f335(f312(x74591),x74592),x74593)),x74594),f335(f335(f312(x74591),x74592),f335(f335(f95(f888(x74591,a879)),x74593),x74594)))+~P1(f335(f335(f337(x74591),x74592),x74594))
% 59.73/59.66 [7460]E(f335(f335(f95(f888(x74601,a879)),f335(f335(f312(x74601),x74602),x74603)),x74604),f335(f335(f312(x74601),x74602),f335(f335(f95(f888(x74601,a879)),x74603),x74604)))+~P1(f335(f335(f337(x74601),x74602),x74604))
% 59.73/59.66 [7737]P1(f335(x77371,x77372))+~P1(f335(f335(f335(f95(f888(x77373,a879)),x77374),x77371),x77372))
% 59.73/59.66 [7738]P1(f335(x77381,x77382))+~P1(f335(f335(f335(f95(f888(x77383,a879)),x77381),x77384),x77382))
% 59.73/59.66 [7739]P1(f335(x77391,x77392))+~P1(f335(f335(f335(f95(f888(x77393,a879)),x77394),x77391),x77392))
% 59.73/59.66 [7740]P1(f335(x77401,x77402))+~P1(f335(f335(f335(f95(f888(x77403,a879)),x77401),x77404),x77402))
% 59.73/59.66 [7743]E(f335(f335(f6(x77431,a881),x77432),f335(f335(f23(f888(x77431,a879)),x77433),f335(f335(f312(x77431),x77434),f188(f888(x77431,a879))))),f335(f335(f6(x77431,a881),x77432),x77433))+P1(f335(f335(f337(x77431),x77434),x77433))
% 59.73/59.66 [7748]~P77(x77481)+E(f335(f159(x77481),f335(f335(f147(a881,x77481),x77482),f132(a881,f335(f304(a881,x77483),x77484)))),f335(f335(f6(a881,x77481),x77482),f335(f166(a881),f132(a881,f335(f304(a881,x77483),x77484)))))
% 59.73/59.66 [7749]~P77(x77491)+E(f335(f335(f6(a881,x77491),x77492),f335(f166(a881),f132(a881,f335(f304(a881,x77493),x77494)))),f335(f159(x77491),f335(f335(f147(a881,x77491),x77492),f132(a881,f335(f304(a881,x77493),x77494)))))
% 59.73/59.66 [7860]~E(x78603,x78604)+P1(f335(f57(x78601,x78602,f335(f335(f312(x78601),x78603),f188(f888(x78601,a879)))),x78604))
% 59.73/59.66 [7960]P1(f335(f335(f337(x79601),x79602),f335(f166(x79601),x79603)))+~P1(f335(f335(f337(x79601),x79602),f335(f166(x79601),f335(f335(f169(x79601),x79604),x79603))))
% 59.73/59.66 [7961]P1(f335(f335(f337(x79611),x79612),f335(f166(x79611),x79613)))+~P1(f335(f335(f337(x79611),x79612),f335(f166(x79611),f335(f335(f131(x79611),x79614),x79613))))
% 59.73/59.66 [8033]P1(f335(f335(f337(x80331),x80332),x80333))+~P1(f335(f335(f337(x80331),x80332),f335(f335(f95(f888(x80331,a879)),x80334),x80333)))
% 59.73/59.66 [8034]P1(f335(f335(f337(x80341),x80342),x80343))+~P1(f335(f335(f337(x80341),x80342),f335(f335(f23(f888(x80341,a879)),x80343),x80344)))
% 59.73/59.66 [8035]P1(f335(f335(f337(x80351),x80352),x80353))+~P1(f335(f335(f337(x80351),x80352),f335(f335(f23(f888(x80351,a879)),x80353),x80354)))
% 59.73/59.66 [8036]P1(f335(f335(f337(x80361),x80362),x80363))+~P1(f335(f335(f337(x80361),x80362),f335(f335(f23(f888(x80361,a879)),x80363),x80364)))
% 59.73/59.66 [8037]P1(f335(f335(f337(x80371),x80372),x80373))+~P1(f335(f335(f337(x80371),x80372),f335(f335(f95(f888(x80371,a879)),x80374),x80373)))
% 59.73/59.66 [8038]P1(f335(f335(f337(x80381),x80382),x80383))+~P1(f335(f335(f337(x80381),x80382),f335(f335(f95(f888(x80381,a879)),x80384),x80383)))
% 59.73/59.66 [8039]P1(f335(f335(f337(x80391),x80392),x80393))+~P1(f335(f335(f337(x80391),x80392),f335(f335(f95(f888(x80391,a879)),x80393),x80394)))
% 59.73/59.66 [8040]P1(f335(f335(f337(x80401),x80402),x80403))+~P1(f335(f335(f337(x80401),x80402),f335(f335(f95(f888(x80401,a879)),x80403),x80404)))
% 59.73/59.66 [8041]P1(f335(f335(f337(x80411),x80412),x80413))+~P1(f335(f335(f337(x80411),x80412),f335(f335(f95(f888(x80411,a879)),x80413),x80414)))
% 59.73/59.66 [8056]E(f335(f335(f127(x80561),f335(f335(f169(x80561),x80562),x80563)),f335(f335(f144(x80561),x80564),f335(f335(f131(x80561),f335(a106,x80562)),x80563))),f335(f335(f152(x80561,x80563),x80562),x80564))+~P1(f335(f335(f243(a881),x80562),f335(f189(f882(x80561)),x80563)))
% 59.73/59.66 [8079]P1(f335(f335(f337(x80791),x80792),x80793))+~P1(f335(f335(f242(f888(x80791,a879)),f335(f335(f312(x80791),x80792),x80794)),x80793))
% 59.73/59.66 [8110]~P1(f335(f335(f337(x81101),x81102),x81103))+~P1(f335(f335(f337(x81101),x81102),f335(f335(f23(f888(x81101,a879)),x81104),x81103)))
% 59.73/59.66 [8111]~P1(f335(f335(f337(x81111),x81112),x81113))+~P1(f335(f335(f337(x81111),x81112),f335(f335(f23(f888(x81111,a879)),x81114),x81113)))
% 59.73/59.66 [8112]~P1(f335(f335(f337(x81121),x81122),x81123))+~P1(f335(f335(f337(x81121),x81122),f335(f335(f23(f888(x81121,a879)),x81124),x81123)))
% 59.73/59.66 [8143]~P1(f335(f335(f243(a881),x81434),f335(f189(f882(x81431)),x81433)))+P1(f335(f335(f337(x81431),x81432),f335(f166(x81431),f335(f335(f152(x81431,x81433),x81434),x81432))))
% 59.73/59.66 [8187]E(f335(f97(a881),x81871),f2(a881))+E(f335(f335(f144(x81872),x81873),f335(f335(f169(x81872),f335(f335(f23(a881),f335(f97(a881),x81871)),f73(a881))),x81874)),f335(f335(f169(x81872),f335(f97(a881),x81871)),f335(f335(f144(x81872),x81873),x81874)))
% 59.73/59.66 [8198]E(f335(f335(f158(x81981),f335(f335(f131(x81981),x81982),x81983)),x81984),f335(f335(f158(x81981),x81983),f335(f335(f75(a881),x81982),x81984)))+~P1(f335(f335(f242(a881),f335(f335(f75(a881),x81982),x81984)),f335(f189(f882(x81981)),x81983)))
% 59.73/59.66 [8208]~P137(x82082)+E(f335(f335(f6(x82081,x82082),f335(f335(f8(a1,x82082,x82081),f96(x82082)),x82083)),x82084),f335(f96(x82082),f335(f335(f6(x82081,a1),x82083),x82084)))
% 59.73/59.66 [8209]~P143(x82092)+E(f335(f335(f6(x82091,x82092),f335(f335(f8(a881,x82092,x82091),f94(x82092)),x82093)),x82094),f335(f94(x82092),f335(f335(f6(x82091,a881),x82093),x82094)))
% 59.73/59.66 [8261]~P69(x82612)+E(f335(f335(f9(x82611,x82612),f335(f335(f8(x82612,x82612,x82611),f70(x82612)),x82613)),x82614),f335(f70(x82612),f335(f335(f9(x82611,x82612),x82613),x82614)))
% 59.73/59.66 [8262]~P64(x82622)+E(f335(f335(f6(x82621,x82622),f335(f335(f8(x82622,x82622,x82621),f74(x82622)),x82623)),x82624),f335(f74(x82622),f335(f335(f6(x82621,x82622),x82623),x82624)))
% 59.73/59.66 [8264]E(f335(f335(f6(x82641,a881),x82642),f335(f335(f23(f888(x82641,a879)),x82643),f335(f335(f312(x82641),x82644),f188(f888(x82641,a879))))),f335(f335(f23(a881),f335(f335(f6(x82641,a881),x82642),x82643)),f335(x82642,x82644)))+~P1(f335(f335(f337(x82641),x82644),x82643))
% 59.73/59.66 [8284]P1(f335(f335(f242(f888(x82841,a879)),x82842),x82843))+~P1(f335(f335(f242(f888(x82841,a879)),f335(f335(f312(x82841),x82844),x82842)),x82843))
% 59.73/59.66 [8407]~E(f335(f313(x84072,x84073,x84071),f252(f888(x84072,a879))),f252(f888(x84073,a879)))+E(f335(x84071,f335(f87(x84072,x84073,f252(f888(x84072,a879)),x84071),x84074)),x84074)
% 59.73/59.66 [8408]~E(f335(f313(x84082,x84083,x84081),f252(f888(x84082,a879))),f252(f888(x84083,a879)))+E(f335(x84081,f335(f87(x84082,x84083,f252(f888(x84082,a879)),x84081),x84084)),x84084)
% 59.73/59.66 [8493]E(f335(f335(f179(x84931,x84932),x84933),x84934),f200(x84932))+P1(f335(f335(f337(x84931),x84934),f335(f313(f887(x84931,x84932),x84931,f263(x84931,x84932)),f335(f166(f887(x84931,x84932)),x84933))))
% 59.73/59.66 [8494]P36(x84941,x84942)+~P36(x84941,f335(f335(f312(f887(x84941,x84941)),f335(f335(f264(x84941,x84941),x84943),x84944)),x84942))
% 59.73/59.66 [8495]P55(x84951,x84952)+~P55(x84951,f335(f335(f312(f887(x84951,x84951)),f335(f335(f264(x84951,x84951),x84953),x84954)),x84952))
% 59.73/59.66 [8500]~P106(x85001)+E(f335(f335(f141(x85001,x85001,f5(x85001)),x85002),f335(f335(f141(x85001,x85001,f5(x85001)),x85003),x85004)),f335(f335(f141(x85001,x85001,f5(x85001)),x85003),f335(f335(f141(x85001,x85001,f5(x85001)),x85002),x85004)))
% 59.73/59.66 [8510]E(x85101,x85102)+~P1(f335(f57(x85103,x85104,f335(f335(f312(x85103),x85101),f188(f888(x85103,a879)))),x85102))
% 59.73/59.66 [8522]E(f335(f335(f127(x85221),f335(f335(f169(x85221),x85222),x85223)),f335(f335(f169(x85221),x85224),f335(f335(f131(x85221),x85222),x85223))),f335(f335(f169(x85221),f335(f335(f75(a881),x85222),x85224)),x85223))+~P1(f335(f335(f242(a881),f335(f335(f75(a881),x85222),x85224)),f335(f189(f882(x85221)),x85223)))
% 59.73/59.66 [8559]P1(f335(f56(x85591),x85592))+~E(x85592,f335(f313(a881,x85591,x85593),f335(f249(a881),f335(f335(f7(a881,a881,a879),f243(a881)),x85594))))
% 59.73/59.66 [8560]P1(f335(f56(x85601),x85602))+~E(x85602,f335(f313(a881,x85601,x85603),f335(f249(a881),f335(f335(f7(a881,a881,a879),f243(a881)),x85604))))
% 59.73/59.66 [8580]~P92(x85801)+E(f335(f135(x85801,x85801,f75(x85801),f335(f335(f75(x85801),x85802),x85803)),x85804),f335(f335(f75(x85801),x85802),f335(f135(x85801,x85801,f75(x85801),x85803),x85804)))
% 59.73/59.66 [8615]P1(f335(f335(f242(f888(x86151,a879)),f335(f262(x86151,x86152),x86153)),f335(f262(x86151,x86152),x86154)))+~P1(f335(f335(f242(f888(f887(x86151,x86152),a879)),x86153),x86154))
% 59.73/59.66 [8628]~P1(f335(f335(f242(a881),x86282),x86284))+P1(f335(f335(f242(f888(x86281,a879)),f335(f166(x86281),f335(f335(f169(x86281),x86282),x86283))),f335(f166(x86281),f335(f335(f169(x86281),x86284),x86283))))
% 59.73/59.66 [8629]~P1(f335(f335(f242(a881),x86294),x86292))+P1(f335(f335(f242(f888(x86291,a879)),f335(f166(x86291),f335(f335(f131(x86291),x86292),x86293))),f335(f166(x86291),f335(f335(f131(x86291),x86294),x86293))))
% 59.73/59.66 [8684]~P1(f335(f56(x86841),f335(f335(f23(f888(x86841,a879)),x86842),x86844)))+P1(f335(f56(x86841),f335(f335(f23(f888(x86841,a879)),x86842),f335(f335(f312(x86841),x86843),x86844))))
% 59.73/59.66 [8721]P1(f335(f335(f337(f887(x87211,x87211)),x87212),f310(x87211,x87213)))+~P1(f335(f335(f337(f887(x87211,x87211)),x87212),f335(f335(f183(f887(x87211,x87211),a879),x87214),x87213)))
% 59.73/59.66 [8722]P1(f335(f335(f337(f887(x87221,x87221)),x87222),f310(x87221,x87223)))+~P1(f335(f335(f337(f887(x87221,x87221)),x87222),f335(f335(f183(f887(x87221,x87221),a879),x87224),x87223)))
% 59.73/59.66 [8803]~P1(f335(f56(x88031),f335(f335(f23(f888(x88031,a879)),x88032),f335(f335(f312(x88031),x88034),x88033))))+P1(f335(f56(x88031),f335(f335(f23(f888(x88031,a879)),x88032),x88033)))
% 59.73/59.66 [8875]P1(f335(f335(f337(f887(x88751,x88752)),f335(f335(f264(x88751,x88752),x88753),x88754)),f188(f888(f887(x88751,x88752),a879))))+~P1(f335(f335(f188(f888(x88751,f888(x88752,a879))),x88753),x88754))
% 59.73/59.66 [8951]~E(f335(f335(f179(x89511,x89512),x89513),x89514),f200(x89512))+~P1(f335(f335(f337(x89511),x89514),f335(f313(f887(x89511,x89512),x89511,f263(x89511,x89512)),f335(f166(f887(x89511,x89512)),x89513))))
% 59.73/59.66 [9012]~P61(x90121)+P1(f335(f335(f242(x90121),f335(f335(f104(x90121),x90122),f335(f335(f95(x90121),x90123),x90124))),f335(f335(f95(x90121),f335(f335(f104(x90121),x90122),x90123)),f335(f335(f104(x90121),x90122),x90124))))
% 59.73/59.66 [9013]~P106(x90131)+P1(f335(f335(f242(x90131),f335(f335(f241(x90131),x90132),f335(f335(f240(x90131),x90133),x90134))),f335(f335(f240(x90131),f335(f335(f241(x90131),x90132),x90133)),f335(f335(f241(x90131),x90132),x90134))))
% 59.73/59.66 [9030]~P1(f335(f335(f337(f887(x90301,x90302)),f335(f335(f264(x90301,x90302),x90303),x90304)),f188(f888(f887(x90301,x90302),a879))))+P1(f335(f335(f188(f888(x90301,f888(x90302,a879))),x90303),x90304))
% 59.73/59.66 [9164]E(x91641,x91642)+~P1(f335(f335(f337(f887(x91643,x91643)),f335(f335(f264(x91643,x91643),x91641),x91642)),f335(f166(f887(x91643,x91643)),f335(f335(f175(x91643,x91643),x91644),x91644))))
% 59.73/59.66 [9194]~P1(f335(f335(f337(f887(x91941,x91941)),f335(f335(f264(x91941,x91941),x91943),x91942)),f310(x91941,x91944)))+~P36(x91941,f335(f335(f312(f887(x91941,x91941)),f335(f335(f264(x91941,x91941),x91942),x91943)),x91944))
% 59.73/59.66 [9195]~P1(f335(f335(f337(f887(x91951,x91951)),f335(f335(f264(x91951,x91951),x91953),x91952)),f310(x91951,x91954)))+~P55(x91951,f335(f335(f312(f887(x91951,x91951)),f335(f335(f264(x91951,x91951),x91952),x91953)),x91954))
% 59.73/59.66 [9200]E(x92001,x92002)+E(f335(f129(x92003,f335(f335(f8(a879,a879,x92003),a330),f335(a332,x92001))),f335(f335(f144(x92003),x92002),x92004)),f335(f335(f144(x92003),x92002),f335(f129(x92003,f335(f335(f8(a879,a879,x92003),a330),f335(a332,x92001))),x92004)))
% 59.73/59.66 [9210]P1(f335(f335(f337(x92101),x92102),f335(f166(x92101),x92103)))+~P1(f335(f335(f337(f887(x92101,x92101)),f335(f335(f264(x92101,x92101),x92102),x92104)),f335(f166(f887(x92101,x92101)),f335(f335(f175(x92101,x92101),x92103),x92103))))
% 59.73/59.66 [9246]~P61(x92461)+P1(f335(f335(f242(x92461),f335(f335(f104(x92461),f335(f335(f95(x92461),x92462),x92463)),f335(f335(f95(x92461),x92462),x92464))),f335(f335(f95(x92461),x92462),f335(f335(f104(x92461),x92463),x92464))))
% 59.73/59.66 [9247]~P106(x92471)+P1(f335(f335(f242(x92471),f335(f335(f241(x92471),f335(f335(f240(x92471),x92472),x92473)),f335(f335(f240(x92471),x92472),x92474))),f335(f335(f240(x92471),x92472),f335(f335(f241(x92471),x92473),x92474))))
% 59.73/59.66 [9283]P1(f335(f335(f337(f887(x92831,x92831)),f335(f335(f264(x92831,x92831),x92832),x92833)),f335(f335(f291(x92831,x92831,x92831),x92834),f310(x92831,x92834))))+~P1(f335(f335(f337(f887(x92831,x92831)),f335(f335(f264(x92831,x92831),x92832),x92833)),x92834))
% 59.73/59.66 [9318]~E(f335(f313(x93182,x93181,x93183),f252(f888(x93182,a879))),f252(f888(x93181,a879)))+P1(f335(f335(f242(f888(x93181,a879)),f335(f74(f888(x93181,a879)),f335(f313(x93182,x93181,x93183),x93184))),f335(f313(x93182,x93181,x93183),f335(f74(f888(x93182,a879)),x93184))))
% 59.73/59.66 [9640]P1(f335(f335(f337(f887(x96401,x96401)),f335(f335(f264(x96401,x96401),x96402),x96403)),f335(f289(x96401,x96401),f335(f335(f291(x96401,x96401,x96401),x96404),f310(x96401,x96404)))))+~P1(f335(f335(f337(f887(x96401,x96401)),f335(f335(f264(x96401,x96401),x96402),x96403)),f335(f335(f291(x96401,x96401,x96401),f335(f289(x96401,x96401),x96404)),f310(x96401,f335(f289(x96401,x96401),x96404)))))
% 59.73/59.66 [9641]~P1(f335(f335(f337(f887(x96411,x96411)),f335(f335(f264(x96411,x96411),x96412),x96413)),f335(f289(x96411,x96411),f335(f335(f291(x96411,x96411,x96411),x96414),f310(x96411,x96414)))))+P1(f335(f335(f337(f887(x96411,x96411)),f335(f335(f264(x96411,x96411),x96412),x96413)),f335(f335(f291(x96411,x96411,x96411),f335(f289(x96411,x96411),x96414)),f310(x96411,f335(f289(x96411,x96411),x96414)))))
% 59.73/59.66 [9662]~P1(f335(f335(f337(x96622),x96624),f335(f260(x96621,x96622),x96623)))+P1(f335(f335(f337(f887(x96621,x96622)),f335(f335(f264(x96621,x96622),f524(x96623,x96621,x96624,x96622)),x96624)),x96623))
% 59.73/59.66 [9663]~P1(f335(f335(f337(x96632),x96634),f335(f260(x96631,x96632),x96633)))+P1(f335(f335(f337(f887(x96631,x96632)),f335(f335(f264(x96631,x96632),f526(x96633,x96631,x96634,x96632)),x96634)),x96633))
% 59.73/59.66 [9691]~P1(f335(f335(f337(x96911),x96914),f335(f335(f104(f888(x96911,a879)),x96912),x96913)))+P1(f335(f335(f335(f104(f888(x96911,a879)),f335(f335(f7(x96911,f888(x96911,a879),a879),f337(x96911)),x96912)),f335(f335(f7(x96911,f888(x96911,a879),a879),f337(x96911)),x96913)),x96914))
% 59.73/59.66 [9692]~P1(f335(f335(f337(x96921),x96924),f335(f335(f95(f888(x96921,a879)),x96922),x96923)))+P1(f335(f335(f335(f95(f888(x96921,a879)),f335(f335(f7(x96921,f888(x96921,a879),a879),f337(x96921)),x96922)),f335(f335(f7(x96921,f888(x96921,a879),a879),f337(x96921)),x96923)),x96924))
% 59.73/59.66 [9774]~P1(f335(f335(f337(f887(x97741,x97741)),f335(f335(f264(x97741,x97741),x97744),x97743)),f335(f335(f291(x97741,x97741,x97741),x97742),f310(x97741,x97742))))+P1(f335(f335(f337(f887(x97741,x97741)),f335(f335(f264(x97741,x97741),f615(x97742,x97743,x97744,x97741)),x97743)),x97742))
% 59.73/59.66 [9822]P1(f335(f335(f337(x98221),x98222),f335(f335(f104(f888(x98221,a879)),x98223),x98224)))+~P1(f335(f335(f335(f104(f888(x98221,a879)),f335(f335(f7(x98221,f888(x98221,a879),a879),f337(x98221)),x98223)),f335(f335(f7(x98221,f888(x98221,a879),a879),f337(x98221)),x98224)),x98222))
% 59.73/59.66 [9823]P1(f335(f335(f337(x98231),x98232),f335(f335(f95(f888(x98231,a879)),x98233),x98234)))+~P1(f335(f335(f335(f95(f888(x98231,a879)),f335(f335(f7(x98231,f888(x98231,a879),a879),f337(x98231)),x98233)),f335(f335(f7(x98231,f888(x98231,a879),a879),f337(x98231)),x98234)),x98232))
% 59.73/59.66 [10097]P31(x100971,f335(f335(f7(x100971,f888(f887(x100971,x100971),a879),f888(x100971,a879)),f335(f335(f8(f888(x100971,f888(f888(f887(x100971,x100971),a879),a879)),f888(f888(f887(x100971,x100971),a879),f888(x100971,a879)),x100971),f7(x100971,f888(f887(x100971,x100971),a879),a879)),f335(f335(f8(f888(x100971,f887(x100971,x100971)),f888(x100971,f888(f888(f887(x100971,x100971),a879),a879)),x100971),f335(f8(f887(x100971,x100971),f888(f888(f887(x100971,x100971),a879),a879),x100971),f337(f887(x100971,x100971)))),f264(x100971,x100971)))),x100972),x100973,x100974)+~P1(f335(f335(f337(f887(f882(x100971),f882(x100971))),f335(f335(f264(f882(x100971),f882(x100971)),x100973),x100974)),f151(x100971,x100972)))
% 59.73/59.66 [10101]P56(x101011,f335(f335(f7(x101011,f888(f887(x101011,x101011),a879),f888(x101011,a879)),f335(f335(f8(f888(x101011,f888(f888(f887(x101011,x101011),a879),a879)),f888(f888(f887(x101011,x101011),a879),f888(x101011,a879)),x101011),f7(x101011,f888(f887(x101011,x101011),a879),a879)),f335(f335(f8(f888(x101011,f887(x101011,x101011)),f888(x101011,f888(f888(f887(x101011,x101011),a879),a879)),x101011),f335(f8(f887(x101011,x101011),f888(f888(f887(x101011,x101011),a879),a879),x101011),f337(f887(x101011,x101011)))),f264(x101011,x101011)))),x101012),x101013,x101014)+~P1(f335(f335(f337(f887(f888(x101011,a879),f888(x101011,a879))),f335(f335(f264(f888(x101011,a879),f888(x101011,a879)),x101013),x101014)),f327(x101011,x101012)))
% 59.73/59.66 [10128]E(x101281,x101282)+~E(f335(f335(f7(x101283,f888(f887(x101283,x101284),a879),f888(x101284,a879)),f335(f335(f8(f888(x101284,f888(f888(f887(x101283,x101284),a879),a879)),f888(f888(f887(x101283,x101284),a879),f888(x101284,a879)),x101283),f7(x101284,f888(f887(x101283,x101284),a879),a879)),f335(f335(f8(f888(x101284,f887(x101283,x101284)),f888(x101284,f888(f888(f887(x101283,x101284),a879),a879)),x101283),f335(f8(f887(x101283,x101284),f888(f888(f887(x101283,x101284),a879),a879),x101284),f337(f887(x101283,x101284)))),f264(x101283,x101284)))),x101281),f335(f335(f7(x101283,f888(f887(x101283,x101284),a879),f888(x101284,a879)),f335(f335(f8(f888(x101284,f888(f888(f887(x101283,x101284),a879),a879)),f888(f888(f887(x101283,x101284),a879),f888(x101284,a879)),x101283),f7(x101284,f888(f887(x101283,x101284),a879),a879)),f335(f335(f8(f888(x101284,f887(x101283,x101284)),f888(x101284,f888(f888(f887(x101283,x101284),a879),a879)),x101283),f335(f8(f887(x101283,x101284),f888(f888(f887(x101283,x101284),a879),a879),x101284),f337(f887(x101283,x101284)))),f264(x101283,x101284)))),x101282))
% 59.73/59.66 [10131]~P31(x101311,f335(f335(f7(x101311,f888(f887(x101311,x101311),a879),f888(x101311,a879)),f335(f335(f8(f888(x101311,f888(f888(f887(x101311,x101311),a879),a879)),f888(f888(f887(x101311,x101311),a879),f888(x101311,a879)),x101311),f7(x101311,f888(f887(x101311,x101311),a879),a879)),f335(f335(f8(f888(x101311,f887(x101311,x101311)),f888(x101311,f888(f888(f887(x101311,x101311),a879),a879)),x101311),f335(f8(f887(x101311,x101311),f888(f888(f887(x101311,x101311),a879),a879),x101311),f337(f887(x101311,x101311)))),f264(x101311,x101311)))),x101314),x101312,x101313)+P1(f335(f335(f337(f887(f882(x101311),f882(x101311))),f335(f335(f264(f882(x101311),f882(x101311)),x101312),x101313)),f151(x101311,x101314)))
% 59.73/59.66 [10132]~P56(x101321,f335(f335(f7(x101321,f888(f887(x101321,x101321),a879),f888(x101321,a879)),f335(f335(f8(f888(x101321,f888(f888(f887(x101321,x101321),a879),a879)),f888(f888(f887(x101321,x101321),a879),f888(x101321,a879)),x101321),f7(x101321,f888(f887(x101321,x101321),a879),a879)),f335(f335(f8(f888(x101321,f887(x101321,x101321)),f888(x101321,f888(f888(f887(x101321,x101321),a879),a879)),x101321),f335(f8(f887(x101321,x101321),f888(f888(f887(x101321,x101321),a879),a879),x101321),f337(f887(x101321,x101321)))),f264(x101321,x101321)))),x101324),x101322,x101323)+P1(f335(f335(f337(f887(f888(x101321,a879),f888(x101321,a879))),f335(f335(f264(f888(x101321,a879),f888(x101321,a879)),x101322),x101323)),f327(x101321,x101324)))
% 59.73/59.66 [7511]~P97(x75111)+E(f335(f335(f76(x75111),f335(f97(x75111),x75112)),f335(f335(f76(x75111),f335(f97(x75111),x75113)),x75114)),f335(f335(f76(x75111),f335(f97(x75111),f335(f335(f76(a1),x75112),x75113))),x75114))
% 59.73/59.66 [7512]~P97(x75121)+E(f335(f335(f75(x75121),f335(f97(x75121),x75122)),f335(f335(f23(x75121),f335(f97(x75121),x75123)),x75124)),f335(f335(f23(x75121),f335(f97(x75121),f335(f335(f75(a1),x75122),x75123))),x75124))
% 59.73/59.66 [7513]~P97(x75131)+E(f335(f335(f75(x75131),f335(f97(x75131),x75132)),f335(f335(f75(x75131),f335(f97(x75131),x75133)),x75134)),f335(f335(f75(x75131),f335(f97(x75131),f335(f335(f75(a1),x75132),x75133))),x75134))
% 59.73/59.66 [7556]~P143(x75561)+E(f335(f159(x75561),f335(f335(f147(x75562,x75561),f335(f16(x75561,x75562),x75563)),x75564)),f335(f335(f76(x75561),f335(f94(x75561),f335(f189(f882(x75562)),x75564))),x75563))
% 59.73/59.66 [7795]E(f335(f276(x77951,f335(f335(f144(f887(a93,x77951)),x77952),x77953)),x77954),f335(f267(a93,x77951),x77952))+~P1(f335(f335(f243(a93),x77954),f335(f263(a93,x77951),x77952)))
% 59.73/59.66 [7837]~P97(x78371)+E(f335(f335(f75(x78371),f335(f97(x78371),x78372)),f335(f335(f23(x78371),x78373),f335(f97(x78371),x78374))),f335(f335(f75(x78371),f335(f97(x78371),f335(f335(f75(a1),x78372),f335(f74(a1),x78374)))),x78373))
% 59.73/59.66 [7975]E(f335(f276(x79751,x79752),f335(f335(f23(a93),x79753),f335(f263(a93,x79751),x79754))),f335(f276(x79751,f335(f335(f144(f887(a93,x79751)),x79754),x79752)),x79753))+P1(f335(f335(f243(a93),x79753),f335(f263(a93,x79751),x79754)))
% 59.73/59.66 [8414]~P1(f335(f335(f337(x84141),x84142),f335(f166(x84141),f108(x84141,x84144))))+P1(f335(f335(f337(x84141),x84142),f335(f166(x84141),f108(x84141,f335(f335(f127(x84141),x84143),x84144)))))
% 59.73/59.66 [8415]~P1(f335(f335(f337(x84151),x84152),f335(f166(x84151),f108(x84151,x84153))))+P1(f335(f335(f337(x84151),x84152),f335(f166(x84151),f108(x84151,f335(f335(f127(x84151),x84153),x84154)))))
% 59.73/59.66 [8433]E(f335(f335(f104(f888(x84331,a879)),f335(f335(f95(f888(x84331,a879)),x84332),x84333)),x84334),f335(f335(f95(f888(x84331,a879)),x84332),f335(f335(f104(f888(x84331,a879)),x84333),x84334)))+~P1(f335(f335(f242(f888(x84331,a879)),x84334),x84332))
% 59.73/59.66 [8735]~E(f335(f335(f104(f888(x87351,a879)),f335(f335(f95(f888(x87351,a879)),x87353),x87354)),x87352),f335(f335(f95(f888(x87351,a879)),x87353),f335(f335(f104(f888(x87351,a879)),x87354),x87352)))+P1(f335(f335(f242(f888(x87351,a879)),x87352),x87353))
% 59.73/59.66 [9017]~P1(f335(f335(f242(f888(x90171,a879)),x90172),f335(f335(f104(f888(x90171,a879)),x90173),x90174)))+P1(f335(f335(f242(f888(x90171,a879)),f335(f335(f23(f888(x90171,a879)),x90172),x90173)),x90174))
% 59.73/59.66 [9134]~E(f335(f313(x91341,x91342,x91343),f252(f888(x91341,a879))),f252(f888(x91342,a879)))+E(f335(f313(x91341,x91342,x91343),f335(f313(x91342,x91341,f87(x91341,x91342,f252(f888(x91341,a879)),x91343)),x91344)),x91344)
% 59.73/59.66 [9139]P1(f335(f335(f242(f888(x91391,a879)),x91392),f335(f335(f104(f888(x91391,a879)),x91393),x91394)))+~P1(f335(f335(f242(f888(x91391,a879)),f335(f335(f23(f888(x91391,a879)),x91392),x91393)),x91394))
% 59.73/59.66 [9227]~P88(x92271)+E(f335(f70(x92271),f335(f335(f6(x92272,x92271),f335(f335(f8(x92271,x92271,x92272),f70(x92271)),x92273)),x92274)),f335(f335(f6(x92272,x92271),f335(f335(f8(x92271,x92271,x92272),f70(x92271)),x92273)),x92274))
% 59.73/59.66 [9395]~P88(x93951)+P1(f335(f335(f242(x93951),f2(x93951)),f335(f335(f6(x93952,x93951),f335(f335(f8(x93951,x93951,x93952),f70(x93951)),x93953)),x93954)))
% 59.73/59.66 [9399]~P64(x93991)+E(f335(f159(x93991),f335(f335(f147(x93992,x93991),f335(f68(x93991,x93991,x93992,f74(x93991)),x93993)),x93994)),f335(f74(x93991),f335(f159(x93991),f335(f335(f147(x93992,x93991),x93993),x93994))))
% 59.73/59.66 [9536]~P88(x95361)+P1(f335(f335(f242(x95361),f335(f70(x95361),f335(f335(f6(x95362,x95361),x95363),x95364))),f335(f335(f6(x95362,x95361),f335(f335(f8(x95361,x95361,x95362),f70(x95361)),x95363)),x95364)))
% 59.73/59.66 [9565]~E(f335(f335(f75(a881),x95651),x95654),f335(f335(f75(a881),x95653),x95652))+P1(f335(f335(f337(f887(f887(a881,a881),f887(a881,a881))),f335(f335(f264(f887(a881,a881),f887(a881,a881)),f335(f335(f264(a881,a881),x95651),x95652)),f335(f335(f264(a881,a881),x95653),x95654))),a102))
% 59.73/59.66 [9566]~P1(f335(f335(f243(a881),x95661),x95663))+P1(f335(f335(f337(f887(f887(a881,a881),f887(a881,a881))),f335(f335(f264(f887(a881,a881),f887(a881,a881)),f335(f335(f264(a881,a881),x95661),x95662)),f335(f335(f264(a881,a881),x95663),x95664))),a26))
% 59.73/59.66 [9567]~P1(f335(f335(f243(a881),x95671),x95673))+P1(f335(f335(f337(f887(f887(a881,a881),f887(a881,a881))),f335(f335(f264(f887(a881,a881),f887(a881,a881)),f335(f335(f264(a881,a881),x95671),x95672)),f335(f335(f264(a881,a881),x95673),x95674))),a65))
% 59.73/59.66 [9717]E(f335(f335(f75(a881),x97171),x97172),f335(f335(f75(a881),x97173),x97174))+~P1(f335(f335(f337(f887(f887(a881,a881),f887(a881,a881))),f335(f335(f264(f887(a881,a881),f887(a881,a881)),f335(f335(f264(a881,a881),x97171),x97174)),f335(f335(f264(a881,a881),x97173),x97172))),a102))
% 59.73/59.66 [9747]E(f335(f335(f158(x97471),f335(f335(f131(x97471),f335(f189(f882(x97471)),f171(x97471,x97472,x97473))),x97473)),x97474),f335(f335(f158(x97471),x97473),f335(f335(f75(a881),x97474),f335(f189(f882(x97471)),f171(x97471,x97472,x97473)))))+~P1(f335(f335(f243(a881),x97474),f335(f189(f882(x97471)),f335(f335(f131(x97471),f335(f189(f882(x97471)),f171(x97471,x97472,x97473))),x97473))))
% 59.73/59.66 [9765]~P1(f335(f335(f337(x97652),x97654),f335(f335(f33(x97651,f888(x97652,a879)),f252(f888(x97651,a879))),x97653)))+P1(f335(f335(f335(f33(x97651,f888(x97652,a879)),f252(f888(x97651,a879))),f335(f335(f8(f888(x97652,a879),f888(x97652,a879),x97651),f335(f7(x97652,f888(x97652,a879),a879),f337(x97652))),x97653)),x97654))
% 59.73/59.66 [9766]~P1(f335(f335(f337(x97662),x97664),f335(f335(f34(x97661,f888(x97662,a879)),f252(f888(x97661,a879))),x97663)))+P1(f335(f335(f335(f34(x97661,f888(x97662,a879)),f252(f888(x97661,a879))),f335(f335(f8(f888(x97662,a879),f888(x97662,a879),x97661),f335(f7(x97662,f888(x97662,a879),a879),f337(x97662))),x97663)),x97664))
% 59.73/59.66 [9849]~P1(f335(f43(x98491,x98492),f335(f335(f264(a1,a1),x98494),x98493)))+P1(f335(f43(f335(f74(a1),x98491),x98492),f335(f335(f264(a1,a1),f335(f335(f335(f88(a1),f335(f335(a332,x98493),f2(a1))),f335(f74(a1),x98494)),f335(f335(f23(a1),f335(f74(a1),x98494)),f73(a1)))),f335(f335(f335(f88(a1),f335(f335(a332,x98493),f2(a1))),f2(a1)),f335(f335(f23(a1),x98492),x98493)))))
% 59.73/59.66 [9859]P1(f335(f335(f337(x98591),x98592),f335(f335(f33(x98593,f888(x98591,a879)),f252(f888(x98593,a879))),x98594)))+~P1(f335(f335(f335(f33(x98593,f888(x98591,a879)),f252(f888(x98593,a879))),f335(f335(f8(f888(x98591,a879),f888(x98591,a879),x98593),f335(f7(x98591,f888(x98591,a879),a879),f337(x98591))),x98594)),x98592))
% 59.73/59.66 [9860]P1(f335(f335(f337(x98601),x98602),f335(f335(f34(x98603,f888(x98601,a879)),f252(f888(x98603,a879))),x98604)))+~P1(f335(f335(f335(f34(x98603,f888(x98601,a879)),f252(f888(x98603,a879))),f335(f335(f8(f888(x98601,a879),f888(x98601,a879),x98603),f335(f7(x98601,f888(x98601,a879),a879),f337(x98601))),x98604)),x98602))
% 59.73/59.66 [9872]E(f335(f335(f33(a881,f888(x98721,a879)),f252(f888(a881,a879))),x98722),f335(f335(f33(a881,f888(x98721,a879)),f252(f888(a881,a879))),x98723))+~E(f335(f335(f33(a881,f888(x98721,a879)),f335(f304(a881,f2(a881)),f487(x98722,x98724,x98723,x98721))),x98723),f335(f335(f33(a881,f888(x98721,a879)),f335(f304(a881,f2(a881)),f335(f335(f75(a881),f487(x98722,x98724,x98723,x98721)),x98724))),x98722))
% 59.73/59.66 [10190]~P1(f335(f335(f242(f888(f887(x101901,x101902),a879)),x101903),x101904))+P1(f335(f335(f242(f888(x101901,f888(x101902,a879))),f335(f335(f7(x101901,f888(f887(x101901,x101902),a879),f888(x101902,a879)),f335(f335(f8(f888(x101902,f888(f888(f887(x101901,x101902),a879),a879)),f888(f888(f887(x101901,x101902),a879),f888(x101902,a879)),x101901),f7(x101902,f888(f887(x101901,x101902),a879),a879)),f335(f335(f8(f888(x101902,f887(x101901,x101902)),f888(x101902,f888(f888(f887(x101901,x101902),a879),a879)),x101901),f335(f8(f887(x101901,x101902),f888(f888(f887(x101901,x101902),a879),a879),x101902),f337(f887(x101901,x101902)))),f264(x101901,x101902)))),x101903)),f335(f335(f7(x101901,f888(f887(x101901,x101902),a879),f888(x101902,a879)),f335(f335(f8(f888(x101902,f888(f888(f887(x101901,x101902),a879),a879)),f888(f888(f887(x101901,x101902),a879),f888(x101902,a879)),x101901),f7(x101902,f888(f887(x101901,x101902),a879),a879)),f335(f335(f8(f888(x101902,f887(x101901,x101902)),f888(x101902,f888(f888(f887(x101901,x101902),a879),a879)),x101901),f335(f8(f887(x101901,x101902),f888(f888(f887(x101901,x101902),a879),a879),x101902),f337(f887(x101901,x101902)))),f264(x101901,x101902)))),x101904)))
% 59.73/59.66 [10207]P1(f335(f335(f242(f888(f887(x102071,x102072),a879)),x102073),x102074))+~P1(f335(f335(f242(f888(x102071,f888(x102072,a879))),f335(f335(f7(x102071,f888(f887(x102071,x102072),a879),f888(x102072,a879)),f335(f335(f8(f888(x102072,f888(f888(f887(x102071,x102072),a879),a879)),f888(f888(f887(x102071,x102072),a879),f888(x102072,a879)),x102071),f7(x102072,f888(f887(x102071,x102072),a879),a879)),f335(f335(f8(f888(x102072,f887(x102071,x102072)),f888(x102072,f888(f888(f887(x102071,x102072),a879),a879)),x102071),f335(f8(f887(x102071,x102072),f888(f888(f887(x102071,x102072),a879),a879),x102072),f337(f887(x102071,x102072)))),f264(x102071,x102072)))),x102073)),f335(f335(f7(x102071,f888(f887(x102071,x102072),a879),f888(x102072,a879)),f335(f335(f8(f888(x102072,f888(f888(f887(x102071,x102072),a879),a879)),f888(f888(f887(x102071,x102072),a879),f888(x102072,a879)),x102071),f7(x102072,f888(f887(x102071,x102072),a879),a879)),f335(f335(f8(f888(x102072,f887(x102071,x102072)),f888(x102072,f888(f888(f887(x102071,x102072),a879),a879)),x102071),f335(f8(f887(x102071,x102072),f888(f888(f887(x102071,x102072),a879),a879),x102072),f337(f887(x102071,x102072)))),f264(x102071,x102072)))),x102074)))
% 59.73/59.66 [9271]~P1(f335(f335(f337(f887(x92711,x92711)),x92712),f310(x92711,x92714)))+P1(f335(f335(f337(f887(x92711,x92711)),x92712),f310(x92711,f335(f335(f104(f888(f887(x92711,x92711),a879)),x92713),x92714))))
% 59.73/59.66 [9272]~P1(f335(f335(f337(f887(x92721,x92721)),x92722),f310(x92721,x92723)))+P1(f335(f335(f337(f887(x92721,x92721)),x92722),f310(x92721,f335(f335(f104(f888(f887(x92721,x92721),a879)),x92723),x92724))))
% 59.73/59.66 [9632]~E(f335(f166(x96321),x96324),f177(x96321,x96322,x96323))+E(f335(f179(x96321,x96322),f335(f335(f147(x96321,f887(x96321,x96322)),f335(f335(f18(x96321,x96322,f887(x96321,x96322)),f264(x96321,x96322)),f335(f335(f8(f885(x96322),x96322,x96321),f239(x96322)),x96323))),x96324)),x96323)
% 59.73/59.66 [9963]~P1(f335(f335(f242(a881),f335(f335(f75(a881),x99631),x99634)),f335(f335(f75(a881),x99633),x99632)))+P1(f335(f335(f242(a1),f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),x99631),x99632)),f188(f888(f887(a881,a881),a879)))))),f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),x99633),x99634)),f188(f888(f887(a881,a881),a879)))))))
% 59.73/59.66 [9964]~P1(f335(f335(f243(a881),f335(f335(f75(a881),x99641),x99644)),f335(f335(f75(a881),x99643),x99642)))+P1(f335(f335(f243(a1),f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),x99641),x99642)),f188(f888(f887(a881,a881),a879)))))),f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),x99643),x99644)),f188(f888(f887(a881,a881),a879)))))))
% 59.73/59.66 [10041]P1(f335(f335(f242(a881),f335(f335(f75(a881),x100411),x100412)),f335(f335(f75(a881),x100413),x100414)))+~P1(f335(f335(f242(a1),f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),x100411),x100414)),f188(f888(f887(a881,a881),a879)))))),f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),x100413),x100412)),f188(f888(f887(a881,a881),a879)))))))
% 59.73/59.66 [10042]P1(f335(f335(f243(a881),f335(f335(f75(a881),x100421),x100422)),f335(f335(f75(a881),x100423),x100424)))+~P1(f335(f335(f243(a1),f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),x100421),x100424)),f188(f888(f887(a881,a881),a879)))))),f335(a84,f335(f288(f887(a881,a881),f887(a881,a881),a102),f335(f335(f312(f887(a881,a881)),f335(f335(f264(a881,a881),x100423),x100422)),f188(f888(f887(a881,a881),a879)))))))
% 59.73/59.66 [10083]P1(f335(f335(f242(f888(x100831,a879)),f335(f335(f33(a881,f888(x100831,a879)),f252(f888(a881,a879))),x100832)),f335(f335(f33(a881,f888(x100831,a879)),f252(f888(a881,a879))),x100833)))+~P1(f335(f335(f242(f888(x100831,a879)),f335(f335(f33(a881,f888(x100831,a879)),f335(f304(a881,f2(a881)),f475(x100833,x100834,x100832,x100831))),x100832)),f335(f335(f33(a881,f888(x100831,a879)),f335(f304(a881,f2(a881)),f335(f335(f75(a881),f475(x100833,x100834,x100832,x100831)),x100834))),x100833)))
% 59.73/59.66 [10134]P1(f335(f335(f242(a93),x101344),f2(a93)))+E(f335(f335(f270(f887(a93,a93),f887(x101341,f888(a884,a331)),f887(a93,a93),f887(f888(a93,f888(a879,f885(f883(x101341)))),f887(a93,a93))),f335(x101342,x101343)),f335(f335(f8(f888(f888(a93,f888(a879,f885(f883(x101341)))),f888(f887(a93,a93),f887(f888(a93,f888(a879,f885(f883(x101341)))),f887(a93,a93)))),f888(f887(a93,a93),f887(f888(a93,f888(a879,f885(f883(x101341)))),f887(a93,a93))),f887(x101341,f888(a884,a331))),f335(f270(f887(a93,a93),f888(a93,f888(a879,f885(f883(x101341)))),f887(a93,a93),f887(f888(a93,f888(a879,f885(f883(x101341)))),f887(a93,a93))),f283(x101341,x101342,f335(f335(f23(a93),x101344),f73(a93)),x101343))),f335(f335(f8(f888(f888(a93,f888(a879,f885(f883(x101341)))),f888(a93,f888(a879,f885(f883(x101341))))),f888(f888(a93,f888(a879,f885(f883(x101341)))),f888(f887(a93,a93),f887(f888(a93,f888(a879,f885(f883(x101341)))),f887(a93,a93)))),f887(x101341,f888(a884,a331))),f335(f8(f888(a93,f888(a879,f885(f883(x101341)))),f888(f887(a93,a93),f887(f888(a93,f888(a879,f885(f883(x101341)))),f887(a93,a93))),f888(a93,f888(a879,f885(f883(x101341))))),f264(f888(a93,f888(a879,f885(f883(x101341)))),f887(a93,a93)))),f335(f335(f8(f888(a93,f888(a879,f885(f883(x101341)))),f888(f888(a93,f888(a879,f885(f883(x101341)))),f888(a93,f888(a879,f885(f883(x101341))))),f887(x101341,f888(a884,a331))),f38(x101341)),f335(f335(f8(x101341,f888(a93,f888(a879,f885(f883(x101341)))),f887(x101341,f888(a884,a331))),f36(x101341)),f263(x101341,f888(a884,a331))))))),f283(x101341,x101342,x101344,x101343))
% 59.73/59.66 [10180]~P1(f335(f335(f337(x101802),x101804),f335(f260(x101801,x101802),x101803)))+P1(f335(f259(x101801,x101802,f335(f335(f7(x101801,f888(f887(x101801,x101802),a879),f888(x101802,a879)),f335(f335(f8(f888(x101802,f888(f888(f887(x101801,x101802),a879),a879)),f888(f888(f887(x101801,x101802),a879),f888(x101802,a879)),x101801),f7(x101802,f888(f887(x101801,x101802),a879),a879)),f335(f335(f8(f888(x101802,f887(x101801,x101802)),f888(x101802,f888(f888(f887(x101801,x101802),a879),a879)),x101801),f335(f8(f887(x101801,x101802),f888(f888(f887(x101801,x101802),a879),a879),x101802),f337(f887(x101801,x101802)))),f264(x101801,x101802)))),x101803)),x101804))
% 59.73/59.66 [10181]~P1(f335(f335(f337(x101811),x101814),f335(f262(x101811,x101812),x101813)))+P1(f335(f258(x101811,x101812,f335(f335(f7(x101811,f888(f887(x101811,x101812),a879),f888(x101812,a879)),f335(f335(f8(f888(x101812,f888(f888(f887(x101811,x101812),a879),a879)),f888(f888(f887(x101811,x101812),a879),f888(x101812,a879)),x101811),f7(x101812,f888(f887(x101811,x101812),a879),a879)),f335(f335(f8(f888(x101812,f887(x101811,x101812)),f888(x101812,f888(f888(f887(x101811,x101812),a879),a879)),x101811),f335(f8(f887(x101811,x101812),f888(f888(f887(x101811,x101812),a879),a879),x101812),f337(f887(x101811,x101812)))),f264(x101811,x101812)))),x101813)),x101814))
% 59.73/59.66 [10193]P1(f335(f335(f337(x101931),x101932),f335(f260(x101933,x101931),x101934)))+~P1(f335(f259(x101933,x101931,f335(f335(f7(x101933,f888(f887(x101933,x101931),a879),f888(x101931,a879)),f335(f335(f8(f888(x101931,f888(f888(f887(x101933,x101931),a879),a879)),f888(f888(f887(x101933,x101931),a879),f888(x101931,a879)),x101933),f7(x101931,f888(f887(x101933,x101931),a879),a879)),f335(f335(f8(f888(x101931,f887(x101933,x101931)),f888(x101931,f888(f888(f887(x101933,x101931),a879),a879)),x101933),f335(f8(f887(x101933,x101931),f888(f888(f887(x101933,x101931),a879),a879),x101931),f337(f887(x101933,x101931)))),f264(x101933,x101931)))),x101934)),x101932))
% 59.73/59.66 [10194]P1(f335(f335(f337(x101941),x101942),f335(f262(x101941,x101943),x101944)))+~P1(f335(f258(x101941,x101943,f335(f335(f7(x101941,f888(f887(x101941,x101943),a879),f888(x101943,a879)),f335(f335(f8(f888(x101943,f888(f888(f887(x101941,x101943),a879),a879)),f888(f888(f887(x101941,x101943),a879),f888(x101943,a879)),x101941),f7(x101943,f888(f887(x101941,x101943),a879),a879)),f335(f335(f8(f888(x101943,f887(x101941,x101943)),f888(x101943,f888(f888(f887(x101941,x101943),a879),a879)),x101941),f335(f8(f887(x101941,x101943),f888(f888(f887(x101941,x101943),a879),a879),x101943),f337(f887(x101941,x101943)))),f264(x101941,x101943)))),x101944)),x101942))
% 59.73/59.66 [9882]P1(f335(f153(x98821,x98822),x98823))+~P1(f335(f153(x98821,f335(f335(f18(x98821,a879,a879),f335(f335(f8(a879,f888(a879,a879),x98821),a333),x98824)),x98822)),x98823))
% 59.73/59.66 [9883]P1(f335(f153(x98831,x98832),x98833))+~P1(f335(f153(x98831,f335(f335(f18(x98831,a879,a879),f335(f335(f8(a879,f888(a879,a879),x98831),a333),x98832)),x98834)),x98833))
% 59.73/59.66 [9965]~P114(x99651)+E(f335(f335(f76(x99651),f335(f335(f75(x99651),f73(x99651)),f73(x99651))),f335(f335(f6(a881,x99651),f335(f335(f8(x99651,x99651,a881),f335(f75(x99651),x99652)),f335(f335(f7(a881,x99651,x99651),f335(f335(f8(x99651,f888(x99651,x99651),a881),f76(x99651)),f94(x99651))),x99653))),f335(f250(a881),x99654))),f335(f335(f76(x99651),f335(f94(x99651),x99654)),f335(f335(f75(x99651),x99652),f335(f335(f75(x99651),x99652),f335(f335(f76(x99651),f335(f94(x99651),f335(f335(f23(a881),x99654),f73(a881)))),x99653)))))
% 59.73/59.66 [10104]P1(f335(x101041,f523(x101042,x101043,x101044,x101041)))+P36(x101042,f335(f249(f887(x101042,x101042)),f335(f268(x101042,x101042,a879),f335(f335(f8(f888(x101042,a879),f888(x101042,a879),x101042),f335(f18(x101042,a879,a879),f335(f335(f8(a879,f888(a879,a879),x101042),a333),x101041))),f335(f335(f7(x101042,f888(x101042,x101042),f888(x101042,a879)),f335(f335(f8(f888(x101042,a879),f888(f888(x101042,x101042),f888(x101042,a879)),x101042),f8(x101042,a879,x101042)),a332)),x101043)))))
% 59.73/59.66 [10116]~P1(f335(f335(f243(a881),f335(x101164,f335(x101163,f523(x101161,x101163,x101164,x101162)))),f335(x101164,f523(x101161,x101163,x101164,x101162))))+P36(x101161,f335(f249(f887(x101161,x101161)),f335(f268(x101161,x101161,a879),f335(f335(f8(f888(x101161,a879),f888(x101161,a879),x101161),f335(f18(x101161,a879,a879),f335(f335(f8(a879,f888(a879,a879),x101161),a333),x101162))),f335(f335(f7(x101161,f888(x101161,x101161),f888(x101161,a879)),f335(f335(f8(f888(x101161,a879),f888(f888(x101161,x101161),f888(x101161,a879)),x101161),f8(x101161,a879,x101161)),a332)),x101163)))))
% 59.73/59.66 [10221]~P1(f335(f335(f337(f887(x102211,x102211)),f335(f335(f264(x102211,x102211),x102213),x102214)),f335(f335(f104(f888(f887(x102211,x102211),a879)),x102212),f310(x102211,f188(f888(f887(x102211,x102211),a879))))))+P1(f335(f335(f335(f335(f104(f888(x102211,f888(x102211,a879))),f335(f335(f7(x102211,f888(f887(x102211,x102211),a879),f888(x102211,a879)),f335(f335(f8(f888(x102211,f888(f888(f887(x102211,x102211),a879),a879)),f888(f888(f887(x102211,x102211),a879),f888(x102211,a879)),x102211),f7(x102211,f888(f887(x102211,x102211),a879),a879)),f335(f335(f8(f888(x102211,f887(x102211,x102211)),f888(x102211,f888(f888(f887(x102211,x102211),a879),a879)),x102211),f335(f8(f887(x102211,x102211),f888(f888(f887(x102211,x102211),a879),a879),x102211),f337(f887(x102211,x102211)))),f264(x102211,x102211)))),x102212)),a332),x102213),x102214))
% 59.73/59.66 [10230]P1(f335(f335(f337(f887(x102301,x102301)),f335(f335(f264(x102301,x102301),x102302),x102303)),f335(f335(f104(f888(f887(x102301,x102301),a879)),x102304),f310(x102301,f188(f888(f887(x102301,x102301),a879))))))+~P1(f335(f335(f335(f335(f104(f888(x102301,f888(x102301,a879))),f335(f335(f7(x102301,f888(f887(x102301,x102301),a879),f888(x102301,a879)),f335(f335(f8(f888(x102301,f888(f888(f887(x102301,x102301),a879),a879)),f888(f888(f887(x102301,x102301),a879),f888(x102301,a879)),x102301),f7(x102301,f888(f887(x102301,x102301),a879),a879)),f335(f335(f8(f888(x102301,f887(x102301,x102301)),f888(x102301,f888(f888(f887(x102301,x102301),a879),a879)),x102301),f335(f8(f887(x102301,x102301),f888(f888(f887(x102301,x102301),a879),a879),x102301),f337(f887(x102301,x102301)))),f264(x102301,x102301)))),x102304)),a332),x102302),x102303))
% 59.73/59.66 [10178]E(f335(f335(f144(f882(x101781)),f335(f335(f144(x101781),x101782),f335(f135(f882(x101781),f882(x101781),f127(x101781),f107(x101781)),f335(f335(f147(f882(x101781),f882(x101781)),f149(f882(x101781),x101781,f107(x101781),f335(f335(f8(f882(x101781),f888(f882(x101781),f882(x101781)),x101781),f16(f882(x101781),f882(x101781))),f335(f335(f7(x101781,f882(x101781),f882(x101781)),f144(x101781)),f107(x101781))))),x101783)))),f173(x101781,f335(f335(f144(f882(x101781)),x101784),f335(f135(f882(f882(x101781)),f882(f882(x101781)),f127(f882(x101781)),f107(f882(x101781))),f335(f335(f147(f882(x101781),f882(f882(x101781))),f149(f882(f882(x101781)),x101781,f107(f882(x101781)),f335(f16(f888(f882(x101781),f882(f882(x101781))),x101781),f335(f335(f7(f882(x101781),f882(f882(x101781)),f882(f882(x101781))),f144(f882(x101781))),f107(f882(x101781)))))),x101783))))),f173(x101781,f335(f335(f144(f882(x101781)),f335(f335(f144(x101781),x101782),x101784)),x101783)))+~P1(f335(f323(f882(f882(x101781)),f174(x101781)),f335(f335(f144(f882(x101781)),f335(f335(f144(x101781),x101782),x101784)),x101783)))
% 59.73/59.66 [10220]~P1(f335(f56(x102202),f335(f249(x102202),x102204)))+P1(f335(f56(x102201),f335(f249(x102201),f335(f335(f8(f888(x102202,a879),a879,x102201),f82(x102202)),f335(f335(f7(x102201,f888(x102202,a879),f888(x102202,a879)),f335(f335(f8(f888(x102202,f888(a879,a879)),f888(f888(x102202,a879),f888(x102202,a879)),x102201),f18(x102202,a879,a879)),f335(f335(f8(f888(x102202,a879),f888(x102202,f888(a879,a879)),x102201),f335(f8(a879,f888(a879,a879),x102202),a333)),f335(f335(f7(x102201,f888(x102202,x102201),f888(x102202,a879)),f335(f335(f8(f888(x102201,a879),f888(f888(x102202,x102201),f888(x102202,a879)),x102201),f8(x102201,a879,x102202)),a332)),x102203)))),x102204)))))
% 59.73/59.66 [5291]E(x52911,x52912)+~E(f120(x52913,x52914,x52911),f120(x52913,x52915,x52912))
% 59.73/59.66 [5292]E(x52921,x52922)+~E(f120(x52923,x52921,x52924),f120(x52923,x52922,x52925))
% 59.73/59.66 [5293]E(x52931,x52932)+~E(f163(x52933,x52931,x52934),f163(x52933,x52932,x52935))
% 59.73/59.66 [5672]E(f335(f335(f312(x56721),x56722),f177(x56721,x56723,x56724)),f177(x56721,x56723,x56724))+~E(f335(x56724,x56722),f335(f235(x56723),x56725))
% 59.73/59.66 [6078]P1(f335(f259(x60781,x60782,x60783),x60784))+~P1(f335(f335(x60783,x60785),x60784))
% 59.73/59.66 [6079]P1(f335(f259(x60791,x60792,x60793),x60794))+~P1(f335(f335(x60793,x60795),x60794))
% 59.73/59.66 [6080]P1(f335(f258(x60801,x60802,x60803),x60804))+~P1(f335(f335(x60803,x60804),x60805))
% 59.73/59.66 [6081]P1(f335(f258(x60811,x60812,x60813),x60814))+~P1(f335(f335(x60813,x60814),x60815))
% 59.73/59.66 [6084]~E(f335(x60844,x60842),f335(f235(x60843),x60845))+P1(f335(f335(f337(x60841),x60842),f177(x60841,x60843,x60844)))
% 59.73/59.66 [6085]~E(f335(x60854,x60855),f335(f235(x60851),x60852))+P1(f335(f335(f337(x60851),x60852),f178(x60853,x60851,x60854)))
% 59.73/59.66 [6551]~E(x65515,f2(a93))+E(f335(f199(x65511,x65512,x65513,x65514),x65515),f109(x65512))
% 59.73/59.66 [6552]~E(x65525,f2(a93))+E(f335(f196(x65521,x65522,x65523,x65524),x65525),f118(x65522))
% 59.73/59.66 [6693]~E(x66933,f2(a93))+E(f335(f279(x66931,x66932,x66933,x66934),x66935),f335(f264(x66931,x66932),x66935))
% 59.73/59.66 [6766]~E(f335(x67664,x67665),f200(x67662))+E(f335(f237(f885(x67661),x67662,f200(x67661),x67663),f335(x67664,x67665)),f200(x67661))
% 59.73/59.66 [6767]~E(f335(x67674,x67675),f200(x67672))+E(f335(f237(f885(x67671),x67672,f200(x67671),x67673),f335(x67674,x67675)),f200(x67671))
% 59.73/59.66 [7393]E(f335(x73931,x73932),f200(x73933))+~E(f335(f180(x73934,x73933,x73935,x73931),x73932),f200(x73933))
% 59.73/59.66 [7394]E(f335(x73941,x73942),f200(x73943))+~E(f335(f180(x73944,x73943,x73941,x73945),x73942),f200(x73943))
% 59.73/59.66 [7430]E(f335(f180(x74301,x74302,x74303,x74304),x74305),f335(x74303,x74305))+P1(f335(f335(f337(x74301),x74305),f177(x74301,x74302,x74304)))
% 59.73/59.66 [7431]E(f335(f180(x74311,x74312,x74313,x74314),x74315),f335(x74314,x74315))+P1(f335(f335(f337(x74311),x74315),f177(x74311,x74312,x74313)))
% 59.73/59.66 [7753]~P22(x77534,x77531,x77532,x77535)+E(f335(f68(x77531,x77531,x77531,f335(x77532,x77533)),f335(x77532,x77533)),f335(x77532,x77533))
% 59.73/59.66 [7797]E(f335(f180(x77971,x77972,x77973,x77974),x77975),f335(x77974,x77975))+~P1(f335(f335(f337(x77971),x77975),f177(x77971,x77972,x77974)))
% 59.73/59.66 [8144]~P18(x81445,x81441,x81442)+E(f335(f68(x81441,x81441,x81441,f335(x81442,x81443)),f335(x81442,x81444)),f335(f68(x81441,x81441,x81441,f335(x81442,x81444)),f335(x81442,x81443)))
% 59.73/59.66 [8476]P1(f335(f335(f337(f887(x84761,x84761)),f335(f335(f264(x84761,x84761),x84762),x84763)),f329(x84761,x84764,x84765)))+~P1(f335(f335(f243(a881),f335(x84764,x84762)),f335(x84764,x84763)))
% 59.73/59.66 [8566]~P1(f335(f335(f337(x85664),x85663),f298(x85664,x85661,x85662,x85665)))+P1(f335(f335(x85661,x85662),x85663))
% 59.73/59.66 [8567]~P1(f335(f335(f337(x85674),x85673),f301(x85674,x85671,x85672,x85675)))+P1(f335(f335(x85671,x85672),x85673))
% 59.73/59.66 [8568]~P1(f335(f335(f337(x85684),x85682),f298(x85684,x85681,x85685,x85683)))+P1(f335(f335(x85681,x85682),x85683))
% 59.73/59.66 [8569]~P1(f335(f335(f337(x85694),x85692),f301(x85694,x85691,x85695,x85693)))+P1(f335(f335(x85691,x85692),x85693))
% 59.73/59.66 [8712]~P54(x87122,x87121,x87125,x87123,x87124)+E(f335(f313(x87121,x87122,x87123),x87124),f252(f888(x87122,a879)))
% 59.73/59.66 [9153]~P33(x91531,x91532,x91533,x91534,x91535)+P33(x91531,x91532,x91533,f335(f162(x91531),x91534),f335(f162(x91532),x91535))
% 59.73/59.66 [9155]~P33(x91551,x91552,x91553,f335(f162(x91551),x91554),x91555)+P33(x91551,x91552,x91553,x91554,f335(f162(x91552),x91555))
% 59.73/59.66 [9156]~P33(x91561,x91562,x91563,x91564,f335(f162(x91562),x91565))+P33(x91561,x91562,x91563,f335(f162(x91561),x91564),x91565)
% 59.73/59.66 [9162]P33(x91621,x91622,x91623,x91624,x91625)+~P33(x91621,x91622,x91623,f335(f162(x91621),x91624),f335(f162(x91622),x91625))
% 59.73/59.66 [9556]P1(f335(f335(f337(f887(f882(x95561),f882(x95561))),f335(f335(f264(f882(x95561),f882(x95561)),f335(f335(f144(x95561),x95562),x95563)),f335(f335(f144(x95561),x95562),x95564))),f150(x95561,x95565)))+~P1(f335(f335(f337(f887(f882(x95561),f882(x95561))),f335(f335(f264(f882(x95561),f882(x95561)),x95563),x95564)),f150(x95561,x95565)))
% 59.73/59.66 [9557]P1(f335(f335(f337(f887(f882(x95571),f882(x95571))),f335(f335(f264(f882(x95571),f882(x95571)),f335(f335(f127(x95571),x95572),x95573)),f335(f335(f127(x95571),x95572),x95574))),f140(x95571,x95575)))+~P1(f335(f335(f337(f887(f882(x95571),f882(x95571))),f335(f335(f264(f882(x95571),f882(x95571)),x95573),x95574)),f140(x95571,x95575)))
% 59.73/59.66 [9754]E(f335(f335(f144(x97541),f678(x97542,x97543,x97544,x97545,x97541)),f679(x97542,x97543,x97544,x97545,x97541)),x97545)+~P1(f335(f335(f337(f887(f882(x97541),f882(x97541))),f335(f335(f264(f882(x97541),f882(x97541)),x97545),f335(f335(f144(x97541),x97544),x97543))),f151(x97541,x97542)))
% 59.73/59.66 [9777]E(f335(f335(f144(x97771),f681(x97772,x97773,x97774,x97775,x97771)),f682(x97772,x97773,x97774,x97775,x97771)),x97773)+~P1(f335(f335(f337(f887(f882(x97771),f882(x97771))),f335(f335(f264(f882(x97771),f882(x97771)),f335(f335(f144(x97771),x97775),x97774)),x97773)),f151(x97771,x97772)))
% 59.73/59.66 [9938]~P1(f335(f335(f337(f887(f882(x99381),f882(x99381))),f335(f335(f264(f882(x99381),f882(x99381)),f335(f335(f144(x99381),x99385),x99382)),x99384)),f151(x99381,x99383)))+P1(f335(f335(f337(f887(f882(x99381),f882(x99381))),f335(f335(f264(f882(x99381),f882(x99381)),x99382),f682(x99383,x99384,x99382,x99385,x99381))),f151(x99381,x99383)))
% 59.73/59.66 [10009]~P1(f335(f335(f337(f887(f882(x100091),f882(x100091))),f335(f335(f264(f882(x100091),f882(x100091)),x100095),f335(f335(f144(x100091),x100094),x100093))),f151(x100091,x100092)))+P1(f335(f335(f337(f887(f882(x100091),f882(x100091))),f335(f335(f264(f882(x100091),f882(x100091)),f679(x100092,x100093,x100094,x100095,x100091)),x100093)),f151(x100091,x100092)))
% 59.73/59.66 [10173]P1(f335(f335(f337(f887(x101731,x101731)),f335(f335(f264(x101731,x101731),f335(x101732,f335(f335(f75(a881),x101733),x101734))),f335(x101732,x101733))),f310(x101731,x101735)))+~P1(f335(f335(f337(f887(x101731,x101731)),f335(f335(f264(x101731,x101731),f335(x101732,f335(a106,f593(x101734,x101733,x101735,x101732,x101731)))),f335(x101732,f593(x101734,x101733,x101735,x101732,x101731)))),f310(x101731,x101735)))
% 59.73/59.66 [5263]E(x52631,x52632)+~E(f335(f335(f144(x52633),x52634),x52631),f335(f335(f144(x52633),x52635),x52632))
% 59.73/59.66 [5264]E(x52641,x52642)+~E(f335(f335(f144(x52643),x52641),x52644),f335(f335(f144(x52643),x52642),x52645))
% 59.73/59.66 [5309]P1(f335(x53091,x53092))+~E(f335(f129(x53093,x53091),x53094),f335(f335(f144(x53093),x53092),x53095))
% 59.73/59.66 [5310]P1(f335(x53101,x53102))+~E(f335(f335(f144(x53103),x53102),x53104),f335(f129(x53103,x53101),x53105))
% 59.73/59.66 [5467]~E(f335(f335(f131(x54671),x54673),x54672),f335(f335(f144(x54671),x54674),x54675))+E(f335(f335(f158(x54671),x54672),x54673),x54674)
% 59.73/59.66 [5601]~P17(x56014,x56015,x56011)+E(f335(f335(x56011,x56012),f335(f335(x56011,x56012),x56013)),f335(f335(x56011,x56012),x56013))
% 59.73/59.66 [5963]~E(f335(x59633,x59634),f335(f235(x59632),x59635))+E(f335(f335(f335(f67(x59631,f885(x59632)),x59633),x59634),f335(f235(x59632),x59635)),x59633)
% 59.73/59.66 [6136]~E(x61364,f2(a93))+E(f335(f335(f111(x61361,x61362,x61363),x61364),x61365),f335(f335(f264(f882(x61362),x61361),f107(x61362)),x61365))
% 59.73/59.66 [6205]~P106(x62052)+~E(f335(f335(f141(x62051,x62052,x62053),x62054),x62055),f107(x62051))
% 59.73/59.66 [6590]E(x65901,x65902)+~E(f335(f335(f127(x65903),x65904),f335(f335(f144(x65903),x65901),f107(x65903))),f335(f335(f127(x65903),x65905),f335(f335(f144(x65903),x65902),f107(x65903))))
% 59.73/59.66 [6591]E(x65911,x65912)+~E(f335(f335(f127(x65913),x65911),f335(f335(f144(x65913),x65914),f107(x65913))),f335(f335(f127(x65913),x65912),f335(f335(f144(x65913),x65915),f107(x65913))))
% 59.73/59.66 [6851]E(f335(f182(x68511,x68512,x68513,x68514),x68515),f200(x68512))+P1(f335(f335(f337(x68511),x68515),x68514))
% 59.73/59.66 [6852]E(f335(f182(x68521,x68522,x68523,x68524),x68525),f200(x68522))+P1(f335(f335(f337(x68521),x68525),x68524))
% 59.73/59.66 [6916]E(f335(f335(f312(x69161),f335(x69162,x69163)),f335(f313(x69164,x69161,x69162),x69165)),f335(f313(x69164,x69161,x69162),x69165))+~P1(f335(f335(f337(x69164),x69163),x69165))
% 59.73/59.66 [6922]~P1(f335(x69224,f335(x69223,x69225)))+P1(f335(f335(f314(x69221,x69222,x69223),x69224),x69225))
% 59.73/59.66 [6923]~P1(f335(f335(x69233,x69235),x69234))+P1(f335(f335(f253(x69231,x69232,x69233),x69234),x69235))
% 59.73/59.66 [6924]~P1(f335(f335(x69243,x69245),x69244))+P1(f335(f335(f253(x69241,x69242,x69243),x69244),x69245))
% 59.73/59.66 [6925]~P1(f335(f335(x69253,x69255),x69254))+P1(f335(f335(f253(x69251,x69252,x69253),x69254),x69255))
% 59.73/59.66 [7018]~E(f335(f313(x70181,x70182,x70183),x70184),x70185)+E(f335(f313(f888(x70181,a879),f888(x70182,a879),f313(x70181,x70182,x70183)),f335(f311(x70181),x70184)),f335(f311(x70182),x70185))
% 59.73/59.66 [7046]E(f335(f182(x70461,x70462,x70463,x70464),x70465),f335(x70463,x70465))+~P1(f335(f335(f337(x70461),x70465),x70464))
% 59.73/59.66 [7047]E(f335(f182(x70471,x70472,x70473,x70474),x70475),f335(x70473,x70475))+~P1(f335(f335(f337(x70471),x70475),x70474))
% 59.73/59.66 [7353]P26(x73531,x73532,x73533,x73534)+~P26(x73531,x73532,x73533,f335(f335(f312(x73531),x73535),x73534))
% 59.73/59.66 [7464]~P1(f335(f335(f337(x74644),x74643),x74645))+P1(f335(f335(f337(x74641),f335(x74642,x74643)),f335(f313(x74644,x74641,x74642),x74645)))
% 59.73/59.66 [7487]~P106(x74872)+E(f143(x74871,x74872,x74873,f335(f129(x74871,x74874),x74875)),f335(f129(x74871,x74874),f143(x74871,x74872,x74873,x74875)))
% 59.73/59.66 [7519]P1(f335(x75191,f335(x75192,x75193)))+~P1(f335(f335(f314(x75194,x75195,x75192),x75191),x75193))
% 59.73/59.66 [7520]P1(f335(f335(x75201,x75202),x75203))+~P1(f335(f335(f253(x75204,x75205,x75201),x75203),x75202))
% 59.73/59.66 [7521]P1(f335(f335(x75211,x75212),x75213))+~P1(f335(f335(f253(x75214,x75215,x75211),x75213),x75212))
% 59.73/59.66 [7522]P1(f335(f335(x75221,x75222),x75223))+~P1(f335(f335(f253(x75224,x75225,x75221),x75223),x75222))
% 59.73/59.66 [7586]~P1(f335(f335(f337(x75863),f335(x75864,x75862)),x75865))+P1(f335(f335(f337(x75861),x75862),f335(f314(x75861,x75863,x75864),x75865)))
% 59.73/59.66 [7587]~P1(f335(f335(f337(x75873),f335(x75874,x75872)),x75875))+P1(f335(f335(f337(x75871),x75872),f335(f314(x75871,x75873,x75874),x75875)))
% 59.73/59.66 [7989]~P1(f335(f335(f337(x79895),x79893),f335(f314(x79895,x79891,x79892),x79894)))+P1(f335(f335(f337(x79891),f335(x79892,x79893)),x79894))
% 59.73/59.66 [7990]~P1(f335(f335(f337(x79905),x79903),f335(f314(x79905,x79901,x79902),x79904)))+P1(f335(f335(f337(x79901),f335(x79902,x79903)),x79904))
% 59.73/59.66 [8210]~E(x82103,f335(f335(f335(f67(x82101,f885(x82102)),f335(f16(f885(x82102),x82101),f200(x82102))),x82104),f335(f235(x82102),x82105)))+E(f177(x82101,x82102,x82103),f335(f335(f312(x82101),x82104),f188(f888(x82101,a879))))
% 59.73/59.66 [8289]~P18(x82892,x82891,x82893)+E(f335(f135(x82891,x82892,f335(f7(x82892,x82891,x82891),x82893),x82894),f145(x82892,x82895)),f335(f335(f59(x82892,x82891,x82893),x82894),f335(f166(x82892),x82895)))
% 59.73/59.66 [8310]E(f335(x83101,f419(x83102,x83101,x83103,x83104)),x83104)+~P1(f335(f335(f337(x83105),x83104),f335(f313(x83103,x83105,x83101),x83102)))
% 59.73/59.66 [8311]E(f335(x83111,f465(x83112,x83111,x83113,x83114)),x83114)+~P1(f335(f335(f337(x83115),x83114),f335(f313(x83113,x83115,x83111),x83112)))
% 59.73/59.66 [8612]~E(x86122,f335(f335(f144(x86121),x86124),x86125))+P1(f335(f335(f337(f887(f882(x86121),f882(x86121))),f335(f335(f264(f882(x86121),f882(x86121)),f107(x86121)),x86122)),f140(x86121,x86123)))
% 59.73/59.66 [8656]E(f335(x86561,f335(f87(x86562,x86563,x86564,x86561),x86565)),x86565)+~P1(f335(f335(f337(x86563),x86565),f335(f313(x86562,x86563,x86561),x86564)))
% 59.73/59.66 [8659]P26(x86591,x86592,f87(x86592,x86591,x86593,x86594),x86595)+~P1(f335(f335(f242(f888(x86591,a879)),x86595),f335(f313(x86592,x86591,x86594),x86593)))
% 59.73/59.66 [8665]~P33(x86651,x86653,x86655,x86652,x86654)+E(f335(f189(f882(x86651)),x86652),f335(f189(f882(x86653)),x86654))
% 59.73/59.66 [8666]~P33(x86661,x86663,x86665,x86662,x86664)+E(f335(f189(f882(x86661)),x86662),f335(f189(f882(x86663)),x86664))
% 59.73/59.66 [8667]~P33(x86671,x86673,x86675,x86672,x86674)+E(f335(f189(f882(x86671)),x86672),f335(f189(f882(x86673)),x86674))
% 59.73/59.66 [8678]P1(f335(f335(f242(f888(x86781,a879)),f335(f335(f34(x86782,f888(x86781,a879)),x86783),x86784)),f335(x86784,x86785)))+~P1(f335(f335(f337(x86782),x86785),x86783))
% 59.73/59.66 [8728]~P54(x87281,x87282,x87283,x87285,x87284)+E(f335(f313(x87281,x87282,x87283),f252(f888(x87281,a879))),x87284)
% 59.73/59.66 [8938]E(f335(f335(f335(f67(x89381,f885(x89382)),f182(x89381,x89382,x89383,x89384)),x89385),f200(x89382)),f182(x89381,x89382,x89383,x89384))+P1(f335(f335(f337(x89381),x89385),x89384))
% 59.73/59.66 [8943]E(f335(f129(x89431,x89432),f770(x89433,x89434,x89435,x89432,x89431)),x89433)+~E(f335(f129(x89431,x89432),x89435),f335(f335(f144(x89431),x89434),x89433))
% 59.73/59.66 [8944]E(f335(f129(x89441,x89442),f773(x89443,x89442,x89444,x89445,x89441)),x89444)+~E(f335(f335(f144(x89441),x89445),x89444),f335(f129(x89441,x89442),x89443))
% 59.73/59.66 [8945]E(f335(x89451,f661(x89452,x89453,x89451,x89454,x89455)),x89452)+~E(f335(f335(f201(x89455,x89454),x89451),x89453),f335(f235(x89454),x89452))
% 59.73/59.66 [8948]E(f335(f235(x89481),f661(x89482,x89483,x89484,x89485,x89481)),x89483)+~E(f335(f335(f201(x89481,x89485),x89484),x89483),f335(f235(x89485),x89482))
% 59.73/59.66 [9039]E(f335(f189(f882(x90391)),x90392),x90393)+~P1(f335(f335(f337(f887(f882(x90391),f882(x90391))),f335(f335(f264(f882(x90391),f882(x90391)),x90394),x90392)),f335(f136(x90391,x90395),x90393)))
% 59.73/59.66 [9040]E(f335(f189(f882(x90401)),x90402),x90403)+~P1(f335(f335(f337(f887(f882(x90401),f882(x90401))),f335(f335(f264(f882(x90401),f882(x90401)),x90402),x90404)),f335(f136(x90401,x90405),x90403)))
% 59.73/59.66 [9108]P1(f335(f335(f337(x91081),f419(x91082,x91083,x91081,x91084)),x91082))+~P1(f335(f335(f337(x91085),x91084),f335(f313(x91081,x91085,x91083),x91082)))
% 59.73/59.66 [9109]P1(f335(f335(f337(x91091),f465(x91092,x91093,x91091,x91094)),x91092))+~P1(f335(f335(f337(x91095),x91094),f335(f313(x91091,x91095,x91093),x91092)))
% 59.73/59.66 [9267]~P37(f888(x92673,a879),f888(x92671,a879),x92672)+P1(f335(f335(f242(f888(x92671,a879)),f335(x92672,f335(f335(f95(f888(x92673,a879)),x92674),x92675))),f335(f335(f95(f888(x92671,a879)),f335(x92672,x92674)),f335(x92672,x92675))))
% 59.73/59.66 [9269]E(f335(f313(x92691,x92692,x92693),f445(x92694,x92693,x92691,x92695,x92692)),x92695)+~P1(f335(f335(f242(f888(x92692,a879)),x92695),f335(f313(x92691,x92692,x92693),x92694)))
% 59.73/59.66 [9525]E(f335(x95251,f847(x95252,x95251,x95253,x95254,x95255)),f335(f235(x95255),x95254))+~P1(f335(f335(f337(x95255),x95254),f178(x95253,x95255,f182(x95253,x95255,x95251,x95252))))
% 59.73/59.66 [9572]P1(f335(f335(f337(f887(f882(x95721),f882(x95721))),f335(f335(f264(f882(x95721),f882(x95721)),f335(f335(f144(x95721),x95722),x95723)),f335(f335(f144(x95721),x95722),x95724))),f310(f882(x95721),f150(x95721,x95725))))+~P1(f335(f335(f337(f887(f882(x95721),f882(x95721))),f335(f335(f264(f882(x95721),f882(x95721)),x95723),x95724)),f310(f882(x95721),f150(x95721,x95725))))
% 59.73/59.66 [9603]~E(f335(x96033,f668(x96035,x96034,x96033,x96032,x96031)),f335(x96035,f668(x96035,x96034,x96033,x96032,x96031)))+E(f335(f335(f147(x96031,x96032),x96033),x96034),f335(f335(f147(x96031,x96032),x96035),x96034))
% 59.73/59.66 [9681]~E(f335(f129(x96811,x96815),x96814),f335(f335(f144(x96811),x96813),x96812))+E(f335(f335(f127(x96811),f771(x96812,x96813,x96814,x96815,x96811)),f335(f335(f144(x96811),x96813),f770(x96812,x96813,x96814,x96815,x96811))),x96814)
% 59.73/59.66 [9682]~E(f335(f335(f144(x96821),x96825),x96824),f335(f129(x96821,x96823),x96822))+E(f335(f335(f127(x96821),f774(x96822,x96823,x96824,x96825,x96821)),f335(f335(f144(x96821),x96825),f773(x96822,x96823,x96824,x96825,x96821))),x96822)
% 59.73/59.66 [9686]E(f335(f335(f147(x96861,x96862),x96863),x96864),f335(f335(f147(x96861,x96862),x96865),x96864))+P1(f335(f335(f337(x96861),f668(x96863,x96864,x96865,x96862,x96861)),f335(f166(x96861),x96864)))
% 59.73/59.66 [9718]~P1(f335(f335(f337(x97185),x97184),f335(f288(x97181,x97185,x97183),x97182)))+P1(f335(f335(f337(x97181),f839(x97182,x97183,x97181,x97184,x97185)),x97182))
% 59.73/59.66 [9719]~P1(f335(f335(f337(x97195),x97194),f335(f288(x97191,x97195,x97193),x97192)))+P1(f335(f335(f337(x97191),f848(x97192,x97193,x97191,x97194,x97195)),x97192))
% 59.73/59.66 [9748]~P1(f335(f335(f242(f888(x97485,a879)),x97484),f335(f313(x97481,x97485,x97483),x97482)))+P1(f335(f335(f242(f888(x97481,a879)),f445(x97482,x97483,x97481,x97484,x97485)),x97482))
% 59.73/59.66 [9801]~P1(f335(f335(f337(x98015),x98014),f178(x98011,x98015,f182(x98011,x98015,x98013,x98012))))+P1(f335(f335(f337(x98011),f847(x98012,x98013,x98011,x98014,x98015)),x98012))
% 59.73/59.66 [10196]E(x101961,f2(a93))+E(f335(f237(f887(f882(x101962),x101963),f887(x101962,x101963),f335(f335(f264(f882(x101962),x101963),f107(x101962)),x101964),f335(f268(x101962,x101963,f887(f882(x101962),x101963)),f335(f335(f7(x101962,f888(x101963,f887(f882(x101962),x101963)),f888(x101963,f887(f882(x101962),x101963))),f335(f335(f8(f888(f887(f882(x101962),x101963),f887(f882(x101962),x101963)),f888(f888(x101963,f887(f882(x101962),x101963)),f888(x101963,f887(f882(x101962),x101963))),x101962),f8(f887(f882(x101962),x101963),f887(f882(x101962),x101963),x101963)),f335(f335(f8(f888(f882(x101962),f888(x101963,f887(f882(x101962),x101963))),f888(f887(f882(x101962),x101963),f887(f882(x101962),x101963)),x101962),f268(f882(x101962),x101963,f887(f882(x101962),x101963))),f335(f335(f8(f888(f882(x101962),f882(x101962)),f888(f882(x101962),f888(x101963,f887(f882(x101962),x101963))),x101962),f335(f8(f882(x101962),f888(x101963,f887(f882(x101962),x101963)),f882(x101962)),f264(f882(x101962),x101963))),f144(x101962))))),f335(f111(x101963,x101962,x101965),f335(f335(f23(a93),x101961),f73(a93)))))),f335(x101965,x101964)),f335(f335(f111(x101963,x101962,x101965),x101961),x101964))
% 59.73/59.66 [5479]~E(f335(x54793,x54794),x54795)+E(f335(f335(f335(f67(x54791,x54792),x54793),x54794),x54795),x54793)
% 59.73/59.66 [5480]~E(f335(x54803,x54804),x54805)+E(f335(f335(f335(f67(x54801,x54802),x54803),x54804),x54805),x54803)
% 59.73/59.66 [5926]E(f335(x59261,x59262),x59263)+~E(f335(f335(f335(f67(x59264,x59265),x59261),x59262),x59263),x59261)
% 59.73/59.66 [6021]E(x60211,x60212)+~E(f335(f267(x60213,x60214),f335(f335(f264(x60213,x60214),x60215),x60211)),x60212)
% 59.73/59.66 [6022]E(x60221,x60222)+~E(f335(f263(x60223,x60224),f335(f335(f264(x60223,x60224),x60221),x60225)),x60222)
% 59.73/59.66 [6281]~E(x62813,f335(f335(f127(x62811),x62814),f335(f335(f144(x62811),x62812),x62815)))+P1(f335(f335(f337(x62811),x62812),f335(f166(x62811),x62813)))
% 59.73/59.66 [6679]E(f335(f313(x66791,x66792,f335(f16(x66792,x66791),x66793)),x66794),f335(f335(f312(x66792),x66793),f188(f888(x66792,a879))))+~P1(f335(f335(f337(x66791),x66795),x66794))
% 59.73/59.66 [6753]E(f335(f335(f104(f888(x67531,a879)),f335(f166(x67531),x67532)),f335(f166(x67531),x67533)),f335(f166(x67531),x67534))+~E(f160(x67531,x67535,x67534),f335(f335(f264(f882(x67531),f882(x67531)),x67532),x67533))
% 59.73/59.66 [6856]~P106(x68562)+E(f335(f189(f882(x68561)),f335(f335(f141(x68561,x68562,x68563),x68564),x68565)),f335(a106,f335(f189(f882(x68561)),x68565)))
% 59.73/59.66 [6870]~P106(x68702)+E(f335(f166(x68701),f335(f335(f141(x68701,x68702,x68703),x68704),x68705)),f335(f335(f312(x68701),x68704),f335(f166(x68701),x68705)))
% 59.73/59.66 [7139]~P114(x71391)+E(f335(f335(f76(x71391),f335(f335(f76(x71391),x71392),x71393)),f335(f335(f76(x71391),x71394),x71395)),f335(f335(f76(x71391),f335(f335(f76(x71391),x71392),x71394)),f335(f335(f76(x71391),x71393),x71395)))
% 59.73/59.66 [7140]~P114(x71401)+E(f335(f335(f75(x71401),f335(f335(f75(x71401),x71402),x71403)),f335(f335(f75(x71401),x71404),x71405)),f335(f335(f75(x71401),f335(f335(f75(x71401),x71402),x71404)),f335(f335(f75(x71401),x71403),x71405)))
% 59.73/59.66 [7141]~P66(x71411)+E(f335(f335(f292(x71411),f335(f335(f76(x71411),x71412),x71413)),f335(f335(f76(x71411),x71414),x71415)),f335(f335(f76(x71411),f335(f335(f292(x71411),x71412),x71414)),f335(f335(f292(x71411),x71413),x71415)))
% 59.73/59.66 [7155]~P106(x71551)+E(f308(x71551,f335(f335(f241(x71551),x71552),x71553),f335(f335(f240(x71551),x71554),x71555)),f335(f335(f95(f888(x71551,a879)),f308(x71551,x71552,x71554)),f308(x71551,x71553,x71555)))
% 59.73/59.66 [7156]~P106(x71561)+E(f307(x71561,f335(f335(f241(x71561),x71562),x71563),f335(f335(f240(x71561),x71564),x71565)),f335(f335(f95(f888(x71561,a879)),f307(x71561,x71562,x71564)),f307(x71561,x71563,x71565)))
% 59.73/59.66 [7157]~P106(x71571)+E(f305(x71571,f335(f335(f241(x71571),x71572),x71573),f335(f335(f240(x71571),x71574),x71575)),f335(f335(f95(f888(x71571,a879)),f305(x71571,x71572,x71574)),f305(x71571,x71573,x71575)))
% 59.73/59.66 [7158]~P106(x71581)+E(f335(f335(f95(f888(x71581,a879)),f335(f304(x71581,x71582),x71583)),f335(f304(x71581,x71584),x71585)),f335(f304(x71581,f335(f335(f241(x71581),x71582),x71584)),f335(f335(f240(x71581),x71583),x71585)))
% 59.73/59.66 [7275]~P1(f335(x72751,f384(x72753,x72752,x72751)))+P1(f335(x72751,f335(f335(f264(x72752,x72753),x72754),x72755)))
% 59.73/59.66 [7366]~E(f335(x73663,x73664),f200(x73662))+E(f178(x73661,x73662,f335(f335(f335(f67(x73661,f885(x73662)),x73663),x73664),f335(f235(x73662),x73665))),f335(f335(f312(x73662),x73665),f178(x73661,x73662,x73663)))
% 59.73/59.66 [7385]~E(x73852,f335(x73854,x73855))+P1(f335(f335(f337(x73851),x73852),f335(f313(x73853,x73851,x73854),f252(f888(x73853,a879)))))
% 59.73/59.66 [7442]~E(f335(x74423,x74424),f200(x74422))+E(f335(f335(f23(f888(x74421,a879)),f177(x74421,x74422,x74423)),f335(f335(f312(x74421),x74424),x74425)),f335(f335(f23(f888(x74421,a879)),f177(x74421,x74422,x74423)),x74425))
% 59.73/59.66 [7461]~P17(x74613,x74612,x74614)+P17(x74611,x74612,f335(f335(f8(x74613,f888(x74612,x74612),x74611),x74614),x74615))
% 59.73/59.66 [7462]~P18(x74623,x74622,x74624)+P18(x74621,x74622,f335(f335(f8(x74623,f888(x74622,x74622),x74621),x74624),x74625))
% 59.73/59.66 [7604]~P26(x76041,x76042,x76043,x76044)+P26(x76041,x76042,x76043,f335(f335(f23(f888(x76041,a879)),x76044),x76045))
% 59.73/59.66 [7761]~P1(f335(f335(x77613,x77614),x77615))+P1(f335(f335(f268(x77611,x77612,a879),x77613),f335(f335(f264(x77611,x77612),x77614),x77615)))
% 59.73/59.66 [7762]~P1(f335(f335(x77623,x77624),x77625))+P1(f335(f335(f268(x77621,x77622,a879),x77623),f335(f335(f264(x77621,x77622),x77624),x77625)))
% 59.73/59.66 [7873]~P1(f335(x78732,x78734))+~E(f335(f335(f131(x78731),f335(f189(f882(x78731)),f171(x78731,x78732,x78733))),x78733),f335(f335(f144(x78731),x78734),x78735))
% 59.73/59.66 [7893]P26(x78931,x78932,x78933,x78934)+~P26(x78931,x78932,x78933,f335(f335(f104(f888(x78931,a879)),x78935),x78934))
% 59.73/59.66 [7894]P26(x78941,x78942,x78943,x78944)+~P26(x78941,x78942,x78943,f335(f335(f104(f888(x78941,a879)),x78944),x78945))
% 59.73/59.66 [7942]~P106(x79422)+E(f335(f335(f141(x79421,x79422,x79423),x79424),f143(x79421,x79422,x79423,x79425)),f143(x79421,x79422,x79423,f335(f335(f144(x79421),x79424),x79425)))
% 59.73/59.66 [8265]~P17(x82652,x82651,x82653)+E(f335(f135(x82651,x82652,f335(f7(x82652,x82651,x82651),x82653),x82654),x82655),f335(f335(f59(x82652,x82651,x82653),x82654),f335(f166(x82652),x82655)))
% 59.73/59.66 [8294]~E(f335(f335(f131(x82941),f335(f189(f882(x82941)),f171(x82941,x82942,x82943))),x82943),f335(f335(f144(x82941),x82944),x82945))+E(f335(f335(f127(x82941),f171(x82941,x82942,x82943)),f335(f335(f144(x82941),x82944),x82945)),x82943)
% 59.73/59.66 [8321]P1(f335(f335(x83211,x83212),x83213))+~P1(f335(f335(f268(x83214,x83215,a879),x83211),f335(f335(f264(x83214,x83215),x83212),x83213)))
% 59.73/59.66 [8382]~E(f335(f335(f179(x83821,x83822),x83825),x83823),f335(f235(x83822),x83824))+P1(f335(f335(f337(f887(x83821,x83822)),f335(f335(f264(x83821,x83822),x83823),x83824)),f335(f166(f887(x83821,x83822)),x83825)))
% 59.73/59.66 [8383]~E(f335(f335(f179(x83831,x83832),x83835),x83833),f335(f235(x83832),x83834))+P1(f335(f335(f337(f887(x83831,x83832)),f335(f335(f264(x83831,x83832),x83833),x83834)),f335(f166(f887(x83831,x83832)),x83835)))
% 59.73/59.66 [8786]P1(f335(f335(f242(f888(x87861,a879)),f335(f313(x87862,x87861,x87863),x87864)),f335(f313(x87862,x87861,x87863),x87865)))+~P1(f335(f335(f242(f888(x87862,a879)),x87864),x87865))
% 59.73/59.66 [8787]P1(f335(f335(f242(f888(x87871,a879)),f335(f314(x87871,x87872,x87873),x87874)),f335(f314(x87871,x87872,x87873),x87875)))+~P1(f335(f335(f242(f888(x87872,a879)),x87874),x87875))
% 59.73/59.66 [8863]E(x88631,f2(a93))+E(f335(f335(f270(x88632,x88633,x88632,f887(x88633,x88632)),f335(x88634,x88635)),f279(x88633,x88632,f335(f335(f23(a93),x88631),f73(a93)),x88634)),f335(f279(x88633,x88632,x88631,x88634),x88635))
% 59.73/59.66 [9379]E(f335(f235(x93791),f721(x93792,x93793,x93794,x93791,x93795)),f335(f335(f179(x93795,x93791),x93792),x93794))+~P1(f335(f335(f337(f887(x93795,x93791)),f335(f335(f264(x93795,x93791),x93794),x93793)),f335(f166(f887(x93795,x93791)),x93792)))
% 59.73/59.66 [9426]~P1(f335(f335(f337(x94262),x94265),f335(f313(x94261,x94262,x94264),x94263)))+P1(f335(f335(f337(x94261),f335(f87(x94261,x94262,x94263,x94264),x94265)),x94263))
% 59.73/59.66 [9517]~P1(f335(f56(x95173),f335(f313(x95172,x95173,x95175),f252(f888(x95172,a879)))))+P1(f335(f56(x95171),f335(f313(x95172,x95171,f335(f335(f8(x95173,x95171,x95172),x95174),x95175)),f252(f888(x95172,a879)))))
% 59.73/59.66 [9542]P1(f335(f335(f242(f888(f888(x95421,a879),a879)),f335(f313(f888(x95422,a879),f888(x95421,a879),f313(x95422,x95421,x95423)),f335(f311(x95422),x95424))),f335(f311(x95421),x95425)))+~P1(f335(f335(f242(f888(x95421,a879)),f335(f313(x95422,x95421,x95423),x95424)),x95425))
% 59.73/59.66 [9552]~P1(f335(f56(f885(x95521)),f335(f313(x95522,f885(x95521),x95523),f252(f888(x95522,a879)))))+P1(f335(f56(f885(x95521)),f335(f313(x95522,f885(x95521),f335(f335(f335(f67(x95522,f885(x95521)),x95523),x95524),f335(f235(x95521),x95525))),f252(f888(x95522,a879)))))
% 59.73/59.66 [9611]E(x96111,x96112)+~P1(f335(f61(x96113,x96114,x96115,x96111,f188(f888(x96113,a879))),x96112))
% 59.73/59.66 [9627]E(f335(f335(f264(x96271,x96272),f539(x96273,x96274,x96275,x96272,x96271)),f540(x96273,x96274,x96275,x96272,x96271)),x96275)+~P1(f335(f335(f337(f887(x96271,x96272)),x96275),f335(f335(f266(x96271,x96272),x96274),x96273)))
% 59.73/59.66 [9723]P1(f335(f335(f337(x97231),f539(x97232,x97233,x97234,x97235,x97231)),x97233))+~P1(f335(f335(f337(f887(x97231,x97235)),x97234),f335(f335(f266(x97231,x97235),x97233),x97232)))
% 59.73/59.66 [9732]P1(f335(f335(f337(x97321),f484(x97322,x97323,x97324,x97325,x97321)),x97325))+P1(f335(f335(f242(f888(x97324,a879)),f335(f313(x97321,x97324,x97323),x97325)),x97322))
% 59.73/59.66 [9891]P1(f335(f335(f337(x98911),f540(x98912,x98913,x98914,x98911,x98915)),f335(x98912,f539(x98912,x98913,x98914,x98911,x98915))))+~P1(f335(f335(f337(f887(x98915,x98911)),x98914),f335(f335(f266(x98915,x98911),x98913),x98912)))
% 59.73/59.66 [9916]P1(f335(f335(f337(f887(x99161,x99161)),f335(f335(f264(x99161,x99161),x99162),f612(x99163,x99164,x99165,x99162,x99161))),x99163))+~P1(f335(f335(f337(f887(x99161,x99161)),f335(f335(f264(x99161,x99161),x99162),x99165)),f335(f335(f183(f887(x99161,x99161),a879),f335(a106,x99164)),x99163)))
% 59.73/59.66 [9917]P1(f335(f335(f337(f887(x99171,x99171)),f335(f335(f264(x99171,x99171),x99172),f613(x99173,x99174,x99175,x99172,x99171))),x99173))+~P1(f335(f335(f337(f887(x99171,x99171)),f335(f335(f264(x99171,x99171),x99172),x99175)),f335(f335(f183(f887(x99171,x99171),a879),f335(a106,x99174)),x99173)))
% 59.73/59.66 [9935]~P1(f335(f335(f337(f887(f882(x99351),f882(x99351))),f335(f335(f264(f882(x99351),f882(x99351)),f335(f335(f144(x99351),x99352),x99355)),x99354)),f151(x99351,x99353)))+P1(f335(f335(f337(f887(x99351,x99351)),f335(f335(f264(x99351,x99351),x99352),f681(x99353,x99354,x99355,x99352,x99351))),x99353))
% 59.73/59.66 [9957]~P1(f335(f335(f337(x99571),f335(x99573,f484(x99575,x99573,x99571,x99574,x99572))),x99575))+P1(f335(f335(f242(f888(x99571,a879)),f335(f313(x99572,x99571,x99573),x99574)),x99575))
% 59.73/59.66 [6356]P1(f335(x63562,x63564))+E(f171(x63561,x63562,f335(f335(f127(x63561),x63563),f335(f335(f144(x63561),x63564),x63565))),f171(x63561,x63562,x63563))
% 59.73/59.66 [6406]~P61(x64062)+E(f335(f335(f335(f104(f888(x64061,x64062)),x64063),x64064),x64065),f335(f335(f104(x64062),f335(x64063,x64065)),f335(x64064,x64065)))
% 59.73/59.66 [6407]~P61(x64072)+E(f335(f335(f335(f104(f888(x64071,x64072)),x64073),x64074),x64075),f335(f335(f104(x64072),f335(x64073,x64075)),f335(x64074,x64075)))
% 59.73/59.66 [6408]~P63(x64082)+E(f335(f335(f335(f23(f888(x64081,x64082)),x64083),x64084),x64085),f335(f335(f23(x64082),f335(x64083,x64085)),f335(x64084,x64085)))
% 59.73/59.66 [6409]~P63(x64092)+E(f335(f335(f335(f23(f888(x64091,x64092)),x64093),x64094),x64095),f335(f335(f23(x64092),f335(x64093,x64095)),f335(x64094,x64095)))
% 59.73/59.66 [6410]~P61(x64102)+E(f335(f335(f335(f95(f888(x64101,x64102)),x64103),x64104),x64105),f335(f335(f95(x64102),f335(x64103,x64105)),f335(x64104,x64105)))
% 59.73/59.66 [6411]~P61(x64112)+E(f335(f335(f335(f95(f888(x64111,x64112)),x64113),x64114),x64115),f335(f335(f95(x64112),f335(x64113,x64115)),f335(x64114,x64115)))
% 59.73/59.66 [6428]E(x64281,x64282)+E(f335(f335(f158(x64283),f335(f335(f152(x64283,x64284),x64281),x64285)),x64282),f335(f335(f158(x64283),x64284),x64282))
% 59.73/59.66 [6698]~E(x66984,f188(f888(x66983,a879)))+E(f335(f335(f104(f888(x66981,a879)),x66982),f335(f335(f33(x66983,f888(x66981,a879)),x66984),x66985)),x66982)
% 59.73/59.66 [6699]~E(x66994,f188(f888(x66993,a879)))+E(f335(f335(f23(f888(x66991,a879)),x66992),f335(f335(f33(x66993,f888(x66991,a879)),x66994),x66995)),x66992)
% 59.73/59.66 [6700]~E(x67004,f188(f888(x67003,a879)))+E(f335(f335(f95(f888(x67001,a879)),x67002),f335(f335(f34(x67003,f888(x67001,a879)),x67004),x67005)),x67002)
% 59.73/59.66 [6716]~E(x67164,f188(f888(x67163,a879)))+E(f335(f335(f312(x67161),x67162),f335(f335(f33(x67163,f888(x67161,a879)),x67164),x67165)),f335(f335(f312(x67161),x67162),f188(f888(x67161,a879))))
% 59.73/59.66 [7138]~P114(x71381)+E(f335(f335(f76(x71381),f335(f335(f76(x71381),x71382),x71383)),f335(f335(f76(x71381),x71384),x71385)),f335(f335(f76(x71381),x71382),f335(f335(f76(x71381),x71383),f335(f335(f76(x71381),x71384),x71385))))
% 59.73/59.66 [7509]E(f335(f335(f158(x75091),f335(f335(f147(x75092,x75091),x75093),x75094)),x75095),f335(x75093,f335(f335(f158(x75092),x75094),x75095)))+~P1(f335(f335(f243(a881),x75095),f335(f189(f882(x75092)),x75094)))
% 59.73/59.66 [7575]E(f335(f335(f104(f888(x75751,a879)),f335(x75752,x75753)),f335(f335(f33(x75754,f888(x75751,a879)),x75755),x75752)),f335(f335(f33(x75754,f888(x75751,a879)),x75755),x75752))+~P1(f335(f335(f337(x75754),x75753),x75755))
% 59.73/59.66 [7576]E(f335(f335(f95(f888(x75761,a879)),f335(x75762,x75763)),f335(f335(f34(x75764,f888(x75761,a879)),x75765),x75762)),f335(f335(f34(x75764,f888(x75761,a879)),x75765),x75762))+~P1(f335(f335(f337(x75764),x75763),x75765))
% 59.73/59.66 [8183]~E(x81833,f188(f888(x81831,a879)))+E(f335(f335(f33(x81831,f888(x81832,a879)),x81833),f335(f335(f8(f888(x81832,a879),f888(x81832,a879),x81831),f335(f312(x81832),x81834)),x81835)),f188(f888(x81832,a879)))
% 59.73/59.66 [8188]~P1(f335(f335(f337(x81884),x81883),x81885))+P1(f335(f335(f242(f888(x81881,a879)),f335(x81882,x81883)),f335(f335(f33(x81884,f888(x81881,a879)),x81885),x81882)))
% 59.73/59.66 [8320]~E(f335(x83204,x83202),x83205)+P1(f335(f335(f337(x83201),x83202),f335(f314(x83201,x83203,x83204),f335(f335(f312(x83203),x83205),f188(f888(x83203,a879))))))
% 59.73/59.66 [8365]~P52(x83651,x83652,f335(f289(x83652,x83651),x83653))+E(f335(f335(f95(f888(x83651,a879)),f335(f288(x83652,x83651,x83653),x83654)),f335(f288(x83652,x83651,x83653),x83655)),f335(f288(x83652,x83651,x83653),f335(f335(f95(f888(x83652,a879)),x83654),x83655)))
% 59.73/59.66 [8442]E(x84421,f2(a93))+E(f335(f112(x84422,x84423,f335(x84424,f335(f335(f23(a93),x84421),f73(a93)))),f335(f335(f7(x84422,a93,f883(x84423)),x84425),x84421)),f335(f199(x84422,x84423,x84424,x84425),x84421))
% 59.73/59.66 [8482]E(x84821,f188(f888(x84822,a879)))+E(f335(f335(f33(x84822,f888(x84823,a879)),x84821),f335(f335(f8(f888(x84823,a879),f888(x84823,a879),x84822),f335(f312(x84823),x84824)),x84825)),f335(f335(f312(x84823),x84824),f335(f335(f33(x84822,f888(x84823,a879)),x84821),x84825)))
% 59.73/59.66 [8483]E(x84831,f188(f888(x84832,a879)))+E(f335(f335(f33(x84832,f888(x84833,a879)),x84831),f335(f335(f8(f888(x84833,a879),f888(x84833,a879),x84832),f335(f312(x84833),x84834)),x84835)),f335(f335(f312(x84833),x84834),f335(f335(f33(x84832,f888(x84833,a879)),x84831),x84835)))
% 59.73/59.66 [8532]~P26(x85322,x85321,x85323,f252(f888(x85322,a879)))+E(f335(f335(f23(f888(x85321,a879)),f335(f313(x85322,x85321,x85323),x85324)),f335(f313(x85322,x85321,x85323),x85325)),f335(f313(x85322,x85321,x85323),f335(f335(f23(f888(x85322,a879)),x85324),x85325)))
% 59.73/59.66 [8533]~P26(x85332,x85331,x85333,f252(f888(x85332,a879)))+E(f335(f335(f95(f888(x85331,a879)),f335(f313(x85332,x85331,x85333),x85334)),f335(f313(x85332,x85331,x85333),x85335)),f335(f313(x85332,x85331,x85333),f335(f335(f95(f888(x85332,a879)),x85334),x85335)))
% 59.73/59.66 [8599]~P1(f335(f335(f62(x85991,x85992,x85995),x85993),x85994))+P1(f335(f335(f337(f887(x85991,x85992)),f335(f335(f264(x85991,x85992),x85993),x85994)),x85995))
% 59.73/59.66 [8630]P1(f335(f335(f337(x86301),x86302),f335(f260(x86303,x86301),x86304)))+~P1(f335(f335(f337(f887(x86303,x86301)),f335(f335(f264(x86303,x86301),x86305),x86302)),x86304))
% 59.73/59.66 [8631]P1(f335(f335(f337(x86311),x86312),f335(f260(x86313,x86311),x86314)))+~P1(f335(f335(f337(f887(x86313,x86311)),f335(f335(f264(x86313,x86311),x86315),x86312)),x86314))
% 59.73/59.66 [8632]P1(f335(f335(f337(x86321),x86322),f335(f262(x86321,x86323),x86324)))+~P1(f335(f335(f337(f887(x86321,x86323)),f335(f335(f264(x86321,x86323),x86322),x86325)),x86324))
% 59.73/59.66 [8633]P1(f335(f335(f337(x86331),x86332),f335(f262(x86331,x86333),x86334)))+~P1(f335(f335(f337(f887(x86331,x86333)),f335(f335(f264(x86331,x86333),x86332),x86335)),x86334))
% 59.73/59.66 [8770]P1(f335(f335(f62(x87701,x87702,x87703),x87704),x87705))+~P1(f335(f335(f337(f887(x87701,x87702)),f335(f335(f264(x87701,x87702),x87704),x87705)),x87703))
% 59.73/59.66 [8809]E(f335(x88091,x88092),x88093)+~P1(f335(f335(f337(x88094),x88092),f335(f314(x88094,x88095,x88091),f335(f335(f312(x88095),x88093),f188(f888(x88095,a879))))))
% 59.73/59.66 [9011]E(x90111,f2(a93))+E(f115(x90112,f116(x90113,f883(f885(x90112)),f335(f335(f7(x90113,a93,f883(f885(x90112))),x90114),x90111),f335(x90115,f335(f335(f23(a93),x90111),f73(a93))))),f335(f196(x90113,x90112,x90115,x90114),x90111))
% 59.73/59.66 [9035]P1(f335(f335(f337(f887(x90351,x90352)),f335(f335(f264(x90351,x90352),x90353),x90354)),f335(f289(x90352,x90351),x90355)))+~P1(f335(f335(f337(f887(x90352,x90351)),f335(f335(f264(x90352,x90351),x90354),x90353)),x90355))
% 59.73/59.66 [9036]P1(f335(f335(f337(f887(x90361,x90362)),f335(f335(f264(x90361,x90362),x90363),x90364)),f335(f289(x90362,x90361),x90365)))+~P1(f335(f335(f337(f887(x90362,x90361)),f335(f335(f264(x90362,x90361),x90364),x90363)),x90365))
% 59.73/59.66 [9054]~P1(f335(f335(x90541,x90545),x90544))+P1(f335(f335(x90541,f335(f267(x90542,x90543),f335(f335(f264(x90542,x90543),x90544),x90545))),f335(f263(x90542,x90543),f335(f335(f264(x90542,x90543),x90544),x90545))))
% 59.73/59.66 [9082]~P1(f335(f335(f337(f887(x90822,x90821)),f335(f335(f264(x90822,x90821),x90824),x90823)),f335(f289(x90821,x90822),x90825)))+P1(f335(f335(f337(f887(x90821,x90822)),f335(f335(f264(x90821,x90822),x90823),x90824)),x90825))
% 59.73/59.66 [9083]~P1(f335(f335(f337(f887(x90832,x90831)),f335(f335(f264(x90832,x90831),x90834),x90833)),f335(f289(x90831,x90832),x90835)))+P1(f335(f335(f337(f887(x90831,x90832)),f335(f335(f264(x90831,x90832),x90833),x90834)),x90835))
% 59.73/59.66 [9116]~P1(f335(f335(f337(f887(x91163,x91161)),f335(f335(f264(x91163,x91161),x91165),x91162)),x91164))+P1(f335(f335(f337(x91161),x91162),f335(f288(x91163,x91161,x91164),f335(f335(f312(x91163),x91165),f188(f888(x91163,a879))))))
% 59.73/59.66 [9166]P1(f335(f335(f337(f887(x91661,x91662)),f335(f335(f264(x91661,x91662),x91663),x91664)),x91665))+~P1(f335(f335(f337(x91662),x91664),f335(f288(x91661,x91662,x91665),f335(f335(f312(x91661),x91663),f188(f888(x91661,a879))))))
% 59.73/59.66 [9186]E(f335(f335(f335(f67(x91861,f885(x91862)),f182(x91861,x91862,x91863,x91864)),x91865),f200(x91862)),f182(x91861,x91862,x91863,f335(f335(f23(f888(x91861,a879)),x91864),f335(f335(f312(x91861),x91865),f188(f888(x91861,a879))))))+~P1(f335(f335(f337(x91861),x91865),x91864))
% 59.73/59.66 [9254]~P77(x92541)+E(f335(f335(f6(a881,x92541),x92542),f305(a881,f335(f335(f75(a881),x92543),x92544),f335(f335(f75(a881),x92545),x92544))),f335(f335(f6(a881,x92541),f335(f335(f8(a881,x92541,a881),x92542),f335(f335(f7(a881,a881,a881),f75(a881)),x92544))),f305(a881,x92543,x92545)))
% 59.73/59.66 [9273]~P77(x92731)+E(f335(f335(f6(a881,x92731),x92732),f335(f304(a881,f335(f335(f75(a881),x92733),x92734)),f335(f335(f75(a881),x92735),x92734))),f335(f335(f6(a881,x92731),f335(f335(f8(a881,x92731,a881),x92732),f335(f335(f7(a881,a881,a881),f75(a881)),x92734))),f335(f304(a881,x92733),x92735)))
% 59.73/59.66 [9329]~P26(x93291,x93292,x93293,f252(f888(x93291,a879)))+E(f335(f335(f147(x93291,x93292),x93293),f335(f129(x93291,f335(f335(f8(a879,a879,x93291),a330),f335(a332,x93294))),x93295)),f335(f129(x93292,f335(f335(f8(a879,a879,x93292),a330),f335(a332,f335(x93293,x93294)))),f335(f335(f147(x93291,x93292),x93293),x93295)))
% 59.73/59.66 [9345]~P26(x93451,x93452,x93453,f335(f335(f312(x93451),x93454),f335(f166(x93451),x93455)))+E(f335(f335(f147(x93451,x93452),x93453),f335(f129(x93451,f335(f335(f8(a879,a879,x93451),a330),f335(a332,x93454))),x93455)),f335(f129(x93452,f335(f335(f8(a879,a879,x93452),a330),f335(a332,f335(x93453,x93454)))),f335(f335(f147(x93451,x93452),x93453),x93455)))
% 59.73/59.66 [9504]P1(f335(f335(f337(f887(f882(x95041),f882(x95041))),f335(f335(f264(f882(x95041),f882(x95041)),f335(f335(f144(x95041),x95042),x95043)),f335(f335(f144(x95041),x95044),x95043))),f150(x95041,x95045)))+~P1(f335(f335(f337(f887(x95041,x95041)),f335(f335(f264(x95041,x95041),x95042),x95044)),x95045))
% 59.73/59.66 [9622]E(f335(f335(f312(x96221),f829(x96222,x96223,x96224,x96225,x96221)),f833(x96222,x96223,x96224,x96225,x96221)),f335(f335(f312(x96221),x96224),x96223))+~P1(f335(f57(x96221,x96225,f335(f335(f312(x96221),x96224),x96223)),x96222))
% 59.73/59.66 [9623]E(f335(f335(f312(x96231),f834(x96232,x96233,x96234,x96235,x96231)),f837(x96232,x96233,x96234,x96235,x96231)),f335(f335(f312(x96231),x96234),x96233))+~P1(f335(f57(x96231,x96235,f335(f335(f312(x96231),x96234),x96233)),x96232))
% 59.73/59.66 [9708]P1(f335(f335(f337(x97081),f633(x97082,x97083,x97084,x97085,x97081)),x97084))+P1(f335(f335(f335(f34(x97081,f888(x97085,a879)),x97084),x97083),x97082))
% 59.73/59.66 [9713]P1(f335(f335(f337(x97131),f620(x97132,x97133,x97131,x97134,x97135)),x97133))+P1(f335(f335(f337(x97135),x97134),f335(f335(f34(x97131,f888(x97135,a879)),x97133),x97132)))
% 59.73/59.66 [9722]P1(f335(f335(f337(x97221),f625(x97222,x97223,x97221,x97224,x97225)),x97223))+P1(f335(f335(f242(f888(x97225,a879)),x97224),f335(f335(f34(x97221,f888(x97225,a879)),x97223),x97222)))
% 59.73/59.66 [9724]P1(f335(f335(x97241,f732(x97242,x97241,x97243,x97244,x97245)),x97242))+~P1(f335(f335(f335(f33(x97245,f888(x97244,a879)),x97243),x97241),x97242))
% 59.73/59.66 [9728]P1(f335(f335(f337(x97281),f732(x97282,x97283,x97284,x97285,x97281)),x97284))+~P1(f335(f335(f335(f33(x97281,f888(x97285,a879)),x97284),x97283),x97282))
% 59.73/59.66 [9729]P46(x97294,f335(f335(f34(x97291,f888(x97294,a879)),x97295),x97293),f335(f335(f34(x97291,f888(f887(x97294,x97294),a879)),x97295),x97292))+P1(f335(f335(f337(x97291),f807(x97292,x97293,x97294,x97295,x97291)),x97295))
% 59.73/59.66 [9740]P1(f335(f335(f337(x97401),f799(x97402,x97403,x97401,x97404,x97405)),x97403))+~P1(f335(f335(f337(x97405),x97404),f335(f335(f33(x97401,f888(x97405,a879)),x97403),x97402)))
% 59.73/59.66 [9746]P1(f335(f335(f337(x97461),x97462),f335(x97463,f799(x97463,x97464,x97465,x97462,x97461))))+~P1(f335(f335(f337(x97461),x97462),f335(f335(f33(x97465,f888(x97461,a879)),x97464),x97463)))
% 59.73/59.66 [9843]~P1(f335(f335(x98434,f633(x98435,x98434,x98433,x98432,x98431)),x98435))+P1(f335(f335(f335(f34(x98431,f888(x98432,a879)),x98433),x98434),x98435))
% 59.73/59.66 [9846]~P1(f335(f335(f337(x98461),x98462),f335(x98465,f620(x98465,x98464,x98463,x98462,x98461))))+P1(f335(f335(f337(x98461),x98462),f335(f335(f34(x98463,f888(x98461,a879)),x98464),x98465)))
% 59.73/59.66 [9850]~P46(x98501,f335(x98504,f807(x98505,x98504,x98501,x98503,x98502)),f335(x98505,f807(x98505,x98504,x98501,x98503,x98502)))+P46(x98501,f335(f335(f34(x98502,f888(x98501,a879)),x98503),x98504),f335(f335(f34(x98502,f888(f887(x98501,x98501),a879)),x98503),x98505))
% 59.73/59.66 [9851]~P1(f335(f335(f242(f888(x98511,a879)),x98512),f335(x98515,f625(x98515,x98514,x98513,x98512,x98511))))+P1(f335(f335(f242(f888(x98511,a879)),x98512),f335(f335(f34(x98513,f888(x98511,a879)),x98514),x98515)))
% 59.73/59.66 [9920]~P1(f335(f335(f337(x99201),f829(x99205,x99204,x99203,x99202,x99201)),f833(x99205,x99204,x99203,x99202,x99201)))+~P1(f335(f57(x99201,x99202,f335(f335(f312(x99201),x99203),x99204)),x99205))
% 59.73/59.66 [9921]~P1(f335(f335(f337(x99211),f834(x99215,x99214,x99213,x99212,x99211)),f837(x99215,x99214,x99213,x99212,x99211)))+~P1(f335(f57(x99211,x99212,f335(f335(f312(x99211),x99213),x99214)),x99215))
% 59.73/59.66 [9922]~P1(f335(f335(f337(f887(x99221,x99221)),f335(f335(f264(x99221,x99221),x99222),x99225)),f335(f335(f183(f887(x99221,x99221),a879),f335(a106,x99224)),x99223)))+P1(f335(f335(f337(f887(x99221,x99221)),f335(f335(f264(x99221,x99221),x99222),f614(x99223,x99224,x99225,x99222,x99221))),f335(f335(f183(f887(x99221,x99221),a879),x99224),x99223)))
% 59.73/59.66 [9929]P1(f335(f61(x99291,x99291,x99292,f829(x99293,x99294,x99295,x99292,x99291),f833(x99293,x99294,x99295,x99292,x99291)),x99293))+~P1(f335(f57(x99291,x99292,f335(f335(f312(x99291),x99295),x99294)),x99293))
% 59.73/59.66 [9930]P1(f335(f61(x99301,x99301,x99302,f834(x99303,x99304,x99305,x99302,x99301),f837(x99303,x99304,x99305,x99302,x99301)),x99303))+~P1(f335(f57(x99301,x99302,f335(f335(f312(x99301),x99305),x99304)),x99303))
% 59.73/59.66 [9940]~P106(x99401)+P15(x99401,f335(f335(f147(x99402,x99401),x99403),f335(f129(x99402,f335(f335(f7(x99402,x99401,a879),f335(f335(f8(x99401,f888(x99401,a879),x99402),a332),x99403)),f335(x99404,x99405))),x99405)))
% 59.73/59.66 [9981]~P1(f335(f335(f337(x99812),x99815),f335(f288(x99811,x99812,x99814),x99813)))+P1(f335(f335(f337(f887(x99811,x99812)),f335(f335(f264(x99811,x99812),f839(x99813,x99814,x99811,x99815,x99812)),x99815)),x99814))
% 59.73/59.66 [9982]~P1(f335(f335(f337(x99822),x99825),f335(f288(x99821,x99822,x99824),x99823)))+P1(f335(f335(f337(f887(x99821,x99822)),f335(f335(f264(x99821,x99822),f848(x99823,x99824,x99821,x99825,x99822)),x99825)),x99824))
% 59.73/59.66 [10002]~P1(f335(f335(f337(f887(x100021,x100021)),f335(f335(f264(x100021,x100021),x100025),x100024)),f335(f335(f183(f887(x100021,x100021),a879),f335(a106,x100023)),x100022)))+P1(f335(f335(f337(f887(x100021,x100021)),f335(f335(f264(x100021,x100021),f614(x100022,x100023,x100024,x100025,x100021)),x100024)),x100022))
% 59.73/59.66 [10005]~P1(f335(f335(f337(f887(x100051,x100051)),f335(f335(f264(x100051,x100051),x100055),x100054)),f335(f335(f183(f887(x100051,x100051),a879),f335(a106,x100053)),x100052)))+P1(f335(f335(f337(f887(x100051,x100051)),f335(f335(f264(x100051,x100051),f612(x100052,x100053,x100054,x100055,x100051)),x100054)),f335(f335(f183(f887(x100051,x100051),a879),x100053),x100052)))
% 59.73/59.66 [10006]~P1(f335(f335(f337(f887(x100061,x100061)),f335(f335(f264(x100061,x100061),x100065),x100064)),f335(f335(f183(f887(x100061,x100061),a879),f335(a106,x100063)),x100062)))+P1(f335(f335(f337(f887(x100061,x100061)),f335(f335(f264(x100061,x100061),f613(x100062,x100063,x100064,x100065,x100061)),x100064)),f335(f335(f183(f887(x100061,x100061),a879),x100063),x100062)))
% 59.73/59.66 [10007]~P1(f335(f335(f337(f887(f882(x100071),f882(x100071))),f335(f335(f264(f882(x100071),f882(x100071)),x100075),f335(f335(f144(x100071),x100074),x100073))),f151(x100071,x100072)))+P1(f335(f335(f337(f887(x100071,x100071)),f335(f335(f264(x100071,x100071),f678(x100072,x100073,x100074,x100075,x100071)),x100074)),x100072))
% 59.73/59.66 [7101]E(x71011,f200(x71012))+E(f177(x71013,x71012,f335(f335(f335(f67(x71013,f885(x71012)),x71014),x71015),x71011)),f335(f335(f312(x71013),x71015),f177(x71013,x71012,x71014)))
% 59.73/59.66 [7596]~E(x75963,f188(f888(x75962,a879)))+E(f335(f335(f104(f888(x75961,a879)),f335(f335(f33(x75962,f888(x75961,a879)),x75963),x75964)),x75965),x75965)
% 59.73/59.66 [7597]~E(x75973,f188(f888(x75972,a879)))+E(f335(f335(f95(f888(x75971,a879)),f335(f335(f34(x75972,f888(x75971,a879)),x75973),x75974)),x75975),x75975)
% 59.73/59.66 [7648]~P114(x76481)+E(f335(f335(f76(x76481),f335(f335(f76(x76481),x76482),x76483)),f335(f335(f76(x76481),x76484),x76485)),f335(f335(f76(x76481),x76484),f335(f335(f76(x76481),f335(f335(f76(x76481),x76482),x76483)),x76485)))
% 59.73/59.66 [7959]~E(x79595,f200(x79592))+E(f177(x79591,x79592,f335(f335(f335(f67(x79591,f885(x79592)),x79593),x79594),x79595)),f335(f335(f23(f888(x79591,a879)),f177(x79591,x79592,x79593)),f335(f335(f312(x79591),x79594),f188(f888(x79591,a879)))))
% 59.73/59.66 [8030]~E(x80303,f188(f888(x80302,a879)))+E(f335(f335(f23(f888(x80301,a879)),f335(f335(f34(x80302,f888(x80301,a879)),x80303),x80304)),x80305),f335(f335(f23(f888(x80301,a879)),f252(f888(x80301,a879))),x80305))
% 59.73/59.66 [8153]E(f335(f335(f152(x81531,f335(f335(f127(x81531),x81532),x81533)),x81534),x81535),f335(f335(f127(x81531),f335(f335(f152(x81531,x81532),x81534),x81535)),x81533))+~P1(f335(f335(f243(a881),x81534),f335(f189(f882(x81531)),x81532)))
% 59.73/59.66 [8154]E(f335(f335(f152(x81541,f335(f335(f127(x81541),x81542),x81543)),x81544),x81545),f335(f335(f127(x81541),f335(f335(f152(x81541,x81542),x81544),x81545)),x81543))+~P1(f335(f335(f243(a881),x81544),f335(f189(f882(x81541)),x81542)))
% 59.73/59.66 [8269]P1(f335(f335(f337(x82691),x82695),f335(f166(x82691),x82693)))+E(f335(f335(f179(x82691,x82692),f335(f335(f175(x82691,x82692),x82693),f335(f335(f147(x82691,x82692),x82694),x82693))),x82695),f200(x82692))
% 59.73/59.66 [8392]~P1(f335(f335(f337(x83921),x83925),f335(f166(x83921),x83923)))+E(f335(f335(f179(x83921,x83922),f335(f335(f175(x83921,x83922),x83923),f335(f335(f147(x83921,x83922),x83924),x83923))),x83925),f335(f235(x83922),f335(x83924,x83925)))
% 59.73/59.66 [8432]E(f335(f335(f158(x84321),f335(f335(f147(a881,x84321),x84322),f132(a881,f335(f304(a881,x84323),x84324)))),x84325),f335(x84322,f335(f335(f75(a881),x84323),x84325)))+~P1(f335(f335(f243(a881),x84325),f335(f335(f23(a881),x84324),x84323)))
% 59.73/59.66 [8473]~E(x84733,f188(f888(x84731,a879)))+E(f335(f335(f33(x84731,f888(x84732,a879)),x84733),f335(f335(f8(f888(x84732,a879),f888(x84732,a879),x84731),f335(f104(f888(x84732,a879)),x84734)),x84735)),f188(f888(x84732,a879)))
% 59.73/59.66 [8474]~E(x84743,f188(f888(x84741,a879)))+E(f335(f335(f34(x84741,f888(x84742,a879)),x84743),f335(f335(f8(f888(x84742,a879),f888(x84742,a879),x84741),f335(f23(f888(x84742,a879)),x84744)),x84745)),f252(f888(x84742,a879)))
% 59.73/59.66 [8475]~E(x84753,f188(f888(x84751,a879)))+E(f335(f335(f34(x84751,f888(x84752,a879)),x84753),f335(f335(f8(f888(x84752,a879),f888(x84752,a879),x84751),f335(f95(f888(x84752,a879)),x84754)),x84755)),f252(f888(x84752,a879)))
% 59.73/59.66 [8477]~P142(x84772)+E(f335(f335(f6(x84771,x84772),f335(f335(f8(x84772,x84772,x84771),f335(f76(x84772),x84773)),x84774)),x84775),f335(f335(f76(x84772),x84773),f335(f335(f6(x84771,x84772),x84774),x84775)))
% 59.73/59.66 [8752]E(x87521,f188(f888(x87522,a879)))+E(f335(f335(f33(x87522,f888(x87523,a879)),x87521),f335(f335(f8(f888(x87523,a879),f888(x87523,a879),x87522),f335(f104(f888(x87523,a879)),x87524)),x87525)),f335(f335(f104(f888(x87523,a879)),x87524),f335(f335(f33(x87522,f888(x87523,a879)),x87521),x87525)))
% 59.73/59.66 [8753]E(x87531,f188(f888(x87532,a879)))+E(f335(f335(f34(x87532,f888(x87533,a879)),x87531),f335(f335(f8(f888(x87533,a879),f888(x87533,a879),x87532),f335(f23(f888(x87533,a879)),x87534)),x87535)),f335(f335(f23(f888(x87533,a879)),x87534),f335(f335(f33(x87532,f888(x87533,a879)),x87531),x87535)))
% 59.73/59.66 [8754]E(x87541,f188(f888(x87542,a879)))+E(f335(f335(f34(x87542,f888(x87543,a879)),x87541),f335(f335(f8(f888(x87543,a879),f888(x87543,a879),x87542),f335(f95(f888(x87543,a879)),x87544)),x87545)),f335(f335(f95(f888(x87543,a879)),x87544),f335(f335(f34(x87542,f888(x87543,a879)),x87541),x87545)))
% 59.73/59.66 [8755]E(x87551,f188(f888(x87552,a879)))+E(f335(f335(f33(x87552,f888(x87553,a879)),x87551),f335(f335(f8(f888(x87553,a879),f888(x87553,a879),x87552),f335(f104(f888(x87553,a879)),x87554)),x87555)),f335(f335(f104(f888(x87553,a879)),x87554),f335(f335(f33(x87552,f888(x87553,a879)),x87551),x87555)))
% 59.73/59.66 [8756]E(x87561,f188(f888(x87562,a879)))+E(f335(f335(f34(x87562,f888(x87563,a879)),x87561),f335(f335(f8(f888(x87563,a879),f888(x87563,a879),x87562),f335(f23(f888(x87563,a879)),x87564)),x87565)),f335(f335(f23(f888(x87563,a879)),x87564),f335(f335(f33(x87562,f888(x87563,a879)),x87561),x87565)))
% 59.73/59.66 [8757]E(x87571,f188(f888(x87572,a879)))+E(f335(f335(f34(x87572,f888(x87573,a879)),x87571),f335(f335(f8(f888(x87573,a879),f888(x87573,a879),x87572),f335(f95(f888(x87573,a879)),x87574)),x87575)),f335(f335(f95(f888(x87573,a879)),x87574),f335(f335(f34(x87572,f888(x87573,a879)),x87571),x87575)))
% 59.73/59.66 [8956]~P1(f335(f335(f243(a881),f335(x89564,x89562)),f335(x89564,x89563)))+P1(f335(f335(f337(f887(x89561,x89561)),f335(f335(f264(x89561,x89561),x89562),x89563)),f146(x89561,f335(f335(f144(f888(x89561,a881)),x89564),x89565))))
% 59.73/59.66 [8957]~P1(f335(f335(f243(a881),f335(x89574,x89572)),f335(x89574,x89573)))+P1(f335(f335(f337(f887(x89571,x89571)),f335(f335(f264(x89571,x89571),x89572),x89573)),f146(x89571,f335(f335(f144(f888(x89571,a881)),x89574),x89575))))
% 59.73/59.66 [9204]~P37(f888(x92045,a879),f888(x92041,a879),x92042)+P1(f335(f335(f242(f888(x92041,a879)),f335(f335(f104(f888(x92041,a879)),f335(x92042,x92043)),f335(x92042,x92044))),f335(x92042,f335(f335(f104(f888(x92045,a879)),x92043),x92044))))
% 59.73/59.66 [9221]~P26(x92212,x92211,x92213,f335(f335(f104(f888(x92212,a879)),x92214),x92215))+E(f335(f335(f95(f888(x92211,a879)),f335(f313(x92212,x92211,x92213),f335(f335(f23(f888(x92212,a879)),x92214),x92215))),f335(f313(x92212,x92211,x92213),f335(f335(f23(f888(x92212,a879)),x92215),x92214))),f188(f888(x92211,a879)))
% 59.73/59.66 [9469]~P26(x94693,x94691,x94695,f252(f888(x94693,a879)))+E(f335(f68(x94691,x94692,x94693,f335(f68(x94693,x94692,x94691,x94694),f87(x94693,x94691,f252(f888(x94693,a879)),x94695))),x94695),x94694)
% 59.73/59.66 [9500]~P1(f335(f335(f242(f888(x95003,a879)),f335(f288(x95001,x95003,x95004),x95002)),x95005))+P1(f335(f335(f242(f888(x95001,a879)),x95002),f335(f74(f888(x95001,a879)),f335(f288(x95003,x95001,f335(f289(x95001,x95003),x95004)),f335(f74(f888(x95003,a879)),x95005)))))
% 59.73/59.66 [9524]~P26(x95241,x95242,x95243,f335(f335(f312(x95241),x95244),x95245))+~P1(f335(f335(f337(x95242),f335(x95243,x95244)),f335(f313(x95241,x95242,x95243),f335(f335(f23(f888(x95241,a879)),x95245),f335(f335(f312(x95241),x95244),f188(f888(x95241,a879)))))))
% 59.73/59.66 [9576]P1(f335(f335(f242(f888(x95761,a879)),f335(f288(x95762,x95761,x95763),x95764)),x95765))+~P1(f335(f335(f242(f888(x95762,a879)),x95764),f335(f74(f888(x95762,a879)),f335(f288(x95761,x95762,f335(f289(x95762,x95761),x95763)),f335(f74(f888(x95761,a879)),x95765)))))
% 59.73/59.66 [9650]~P88(x96501)+P1(f335(f335(f242(x96501),f335(f70(x96501),f335(f335(f23(x96501),f335(f335(f75(x96501),x96502),x96503)),f335(f335(f75(x96501),x96504),x96505)))),f335(f335(f75(x96501),f335(f70(x96501),f335(f335(f23(x96501),x96502),x96504))),f335(f70(x96501),f335(f335(f23(x96501),x96503),x96505)))))
% 59.73/59.66 [9761]P1(f335(f335(f337(x97611),f828(x97612,x97613,x97614,x97611,x97615)),x97614))+P1(f335(f335(f242(f888(x97615,a879)),f335(f335(f33(x97611,f888(x97615,a879)),x97614),x97613)),x97612))
% 59.73/59.66 [9959]~P1(f335(f335(f242(f888(x99591,a879)),f335(x99594,f828(x99595,x99594,x99593,x99592,x99591))),x99595))+P1(f335(f335(f242(f888(x99591,a879)),f335(f335(f33(x99592,f888(x99591,a879)),x99593),x99594)),x99595))
% 59.73/59.66 [8579]E(f335(f335(f127(x85791),x85792),f335(f335(f152(x85791,x85793),f335(f335(f23(a881),x85794),f335(f189(f882(x85791)),x85792))),x85795)),f335(f335(f152(x85791,f335(f335(f127(x85791),x85792),x85793)),x85794),x85795))+P1(f335(f335(f243(a881),x85794),f335(f189(f882(x85791)),x85792)))
% 59.73/59.66 [8606]~P139(x86061)+E(f335(f335(f75(x86061),f335(f335(f76(x86061),x86062),x86063)),f335(f335(f75(x86061),f335(f335(f76(x86061),x86064),x86063)),x86065)),f335(f335(f75(x86061),f335(f335(f76(x86061),f335(f335(f75(x86061),x86062),x86064)),x86063)),x86065))
% 59.73/59.66 [9176]~P142(x91761)+E(f335(f159(x91761),f335(f335(f147(x91762,x91761),f335(f335(f8(x91761,x91761,x91762),f335(f76(x91761),x91763)),x91764)),x91765)),f335(f335(f76(x91761),x91763),f335(f159(x91761),f335(f335(f147(x91762,x91761),x91764),x91765))))
% 59.73/59.66 [9344]E(f335(f189(f882(x93441)),f335(f335(f169(x93441),f335(f335(f240(a881),f335(f189(f882(x93441)),x93442)),f335(f189(f882(x93443)),x93444))),x93442)),f335(f189(f882(x93443)),f335(f335(f169(x93443),f335(f335(f240(a881),f335(f189(f882(x93441)),x93442)),f335(f189(f882(x93443)),x93444))),x93444)))+P1(f335(x93445,f335(f335(f175(x93441,x93443),x93442),x93444)))
% 59.73/59.66 [9587]~P142(x95872)+E(f335(f335(f6(x95871,x95872),f335(f335(f7(x95871,x95872,x95872),f335(f335(f8(x95872,f888(x95872,x95872),x95871),f76(x95872)),x95873)),x95874)),x95875),f335(f335(f76(x95872),f335(f335(f6(x95871,x95872),x95873),x95875)),x95874))
% 59.73/59.66 [9588]~P67(x95882)+E(f335(f335(f6(x95881,x95882),f335(f335(f7(x95881,x95882,x95882),f335(f335(f8(x95882,f888(x95882,x95882),x95881),f292(x95882)),x95883)),x95884)),x95885),f335(f335(f292(x95882),f335(f335(f6(x95881,x95882),x95883),x95885)),x95884))
% 59.73/59.66 [9595]~P73(x95952)+E(f335(f335(f9(x95951,x95952),f335(f335(f18(x95951,x95952,x95952),f335(f335(f8(x95952,f888(x95952,x95952),x95951),f76(x95952)),x95953)),x95954)),x95955),f335(f335(f76(x95952),f335(f335(f9(x95951,x95952),x95953),x95955)),f335(f335(f9(x95951,x95952),x95954),x95955)))
% 59.73/59.66 [9596]~P64(x95962)+E(f335(f335(f6(x95961,x95962),f335(f335(f18(x95961,x95962,x95962),f335(f335(f8(x95962,f888(x95962,x95962),x95961),f23(x95962)),x95963)),x95964)),x95965),f335(f335(f23(x95962),f335(f335(f6(x95961,x95962),x95963),x95965)),f335(f335(f6(x95961,x95962),x95964),x95965)))
% 59.73/59.66 [9597]~P77(x95972)+E(f335(f335(f6(x95971,x95972),f335(f335(f18(x95971,x95972,x95972),f335(f335(f8(x95972,f888(x95972,x95972),x95971),f75(x95972)),x95973)),x95974)),x95975),f335(f335(f75(x95972),f335(f335(f6(x95971,x95972),x95973),x95975)),f335(f335(f6(x95971,x95972),x95974),x95975)))
% 59.73/59.66 [9635]~E(x96353,f188(f888(x96351,a879)))+E(f335(f335(f33(x96351,f888(x96352,a879)),x96353),f335(f335(f7(x96351,f888(x96352,a879),f888(x96352,a879)),f335(f335(f8(f888(x96352,a879),f888(f888(x96352,a879),f888(x96352,a879)),x96351),f104(f888(x96352,a879))),x96354)),x96355)),f188(f888(x96352,a879)))
% 59.73/59.66 [9636]~E(x96363,f188(f888(x96361,a879)))+E(f335(f335(f34(x96361,f888(x96362,a879)),x96363),f335(f335(f7(x96361,f888(x96362,a879),f888(x96362,a879)),f335(f335(f8(f888(x96362,a879),f888(f888(x96362,a879),f888(x96362,a879)),x96361),f23(f888(x96362,a879))),x96364)),x96365)),f252(f888(x96362,a879)))
% 59.73/59.66 [9637]~E(x96373,f188(f888(x96371,a879)))+E(f335(f335(f34(x96371,f888(x96372,a879)),x96373),f335(f335(f7(x96371,f888(x96372,a879),f888(x96372,a879)),f335(f335(f8(f888(x96372,a879),f888(f888(x96372,a879),f888(x96372,a879)),x96371),f95(f888(x96372,a879))),x96374)),x96375)),f252(f888(x96372,a879)))
% 59.73/59.66 [9655]E(x96551,f188(f888(x96552,a879)))+E(f335(f335(f33(x96552,f888(x96553,a879)),x96551),f335(f335(f7(x96552,f888(x96553,a879),f888(x96553,a879)),f335(f335(f8(f888(x96553,a879),f888(f888(x96553,a879),f888(x96553,a879)),x96552),f104(f888(x96553,a879))),x96554)),x96555)),f335(f335(f104(f888(x96553,a879)),f335(f335(f33(x96552,f888(x96553,a879)),x96551),x96554)),x96555))
% 59.73/59.66 [9656]E(x96561,f188(f888(x96562,a879)))+E(f335(f335(f34(x96562,f888(x96563,a879)),x96561),f335(f335(f7(x96562,f888(x96563,a879),f888(x96563,a879)),f335(f335(f8(f888(x96563,a879),f888(f888(x96563,a879),f888(x96563,a879)),x96562),f23(f888(x96563,a879))),x96564)),x96565)),f335(f335(f23(f888(x96563,a879)),f335(f335(f34(x96562,f888(x96563,a879)),x96561),x96564)),x96565))
% 59.73/59.66 [9657]E(x96571,f188(f888(x96572,a879)))+E(f335(f335(f34(x96572,f888(x96573,a879)),x96571),f335(f335(f7(x96572,f888(x96573,a879),f888(x96573,a879)),f335(f335(f8(f888(x96573,a879),f888(f888(x96573,a879),f888(x96573,a879)),x96572),f95(f888(x96573,a879))),x96574)),x96575)),f335(f335(f95(f888(x96573,a879)),f335(f335(f34(x96572,f888(x96573,a879)),x96571),x96574)),x96575))
% 59.73/59.66 [9658]E(x96581,f188(f888(x96582,a879)))+E(f335(f335(f33(x96582,f888(x96583,a879)),x96581),f335(f335(f7(x96582,f888(x96583,a879),f888(x96583,a879)),f335(f335(f8(f888(x96583,a879),f888(f888(x96583,a879),f888(x96583,a879)),x96582),f104(f888(x96583,a879))),x96584)),x96585)),f335(f335(f104(f888(x96583,a879)),f335(f335(f33(x96582,f888(x96583,a879)),x96581),x96584)),x96585))
% 59.73/59.66 [9659]E(x96591,f188(f888(x96592,a879)))+E(f335(f335(f34(x96592,f888(x96593,a879)),x96591),f335(f335(f7(x96592,f888(x96593,a879),f888(x96593,a879)),f335(f335(f8(f888(x96593,a879),f888(f888(x96593,a879),f888(x96593,a879)),x96592),f23(f888(x96593,a879))),x96594)),x96595)),f335(f335(f23(f888(x96593,a879)),f335(f335(f34(x96592,f888(x96593,a879)),x96591),x96594)),x96595))
% 59.73/59.66 [9660]E(x96601,f188(f888(x96602,a879)))+E(f335(f335(f34(x96602,f888(x96603,a879)),x96601),f335(f335(f7(x96602,f888(x96603,a879),f888(x96603,a879)),f335(f335(f8(f888(x96603,a879),f888(f888(x96603,a879),f888(x96603,a879)),x96602),f95(f888(x96603,a879))),x96604)),x96605)),f335(f335(f95(f888(x96603,a879)),f335(f335(f34(x96602,f888(x96603,a879)),x96601),x96604)),x96605))
% 59.73/59.66 [9228]~P1(f335(f335(f242(a881),x92281),x92284))+E(f335(f335(f23(a881),f335(f335(f75(a881),f335(f335(f76(a881),x92281),x92282)),x92283)),f335(f335(f75(a881),f335(f335(f76(a881),x92284),x92282)),x92285)),f335(f335(f23(a881),x92283),f335(f335(f75(a881),f335(f335(f76(a881),f335(f335(f23(a881),x92284),x92281)),x92282)),x92285)))
% 59.73/59.66 [9825]~P142(x98251)+E(f335(f159(x98251),f335(f335(f147(x98252,x98251),f335(f335(f7(x98252,x98251,x98251),f335(f335(f8(x98251,f888(x98251,x98251),x98252),f76(x98251)),x98253)),x98254)),x98255)),f335(f335(f76(x98251),f335(f159(x98251),f335(f335(f147(x98252,x98251),x98253),x98255))),x98254))
% 59.73/59.66 [9831]~P64(x98311)+E(f335(f159(x98311),f335(f335(f147(x98312,x98311),f335(f335(f18(x98312,x98311,x98311),f335(f335(f8(x98311,f888(x98311,x98311),x98312),f23(x98311)),x98313)),x98314)),x98315)),f335(f335(f23(x98311),f335(f159(x98311),f335(f335(f147(x98312,x98311),x98313),x98315))),f335(f159(x98311),f335(f335(f147(x98312,x98311),x98314),x98315))))
% 59.73/59.66 [9832]~P77(x98321)+E(f335(f159(x98321),f335(f335(f147(x98322,x98321),f335(f335(f18(x98322,x98321,x98321),f335(f335(f8(x98321,f888(x98321,x98321),x98322),f75(x98321)),x98323)),x98324)),x98325)),f335(f335(f75(x98321),f335(f159(x98321),f335(f335(f147(x98322,x98321),x98323),x98325))),f335(f159(x98321),f335(f335(f147(x98322,x98321),x98324),x98325))))
% 59.73/59.66 [9972]P1(f335(x99721,f335(f335(f175(x99722,x99723),x99724),x99725)))+~P1(f335(x99721,f335(f335(f175(x99722,x99723),f335(f335(f169(x99722),f335(f335(f240(a881),f335(f189(f882(x99722)),x99724)),f335(f189(f882(x99723)),x99725))),x99724)),f335(f335(f169(x99723),f335(f335(f240(a881),f335(f189(f882(x99722)),x99724)),f335(f189(f882(x99723)),x99725))),x99725))))
% 59.73/59.66 [10206]~P1(f335(f335(f337(f887(x102062,x102061)),f335(f335(f264(x102062,x102061),x102064),x102065)),f335(f289(x102061,x102062),x102063)))+P1(f335(f335(f253(x102061,x102062,f335(f335(f7(x102061,f888(f887(x102061,x102062),a879),f888(x102062,a879)),f335(f335(f8(f888(x102062,f888(f888(f887(x102061,x102062),a879),a879)),f888(f888(f887(x102061,x102062),a879),f888(x102062,a879)),x102061),f7(x102062,f888(f887(x102061,x102062),a879),a879)),f335(f335(f8(f888(x102062,f887(x102061,x102062)),f888(x102062,f888(f888(f887(x102061,x102062),a879),a879)),x102061),f335(f8(f887(x102061,x102062),f888(f888(f887(x102061,x102062),a879),a879),x102062),f337(f887(x102061,x102062)))),f264(x102061,x102062)))),x102063)),x102064),x102065))
% 59.73/59.66 [10217]P1(f335(f335(f337(f887(x102171,x102172)),f335(f335(f264(x102171,x102172),x102173),x102174)),f335(f289(x102172,x102171),x102175)))+~P1(f335(f335(f253(x102172,x102171,f335(f335(f7(x102172,f888(f887(x102172,x102171),a879),f888(x102171,a879)),f335(f335(f8(f888(x102171,f888(f888(f887(x102172,x102171),a879),a879)),f888(f888(f887(x102172,x102171),a879),f888(x102171,a879)),x102172),f7(x102171,f888(f887(x102172,x102171),a879),a879)),f335(f335(f8(f888(x102171,f887(x102172,x102171)),f888(x102171,f888(f888(f887(x102172,x102171),a879),a879)),x102172),f335(f8(f887(x102172,x102171),f888(f888(f887(x102172,x102171),a879),a879),x102171),f337(f887(x102172,x102171)))),f264(x102172,x102171)))),x102175)),x102173),x102174))
% 59.73/59.66 [9468]~P1(f335(f335(f242(a881),x94684),x94681))+E(f335(f335(f23(a881),f335(f335(f75(a881),f335(f335(f76(a881),x94681),x94682)),x94683)),f335(f335(f75(a881),f335(f335(f76(a881),x94684),x94682)),x94685)),f335(f335(f23(a881),f335(f335(f75(a881),f335(f335(f76(a881),f335(f335(f23(a881),x94681),x94684)),x94682)),x94683)),x94685))
% 59.73/59.66 [7283]E(x72831,x72832)+~E(f223(x72833,x72834,x72835,x72831),f223(x72833,x72834,x72836,x72832))
% 59.73/59.66 [7284]E(x72841,x72842)+~E(f223(x72843,x72844,x72841,x72845),f223(x72843,x72844,x72842,x72846))
% 59.73/59.66 [6743]E(f335(f180(x67431,x67432,x67433,x67434),x67435),f335(f235(x67432),x67436))+~E(f335(x67434,x67435),f335(f235(x67432),x67436))
% 59.73/59.66 [6744]E(f335(f180(x67441,x67442,x67443,x67444),x67445),f335(f235(x67442),x67446))+~E(f335(x67444,x67445),f335(f235(x67442),x67446))
% 59.73/59.66 [6890]E(f335(f237(f885(x68901),x68902,f200(x68901),x68903),f335(x68904,x68905)),f335(x68903,x68906))+~E(f335(x68904,x68905),f335(f235(x68902),x68906))
% 59.73/59.66 [8417]~P21(x84175,x84171,x84172,x84176)+E(f335(f68(x84171,x84171,x84171,f335(x84172,x84173)),f335(x84172,x84174)),f335(f68(x84171,x84171,x84171,f335(x84172,x84174)),f335(x84172,x84173)))
% 59.73/59.66 [8648]~P54(x86484,x86485,x86482,x86481,x86486)+E(f335(x86481,f335(x86482,x86483)),x86483)
% 59.73/59.66 [8807]P26(x88071,x88072,x88073,x88074)+~P26(x88071,x88075,f335(f68(x88072,x88075,x88071,x88076),x88073),x88074)
% 59.73/59.66 [8891]~P26(x88914,x88912,f335(f68(x88911,x88912,x88914,x88913),x88915),x88916)+P26(x88911,x88912,x88913,f335(f313(x88914,x88911,x88915),x88916))
% 59.73/59.66 [9538]P51(x95381,x95382,x95383,x95384,x95385,x95386)+~P1(f335(f335(x95383,f335(x95384,x95385)),f335(x95384,x95386)))
% 59.73/59.66 [9539]P51(x95391,x95392,x95393,x95394,x95395,x95396)+~P1(f335(f335(x95393,f335(x95394,x95395)),f335(x95394,x95396)))
% 59.73/59.66 [9598]P1(f335(f56(x95981),x95982))+~P1(f335(f61(x95981,x95983,x95984,x95985,x95982),x95986))
% 59.73/59.66 [9606]~P1(f335(f335(f337(x96064),x96063),f302(x96064,x96065,x96061,x96062,x96066)))+P1(f335(f335(x96061,x96062),x96063))
% 59.73/59.66 [9607]~P1(f335(f335(f337(x96074),x96073),f299(x96074,x96071,x96075,x96072,x96076)))+P1(f335(f335(x96071,x96072),x96073))
% 59.73/59.66 [9608]~P1(f335(f335(f337(x96084),x96082),f302(x96084,x96081,x96085,x96086,x96083)))+P1(f335(f335(x96081,x96082),x96083))
% 59.73/59.66 [9609]~P1(f335(f335(f337(x96094),x96092),f299(x96094,x96095,x96091,x96096,x96093)))+P1(f335(f335(x96091,x96092),x96093))
% 59.73/59.66 [9671]~P51(x96715,x96716,x96711,x96712,x96713,x96714)+P1(f335(f335(x96711,f335(x96712,x96713)),f335(x96712,x96714)))
% 59.73/59.66 [9672]~P51(x96725,x96726,x96721,x96722,x96723,x96724)+P1(f335(f335(x96721,f335(x96722,x96723)),f335(x96722,x96724)))
% 59.73/59.66 [5790]E(x57901,x57902)+~E(f335(f335(f264(x57903,x57904),x57905),x57901),f335(f335(f264(x57903,x57904),x57906),x57902))
% 59.73/59.66 [5791]E(x57911,x57912)+~E(f335(f335(f264(x57913,x57914),x57915),x57911),f335(f335(f264(x57913,x57914),x57916),x57912))
% 59.73/59.66 [5792]E(x57921,x57922)+~E(f335(f335(f264(x57923,x57924),x57921),x57925),f335(f335(f264(x57923,x57924),x57922),x57926))
% 59.73/59.66 [5793]E(x57931,x57932)+~E(f335(f335(f264(x57933,x57934),x57931),x57935),f335(f335(f264(x57933,x57934),x57932),x57936))
% 59.73/59.66 [5920]~P18(x59205,x59206,x59201)+E(f335(f335(x59201,x59202),f335(f335(x59201,x59203),x59204)),f335(f335(x59201,x59203),f335(f335(x59201,x59202),x59204)))
% 59.73/59.66 [7347]~P31(x73474,x73471,f335(f335(f144(x73474),x73472),x73475),f335(f335(f144(x73474),x73473),x73476))+P1(f335(f335(x73471,x73472),x73473))
% 59.73/59.66 [7712]P31(x77121,x77122,x77123,x77124)+~P31(x77121,x77122,f335(f335(f144(x77121),x77125),x77123),f335(f335(f144(x77121),x77126),x77124))
% 59.73/59.66 [8746]~P54(x87465,x87461,x87462,x87466,x87464)+P1(f335(f335(f337(x87461),f335(x87462,x87463)),x87464))
% 59.73/59.66 [8917]E(f335(f71(x89171,x89172,x89173,x89174,x89175),x89176),f335(x89173,x89176))+P1(f335(f335(f337(x89171),x89176),x89175))
% 59.73/59.66 [8918]E(f335(f71(x89181,x89182,x89183,x89184,x89185),x89186),f335(x89183,x89186))+P1(f335(f335(f337(x89181),x89186),x89185))
% 59.73/59.66 [8941]~E(x89413,f335(f335(f144(x89411),x89415),x89416))+P1(f335(f335(f337(f887(f882(x89411),f882(x89411))),f335(f335(f264(f882(x89411),f882(x89411)),x89412),f335(f335(f127(x89411),x89412),x89413))),f140(x89411,x89414)))
% 59.73/59.66 [8946]E(f335(f71(x89461,x89462,x89463,x89464,x89465),x89466),f335(x89464,x89466))+~P1(f335(f335(f337(x89461),x89466),x89465))
% 59.73/59.66 [8947]E(f335(f71(x89471,x89472,x89473,x89474,x89475),x89476),f335(x89474,x89476))+~P1(f335(f335(f337(x89471),x89476),x89475))
% 59.73/59.66 [8952]E(f335(f181(x89521,x89522,x89523,x89524,x89525),x89526),f335(x89523,x89526))+P1(f335(f335(f337(x89521),x89526),f335(f166(x89521),x89524)))
% 59.73/59.66 [9180]~P33(x91801,x91802,x91803,x91805,x91806)+P33(x91801,x91802,x91803,f335(f335(f169(x91801),x91804),x91805),f335(f335(f169(x91802),x91804),x91806))
% 59.73/59.66 [9181]~P33(x91811,x91812,x91813,x91815,x91816)+P33(x91811,x91812,x91813,f335(f335(f131(x91811),x91814),x91815),f335(f335(f131(x91812),x91814),x91816))
% 59.73/59.66 [9670]~P25(x96704,x96702,x96705,x96703,x96706,x96701)+E(f335(x96701,f188(f888(x96702,a879))),x96703)
% 59.73/59.66 [9923]~E(f335(x99234,f335(f263(x99231,x99233),x99235)),f335(x99236,f335(f263(x99231,x99233),x99235)))+E(f335(f269(x99231,x99232,x99233,x99233,x99234,f25(x99233)),x99235),f335(f269(x99231,x99232,x99233,x99233,x99236,f25(x99233)),x99235))
% 59.73/59.66 [9924]~E(f335(x99244,f335(f267(x99241,x99242),x99245)),f335(x99246,f335(f267(x99241,x99242),x99245)))+E(f335(f269(x99241,x99241,x99242,x99243,f25(x99241),x99244),x99245),f335(f269(x99241,x99241,x99242,x99243,f25(x99241),x99246),x99245))
% 59.73/59.66 [9968]~E(f335(f269(x99682,x99686,x99683,x99683,x99681,f25(x99683)),x99684),f335(f269(x99682,x99686,x99683,x99683,x99685,f25(x99683)),x99684))+E(f335(x99681,f335(f263(x99682,x99683),x99684)),f335(x99685,f335(f263(x99682,x99683),x99684)))
% 59.73/59.66 [9969]~E(f335(f269(x99692,x99692,x99693,x99696,f25(x99692),x99691),x99694),f335(f269(x99692,x99692,x99693,x99696,f25(x99692),x99695),x99694))+E(f335(x99691,f335(f267(x99692,x99693),x99694)),f335(x99695,f335(f267(x99692,x99693),x99694)))
% 59.73/59.66 [8844]P1(f335(f335(f337(x88441),x88442),x88443))+~P1(f335(f335(f337(f887(x88441,x88444)),f335(f335(f264(x88441,x88444),x88442),x88445)),f335(f335(f266(x88441,x88444),x88443),x88446)))
% 59.73/59.66 [8845]P1(f335(f335(f337(x88451),x88452),x88453))+~P1(f335(f335(f337(f887(x88451,x88454)),f335(f335(f264(x88451,x88454),x88452),x88455)),f335(f335(f266(x88451,x88454),x88453),x88456)))
% 59.73/59.66 [8846]P1(f335(f335(f337(x88461),x88462),x88463))+~P1(f335(f335(f337(f887(x88461,x88464)),f335(f335(f264(x88461,x88464),x88462),x88465)),f335(f335(f266(x88461,x88464),x88463),x88466)))
% 59.73/59.66 [8858]P1(f335(f335(f337(x88581),x88582),f335(x88583,x88584)))+~P1(f335(f335(f337(f887(x88585,x88581)),f335(f335(f264(x88585,x88581),x88584),x88582)),f335(f335(f266(x88585,x88581),x88586),x88583)))
% 59.73/59.66 [8859]P1(f335(f335(f337(x88591),x88592),f335(x88593,x88594)))+~P1(f335(f335(f337(f887(x88595,x88591)),f335(f335(f264(x88595,x88591),x88594),x88592)),f335(f335(f266(x88595,x88591),x88596),x88593)))
% 59.73/59.66 [8860]P1(f335(f335(f337(x88601),x88602),f335(x88603,x88604)))+~P1(f335(f335(f337(f887(x88605,x88601)),f335(f335(f264(x88605,x88601),x88604),x88602)),f335(f335(f266(x88605,x88601),x88606),x88603)))
% 59.73/59.66 [8949]~E(f335(f189(f882(x89491)),x89494),f335(f189(f882(x89492)),x89495))+E(f181(x89491,x89492,x89493,x89494,f335(f335(f127(x89492),x89495),x89496)),f181(x89491,x89492,x89493,x89494,x89495))
% 59.73/59.66 [8950]~E(f335(f189(f882(x89501)),x89504),f335(f189(f882(x89502)),x89506))+E(f181(x89501,x89502,x89503,f335(f335(f127(x89501),x89504),x89505),x89506),f181(x89501,x89502,x89503,x89504,x89506))
% 59.73/59.66 [9198]P1(f335(f335(f337(x91981),x91984),f177(x91981,x91982,x91986)))+E(f180(x91981,x91982,f335(f335(f335(f67(x91981,f885(x91982)),x91983),x91984),f335(f235(x91982),x91985)),x91986),f335(f335(f335(f67(x91981,f885(x91982)),f180(x91981,x91982,x91983,x91986)),x91984),f335(f235(x91982),x91985)))
% 59.73/59.66 [9299]P1(f335(f335(f337(f887(x92991,x92991)),f335(f335(f264(x92991,x92991),f335(x92992,x92993)),f335(x92992,x92994))),x92995))+~P1(f335(f335(f337(f887(x92996,x92996)),f335(f335(f264(x92996,x92996),x92993),x92994)),f335(f335(f290(x92991,x92996),x92995),x92992)))
% 59.73/59.66 [9316]~P1(f335(f335(f337(f887(x93164,x93164)),f335(f335(f264(x93164,x93164),f335(x93166,x93162)),f335(x93166,x93163))),x93165))+P1(f335(f335(f337(f887(x93161,x93161)),f335(f335(f264(x93161,x93161),x93162),x93163)),f335(f335(f290(x93164,x93161),x93165),x93166)))
% 59.73/59.66 [9971]E(f335(f335(f264(x99711,x99712),f663(x99713,x99714,x99715,x99716,x99712,x99711)),f664(x99713,x99714,x99715,x99716,x99712,x99711)),x99716)+~P1(f335(f335(f337(f887(x99711,x99712)),x99716),f335(f335(f291(x99711,x99715,x99712),x99714),x99713)))
% 59.73/59.66 [10170]~P1(f335(f335(f337(f887(x101701,x101706)),x101705),f335(f335(f291(x101701,x101702,x101706),x101704),x101703)))+P1(f335(f335(f337(f887(x101701,x101702)),f335(f335(f264(x101701,x101702),f663(x101703,x101704,x101702,x101705,x101706,x101701)),f665(x101703,x101704,x101702,x101705,x101706,x101701))),x101704))
% 59.73/59.66 [10171]~P1(f335(f335(f337(f887(x101716,x101712)),x101715),f335(f335(f291(x101716,x101711,x101712),x101714),x101713)))+P1(f335(f335(f337(f887(x101711,x101712)),f335(f335(f264(x101711,x101712),f665(x101713,x101714,x101711,x101715,x101712,x101716)),f664(x101713,x101714,x101711,x101715,x101712,x101716))),x101713))
% 59.73/59.66 [6192]~E(x61926,x61924)+E(f335(f335(f335(f335(f67(x61921,x61922),x61923),x61924),x61925),x61926),x61925)
% 59.73/59.66 [6193]~E(x61936,x61934)+E(f335(f335(f335(f335(f67(x61931,x61932),x61933),x61934),x61935),x61936),x61935)
% 59.73/59.66 [6242]E(x62421,x62422)+E(f335(f335(f335(f335(f67(x62423,x62424),x62425),x62422),x62426),x62421),f335(x62425,x62421))
% 59.73/59.66 [6243]E(x62431,x62432)+E(f335(f335(f335(f335(f67(x62433,x62434),x62435),x62432),x62436),x62431),f335(x62435,x62431))
% 59.73/59.66 [6244]E(x62441,x62442)+E(f335(f335(f335(f335(f67(x62443,x62444),x62445),x62442),x62446),x62441),f335(x62445,x62441))
% 59.73/59.66 [7783]~P5(x77832)+E(f335(f335(f33(x77831,x77832),x77833),f335(f335(f7(x77831,x77834,x77832),x77835),x77836)),f335(f335(f335(f33(x77831,f888(x77834,x77832)),x77833),x77835),x77836))
% 59.73/59.66 [7784]~P5(x77842)+E(f335(f335(f34(x77841,x77842),x77843),f335(f335(f7(x77841,x77844,x77842),x77845),x77846)),f335(f335(f335(f34(x77841,f888(x77844,x77842)),x77843),x77845),x77846))
% 59.73/59.66 [8381]E(f335(f313(x83811,f885(x83812),f335(f335(f335(f67(x83811,f885(x83812)),x83813),x83814),f335(f235(x83812),x83815))),x83816),f335(f313(x83811,f885(x83812),x83813),x83816))+P1(f335(f335(f337(x83811),x83814),x83816))
% 59.73/59.66 [8561]E(f335(f335(f33(x85611,f888(x85612,a879)),x85613),f335(f335(f8(f888(x85612,a879),f888(x85612,a879),x85611),f335(f312(x85612),x85614)),x85615)),f335(f335(f312(x85612),x85614),f335(f335(f33(x85611,f888(x85612,a879)),x85613),x85615)))+~P1(f335(f335(f337(x85611),x85616),x85613))
% 59.73/59.66 [8562]E(f335(f335(f34(x85621,f888(x85622,a879)),x85623),f335(f335(f8(f888(x85622,a879),f888(x85622,a879),x85621),f335(f312(x85622),x85624)),x85625)),f335(f335(f312(x85622),x85624),f335(f335(f34(x85621,f888(x85622,a879)),x85623),x85625)))+~P1(f335(f335(f337(x85621),x85626),x85623))
% 59.73/59.66 [8996]~P5(x89962)+E(f335(f335(f33(x89961,x89962),x89963),f335(f335(f8(f888(x89964,x89962),x89962,x89961),f335(f33(x89964,x89962),x89965)),f335(f7(x89964,x89961,x89962),x89966))),f335(f335(f33(x89964,x89962),x89965),f335(f335(f8(f888(x89961,x89962),x89962,x89964),f335(f33(x89961,x89962),x89963)),x89966)))
% 59.73/59.66 [8997]~P5(x89972)+E(f335(f335(f34(x89971,x89972),x89973),f335(f335(f8(f888(x89974,x89972),x89972,x89971),f335(f34(x89974,x89972),x89975)),f335(f7(x89974,x89971,x89972),x89976))),f335(f335(f34(x89974,x89972),x89975),f335(f335(f8(f888(x89971,x89972),x89972,x89974),f335(f34(x89971,x89972),x89973)),x89976)))
% 59.73/59.66 [9206]P1(f335(f335(f337(x92061),x92062),f335(f166(x92061),x92063)))+~P1(f335(f335(f337(f887(x92064,x92061)),f335(f335(f264(x92064,x92061),x92065),x92062)),f335(f166(f887(x92064,x92061)),f335(f335(f175(x92064,x92061),x92066),x92063))))
% 59.73/59.66 [9207]P1(f335(f335(f337(x92071),x92072),f335(f166(x92071),x92073)))+~P1(f335(f335(f337(f887(x92071,x92074)),f335(f335(f264(x92071,x92074),x92072),x92075)),f335(f166(f887(x92071,x92074)),f335(f335(f175(x92071,x92074),x92073),x92076))))
% 59.73/59.66 [9208]P1(f335(f335(f337(x92081),x92082),f335(f166(x92081),x92083)))+~P1(f335(f335(f337(f887(x92084,x92081)),f335(f335(f264(x92084,x92081),x92085),x92082)),f335(f166(f887(x92084,x92081)),f335(f335(f175(x92084,x92081),x92086),x92083))))
% 59.73/59.66 [9209]P1(f335(f335(f337(x92091),x92092),f335(f166(x92091),x92093)))+~P1(f335(f335(f337(f887(x92091,x92094)),f335(f335(f264(x92091,x92094),x92092),x92095)),f335(f166(f887(x92091,x92094)),f335(f335(f175(x92091,x92094),x92093),x92096))))
% 59.73/59.66 [9313]P1(f335(f335(f242(f888(x93131,a879)),f335(f288(x93132,x93131,x93133),x93134)),x93135))+~P1(f335(f335(f242(f888(f887(x93132,x93131),a879)),x93133),f335(f335(f266(x93132,x93131),x93136),f335(f16(f888(x93131,a879),x93132),x93135))))
% 59.73/59.66 [9503]P1(f335(f335(f337(f887(f882(x95031),f882(x95031))),f335(f335(f264(f882(x95031),f882(x95031)),f335(f335(f144(x95031),x95032),x95033)),f335(f335(f144(x95031),x95034),x95035))),f140(x95031,x95036)))+~P1(f335(f335(f337(f887(x95031,x95031)),f335(f335(f264(x95031,x95031),x95032),x95034)),x95036))
% 59.73/59.66 [9967]E(f335(f335(f264(x99671,x99672),f568(x99673,x99674,x99675,x99672,x99671,x99676)),f569(x99673,x99674,x99675,x99672,x99671,x99676)),x99676)+P1(f335(f335(f337(x99675),x99674),f335(f335(f268(x99671,x99672,f888(x99675,a879)),x99673),x99676)))
% 59.73/59.66 [9973]E(f335(f335(f264(x99731,x99732),f570(x99733,x99734,x99732,x99731,x99735,x99736)),f571(x99733,x99734,x99732,x99731,x99735,x99736)),x99733)+~P1(f335(f335(f337(x99736),x99735),f335(f335(f268(x99731,x99732,f888(x99736,a879)),x99734),x99733)))
% 59.73/59.66 [10127]P1(f335(f335(f337(x101271),x101272),f335(f335(x101273,f570(x101274,x101273,x101275,x101276,x101272,x101271)),f571(x101274,x101273,x101275,x101276,x101272,x101271))))+~P1(f335(f335(f337(x101271),x101272),f335(f335(f268(x101276,x101275,f888(x101271,a879)),x101273),x101274)))
% 59.73/59.66 [10146]~P1(f335(f335(f337(x101461),x101462),f335(f335(x101465,f568(x101465,x101462,x101461,x101464,x101463,x101466)),f569(x101465,x101462,x101461,x101464,x101463,x101466))))+P1(f335(f335(f337(x101461),x101462),f335(f335(f268(x101463,x101464,f888(x101461,a879)),x101465),x101466)))
% 59.73/59.66 [7902]P1(f335(f335(f337(x79021),x79024),x79026))+E(f182(x79021,x79022,f335(f335(f335(f67(x79021,f885(x79022)),x79023),x79024),x79025),x79026),f182(x79021,x79022,x79023,x79026))
% 59.73/59.66 [7984]P1(f335(f335(f337(x79841),x79844),x79846))+E(f335(f313(x79841,x79842,f335(f335(f335(f67(x79841,x79842),x79843),x79844),x79845)),x79846),f335(f313(x79841,x79842,x79843),x79846))
% 59.73/59.66 [8013]P1(f335(f335(f337(x80131),x80134),f335(f166(x80131),x80136)))+E(f335(f335(f147(x80131,x80132),f335(f335(f335(f67(x80131,x80132),x80133),x80134),x80135)),x80136),f335(f335(f147(x80131,x80132),x80133),x80136))
% 59.73/59.66 [8463]E(x84631,x84632)+E(f335(f335(f152(x84633,f335(f335(f152(x84633,x84634),x84631),x84635)),x84632),x84636),f335(f335(f152(x84633,f335(f335(f152(x84633,x84634),x84632),x84636)),x84631),x84635))
% 59.73/59.66 [9002]~P1(f335(f335(f337(x90023),x90026),x90025))+E(f335(f335(f312(x90021),x90022),f335(f313(x90023,x90021,x90024),f335(f335(f23(f888(x90023,a879)),x90025),f335(f335(f312(x90023),x90026),f188(f888(x90023,a879)))))),f335(f313(x90023,x90021,f335(f335(f335(f67(x90023,x90021),x90024),x90026),x90022)),x90025))
% 59.73/59.66 [9785]E(f181(x97851,x97852,x97853,f335(f335(f127(x97851),x97854),f335(f335(f144(x97851),x97855),f107(x97851))),x97856),f335(f335(f335(f67(x97851,f885(x97852)),f181(x97851,x97852,x97853,x97854,x97856)),x97855),f335(f235(x97852),f335(f335(f158(x97852),x97856),f335(f189(f882(x97851)),x97854)))))+~P1(f335(f335(f243(a881),f335(f189(f882(x97851)),x97854)),f335(f189(f882(x97852)),x97856)))
% 59.73/59.66 [8788]~E(x87883,x87886)+E(f335(f335(f179(x87881,x87882),f335(f335(f144(f887(x87881,x87882)),f335(f335(f264(x87881,x87882),x87883),x87884)),x87885)),x87886),f335(f235(x87882),x87884))
% 59.73/59.66 [8816]E(x88161,x88162)+E(f335(f335(f179(x88163,x88164),f335(f335(f144(f887(x88163,x88164)),f335(f335(f264(x88163,x88164),x88161),x88165)),x88166)),x88162),f335(f335(f179(x88163,x88164),x88166),x88162))
% 59.73/59.66 [9076]~P1(f335(f335(x90764,x90765),x90766))+P1(f335(f335(f335(f335(f104(f888(x90761,f888(x90762,a879))),x90763),x90764),x90765),x90766))
% 59.73/59.66 [9077]~P1(f335(f335(x90774,x90775),x90776))+P1(f335(f335(f335(f335(f104(f888(x90771,f888(x90772,a879))),x90773),x90774),x90775),x90776))
% 59.73/59.66 [9078]~P1(f335(f335(x90783,x90785),x90786))+P1(f335(f335(f335(f335(f104(f888(x90781,f888(x90782,a879))),x90783),x90784),x90785),x90786))
% 59.73/59.66 [9079]~P1(f335(f335(x90793,x90795),x90796))+P1(f335(f335(f335(f335(f104(f888(x90791,f888(x90792,a879))),x90793),x90794),x90795),x90796))
% 59.73/59.66 [9364]P1(f335(f335(x93641,x93642),x93643))+~P1(f335(f335(f335(f335(f95(f888(x93644,f888(x93645,a879))),x93646),x93641),x93642),x93643))
% 59.73/59.66 [9365]P1(f335(f335(x93651,x93652),x93653))+~P1(f335(f335(f335(f335(f95(f888(x93654,f888(x93655,a879))),x93651),x93656),x93652),x93653))
% 59.73/59.66 [9366]P1(f335(f335(x93661,x93662),x93663))+~P1(f335(f335(f335(f335(f95(f888(x93664,f888(x93665,a879))),x93666),x93661),x93662),x93663))
% 59.73/59.66 [9367]P1(f335(f335(x93671,x93672),x93673))+~P1(f335(f335(f335(f335(f95(f888(x93674,f888(x93675,a879))),x93671),x93676),x93672),x93673))
% 59.73/59.66 [9809]~P73(x98092)+E(f335(f335(f9(x98091,x98092),f335(f335(f7(x98091,f888(x98093,a879),x98092),f335(f335(f8(f888(x98093,x98092),f888(f888(x98093,a879),x98092),x98091),f9(x98093,x98092)),x98094)),x98095)),x98096),f335(f335(f9(f887(x98091,x98093),x98092),f335(f268(x98091,x98093,x98092),x98094)),f335(f335(f266(x98091,x98093),x98096),f335(f16(f888(x98093,a879),x98091),x98095))))
% 59.73/59.66 [9810]~P77(x98102)+E(f335(f335(f6(x98101,x98102),f335(f335(f7(x98101,f888(x98103,a879),x98102),f335(f335(f8(f888(x98103,x98102),f888(f888(x98103,a879),x98102),x98101),f6(x98103,x98102)),x98104)),x98105)),x98106),f335(f335(f6(f887(x98101,x98103),x98102),f335(f268(x98101,x98103,x98102),x98104)),f335(f335(f266(x98101,x98103),x98106),f335(f16(f888(x98103,a879),x98101),x98105))))
% 59.73/59.66 [9949]~P77(x99492)+E(f335(f335(f6(x99491,x99492),f335(f335(f7(x99491,f888(x99493,a879),x99492),f335(f335(f8(f888(x99493,x99492),f888(f888(x99493,a879),x99492),x99491),f6(x99493,x99492)),f335(f7(x99493,x99491,x99492),x99494))),x99495)),x99496),f335(f335(f6(x99493,x99492),f335(f335(f7(x99493,f888(x99491,a879),x99492),f335(f335(f8(f888(x99491,x99492),f888(f888(x99491,a879),x99492),x99493),f6(x99491,x99492)),x99494)),x99496)),x99495))
% 59.73/59.66 [9639]~P1(f335(f335(f337(x96391),x96395),x96394))+E(f335(f335(f335(f67(x96391,f885(x96392)),f182(x96391,x96392,x96393,f335(f335(f23(f888(x96391,a879)),x96394),f335(f335(f312(x96391),x96395),f188(f888(x96391,a879)))))),x96395),x96396),f182(x96391,x96392,f335(f335(f335(f67(x96391,f885(x96392)),x96393),x96395),x96396),x96394))
% 59.73/59.66 [9697]~P1(f335(f335(f337(x96971),x96975),x96974))+E(f335(f335(f335(f67(x96971,f885(x96972)),f182(x96971,x96972,x96973,f335(f335(f23(f888(x96971,a879)),x96974),f335(f335(f312(x96971),x96975),f188(f888(x96971,a879)))))),x96975),x96976),f335(f335(f335(f67(x96971,f885(x96972)),f182(x96971,x96972,x96973,x96974)),x96975),x96976))
% 59.73/59.66 [10227]~P1(f335(f335(f337(f887(x102271,x102272)),f335(f335(f264(x102271,x102272),x102275),x102276)),f335(f335(f104(f888(f887(x102271,x102272),a879)),x102273),x102274)))+P1(f335(f335(f335(f335(f104(f888(x102271,f888(x102272,a879))),f335(f335(f7(x102271,f888(f887(x102271,x102272),a879),f888(x102272,a879)),f335(f335(f8(f888(x102272,f888(f888(f887(x102271,x102272),a879),a879)),f888(f888(f887(x102271,x102272),a879),f888(x102272,a879)),x102271),f7(x102272,f888(f887(x102271,x102272),a879),a879)),f335(f335(f8(f888(x102272,f887(x102271,x102272)),f888(x102272,f888(f888(f887(x102271,x102272),a879),a879)),x102271),f335(f8(f887(x102271,x102272),f888(f888(f887(x102271,x102272),a879),a879),x102272),f337(f887(x102271,x102272)))),f264(x102271,x102272)))),x102273)),f335(f335(f7(x102271,f888(f887(x102271,x102272),a879),f888(x102272,a879)),f335(f335(f8(f888(x102272,f888(f888(f887(x102271,x102272),a879),a879)),f888(f888(f887(x102271,x102272),a879),f888(x102272,a879)),x102271),f7(x102272,f888(f887(x102271,x102272),a879),a879)),f335(f335(f8(f888(x102272,f887(x102271,x102272)),f888(x102272,f888(f888(f887(x102271,x102272),a879),a879)),x102271),f335(f8(f887(x102271,x102272),f888(f888(f887(x102271,x102272),a879),a879),x102272),f337(f887(x102271,x102272)))),f264(x102271,x102272)))),x102274)),x102275),x102276))
% 59.73/59.66 [10228]~P1(f335(f335(f337(f887(x102281,x102282)),f335(f335(f264(x102281,x102282),x102285),x102286)),f335(f335(f95(f888(f887(x102281,x102282),a879)),x102283),x102284)))+P1(f335(f335(f335(f335(f95(f888(x102281,f888(x102282,a879))),f335(f335(f7(x102281,f888(f887(x102281,x102282),a879),f888(x102282,a879)),f335(f335(f8(f888(x102282,f888(f888(f887(x102281,x102282),a879),a879)),f888(f888(f887(x102281,x102282),a879),f888(x102282,a879)),x102281),f7(x102282,f888(f887(x102281,x102282),a879),a879)),f335(f335(f8(f888(x102282,f887(x102281,x102282)),f888(x102282,f888(f888(f887(x102281,x102282),a879),a879)),x102281),f335(f8(f887(x102281,x102282),f888(f888(f887(x102281,x102282),a879),a879),x102282),f337(f887(x102281,x102282)))),f264(x102281,x102282)))),x102283)),f335(f335(f7(x102281,f888(f887(x102281,x102282),a879),f888(x102282,a879)),f335(f335(f8(f888(x102282,f888(f888(f887(x102281,x102282),a879),a879)),f888(f888(f887(x102281,x102282),a879),f888(x102282,a879)),x102281),f7(x102282,f888(f887(x102281,x102282),a879),a879)),f335(f335(f8(f888(x102282,f887(x102281,x102282)),f888(x102282,f888(f888(f887(x102281,x102282),a879),a879)),x102281),f335(f8(f887(x102281,x102282),f888(f888(f887(x102281,x102282),a879),a879),x102282),f337(f887(x102281,x102282)))),f264(x102281,x102282)))),x102284)),x102285),x102286))
% 59.73/59.66 [10235]P1(f335(f335(f337(f887(x102351,x102352)),f335(f335(f264(x102351,x102352),x102353),x102354)),f335(f335(f104(f888(f887(x102351,x102352),a879)),x102355),x102356)))+~P1(f335(f335(f335(f335(f104(f888(x102351,f888(x102352,a879))),f335(f335(f7(x102351,f888(f887(x102351,x102352),a879),f888(x102352,a879)),f335(f335(f8(f888(x102352,f888(f888(f887(x102351,x102352),a879),a879)),f888(f888(f887(x102351,x102352),a879),f888(x102352,a879)),x102351),f7(x102352,f888(f887(x102351,x102352),a879),a879)),f335(f335(f8(f888(x102352,f887(x102351,x102352)),f888(x102352,f888(f888(f887(x102351,x102352),a879),a879)),x102351),f335(f8(f887(x102351,x102352),f888(f888(f887(x102351,x102352),a879),a879),x102352),f337(f887(x102351,x102352)))),f264(x102351,x102352)))),x102355)),f335(f335(f7(x102351,f888(f887(x102351,x102352),a879),f888(x102352,a879)),f335(f335(f8(f888(x102352,f888(f888(f887(x102351,x102352),a879),a879)),f888(f888(f887(x102351,x102352),a879),f888(x102352,a879)),x102351),f7(x102352,f888(f887(x102351,x102352),a879),a879)),f335(f335(f8(f888(x102352,f887(x102351,x102352)),f888(x102352,f888(f888(f887(x102351,x102352),a879),a879)),x102351),f335(f8(f887(x102351,x102352),f888(f888(f887(x102351,x102352),a879),a879),x102352),f337(f887(x102351,x102352)))),f264(x102351,x102352)))),x102356)),x102353),x102354))
% 59.73/59.66 [10236]P1(f335(f335(f337(f887(x102361,x102362)),f335(f335(f264(x102361,x102362),x102363),x102364)),f335(f335(f95(f888(f887(x102361,x102362),a879)),x102365),x102366)))+~P1(f335(f335(f335(f335(f95(f888(x102361,f888(x102362,a879))),f335(f335(f7(x102361,f888(f887(x102361,x102362),a879),f888(x102362,a879)),f335(f335(f8(f888(x102362,f888(f888(f887(x102361,x102362),a879),a879)),f888(f888(f887(x102361,x102362),a879),f888(x102362,a879)),x102361),f7(x102362,f888(f887(x102361,x102362),a879),a879)),f335(f335(f8(f888(x102362,f887(x102361,x102362)),f888(x102362,f888(f888(f887(x102361,x102362),a879),a879)),x102361),f335(f8(f887(x102361,x102362),f888(f888(f887(x102361,x102362),a879),a879),x102362),f337(f887(x102361,x102362)))),f264(x102361,x102362)))),x102365)),f335(f335(f7(x102361,f888(f887(x102361,x102362),a879),f888(x102362,a879)),f335(f335(f8(f888(x102362,f888(f888(f887(x102361,x102362),a879),a879)),f888(f888(f887(x102361,x102362),a879),f888(x102362,a879)),x102361),f7(x102362,f888(f887(x102361,x102362),a879),a879)),f335(f335(f8(f888(x102362,f887(x102361,x102362)),f888(x102362,f888(f888(f887(x102361,x102362),a879),a879)),x102361),f335(f8(f887(x102361,x102362),f888(f888(f887(x102361,x102362),a879),a879),x102362),f337(f887(x102361,x102362)))),f264(x102361,x102362)))),x102366)),x102363),x102364))
% 59.73/59.66 [10223]~P1(f335(f335(f337(f887(x102232,x102233)),f335(f335(f264(x102232,x102233),x102235),x102236)),f335(f335(f33(x102231,f888(f887(x102232,x102233),a879)),f252(f888(x102231,a879))),x102234)))+P1(f335(f335(f335(f335(f33(x102231,f888(x102232,f888(x102233,a879))),f252(f888(x102231,a879))),f335(f335(f8(f888(f887(x102232,x102233),a879),f888(x102232,f888(x102233,a879)),x102231),f335(f7(x102232,f888(f887(x102232,x102233),a879),f888(x102233,a879)),f335(f335(f8(f888(x102233,f888(f888(f887(x102232,x102233),a879),a879)),f888(f888(f887(x102232,x102233),a879),f888(x102233,a879)),x102232),f7(x102233,f888(f887(x102232,x102233),a879),a879)),f335(f335(f8(f888(x102233,f887(x102232,x102233)),f888(x102233,f888(f888(f887(x102232,x102233),a879),a879)),x102232),f335(f8(f887(x102232,x102233),f888(f888(f887(x102232,x102233),a879),a879),x102233),f337(f887(x102232,x102233)))),f264(x102232,x102233))))),x102234)),x102235),x102236))
% 59.73/59.66 [10224]~P1(f335(f335(f337(f887(x102242,x102243)),f335(f335(f264(x102242,x102243),x102245),x102246)),f335(f335(f34(x102241,f888(f887(x102242,x102243),a879)),f252(f888(x102241,a879))),x102244)))+P1(f335(f335(f335(f335(f34(x102241,f888(x102242,f888(x102243,a879))),f252(f888(x102241,a879))),f335(f335(f8(f888(f887(x102242,x102243),a879),f888(x102242,f888(x102243,a879)),x102241),f335(f7(x102242,f888(f887(x102242,x102243),a879),f888(x102243,a879)),f335(f335(f8(f888(x102243,f888(f888(f887(x102242,x102243),a879),a879)),f888(f888(f887(x102242,x102243),a879),f888(x102243,a879)),x102242),f7(x102243,f888(f887(x102242,x102243),a879),a879)),f335(f335(f8(f888(x102243,f887(x102242,x102243)),f888(x102243,f888(f888(f887(x102242,x102243),a879),a879)),x102242),f335(f8(f887(x102242,x102243),f888(f888(f887(x102242,x102243),a879),a879),x102243),f337(f887(x102242,x102243)))),f264(x102242,x102243))))),x102244)),x102245),x102246))
% 59.73/59.66 [10232]P1(f335(f335(f337(f887(x102321,x102322)),f335(f335(f264(x102321,x102322),x102323),x102324)),f335(f335(f33(x102325,f888(f887(x102321,x102322),a879)),f252(f888(x102325,a879))),x102326)))+~P1(f335(f335(f335(f335(f33(x102325,f888(x102321,f888(x102322,a879))),f252(f888(x102325,a879))),f335(f335(f8(f888(f887(x102321,x102322),a879),f888(x102321,f888(x102322,a879)),x102325),f335(f7(x102321,f888(f887(x102321,x102322),a879),f888(x102322,a879)),f335(f335(f8(f888(x102322,f888(f888(f887(x102321,x102322),a879),a879)),f888(f888(f887(x102321,x102322),a879),f888(x102322,a879)),x102321),f7(x102322,f888(f887(x102321,x102322),a879),a879)),f335(f335(f8(f888(x102322,f887(x102321,x102322)),f888(x102322,f888(f888(f887(x102321,x102322),a879),a879)),x102321),f335(f8(f887(x102321,x102322),f888(f888(f887(x102321,x102322),a879),a879),x102322),f337(f887(x102321,x102322)))),f264(x102321,x102322))))),x102326)),x102323),x102324))
% 59.73/59.67 [10233]P1(f335(f335(f337(f887(x102331,x102332)),f335(f335(f264(x102331,x102332),x102333),x102334)),f335(f335(f34(x102335,f888(f887(x102331,x102332),a879)),f252(f888(x102335,a879))),x102336)))+~P1(f335(f335(f335(f335(f34(x102335,f888(x102331,f888(x102332,a879))),f252(f888(x102335,a879))),f335(f335(f8(f888(f887(x102331,x102332),a879),f888(x102331,f888(x102332,a879)),x102335),f335(f7(x102331,f888(f887(x102331,x102332),a879),f888(x102332,a879)),f335(f335(f8(f888(x102332,f888(f888(f887(x102331,x102332),a879),a879)),f888(f888(f887(x102331,x102332),a879),f888(x102332,a879)),x102331),f7(x102332,f888(f887(x102331,x102332),a879),a879)),f335(f335(f8(f888(x102332,f887(x102331,x102332)),f888(x102332,f888(f888(f887(x102331,x102332),a879),a879)),x102331),f335(f8(f887(x102331,x102332),f888(f888(f887(x102331,x102332),a879),a879),x102332),f337(f887(x102331,x102332)))),f264(x102331,x102332))))),x102336)),x102333),x102334))
% 59.73/59.67 [9278]E(x92781,x92782)+~E(f322(x92783,x92784,x92785,x92786,x92781),f322(x92783,x92784,x92785,x92787,x92782))
% 59.73/59.67 [9279]E(x92791,x92792)+~E(f322(x92793,x92794,x92795,x92791,x92796),f322(x92793,x92794,x92795,x92792,x92797))
% 59.73/59.67 [7457]E(f335(x74571,f335(x74572,x74573)),f335(x74574,x74573))+~E(f335(f68(x74575,x74576,x74577,x74571),x74572),x74574)
% 59.73/59.67 [9669]~P24(x96693,x96694,x96691,x96695,x96696,x96697)+E(f335(f335(x96691,x96692),x96692),x96692)
% 59.73/59.67 [10047]~E(f335(f237(f885(x100477),x100471,f200(x100477),x100475),f335(x100474,x100473)),f335(f235(x100477),x100472))+E(f335(f235(x100471),f670(x100472,x100473,x100474,x100475,x100476,x100477,x100471)),f335(x100474,x100473))
% 59.73/59.67 [10048]~E(f335(f237(f885(x100486),x100487,f200(x100486),x100481),f335(x100484,x100483)),f335(f235(x100486),x100482))+E(f335(x100481,f670(x100482,x100483,x100484,x100481,x100485,x100486,x100487)),f335(f235(x100486),x100482))
% 59.73/59.67 [6023]~E(f335(f335(f147(x60231,x60235),x60236),x60232),f335(f335(f147(x60233,x60235),x60237),x60234))+E(f335(f189(f882(x60231)),x60232),f335(f189(f882(x60233)),x60234))
% 59.73/59.67 [7532]E(x75321,x75322)+~E(f335(f335(f335(f67(x75323,f885(x75324)),x75325),x75326),f335(f235(x75324),x75321)),f335(f335(f335(f67(x75323,f885(x75324)),x75327),x75326),f335(f235(x75324),x75322)))
% 59.73/59.67 [8497]E(f335(x84971,f335(x84972,x84973)),f335(x84974,x84973))+~E(f335(f68(x84975,x84976,x84977,x84971),x84972),f335(f68(x84976,x84976,x84977,f25(x84976)),x84974))
% 59.73/59.67 [8835]~P33(x88354,x88355,x88351,f335(f335(f144(x88354),x88352),x88356),f335(f335(f144(x88355),x88353),x88357))+P1(f335(f335(x88351,x88352),x88353))
% 59.73/59.67 [9215]P33(x92151,x92152,x92153,x92154,x92155)+~P33(x92151,x92152,x92153,f335(f335(f144(x92151),x92156),x92154),f335(f335(f144(x92152),x92157),x92155))
% 59.73/59.67 [9847]P1(f335(f335(x98471,x98472),f515(x98473,x98472,x98474,x98471)))+~P1(f335(f335(f265(x98475,x98476,x98477,x98471,x98474),x98472),x98473))
% 59.73/59.67 [9869]P1(f335(f335(x98691,f515(x98692,x98693,x98691,x98694)),x98692))+~P1(f335(f335(f265(x98695,x98696,x98697,x98694,x98691),x98693),x98692))
% 59.73/59.67 [8955]~P22(x89556,x89551,x89553,x89557)+E(f335(f68(x89551,x89551,x89552,f335(x89553,x89554)),f335(f68(x89551,x89551,x89552,f335(x89553,x89554)),x89555)),f335(f68(x89551,x89551,x89552,f335(x89553,x89554)),x89555))
% 59.73/59.67 [9319]~P33(x93193,x93192,x93194,f335(f335(f147(x93191,x93193),x93195),x93196),x93197)+P33(x93191,x93192,f335(f335(f8(x93193,f888(x93192,a879),x93191),x93194),x93195),x93196,x93197)
% 59.73/59.67 [9341]P33(x93411,x93412,x93413,f335(f335(f147(x93414,x93411),x93415),x93416),x93417)+~P33(x93414,x93412,f335(f335(f8(x93411,f888(x93412,a879),x93414),x93413),x93415),x93416,x93417)
% 59.73/59.67 [9764]E(f181(x97641,x97642,f335(f335(f335(f67(x97641,f885(x97642)),x97643),x97644),f335(f235(x97642),x97645)),x97646,x97647),f335(f335(f335(f67(x97641,f885(x97642)),f181(x97641,x97642,x97643,x97646,x97647)),x97644),f335(f235(x97642),x97645)))+P1(f335(f335(f337(x97641),x97644),f335(f166(x97641),x97646)))
% 59.73/59.67 [8954]~P1(f335(f335(f337(x89541),x89542),f335(f335(x89545,x89546),x89547)))+P1(f335(f335(f337(x89541),x89542),f335(f335(f268(x89543,x89544,f888(x89541,a879)),x89545),f335(f335(f264(x89543,x89544),x89546),x89547))))
% 59.73/59.67 [9242]P1(f335(f335(f335(x92421,x92422),x92423),x92424))+~P1(f335(f335(f335(f268(x92425,x92426,f888(x92427,a879)),x92421),f335(f335(f264(x92425,x92426),x92422),x92423)),x92424))
% 59.73/59.67 [9382]P1(f335(f335(f337(x93821),f335(f335(x93822,x93823),x93824)),f335(f313(f887(x93825,x93826),x93821,f335(f268(x93825,x93826,x93821),x93822)),x93827)))+~P1(f335(f335(f337(f887(x93825,x93826)),f335(f335(f264(x93825,x93826),x93823),x93824)),x93827))
% 59.73/59.67 [9720]P1(f335(f335(f337(f887(f882(x97201),f882(x97201))),f335(f335(f264(f882(x97201),f882(x97201)),f335(f335(f127(x97201),x97202),f335(f335(f144(x97201),x97203),x97204))),f335(f335(f127(x97201),x97202),f335(f335(f144(x97201),x97205),x97206)))),f140(x97201,x97207)))+~P1(f335(f335(f337(f887(x97201,x97201)),f335(f335(f264(x97201,x97201),x97203),x97205)),x97207))
% 59.73/59.67 [9787]~P33(x97871,x97873,x97874,x97876,f335(f335(f147(x97872,x97873),x97875),x97877))+P33(x97871,x97872,f335(f335(f7(x97871,f888(x97872,x97873),f888(x97872,a879)),f335(f335(f8(f888(x97873,a879),f888(f888(x97872,x97873),f888(x97872,a879)),x97871),f8(x97873,a879,x97872)),x97874)),x97875),x97876,x97877)
% 59.73/59.67 [9873]P33(x98731,x98732,x98733,x98734,f335(f335(f147(x98735,x98732),x98736),x98737))+~P33(x98731,x98735,f335(f335(f7(x98731,f888(x98735,x98732),f888(x98735,a879)),f335(f335(f8(f888(x98732,a879),f888(f888(x98735,x98732),f888(x98735,a879)),x98731),f8(x98732,a879,x98735)),x98733)),x98736),x98734,x98737)
% 59.73/59.67 [9234]E(x92341,x92342)+E(f335(f335(f335(f67(x92343,x92344),f335(f335(f335(f67(x92343,x92344),x92345),x92341),x92346)),x92342),x92347),f335(f335(f335(f67(x92343,x92344),f335(f335(f335(f67(x92343,x92344),x92345),x92342),x92347)),x92341),x92346))
% 59.73/59.67 [9480]E(f181(x94801,x94802,f335(f335(f335(f67(x94801,f885(x94802)),x94803),x94804),f335(f235(x94802),x94805)),x94806,x94807),f181(x94801,x94802,x94803,x94806,x94807))+~P1(f335(f335(f337(x94801),x94804),f335(f166(x94801),f335(f335(f169(x94801),f335(f189(f882(x94802)),x94807)),x94806))))
% 59.73/59.67 [9798]E(f181(x97981,x97982,f335(f335(f335(f67(x97981,f885(x97982)),x97983),x97984),f335(f235(x97982),x97985)),x97986,x97987),f335(f335(f335(f67(x97981,f885(x97982)),f181(x97981,x97982,x97983,x97986,x97987)),x97984),f335(f235(x97982),x97985)))+P1(f335(f335(f337(x97981),x97984),f335(f166(x97981),f335(f335(f169(x97981),f335(f189(f882(x97982)),x97987)),x97986))))
% 59.73/59.67 [10157]P1(f335(f335(f337(x101571),f626(x101572,x101573,x101574,x101575,x101576,x101577,x101571)),x101575))+P1(f335(f335(f335(f335(f34(x101571,f888(x101577,f888(x101576,a879))),x101575),x101574),x101573),x101572))
% 59.73/59.67 [10158]P1(f335(f335(f337(x101581),f819(x101582,x101583,x101584,x101585,x101586,x101587,x101581)),x101587))+P1(f335(f335(f335(f335(f34(x101581,f888(x101583,f888(x101582,a879))),x101587),x101586),x101585),x101584))
% 59.73/59.67 [10159]P1(f335(f335(f337(x101591),f845(x101592,x101593,x101594,x101595,x101596,x101597,x101591)),x101595))+~P1(f335(f335(f335(f335(f33(x101591,f888(x101597,f888(x101596,a879))),x101595),x101594),x101593),x101592))
% 59.73/59.67 [10160]P1(f335(f335(f337(x101601),f818(x101602,x101603,x101604,x101605,x101606,x101607,x101601)),x101605))+~P1(f335(f335(f335(f335(f33(x101601,f888(x101607,f888(x101606,a879))),x101605),x101604),x101603),x101602))
% 59.73/59.67 [10186]P1(f335(f335(f335(x101861,f845(x101862,x101863,x101861,x101864,x101865,x101866,x101867)),x101863),x101862))+~P1(f335(f335(f335(f335(f33(x101867,f888(x101866,f888(x101865,a879))),x101864),x101861),x101863),x101862))
% 59.73/59.67 [10187]P1(f335(f335(f335(x101871,f818(x101872,x101873,x101871,x101874,x101875,x101876,x101877)),x101873),x101872))+~P1(f335(f335(f335(f335(f33(x101877,f888(x101876,f888(x101875,a879))),x101874),x101871),x101873),x101872))
% 59.73/59.67 [10203]~P1(f335(f335(f335(x102035,f626(x102037,x102036,x102035,x102034,x102033,x102032,x102031)),x102036),x102037))+P1(f335(f335(f335(f335(f34(x102031,f888(x102032,f888(x102033,a879))),x102034),x102035),x102036),x102037))
% 59.73/59.67 [10204]~P1(f335(f335(f335(x102045,f819(x102043,x102042,x102047,x102046,x102045,x102044,x102041)),x102046),x102047))+P1(f335(f335(f335(f335(f34(x102041,f888(x102042,f888(x102043,a879))),x102044),x102045),x102046),x102047))
% 59.73/59.67 [10222]~P1(f335(f335(f337(f887(x102221,x102223)),f335(f335(f264(x102221,x102223),x102226),x102227)),f335(f335(f291(x102221,x102222,x102223),x102224),x102225)))+P1(f335(f335(f265(x102221,x102222,x102223,f335(f335(f7(x102221,f888(f887(x102221,x102222),a879),f888(x102222,a879)),f335(f335(f8(f888(x102222,f888(f888(f887(x102221,x102222),a879),a879)),f888(f888(f887(x102221,x102222),a879),f888(x102222,a879)),x102221),f7(x102222,f888(f887(x102221,x102222),a879),a879)),f335(f335(f8(f888(x102222,f887(x102221,x102222)),f888(x102222,f888(f888(f887(x102221,x102222),a879),a879)),x102221),f335(f8(f887(x102221,x102222),f888(f888(f887(x102221,x102222),a879),a879),x102222),f337(f887(x102221,x102222)))),f264(x102221,x102222)))),x102224),f335(f335(f7(x102222,f888(f887(x102222,x102223),a879),f888(x102223,a879)),f335(f335(f8(f888(x102223,f888(f888(f887(x102222,x102223),a879),a879)),f888(f888(f887(x102222,x102223),a879),f888(x102223,a879)),x102222),f7(x102223,f888(f887(x102222,x102223),a879),a879)),f335(f335(f8(f888(x102223,f887(x102222,x102223)),f888(x102223,f888(f888(f887(x102222,x102223),a879),a879)),x102222),f335(f8(f887(x102222,x102223),f888(f888(f887(x102222,x102223),a879),a879),x102223),f337(f887(x102222,x102223)))),f264(x102222,x102223)))),x102225)),x102226),x102227))
% 59.73/59.67 [10231]P1(f335(f335(f337(f887(x102311,x102312)),f335(f335(f264(x102311,x102312),x102313),x102314)),f335(f335(f291(x102311,x102315,x102312),x102316),x102317)))+~P1(f335(f335(f265(x102311,x102315,x102312,f335(f335(f7(x102311,f888(f887(x102311,x102315),a879),f888(x102315,a879)),f335(f335(f8(f888(x102315,f888(f888(f887(x102311,x102315),a879),a879)),f888(f888(f887(x102311,x102315),a879),f888(x102315,a879)),x102311),f7(x102315,f888(f887(x102311,x102315),a879),a879)),f335(f335(f8(f888(x102315,f887(x102311,x102315)),f888(x102315,f888(f888(f887(x102311,x102315),a879),a879)),x102311),f335(f8(f887(x102311,x102315),f888(f888(f887(x102311,x102315),a879),a879),x102315),f337(f887(x102311,x102315)))),f264(x102311,x102315)))),x102316),f335(f335(f7(x102315,f888(f887(x102315,x102312),a879),f888(x102312,a879)),f335(f335(f8(f888(x102312,f888(f888(f887(x102315,x102312),a879),a879)),f888(f888(f887(x102315,x102312),a879),f888(x102312,a879)),x102315),f7(x102312,f888(f887(x102315,x102312),a879),a879)),f335(f335(f8(f888(x102312,f887(x102315,x102312)),f888(x102312,f888(f888(f887(x102315,x102312),a879),a879)),x102315),f335(f8(f887(x102315,x102312),f888(f888(f887(x102315,x102312),a879),a879),x102312),f337(f887(x102315,x102312)))),f264(x102315,x102312)))),x102317)),x102313),x102314))
% 59.73/59.67 [10169]~P142(x101692)+E(f335(f335(f6(x101691,x101692),f335(f335(f7(x101691,f888(x101693,a879),x101692),f335(f335(f8(f888(x101693,x101692),f888(f888(x101693,a879),x101692),x101691),f6(x101693,x101692)),f335(f335(f7(x101691,f888(x101693,x101692),f888(x101693,x101692)),f335(f335(f8(f888(x101692,x101692),f888(f888(x101693,x101692),f888(x101693,x101692)),x101691),f8(x101692,x101692,x101693)),f335(f335(f8(x101692,f888(x101692,x101692),x101691),f76(x101692)),x101694))),x101695))),x101696)),x101697),f335(f335(f76(x101692),f335(f335(f6(x101691,x101692),x101694),x101697)),f335(f335(f6(x101693,x101692),x101695),x101696)))
% 59.73/59.67 [9270]~P21(x92707,x92701,x92703,x92708)+E(f335(f68(x92701,x92701,x92702,f335(x92703,x92704)),f335(f68(x92701,x92701,x92702,f335(x92703,x92705)),x92706)),f335(f68(x92701,x92701,x92702,f335(x92703,x92705)),f335(f68(x92701,x92701,x92702,f335(x92703,x92704)),x92706)))
% 59.73/59.67 [10225]E(f335(f335(f264(x102251,x102252),f335(x102253,f541(x102254,x102255,x102253,x102256,x102257,x102258,x102252,x102251))),f335(x102255,f543(x102254,x102255,x102253,x102256,x102257,x102258,x102252,x102251))),x102258)+~P1(f335(f335(f337(f887(x102251,x102252)),x102258),f335(f313(f887(x102257,x102256),f887(x102251,x102252),f269(x102257,x102251,x102256,x102252,x102253,x102255)),x102254)))
% 59.73/59.67 [10240]~P1(f335(f335(f337(f887(x102408,x102407)),x102406),f335(f313(f887(x102401,x102402),f887(x102408,x102407),f269(x102401,x102408,x102402,x102407,x102405,x102404)),x102403)))+P1(f335(f335(f337(f887(x102401,x102402)),f335(f335(f264(x102401,x102402),f541(x102403,x102404,x102405,x102402,x102401,x102406,x102407,x102408)),f543(x102403,x102404,x102405,x102402,x102401,x102406,x102407,x102408))),x102403))
% 59.73/59.67 [9709]P1(f335(f335(f337(f887(f887(x97091,x97092),f887(x97091,x97092))),f335(f335(f264(f887(x97091,x97092),f887(x97091,x97092)),f335(f335(f264(x97091,x97092),x97093),x97094)),f335(f335(f264(x97091,x97092),x97095),x97096))),f328(x97091,x97092,x97097,x97098)))+~P1(f335(f335(f337(f887(x97091,x97091)),f335(f335(f264(x97091,x97091),x97093),x97095)),x97097))
% 59.73/59.67 [10216]E(f335(f135(x102161,x102162,f335(f7(x102162,x102161,x102161),x102163),f335(x102164,x102165)),x102166),f335(x102164,f335(f135(x102167,x102162,f335(f7(x102162,x102167,x102167),x102168),x102165),x102166)))+P1(f335(f335(f337(x102162),f759(x102165,x102168,x102164,x102163,x102167,x102161,x102166,x102162)),f335(f166(x102162),x102166)))
% 59.73/59.67 [10234]~E(f335(f68(x102341,x102341,x102347,f335(x102343,f759(x102345,x102348,x102344,x102343,x102347,x102341,x102346,x102342))),x102344),f335(f68(x102347,x102341,x102347,x102344),f335(x102348,f759(x102345,x102348,x102344,x102343,x102347,x102341,x102346,x102342))))+E(f335(f135(x102341,x102342,f335(f7(x102342,x102341,x102341),x102343),f335(x102344,x102345)),x102346),f335(x102344,f335(f135(x102347,x102342,f335(f7(x102342,x102347,x102347),x102348),x102345),x102346)))
% 59.73/59.67 [8501]E(f335(x85011,f335(x85012,x85013)),f335(x85014,f335(x85015,x85013)))+~E(f335(f68(x85016,x85017,x85018,x85011),x85012),f335(f68(x85019,x85017,x85018,x85014),x85015))
% 59.73/59.67 [8502]E(f335(x85021,f335(x85022,x85023)),f335(x85024,f335(x85025,x85023)))+~E(f335(f68(x85026,x85027,x85028,x85021),x85022),f335(f68(x85029,x85027,x85028,x85024),x85025))
% 59.73/59.67 [10098]P1(f335(f335(f337(f887(x100981,x100982)),f335(f335(f264(x100981,x100982),f335(x100983,x100984)),f335(x100985,x100986))),f335(f313(f887(x100987,x100988),f887(x100981,x100982),f269(x100987,x100981,x100988,x100982,x100983,x100985)),x100989)))+~P1(f335(f335(f337(f887(x100987,x100988)),f335(f335(f264(x100987,x100988),x100984),x100986)),x100989))
% 59.73/59.67 [8781]~E(f335(x87814,f335(x87815,x87816)),f335(x87819,f335(x878110,x878111)))+E(f335(f335(f68(x87811,x87812,x87813,x87814),x87815),x87816),f335(f335(f68(x87817,x87812,x87818,x87819),x878110),x878111))
% 59.73/59.67 [9351]~P21(x93518,x93519,x935110,x935111)+E(f335(f68(x93511,x93512,x93513,x93514),f335(f68(x93515,x93511,x93513,x93516),x93517)),f335(f68(x93515,x93512,x93513,f335(f68(x93511,x93512,x93515,x93514),x93516)),x93517))
% 59.73/59.67 [4626]~P106(x46261)+~P102(x46261)+E(f95(x46261),f240(x46261))
% 59.73/59.67 [4627]~P106(x46271)+~P60(x46271)+E(f104(x46271),f241(x46271))
% 59.73/59.67 [4866]~P119(x48661)+~P97(x48661)+E(f335(f70(x48661),f335(f97(x48661),a91)),f73(x48661))
% 59.73/59.67 [5145]E(x51451,f2(a1))+E(f77(a1,x51451),f335(f74(a1),f73(a1)))+P1(f335(f335(f243(a1),f2(a1)),x51451))
% 59.73/59.67 [5351]E(x53511,f2(a1))+E(f77(a1,x53511),f73(a1))+~P1(f335(f335(f243(a1),f2(a1)),x53511))
% 59.73/59.67 [6649]~P38(x66491)+~P1(f335(f56(a1),x66491))+P1(f335(f56(a881),f335(f313(a1,a881,a98),x66491)))
% 59.73/59.67 [7015]E(f41(f73(a1),f335(f97(a1),x70151)),f335(f335(f264(a1,a1),f2(a1)),f73(a1)))+~P1(f335(f335(f243(a1),f2(a1)),f335(f97(a1),x70151)))+~P1(f335(f335(f243(a1),f73(a1)),f335(f97(a1),x70151)))
% 59.73/59.67 [7351]~P38(x73511)+P1(f335(f56(a1),x73511))+~P1(f335(f56(a881),f335(f313(a1,a881,a98),x73511)))
% 59.73/59.67 [8200]E(f335(f335(f264(a1,a1),f335(f97(a1),a91)),f335(f335(f75(a1),f73(a1)),f335(f97(a1),x82001))),f44(f73(a1),f335(f97(a1),x82001)))+~P1(f335(f335(f243(a1),f2(a1)),f335(f97(a1),x82001)))+~P1(f335(f335(f242(a1),f2(a1)),f335(f335(f75(a1),f73(a1)),f335(f97(a1),x82001))))
% 59.73/59.67 [9991]E(f335(f37(f335(f97(a1),x99911)),f41(f73(a1),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(f97(a1),x99911)))),f41(f73(a1),f335(f97(a1),x99911)))+~P1(f335(f335(f243(a1),f2(a1)),f335(f97(a1),x99911)))+P1(f335(f335(f243(a1),f73(a1)),f335(f97(a1),x99911)))
% 59.73/59.67 [9997]E(f335(f37(f335(f97(a1),x99971)),f44(f73(a1),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(f97(a1),x99971)))),f44(f73(a1),f335(f97(a1),x99971)))+~P1(f335(f335(f243(a1),f2(a1)),f335(f97(a1),x99971)))+P1(f335(f335(f242(a1),f2(a1)),f335(f335(f75(a1),f73(a1)),f335(f97(a1),x99971))))
% 59.73/59.67 [9668]E(x96681,f188(f888(f887(a881,a881),a879)))+~P1(f335(f56(f887(a881,a881)),x96681))+P1(f335(f335(f337(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879))),f335(f335(f264(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),f188(f888(f887(a881,a881),a879))),x96681)),a28))
% 59.73/59.67 [9848]E(x98481,f2(a881))+E(x98481,f335(a106,f2(a881)))+~P1(f335(f335(f243(a881),x98481),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))
% 59.73/59.67 [10124]E(x101241,f2(a93))+E(f335(f335(f75(a1),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(a21,f335(f335(f30(a93),x101241),f335(f97(a93),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))))),f73(a1)),f335(a21,x101241))+E(f39(a93,x101241,f335(f97(a93),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f2(a93))
% 59.73/59.67 [9978]E(x99781,f2(a93))+~E(f39(a93,x99781,f335(f97(a93),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f2(a93))+E(f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(a21,f335(f335(f30(a93),x99781),f335(f97(a93),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))),f335(a21,x99781))
% 59.73/59.67 [4698]~P55(x46981,x46982)+P41(x46981,x46982)+~P42(a879)
% 59.73/59.67 [4636]~P143(x46361)+P28(x46361,x46362)+~E(x46362,f2(x46361))
% 59.73/59.67 [4637]~P106(x46371)+P15(x46371,x46372)+~E(x46372,f107(x46371))
% 59.73/59.67 [4646]~P119(x46461)+~E(x46462,f2(x46461))+E(f77(x46461,x46462),f2(x46461))
% 59.73/59.67 [4647]~P91(x46471)+~E(x46472,f2(x46471))+E(f77(x46471,x46472),f2(x46471))
% 59.73/59.67 [4655]~P143(x46552)+~P28(x46552,x46551)+E(x46551,f2(x46552))
% 59.73/59.67 [4689]~P119(x46892)+~E(f77(x46892,x46891),f2(x46892))+E(x46891,f2(x46892))
% 59.73/59.67 [4705]~P4(x47052)+~P4(x47051)+P4(f888(x47051,x47052))
% 59.73/59.67 [4706]~P4(x47062)+~P4(x47061)+P4(f887(x47061,x47062))
% 59.73/59.67 [4707]~P4(x47072)+~P4(x47071)+P4(f889(x47071,x47072))
% 59.73/59.67 [4708]~P65(x47082)+~P65(x47081)+P65(f888(x47081,x47082))
% 59.73/59.67 [4709]~P65(x47092)+~P65(x47091)+P65(f887(x47091,x47092))
% 59.73/59.67 [4710]~P65(x47102)+~P65(x47101)+P65(f889(x47101,x47102))
% 59.73/59.67 [4711]~P6(x47112)+~P6(x47111)+P6(f194(x47111,x47112))
% 59.73/59.67 [4712]~P144(x47122)+~P144(x47121)+P144(f887(x47121,x47122))
% 59.73/59.67 [4713]~P4(x47131)+~P96(x47132)+P96(f888(x47131,x47132))
% 59.73/59.67 [4714]~P104(x47142)+~P104(x47141)+P104(f887(x47141,x47142))
% 59.73/59.67 [4838]~P106(x48381)+~P15(x48381,x48382)+P15(x48381,f145(x48381,x48382))
% 59.73/59.67 [5073]~P6(x50732)+~P6(x50731)+P6(f39(a1,x50731,x50732))
% 59.73/59.67 [4656]~P79(x46561)+~E(x46562,f2(x46561))+E(f335(f74(x46561),x46562),x46562)
% 59.73/59.67 [4657]~P79(x46571)+~E(x46572,f2(x46571))+E(f335(f74(x46571),x46572),x46572)
% 59.73/59.67 [4660]~P94(x46601)+~E(x46602,f2(a1))+E(f335(f96(x46601),x46602),f2(x46601))
% 59.73/59.67 [4661]~P137(x46611)+~E(x46612,f2(a1))+E(f335(f96(x46611),x46612),f2(x46611))
% 59.73/59.67 [4662]~P94(x46621)+~E(x46622,f2(a1))+E(f335(f96(x46621),x46622),f2(x46621))
% 59.73/59.67 [4686]~P72(x46861)+~E(f2(x46861),x46862)+E(f335(f74(x46861),x46862),f2(x46861))
% 59.73/59.67 [4687]~P72(x46871)+~E(x46872,f2(x46871))+E(f335(f74(x46871),x46872),f2(x46871))
% 59.73/59.67 [4688]~P88(x46881)+~E(x46882,f2(x46881))+E(f335(f70(x46881),x46882),f2(x46881))
% 59.73/59.67 [4715]~P79(x47152)+E(x47151,f2(x47152))+~E(f335(f74(x47152),x47151),x47151)
% 59.73/59.67 [4716]~P79(x47162)+E(x47161,f2(x47162))+~E(f335(f74(x47162),x47161),x47161)
% 59.73/59.67 [4718]E(x47181,f335(a98,x47182))+~E(x47181,f2(a881))+~E(x47182,f335(f94(a1),x47181))
% 59.73/59.67 [4719]E(f335(a98,x47191),x47192)+~E(x47192,f2(a881))+~E(x47191,f335(f94(a1),x47192))
% 59.73/59.67 [4722]~P94(x47222)+E(x47221,f2(a1))+~E(f335(f96(x47222),x47221),f2(x47222))
% 59.73/59.67 [4723]~P94(x47232)+E(x47231,f2(a1))+~E(f335(f96(x47232),x47231),f2(x47232))
% 59.73/59.67 [4728]~P72(x47282)+E(x47281,f2(x47282))+~E(f335(f74(x47282),x47281),f2(x47282))
% 59.73/59.67 [4729]~P88(x47292)+E(x47291,f2(x47292))+~E(f335(f70(x47292),x47291),f2(x47292))
% 59.73/59.67 [4730]~P72(x47301)+E(f2(x47301),x47302)+~E(f335(f74(x47301),x47302),f2(x47301))
% 59.73/59.67 [4912]~P106(x49121)+~P15(x49121,x49122)+P15(x49121,f335(f165(x49121),x49122))
% 59.73/59.67 [4937]~P1(x49372)+~P1(x49371)+P1(f335(f335(a333,x49371),x49372))
% 59.73/59.67 [4971]~E(f73(a881),f2(a881))+E(f335(f29(x49711),x49712),f2(a881))+~P1(f335(f56(x49711),x49712))
% 59.73/59.67 [5005]~P113(x50051)+~P142(x50051)+E(f335(f335(f254(x50051),f2(x50051)),f335(a106,x50052)),f2(x50051))
% 59.73/59.67 [5043]~P106(x50431)+P15(x50431,f132(x50431,x50432))+~P1(f335(f56(x50431),x50432))
% 59.73/59.67 [5044]~P106(x50441)+P15(x50441,f748(x50442,x50441))+~P1(f335(f56(x50441),x50442))
% 59.73/59.67 [5065]~P106(x50651)+E(f335(f166(x50651),f132(x50651,x50652)),x50652)+~P1(f335(f56(x50651),x50652))
% 59.73/59.67 [5066]~P106(x50661)+E(f335(f166(x50661),f748(x50662,x50661)),x50662)+~P1(f335(f56(x50661),x50662))
% 59.73/59.67 [5094]P1(x50941)+P1(x50942)+~P1(f335(f335(a334,x50942),x50941))
% 59.73/59.67 [5106]E(x51061,f188(f888(x51062,a879)))+~E(f335(f29(x51062),x51061),f2(a881))+~P1(f335(f56(x51062),x51061))
% 59.73/59.67 [5111]P1(x51111)+~P1(x51112)+~P1(f335(f335(a338,x51112),x51111))
% 59.73/59.67 [5164]~P76(x51641)+E(f335(f70(x51641),x51642),x51642)+P1(f335(f335(f243(x51641),x51642),f2(x51641)))
% 59.73/59.67 [5165]~P5(x51652)+~P37(x51652,x51652,x51651)+E(f335(x51651,f90(x51652,x51651)),f90(x51652,x51651))
% 59.73/59.67 [5166]~P5(x51662)+~P37(x51662,x51662,x51661)+E(f335(x51661,f89(x51662,x51661)),f89(x51662,x51661))
% 59.73/59.67 [5229]~P4(x52292)+~P1(f335(f52(x52292),x52291))+P1(f335(x52291,f574(x52291,x52292)))
% 59.73/59.67 [5230]~P4(x52302)+~P1(f335(f52(x52302),x52301))+P1(f335(x52301,f616(x52301,x52302)))
% 59.73/59.67 [5267]E(x52671,f107(x52672))+P1(f335(f130(x52672),f108(x52672,x52671)))+~P1(f335(f130(x52672),x52671))
% 59.73/59.67 [5272]~P106(x52721)+~P1(f335(f56(x52721),x52722))+P1(f335(f130(x52721),f132(x52721,x52722)))
% 59.73/59.67 [5273]~P106(x52731)+~P1(f335(f56(x52731),x52732))+P1(f335(f130(x52731),f748(x52732,x52731)))
% 59.73/59.67 [5279]~P137(x52791)+E(f335(f94(x52791),f335(a98,x52792)),f335(f96(x52791),x52792))+P1(f335(f335(f243(a1),x52792),f2(a1)))
% 59.73/59.67 [5301]P7(x53012,x53011)+E(f335(x53011,f846(x53011)),f335(x53011,f849(x53011)))+P1(f335(f335(x53011,f846(x53011)),f849(x53011)))
% 59.73/59.67 [5315]E(f335(f94(a1),f398(x53151,x53152)),x53151)+P1(f335(x53152,f335(a98,x53151)))+~P1(f335(x53152,f2(a881)))
% 59.73/59.67 [5327]~P4(x53271)+~P1(f335(x53272,f765(x53272,x53271)))+P1(f335(f53(x53271),x53272))
% 59.73/59.67 [5328]~P4(x53281)+~P1(f335(x53282,f810(x53282,x53281)))+P1(f335(f53(x53281),x53282))
% 59.73/59.67 [5344]~P4(x53442)+~P34(x53442,x53441,f50(x53442))+P1(f335(x53441,f764(x53441,x53442)))
% 59.73/59.67 [5360]~P119(x53601)+~E(f77(x53601,x53602),f335(f74(x53601),f73(x53601)))+P1(f335(f335(f243(x53601),x53602),f2(x53601)))
% 59.73/59.67 [5436]~E(x54362,f2(a1))+E(f218(x54361,x54362),f335(f335(f264(a1,a1),f2(a1)),f73(a1)))+P1(f335(f335(f243(a1),x54362),f2(a1)))
% 59.73/59.67 [5437]~E(x54371,f2(a1))+E(f218(x54371,x54372),f335(f335(f264(a1,a1),f2(a1)),f73(a1)))+P1(f335(f335(f243(a1),x54372),f2(a1)))
% 59.73/59.67 [5489]E(f335(f94(a1),f398(x54891,x54892)),x54891)+P1(f335(x54892,f335(a98,x54891)))+P1(f335(f335(f243(a1),x54891),f2(a1)))
% 59.73/59.67 [5551]~P119(x55511)+E(f77(x55511,x55512),f335(f74(x55511),f73(x55511)))+~P1(f335(f335(f243(x55511),x55512),f2(x55511)))
% 59.73/59.67 [5552]~P119(x55521)+E(f77(x55521,x55522),f335(f74(x55521),f73(x55521)))+~P1(f335(f335(f243(x55521),x55522),f2(x55521)))
% 59.73/59.67 [5553]~P88(x55531)+E(f335(f70(x55531),x55532),f335(f74(x55531),x55532))+~P1(f335(f335(f242(x55531),x55532),f2(x55531)))
% 59.73/59.67 [5554]~P88(x55541)+E(f335(f70(x55541),x55542),f335(f74(x55541),x55542))+~P1(f335(f335(f243(x55541),x55542),f2(x55541)))
% 59.73/59.67 [5555]~P76(x55551)+E(f335(f70(x55551),x55552),f335(f74(x55551),x55552))+~P1(f335(f335(f243(x55551),x55552),f2(x55551)))
% 59.73/59.67 [5652]~P1(f335(x56521,f398(x56522,x56521)))+P1(f335(x56521,f335(a98,x56522)))+~P1(f335(x56521,f2(a881)))
% 59.73/59.67 [5659]E(x56591,f2(a881))+E(f335(a106,f354(x56592,x56591)),x56591)+~P1(f335(f335(f243(a881),x56591),f335(a106,x56592)))
% 59.73/59.67 [5663]P7(x56631,x56632)+~E(f335(x56632,f846(x56632)),f335(x56632,f849(x56632)))+~P1(f335(f335(x56632,f846(x56632)),f849(x56632)))
% 59.73/59.67 [5684]~P106(x56841)+P15(x56841,x56842)+P1(f335(f335(f242(a881),f723(x56842,x56841)),f724(x56842,x56841)))
% 59.73/59.67 [5685]~P106(x56851)+P15(x56851,x56852)+P1(f335(f335(f242(a881),f738(x56852,x56851)),f740(x56852,x56851)))
% 59.73/59.67 [5771]~P88(x57711)+~E(x57712,f2(x57711))+P1(f335(f335(f242(x57711),f335(f70(x57711),x57712)),f2(x57711)))
% 59.73/59.67 [5851]~P4(x58512)+~P4(x58511)+E(f54(x58511,x58512,f50(x58511),f50(x58512)),f50(f887(x58511,x58512)))
% 59.73/59.67 [5856]~P1(f335(x58561,f398(x58562,x58561)))+P1(f335(x58561,f335(a98,x58562)))+P1(f335(f335(f243(a1),x58562),f2(a1)))
% 59.73/59.67 [5880]~P1(f335(x58801,f335(a98,x58802)))+P1(f335(x58801,f2(a881)))+~P1(f335(f335(f243(a1),x58802),f2(a1)))
% 59.73/59.67 [6216]~P119(x62161)+~P1(f335(f335(f243(x62161),x62162),f2(x62161)))+P1(f335(f335(f243(x62161),f77(x62161,x62162)),f2(x62161)))
% 59.73/59.67 [6329]~P119(x63291)+P1(f335(f335(f242(x63291),f335(f96(x63291),x63292)),f2(x63291)))+~P1(f335(f335(f242(a1),x63292),f2(a1)))
% 59.73/59.67 [6330]~P119(x63301)+P1(f335(f335(f243(x63301),f335(f96(x63301),x63302)),f2(x63301)))+~P1(f335(f335(f243(a1),x63302),f2(a1)))
% 59.73/59.67 [6338]~P88(x63382)+E(x63381,f2(x63382))+~P1(f335(f335(f242(x63382),f335(f70(x63382),x63381)),f2(x63382)))
% 59.73/59.67 [6417]~P137(x64171)+~P1(f335(f335(f337(x64171),x64172),f103(x64171)))+P1(f335(f335(f337(x64171),f335(f74(x64171),x64172)),f103(x64171)))
% 59.73/59.67 [6450]~P119(x64501)+~P1(f335(f335(f243(x64501),f77(x64501,x64502)),f2(x64501)))+P1(f335(f335(f243(x64501),x64502),f2(x64501)))
% 59.73/59.67 [6625]~P119(x66252)+~P1(f335(f335(f242(x66252),f335(f96(x66252),x66251)),f2(x66252)))+P1(f335(f335(f242(a1),x66251),f2(a1)))
% 59.73/59.67 [6626]~P119(x66262)+~P1(f335(f335(f243(x66262),f335(f96(x66262),x66261)),f2(x66262)))+P1(f335(f335(f243(a1),x66261),f2(a1)))
% 59.73/59.67 [6710]~P5(x67101)+~P37(x67101,x67101,x67102)+P1(f335(f335(f242(x67101),f335(x67102,f90(x67101,x67102))),f90(x67101,x67102)))
% 59.73/59.67 [6711]~P5(x67111)+~P37(x67111,x67111,x67112)+P1(f335(f335(f242(x67111),f335(x67112,f89(x67111,x67112))),f89(x67111,x67112)))
% 59.73/59.67 [7131]~P79(x71311)+~P1(f335(f335(f242(x71311),x71312),f2(x71311)))+P1(f335(f335(f242(x71311),f335(f335(f75(x71311),x71312),x71312)),f2(x71311)))
% 59.73/59.67 [7133]~P119(x71331)+~P1(f335(f335(f243(x71331),x71332),f2(x71331)))+P1(f335(f335(f243(x71331),f335(f335(f75(x71331),x71332),x71332)),f2(x71331)))
% 59.73/59.67 [7134]~P79(x71341)+~P1(f335(f335(f243(x71341),x71342),f2(x71341)))+P1(f335(f335(f243(x71341),f335(f335(f75(x71341),x71342),x71342)),f2(x71341)))
% 59.73/59.67 [7706]~P79(x77061)+~P1(f335(f335(f242(x77061),f335(f335(f75(x77061),x77062),x77062)),f2(x77061)))+P1(f335(f335(f242(x77061),x77062),f2(x77061)))
% 59.73/59.67 [7707]~P119(x77071)+~P1(f335(f335(f243(x77071),f335(f335(f75(x77071),x77072),x77072)),f2(x77071)))+P1(f335(f335(f243(x77071),x77072),f2(x77071)))
% 59.73/59.67 [7708]~P79(x77081)+~P1(f335(f335(f243(x77081),f335(f335(f75(x77081),x77082),x77082)),f2(x77081)))+P1(f335(f335(f243(x77081),x77082),f2(x77081)))
% 59.73/59.67 [4767]~E(x47672,f73(a881))+~E(x47671,f73(a881))+E(f335(f335(f76(a881),x47671),x47672),f73(a881))
% 59.73/59.67 [4768]~E(x47682,f73(a881))+~E(x47681,f73(a881))+E(f335(f335(f76(a881),x47681),x47682),f73(a881))
% 59.73/59.67 [4769]~E(x47692,f73(a1))+~E(x47691,f73(a1))+E(f335(f335(f76(a1),x47691),x47692),f73(a1))
% 59.73/59.67 [4770]~E(x47702,f2(a881))+~E(x47701,f2(a881))+E(f335(f335(f75(a881),x47701),x47702),f2(a881))
% 59.73/59.67 [4824]~P58(x48242)+E(x48241,f2(x48242))+E(f335(f335(f30(x48242),x48241),x48241),f73(x48242))
% 59.73/59.67 [4825]~P116(x48252)+E(x48251,f2(x48252))+E(f335(f335(f292(x48252),x48251),x48251),f73(x48252))
% 59.73/59.67 [4826]~P117(x48262)+E(x48261,f2(x48262))+E(f335(f335(f292(x48262),x48261),x48261),f73(x48262))
% 59.73/59.67 [4841]~P79(x48411)+~E(x48412,f2(x48411))+E(f335(f335(f75(x48411),x48412),x48412),f2(x48411))
% 59.73/59.67 [4844]~P136(x48441)+~E(x48442,f73(x48441))+E(f335(f335(f76(x48441),x48442),x48442),f73(x48441))
% 59.73/59.67 [4845]~P79(x48451)+~E(x48452,f2(x48451))+E(f335(f335(f75(x48451),x48452),x48452),f2(x48451))
% 59.73/59.67 [4846]~P117(x48461)+~E(x48462,f2(x48461))+E(f335(f335(f292(x48461),x48462),x48462),f2(x48461))
% 59.73/59.67 [4891]~E(x48912,f2(a881))+~E(x48911,f2(a881))+E(f335(f74(a1),f335(f94(a1),x48911)),f335(f94(a1),x48912))
% 59.73/59.67 [4909]E(x49091,f73(a881))+E(x49092,f2(a881))+~E(f335(f335(f76(a881),x49092),x49091),x49092)
% 59.73/59.67 [4919]E(x49191,f2(a881))+E(x49192,f2(a881))+~E(f335(f335(f76(a881),x49192),x49191),f2(a881))
% 59.73/59.67 [4944]~E(x49442,f2(a881))+~E(x49441,f335(a106,f2(a881)))+E(f335(f335(f75(a881),x49441),x49442),f335(a106,f2(a881)))
% 59.73/59.67 [4945]~E(x49451,f2(a881))+~E(x49452,f335(a106,f2(a881)))+E(f335(f335(f75(a881),x49451),x49452),f335(a106,f2(a881)))
% 59.73/59.67 [4946]~E(x49462,f2(a881))+~E(x49461,f335(a106,f2(a881)))+E(f335(f335(f75(a881),x49461),x49462),f335(a106,f2(a881)))
% 59.73/59.67 [4947]~E(x49471,f2(a881))+~E(x49472,f335(a106,f2(a881)))+E(f335(f335(f75(a881),x49471),x49472),f335(a106,f2(a881)))
% 59.73/59.67 [4954]E(x49541,f73(a1))+E(x49542,f335(f97(a1),a91))+~E(f335(f335(f76(a1),x49541),x49542),f73(a1))
% 59.73/59.67 [4955]E(x49551,f73(a1))+E(x49552,f335(f97(a1),a91))+~E(f335(f335(f76(a1),x49552),x49551),f73(a1))
% 59.73/59.67 [4956]E(x49561,f73(a1))+E(x49561,f335(f97(a1),a91))+~E(f335(f335(f76(a1),x49562),x49561),f73(a1))
% 59.73/59.67 [4957]E(x49571,f73(a1))+E(x49571,f335(f97(a1),a91))+~E(f335(f335(f76(a1),x49571),x49572),f73(a1))
% 59.73/59.67 [4958]E(x49581,f73(a1))+E(x49581,f335(f97(a1),a91))+~E(f335(f335(f76(a1),x49581),x49582),f73(a1))
% 59.73/59.67 [4975]~P79(x49752)+E(x49751,f2(x49752))+~E(f335(f335(f75(x49752),x49751),x49751),f2(x49752))
% 59.73/59.67 [4976]~P79(x49762)+E(x49761,f2(x49762))+~E(f335(f335(f75(x49762),x49761),x49761),f2(x49762))
% 59.73/59.67 [4982]~E(x49821,f335(f97(a1),a91))+~E(x49822,f335(f97(a1),a91))+E(f335(f335(f76(a1),x49821),x49822),f73(a1))
% 59.73/59.67 [4993]E(x49931,f2(a881))+E(x49932,f2(a881))+~E(f335(f335(f75(a881),x49932),x49931),f335(a106,f2(a881)))
% 59.73/59.67 [4994]E(x49941,f2(a881))+E(x49942,f2(a881))+~E(f335(f335(f75(a881),x49942),x49941),f335(a106,f2(a881)))
% 59.73/59.67 [5004]~P97(x50041)+~P66(x50041)+E(f335(f335(f292(x50041),x50042),f335(f97(x50041),a78)),f2(x50041))
% 59.73/59.67 [5010]~P136(x50101)+~E(x50102,f335(f74(x50101),f73(x50101)))+E(f335(f335(f76(x50101),x50102),x50102),f73(x50101))
% 59.73/59.67 [5015]~P6(x50152)+~P6(x50151)+P6(f335(f335(f76(a1),x50151),x50152))
% 59.73/59.67 [5016]~P6(x50162)+~P6(x50161)+P6(f335(f335(f75(a1),x50161),x50162))
% 59.73/59.67 [5017]~P6(x50172)+~P6(x50171)+P6(f335(f335(f30(a1),x50171),x50172))
% 59.73/59.67 [5018]~E(x50182,f2(a1))+E(x50181,f2(a1))+E(f40(x50181,x50182),f335(f335(f264(a1,a1),f2(a1)),x50181))
% 59.73/59.67 [5019]~E(x50192,f2(a1))+E(x50191,f2(a1))+E(f40(x50191,x50192),f335(f335(f264(a1,a1),f2(a1)),x50191))
% 59.73/59.67 [5041]~E(x50412,f335(a106,f2(a881)))+~E(x50411,f335(a106,f2(a881)))+E(f335(f335(f76(a881),x50411),x50412),f335(a106,f2(a881)))
% 59.73/59.67 [5054]E(x50541,f2(a881))+E(x50541,f335(a106,f2(a881)))+~E(f335(f335(f75(a881),x50542),x50541),f335(a106,f2(a881)))
% 59.73/59.67 [5055]E(x50551,f2(a881))+E(x50551,f335(a106,f2(a881)))+~E(f335(f335(f75(a881),x50551),x50552),f335(a106,f2(a881)))
% 59.73/59.67 [5056]E(x50561,f2(a881))+E(x50562,f335(a106,f2(a881)))+~E(f335(f335(f254(a881),x50562),x50561),f335(a106,f2(a881)))
% 59.73/59.67 [5057]E(x50571,f2(a881))+E(x50571,f335(a106,f2(a881)))+~E(f335(f335(f75(a881),x50572),x50571),f335(a106,f2(a881)))
% 59.73/59.67 [5058]E(x50581,f2(a881))+E(x50581,f335(a106,f2(a881)))+~E(f335(f335(f75(a881),x50581),x50582),f335(a106,f2(a881)))
% 59.73/59.67 [5067]~P97(x50671)+~P66(x50671)+E(f335(f335(f292(x50671),x50672),f335(f97(x50671),a91)),f335(f74(x50671),x50672))
% 59.73/59.67 [5086]E(x50861,f335(a98,x50862))+~E(x50861,f2(a881))+P1(f335(f335(f242(a1),f2(a1)),x50862))
% 59.73/59.67 [5087]E(f335(a98,x50871),x50872)+~E(x50872,f2(a881))+P1(f335(f335(f242(a1),f2(a1)),x50871))
% 59.73/59.67 [5101]E(x51011,f335(a106,f2(a881)))+E(x51012,f335(a106,f2(a881)))+~E(f335(f335(f75(a881),x51011),x51012),f335(a106,f2(a881)))
% 59.73/59.67 [5102]E(x51021,f335(a106,f2(a881)))+E(x51022,f335(a106,f2(a881)))+~E(f335(f335(f75(a881),x51021),x51022),f335(a106,f2(a881)))
% 59.73/59.67 [5113]~E(x51131,f335(a98,x51132))+E(x51131,f2(a881))+P1(f335(f335(f242(a1),f2(a1)),x51132))
% 59.73/59.67 [5114]~E(f335(a98,x51142),x51141)+E(x51141,f2(a881))+P1(f335(f335(f242(a1),f2(a1)),x51142))
% 59.73/59.67 [5140]~P61(x51401)+E(f335(f58(x51401,f95(x51401)),x51402),f10(x51401,x51402))+~P1(f335(f56(x51401),x51402))
% 59.73/59.67 [5141]~P61(x51411)+E(f335(f58(x51411,f104(x51411)),x51412),f13(x51411,x51412))+~P1(f335(f56(x51411),x51412))
% 59.73/59.67 [5142]~P106(x51421)+E(f335(f58(x51421,f241(x51421)),x51422),f14(x51421,x51422))+~P1(f335(f56(x51421),x51422))
% 59.73/59.67 [5143]~P106(x51431)+E(f335(f58(x51431,f240(x51431)),x51432),f15(x51431,x51432))+~P1(f335(f56(x51431),x51432))
% 59.73/59.67 [5144]~P4(x51441)+~P1(f335(x51442,f200(x51441)))+P1(f335(f52(f885(x51441)),x51442))
% 59.73/59.67 [5221]~P4(x52212)+P1(f335(x52211,f200(x52212)))+~P1(f335(f53(f885(x52212)),x52211))
% 59.73/59.67 [5223]E(x52231,x52232)+~E(f335(f335(f23(a881),x52232),x52231),f2(a881))+~E(f335(f335(f23(a881),x52231),x52232),f2(a881))
% 59.73/59.67 [5238]P6(x52381)+~P38(x52382)+~P1(f335(f335(f337(a1),x52381),x52382))
% 59.73/59.67 [5268]~P119(x52681)+~E(f77(x52681,x52682),f73(x52681))+P1(f335(f335(f243(x52681),f2(x52681)),x52682))
% 59.73/59.67 [5280]~P97(x52801)+E(f335(f94(x52801),f335(f97(a881),x52802)),f335(f97(x52801),x52802))+P1(f335(a193,f335(f97(a1),x52802)))
% 59.73/59.67 [5286]~P41(x52861,x52862)+P42(a879)+P1(f335(f56(f887(x52861,x52861)),x52862))
% 59.73/59.67 [5353]~P106(x53531)+E(f335(f58(x53531,f240(x53531)),x53532),f11(x53531,f240(x53531),x53532))+~P1(f335(f56(x53531),x53532))
% 59.73/59.67 [5354]~P106(x53541)+E(f335(f58(x53541,f241(x53541)),x53542),f12(x53541,f241(x53541),x53542))+~P1(f335(f56(x53541),x53542))
% 59.73/59.67 [5366]E(x53661,x53662)+P1(f335(f335(f243(a881),x53662),x53661))+P1(f335(f335(f243(a881),x53661),x53662))
% 59.73/59.67 [5367]E(x53671,x53672)+P1(f335(f335(f243(a881),x53672),x53671))+P1(f335(f335(f243(a881),x53671),x53672))
% 59.73/59.67 [5368]E(x53681,x53682)+P1(f335(f335(f243(a1),x53682),x53681))+P1(f335(f335(f243(a1),x53681),x53682))
% 59.73/59.67 [5423]~P97(x54231)+E(f335(f94(x54231),f335(f97(a881),x54232)),f2(x54231))+~P1(f335(a193,f335(f97(a1),x54232)))
% 59.73/59.67 [5426]~E(x54262,f335(a98,x54261))+E(x54261,f335(f94(a1),x54262))+~P1(f335(f335(f242(a1),f2(a1)),x54261))
% 59.73/59.67 [5427]~E(f335(a98,x54271),x54272)+E(x54271,f335(f94(a1),x54272))+~P1(f335(f335(f242(a1),f2(a1)),x54271))
% 59.73/59.67 [5428]~E(x54281,f335(a98,x54282))+E(f335(f94(a1),x54281),x54282)+~P1(f335(f335(f242(a1),f2(a1)),x54282))
% 59.73/59.67 [5438]E(x54381,f335(a98,x54382))+~E(x54382,f335(f94(a1),x54381))+~P1(f335(f335(f242(a1),f2(a1)),x54382))
% 59.73/59.67 [5439]E(f335(a98,x54391),x54392)+~E(x54391,f335(f94(a1),x54392))+~P1(f335(f335(f242(a1),f2(a1)),x54391))
% 59.73/59.67 [5478]~P88(x54782)+E(x54781,f2(x54782))+P1(f335(f335(f243(x54782),f2(x54782)),f335(f70(x54782),x54781)))
% 59.73/59.67 [5544]~P119(x55441)+E(f77(x55441,x55442),f73(x55441))+~P1(f335(f335(f243(x55441),f2(x55441)),x55442))
% 59.73/59.67 [5545]~P119(x55451)+E(f77(x55451,x55452),f73(x55451))+~P1(f335(f335(f243(x55451),f2(x55451)),x55452))
% 59.73/59.67 [5549]~P97(x55491)+E(f335(f94(x55491),f335(f97(a881),x55492)),f2(x55491))+P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),x55492)))
% 59.73/59.67 [5556]~P88(x55561)+E(f335(f70(x55561),x55562),x55562)+~P1(f335(f335(f242(x55561),f2(x55561)),x55562))
% 59.73/59.67 [5557]~P88(x55571)+E(f335(f70(x55571),x55572),x55572)+~P1(f335(f335(f243(x55571),f2(x55571)),x55572))
% 59.73/59.67 [5566]E(x55661,f2(a881))+~E(f132(a881,f335(f304(a881,x55662),x55661)),f107(a881))+P1(f335(f335(f242(a881),x55661),x55662))
% 59.73/59.67 [5576]~P77(x55761)+E(f335(f335(f6(x55761,x55761),f5(x55761)),f335(f166(x55761),x55762)),f335(f159(x55761),x55762))+~P1(f335(f130(x55761),x55762))
% 59.73/59.67 [5579]~P137(x55791)+E(f335(f94(x55791),f335(a98,x55792)),f335(f96(x55791),x55792))+~P1(f335(f335(f242(a1),f2(a1)),x55792))
% 59.73/59.67 [5581]~E(x55811,x55812)+P1(f335(f335(f243(a881),x55811),f335(a106,x55812)))+P1(f335(f335(f243(a881),x55811),x55812))
% 59.73/59.67 [5604]E(x56041,x56042)+P1(f335(f335(f243(a881),x56041),x56042))+~P1(f335(f335(f242(a881),x56041),x56042))
% 59.73/59.67 [5605]E(x56051,x56052)+P1(f335(f335(f243(a881),x56051),x56052))+~P1(f335(f335(f242(a881),x56051),x56052))
% 59.73/59.67 [5606]E(x56061,x56062)+P1(f335(f335(f243(a881),x56061),x56062))+~P1(f335(f335(f242(a881),x56061),x56062))
% 59.73/59.67 [5607]E(x56071,x56072)+P1(f335(f335(f243(a1),x56071),x56072))+~P1(f335(f335(f242(a1),x56071),x56072))
% 59.73/59.67 [5610]E(x56101,f73(a1))+~E(f335(f335(f76(a1),x56102),x56101),f73(a1))+~P1(f335(f335(f243(a1),f2(a1)),x56102))
% 59.73/59.67 [5611]E(x56111,f73(a1))+~E(f335(f335(f76(a1),x56111),x56112),f73(a1))+~P1(f335(f335(f243(a1),f2(a1)),x56111))
% 59.73/59.67 [5648]~P38(x56482)+P1(f335(f335(f242(a1),f2(a1)),x56481))+~P1(f335(f335(f337(a1),x56481),x56482))
% 59.73/59.67 [5649]~P38(x56492)+P1(f335(f335(f242(a1),f2(a1)),x56491))+~P1(f335(f335(f337(a1),x56491),x56492))
% 59.73/59.67 [5668]~P55(x56681,x56682)+P36(x56681,x56682)+~P1(f335(f56(f887(x56681,x56681)),x56682))
% 59.73/59.67 [5669]~P55(x56691,x56692)+P36(x56691,x56692)+~P1(f335(f56(f887(x56691,x56691)),x56692))
% 59.73/59.67 [5670]~P36(x56701,x56702)+P55(x56701,x56702)+~P1(f335(f56(f887(x56701,x56701)),x56702))
% 59.73/59.67 [5671]~P55(x56711,x56712)+P41(x56711,x56712)+~P1(f335(f56(f887(x56711,x56711)),x56712))
% 59.73/59.67 [5715]E(x57151,f188(f888(x57152,a879)))+~P1(f335(f56(x57152),x57151))+P1(f335(f335(f243(a881),f2(a881)),f335(f29(x57152),x57151)))
% 59.73/59.67 [5742]~P1(f335(x57421,x57422))+P1(f335(x57421,f2(a881)))+P1(f335(f335(f243(a881),f364(x57422,x57421)),x57422))
% 59.73/59.67 [5765]E(x57651,f2(a881))+~E(f335(f159(a881),x57652),f2(a881))+~P1(f335(f335(f337(a881),x57651),f335(f166(a881),x57652)))
% 59.73/59.67 [5800]~E(x58001,x58002)+P1(f335(f335(f243(a881),x58001),f335(a106,x58002)))+~P1(f335(f335(f242(a881),x58002),x58001))
% 59.73/59.67 [5831]E(x58311,x58312)+~P1(f335(f335(f242(a881),x58312),x58311))+~P1(f335(f335(f242(a881),x58311),x58312))
% 59.73/59.67 [5832]E(x58321,x58322)+~P1(f335(f335(f242(a1),x58322),x58321))+~P1(f335(f335(f242(a1),x58321),x58322))
% 59.73/59.67 [5834]E(f335(f29(x58341),x58342),f2(a881))+~P1(f335(f56(x58341),x58342))+P1(f335(f335(f337(x58341),f577(x58342,x58341)),x58342))
% 59.73/59.67 [5843]E(f44(x58431,x58432),f40(x58431,x58432))+P1(f335(f335(f242(a1),f2(a1)),x58431))+~P1(f335(f335(f243(a1),f2(a1)),x58432))
% 59.73/59.67 [5868]~P1(f335(x58681,f381(x58681)))+P1(f335(x58681,f335(a98,x58682)))+~P1(f335(f335(f242(a1),f2(a1)),x58682))
% 59.73/59.67 [5870]P1(f335(f335(f242(a881),x58701),f851(x58702)))+~P1(f335(f56(a881),x58702))+~P1(f335(f335(f337(a881),x58701),x58702))
% 59.73/59.67 [5871]P1(f335(f335(f243(a881),x58711),f855(x58712)))+~P1(f335(f56(a881),x58712))+~P1(f335(f335(f337(a881),x58711),x58712))
% 59.73/59.67 [5898]E(x58981,x58982)+~P1(f335(f335(f243(a881),x58981),f335(a106,x58982)))+P1(f335(f335(f243(a881),x58981),x58982))
% 59.73/59.67 [5899]E(x58991,x58992)+~P1(f335(f335(f243(a881),x58991),f335(a106,x58992)))+P1(f335(f335(f243(a881),x58991),x58992))
% 59.73/59.67 [5900]E(x59001,x59002)+~P1(f335(f335(f243(a881),x59001),f335(a106,x59002)))+P1(f335(f335(f243(a881),x59001),x59002))
% 59.73/59.67 [5901]E(x59011,x59012)+~P1(f335(f335(f243(a881),x59011),f335(a106,x59012)))+P1(f335(f335(f243(a881),x59011),x59012))
% 59.73/59.67 [5932]E(x59321,f335(a106,x59322))+~P1(f335(f335(f242(a881),x59321),f335(a106,x59322)))+P1(f335(f335(f242(a881),x59321),x59322))
% 59.73/59.67 [5933]E(x59331,f335(a106,x59332))+~P1(f335(f335(f242(a881),x59331),f335(a106,x59332)))+P1(f335(f335(f242(a881),x59331),x59332))
% 59.73/59.67 [5947]P1(f335(x59471,f394(x59471)))+~P1(f335(x59471,f335(a98,x59472)))+~P1(f335(f335(f242(a1),f2(a1)),x59472))
% 59.73/59.67 [5961]~P1(f335(x59611,x59612))+~P1(f335(f335(f242(a1),f2(a1)),x59612))+P1(f335(x59611,f335(f94(a1),f400(x59611))))
% 59.73/59.67 [5975]~P88(x59752)+~E(x59751,f2(x59752))+~P1(f335(f335(f243(x59752),f2(x59752)),f335(f70(x59752),x59751)))
% 59.73/59.67 [5999]~P55(x59991,x59992)+P36(x59991,f335(f289(x59991,x59991),x59992))+~P1(f335(f56(f887(x59991,x59991)),x59992))
% 59.73/59.67 [6009]~P97(x60091)+E(f335(f94(x60091),f335(f97(a881),x60092)),f335(f97(x60091),x60092))+~P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),x60092)))
% 59.73/59.67 [6012]E(f335(a106,x60121),x60122)+~P1(f335(f335(f243(a881),x60121),x60122))+P1(f335(f335(f243(a881),f335(a106,x60121)),x60122))
% 59.73/59.67 [6028]E(f335(f335(f30(a1),x60281),x60282),f2(a1))+~P1(f335(f335(f242(a1),x60281),f2(a1)))+~P1(f335(f335(f243(a1),x60282),x60281))
% 59.73/59.67 [6029]E(f335(f335(f30(a1),x60291),x60292),f2(a1))+~P1(f335(f335(f242(a1),x60291),f2(a1)))+~P1(f335(f335(f243(a1),x60292),x60291))
% 59.73/59.67 [6040]E(f39(a1,x60401,x60402),x60401)+~P1(f335(f335(f242(a1),x60401),f2(a1)))+~P1(f335(f335(f243(a1),x60402),x60401))
% 59.73/59.67 [6053]E(f41(x60531,x60532),f40(x60531,x60532))+~P1(f335(f335(f242(a1),f2(a1)),x60531))+~P1(f335(f335(f242(a1),f2(a1)),x60532))
% 59.73/59.67 [6059]E(f335(f335(f30(a881),x60591),x60592),f2(a881))+~P1(f335(f335(f243(a881),f2(a881)),x60592))+~P1(f335(f335(f243(a881),x60591),x60592))
% 59.73/59.67 [6060]E(f335(f335(f30(a1),x60601),x60602),f2(a1))+~P1(f335(f335(f242(a1),f2(a1)),x60601))+~P1(f335(f335(f243(a1),x60601),x60602))
% 59.73/59.67 [6061]E(f335(f335(f30(a1),x60611),x60612),f2(a1))+~P1(f335(f335(f242(a1),f2(a1)),x60611))+~P1(f335(f335(f243(a1),x60611),x60612))
% 59.73/59.67 [6070]E(f39(a881,f335(f97(a881),x60701),f335(f97(a881),x60702)),f335(f97(a881),x60701))+P1(f335(a193,f335(f97(a1),x60701)))+~P1(f335(a193,f335(f97(a1),x60702)))
% 59.73/59.67 [6072]E(f39(a1,x60721,x60722),x60721)+~P1(f335(f335(f242(a1),f2(a1)),x60721))+~P1(f335(f335(f243(a1),x60721),x60722))
% 59.73/59.67 [6073]E(x60731,x60732)+~P1(f335(f335(f243(a881),x60731),f335(a106,x60732)))+~P1(f335(f335(f242(a881),x60732),x60731))
% 59.73/59.67 [6086]E(f335(f94(a1),x60861),f335(f97(a1),x60862))+~E(x60861,f335(a98,f335(f97(a1),x60862)))+~P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),x60862)))
% 59.73/59.67 [6090]~P79(x60901)+~P1(f335(f335(f242(x60901),x60902),f2(x60901)))+P1(f335(f335(f242(x60901),x60902),f335(f74(x60901),x60902)))
% 59.73/59.67 [6091]~P119(x60911)+~P1(f335(f335(f243(x60911),x60912),f2(x60911)))+P1(f335(f335(f243(x60911),x60912),f335(f74(x60911),x60912)))
% 59.73/59.67 [6100]~P5(x61001)+E(f335(f335(f59(x61001,x61001,f95(x61001)),f252(x61001)),x61002),f32(x61001,x61002))+~P1(f335(f56(x61001),x61002))
% 59.73/59.67 [6101]~P5(x61011)+E(f335(f335(f59(x61011,x61011,f104(x61011)),f188(x61011)),x61012),f31(x61011,x61012))+~P1(f335(f56(x61011),x61012))
% 59.73/59.67 [6115]~P119(x61151)+~P1(f335(f335(f242(a1),f2(a1)),x61152))+P1(f335(f335(f242(x61151),f2(x61151)),f335(f96(x61151),x61152)))
% 59.73/59.67 [6116]~P119(x61161)+~P1(f335(f335(f243(a1),f2(a1)),x61162))+P1(f335(f335(f243(x61161),f2(x61161)),f335(f96(x61161),x61162)))
% 59.73/59.67 [6117]~P122(x61171)+~P1(f335(f335(f243(a881),f2(a881)),x61172))+P1(f335(f335(f243(x61171),f2(x61171)),f335(f94(x61171),x61172)))
% 59.73/59.67 [6120]~P6(x61202)+~P6(x61201)+E(f335(f313(a881,a1,f94(a1)),f305(a881,f335(a98,x61201),f335(a98,x61202))),f305(a1,x61201,x61202))
% 59.73/59.67 [6126]P1(f335(x61261,x61262))+~P1(f335(f335(f242(a1),f2(a1)),x61262))+~P1(f335(x61261,f335(f94(a1),f401(x61261))))
% 59.73/59.67 [6153]E(f335(f335(f75(a881),f335(f97(a881),x61531)),f335(f97(a881),x61532)),f335(f97(a881),x61531))+P1(f335(f335(f243(a1),x61531),a78))+~P1(f335(f335(f243(a1),x61532),a78))
% 59.73/59.67 [6157]~P119(x61571)+P1(f335(f335(f243(x61571),f2(x61571)),f77(x61571,x61572)))+~P1(f335(f335(f243(x61571),f2(x61571)),x61572))
% 59.73/59.67 [6168]~P80(x61681)+~P1(f335(f335(f242(x61681),x61682),f2(x61681)))+P1(f335(f335(f242(x61681),f2(x61681)),f335(f74(x61681),x61682)))
% 59.73/59.67 [6169]~P80(x61691)+~P1(f335(f335(f243(x61691),x61692),f2(x61691)))+P1(f335(f335(f243(x61691),f2(x61691)),f335(f74(x61691),x61692)))
% 59.73/59.67 [6172]E(x61721,f252(f888(x61722,a879)))+~E(f335(f29(x61722),x61721),f335(f29(x61722),f252(f888(x61722,a879))))+~P1(f335(f56(x61722),f252(f888(x61722,a879))))
% 59.73/59.67 [6207]~P79(x62071)+P1(f335(f335(f242(x62071),x62072),f2(x62071)))+~P1(f335(f335(f242(x62071),x62072),f335(f74(x62071),x62072)))
% 59.73/59.67 [6208]~P119(x62081)+P1(f335(f335(f243(x62081),x62082),f2(x62081)))+~P1(f335(f335(f243(x62081),x62082),f335(f74(x62081),x62082)))
% 59.73/59.67 [6215]E(f41(x62151,x62152),f335(f335(f264(a1,a1),f2(a1)),x62151))+~P1(f335(f335(f243(a1),f2(a1)),x62152))+~P1(f335(f335(f243(a1),x62151),x62152))
% 59.73/59.67 [6218]~P97(x62181)+P1(f335(f335(f337(x62181),f335(f97(x62181),x62182)),f186(x62181)))+~P1(f335(f335(f242(a1),a78),x62182))
% 59.73/59.67 [6249]E(x62491,f2(a881))+~P1(f335(f335(f243(a881),x62491),f335(a106,x62492)))+P1(f335(f335(f243(a881),f354(x62492,x62491)),x62492))
% 59.73/59.67 [6271]~P119(x62711)+~P1(f335(f335(f243(x62711),f2(x62711)),f77(x62711,x62712)))+P1(f335(f335(f243(x62711),f2(x62711)),x62712))
% 59.73/59.67 [6273]~E(f335(f97(a881),x62732),f335(f97(a881),x62731))+P1(f335(f335(f242(a1),f335(f97(a1),x62731)),f2(a1)))+~P1(f335(a193,f335(f97(a1),x62732)))
% 59.73/59.67 [6302]E(f335(f263(a1,a1),f44(x63021,x63022)),f335(f335(f30(a1),x63021),x63022))+~P1(f335(f335(f243(a1),x63021),f2(a1)))+~P1(f335(f335(f243(a1),f2(a1)),x63022))
% 59.73/59.67 [6336]E(f335(f267(a1,a1),f44(x63361,x63362)),f39(a1,x63361,x63362))+~P1(f335(f335(f243(a1),x63361),f2(a1)))+~P1(f335(f335(f243(a1),f2(a1)),x63362))
% 59.73/59.67 [6339]~P119(x63392)+~P1(f335(f335(f242(x63392),f2(x63392)),f335(f96(x63392),x63391)))+P1(f335(f335(f242(a1),f2(a1)),x63391))
% 59.73/59.67 [6340]~P122(x63402)+~P1(f335(f335(f243(x63402),f2(x63402)),f335(f94(x63402),x63401)))+P1(f335(f335(f243(a881),f2(a881)),x63401))
% 59.73/59.67 [6341]~P119(x63412)+~P1(f335(f335(f243(x63412),f2(x63412)),f335(f96(x63412),x63411)))+P1(f335(f335(f243(a1),f2(a1)),x63411))
% 59.73/59.67 [6344]E(f335(f263(a1,a1),f41(x63441,x63442)),f335(f335(f30(a1),x63441),x63442))+~P1(f335(f335(f242(a1),f2(a1)),x63442))+~P1(f335(f335(f243(a1),f2(a1)),x63441))
% 59.73/59.67 [6360]E(f335(f267(a1,a1),f41(x63601,x63602)),f39(a1,x63601,x63602))+~P1(f335(f335(f242(a1),f2(a1)),x63602))+~P1(f335(f335(f243(a1),f2(a1)),x63601))
% 59.73/59.67 [6375]~P80(x63751)+P1(f335(f335(f242(x63751),x63752),f2(x63751)))+~P1(f335(f335(f242(x63751),f2(x63751)),f335(f74(x63751),x63752)))
% 59.73/59.67 [6376]~P80(x63761)+P1(f335(f335(f243(x63761),x63762),f2(x63761)))+~P1(f335(f335(f243(x63761),f2(x63761)),f335(f74(x63761),x63762)))
% 59.73/59.67 [6399]~P5(x63991)+~P37(x63991,x63991,x63992)+P1(f335(f335(f242(x63991),f90(x63991,x63992)),f335(x63992,f90(x63991,x63992))))
% 59.73/59.67 [6400]~P5(x64001)+~P37(x64001,x64001,x64002)+P1(f335(f335(f242(x64001),f89(x64001,x64002)),f335(x64002,f89(x64001,x64002))))
% 59.73/59.67 [6405]P1(f335(f43(x64051,x64052),f44(x64051,x64052)))+~P1(f335(f335(f243(a1),x64051),f2(a1)))+~P1(f335(f335(f243(a1),f2(a1)),x64052))
% 59.73/59.67 [6429]P1(f335(f43(x64291,x64292),f41(x64291,x64292)))+~P1(f335(f335(f242(a1),f2(a1)),x64291))+~P1(f335(f335(f243(a1),f2(a1)),x64292))
% 59.73/59.67 [6473]~P80(x64731)+P1(f335(f335(f242(x64731),f335(f74(x64731),x64732)),f2(x64731)))+~P1(f335(f335(f242(x64731),f2(x64731)),x64732))
% 59.73/59.67 [6474]~P80(x64741)+P1(f335(f335(f243(x64741),f335(f74(x64741),x64742)),f2(x64741)))+~P1(f335(f335(f243(x64741),f2(x64741)),x64742))
% 59.73/59.67 [6490]E(f335(f335(f23(a881),f335(a98,x64901)),f335(a98,x64902)),f335(a98,f194(x64901,x64902)))+~P1(f335(f335(f242(a1),f2(a1)),x64902))+~P1(f335(f335(f242(a1),f2(a1)),x64901))
% 59.73/59.67 [6507]P1(f335(f335(f242(a1),f2(a1)),f194(x65071,x65072)))+~P1(f335(f335(f242(a1),f2(a1)),x65072))+~P1(f335(f335(f242(a1),f2(a1)),x65071))
% 59.73/59.67 [6545]~P1(f335(x65451,x65452))+P1(f335(x65451,f2(a881)))+P1(f335(x65451,f335(f335(f75(a881),f364(x65452,x65451)),f73(a881))))
% 59.73/59.67 [6632]E(f335(f97(a881),x66321),f335(f97(a881),x66322))+~P1(f335(f335(f242(a1),f335(f97(a1),x66322)),f2(a1)))+~P1(f335(a193,f335(f97(a1),x66321)))
% 59.73/59.67 [6642]~E(x66421,f2(a881))+~E(f690(x66422,x66421),f2(a881))+E(f335(f135(a881,a881,f75(a881),x66421),x66422),f2(a881))
% 59.73/59.67 [6667]~P1(f335(f56(x66671),f629(x66672,x66671)))+~P1(f335(f56(f888(x66671,a879)),x66672))+P1(f335(f56(x66671),f31(f888(x66671,a879),x66672)))
% 59.73/59.67 [6673]E(x66731,x66732)+P1(f335(f335(f243(a1),x66731),x66732))+~P1(f335(f335(f243(a1),x66731),f335(f335(f75(a1),x66732),f73(a1))))
% 59.73/59.67 [6674]P1(f335(f335(f242(a881),f335(a98,x66741)),f335(a98,x66742)))+~P1(f335(f335(f242(a1),f2(a1)),x66742))+~P1(f335(f335(f242(a1),x66741),x66742))
% 59.73/59.67 [6675]P1(f335(f335(f242(a881),f335(a98,x66751)),f335(a98,x66752)))+~P1(f335(f335(f243(a1),f2(a1)),x66751))+~P1(f335(f335(f242(a1),x66751),x66752))
% 59.73/59.67 [6676]P1(f335(f335(f243(a881),f335(a98,x66761)),f335(a98,x66762)))+~P1(f335(f335(f243(a1),f2(a1)),x66762))+~P1(f335(f335(f243(a1),x66761),x66762))
% 59.73/59.67 [6677]P1(f335(f335(f243(a881),f335(a98,x66771)),f335(a98,x66772)))+~P1(f335(f335(f242(a1),f2(a1)),x66771))+~P1(f335(f335(f243(a1),x66771),x66772))
% 59.73/59.67 [6678]P1(f335(f335(f243(a881),f335(a98,x66781)),f335(a98,x66782)))+~P1(f335(f335(f243(a1),f2(a1)),x66782))+~P1(f335(f335(f243(a1),x66781),x66782))
% 59.73/59.67 [6689]E(f39(a881,f335(a98,x66891),f335(a98,x66892)),f335(a98,f39(a1,x66891,x66892)))+~P1(f335(f335(f242(a1),f2(a1)),x66892))+~P1(f335(f335(f242(a1),f2(a1)),x66891))
% 59.73/59.67 [6690]E(f39(a881,f335(a98,x66901),f335(a98,x66902)),f335(a98,f39(a1,x66901,x66902)))+~P1(f335(f335(f242(a1),f2(a1)),x66902))+~P1(f335(f335(f242(a1),f2(a1)),x66901))
% 59.73/59.67 [6714]~P80(x67141)+~P1(f335(f335(f242(x67141),f335(f74(x67141),x67142)),f2(x67141)))+P1(f335(f335(f242(x67141),f2(x67141)),x67142))
% 59.73/59.67 [6715]~P80(x67151)+~P1(f335(f335(f243(x67151),f335(f74(x67151),x67152)),f2(x67151)))+P1(f335(f335(f243(x67151),f2(x67151)),x67152))
% 59.73/59.67 [6731]~P1(f335(f335(f243(a1),a78),x67312))+~P1(f335(f335(f243(a1),x67311),x67312))+P1(f335(f335(f243(a881),f335(f97(a881),x67311)),f335(f97(a881),x67312)))
% 59.73/59.67 [6822]~P1(f335(f335(f242(a1),f2(a1)),x68221))+P1(f335(f335(f243(a881),f335(a98,x68221)),x68222))+~P1(f335(f335(f243(a1),x68221),f335(f94(a1),x68222)))
% 59.73/59.67 [6839]E(x68391,f2(a1))+E(f39(a1,x68392,x68391),f2(a1))+E(f335(f335(f23(a1),f335(f74(a1),f335(f335(f30(a1),x68392),x68391))),f73(a1)),f335(f335(f30(a1),x68392),f335(f74(a1),x68391)))
% 59.73/59.67 [6855]~P1(f335(f335(f242(a1),f2(a1)),x68551))+~P1(f335(f335(f243(a881),f335(a98,x68551)),x68552))+P1(f335(f335(f243(a1),x68551),f335(f94(a1),x68552)))
% 59.73/59.67 [6892]~P1(f335(f335(f242(a881),f335(a98,x68921)),f335(a98,x68922)))+~P1(f335(f335(f242(a1),f2(a1)),x68922))+P1(f335(f335(f242(a1),x68921),x68922))
% 59.73/59.67 [6893]~P1(f335(f335(f242(a881),f335(a98,x68931)),f335(a98,x68932)))+~P1(f335(f335(f243(a1),f2(a1)),x68931))+P1(f335(f335(f242(a1),x68931),x68932))
% 59.73/59.67 [6894]~P1(f335(f335(f243(a881),f335(a98,x68941)),f335(a98,x68942)))+~P1(f335(f335(f242(a1),f2(a1)),x68941))+P1(f335(f335(f243(a1),x68941),x68942))
% 59.73/59.67 [6895]~P1(f335(f335(f243(a881),f335(a98,x68951)),f335(a98,x68952)))+~P1(f335(f335(f243(a1),f2(a1)),x68952))+P1(f335(f335(f243(a1),x68951),x68952))
% 59.73/59.67 [6921]P1(f335(f335(f242(a1),x69211),x69212))+~P1(f335(f335(f242(a881),f335(f97(a881),x69211)),f335(f97(a881),x69212)))+P1(f335(f335(f242(a1),x69211),a78))
% 59.73/59.67 [6945]P1(f335(f335(f242(a1),f2(a1)),f39(a1,x69451,x69452)))+~P1(f335(f335(f242(a1),f2(a1)),x69452))+~P1(f335(f335(f242(a1),f2(a1)),x69451))
% 59.73/59.67 [7042]P1(f335(f335(f243(a1),a78),x70421))+~P1(f335(f335(f243(a1),x70422),x70421))+~P1(f335(f335(f243(a881),f335(f97(a881),x70422)),f335(f97(a881),x70421)))
% 59.73/59.67 [7094]E(f335(f335(f264(a1,a1),f335(f335(f30(a1),x70941),x70942)),f39(a1,x70941,x70942)),f44(x70941,x70942))+~P1(f335(f335(f243(a1),x70941),f2(a1)))+~P1(f335(f335(f243(a1),f2(a1)),x70942))
% 59.73/59.67 [7115]E(f335(f335(f264(a1,a1),f335(f335(f30(a1),x71151),x71152)),f39(a1,x71151,x71152)),f41(x71151,x71152))+~P1(f335(f335(f242(a1),f2(a1)),x71152))+~P1(f335(f335(f242(a1),f2(a1)),x71151))
% 59.73/59.67 [7166]~P98(x71662)+E(x71661,f107(x71662))+E(f335(f135(x71662,x71662,f76(x71662),f335(f134(x71662),x71661)),f335(f165(x71662),x71661)),f335(f58(x71662,f76(x71662)),f335(f166(x71662),x71661)))
% 59.73/59.67 [7280]~E(x72801,f2(a881))+E(f335(f135(a881,a881,f75(a881),x72801),x72802),f2(a881))+P1(f335(f335(f337(a881),f690(x72802,x72801)),f335(f166(a881),x72802)))
% 59.73/59.67 [7331]~P1(f335(f335(f242(a1),x73311),f2(a1)))+P1(f335(f335(f242(a1),f335(f335(f30(a1),x73311),x73312)),f2(a1)))+~P1(f335(f335(f243(a1),f2(a1)),x73312))
% 59.73/59.67 [7332]~P1(f335(f335(f243(a1),x73322),f2(a1)))+P1(f335(f335(f242(a1),f335(f335(f30(a1),x73321),x73322)),f2(a1)))+~P1(f335(f335(f242(a1),f2(a1)),x73321))
% 59.73/59.67 [7333]~P1(f335(f335(f243(a1),x73332),f2(a1)))+P1(f335(f335(f243(a1),f335(f335(f30(a1),x73331),x73332)),f2(a1)))+~P1(f335(f335(f243(a1),f2(a1)),x73331))
% 59.73/59.67 [7334]~P1(f335(f335(f243(a1),x73341),f2(a1)))+P1(f335(f335(f243(a1),f335(f335(f30(a1),x73341),x73342)),f2(a1)))+~P1(f335(f335(f243(a1),f2(a1)),x73342))
% 59.73/59.67 [7335]~P1(f335(f335(f243(a1),x73351),f2(a1)))+P1(f335(f335(f243(a1),f335(f335(f30(a1),x73351),x73352)),f2(a1)))+~P1(f335(f335(f243(a1),f2(a1)),x73352))
% 59.73/59.67 [7341]P1(f335(f335(f337(f888(x73411,a879)),f629(x73412,x73411)),x73412))+~P1(f335(f56(f888(x73411,a879)),x73412))+P1(f335(f56(x73411),f31(f888(x73411,a879),x73412)))
% 59.73/59.67 [7435]P26(x74351,x74351,x74352,f252(f888(x74351,a879)))+~E(f335(f313(x74351,x74351,x74352),f252(f888(x74351,a879))),f252(f888(x74351,a879)))+~P1(f335(f56(x74351),f252(f888(x74351,a879))))
% 59.73/59.67 [7560]~P26(x75601,x75601,x75602,f252(f888(x75601,a879)))+E(f335(f313(x75601,x75601,x75602),f252(f888(x75601,a879))),f252(f888(x75601,a879)))+~P1(f335(f56(x75601),f252(f888(x75601,a879))))
% 59.73/59.67 [7584]E(f41(f335(f97(a1),x75841),f335(f97(a1),x75842)),f335(f335(f264(a1,a1),f2(a1)),f335(f97(a1),x75841)))+~P1(f335(f335(f243(a1),f2(a1)),f335(f97(a1),x75842)))+~P1(f335(f335(f243(a1),f335(f97(a1),x75841)),f335(f97(a1),x75842)))
% 59.73/59.67 [7699]E(f335(f335(f30(a1),x76991),x76992),f335(f97(a1),a91))+~P1(f335(f335(f242(a1),f335(f335(f75(a1),x76991),x76992)),f2(a1)))+~P1(f335(f335(f243(a1),f2(a1)),x76991))
% 59.73/59.67 [7759]~P1(f335(f335(f243(a1),x77592),f2(a1)))+~P1(f335(f335(f243(a1),f335(f335(f30(a1),x77591),x77592)),f2(a1)))+P1(f335(f335(f243(a1),f2(a1)),x77591))
% 59.73/59.67 [7764]E(f335(f335(f75(a1),x77641),x77642),f39(a1,x77641,x77642))+~P1(f335(f335(f242(a1),f335(f335(f75(a1),x77641),x77642)),f2(a1)))+~P1(f335(f335(f243(a1),f2(a1)),x77641))
% 59.73/59.67 [7767]P1(f335(f335(f243(a1),x77671),f2(a1)))+~P1(f335(f335(f243(a1),f335(f335(f30(a1),x77671),x77672)),f2(a1)))+~P1(f335(f335(f243(a1),f2(a1)),x77672))
% 59.73/59.67 [8157]~P4(x81571)+~P1(f335(f53(f885(x81571)),x81572))+P1(f335(f53(x81571),f335(f335(f8(f885(x81571),a879,x81571),x81572),f235(x81571))))
% 59.73/59.67 [8468]~P106(x84681)+P15(x84681,x84682)+~P1(f335(f335(f242(x84681),f335(f335(f158(x84681),x84682),f723(x84682,x84681))),f335(f335(f158(x84681),x84682),f724(x84682,x84681))))
% 59.73/59.67 [8469]~P106(x84691)+P15(x84691,x84692)+~P1(f335(f335(f242(x84691),f335(f335(f158(x84691),x84692),f738(x84692,x84691))),f335(f335(f158(x84691),x84692),f740(x84692,x84691))))
% 59.73/59.67 [8618]~P4(x86181)+P1(f335(f52(f885(x86181)),x86182))+~P1(f335(f52(x86181),f335(f335(f8(f885(x86181),a879,x86181),x86182),f235(x86181))))
% 59.73/59.67 [9795]~P4(x97951)+~P4(x97952)+E(f335(f335(f147(f882(x97951),f888(x97952,x97951)),f335(f335(f8(f888(x97952,f885(x97951)),f888(x97952,x97951),f882(x97951)),f68(f885(x97951),x97951,x97952,f239(x97951))),f335(f335(f8(f882(f887(x97952,x97951)),f888(x97952,f885(x97951)),f882(x97951)),f179(x97952,x97951)),f335(f175(x97952,x97951),f50(x97952))))),f49(x97951,f335(f189(f882(x97952)),f50(x97952)),f50(x97951))),f50(f888(x97952,x97951)))
% 59.73/59.67 [5708]E(x57081,f2(a1))+~E(f39(a1,x57082,x57081),f2(a1))+E(f335(f335(f30(a1),x57082),f335(f74(a1),x57081)),f335(f74(a1),f335(f335(f30(a1),x57082),x57081)))
% 59.73/59.67 [5726]~P38(x57262)+~P38(x57261)+P38(f335(f335(f104(f888(a1,a879)),x57261),x57262))
% 59.73/59.67 [5727]~P38(x57272)+~P38(x57271)+P38(f335(f335(f95(f888(a1,a879)),x57271),x57272))
% 59.73/59.67 [5745]~P97(x57451)+~P66(x57451)+E(f335(f74(x57451),f335(f335(f292(x57451),f73(x57451)),x57452)),f335(f335(f292(x57451),f335(f97(x57451),a91)),x57452))
% 59.73/59.67 [5860]E(x58601,f2(a1))+~E(f39(a1,x58602,x58601),f2(a1))+E(f335(f335(f30(a1),f335(f74(a1),x58602)),x58601),f335(f74(a1),f335(f335(f30(a1),x58602),x58601)))
% 59.73/59.67 [5993]~P106(x59931)+P15(x59931,x59932)+P1(f335(f335(f243(a881),f724(x59932,x59931)),f335(f189(f882(x59931)),x59932)))
% 59.73/59.67 [5994]~P106(x59941)+P15(x59941,x59942)+P1(f335(f335(f243(a881),f740(x59942,x59941)),f335(f189(f882(x59941)),x59942)))
% 59.73/59.67 [6147]~P97(x61471)+~E(f335(f97(x61471),x61472),f2(x61471))+P28(x61471,f335(f97(x61471),f335(f335(f75(a1),x61472),f335(f74(a1),a78))))
% 59.73/59.67 [6148]~P97(x61481)+~E(f335(f97(x61481),x61482),f2(x61481))+P28(x61481,f335(f97(x61481),f335(f335(f75(a1),a78),f335(f74(a1),x61482))))
% 59.73/59.67 [6150]E(f335(a45,f41(f335(f74(a1),x61501),f335(f74(a1),x61502))),f40(x61501,x61502))+P1(f335(f335(f242(a1),f2(a1)),x61501))+P1(f335(f335(f243(a1),f2(a1)),x61502))
% 59.73/59.67 [6279]~E(x62792,f2(a881))+~E(x62791,f2(a881))+P1(f335(f335(f242(a1),f335(f94(a1),x62791)),f335(f74(a1),f335(f94(a1),x62792))))
% 59.73/59.67 [6306]E(f335(f335(f75(a881),f335(f97(a881),x63061)),f335(f97(a881),x63062)),f335(f97(a881),f335(f335(f75(a1),x63061),x63062)))+P1(f335(f335(f243(a1),x63061),a78))+P1(f335(f335(f243(a1),x63062),a78))
% 59.73/59.67 [6439]~P79(x64391)+~P1(f335(f335(f242(x64391),f2(x64391)),x64392))+P1(f335(f335(f242(x64391),f335(f74(x64391),x64392)),x64392))
% 59.73/59.67 [6440]~P79(x64401)+~P1(f335(f335(f243(x64401),f2(x64401)),x64402))+P1(f335(f335(f243(x64401),f335(f74(x64401),x64402)),x64402))
% 59.73/59.67 [6618]E(f335(f335(f23(a881),f335(a98,x66181)),f335(a98,x66182)),f335(a98,f335(f335(f23(a1),x66181),x66182)))+~P1(f335(f335(f242(a1),f2(a1)),x66182))+~P1(f335(f335(f242(a1),x66182),x66181))
% 59.73/59.67 [6650]E(f335(a98,f39(a1,f335(f97(a1),x66501),f335(f97(a1),x66502))),f39(a881,f335(f97(a881),x66501),f335(f97(a881),x66502)))+P1(f335(a193,f335(f97(a1),x66501)))+P1(f335(a193,f335(f97(a1),x66502)))
% 59.73/59.67 [6668]~P79(x66681)+P1(f335(f335(f242(x66681),f2(x66681)),x66682))+~P1(f335(f335(f242(x66681),f335(f74(x66681),x66682)),x66682))
% 59.73/59.67 [6669]~P79(x66691)+P1(f335(f335(f243(x66691),f2(x66691)),x66692))+~P1(f335(f335(f243(x66691),f335(f74(x66691),x66692)),x66692))
% 59.73/59.67 [6682]~P79(x66821)+~P1(f335(f335(f242(x66821),f2(x66821)),x66822))+P1(f335(f335(f242(x66821),f2(x66821)),f335(f335(f75(x66821),x66822),x66822)))
% 59.73/59.67 [6684]~P79(x66841)+~P1(f335(f335(f243(x66841),f2(x66841)),x66842))+P1(f335(f335(f243(x66841),f2(x66841)),f335(f335(f75(x66841),x66842),x66842)))
% 59.73/59.67 [6694]E(f335(f335(f75(a881),f335(a98,x66941)),f335(a98,x66942)),f335(a98,f335(f335(f75(a1),x66941),x66942)))+~P1(f335(f335(f242(a1),f2(a1)),x66942))+~P1(f335(f335(f242(a1),f2(a1)),x66941))
% 59.73/59.67 [6695]E(f335(f335(f76(a881),f335(a98,x66951)),f335(a98,x66952)),f335(a98,f335(f335(f76(a1),x66951),x66952)))+~P1(f335(f335(f242(a1),f2(a1)),x66952))+~P1(f335(f335(f242(a1),f2(a1)),x66951))
% 59.73/59.67 [6696]E(f335(f335(f75(a881),f335(a98,x66961)),f335(a98,x66962)),f335(a98,f335(f335(f75(a1),x66961),x66962)))+~P1(f335(f335(f242(a1),f2(a1)),x66962))+~P1(f335(f335(f242(a1),f2(a1)),x66961))
% 59.73/59.67 [6697]E(f335(f335(f30(a881),f335(a98,x66971)),f335(a98,x66972)),f335(a98,f335(f335(f30(a1),x66971),x66972)))+~P1(f335(f335(f242(a1),f2(a1)),x66972))+~P1(f335(f335(f242(a1),f2(a1)),x66971))
% 59.73/59.67 [6707]E(x67071,f2(a881))+P1(f335(f335(f243(a881),f2(a881)),x67072))+~P1(f335(f335(f243(a881),f2(a881)),f335(f335(f254(a881),x67072),x67071)))
% 59.73/59.67 [6740]~P97(x67401)+E(f335(f97(x67401),x67402),f2(x67401))+~P28(x67401,f335(f97(x67401),f335(f335(f75(a1),a78),f335(f74(a1),x67402))))
% 59.73/59.67 [6741]~P97(x67411)+E(f335(f97(x67411),x67412),f2(x67411))+~P28(x67411,f335(f97(x67411),f335(f335(f75(a1),x67412),f335(f74(a1),a78))))
% 59.73/59.67 [6800]~P1(f335(f56(x68001),x68002))+~P1(f335(f56(x68001),f252(f888(x68001,a879))))+P1(f335(f56(x68001),f335(f74(f888(x68001,a879)),x68002)))
% 59.73/59.67 [6823]~P1(f335(f335(f243(a1),f2(a1)),x68232))+~P1(f335(f335(f242(a1),x68232),x68231))+P1(f335(f335(f243(a1),f2(a1)),f335(f335(f30(a1),x68231),x68232)))
% 59.73/59.67 [6824]~P1(f335(f335(f242(a1),x68241),f2(a1)))+~P1(f335(f335(f243(a1),x68242),f2(a1)))+P1(f335(f335(f242(a1),f2(a1)),f335(f335(f30(a1),x68241),x68242)))
% 59.73/59.67 [6865]~P1(f335(f335(f242(a1),f2(a1)),x68652))+~P1(f335(f335(f242(a1),f2(a1)),x68651))+P1(f335(f335(f242(a1),f2(a1)),f335(f335(f76(a1),x68651),x68652)))
% 59.73/59.67 [6866]~P1(f335(f335(f242(a1),f2(a1)),x68662))+~P1(f335(f335(f242(a1),f2(a1)),x68661))+P1(f335(f335(f242(a1),f2(a1)),f335(f335(f75(a1),x68661),x68662)))
% 59.73/59.67 [6867]~P1(f335(f335(f242(a1),f2(a1)),x68672))+~P1(f335(f335(f242(a1),f2(a1)),x68671))+P1(f335(f335(f242(a1),f2(a1)),f335(f335(f30(a1),x68671),x68672)))
% 59.73/59.67 [6868]~P1(f335(f335(f242(a1),f2(a1)),x68681))+~P1(f335(f335(f243(a1),f2(a1)),x68682))+P1(f335(f335(f242(a1),f2(a1)),f335(f335(f30(a1),x68681),x68682)))
% 59.73/59.67 [6869]~P1(f335(f335(f243(a881),f2(a881)),x68692))+~P1(f335(f335(f243(a881),f2(a881)),x68691))+P1(f335(f335(f243(a881),f2(a881)),f335(f335(f76(a881),x68691),x68692)))
% 59.73/59.67 [6933]E(x69331,f2(a1))+E(f39(a1,x69332,x69331),f2(a1))+E(f335(f335(f23(a1),f335(f74(a1),f335(f335(f30(a1),x69332),x69331))),f73(a1)),f335(f335(f30(a1),f335(f74(a1),x69332)),x69331))
% 59.73/59.67 [6986]P1(f335(f335(f243(a881),f2(a881)),x69861))+P1(f335(f335(f243(a881),f2(a881)),x69862))+~P1(f335(f335(f243(a881),f2(a881)),f335(f335(f75(a881),x69862),x69861)))
% 59.73/59.67 [6990]~P79(x69901)+P1(f335(f335(f242(x69901),f2(x69901)),x69902))+~P1(f335(f335(f242(x69901),f2(x69901)),f335(f335(f75(x69901),x69902),x69902)))
% 59.73/59.67 [6991]~P79(x69911)+P1(f335(f335(f243(x69911),f2(x69911)),x69912))+~P1(f335(f335(f243(x69911),f2(x69911)),f335(f335(f75(x69911),x69912),x69912)))
% 59.73/59.67 [7043]~P1(f335(f56(x70431),x70432))+P1(f335(f56(x70431),f252(f888(x70431,a879))))+~P1(f335(f56(x70431),f335(f74(f888(x70431,a879)),x70432)))
% 59.73/59.67 [7107]P1(f335(f335(f242(a1),x71071),f2(a1)))+~P1(f335(f335(f243(a1),x71072),f2(a1)))+~P1(f335(f335(f242(a1),f2(a1)),f335(f335(f30(a1),x71071),x71072)))
% 59.73/59.67 [7113]~P1(f335(f335(f243(a1),f2(a1)),x71131))+P1(f335(f335(f242(a1),x71131),x71132))+~P1(f335(f335(f243(a1),f2(a1)),f335(f335(f30(a1),x71132),x71131)))
% 59.73/59.67 [7114]~P1(f335(f335(f242(a1),f2(a1)),x71142))+P1(f335(f335(f242(a1),x71141),x71142))+~P1(f335(f335(f243(a1),f2(a1)),f335(f335(f30(a1),x71142),x71141)))
% 59.73/59.67 [7143]P1(f335(f335(f242(a1),f2(a1)),x71431))+~P1(f335(f335(f243(a1),f2(a1)),x71432))+~P1(f335(f335(f242(a1),f2(a1)),f335(f335(f30(a1),x71431),x71432)))
% 59.73/59.67 [7144]P1(f335(f335(f243(a1),f2(a1)),x71441))+~P1(f335(f335(f242(a1),f2(a1)),x71442))+~P1(f335(f335(f243(a1),f2(a1)),f335(f335(f30(a1),x71442),x71441)))
% 59.73/59.67 [7245]E(f219(x72451,x72452),x72451)+~E(x72452,f2(a881))+~P1(f335(f323(f887(a881,a881),a222),f335(f335(f264(a881,a881),x72451),x72452)))
% 59.73/59.67 [7455]E(f172(x74551,x74552),f107(a1))+P1(f335(f335(f242(a1),x74551),x74552))+~P1(f335(f323(f887(a1,a1),a176),f335(f335(f264(a1,a1),x74551),x74552)))
% 59.73/59.67 [7477]E(f335(f335(f264(a1,a1),f335(f97(a1),a91)),f335(f335(f75(a1),x74771),x74772)),f44(x74771,x74772))+~P1(f335(f335(f243(a1),f2(a1)),x74772))+~P1(f335(f335(f242(a1),f2(a1)),f335(f335(f75(a1),x74771),x74772)))
% 59.73/59.67 [7508]E(x75081,f2(a881))+E(f219(x75081,f39(a881,x75082,x75081)),f219(x75082,x75081))+~P1(f335(f323(f887(a881,a881),a222),f335(f335(f264(a881,a881),x75082),x75081)))
% 59.73/59.67 [7563]E(f122(x75631,x75632),f109(a1))+~P1(f335(f335(f243(a1),x75631),x75632))+~P1(f335(f323(f887(a1,a1),a126),f335(f335(f264(a1,a1),x75631),x75632)))
% 59.73/59.67 [7592]~P1(f335(f56(x75922),f252(f888(x75922,a879))))+~P1(f335(f56(x75921),f252(f888(x75921,a879))))+P1(f335(f56(f887(x75921,x75922)),f252(f888(f887(x75921,x75922),a879))))
% 59.73/59.67 [7593]~P1(f335(f56(x75932),f252(f888(x75932,a879))))+~P1(f335(f56(x75931),f252(f888(x75931,a879))))+P1(f335(f56(f889(x75931,x75932)),f252(f888(f889(x75931,x75932),a879))))
% 59.73/59.67 [7663]~P1(f335(f335(f243(a881),f335(a106,f2(a881))),x76631))+~P1(f335(f335(f243(a881),f335(a106,f2(a881))),x76632))+P1(f335(f335(f243(a881),x76631),f335(f335(f76(a881),x76632),x76631)))
% 59.73/59.67 [7664]~P1(f335(f335(f243(a881),f335(a106,f2(a881))),x76641))+~P1(f335(f335(f243(a881),f335(a106,f2(a881))),x76642))+P1(f335(f335(f243(a881),x76641),f335(f335(f76(a881),x76641),x76642)))
% 59.73/59.67 [7698]E(f335(f29(x76981),f252(f888(x76981,a879))),f335(a106,f2(a881)))+P1(f335(f56(x76982),f252(f888(x76982,a879))))+~P1(f335(f56(f888(x76982,x76981)),f252(f888(f888(x76982,x76981),a879))))
% 59.73/59.67 [7752]E(f41(x77521,x77522),f335(f335(f264(a1,a1),f2(a1)),x77521))+~P1(f335(f335(f243(a1),x77521),x77522))+~P1(f335(f323(f887(a1,a1),a51),f335(f335(f264(a1,a1),x77521),x77522)))
% 59.73/59.67 [7756]E(f218(f335(f74(a1),x77561),f335(f74(a1),x77562)),f218(x77561,x77562))+~P1(f335(f335(f243(a1),x77562),f2(a1)))+~P1(f335(f323(f887(a1,a1),a224),f335(f335(f264(a1,a1),x77561),x77562)))
% 59.73/59.67 [7775]E(f41(x77751,x77752),f335(f335(f264(a1,a1),f2(a1)),x77751))+~P1(f335(f335(f242(a1),x77752),f2(a1)))+~P1(f335(f323(f887(a1,a1),a51),f335(f335(f264(a1,a1),x77751),x77752)))
% 59.73/59.67 [7827]~P1(f335(f335(f242(a881),f335(a106,f2(a881))),x78271))+~P1(f335(f335(f242(a881),f335(a106,f2(a881))),x78272))+P1(f335(f335(f242(a881),f335(a106,f2(a881))),f335(f335(f76(a881),x78271),x78272)))
% 59.73/59.67 [7828]~P1(f335(f335(f243(a881),f335(a106,f2(a881))),x78282))+~P1(f335(f335(f243(a881),f335(a106,f2(a881))),x78281))+P1(f335(f335(f243(a881),f335(a106,f2(a881))),f335(f335(f76(a881),x78281),x78282)))
% 59.73/59.67 [7995]E(f335(f335(f264(a1,a1),f335(f97(a1),a91)),f335(f335(f75(a1),x79951),x79952)),f44(x79951,x79952))+~P1(f335(f335(f242(a1),x79952),f2(a1)))+~P1(f335(f323(f887(a1,a1),a46),f335(f335(f264(a1,a1),x79951),x79952)))
% 59.73/59.67 [8018]E(f110(a1,f335(f123(a1),x80181),f122(x80182,f335(f335(f75(a1),x80181),f73(a1)))),f122(x80182,x80181))+P1(f335(f335(f243(a1),x80182),x80181))+~P1(f335(f323(f887(a1,a1),a126),f335(f335(f264(a1,a1),x80182),x80181)))
% 59.73/59.67 [8031]E(f335(f335(f144(a1),x80311),f172(f335(f335(f75(a1),x80311),f73(a1)),x80312)),f172(x80311,x80312))+~P1(f335(f335(f242(a1),x80311),x80312))+~P1(f335(f323(f887(a1,a1),a176),f335(f335(f264(a1,a1),x80311),x80312)))
% 59.73/59.67 [8171]~P107(x81711)+P37(a881,x81711,x81712)+~P1(f335(f335(f242(x81711),f335(x81712,f353(x81712,x81711))),f335(x81712,f335(a106,f353(x81712,x81711)))))
% 59.73/59.67 [8313]E(f335(f335(f264(a1,a1),f335(f97(a1),a91)),f335(f335(f75(a1),x83131),x83132)),f44(x83131,x83132))+~P1(f335(f335(f242(a1),f2(a1)),f335(f335(f75(a1),x83131),x83132)))+~P1(f335(f323(f887(a1,a1),a46),f335(f335(f264(a1,a1),x83131),x83132)))
% 59.73/59.67 [8513]E(x85131,f107(x85132))+~P1(f335(f130(x85132),x85131))+E(f171(x85132,f335(f335(f8(a879,a879,x85132),a330),f335(f335(f7(x85132,x85132,a879),a332),f137(x85132,x85131))),x85131),f108(x85132,x85131))
% 59.73/59.67 [8585]E(f335(f335(f264(a1,a1),f335(f97(a1),a91)),f335(f335(f75(a1),f335(f97(a1),x85851)),f335(f97(a1),x85852))),f44(f335(f97(a1),x85851),f335(f97(a1),x85852)))+~P1(f335(f335(f243(a1),f2(a1)),f335(f97(a1),x85852)))+~P1(f335(f335(f242(a1),f2(a1)),f335(f335(f75(a1),f335(f97(a1),x85851)),f335(f97(a1),x85852))))
% 59.73/59.67 [8608]~P38(x86082)+~P38(x86081)+E(f335(f313(a881,a1,f94(a1)),f335(f335(f104(f888(a881,a879)),f335(f313(a1,a881,a98),x86081)),f335(f313(a1,a881,a98),x86082))),f335(f335(f104(f888(a1,a879)),x86081),x86082))
% 59.73/59.67 [8609]~P38(x86092)+~P38(x86091)+E(f335(f313(a881,a1,f94(a1)),f335(f335(f95(f888(a881,a879)),f335(f313(a1,a881,a98),x86091)),f335(f313(a1,a881,a98),x86092))),f335(f335(f95(f888(a1,a879)),x86091),x86092))
% 59.73/59.67 [9263]~P97(x92631)+~E(f335(f97(x92631),x92632),f73(x92631))+P28(x92631,f335(f97(x92631),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f74(a1),x92632))))
% 59.73/59.67 [9501]~P97(x95011)+E(f335(f97(x95011),x95012),f73(x95011))+~P28(x95011,f335(f97(x95011),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f74(a1),x95012))))
% 59.73/59.67 [10238]E(x102381,f2(a1))+E(x102382,f2(a1))+E(f335(f269(a1,a1,a1,a1,f25(a1),f335(f76(a1),f77(a1,x102382))),f335(f335(f335(f88(f887(a1,a1)),f335(f335(a332,f77(a1,x102381)),f77(a1,x102382))),f47(x102381,x102382)),f335(f335(f268(a1,a1,f887(a1,a1)),f335(f335(f18(a1,f888(a1,f887(a1,a1)),f888(a1,f887(a1,a1))),f335(f335(f8(f888(a1,f888(f887(a1,a1),f887(a1,a1))),f888(f888(a1,f887(a1,a1)),f888(a1,f887(a1,a1))),a1),f18(a1,f887(a1,a1),f887(a1,a1))),f335(f335(f8(f887(a1,a1),f888(a1,f888(f887(a1,a1),f887(a1,a1))),a1),f335(f7(a1,f887(a1,a1),f888(f887(a1,a1),f887(a1,a1))),f335(f335(f8(a879,f888(f887(a1,a1),f888(f887(a1,a1),f887(a1,a1))),a1),f88(f887(a1,a1))),f335(f335(f7(a1,a1,a879),a332),f2(a1))))),f335(f335(f7(a1,a1,f887(a1,a1)),f335(f335(f8(a1,f888(a1,f887(a1,a1)),a1),f264(a1,a1)),f74(a1))),f2(a1))))),f335(f335(f7(a1,f888(a1,a1),f888(a1,f887(a1,a1))),f335(f335(f8(f888(a1,f887(a1,a1)),f888(f888(a1,a1),f888(a1,f887(a1,a1))),a1),f8(a1,f887(a1,a1),a1)),f335(f335(f8(a1,f888(a1,f887(a1,a1)),a1),f264(a1,a1)),f335(f335(f7(a1,a1,a1),f335(f335(f8(a1,f888(a1,a1),a1),f23(a1)),f74(a1))),f73(a1))))),f335(f23(a1),f335(f70(a1),x102382))))),f47(x102381,x102382)))),f40(x102381,x102382))
% 59.73/59.67 [10239]E(x102391,f2(a1))+E(x102392,f2(a1))+E(f335(f269(a1,a1,a1,a1,f25(a1),f335(f76(a1),f77(a1,x102392))),f335(f335(f335(f88(f887(a1,a1)),f335(f335(a334,f335(f335(a333,f335(f335(f243(a1),f2(a1)),x102392)),f335(f335(f242(a1),f2(a1)),x102391))),f335(f335(a333,f335(f335(f243(a1),x102392),f2(a1))),f335(f335(f243(a1),x102391),f2(a1))))),f47(x102391,x102392)),f335(f335(f268(a1,a1,f887(a1,a1)),f335(f335(f18(a1,f888(a1,f887(a1,a1)),f888(a1,f887(a1,a1))),f335(f335(f8(f888(a1,f888(f887(a1,a1),f887(a1,a1))),f888(f888(a1,f887(a1,a1)),f888(a1,f887(a1,a1))),a1),f18(a1,f887(a1,a1),f887(a1,a1))),f335(f335(f8(f887(a1,a1),f888(a1,f888(f887(a1,a1),f887(a1,a1))),a1),f335(f7(a1,f887(a1,a1),f888(f887(a1,a1),f887(a1,a1))),f335(f335(f8(a879,f888(f887(a1,a1),f888(f887(a1,a1),f887(a1,a1))),a1),f88(f887(a1,a1))),f335(f335(f7(a1,a1,a879),a332),f2(a1))))),f335(f335(f7(a1,a1,f887(a1,a1)),f335(f335(f8(a1,f888(a1,f887(a1,a1)),a1),f264(a1,a1)),f74(a1))),f2(a1))))),f335(f335(f7(a1,f888(a1,a1),f888(a1,f887(a1,a1))),f335(f335(f8(f888(a1,f887(a1,a1)),f888(f888(a1,a1),f888(a1,f887(a1,a1))),a1),f8(a1,f887(a1,a1),a1)),f335(f335(f8(a1,f888(a1,f887(a1,a1)),a1),f264(a1,a1)),f335(f335(f7(a1,a1,a1),f335(f335(f8(a1,f888(a1,a1),a1),f23(a1)),f74(a1))),f73(a1))))),f335(f23(a1),f335(f70(a1),x102392))))),f47(x102391,x102392)))),f40(x102391,x102392))
% 59.73/59.67 [5734]~P119(x57341)+~P97(x57341)+E(f335(f70(x57341),f335(f335(f254(x57341),f335(f97(x57341),a91)),x57342)),f73(x57341))
% 59.73/59.67 [6219]~P137(x62191)+~P1(f335(f335(f243(a1),x62192),f2(a1)))+E(f335(f74(x62191),f335(f94(x62191),f335(a98,f335(f74(a1),x62192)))),f335(f96(x62191),x62192))
% 59.73/59.67 [6422]P1(f335(f335(f242(a93),x64221),f73(a93)))+E(f335(f335(f75(a93),f73(a93)),f278(x64221,f335(f335(f30(a93),x64222),x64221))),f278(x64221,x64222))+P1(f335(f335(f243(a93),x64222),x64221))
% 59.73/59.67 [7031]~P94(x70311)+~P1(f335(f335(f337(x70311),x70312),f103(x70311)))+~E(f335(f335(f75(x70311),f335(f335(f75(x70311),f73(x70311)),x70312)),x70312),f2(x70311))
% 59.73/59.67 [7145]~P1(f335(f335(f242(a1),x71452),f2(a1)))+~P1(f335(f335(f243(a1),x71451),f2(a1)))+E(f335(f263(a1,a1),f335(a45,f41(f335(f74(a1),x71451),f335(f74(a1),x71452)))),f335(f335(f30(a1),x71451),x71452))
% 59.73/59.67 [7162]~P1(f335(f335(f242(a1),x71622),f2(a1)))+~P1(f335(f335(f243(a1),x71621),f2(a1)))+E(f335(f267(a1,a1),f335(a45,f41(f335(f74(a1),x71621),f335(f74(a1),x71622)))),f39(a1,x71621,x71622))
% 59.73/59.67 [7168]~P1(f335(f335(f243(a1),x71682),f2(a1)))+E(f335(f263(a1,a1),f335(a45,f44(f335(f74(a1),x71681),f335(f74(a1),x71682)))),f335(f335(f30(a1),x71681),x71682))+~P1(f335(f335(f243(a1),f2(a1)),x71681))
% 59.73/59.67 [7186]~P1(f335(f335(f243(a1),x71862),f2(a1)))+E(f335(f267(a1,a1),f335(a45,f44(f335(f74(a1),x71861),f335(f74(a1),x71862)))),f39(a1,x71861,x71862))+~P1(f335(f335(f243(a1),f2(a1)),x71861))
% 59.73/59.67 [7239]E(f335(f335(f30(a1),f335(f335(f254(a1),x72391),x72392)),x72391),f335(f335(f254(a1),x72391),f335(f335(f23(a881),x72392),f335(a106,f2(a881)))))+~P1(f335(f335(f243(a881),f2(a881)),x72392))+~P1(f335(f335(f243(a1),f2(a1)),x72391))
% 59.73/59.67 [7338]~P1(f335(f335(f243(a881),f2(a881)),x73381))+~P1(f335(f335(f243(a881),f2(a881)),x73382))+P1(f335(f335(f243(a881),f335(f335(f23(a881),x73381),x73382)),x73381))
% 59.73/59.67 [7339]~P1(f335(f335(f243(a881),f2(a881)),x73391))+~P1(f335(f335(f243(a881),f73(a881)),x73392))+P1(f335(f335(f243(a881),f335(f335(f30(a881),x73391),x73392)),x73391))
% 59.73/59.67 [7340]~P1(f335(f335(f243(a1),f2(a1)),x73401))+~P1(f335(f335(f243(a1),f73(a1)),x73402))+P1(f335(f335(f243(a1),f335(f335(f30(a1),x73401),x73402)),x73401))
% 59.73/59.67 [7484]E(x74841,f2(a881))+~E(x74842,f2(a1))+~P1(f335(f335(f243(a1),f2(a1)),f335(f335(f254(a1),f335(f70(a1),x74842)),x74841)))
% 59.73/59.67 [7856]~P1(f335(x78561,x78562))+P1(f335(x78561,f2(a881)))+E(f335(a106,f246(a881,f335(f335(f8(a881,a879,a881),x78561),a106))),f246(a881,x78561))
% 59.73/59.67 [7906]~E(x79062,f107(f882(x79061)))+E(f335(f189(f882(f882(x79061))),f173(x79061,x79062)),f2(a881))+~P15(a881,f335(f162(a881),f335(f335(f147(f882(x79061),a881),f189(f882(x79061))),x79062)))
% 59.73/59.67 [8156]P1(f335(x81561,x81562))+~P1(f335(x81561,f335(a101,f547(x81561,x81562))))+~P1(f335(f335(f337(f888(f887(a881,a881),a879)),x81562),a92))
% 59.73/59.67 [8175]E(x81751,f107(f882(x81752)))+E(f335(f189(f882(x81752)),f335(f335(f158(f882(x81752)),x81751),f2(a881))),f335(f189(f882(f882(x81752))),f173(x81752,x81751)))+~P15(a881,f335(f162(a881),f335(f335(f147(f882(x81752),a881),f189(f882(x81752))),x81751)))
% 59.73/59.67 [8879]~P1(f335(f56(x88791),f335(f249(x88791),x88792)))+~P1(f335(f56(x88791),f252(f888(x88791,a879))))+P1(f335(f56(x88791),f335(f249(x88791),f335(f335(f8(a879,a879,x88791),a330),x88792))))
% 59.73/59.67 [8942]E(f335(f335(f264(a881,a881),f335(a106,f335(f335(f30(a881),f335(f335(f23(a881),x89421),x89422)),x89422))),f39(a881,f335(f335(f23(a881),x89421),x89422),x89422)),f80(f887(a881,a881),f42(x89421,x89422)))+~P1(f335(f335(f243(a881),f2(a881)),x89422))+~P1(f335(f335(f242(a881),x89422),x89421))
% 59.73/59.67 [9232]~P1(f335(f56(x92321),f335(f249(x92321),x92322)))+P1(f335(f56(x92321),f252(f888(x92321,a879))))+~P1(f335(f56(x92321),f335(f249(x92321),f335(f335(f8(a879,a879,x92321),a330),x92322))))
% 59.73/59.67 [9961]P27(x99611,x99612)+~P36(x99611,f335(f263(f888(f887(x99611,x99611),a879),f888(f887(x99611,x99611),a879)),x99612))+~P1(f335(f335(f242(f888(f887(x99611,x99611),a879)),f335(f335(f291(x99611,x99611,x99611),f335(f263(f888(f887(x99611,x99611),a879),f888(f887(x99611,x99611),a879)),x99612)),f335(f267(f888(f887(x99611,x99611),a879),f888(f887(x99611,x99611),a879)),x99612))),f335(f263(f888(f887(x99611,x99611),a879),f888(f887(x99611,x99611),a879)),x99612)))
% 59.73/59.67 [9995]E(f335(f37(f335(f97(a1),x99951)),f41(f335(f97(a1),x99952),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(f97(a1),x99951)))),f41(f335(f97(a1),x99952),f335(f97(a1),x99951)))+~P1(f335(f335(f243(a1),f2(a1)),f335(f97(a1),x99951)))+P1(f335(f335(f243(a1),f335(f97(a1),x99952)),f335(f97(a1),x99951)))
% 59.73/59.67 [10001]E(f335(f37(f335(f97(a1),x100011)),f44(f335(f97(a1),x100012),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(f97(a1),x100011)))),f44(f335(f97(a1),x100012),f335(f97(a1),x100011)))+~P1(f335(f335(f243(a1),f2(a1)),f335(f97(a1),x100011)))+P1(f335(f335(f242(a1),f2(a1)),f335(f335(f75(a1),f335(f97(a1),x100012)),f335(f97(a1),x100011))))
% 59.73/59.67 [7265]~P1(f335(f335(f243(a881),f2(a881)),x72652))+P1(f335(f335(f243(a881),x72651),x72652))+E(f335(a106,f335(f335(f30(a881),f335(f335(f23(a881),x72651),x72652)),x72652)),f335(f335(f30(a881),x72651),x72652))
% 59.73/59.67 [7266]~P1(f335(f335(f243(a881),f2(a881)),x72662))+P1(f335(f335(f243(a881),x72661),x72662))+E(f335(a106,f335(f335(f30(a881),f335(f335(f23(a881),x72661),x72662)),x72662)),f335(f335(f30(a881),x72661),x72662))
% 59.73/59.67 [7406]~P1(f335(f335(f243(a881),f2(a881)),x74062))+~P1(f335(f335(f242(a881),x74062),x74061))+E(f335(a106,f335(f335(f30(a881),f335(f335(f23(a881),x74061),x74062)),x74062)),f335(f335(f30(a881),x74061),x74062))
% 59.73/59.67 [8385]~P97(x83851)+~P94(x83851)+~P28(x83851,f335(f97(x83851),f335(f335(f23(a1),f335(f335(f75(a1),x83852),x83852)),a91)))
% 59.73/59.67 [9136]E(x91361,f2(a881))+E(f335(f335(f268(a881,a881,f887(a881,a881)),f335(f335(f8(a881,f888(a881,f887(a881,a881)),a881),f264(a881,a881)),a106)),f80(f887(a881,a881),f42(f335(f335(f23(a881),x91362),x91361),x91361))),f80(f887(a881,a881),f42(x91362,x91361)))+P1(f335(f335(f243(a881),x91362),x91361))
% 59.73/59.67 [9564]P1(f335(x95642,f656(x95642,x95641)))+P1(f335(x95641,f656(x95642,x95641)))+E(f335(f249(a1),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f242(a1),f2(a1)))),x95641)),f335(f249(a1),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f242(a1),f2(a1)))),x95642)))
% 59.73/59.67 [9568]~P1(f335(x95682,f656(x95682,x95681)))+~P1(f335(x95681,f656(x95682,x95681)))+E(f335(f249(a1),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f242(a1),f2(a1)))),x95681)),f335(f249(a1),f335(f335(f18(a1,a879,a879),f335(f335(f8(a879,f888(a879,a879),a1),a333),f335(f242(a1),f2(a1)))),x95682)))
% 59.73/59.67 [7620]~P97(x76201)+~P67(x76201)+E(f335(f335(f292(x76201),x76202),f335(f97(x76201),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),x76202)
% 59.73/59.67 [7621]~P97(x76211)+~P67(x76211)+E(f335(f335(f292(x76211),x76212),f335(f97(x76211),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))),x76212)
% 59.73/59.67 [9262]~P97(x92621)+~E(f335(f97(x92621),x92622),f73(x92621))+P28(x92621,f335(f97(x92621),f335(f335(f75(a1),x92622),f335(f74(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))
% 59.73/59.67 [9441]~P136(x94411)+~E(x94412,f73(x94411))+E(f335(f335(f254(x94411),x94412),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f73(x94411))
% 59.73/59.67 [9442]~P136(x94421)+~E(x94422,f2(x94421))+E(f335(f335(f254(x94421),x94422),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f2(x94421))
% 59.73/59.67 [9457]~P136(x94571)+~E(x94572,f335(f74(x94571),f73(x94571)))+E(f335(f335(f254(x94571),x94572),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f73(x94571))
% 59.73/59.67 [9477]~P82(x94771)+~P95(x94771)+E(f335(f335(f254(x94771),f335(f97(x94771),x94772)),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(f335(f76(x94771),f335(f97(x94771),x94772)),f335(f97(x94771),x94772)))
% 59.73/59.67 [9502]~P97(x95021)+E(f335(f97(x95021),x95022),f73(x95021))+~P28(x95021,f335(f97(x95021),f335(f335(f75(a1),x95022),f335(f74(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))
% 59.73/59.67 [9618]~P136(x96182)+E(x96181,f2(x96182))+~E(f335(f335(f254(x96182),x96181),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f2(x96182))
% 59.73/59.67 [9898]~P119(x98982)+E(x98981,f2(x98982))+P1(f335(f335(f243(x98982),f2(x98982)),f335(f335(f254(x98982),x98981),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))))
% 59.73/59.67 [9960]~P119(x99602)+~E(x99601,f2(x99602))+~P1(f335(f335(f243(x99602),f2(x99602)),f335(f335(f254(x99602),x99601),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))))
% 59.73/59.67 [9986]P1(f335(f335(f242(a1),x99861),f2(a1)))+P1(f335(f335(f243(a1),x99862),x99861))+E(f335(f37(x99861),f41(x99862,f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x99861))),f41(x99862,x99861))
% 59.73/59.67 [9987]~P1(f335(f335(f243(a1),f2(a1)),x99871))+P1(f335(f335(f243(a1),x99872),x99871))+E(f335(f37(x99871),f41(x99872,f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x99871))),f41(x99872,x99871))
% 59.73/59.67 [9988]P1(f335(f335(f242(a1),x99881),f2(a1)))+P1(f335(f335(f242(a1),f2(a1)),f335(f335(f75(a1),x99882),x99881)))+E(f335(f37(x99881),f44(x99882,f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x99881))),f44(x99882,x99881))
% 59.73/59.67 [9989]~P1(f335(f335(f243(a1),f2(a1)),x99891))+P1(f335(f335(f242(a1),f2(a1)),f335(f335(f75(a1),x99892),x99891)))+E(f335(f37(x99891),f44(x99892,f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x99891))),f44(x99892,x99891))
% 59.73/59.67 [9990]~P143(x99901)+~P1(f335(f335(f242(a1),f2(a1)),x99902))+E(f335(f94(x99901),f335(a98,f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x99902))),f335(f335(f75(x99901),f335(f94(x99901),f335(a98,x99902))),f335(f94(x99901),f335(a98,x99902))))
% 59.73/59.67 [5074]~P145(x50741,x50743,x50742)+~E(x50743,f2(a1))+P1(f335(x50741,x50742))
% 59.73/59.67 [5200]~P106(x52001)+~P15(x52001,x52003)+P15(x52001,f164(x52001,x52002,x52003))
% 59.73/59.67 [5201]~P106(x52011)+~P15(x52011,x52013)+P15(x52011,f171(x52011,x52012,x52013))
% 59.73/59.67 [4778]~P72(x47782)+~E(x47783,f335(f74(x47782),x47781))+E(x47781,f335(f74(x47782),x47783))
% 59.73/59.67 [4779]~P72(x47792)+~E(x47793,f335(f74(x47792),x47791))+E(x47791,f335(f74(x47792),x47793))
% 59.73/59.67 [4780]~P72(x47801)+~E(f335(f74(x47801),x47803),x47802)+E(f335(f74(x47801),x47802),x47803)
% 59.73/59.67 [4781]~P72(x47811)+~E(f335(f74(x47811),x47813),x47812)+E(f335(f74(x47811),x47812),x47813)
% 59.73/59.67 [4856]~P72(x48563)+E(x48561,x48562)+~E(f335(f74(x48563),x48561),f335(f74(x48563),x48562))
% 59.73/59.67 [4857]~P84(x48573)+E(x48571,x48572)+~E(f335(f74(x48573),x48571),f335(f74(x48573),x48572))
% 59.73/59.67 [4858]~P94(x48583)+E(x48581,x48582)+~E(f335(f96(x48583),x48581),f335(f96(x48583),x48582))
% 59.73/59.67 [4859]~P103(x48593)+E(x48591,x48592)+~E(f335(f94(x48593),x48591),f335(f94(x48593),x48592))
% 59.73/59.67 [4860]~P106(x48603)+E(x48601,x48602)+~E(f335(f250(x48603),x48601),f335(f250(x48603),x48602))
% 59.73/59.67 [4861]~P106(x48613)+E(x48611,x48612)+~E(f335(f303(x48613),x48611),f335(f303(x48613),x48612))
% 59.73/59.67 [4862]~P106(x48623)+E(x48621,x48622)+~E(f335(f306(x48623),x48621),f335(f306(x48623),x48622))
% 59.73/59.67 [4863]~P106(x48633)+E(x48631,x48632)+~E(f335(f251(x48633),x48631),f335(f251(x48633),x48632))
% 59.73/59.67 [4961]~P4(x49611)+~P1(f335(x49612,x49613))+P1(f335(f52(x49611),x49612))
% 59.73/59.67 [4962]~P4(x49621)+~P1(f335(x49622,x49623))+P1(f335(f52(x49621),x49622))
% 59.73/59.67 [4995]~P4(x49953)+P1(f335(x49951,x49952))+~P1(f335(f53(x49953),x49951))
% 59.73/59.67 [4996]~P4(x49963)+P1(f335(x49961,x49962))+~P1(f335(f53(x49963),x49961))
% 59.73/59.67 [5093]~P146(x50931,x50932,x50933)+~E(x50932,f2(a1))+P1(f335(x50931,f2(a1)))
% 59.73/59.67 [5127]~P109(x51272)+~P1(f335(x51271,x51273))+P1(f335(x51271,f246(x51272,x51271)))
% 59.73/59.67 [5128]~P109(x51282)+~P1(f335(x51281,x51283))+P1(f335(x51281,f246(x51282,x51281)))
% 59.73/59.67 [5135]~E(x51351,f2(a881))+E(f342(x51351,x51352,x51353),f188(f888(x51353,a879)))+~E(f335(f29(x51353),x51352),f335(a106,x51351))
% 59.73/59.67 [5285]~E(x52852,f2(a881))+E(f335(f263(a881,a881),x52851),f2(a881))+~P1(f335(f42(x52853,x52852),x52851))
% 59.73/59.67 [5324]P1(f335(x53241,x53242))+~E(x53243,f335(f94(a1),x53242))+~P1(f335(x53241,f335(a98,x53243)))
% 59.73/59.67 [5797]~E(x57973,f2(a881))+~P1(f335(x57971,x57972))+P1(f335(x57971,f39(a881,x57972,x57973)))
% 59.73/59.67 [5852]~P109(x58521)+~P1(f335(x58522,x58523))+~P1(f335(f335(f243(x58521),x58523),f246(x58521,x58522)))
% 59.73/59.67 [5962]~P4(x59623)+~P11(x59623,x59621,x59622)+P1(f335(x59621,f675(x59622,x59621,x59623)))
% 59.73/59.67 [6024]~P104(x60242)+~P104(x60241)+E(f124(x60241,x60242,f125(x60241,x60243),f125(x60242,x60243)),f125(f887(x60241,x60242),x60243))
% 59.73/59.67 [6200]~E(x62003,f2(a881))+P1(f335(x62001,x62002))+~P1(f335(x62001,f39(a881,x62002,x62003)))
% 59.73/59.67 [6212]~P5(x62121)+~P1(f335(f335(f242(x62121),x62122),f335(x62123,x62122)))+P1(f335(f335(f242(x62121),x62122),f90(x62121,x62123)))
% 59.73/59.67 [6351]~P4(x63511)+P12(x63511,x63512,x63513)+~P1(f335(x63512,f683(x63513,x63512,x63511)))
% 59.73/59.67 [6891]E(x68911,f2(a881))+~P1(f335(x68912,f382(x68911,x68913,x68912)))+P1(f335(x68912,f39(a881,x68913,x68911)))
% 59.73/59.67 [6996]~P5(x69961)+~P1(f335(f335(f242(x69961),x69962),f631(x69963,x69962,x69961)))+P1(f335(f335(f242(x69961),x69962),f32(x69961,x69963)))
% 59.73/59.67 [6998]~P1(f335(x69981,x69982))+~P1(f335(x69981,f382(x69983,x69982,x69981)))+P1(f335(x69981,f39(a881,x69982,x69983)))
% 59.73/59.67 [7100]E(x71001,f107(x71002))+E(f335(f335(f144(x71002),f710(x71003,x71001,x71002)),f718(x71003,x71001,x71002)),x71001)+~P1(f335(f335(f337(f882(x71002)),x71001),f154(x71002,x71003)))
% 59.73/59.67 [7132]~P137(x71321)+~P1(f335(f335(f337(x71321),x71322),f103(x71321)))+P1(f335(f335(f337(x71321),f335(f335(f254(x71321),x71322),x71323)),f103(x71321)))
% 59.73/59.67 [7454]P36(x74541,x74542)+~P1(f335(f335(f337(x74541),x74543),f628(x74542,x74541)))+P1(f335(f335(f337(x74541),f655(x74542,x74541,x74543)),f628(x74542,x74541)))
% 59.73/59.67 [7726]E(x77261,f107(x77262))+~P1(f335(f335(f337(f882(x77262)),x77261),f154(x77262,x77263)))+P1(f335(f335(f337(f882(x77262)),f718(x77263,x77261,x77262)),f154(x77262,x77263)))
% 59.73/59.67 [7779]E(x77791,f2(a881))+E(f335(f335(f75(a881),f335(f335(f76(a881),x77791),f383(x77791,x77792,x77793))),f382(x77791,x77792,x77793)),x77792)+P1(f335(x77793,f39(a881,x77792,x77791)))
% 59.73/59.67 [7822]~P1(f335(x78223,x78222))+E(f335(f335(f75(a881),f335(f335(f76(a881),x78221),f383(x78221,x78222,x78223))),f382(x78221,x78222,x78223)),x78222)+P1(f335(x78223,f39(a881,x78222,x78221)))
% 59.73/59.67 [7965]P1(f335(f335(f243(a1),x79651),f375(x79652,x79653,x79651)))+P1(f335(f335(x79653,f335(f335(f30(a1),x79652),x79651)),f39(a1,x79652,x79651)))+~P1(f335(f335(f243(a1),x79651),f2(a1)))
% 59.73/59.67 [8236]P1(f335(f335(x82362,f335(f335(f30(a1),x82361),x82363)),f39(a1,x82361,x82363)))+~P1(f335(f335(f243(a1),x82363),f2(a1)))+P1(f335(f335(f242(a1),f375(x82361,x82362,x82363)),f2(a1)))
% 59.73/59.67 [8421]E(f335(f335(f75(a1),f335(f335(f76(a1),x84211),f376(x84212,x84213,x84211))),f375(x84212,x84213,x84211)),x84212)+P1(f335(f335(x84213,f335(f335(f30(a1),x84212),x84211)),f39(a1,x84212,x84211)))+~P1(f335(f335(f243(a1),x84211),f2(a1)))
% 59.73/59.67 [8654]~P1(f335(f335(x86541,f376(x86542,x86541,x86543)),f375(x86542,x86541,x86543)))+P1(f335(f335(x86541,f335(f335(f30(a1),x86542),x86543)),f39(a1,x86542,x86543)))+~P1(f335(f335(f243(a1),x86543),f2(a1)))
% 59.73/59.67 [8889]~P106(x88891)+~P15(x88891,x88893)+P15(x88891,f142(x88891,x88891,f5(x88891),x88892,x88893))
% 59.73/59.67 [9392]~P123(x93922)+E(x93921,f2(x93922))+~P1(f335(f335(f242(x93922),f335(f335(f75(x93922),f335(f335(f76(x93922),x93923),x93923)),f335(f335(f76(x93922),x93921),x93921))),f2(x93922)))
% 59.73/59.67 [9393]~P123(x93932)+E(x93931,f2(x93932))+~P1(f335(f335(f242(x93932),f335(f335(f75(x93932),f335(f335(f76(x93932),x93931),x93931)),f335(f335(f76(x93932),x93933),x93933))),f2(x93932)))
% 59.73/59.67 [10176]~P119(x101761)+~P1(f335(f335(f243(x101761),x101762),f2(x101761)))+P1(f335(f335(f243(x101761),f335(f335(f254(x101761),x101762),f335(a106,f335(f335(f76(a881),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x101763)))),f2(x101761)))
% 59.73/59.67 [10184]~P119(x101842)+E(x101841,f2(x101842))+~P1(f335(f335(f242(x101842),f335(f335(f75(x101842),f335(f335(f254(x101842),x101843),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f335(f335(f254(x101842),x101841),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))),f2(x101842)))
% 59.73/59.67 [10185]~P119(x101852)+E(x101851,f2(x101852))+~P1(f335(f335(f242(x101852),f335(f335(f75(x101852),f335(f335(f254(x101852),x101851),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f335(f335(f254(x101852),x101853),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))),f2(x101852)))
% 59.73/59.67 [4813]~E(x48132,x48133)+~P64(x48131)+E(f335(f335(f23(x48131),x48132),x48133),f2(x48131))
% 59.73/59.67 [4814]~E(x48142,x48143)+~P72(x48141)+E(f335(f335(f23(x48141),x48142),x48143),f2(x48141))
% 59.73/59.67 [4827]~P138(x48271)+~E(x48273,f2(x48271))+E(f335(f335(f75(x48271),x48272),x48273),x48272)
% 59.73/59.67 [4842]~P140(x48421)+~E(x48423,f2(x48421))+E(f335(f335(f76(x48421),x48422),x48423),f2(x48421))
% 59.73/59.67 [4843]~P140(x48431)+~E(x48432,f2(x48431))+E(f335(f335(f76(x48431),x48432),x48433),f2(x48431))
% 59.73/59.67 [4864]~E(x48643,f107(x48641))+~E(x48642,f107(x48641))+E(f335(f335(f127(x48641),x48642),x48643),f107(x48641))
% 59.73/59.67 [4865]~E(x48653,f107(x48651))+~E(x48652,f107(x48651))+E(f335(f335(f127(x48651),x48652),x48653),f107(x48651))
% 59.73/59.67 [4952]~P138(x49522)+E(x49521,f2(x49522))+~E(f335(f335(f75(x49522),x49523),x49521),x49523)
% 59.73/59.67 [4953]~P72(x49531)+~E(x49532,f335(f74(x49531),x49533))+E(f335(f335(f75(x49531),x49532),x49533),f2(x49531))
% 59.73/59.67 [4960]E(x49601,f107(x49602))+E(x49603,f2(a881))+~E(f335(f335(f169(x49602),x49603),x49601),f107(x49602))
% 59.73/59.67 [4966]~P64(x49663)+E(x49661,x49662)+~E(f335(f335(f23(x49663),x49661),x49662),f2(x49663))
% 59.73/59.67 [4967]~P72(x49673)+E(x49671,x49672)+~E(f335(f335(f23(x49673),x49671),x49672),f2(x49673))
% 59.73/59.67 [4977]~P136(x49772)+E(x49771,f2(x49772))+~E(f335(f335(f254(x49772),x49771),x49773),f2(x49772))
% 59.73/59.67 [4978]~P62(x49782)+E(x49781,f188(x49782))+~E(f335(f335(f104(x49782),x49783),x49781),f188(x49782))
% 59.73/59.67 [4979]~P62(x49792)+E(x49791,f188(x49792))+~E(f335(f335(f104(x49792),x49791),x49793),f188(x49792))
% 59.73/59.67 [4980]~P101(x49802)+E(x49801,f252(x49802))+~E(f335(f335(f95(x49802),x49803),x49801),f252(x49802))
% 59.73/59.67 [4981]~P101(x49812)+E(x49811,f252(x49812))+~E(f335(f335(f95(x49812),x49811),x49813),f252(x49812))
% 59.73/59.67 [5047]~P72(x50472)+E(x50471,f335(f74(x50472),x50473))+~E(f335(f335(f75(x50472),x50471),x50473),f2(x50472))
% 59.73/59.67 [5048]~P72(x50481)+E(f335(f74(x50481),x50482),x50483)+~E(f335(f335(f75(x50481),x50482),x50483),f2(x50481))
% 59.73/59.67 [5049]~E(x50492,x50493)+~P107(x50491)+P1(f335(f335(f242(x50491),x50492),x50493))
% 59.73/59.67 [5050]~E(x50502,x50503)+~P2(x50501)+P1(f335(f335(f242(x50501),x50502),x50503))
% 59.73/59.67 [5051]~E(x50512,x50513)+~P107(x50511)+P1(f335(f335(f242(x50511),x50512),x50513))
% 59.73/59.67 [5052]~E(x50522,x50523)+~P107(x50521)+P1(f335(f335(f242(x50521),x50522),x50523))
% 59.73/59.67 [5053]~E(x50532,x50533)+~P96(x50531)+P1(f335(f335(f86(x50531),x50532),x50533))
% 59.73/59.67 [5150]~P111(x51501)+~E(x51502,f335(f74(x51501),x51503))+E(f335(f335(f76(x51501),x51502),x51502),f335(f335(f76(x51501),x51503),x51503))
% 59.73/59.67 [5158]~P106(x51581)+~P15(x51581,x51583)+P15(x51581,f335(f335(f169(x51581),x51582),x51583))
% 59.73/59.67 [5159]~P106(x51591)+~P15(x51591,x51593)+P15(x51591,f335(f335(f131(x51591),x51592),x51593))
% 59.73/59.67 [5197]E(x51971,x51972)+E(x51973,f2(a881))+~E(f335(f335(f76(a881),x51973),x51971),f335(f335(f76(a881),x51973),x51972))
% 59.73/59.67 [5198]E(x51981,x51982)+E(x51983,f2(a881))+~E(f335(f335(f76(a881),x51983),x51981),f335(f335(f76(a881),x51983),x51982))
% 59.73/59.67 [5199]E(x51991,x51992)+E(x51993,f2(a881))+~E(f335(f335(f76(a881),x51991),x51993),f335(f335(f76(a881),x51992),x51993))
% 59.73/59.67 [5276]~E(x52762,x52763)+~P107(x52761)+E(f305(x52761,x52762,x52763),f335(f335(f312(x52761),x52762),f188(f888(x52761,a879))))
% 59.73/59.67 [5311]E(x53111,x53112)+~P96(x53113)+~P1(f335(f335(f86(x53113),x53111),x53112))
% 59.73/59.67 [5317]~E(x53171,x53172)+~P106(x53173)+~P1(f335(f335(f243(x53173),x53171),x53172))
% 59.73/59.67 [5318]~E(x53181,x53182)+~P106(x53183)+~P1(f335(f335(f243(x53183),x53181),x53182))
% 59.73/59.67 [5319]~E(x53191,x53192)+~P107(x53193)+~P1(f335(f335(f243(x53193),x53191),x53192))
% 59.73/59.67 [5320]~E(x53201,x53202)+~P107(x53203)+~P1(f335(f335(f243(x53203),x53201),x53202))
% 59.73/59.67 [5321]~E(x53211,x53212)+~P107(x53213)+~P1(f335(f335(f243(x53213),x53211),x53212))
% 59.73/59.67 [5322]~E(x53221,x53222)+~P106(x53223)+~P1(f335(f335(f243(x53223),x53221),x53222))
% 59.73/59.67 [5323]~E(x53231,x53232)+~P107(x53233)+~P1(f335(f335(f243(x53233),x53231),x53232))
% 59.73/59.67 [5333]~P107(x53331)+E(f335(f304(x53331,x53332),x53333),f188(f888(x53331,a879)))+P1(f335(f335(f243(x53331),x53332),x53333))
% 59.73/59.67 [5334]~P107(x53341)+E(f335(f304(x53341,x53342),x53343),f188(f888(x53341,a879)))+P1(f335(f335(f243(x53341),x53342),x53343))
% 59.73/59.67 [5381]~P107(x53811)+E(f307(x53811,x53812,x53813),f188(f888(x53811,a879)))+P1(f335(f335(f243(x53811),x53812),x53813))
% 59.73/59.67 [5382]~P107(x53821)+E(f305(x53821,x53822,x53823),f188(f888(x53821,a879)))+P1(f335(f335(f242(x53821),x53822),x53823))
% 59.73/59.67 [5383]~P107(x53831)+E(f188(f888(x53831,a879)),f307(x53831,x53832,x53833))+P1(f335(f335(f243(x53831),x53832),x53833))
% 59.73/59.67 [5384]~P107(x53841)+E(f188(f888(x53841,a879)),f305(x53841,x53842,x53843))+P1(f335(f335(f242(x53841),x53842),x53843))
% 59.73/59.67 [5392]~P60(x53921)+~E(f335(f335(f104(x53921),x53922),x53923),x53923)+P1(f335(f335(f242(x53921),x53922),x53923))
% 59.73/59.67 [5393]~P102(x53931)+~E(f335(f335(f95(x53931),x53932),x53933),x53932)+P1(f335(f335(f242(x53931),x53932),x53933))
% 59.73/59.67 [5394]~P106(x53941)+~E(f335(f335(f240(x53941),x53942),x53943),x53942)+P1(f335(f335(f242(x53941),x53942),x53943))
% 59.73/59.67 [5395]~P106(x53951)+~E(f335(f335(f241(x53951),x53952),x53953),x53953)+P1(f335(f335(f242(x53951),x53952),x53953))
% 59.73/59.67 [5414]~P106(x54141)+P15(x54141,x54142)+~P15(x54141,f335(f335(f144(x54141),x54143),x54142))
% 59.73/59.67 [5415]~P106(x54151)+P15(x54151,x54152)+~P15(x54151,f335(f335(f144(x54151),x54153),x54152))
% 59.73/59.67 [5416]~P106(x54161)+P15(x54161,x54162)+~P15(x54161,f335(f335(f127(x54161),x54163),x54162))
% 59.73/59.67 [5417]~P106(x54171)+P15(x54171,x54172)+~P15(x54171,f335(f335(f127(x54171),x54172),x54173))
% 59.73/59.67 [5481]~P106(x54811)+P1(f335(f335(f242(x54811),x54813),x54812))+P1(f335(f335(f242(x54811),x54812),x54813))
% 59.73/59.67 [5482]~P106(x54821)+P1(f335(f335(f242(x54821),x54823),x54822))+P1(f335(f335(f242(x54821),x54822),x54823))
% 59.73/59.67 [5483]~P106(x54831)+P1(f335(f335(f243(x54831),x54833),x54832))+P1(f335(f335(f242(x54831),x54832),x54833))
% 59.73/59.67 [5484]~P106(x54841)+P1(f335(f335(f243(x54841),x54843),x54842))+P1(f335(f335(f242(x54841),x54842),x54843))
% 59.73/59.67 [5485]~P106(x54851)+P1(f335(f335(f243(x54851),x54853),x54852))+P1(f335(f335(f242(x54851),x54852),x54853))
% 59.73/59.67 [5486]~P106(x54861)+P1(f335(f335(f243(x54861),x54863),x54862))+P1(f335(f335(f242(x54861),x54862),x54863))
% 59.73/59.67 [5487]~P106(x54871)+P1(f335(f335(f243(x54871),x54873),x54872))+P1(f335(f335(f242(x54871),x54872),x54873))
% 59.73/59.67 [5525]~P60(x55251)+E(f335(f335(f104(x55251),x55252),x55253),x55252)+~P1(f335(f335(f242(x55251),x55253),x55252))
% 59.73/59.67 [5526]~P60(x55261)+E(f335(f335(f104(x55261),x55262),x55263),x55263)+~P1(f335(f335(f242(x55261),x55262),x55263))
% 59.73/59.67 [5527]~P60(x55271)+E(f335(f335(f104(x55271),x55272),x55273),x55273)+~P1(f335(f335(f242(x55271),x55272),x55273))
% 59.73/59.67 [5528]~P102(x55281)+E(f335(f335(f95(x55281),x55282),x55283),x55283)+~P1(f335(f335(f242(x55281),x55283),x55282))
% 59.73/59.67 [5529]~P102(x55291)+E(f335(f335(f95(x55291),x55292),x55293),x55292)+~P1(f335(f335(f242(x55291),x55292),x55293))
% 59.73/59.67 [5530]~P102(x55301)+E(f335(f335(f95(x55301),x55302),x55303),x55302)+~P1(f335(f335(f242(x55301),x55302),x55303))
% 59.73/59.67 [5531]~P106(x55311)+E(f335(f335(f240(x55311),x55312),x55313),x55313)+~P1(f335(f335(f242(x55311),x55313),x55312))
% 59.73/59.67 [5532]~P106(x55321)+E(f335(f335(f240(x55321),x55322),x55323),x55322)+~P1(f335(f335(f242(x55321),x55322),x55323))
% 59.73/59.67 [5533]~P106(x55331)+E(f335(f335(f240(x55331),x55332),x55333),x55332)+~P1(f335(f335(f242(x55331),x55332),x55333))
% 59.73/59.67 [5534]~P106(x55341)+E(f335(f335(f241(x55341),x55342),x55343),x55342)+~P1(f335(f335(f242(x55341),x55343),x55342))
% 59.73/59.67 [5535]~P106(x55351)+E(f335(f335(f241(x55351),x55352),x55353),x55353)+~P1(f335(f335(f242(x55351),x55352),x55353))
% 59.73/59.67 [5536]~P106(x55361)+E(f335(f335(f241(x55361),x55362),x55363),x55363)+~P1(f335(f335(f242(x55361),x55362),x55363))
% 59.73/59.67 [5543]~P116(x55432)+E(x55431,f2(x55432))+E(f335(f335(f292(x55432),f335(f74(x55432),x55433)),f335(f74(x55432),x55431)),f335(f335(f292(x55432),x55433),x55431))
% 59.73/59.67 [5590]~P107(x55901)+E(f335(f304(x55901,x55902),x55903),f188(f888(x55901,a879)))+~P1(f335(f335(f242(x55901),x55903),x55902))
% 59.73/59.67 [5622]~P107(x56221)+E(f308(x56221,x56222,x56223),f188(f888(x56221,a879)))+~P1(f335(f335(f242(x56221),x56223),x56222))
% 59.73/59.67 [5623]~P107(x56231)+E(f307(x56231,x56232,x56233),f188(f888(x56231,a879)))+~P1(f335(f335(f242(x56231),x56233),x56232))
% 59.73/59.67 [5624]~P107(x56241)+E(f305(x56241,x56242,x56243),f188(f888(x56241,a879)))+~P1(f335(f335(f243(x56241),x56243),x56242))
% 59.73/59.67 [5665]~P109(x56651)+~P1(f335(x56652,x56653))+P1(f335(f335(f242(x56651),f246(x56651,x56652)),x56653))
% 59.73/59.67 [5676]~E(f335(f335(f23(a881),x56761),x56763),x56762)+E(x56761,f335(f335(f75(a881),x56762),x56763))+~P1(f335(f335(f242(a881),x56763),x56761))
% 59.73/59.67 [5677]~E(x56771,f335(f335(f75(a881),x56773),x56772))+E(f335(f335(f23(a881),x56771),x56772),x56773)+~P1(f335(f335(f242(a881),x56772),x56771))
% 59.73/59.67 [5723]~P1(f335(x57231,x57233))+P1(f335(x57231,f440(x57231,x57232)))+~P1(f335(f335(f242(a881),x57233),x57232))
% 59.73/59.67 [5724]~P1(f335(x57241,x57243))+P1(f335(x57241,f452(x57241,x57242)))+~P1(f335(f335(f243(a881),x57243),x57242))
% 59.73/59.67 [5731]~P107(x57311)+~E(f335(f304(x57311,x57312),x57313),f188(f888(x57311,a879)))+~P1(f335(f335(f243(x57311),x57312),x57313))
% 59.73/59.67 [5732]~P107(x57321)+~E(f335(f304(x57321,x57322),x57323),f188(f888(x57321,a879)))+~P1(f335(f335(f243(x57321),x57322),x57323))
% 59.73/59.67 [5736]~P2(x57361)+~P1(f335(f335(f243(x57361),x57362),x57363))+P1(f335(f335(f242(x57361),x57362),x57363))
% 59.73/59.67 [5737]~P2(x57371)+~P1(f335(f335(f243(x57371),x57372),x57373))+P1(f335(f335(f242(x57371),x57372),x57373))
% 59.73/59.67 [5738]~P107(x57381)+~P1(f335(f335(f243(x57381),x57382),x57383))+P1(f335(f335(f242(x57381),x57382),x57383))
% 59.73/59.67 [5739]~P107(x57391)+~P1(f335(f335(f243(x57391),x57392),x57393))+P1(f335(f335(f242(x57391),x57392),x57393))
% 59.73/59.67 [5846]~P107(x58461)+~E(f307(x58461,x58462,x58463),f188(f888(x58461,a879)))+~P1(f335(f335(f243(x58461),x58462),x58463))
% 59.73/59.67 [5847]~P107(x58471)+~E(f305(x58471,x58472,x58473),f188(f888(x58471,a879)))+~P1(f335(f335(f242(x58471),x58472),x58473))
% 59.73/59.67 [5848]~P107(x58481)+~E(f188(f888(x58481,a879)),f307(x58481,x58482,x58483))+~P1(f335(f335(f243(x58481),x58482),x58483))
% 59.73/59.67 [5849]~P107(x58491)+~E(f188(f888(x58491,a879)),f305(x58491,x58492,x58493))+~P1(f335(f335(f242(x58491),x58492),x58493))
% 59.73/59.67 [5858]P1(f335(x58581,x58582))+~P1(f335(x58581,f448(x58581,x58583)))+~P1(f335(f335(f242(a881),x58582),x58583))
% 59.73/59.67 [5859]P1(f335(x58591,x58592))+~P1(f335(x58591,f453(x58591,x58593)))+~P1(f335(f335(f243(a881),x58592),x58593))
% 59.73/59.67 [5867]~E(x58671,f335(a106,x58673))+P1(f335(f335(f243(a881),x58671),f335(a106,x58672)))+~P1(f335(f335(f243(a881),x58673),x58672))
% 59.73/59.67 [5884]E(x58841,x58842)+~E(f335(f335(f76(a881),x58843),x58841),f335(f335(f76(a881),x58843),x58842))+~P1(f335(f335(f243(a881),f2(a881)),x58843))
% 59.73/59.67 [5940]E(f335(x59401,f463(x59401,x59402,x59403)),f73(a881))+~E(f335(f335(f6(x59403,a881),x59401),x59402),f73(a881))+~P1(f335(f56(x59403),x59402))
% 59.73/59.67 [5953]~P5(x59531)+P1(f335(f335(f242(x59531),x59532),f31(x59531,x59533)))+~P1(f335(f335(f337(x59531),x59532),x59533))
% 59.73/59.67 [5979]~P2(x59791)+~P1(f335(f335(f243(x59791),x59793),x59792))+~P1(f335(f335(f242(x59791),x59792),x59793))
% 59.73/59.67 [5980]~P2(x59801)+~P1(f335(f335(f243(x59801),x59803),x59802))+~P1(f335(f335(f243(x59801),x59802),x59803))
% 59.73/59.67 [5981]~P2(x59811)+~P1(f335(f335(f243(x59811),x59813),x59812))+~P1(f335(f335(f243(x59811),x59812),x59813))
% 59.73/59.67 [5982]~P2(x59821)+~P1(f335(f335(f243(x59821),x59823),x59822))+~P1(f335(f335(f243(x59821),x59822),x59823))
% 59.73/59.67 [5983]~P2(x59831)+~P1(f335(f335(f243(x59831),x59833),x59832))+~P1(f335(f335(f243(x59831),x59832),x59833))
% 59.73/59.67 [5984]~P106(x59841)+~P1(f335(f335(f243(x59841),x59843),x59842))+~P1(f335(f335(f242(x59841),x59842),x59843))
% 59.73/59.67 [5985]~P106(x59851)+~P1(f335(f335(f243(x59851),x59853),x59852))+~P1(f335(f335(f242(x59851),x59852),x59853))
% 59.73/59.67 [5986]~P106(x59861)+~P1(f335(f335(f243(x59861),x59863),x59862))+~P1(f335(f335(f242(x59861),x59862),x59863))
% 59.73/59.67 [5987]~P106(x59871)+~P1(f335(f335(f243(x59871),x59873),x59872))+~P1(f335(f335(f243(x59871),x59872),x59873))
% 59.73/59.67 [5988]~P107(x59881)+~P1(f335(f335(f243(x59881),x59883),x59882))+~P1(f335(f335(f243(x59881),x59882),x59883))
% 59.73/59.67 [6016]~E(f335(x60162,f365(x60162,x60163,x60161)),f73(a881))+E(f335(f335(f9(x60161,a881),x60162),x60163),f73(a881))+~P1(f335(f56(x60161),x60163))
% 59.73/59.67 [6017]~E(f335(x60172,f464(x60172,x60173,x60171)),f2(a881))+E(f335(f335(f6(x60171,a881),x60172),x60173),f2(a881))+~P1(f335(f56(x60171),x60173))
% 59.73/59.67 [6033]~P108(x60331)+~P1(f335(f335(f243(x60331),x60333),x60332))+P1(f335(f335(f337(x60331),x60332),f335(f306(x60331),x60333)))
% 59.73/59.67 [6034]~P108(x60341)+~P1(f335(f335(f242(x60341),x60343),x60342))+P1(f335(f335(f337(x60341),x60342),f335(f251(x60341),x60343)))
% 59.73/59.67 [6035]~P108(x60351)+~P1(f335(f335(f243(x60351),x60352),x60353))+P1(f335(f335(f337(x60351),x60352),f335(f250(x60351),x60353)))
% 59.73/59.67 [6036]~P108(x60361)+~P1(f335(f335(f242(x60361),x60362),x60363))+P1(f335(f335(f337(x60361),x60362),f335(f303(x60361),x60363)))
% 59.73/59.67 [6048]E(f335(x60481,f489(x60481,x60482,x60483)),f335(a106,f2(a881)))+~E(f335(f335(f6(x60483,a881),x60481),x60482),f335(a106,f2(a881)))+~P1(f335(f56(x60483),x60482))
% 59.73/59.67 [6127]~P5(x61271)+~P1(f335(f335(f337(x61271),x61273),x61272))+P1(f335(f335(f242(x61271),f32(x61271,x61272)),x61273))
% 59.73/59.67 [6144]~P1(f335(f335(f242(a881),x61441),x61443))+P1(f335(f335(f242(a881),x61441),x61442))+~P1(f335(f335(f242(a881),x61443),x61442))
% 59.73/59.67 [6145]~P1(f335(f335(f242(a1),x61451),x61453))+P1(f335(f335(f242(a1),x61451),x61452))+~P1(f335(f335(f242(a1),x61453),x61452))
% 59.73/59.67 [6164]~P108(x61641)+~P1(f335(f335(f337(x61641),x61643),f335(f251(x61641),x61642)))+P1(f335(f335(f242(x61641),x61642),x61643))
% 59.73/59.67 [6165]~P108(x61651)+~P1(f335(f335(f337(x61651),x61652),f335(f303(x61651),x61653)))+P1(f335(f335(f242(x61651),x61652),x61653))
% 59.73/59.67 [6166]~P108(x61661)+~P1(f335(f335(f337(x61661),x61663),f335(f306(x61661),x61662)))+P1(f335(f335(f243(x61661),x61662),x61663))
% 59.73/59.67 [6167]~P108(x61671)+~P1(f335(f335(f337(x61671),x61672),f335(f250(x61671),x61673)))+P1(f335(f335(f243(x61671),x61672),x61673))
% 59.73/59.67 [6350]~P107(x63501)+~P37(a881,x63501,x63502)+P1(f335(f335(f242(x63501),f335(x63502,x63503)),f335(x63502,f335(a106,x63503))))
% 59.73/59.67 [6385]~P68(x63851)+P1(f335(f335(f243(x63851),f2(x63851)),f507(x63853,x63852,x63851)))+P1(f335(f335(f242(x63851),x63852),x63853))
% 59.73/59.67 [6386]~P69(x63861)+P1(f335(f335(f243(x63861),f2(x63861)),f794(x63863,x63862,x63861)))+P1(f335(f335(f242(x63861),x63862),x63863))
% 59.73/59.67 [6455]~P80(x64551)+~P1(f335(f335(f242(x64551),x64553),f335(f74(x64551),x64552)))+P1(f335(f335(f242(x64551),x64552),f335(f74(x64551),x64553)))
% 59.73/59.67 [6456]~P80(x64561)+~P1(f335(f335(f242(x64561),x64563),f335(f74(x64561),x64562)))+P1(f335(f335(f242(x64561),x64562),f335(f74(x64561),x64563)))
% 59.73/59.67 [6457]~P80(x64571)+~P1(f335(f335(f243(x64571),x64573),f335(f74(x64571),x64572)))+P1(f335(f335(f243(x64571),x64572),f335(f74(x64571),x64573)))
% 59.73/59.67 [6458]~P80(x64581)+~P1(f335(f335(f243(x64581),x64583),f335(f74(x64581),x64582)))+P1(f335(f335(f243(x64581),x64582),f335(f74(x64581),x64583)))
% 59.73/59.67 [6470]~P1(f335(f335(f243(a881),x64701),x64703))+~P1(f335(f335(f243(a881),x64703),x64702))+P1(f335(f335(f243(a881),f335(a106,x64701)),x64702))
% 59.73/59.67 [6495]~P119(x64951)+P1(f335(f335(f242(x64951),f335(f96(x64951),x64952)),f335(f96(x64951),x64953)))+~P1(f335(f335(f242(a1),x64952),x64953))
% 59.73/59.67 [6496]~P122(x64961)+P1(f335(f335(f242(x64961),f335(f94(x64961),x64962)),f335(f94(x64961),x64963)))+~P1(f335(f335(f242(a881),x64962),x64963))
% 59.73/59.67 [6497]~P119(x64971)+P1(f335(f335(f243(x64971),f335(f96(x64971),x64972)),f335(f96(x64971),x64973)))+~P1(f335(f335(f243(a1),x64972),x64973))
% 59.73/59.67 [6498]~P122(x64981)+P1(f335(f335(f243(x64981),f335(f94(x64981),x64982)),f335(f94(x64981),x64983)))+~P1(f335(f335(f243(a881),x64982),x64983))
% 59.73/59.67 [6499]~P122(x64991)+P1(f335(f335(f243(x64991),f335(f94(x64991),x64992)),f335(f94(x64991),x64993)))+~P1(f335(f335(f243(a881),x64992),x64993))
% 59.73/59.67 [6505]~P106(x65051)+E(f335(f335(f104(f888(x65051,a879)),f335(f250(x65051),x65052)),f335(f304(x65051,x65052),x65053)),f335(f250(x65051),x65053))+~P1(f335(f335(f242(x65051),x65052),x65053))
% 59.73/59.67 [6535]~P80(x65351)+~P1(f335(f335(f242(x65351),x65353),x65352))+P1(f335(f335(f242(x65351),f335(f74(x65351),x65352)),f335(f74(x65351),x65353)))
% 59.73/59.67 [6536]~P80(x65361)+~P1(f335(f335(f242(x65361),x65363),x65362))+P1(f335(f335(f242(x65361),f335(f74(x65361),x65362)),f335(f74(x65361),x65363)))
% 59.73/59.67 [6537]~P84(x65371)+~P1(f335(f335(f242(x65371),x65373),x65372))+P1(f335(f335(f242(x65371),f335(f74(x65371),x65372)),f335(f74(x65371),x65373)))
% 59.73/59.67 [6538]~P84(x65381)+~P1(f335(f335(f242(x65381),x65383),x65382))+P1(f335(f335(f242(x65381),f335(f74(x65381),x65382)),f335(f74(x65381),x65383)))
% 59.73/59.67 [6539]~P80(x65391)+~P1(f335(f335(f243(x65391),x65393),x65392))+P1(f335(f335(f243(x65391),f335(f74(x65391),x65392)),f335(f74(x65391),x65393)))
% 59.73/59.67 [6573]~P106(x65731)+E(f335(f335(f104(f888(x65731,a879)),f335(f250(x65731),x65732)),f305(x65731,x65732,x65733)),f335(f303(x65731),x65733))+~P1(f335(f335(f242(x65731),x65732),x65733))
% 59.73/59.67 [6574]~P106(x65741)+E(f335(f335(f104(f888(x65741,a879)),f335(f303(x65741),x65742)),f308(x65741,x65742,x65743)),f335(f250(x65741),x65743))+~P1(f335(f335(f243(x65741),x65742),x65743))
% 59.73/59.67 [6575]~P106(x65751)+E(f335(f335(f104(f888(x65751,a879)),f335(f303(x65751),x65752)),f307(x65751,x65752,x65753)),f335(f303(x65751),x65753))+~P1(f335(f335(f242(x65751),x65752),x65753))
% 59.73/59.67 [6613]~P106(x66131)+E(f335(f335(f104(f888(x66131,a879)),f335(f304(x66131,x66132),x66133)),f335(f251(x66131),x66133)),f335(f251(x66131),x66132))+~P1(f335(f335(f242(x66131),x66132),x66133))
% 59.73/59.67 [6680]~P5(x66801)+~P1(f335(f335(f242(x66801),f335(x66802,x66803)),x66803))+P1(f335(f335(f242(x66801),f89(x66801,x66802)),x66803))
% 59.73/59.67 [6770]~P106(x67701)+E(f335(f335(f104(f888(x67701,a879)),f308(x67701,x67702,x67703)),f335(f251(x67701),x67703)),f335(f306(x67701),x67702))+~P1(f335(f335(f243(x67701),x67702),x67703))
% 59.73/59.67 [6771]~P106(x67711)+E(f335(f335(f104(f888(x67711,a879)),f307(x67711,x67712,x67713)),f335(f306(x67711),x67713)),f335(f306(x67711),x67712))+~P1(f335(f335(f242(x67711),x67712),x67713))
% 59.73/59.67 [6772]~P106(x67721)+E(f335(f335(f104(f888(x67721,a879)),f305(x67721,x67722,x67723)),f335(f306(x67721),x67723)),f335(f251(x67721),x67722))+~P1(f335(f335(f242(x67721),x67722),x67723))
% 59.73/59.67 [6791]P1(f335(x67911,x67912))+~P1(f335(f335(f242(a881),x67912),x67913))+P1(f335(f335(f337(a881),f448(x67911,x67913)),f305(a881,f2(a881),x67913)))
% 59.73/59.67 [6825]E(x68251,x68252)+~E(f335(f335(f158(x68253),x68251),f684(x68253,x68252,x68251)),f335(f335(f158(x68253),x68252),f684(x68253,x68252,x68251)))+~E(f335(f189(f882(x68253)),x68251),f335(f189(f882(x68253)),x68252))
% 59.73/59.67 [6830]~E(x68303,f335(f335(f30(a881),x68301),x68302))+~P1(f335(f335(f243(a881),f2(a881)),x68302))+P1(f335(f335(f243(a881),x68301),f335(f335(f76(a881),x68302),f335(a106,x68303))))
% 59.73/59.67 [6847]~P1(f335(x68471,x68473))+~P1(f335(f335(f242(a881),x68473),x68472))+P1(f335(f335(f337(a881),f440(x68471,x68472)),f305(a881,f2(a881),x68472)))
% 59.73/59.67 [6888]~P1(f335(x68881,x68883))+P1(f335(x68881,f449(x68881,x68882)))+~P1(f335(f335(f337(a881),x68883),f305(a881,f2(a881),x68882)))
% 59.73/59.67 [6907]~P122(x69073)+~P1(f335(f335(f242(x69073),f335(f94(x69073),x69071)),f335(f94(x69073),x69072)))+P1(f335(f335(f242(a881),x69071),x69072))
% 59.73/59.67 [6908]~P119(x69083)+~P1(f335(f335(f242(x69083),f335(f96(x69083),x69081)),f335(f96(x69083),x69082)))+P1(f335(f335(f242(a1),x69081),x69082))
% 59.73/59.67 [6909]~P122(x69093)+~P1(f335(f335(f243(x69093),f335(f94(x69093),x69091)),f335(f94(x69093),x69092)))+P1(f335(f335(f243(a881),x69091),x69092))
% 59.73/59.67 [6910]~P122(x69103)+~P1(f335(f335(f243(x69103),f335(f94(x69103),x69101)),f335(f94(x69103),x69102)))+P1(f335(f335(f243(a881),x69101),x69102))
% 59.73/59.67 [6911]~P119(x69113)+~P1(f335(f335(f243(x69113),f335(f96(x69113),x69111)),f335(f96(x69113),x69112)))+P1(f335(f335(f243(a1),x69111),x69112))
% 59.73/59.67 [6927]~P122(x69271)+~P1(f335(f335(f243(x69271),f73(x69271)),x69272))+P1(f335(f335(f243(x69271),f73(x69271)),f335(f335(f254(x69271),x69272),f335(a106,x69273))))
% 59.73/59.67 [6929]~P80(x69291)+~P1(f335(f335(f242(x69291),f335(f74(x69291),x69293)),f335(f74(x69291),x69292)))+P1(f335(f335(f242(x69291),x69292),x69293))
% 59.73/59.67 [6930]~P84(x69301)+~P1(f335(f335(f242(x69301),f335(f74(x69301),x69303)),f335(f74(x69301),x69302)))+P1(f335(f335(f242(x69301),x69302),x69303))
% 59.73/59.67 [6931]~P80(x69311)+~P1(f335(f335(f243(x69311),f335(f74(x69311),x69313)),f335(f74(x69311),x69312)))+P1(f335(f335(f243(x69311),x69312),x69313))
% 59.73/59.67 [6955]P1(f335(x69551,x69552))+~P1(f335(x69551,f450(x69551,x69553)))+~P1(f335(f335(f337(a881),x69552),f305(a881,f2(a881),x69553)))
% 59.73/59.67 [6974]~P68(x69741)+P1(f335(f335(f243(x69741),f507(x69743,x69742,x69741)),f73(x69741)))+P1(f335(f335(f242(x69741),x69742),x69743))
% 59.73/59.67 [6993]~E(f39(a881,x69933,x69932),f39(a881,x69931,x69932))+E(f335(f335(f75(a881),x69931),f335(f335(f76(a881),x69932),f572(x69931,x69932,x69933))),x69933)+~P1(f335(f335(f242(a881),x69931),x69933))
% 59.73/59.67 [7012]E(f335(x70121,f559(x70121,x70122,x70123)),f200(x70122))+~P1(f335(f56(x70123),f177(x70123,x70122,x70121)))+P1(f335(f56(x70123),f252(f888(x70123,a879))))
% 59.73/59.67 [7050]E(f335(f335(f9(x70501,a881),x70502),x70503),f73(a881))+~P1(f335(f56(x70501),x70503))+P1(f335(f335(f337(x70501),f365(x70502,x70503,x70501)),x70503))
% 59.73/59.67 [7051]E(f335(f335(f6(x70511,a881),x70512),x70513),f2(a881))+~P1(f335(f56(x70511),x70513))+P1(f335(f335(f337(x70511),f464(x70512,x70513,x70511)),x70513))
% 59.73/59.67 [7073]~P106(x70731)+~P1(f335(f335(f242(x70731),x70732),x70733))+P1(f335(f335(f242(f888(x70731,a879)),f335(f250(x70731),x70732)),f335(f250(x70731),x70733)))
% 59.73/59.67 [7074]~P107(x70741)+~P1(f335(f335(f242(x70741),x70742),x70743))+P1(f335(f335(f242(f888(x70741,a879)),f335(f303(x70741),x70742)),f335(f303(x70741),x70743)))
% 59.73/59.67 [7075]~P106(x70751)+~P1(f335(f335(f242(x70751),x70753),x70752))+P1(f335(f335(f242(f888(x70751,a879)),f335(f306(x70751),x70752)),f335(f306(x70751),x70753)))
% 59.73/59.67 [7076]~P107(x70761)+~P1(f335(f335(f242(x70761),x70763),x70762))+P1(f335(f335(f242(f888(x70761,a879)),f335(f251(x70761),x70762)),f335(f251(x70761),x70763)))
% 59.73/59.67 [7077]~P106(x70771)+~P1(f335(f335(f243(x70771),x70772),x70773))+P1(f335(f335(f243(f888(x70771,a879)),f335(f250(x70771),x70772)),f335(f250(x70771),x70773)))
% 59.73/59.67 [7086]~P5(x70861)+P1(f335(f335(f242(x70861),x70862),f32(x70861,x70863)))+P1(f335(f335(f337(x70861),f631(x70863,x70862,x70861)),x70863))
% 59.73/59.67 [7092]~P80(x70921)+P1(f335(f335(f242(x70921),f335(f335(f23(x70921),x70922),x70923)),f2(x70921)))+~P1(f335(f335(f242(x70921),x70922),x70923))
% 59.73/59.67 [7093]~P80(x70931)+P1(f335(f335(f243(x70931),f335(f335(f23(x70931),x70932),x70933)),f2(x70931)))+~P1(f335(f335(f243(x70931),x70932),x70933))
% 59.73/59.67 [7135]P1(f335(x71351,x71352))+P1(f335(f335(f242(a881),f450(x71351,x71353)),x71353))+~P1(f335(f335(f337(a881),x71352),f305(a881,f2(a881),x71353)))
% 59.73/59.67 [7175]~E(f335(f335(f6(x71751,a881),x71752),x71753),f73(a881))+~P1(f335(f56(x71751),x71753))+P1(f335(f335(f337(x71751),f463(x71752,x71753,x71751)),x71753))
% 59.73/59.67 [7176]~P1(f335(x71761,x71763))+P1(f335(f335(f242(a881),f449(x71761,x71762)),x71762))+~P1(f335(f335(f337(a881),x71763),f305(a881,f2(a881),x71762)))
% 59.73/59.67 [7216]~P5(x72161)+P1(f335(f335(f337(x72161),f632(x72163,x72162,x72161)),x72162))+P1(f335(f335(f242(x72161),f31(x72161,x72162)),x72163))
% 59.73/59.67 [7247]~E(f335(f335(f6(x72471,a881),x72472),x72473),f335(a106,f2(a881)))+~P1(f335(f56(x72471),x72473))+P1(f335(f335(f337(x72471),f489(x72472,x72473,x72471)),x72473))
% 59.73/59.67 [7259]E(x72591,f2(a881))+P1(f335(x72592,f39(a881,x72593,x72591)))+P1(f335(f335(f243(a881),f382(x72591,x72593,x72592)),x72591))
% 59.73/59.67 [7369]~P1(f335(x73691,x73692))+P1(f335(x73691,f39(a881,x73692,x73693)))+P1(f335(f335(f243(a881),f382(x73693,x73692,x73691)),x73693))
% 59.73/59.67 [7488]E(x74881,f107(x74882))+~P1(f335(f335(f337(f882(x74882)),x74881),f154(x74882,x74883)))+P1(f335(f335(f337(x74882),f710(x74883,x74881,x74882)),x74883))
% 59.73/59.67 [7510]~P106(x75101)+E(f335(f335(f104(f888(x75101,a879)),f335(f335(f312(x75101),x75102),f188(f888(x75101,a879)))),f308(x75101,x75102,x75103)),f335(f304(x75101,x75102),x75103))+~P1(f335(f335(f243(x75101),x75102),x75103))
% 59.73/59.67 [7534]~P106(x75341)+E(f335(f335(f104(f888(x75341,a879)),f335(f335(f312(x75341),x75342),f188(f888(x75341,a879)))),f307(x75341,x75342,x75343)),f305(x75341,x75342,x75343))+~P1(f335(f335(f242(x75341),x75342),x75343))
% 59.73/59.67 [7643]~P106(x76431)+P1(f335(f335(f242(x76431),x76432),x76433))+~P1(f335(f335(f242(f888(x76431,a879)),f335(f306(x76431),x76433)),f335(f306(x76431),x76432)))
% 59.73/59.67 [7644]~P107(x76441)+P1(f335(f335(f242(x76441),x76442),x76443))+~P1(f335(f335(f242(f888(x76441,a879)),f335(f251(x76441),x76443)),f335(f251(x76441),x76442)))
% 59.73/59.67 [7645]~P106(x76451)+P1(f335(f335(f242(x76451),x76452),x76453))+~P1(f335(f335(f242(f888(x76451,a879)),f335(f250(x76451),x76452)),f335(f250(x76451),x76453)))
% 59.73/59.67 [7646]~P107(x76461)+P1(f335(f335(f242(x76461),x76462),x76463))+~P1(f335(f335(f242(f888(x76461,a879)),f335(f303(x76461),x76462)),f335(f303(x76461),x76463)))
% 59.73/59.67 [7647]~P106(x76471)+P1(f335(f335(f243(x76471),x76472),x76473))+~P1(f335(f335(f243(f888(x76471,a879)),f335(f250(x76471),x76472)),f335(f250(x76471),x76473)))
% 59.73/59.67 [7670]~P80(x76701)+~P1(f335(f335(f242(x76701),f335(f335(f23(x76701),x76702),x76703)),f2(x76701)))+P1(f335(f335(f242(x76701),x76702),x76703))
% 59.73/59.67 [7671]~P80(x76711)+~P1(f335(f335(f243(x76711),f335(f335(f23(x76711),x76712),x76713)),f2(x76711)))+P1(f335(f335(f243(x76711),x76712),x76713))
% 59.73/59.67 [7829]E(x78291,f2(a881))+~E(f335(f135(a881,a881,f75(a881),x78292),x78293),f2(a881))+~P1(f335(f335(f337(a881),x78291),f335(f166(a881),x78293)))
% 59.73/59.67 [7833]~P5(x78331)+~P1(f335(f335(f242(x78331),f632(x78333,x78332,x78331)),x78333))+P1(f335(f335(f242(x78331),f31(x78331,x78332)),x78333))
% 59.73/59.67 [7994]P1(f335(f335(f242(a1),f2(a1)),f377(x79941,x79942,x79943)))+P1(f335(f335(x79942,f335(f335(f30(a1),x79941),x79943)),f39(a1,x79941,x79943)))+~P1(f335(f335(f243(a1),f2(a1)),x79943))
% 59.73/59.67 [8082]E(x80821,x80822)+~E(f335(f189(f882(x80823)),x80821),f335(f189(f882(x80823)),x80822))+~P1(f335(f335(f268(x80823,x80823,a879),a332),f676(x80823,x80821,x80822)))
% 59.73/59.67 [8147]~P36(x81472,x81473)+E(x81471,f188(f888(x81472,a879)))+~P1(f335(f335(f242(f888(x81472,a879)),x81471),f335(f288(x81472,x81472,x81473),x81471)))
% 59.73/59.67 [8177]~P69(x81771)+~P1(f335(f335(f242(x81771),x81772),f335(f335(f75(x81771),x81773),f794(x81773,x81772,x81771))))+P1(f335(f335(f242(x81771),x81772),x81773))
% 59.73/59.67 [8217]P46(x82171,x82172,x82173)+P1(f335(f335(f337(x82171),f551(x82173,x82172,x82171)),x82172))+P1(f335(f335(f337(f887(x82171,x82171)),f552(x82173,x82172,x82171)),x82173))
% 59.73/59.67 [8239]P1(f335(f335(x82392,f335(f335(f30(a1),x82391),x82393)),f39(a1,x82391,x82393)))+~P1(f335(f335(f243(a1),f2(a1)),x82393))+P1(f335(f335(f243(a1),f377(x82391,x82392,x82393)),x82393))
% 59.73/59.67 [8263]E(f335(f313(a881,a881,f335(f335(f7(a881,a881,a881),f23(a881)),x82631)),f335(f304(a881,x82632),x82633)),f188(f888(a881,a879)))+P1(f335(f335(f243(a881),x82631),x82633))+P1(f335(f335(f243(a881),x82632),x82633))
% 59.73/59.67 [8371]E(f335(f313(a881,a881,f335(f335(f7(a881,a881,a881),f23(a881)),x83711)),f335(f304(a881,x83712),x83713)),f335(f335(f312(a881),f2(a881)),f188(f888(a881,a879))))+P1(f335(f335(f243(a881),x83711),x83713))+~P1(f335(f335(f243(a881),x83712),x83713))
% 59.73/59.67 [8388]~P106(x83881)+E(f142(x83881,x83881,f5(x83881),x83882,x83883),x83883)+~P1(f335(f335(f337(x83881),x83882),f335(f166(x83881),x83883)))
% 59.73/59.67 [8402]P26(x84021,x84021,x84022,x84023)+~P1(f335(f56(x84021),x84023))+~P1(f335(f335(f242(f888(x84021,a879)),x84023),f335(f313(x84021,x84021,x84022),x84023)))
% 59.73/59.67 [8428]E(f335(f335(f75(a1),f335(f335(f76(a1),x84281),f378(x84282,x84283,x84281))),f377(x84282,x84283,x84281)),x84282)+P1(f335(f335(x84283,f335(f335(f30(a1),x84282),x84281)),f39(a1,x84282,x84281)))+~P1(f335(f335(f243(a1),f2(a1)),x84281))
% 59.73/59.67 [8662]~P1(f335(f335(x86621,f378(x86622,x86621,x86623)),f377(x86622,x86621,x86623)))+P1(f335(f335(x86621,f335(f335(f30(a1),x86622),x86623)),f39(a1,x86622,x86623)))+~P1(f335(f335(f243(a1),f2(a1)),x86623))
% 59.73/59.67 [9532]~P1(f335(f56(x95321),x95322))+~P1(f335(f335(f337(x95321),x95323),x95322))+P1(f335(f335(f243(a881),f335(f29(x95321),f335(f335(f23(f888(x95321,a879)),x95322),f335(f335(f312(x95321),x95323),f188(f888(x95321,a879)))))),f335(f29(x95321),x95322)))
% 59.73/59.67 [10133]P46(x101331,x101332,x101333)+~P1(f335(f335(f268(x101331,x101331,a879),f335(f335(f7(x101331,f888(x101331,a879),f888(x101331,a879)),f335(f335(f8(f888(a879,a879),f888(f888(x101331,a879),f888(x101331,a879)),x101331),f8(a879,a879,x101331)),f335(f335(f8(a879,f888(a879,a879),x101331),a333),f335(f335(f7(x101331,f888(x101331,a879),a879),f337(x101331)),x101332)))),f335(f335(f7(x101331,f888(x101331,a879),a879),f337(x101331)),x101332))),f552(x101333,x101332,x101331)))+P1(f335(f335(f337(x101331),f551(x101333,x101332,x101331)),x101332))
% 59.73/59.67 [5504]~P116(x55042)+E(x55041,f2(x55042))+E(f335(f335(f292(x55042),x55043),f335(f74(x55042),x55041)),f335(f74(x55042),f335(f335(f292(x55042),x55043),x55041)))
% 59.73/59.67 [5638]~E(x56383,f188(f888(x56381,a879)))+~E(x56382,f188(f888(x56381,a879)))+E(f335(f335(f104(f888(x56381,a879)),x56382),x56383),f188(f888(x56381,a879)))
% 59.73/59.67 [5696]~E(x56963,f2(a881))+~P1(f335(x56961,f2(a881)))+P1(f335(x56961,f335(f335(f30(a881),x56962),x56963)))
% 59.73/59.67 [5697]~E(x56973,f2(a881))+~P1(f335(x56971,f2(a881)))+P1(f335(x56971,f335(f335(f30(a881),x56972),x56973)))
% 59.73/59.67 [5838]~P69(x58382)+E(x58381,f2(x58382))+E(f335(f335(f292(x58382),f335(f70(x58382),x58383)),f335(f70(x58382),x58381)),f335(f70(x58382),f335(f335(f292(x58382),x58383),x58381)))
% 59.73/59.67 [6002]~P1(f335(f56(x60021),x60023))+E(f335(f29(x60021),f335(f335(f312(x60021),x60022),x60023)),f335(a106,f335(f29(x60021),x60023)))+P1(f335(f335(f337(x60021),x60022),x60023))
% 59.73/59.67 [6003]~P1(f335(f56(x60031),x60033))+E(f335(f29(x60031),f335(f335(f312(x60031),x60032),x60033)),f335(a106,f335(f29(x60031),x60033)))+P1(f335(f335(f337(x60031),x60032),x60033))
% 59.73/59.67 [6077]~E(x60772,f2(a881))+P1(f335(x60771,f2(a881)))+~P1(f335(x60771,f335(f335(f30(a881),x60773),x60772)))
% 59.73/59.67 [6096]~P1(f335(f56(x60961),x60963))+E(f335(f29(x60961),f335(f335(f312(x60961),x60962),x60963)),f335(f29(x60961),x60963))+~P1(f335(f335(f337(x60961),x60962),x60963))
% 59.73/59.67 [6129]~P1(f335(f56(x61291),x61293))+E(f335(f29(x61291),f335(f335(f312(x61291),x61292),x61293)),f335(f335(f75(a881),f73(a881)),f335(f29(x61291),x61293)))+P1(f335(f335(f337(x61291),x61292),x61293))
% 59.73/59.67 [6247]E(f335(f335(f75(a881),x62471),f356(x62471,x62472,x62473)),x62472)+~P1(f335(x62473,f2(a881)))+P1(f335(x62473,f335(f335(f23(a881),x62472),x62471)))
% 59.73/59.67 [6248]E(f335(f335(f75(a881),x62481),f357(x62481,x62482,x62483)),x62482)+~P1(f335(x62483,f2(a881)))+P1(f335(x62483,f335(f335(f23(a881),x62482),x62481)))
% 59.73/59.67 [6294]~P5(x62941)+~P1(f335(f56(x62941),x62943))+E(f335(f335(f59(x62941,x62941,f104(x62941)),x62942),x62943),f335(f335(f104(x62941),x62942),f31(x62941,x62943)))
% 59.73/59.67 [6295]~P5(x62951)+~P1(f335(f56(x62951),x62953))+E(f335(f335(f59(x62951,x62951,f95(x62951)),x62952),x62953),f335(f335(f95(x62951),x62952),f32(x62951,x62953)))
% 59.73/59.67 [6301]~P97(x63011)+~E(f335(f97(x63011),x63012),f335(f97(x63011),x63013))+P28(x63011,f335(f97(x63011),f335(f335(f75(a1),x63012),f335(f74(a1),x63013))))
% 59.73/59.67 [6308]~P137(x63081)+E(f335(f335(f23(x63081),f335(f94(x63081),x63082)),f335(f94(x63081),x63083)),f335(f94(x63081),f335(f335(f23(a881),x63082),x63083)))+~P1(f335(f335(f242(a881),x63083),x63082))
% 59.73/59.67 [6396]E(f335(f335(f75(a881),x63961),f356(x63961,x63962,x63963)),x63962)+P1(f335(f335(f243(a881),x63962),x63961))+P1(f335(x63963,f335(f335(f23(a881),x63962),x63961)))
% 59.73/59.67 [6397]E(f335(f335(f75(a881),x63971),f357(x63971,x63972,x63973)),x63972)+P1(f335(f335(f243(a881),x63972),x63971))+P1(f335(x63973,f335(f335(f23(a881),x63972),x63971)))
% 59.73/59.67 [6414]~P119(x64141)+E(f335(f335(f76(x64141),f335(f70(x64141),x64142)),x64143),f335(f70(x64141),f335(f335(f76(x64141),x64142),x64143)))+~P1(f335(f335(f242(x64141),f2(x64141)),x64143))
% 59.73/59.67 [6415]~P68(x64151)+E(f335(f335(f292(x64151),f335(f70(x64151),x64152)),x64153),f335(f70(x64151),f335(f335(f292(x64151),x64152),x64153)))+~P1(f335(f335(f243(x64151),f2(x64151)),x64153))
% 59.73/59.67 [6423]~P61(x64231)+~P1(f335(f56(x64231),x64233))+E(f335(f335(f59(x64231,x64231,f95(x64231)),x64232),x64233),f10(x64231,f335(f335(f312(x64231),x64232),x64233)))
% 59.73/59.67 [6424]~P61(x64241)+~P1(f335(f56(x64241),x64243))+E(f335(f335(f59(x64241,x64241,f104(x64241)),x64242),x64243),f13(x64241,f335(f335(f312(x64241),x64242),x64243)))
% 59.73/59.67 [6425]~P106(x64251)+~P1(f335(f56(x64251),x64253))+E(f335(f335(f59(x64251,x64251,f241(x64251)),x64252),x64253),f14(x64251,f335(f335(f312(x64251),x64252),x64253)))
% 59.73/59.67 [6426]~P106(x64261)+~P1(f335(f56(x64261),x64263))+E(f335(f335(f59(x64261,x64261,f240(x64261)),x64262),x64263),f15(x64261,f335(f335(f312(x64261),x64262),x64263)))
% 59.73/59.67 [6472]E(x64721,f107(x64722))+~E(f173(x64722,x64723),f107(f882(x64722)))+~P1(f335(f335(f337(f882(x64722)),x64721),f335(f166(f882(x64722)),x64723)))
% 59.73/59.67 [6513]~P1(f335(f130(x65131),x65133))+P1(f335(f335(f337(x65131),x65132),f335(f166(x65131),x65133)))+P1(f335(f130(x65131),f335(f335(f144(x65131),x65132),x65133)))
% 59.73/59.67 [6524]~P98(x65241)+~P1(f335(f56(x65241),x65243))+E(f335(f58(x65241,f76(x65241)),f335(f335(f312(x65241),x65242),x65243)),f335(f335(f59(x65241,x65241,f76(x65241)),x65242),x65243))
% 59.73/59.67 [6547]~P106(x65471)+~P1(f335(f56(x65471),x65473))+E(f11(x65471,f240(x65471),f335(f335(f312(x65471),x65472),x65473)),f335(f335(f59(x65471,x65471,f240(x65471)),x65472),x65473))
% 59.73/59.67 [6548]~P106(x65481)+~P1(f335(f56(x65481),x65483))+E(f12(x65481,f241(x65481),f335(f335(f312(x65481),x65482),x65483)),f335(f335(f59(x65481,x65481,f241(x65481)),x65482),x65483))
% 59.73/59.67 [6549]P1(f335(x65491,f2(a881)))+~P1(f335(f335(f243(a881),x65492),x65493))+~P1(f335(x65491,f335(f335(f23(a881),x65492),x65493)))
% 59.73/59.67 [6550]P1(f335(x65501,f2(a881)))+~P1(f335(f335(f243(a881),x65502),x65503))+~P1(f335(x65501,f335(f335(f23(a881),x65502),x65503)))
% 59.73/59.67 [6570]~P88(x65701)+P1(f335(f335(f242(x65701),x65702),x65703))+~P1(f335(f335(f242(x65701),f335(f70(x65701),x65702)),x65703))
% 59.73/59.67 [6571]~P88(x65711)+P1(f335(f335(f242(x65711),x65712),x65713))+~P1(f335(f335(f242(x65711),f335(f70(x65711),x65712)),x65713))
% 59.73/59.67 [6572]~P119(x65721)+P1(f335(f335(f243(x65721),x65722),x65723))+~P1(f335(f335(f243(x65721),f335(f70(x65721),x65722)),x65723))
% 59.73/59.67 [6589]E(x65891,f107(x65892))+E(f335(f134(x65892),f335(f335(f131(x65892),x65893),x65891)),f335(f335(f158(x65892),x65891),x65893))+~P1(f335(f335(f243(a881),x65893),f335(f189(f882(x65892)),x65891)))
% 59.73/59.67 [6644]~P1(f335(x66441,x66443))+P1(f335(x66441,f455(x66441,x66442)))+~P1(f335(f335(f337(a881),x66443),f335(f304(a881,f2(a881)),x66442)))
% 59.73/59.67 [6665]P1(f335(x66651,x66652))+~P1(f335(f335(f243(a881),x66652),x66653))+P1(f335(f335(f337(a881),f453(x66651,x66653)),f335(f304(a881,f2(a881)),x66653)))
% 59.73/59.67 [6681]~P122(x66811)+~P1(f335(f335(f242(x66811),f73(x66811)),x66812))+P1(f335(f335(f242(x66811),f73(x66811)),f335(f335(f254(x66811),x66812),x66813)))
% 59.73/59.67 [6683]~P122(x66831)+~P1(f335(f335(f242(x66831),f2(x66831)),x66832))+P1(f335(f335(f242(x66831),f2(x66831)),f335(f335(f254(x66831),x66832),x66833)))
% 59.73/59.67 [6685]~P122(x66851)+~P1(f335(f335(f243(x66851),f2(x66851)),x66852))+P1(f335(f335(f243(x66851),f2(x66851)),f335(f335(f254(x66851),x66852),x66853)))
% 59.73/59.67 [6709]~P1(f335(x67091,x67093))+~P1(f335(f335(f243(a881),x67093),x67092))+P1(f335(f335(f337(a881),f452(x67091,x67092)),f335(f304(a881,f2(a881)),x67092)))
% 59.73/59.67 [6717]P1(f335(f56(x67171),x67172))+~P1(f335(f56(x67171),x67173))+~P1(f335(f335(f242(f888(x67171,a879)),x67172),x67173))
% 59.73/59.67 [6718]P1(f335(f56(x67181),x67182))+~P1(f335(f56(x67181),x67183))+~P1(f335(f335(f242(f888(x67181,a879)),x67182),x67183))
% 59.73/59.67 [6726]P1(f335(x67261,x67262))+~P1(f335(x67261,f454(x67261,x67263)))+~P1(f335(f335(f337(a881),x67262),f335(f304(a881,f2(a881)),x67263)))
% 59.73/59.67 [6738]E(x67381,f2(a881))+P1(f335(x67382,f372(x67381,x67383,x67382)))+~P1(f335(x67382,f335(f335(f30(a881),x67383),x67381)))
% 59.73/59.67 [6746]~P123(x67462)+E(x67461,f2(x67462))+~E(f335(f335(f75(x67462),f335(f335(f76(x67462),x67463),x67463)),f335(f335(f76(x67462),x67461),x67461)),f2(x67462))
% 59.73/59.67 [6747]~P123(x67472)+E(x67471,f2(x67472))+~E(f335(f335(f75(x67472),f335(f335(f76(x67472),x67471),x67471)),f335(f335(f76(x67472),x67473),x67473)),f2(x67472))
% 59.73/59.67 [6792]E(x67921,f2(a881))+~P1(f335(x67922,f373(x67921,x67923,x67922)))+P1(f335(x67922,f335(f335(f30(a881),x67923),x67921)))
% 59.73/59.67 [6797]~P106(x67971)+~P15(x67971,x67973)+P15(x67971,f335(f335(f141(x67971,x67971,f5(x67971)),x67972),x67973))
% 59.73/59.67 [6840]P1(f335(x68401,f372(x68402,x68403,x68401)))+P1(f335(x68401,f2(a881)))+~P1(f335(x68401,f335(f335(f30(a881),x68403),x68402)))
% 59.73/59.67 [6846]~P97(x68461)+E(f335(f97(x68461),x68462),f335(f97(x68461),x68463))+~P28(x68461,f335(f97(x68461),f335(f335(f75(a1),x68462),f335(f74(a1),x68463))))
% 59.73/59.67 [6914]E(x69141,f2(a1))+E(x69142,f2(a1))+~P1(f335(f43(x69142,x69142),f335(f335(f264(a1,a1),x69143),x69141)))
% 59.73/59.67 [6915]E(x69151,f73(a1))+E(x69152,f2(a1))+~P1(f335(f43(x69152,x69152),f335(f335(f264(a1,a1),x69151),x69153)))
% 59.73/59.67 [6928]P1(f335(x69281,x69282))+P1(f335(f335(f243(a881),f454(x69281,x69283)),x69283))+~P1(f335(f335(f337(a881),x69282),f335(f304(a881,f2(a881)),x69283)))
% 59.73/59.67 [6950]~P1(f335(x69501,f356(x69503,x69502,x69501)))+~P1(f335(x69501,f2(a881)))+P1(f335(x69501,f335(f335(f23(a881),x69502),x69503)))
% 59.73/59.67 [6951]~P1(f335(x69511,f357(x69513,x69512,x69511)))+~P1(f335(x69511,f2(a881)))+P1(f335(x69511,f335(f335(f23(a881),x69512),x69513)))
% 59.73/59.67 [6952]~P1(f335(x69521,f373(x69523,x69522,x69521)))+~P1(f335(x69521,f2(a881)))+P1(f335(x69521,f335(f335(f30(a881),x69522),x69523)))
% 59.73/59.67 [6970]~P1(f335(x69701,x69703))+P1(f335(f335(f243(a881),f455(x69701,x69702)),x69702))+~P1(f335(f335(f337(a881),x69703),f335(f304(a881,f2(a881)),x69702)))
% 59.73/59.67 [6971]E(f335(f335(f23(a881),f335(f335(f23(a881),x69711),x69712)),f335(f335(f23(a881),x69713),x69712)),f335(f335(f23(a881),x69711),x69713))+~P1(f335(f335(f242(a881),x69712),x69711))+~P1(f335(f335(f242(a881),x69712),x69713))
% 59.73/59.67 [7005]~P80(x70051)+~P1(f335(f335(f242(x70051),f335(f74(x70051),x70053)),x70052))+P1(f335(f335(f242(x70051),f335(f74(x70051),x70052)),x70053))
% 59.73/59.67 [7006]~P80(x70061)+~P1(f335(f335(f242(x70061),f335(f74(x70061),x70063)),x70062))+P1(f335(f335(f242(x70061),f335(f74(x70061),x70062)),x70063))
% 59.73/59.67 [7007]~P88(x70071)+~P1(f335(f335(f242(x70071),f335(f70(x70071),x70072)),x70073))+P1(f335(f335(f242(x70071),f335(f74(x70071),x70072)),x70073))
% 59.73/59.67 [7008]~P88(x70081)+~P1(f335(f335(f242(x70081),f335(f70(x70081),x70082)),x70083))+P1(f335(f335(f242(x70081),f335(f74(x70081),x70082)),x70083))
% 59.73/59.67 [7009]~P80(x70091)+~P1(f335(f335(f243(x70091),f335(f74(x70091),x70093)),x70092))+P1(f335(f335(f243(x70091),f335(f74(x70091),x70092)),x70093))
% 59.73/59.67 [7010]~P80(x70101)+~P1(f335(f335(f243(x70101),f335(f74(x70101),x70103)),x70102))+P1(f335(f335(f243(x70101),f335(f74(x70101),x70102)),x70103))
% 59.73/59.67 [7011]~P119(x70111)+~P1(f335(f335(f243(x70111),f335(f70(x70111),x70112)),x70113))+P1(f335(f335(f243(x70111),f335(f74(x70111),x70112)),x70113))
% 59.73/59.67 [7044]~P1(f335(x70443,f356(x70442,x70441,x70443)))+P1(f335(f335(f243(a881),x70441),x70442))+P1(f335(x70443,f335(f335(f23(a881),x70441),x70442)))
% 59.73/59.67 [7045]~P1(f335(x70453,f357(x70452,x70451,x70453)))+P1(f335(f335(f243(a881),x70451),x70452))+P1(f335(x70453,f335(f335(f23(a881),x70451),x70452)))
% 59.73/59.67 [7096]~E(f641(x70963,x70962,x70961),f642(x70963,x70962,x70961))+E(f335(f335(f95(f888(x70961,a879)),x70962),f31(f888(x70961,a879),x70963)),f188(f888(x70961,a879)))+P1(f335(f335(f337(f888(x70961,a879)),x70962),x70963))
% 59.73/59.67 [7105]~P1(f335(f56(x71051),x71053))+P1(f335(f56(x71051),f32(f888(x71051,a879),x71052)))+~P1(f335(f335(f337(f888(x71051,a879)),x71053),x71052))
% 59.73/59.67 [7164]~P106(x71641)+E(f335(f335(f104(f888(x71641,a879)),f335(f304(x71641,x71642),x71643)),f335(f335(f312(x71641),x71643),f188(f888(x71641,a879)))),f305(x71641,x71642,x71643))+~P1(f335(f335(f242(x71641),x71642),x71643))
% 59.73/59.67 [7165]E(x71651,f2(a881))+P1(f335(f335(f243(a881),f374(x71651,x71653,x71652)),x71651))+P1(f335(x71652,f335(f335(f30(a881),x71653),x71651)))
% 59.73/59.67 [7195]P1(f335(f335(f243(a881),f335(f189(f882(x71951)),x71952)),f812(x71953,x71951)))+~P1(f335(f56(f882(x71951)),x71953))+~P1(f335(f335(f337(f882(x71951)),x71952),x71953))
% 59.73/59.67 [7200]E(x72001,x72002)+~P1(f335(f335(f242(f888(x72003,a879)),x72001),x72002))+P1(f335(f335(f243(f888(x72003,a879)),x72001),x72002))
% 59.73/59.67 [7201]E(x72011,x72012)+~P1(f335(f335(f242(f888(x72013,a879)),x72011),x72012))+P1(f335(f335(f243(f888(x72013,a879)),x72011),x72012))
% 59.73/59.67 [7213]E(x72131,x72132)+~E(f335(f189(f882(x72133)),x72131),f335(f189(f882(x72133)),x72132))+P1(f335(f335(f243(a881),f684(x72133,x72131,x72132)),f335(f189(f882(x72133)),x72132)))
% 59.73/59.67 [7260]P8(x72601,x72602,x72603)+~E(f335(f262(x72601,x72601),x72603),x72602)+~E(f335(f335(f291(x72601,x72601,x72601),f335(f289(x72601,x72601),x72603)),x72603),x72603)
% 59.73/59.67 [7337]~P1(f335(x73371,f2(a881)))+P1(f335(f335(f243(a881),f374(x73373,x73372,x73371)),x73373))+P1(f335(x73371,f335(f335(f30(a881),x73372),x73373)))
% 59.73/59.67 [7346]~P106(x73461)+E(f335(f335(f104(f888(x73461,a879)),f308(x73461,x73462,x73463)),f335(f335(f312(x73461),x73463),f188(f888(x73461,a879)))),f307(x73461,x73462,x73463))+~P1(f335(f335(f243(x73461),x73462),x73463))
% 59.73/59.67 [7443]~P1(f335(f56(x74431),x74433))+P1(f335(f335(f242(a881),f335(f29(x74431),x74432)),f335(f29(x74431),x74433)))+~P1(f335(f335(f242(f888(x74431,a879)),x74432),x74433))
% 59.73/59.67 [7444]~P1(f335(f56(x74441),x74443))+P1(f335(f335(f243(a881),f335(f29(x74441),x74442)),f335(f29(x74441),x74443)))+~P1(f335(f335(f243(f888(x74441,a879)),x74442),x74443))
% 59.73/59.67 [7579]E(x75791,x75792)+~P1(f335(f335(f242(f888(x75793,a879)),x75792),x75791))+~P1(f335(f335(f242(f888(x75793,a879)),x75791),x75792))
% 59.73/59.67 [7580]E(x75801,x75802)+~P1(f335(f335(f242(f888(x75803,a879)),x75802),x75801))+~P1(f335(f335(f242(f888(x75803,a879)),x75801),x75802))
% 59.73/59.67 [7583]~P106(x75831)+P15(x75831,x75832)+~P15(x75831,f335(f335(f141(x75831,x75831,f5(x75831)),x75833),x75832))
% 59.73/59.67 [7652]~P1(f335(f335(f243(a881),x76523),x76522))+~P1(f335(f335(f243(a881),x76523),x76521))+P1(f335(f335(f243(a881),f335(f335(f23(a881),x76521),x76522)),f335(f335(f23(a881),x76521),x76523)))
% 59.73/59.67 [7653]~P1(f335(f335(f242(a881),x76532),x76531))+~P1(f335(f335(f243(a881),x76531),x76533))+P1(f335(f335(f243(a881),f335(f335(f23(a881),x76531),x76532)),f335(f335(f23(a881),x76533),x76532)))
% 59.73/59.67 [7668]~P1(f335(f335(f243(a1),x76682),f2(a1)))+~P1(f335(f335(f242(a1),x76683),x76681))+P1(f335(f335(f242(a1),f335(f335(f30(a1),x76681),x76682)),f335(f335(f30(a1),x76683),x76682)))
% 59.73/59.67 [7685]~P1(f335(f335(f243(a881),f2(a881)),x76851))+~P1(f335(f335(f242(a881),x76852),x76853))+P1(f335(f335(f242(a881),f335(f335(f76(a881),x76851),x76852)),f335(f335(f76(a881),x76851),x76853)))
% 59.73/59.67 [7686]~P1(f335(f335(f243(a881),f2(a881)),x76863))+~P1(f335(f335(f242(a881),x76863),x76862))+P1(f335(f335(f242(a881),f335(f335(f30(a881),x76861),x76862)),f335(f335(f30(a881),x76861),x76863)))
% 59.73/59.67 [7687]~P1(f335(f335(f243(a1),f2(a1)),x76872))+~P1(f335(f335(f242(a1),x76871),x76873))+P1(f335(f335(f242(a1),f335(f335(f30(a1),x76871),x76872)),f335(f335(f30(a1),x76873),x76872)))
% 59.73/59.67 [7688]~P1(f335(f335(f243(a881),f2(a881)),x76881))+~P1(f335(f335(f243(a881),x76882),x76883))+P1(f335(f335(f243(a881),f335(f335(f76(a881),x76881),x76882)),f335(f335(f76(a881),x76881),x76883)))
% 59.73/59.67 [7689]~P1(f335(f335(f243(a881),f2(a881)),x76891))+~P1(f335(f335(f243(a881),x76892),x76893))+P1(f335(f335(f243(a881),f335(f335(f76(a881),x76891),x76892)),f335(f335(f76(a881),x76891),x76893)))
% 59.73/59.67 [7690]~P1(f335(f335(f243(a881),f2(a881)),x76902))+~P1(f335(f335(f243(a881),x76901),x76903))+P1(f335(f335(f243(a881),f335(f335(f76(a881),x76901),x76902)),f335(f335(f76(a881),x76903),x76902)))
% 59.73/59.67 [7691]~P1(f335(f335(f243(a881),f2(a881)),x76912))+~P1(f335(f335(f243(a881),x76911),x76913))+P1(f335(f335(f243(a881),f335(f335(f76(a881),x76911),x76912)),f335(f335(f76(a881),x76913),x76912)))
% 59.73/59.67 [7692]~P1(f335(f335(f243(a881),f2(a881)),x76921))+~P1(f335(f335(f243(a881),x76922),x76923))+P1(f335(f335(f243(a881),f335(f335(f76(a881),x76921),x76922)),f335(f335(f76(a881),x76921),x76923)))
% 59.73/59.67 [7693]~P1(f335(f335(f243(a1),f2(a1)),x76931))+~P1(f335(f335(f243(a1),x76932),x76933))+P1(f335(f335(f243(a1),f335(f335(f76(a1),x76931),x76932)),f335(f335(f76(a1),x76931),x76933)))
% 59.73/59.67 [7744]E(x77441,f2(a881))+E(f335(f335(f75(a881),f335(f335(f76(a881),x77441),f373(x77441,x77442,x77443))),f374(x77441,x77442,x77443)),x77442)+P1(f335(x77443,f335(f335(f30(a881),x77442),x77441)))
% 59.73/59.67 [7802]E(f335(f335(f75(a881),f335(f335(f76(a881),x78021),f373(x78021,x78022,x78023))),f374(x78021,x78022,x78023)),x78022)+~P1(f335(x78023,f2(a881)))+P1(f335(x78023,f335(f335(f30(a881),x78022),x78021)))
% 59.73/59.67 [7820]~P1(f335(f56(x78201),x78203))+P1(f335(f335(f337(x78201),f367(x78202,x78203,x78201)),x78203))+P1(f335(f335(f243(a881),f2(a881)),f335(f335(f9(x78201,a881),x78202),x78203)))
% 59.73/59.67 [7821]~P1(f335(f56(x78211),x78213))+P1(f335(f335(f337(x78211),f530(x78212,x78213,x78211)),x78213))+P1(f335(f335(f243(a881),f2(a881)),f335(f335(f9(x78211,a881),x78212),x78213)))
% 59.73/59.67 [8114]E(x81141,f188(f888(x81142,a879)))+E(x81141,f335(f335(f312(x81142),x81143),f188(f888(x81142,a879))))+~P1(f335(f335(f242(f888(x81142,a879)),x81141),f335(f335(f312(x81142),x81143),f188(f888(x81142,a879)))))
% 59.73/59.67 [8131]~P4(x81311)+P12(x81311,x81312,x81313)+P1(f335(f335(f337(f882(x81311)),f683(x81313,x81312,x81311)),f335(f166(f882(x81311)),f49(x81311,x81313,f50(x81311)))))
% 59.73/59.67 [8137]~P106(x81371)+~P15(x81371,x81373)+P15(x81371,f335(f335(f131(x81371),f335(f189(f882(x81371)),f171(x81371,x81372,x81373))),x81373))
% 59.73/59.67 [8148]~P1(f335(f335(f243(a881),f2(a881)),x81483))+P1(f335(f335(f242(a881),x81481),x81482))+~P1(f335(f335(f242(a881),f335(f335(f76(a881),x81483),x81481)),f335(f335(f76(a881),x81483),x81482)))
% 59.73/59.67 [8149]~P1(f335(f335(f243(a881),f2(a881)),x81493))+P1(f335(f335(f242(a881),x81491),x81492))+~P1(f335(f335(f242(a881),f335(f335(f76(a881),x81493),x81491)),f335(f335(f76(a881),x81493),x81492)))
% 59.73/59.67 [8150]~P1(f335(f335(f243(a881),f2(a881)),x81503))+P1(f335(f335(f242(a881),x81501),x81502))+~P1(f335(f335(f242(a881),f335(f335(f76(a881),x81501),x81503)),f335(f335(f76(a881),x81502),x81503)))
% 59.73/59.67 [8151]~P1(f335(f335(f243(a881),f2(a881)),x81513))+P1(f335(f335(f243(a881),x81511),x81512))+~P1(f335(f335(f243(a881),f335(f335(f76(a881),x81513),x81511)),f335(f335(f76(a881),x81513),x81512)))
% 59.73/59.67 [8152]~P1(f335(f335(f243(a881),f2(a881)),x81523))+P1(f335(f335(f243(a881),x81521),x81522))+~P1(f335(f335(f243(a881),f335(f335(f254(a881),x81523),x81521)),f335(f335(f254(a881),x81523),x81522)))
% 59.73/59.67 [8179]~P4(x81791)+~P11(x81791,x81793,x81792)+P1(f335(f335(f337(f882(x81791)),f675(x81792,x81793,x81791)),f335(f166(f882(x81791)),f49(x81791,x81792,f50(x81791)))))
% 59.73/59.67 [8195]~E(f335(f335(f95(f888(x81951,a879)),f642(x81953,x81952,x81951)),f641(x81953,x81952,x81951)),f188(f888(x81951,a879)))+E(f335(f335(f95(f888(x81951,a879)),x81952),f31(f888(x81951,a879),x81953)),f188(f888(x81951,a879)))+P1(f335(f335(f337(f888(x81951,a879)),x81952),x81953))
% 59.73/59.67 [8211]E(x82111,f107(x82112))+~E(f335(f135(f882(x82112),f882(x82112),f127(x82112),f107(x82112)),x82113),f107(x82112))+~P1(f335(f335(f337(f882(x82112)),x82111),f335(f166(f882(x82112)),x82113)))
% 59.73/59.67 [8212]E(x82121,f107(x82122))+~E(f335(f135(f882(x82122),f882(x82122),f127(x82122),f107(x82122)),x82123),f107(x82122))+~P1(f335(f335(f337(f882(x82122)),x82121),f335(f166(f882(x82122)),x82123)))
% 59.73/59.67 [8268]E(x82681,f188(f888(f888(x82682,a879),a879)))+P1(f335(f335(f337(f888(x82682,a879)),f645(x82683,x82681,x82682)),x82681))+P1(f335(f335(f242(f888(x82682,a879)),f32(f888(x82682,a879),x82681)),x82683))
% 59.73/59.67 [8275]~P73(x82751)+~P77(x82751)+E(f335(f335(f9(a1,x82751),f335(f335(f8(a881,x82751,a1),x82752),a98)),f335(f313(a881,a1,f94(a1)),x82753)),f335(f335(f9(a881,x82751),x82752),x82753))
% 59.73/59.67 [8276]~P73(x82761)+~P77(x82761)+E(f335(f335(f6(a1,x82761),f335(f335(f8(a881,x82761,a1),x82762),a98)),f335(f313(a881,a1,f94(a1)),x82763)),f335(f335(f6(a881,x82761),x82762),x82763))
% 59.73/59.67 [8318]~P1(f335(f56(x83181),x83183))+~P1(f335(f335(f243(a881),f2(a881)),f335(x83182,f367(x83182,x83183,x83181))))+P1(f335(f335(f243(a881),f2(a881)),f335(f335(f9(x83181,a881),x83182),x83183)))
% 59.73/59.67 [8319]~P1(f335(f56(x83191),x83193))+~P1(f335(f335(f243(a881),f2(a881)),f335(x83192,f530(x83192,x83193,x83191))))+P1(f335(f335(f243(a881),f2(a881)),f335(f335(f9(x83191,a881),x83192),x83193)))
% 59.73/59.67 [8353]~P67(x83532)+E(x83531,f73(x83532))+E(f335(f335(f292(x83532),f335(f335(f23(x83532),f335(f335(f254(x83532),x83531),x83533)),f73(x83532))),f335(f335(f23(x83532),x83531),f73(x83532))),f335(f335(f6(a881,x83532),f335(f254(x83532),x83531)),f335(f304(a881,f2(a881)),x83533)))
% 59.73/59.67 [8413]E(x84131,f2(a881))+~P1(f335(x84133,f335(f335(f30(a881),x84132),x84131)))+P1(f335(f335(f243(a881),x84132),f335(f335(f76(a881),x84131),f335(a106,f372(x84131,x84132,x84133)))))
% 59.73/59.67 [8431]P1(f335(x84311,f2(a881)))+~P1(f335(x84311,f335(f335(f30(a881),x84312),x84313)))+P1(f335(f335(f243(a881),x84312),f335(f335(f76(a881),x84313),f335(a106,f372(x84313,x84312,x84311)))))
% 59.73/59.67 [8470]E(x84701,f2(a881))+~P1(f335(x84703,f335(f335(f30(a881),x84702),x84701)))+P1(f335(f335(f242(a881),f335(f335(f76(a881),x84701),f372(x84701,x84702,x84703))),x84702))
% 59.73/59.67 [8504]P1(f335(x85041,f2(a881)))+~P1(f335(x85041,f335(f335(f30(a881),x85043),x85042)))+P1(f335(f335(f242(a881),f335(f335(f76(a881),x85042),f372(x85042,x85043,x85041))),x85043))
% 59.73/59.67 [8507]~P106(x85071)+E(f335(f335(f141(x85071,x85071,f5(x85071)),x85072),x85073),f142(x85071,x85071,f5(x85071),x85072,x85073))+P1(f335(f335(f337(x85071),x85072),f335(f166(x85071),x85073)))
% 59.73/59.67 [8544]~E(f335(x85443,f562(x85442,x85443,x85441)),f335(x85443,f566(x85442,x85443,x85441)))+~P57(x85441,f335(x85443,f563(x85442,x85443,x85441)))+P57(x85441,f335(f335(f33(x85442,f888(x85441,f888(x85441,a879))),f252(f888(x85442,a879))),x85443))
% 59.73/59.67 [8553]E(x85531,f188(f888(f888(x85532,a879),a879)))+~P1(f335(f335(f242(f888(x85532,a879)),f645(x85533,x85531,x85532)),x85533))+P1(f335(f335(f242(f888(x85532,a879)),f32(f888(x85532,a879),x85531)),x85533))
% 59.73/59.67 [8611]~P69(x86111)+~P1(f335(f335(f243(x86111),x86112),x86113))+P1(f335(f335(f243(x86111),x86112),f335(f335(f292(x86111),f335(f335(f75(x86111),x86112),x86113)),f335(f335(f75(x86111),f73(x86111)),f73(x86111)))))
% 59.73/59.67 [8668]~P1(f335(f335(x86681,f385(x86681,x86683,x86682)),f386(x86681,x86683,x86682)))+P1(f335(f335(x86681,x86682),x86683))+~P1(f335(f323(f887(a1,a1),a224),f335(f335(f264(a1,a1),x86682),x86683)))
% 59.73/59.67 [8669]~P1(f335(f335(x86691,f395(x86691,x86693,x86692)),f396(x86691,x86693,x86692)))+P1(f335(f335(x86691,x86692),x86693))+~P1(f335(f323(f887(a1,a1),a51),f335(f335(f264(a1,a1),x86692),x86693)))
% 59.73/59.67 [8670]~P1(f335(f335(x86701,f405(x86701,x86703,x86702)),f406(x86701,x86703,x86702)))+P1(f335(f335(x86701,x86702),x86703))+~P1(f335(f323(f887(a1,a1),a46),f335(f335(f264(a1,a1),x86702),x86703)))
% 59.73/59.67 [8671]~P1(f335(f335(x86711,f509(x86711,x86713,x86712)),f511(x86711,x86713,x86712)))+P1(f335(f335(x86711,x86712),x86713))+~P1(f335(f323(f887(a881,a881),a222),f335(f335(f264(a881,a881),x86712),x86713)))
% 59.73/59.67 [8672]~P1(f335(f335(x86721,f692(x86721,x86723,x86722)),f699(x86721,x86723,x86722)))+P1(f335(f335(x86721,x86722),x86723))+~P1(f335(f323(f887(a1,a1),a176),f335(f335(f264(a1,a1),x86722),x86723)))
% 59.73/59.67 [8673]~P1(f335(f335(x86731,f803(x86731,x86733,x86732)),f804(x86731,x86733,x86732)))+P1(f335(f335(x86731,x86732),x86733))+~P1(f335(f323(f887(a1,a1),a126),f335(f335(f264(a1,a1),x86732),x86733)))
% 59.73/59.67 [8931]P1(f335(f335(x89311,x89312),x89313))+P1(f335(f323(f887(a881,a881),a222),f335(f335(f264(a881,a881),f509(x89311,x89313,x89312)),f511(x89311,x89313,x89312))))+~P1(f335(f323(f887(a881,a881),a222),f335(f335(f264(a881,a881),x89312),x89313)))
% 59.73/59.67 [8932]P1(f335(f335(x89321,x89322),x89323))+P1(f335(f323(f887(a1,a1),a224),f335(f335(f264(a1,a1),f385(x89321,x89323,x89322)),f386(x89321,x89323,x89322))))+~P1(f335(f323(f887(a1,a1),a224),f335(f335(f264(a1,a1),x89322),x89323)))
% 59.73/59.67 [8933]P1(f335(f335(x89331,x89332),x89333))+P1(f335(f323(f887(a1,a1),a51),f335(f335(f264(a1,a1),f395(x89331,x89333,x89332)),f396(x89331,x89333,x89332))))+~P1(f335(f323(f887(a1,a1),a51),f335(f335(f264(a1,a1),x89332),x89333)))
% 59.73/59.67 [8934]P1(f335(f335(x89341,x89342),x89343))+P1(f335(f323(f887(a1,a1),a46),f335(f335(f264(a1,a1),f405(x89341,x89343,x89342)),f406(x89341,x89343,x89342))))+~P1(f335(f323(f887(a1,a1),a46),f335(f335(f264(a1,a1),x89342),x89343)))
% 59.73/59.67 [8935]P1(f335(f335(x89351,x89352),x89353))+P1(f335(f323(f887(a1,a1),a176),f335(f335(f264(a1,a1),f692(x89351,x89353,x89352)),f699(x89351,x89353,x89352))))+~P1(f335(f323(f887(a1,a1),a176),f335(f335(f264(a1,a1),x89352),x89353)))
% 59.73/59.67 [8936]P1(f335(f335(x89361,x89362),x89363))+P1(f335(f323(f887(a1,a1),a126),f335(f335(f264(a1,a1),f803(x89361,x89363,x89362)),f804(x89361,x89363,x89362))))+~P1(f335(f323(f887(a1,a1),a126),f335(f335(f264(a1,a1),x89362),x89363)))
% 59.73/59.67 [9275]~P1(f335(f56(x92751),x92753))+P1(f335(f335(f337(f887(f888(x92751,a879),f888(x92751,a879))),f335(f335(f264(f888(x92751,a879),f888(x92751,a879)),x92752),x92753)),f309(x92751)))+~P1(f335(f335(f243(f888(x92751,a879)),x92752),x92753))
% 59.73/59.67 [9346]~P57(x93461,f335(x93463,f563(x93462,x93463,x93461)))+P57(x93461,f335(f335(f33(x93462,f888(x93461,f888(x93461,a879))),f252(f888(x93462,a879))),x93463))+~E(f335(f335(f95(f888(x93461,a879)),f258(x93461,x93461,f335(x93463,f562(x93462,x93463,x93461)))),f259(x93461,x93461,f335(x93463,f566(x93462,x93463,x93461)))),f188(f888(x93461,a879)))
% 59.73/59.67 [9546]P46(x95461,x95462,x95463)+P1(f335(f335(f337(f887(x95461,x95461)),f552(x95463,x95462,x95461)),x95463))+~P1(f335(f335(f337(f887(x95461,x95461)),f335(f335(f264(x95461,x95461),f551(x95463,x95462,x95461)),f551(x95463,x95462,x95461))),x95463))
% 59.73/59.67 [10135]P46(x101351,x101352,x101353)+~P1(f335(f335(f268(x101351,x101351,a879),f335(f335(f7(x101351,f888(x101351,a879),f888(x101351,a879)),f335(f335(f8(f888(a879,a879),f888(f888(x101351,a879),f888(x101351,a879)),x101351),f8(a879,a879,x101351)),f335(f335(f8(a879,f888(a879,a879),x101351),a333),f335(f335(f7(x101351,f888(x101351,a879),a879),f337(x101351)),x101352)))),f335(f335(f7(x101351,f888(x101351,a879),a879),f337(x101351)),x101352))),f552(x101353,x101352,x101351)))+~P1(f335(f335(f337(f887(x101351,x101351)),f335(f335(f264(x101351,x101351),f551(x101353,x101352,x101351)),f551(x101353,x101352,x101351))),x101353))
% 59.73/59.67 [5678]~P58(x56782)+E(x56781,f2(x56782))+E(f335(f335(f30(x56782),f335(f335(f76(x56782),x56783),x56781)),x56781),x56783)
% 59.73/59.67 [5679]~P58(x56792)+E(x56791,f2(x56792))+E(f335(f335(f30(x56792),f335(f335(f76(x56792),x56791),x56793)),x56791),x56793)
% 59.73/59.67 [6471]~P77(x64711)+~E(f335(x64712,f2(a881)),f2(x64711))+E(f335(f335(f6(a881,x64711),x64712),f335(f304(a881,f335(a106,f2(a881))),x64713)),f335(f335(f6(a881,x64711),x64712),f335(f304(a881,f2(a881)),x64713)))
% 59.73/59.67 [6605]~P58(x66052)+E(x66051,f2(x66052))+E(f335(f335(f30(x66052),f335(f335(f75(x66052),x66053),x66051)),x66051),f335(f335(f75(x66052),f335(f335(f30(x66052),x66053),x66051)),f73(x66052)))
% 59.73/59.67 [6606]~P58(x66062)+E(x66061,f2(x66062))+E(f335(f335(f30(x66062),f335(f335(f75(x66062),x66061),x66063)),x66061),f335(f335(f75(x66062),f335(f335(f30(x66062),x66063),x66061)),f73(x66062)))
% 59.73/59.67 [6828]~P1(f335(x68283,f2(a1)))+P1(f335(f335(f242(a881),x68281),x68282))+P1(f335(x68283,f335(f94(a1),f335(f335(f23(a881),x68282),x68281))))
% 59.73/59.67 [6934]P1(f335(f335(f243(a881),x69342),x69341))+P1(f335(f335(f242(a881),x69341),x69342))+P1(f335(x69343,f335(f94(a1),f335(f335(f23(a881),x69342),x69341))))
% 59.73/59.67 [7004]E(f335(f335(f75(a881),f335(f97(a881),x70041)),f335(f335(f75(a881),f335(f97(a881),x70042)),x70043)),f335(f335(f75(a881),f335(f97(a881),x70041)),x70043))+P1(f335(a193,f335(f97(a1),x70041)))+~P1(f335(a193,f335(f97(a1),x70042)))
% 59.73/59.67 [7083]~E(x70832,f335(f335(f30(a881),x70833),x70831))+~P1(f335(f335(f243(a881),f2(a881)),x70831))+P1(f335(f335(f242(a881),f335(f335(f76(a881),x70831),x70832)),x70833))
% 59.73/59.67 [7197]~P1(f335(f56(x71971),x71973))+~P1(f335(f56(x71971),x71972))+P1(f335(f56(x71971),f335(f335(f104(f888(x71971,a879)),x71972),x71973)))
% 59.73/59.67 [7198]~P1(f335(f56(x71981),x71983))+~P1(f335(f56(x71981),x71982))+P1(f335(f56(x71981),f335(f335(f104(f888(x71981,a879)),x71982),x71983)))
% 59.73/59.67 [7199]~P1(f335(f56(x71991),x71993))+~P1(f335(f56(x71991),x71992))+P1(f335(f56(x71991),f335(f335(f23(f888(x71991,a879)),x71992),x71993)))
% 59.73/59.67 [7494]~P106(x74941)+~P1(f335(f56(x74941),x74942))+E(f132(x74941,f335(f335(f23(f888(x74941,a879)),x74942),f335(f335(f312(x74941),x74943),f188(f888(x74941,a879))))),f164(x74941,x74943,f132(x74941,x74942)))
% 59.73/59.67 [7558]P1(f335(x75581,f2(a1)))+~P1(f335(f335(f243(a881),x75582),x75583))+~P1(f335(x75581,f335(f94(a1),f335(f335(f23(a881),x75582),x75583))))
% 59.73/59.67 [7577]~P1(f335(f56(x75771),x75772))+E(f335(f29(x75771),f335(f335(f23(f888(x75771,a879)),x75772),f335(f335(f312(x75771),x75773),f188(f888(x75771,a879))))),f335(f29(x75771),x75772))+P1(f335(f335(f337(x75771),x75773),x75772))
% 59.73/59.67 [7709]~P122(x77091)+~P1(f335(f335(f243(x77091),f73(x77091)),x77092))+P1(f335(f335(f243(x77091),f73(x77091)),f335(f335(f76(x77091),x77092),f335(f335(f254(x77091),x77092),x77093))))
% 59.73/59.67 [7754]~P1(f335(f56(x77541),x77543))+E(f335(f335(f23(a881),f335(f29(x77541),x77542)),f335(f29(x77541),x77543)),f335(f29(x77541),f335(f335(f23(f888(x77541,a879)),x77542),x77543)))+~P1(f335(f335(f242(f888(x77541,a879)),x77543),x77542))
% 59.73/59.67 [7811]~P1(f335(f335(f242(a881),x78112),x78113))+~P1(f335(f335(f242(a881),x78111),f335(f335(f23(a881),x78113),x78112)))+P1(f335(f335(f242(a881),f335(f335(f75(a881),x78111),x78112)),x78113))
% 59.73/59.67 [7863]P1(f335(f56(x78631),x78632))+~P1(f335(f56(x78631),x78633))+~P1(f335(f56(x78631),f335(f335(f23(f888(x78631,a879)),x78632),x78633)))
% 59.73/59.67 [7868]~P1(f335(f56(x78681),x78682))+E(f335(f29(x78681),f335(f335(f23(f888(x78681,a879)),x78682),f335(f335(f312(x78681),x78683),f188(f888(x78681,a879))))),f335(f335(f23(a881),f335(f29(x78681),x78682)),f73(a881)))+~P1(f335(f335(f337(x78681),x78683),x78682))
% 59.73/59.67 [7869]~P1(f335(f56(x78691),x78692))+E(f335(f29(x78691),f335(f335(f23(f888(x78691,a879)),x78692),f335(f335(f312(x78691),x78693),f188(f888(x78691,a879))))),f335(f335(f23(a881),f335(f29(x78691),x78692)),f73(a881)))+~P1(f335(f335(f337(x78691),x78693),x78692))
% 59.73/59.67 [7946]P57(x79461,x79462)+~P57(x79461,x79463)+~P1(f335(f335(f242(f888(x79461,f888(x79461,a879))),x79462),x79463))
% 59.73/59.67 [7993]~P1(f335(f335(f242(a881),x79933),x79932))+P1(f335(f335(f242(a881),x79931),f335(f335(f23(a881),x79932),x79933)))+~P1(f335(f335(f242(a881),f335(f335(f75(a881),x79931),x79933)),x79932))
% 59.73/59.67 [8011]P36(x80111,x80112)+~P36(x80111,x80113)+~P1(f335(f335(f242(f888(f887(x80111,x80111),a879)),x80112),x80113))
% 59.73/59.67 [8012]P55(x80121,x80122)+~P55(x80121,x80123)+~P1(f335(f335(f242(f888(f887(x80121,x80121),a879)),x80122),x80123))
% 59.73/59.67 [8246]~P122(x82461)+~P1(f335(f335(f243(x82461),f73(x82461)),x82462))+P1(f335(f335(f243(x82461),f335(f335(f254(x82461),x82462),x82463)),f335(f335(f76(x82461),x82462),f335(f335(f254(x82461),x82462),x82463))))
% 59.73/59.67 [8336]~P1(f335(x83361,f2(a1)))+~P1(f335(x83361,f335(f335(f23(a1),f335(f94(a1),x83362)),f335(f94(a1),x83363))))+P1(f335(x83361,f335(f94(a1),f335(f335(f23(a881),x83362),x83363))))
% 59.73/59.67 [8349]~P1(f335(f335(f242(a881),x83493),x83492))+P1(f335(x83491,f335(f335(f23(a1),f335(f94(a1),x83492)),f335(f94(a1),x83493))))+~P1(f335(x83491,f335(f94(a1),f335(f335(f23(a881),x83492),x83493))))
% 59.73/59.67 [8368]P1(f335(f335(f243(a881),x83681),x83682))+~P1(f335(x83683,f335(f335(f23(a1),f335(f94(a1),x83681)),f335(f94(a1),x83682))))+P1(f335(x83683,f335(f94(a1),f335(f335(f23(a881),x83681),x83682))))
% 59.73/59.67 [8425]~P123(x84252)+E(x84251,f2(x84252))+P1(f335(f335(f243(x84252),f2(x84252)),f335(f335(f75(x84252),f335(f335(f76(x84252),x84253),x84253)),f335(f335(f76(x84252),x84251),x84251))))
% 59.73/59.67 [8426]~P123(x84262)+E(x84261,f2(x84262))+P1(f335(f335(f243(x84262),f2(x84262)),f335(f335(f75(x84262),f335(f335(f76(x84262),x84261),x84261)),f335(f335(f76(x84262),x84263),x84263))))
% 59.73/59.67 [8527]~P1(f335(f335(f243(a881),f2(a881)),x85271))+~P1(f335(f335(f243(a1),x85272),x85273))+P1(f335(f335(f243(a1),f335(f335(f76(a1),f335(f94(a1),x85271)),x85272)),f335(f335(f76(a1),f335(f94(a1),x85271)),x85273)))
% 59.73/59.67 [8581]E(f335(f335(f95(f888(x85811,a879)),x85812),f31(f888(x85811,a879),x85813)),f188(f888(x85811,a879)))+P1(f335(f335(f337(f888(x85811,a879)),x85812),x85813))+P1(f335(f335(f337(f888(x85811,a879)),f642(x85813,x85812,x85811)),f335(f335(f312(f888(x85811,a879)),x85812),x85813)))
% 59.73/59.67 [8582]E(f335(f335(f95(f888(x85821,a879)),x85822),f31(f888(x85821,a879),x85823)),f188(f888(x85821,a879)))+P1(f335(f335(f337(f888(x85821,a879)),x85822),x85823))+P1(f335(f335(f337(f888(x85821,a879)),f641(x85823,x85822,x85821)),f335(f335(f312(f888(x85821,a879)),x85822),x85823)))
% 59.73/59.67 [8610]E(x86101,x86102)+~E(f335(f189(f882(x86103)),x86101),f335(f189(f882(x86103)),x86102))+P1(f335(f335(f337(f887(x86103,x86103)),f676(x86103,x86101,x86102)),f335(f166(f887(x86103,x86103)),f335(f335(f175(x86103,x86103),x86102),x86101))))
% 59.73/59.67 [8849]E(f310(x88491,x88492),f310(x88491,x88493))+~P1(f335(f335(f242(f888(f887(x88491,x88491),a879)),x88493),f310(x88491,x88492)))+~P1(f335(f335(f242(f888(f887(x88491,x88491),a879)),x88492),x88493))
% 59.73/59.67 [8909]~P46(x89091,f252(f888(x89091,a879)),x89093)+P1(f335(f335(f242(f888(f887(f882(x89091),f882(x89091)),a879)),f150(x89091,x89092)),f151(x89091,x89093)))+~P1(f335(f335(f242(f888(f887(x89091,x89091),a879)),x89092),x89093))
% 59.73/59.67 [9111]P36(x91111,x91112)+~P1(f335(f335(f337(x91111),x91113),f628(x91112,x91111)))+P1(f335(f335(f337(f887(x91111,x91111)),f335(f335(f264(x91111,x91111),f655(x91112,x91111,x91113)),x91113)),x91112))
% 59.73/59.67 [9149]~P1(f335(f56(x91491),x91492))+P1(f335(f56(f888(x91491,a879)),f335(f335(f55(x91491),x91492),x91493)))+~P1(f335(f335(f242(f888(f887(x91491,x91491),a879)),x91493),f335(f335(f266(x91491,x91491),x91492),f335(f16(f888(x91491,a879),x91491),x91492))))
% 59.73/59.67 [9184]P46(x91841,x91842,x91843)+P1(f335(f335(f337(x91841),f542(x91843,x91842,x91841)),x91842))+~P1(f335(f335(f242(f888(f887(x91841,x91841),a879)),x91843),f335(f335(f266(x91841,x91841),x91842),f335(f16(f888(x91841,a879),x91841),x91842))))
% 59.73/59.67 [9185]P46(x91851,x91852,x91853)+P1(f335(f335(f337(x91851),f546(x91852,x91853,x91851)),x91852))+~P1(f335(f335(f242(f888(f887(x91851,x91851),a879)),x91853),f335(f335(f266(x91851,x91851),x91852),f335(f16(f888(x91851,a879),x91851),x91852))))
% 59.73/59.67 [9220]~P69(x92201)+~P1(f335(f335(f243(x92201),x92202),x92203))+P1(f335(f335(f243(x92201),f335(f335(f292(x92201),f335(f335(f75(x92201),x92202),x92203)),f335(f335(f75(x92201),f73(x92201)),f73(x92201)))),x92203))
% 59.73/59.67 [9249]~P68(x92491)+P1(f335(f335(f242(x92491),x92492),x92493))+~P1(f335(f335(f242(x92491),f335(f335(f76(x92491),f507(x92493,x92492,x92491)),x92492)),x92493))
% 59.73/59.67 [9378]E(f316(x93781,x93782,x93783),f200(f882(a331)))+~P1(f335(f335(f243(a1),x93782),x93783))+~P1(f335(f323(f887(f888(a1,f885(f882(a331))),f887(a1,a1)),a320),f335(f335(f264(f888(a1,f885(f882(a331))),f887(a1,a1)),x93781),f335(f335(f264(a1,a1),x93782),x93783))))
% 59.73/59.67 [9383]E(f335(f189(f882(f882(x93831))),f335(f129(f882(x93831),f335(f335(f8(a881,a879,f882(x93831)),f335(f243(a881),x93832)),f189(f882(x93831)))),f173(x93831,x93833))),f335(f189(f882(x93831)),f335(f335(f158(f882(x93831)),x93833),x93832)))+~P15(a881,f335(f162(a881),f335(f335(f147(f882(x93831),a881),f189(f882(x93831))),x93833)))+~P1(f335(f335(f243(a881),x93832),f335(f189(f882(f882(x93831))),x93833)))
% 59.73/59.67 [9493]~P36(x94931,x94932)+P27(x94931,f335(f335(f264(f888(f887(x94931,x94931),a879),f888(f887(x94931,x94931),a879)),x94932),x94933))+~P1(f335(f335(f242(f888(f887(x94931,x94931),a879)),f335(f335(f291(x94931,x94931,x94931),x94932),x94933)),x94932))
% 59.73/59.67 [9495]E(f335(f237(f885(f882(a331)),f882(a331),f316(x94951,x94952,f335(f335(f75(a1),x94953),f73(a1))),f235(f882(a331))),f335(x94951,x94953)),f316(x94951,x94952,x94953))+P1(f335(f335(f243(a1),x94952),x94953))+~P1(f335(f323(f887(f888(a1,f885(f882(a331))),f887(a1,a1)),a320),f335(f335(f264(f888(a1,f885(f882(a331))),f887(a1,a1)),x94951),f335(f335(f264(a1,a1),x94952),x94953))))
% 59.73/59.67 [9499]E(f335(f335(f147(f882(x94991),x94991),f335(f335(f7(f882(x94991),a881,x94991),f158(x94991)),x94992)),f335(f129(f882(x94991),f335(f335(f8(a881,a879,f882(x94991)),f335(f243(a881),x94992)),f189(f882(x94991)))),f173(x94991,x94993))),f335(f335(f158(f882(x94991)),x94993),x94992))+~P15(a881,f335(f162(a881),f335(f335(f147(f882(x94991),a881),f189(f882(x94991))),x94993)))+~P1(f335(f335(f243(a881),x94992),f335(f189(f882(f882(x94991))),x94993)))
% 59.73/59.67 [9633]P46(x96331,x96332,x96333)+~P1(f335(f335(f337(f887(x96331,x96331)),f335(f335(f264(x96331,x96331),f542(x96333,x96332,x96331)),f542(x96333,x96332,x96331))),x96333))+~P1(f335(f335(f242(f888(f887(x96331,x96331),a879)),x96333),f335(f335(f266(x96331,x96331),x96332),f335(f16(f888(x96331,a879),x96331),x96332))))
% 59.73/59.67 [9634]P46(x96341,x96342,x96343)+~P1(f335(f335(f337(f887(x96341,x96341)),f335(f335(f264(x96341,x96341),f546(x96342,x96343,x96341)),f546(x96342,x96343,x96341))),x96343))+~P1(f335(f335(f242(f888(f887(x96341,x96341),a879)),x96343),f335(f335(f266(x96341,x96341),x96342),f335(f16(f888(x96341,a879),x96341),x96342))))
% 59.73/59.67 [9820]~P137(x98201)+~P121(x98201)+E(f335(f335(f292(x98201),f335(f96(x98201),f335(f335(f68(f887(a1,a1),a1,x98202,f263(a1,a1)),f215(x98202)),x98203))),f335(f96(x98201),f335(f335(f68(f887(a1,a1),a1,x98202,f267(a1,a1)),f215(x98202)),x98203))),f225(x98202,x98201,x98203))
% 59.73/59.67 [10018]~E(x100183,f2(a881))+~E(f335(f189(f882(x100181)),f335(f335(f158(f882(x100181)),x100182),f734(x100183,x100181,x100182))),x100183)+E(f335(f335(f147(a881,f882(x100181)),f335(f335(f7(a881,f882(a881),f882(x100181)),f335(f335(f8(f888(a881,x100181),f888(f882(a881),f882(x100181)),a881),f147(a881,x100181)),f335(f7(a881,a881,x100181),f335(f335(f8(f882(x100181),f888(a881,x100181),a881),f158(x100181)),f335(f158(f882(x100181)),x100182))))),f132(a881,f335(f304(a881,f2(a881)),f335(f189(f882(f882(x100181))),x100182))))),f132(a881,f335(f304(a881,f2(a881)),x100183))),f173(x100181,x100182))
% 59.73/59.67 [10019]E(x100191,f107(f882(x100192)))+~E(f335(f189(f882(x100192)),f335(f335(f158(f882(x100192)),x100191),f734(x100193,x100192,x100191))),x100193)+E(f335(f335(f147(a881,f882(x100192)),f335(f335(f7(a881,f882(a881),f882(x100192)),f335(f335(f8(f888(a881,x100192),f888(f882(a881),f882(x100192)),a881),f147(a881,x100192)),f335(f7(a881,a881,x100192),f335(f335(f8(f882(x100192),f888(a881,x100192),a881),f158(x100192)),f335(f158(f882(x100192)),x100191))))),f132(a881,f335(f304(a881,f2(a881)),f335(f189(f882(f882(x100192))),x100191))))),f132(a881,f335(f304(a881,f2(a881)),x100193))),f173(x100192,x100191))
% 59.73/59.67 [10020]~E(x100203,f2(a881))+E(f335(f335(f147(a881,f882(x100201)),f335(f335(f7(a881,f882(a881),f882(x100201)),f335(f335(f8(f888(a881,x100201),f888(f882(a881),f882(x100201)),a881),f147(a881,x100201)),f335(f7(a881,a881,x100201),f335(f335(f8(f882(x100201),f888(a881,x100201),a881),f158(x100201)),f335(f158(f882(x100201)),x100202))))),f132(a881,f335(f304(a881,f2(a881)),f335(f189(f882(f882(x100201))),x100202))))),f132(a881,f335(f304(a881,f2(a881)),x100203))),f173(x100201,x100202))+P1(f335(f335(f243(a881),f734(x100203,x100201,x100202)),f335(f189(f882(f882(x100201))),x100202)))
% 59.73/59.67 [10021]E(x100211,f107(f882(x100212)))+E(f335(f335(f147(a881,f882(x100212)),f335(f335(f7(a881,f882(a881),f882(x100212)),f335(f335(f8(f888(a881,x100212),f888(f882(a881),f882(x100212)),a881),f147(a881,x100212)),f335(f7(a881,a881,x100212),f335(f335(f8(f882(x100212),f888(a881,x100212),a881),f158(x100212)),f335(f158(f882(x100212)),x100211))))),f132(a881,f335(f304(a881,f2(a881)),f335(f189(f882(f882(x100212))),x100211))))),f132(a881,f335(f304(a881,f2(a881)),x100213))),f173(x100212,x100211))+P1(f335(f335(f243(a881),f734(x100213,x100212,x100211)),f335(f189(f882(f882(x100212))),x100211)))
% 59.73/59.67 [7751]E(f335(f335(f75(a881),f335(f97(a881),x77511)),f335(f335(f75(a881),f335(f97(a881),x77512)),x77513)),f335(f335(f75(a881),f335(f97(a881),f335(f335(f75(a1),x77511),x77512))),x77513))+P1(f335(a193,f335(f97(a1),x77511)))+P1(f335(a193,f335(f97(a1),x77512)))
% 59.73/59.67 [8518]~P1(f335(f56(x85181),x85182))+~P1(f335(f335(f337(x85181),x85183),x85182))+E(f335(a106,f335(f29(x85181),f335(f335(f23(f888(x85181,a879)),x85182),f335(f335(f312(x85181),x85183),f188(f888(x85181,a879)))))),f335(f29(x85181),x85182))
% 59.73/59.67 [8534]~P1(f335(f56(x85341),x85342))+~P1(f335(f335(f337(x85341),x85343),x85342))+E(f335(f335(f75(a881),f73(a881)),f335(f29(x85341),f335(f335(f23(f888(x85341,a879)),x85342),f335(f335(f312(x85341),x85343),f188(f888(x85341,a879)))))),f335(f29(x85341),x85342))
% 59.73/59.67 [8620]~P106(x86201)+~P1(f335(f56(x86201),x86203))+E(f335(f335(f141(x86201,x86201,f5(x86201)),x86202),f132(x86201,f335(f335(f23(f888(x86201,a879)),x86203),f335(f335(f312(x86201),x86202),f188(f888(x86201,a879)))))),f132(x86201,f335(f335(f312(x86201),x86202),x86203)))
% 59.73/59.67 [8774]~P1(f335(f56(x87741),x87743))+~P1(f335(f56(x87741),x87742))+E(f335(f335(f75(a881),f335(f29(x87741),f335(f335(f104(f888(x87741,a879)),x87742),x87743))),f335(f29(x87741),f335(f335(f95(f888(x87741,a879)),x87742),x87743))),f335(f335(f75(a881),f335(f29(x87741),x87742)),f335(f29(x87741),x87743)))
% 59.73/59.67 [8775]~P1(f335(f56(x87751),x87753))+~P1(f335(f56(x87751),x87752))+E(f335(f335(f75(a881),f335(f29(x87751),f335(f335(f104(f888(x87751,a879)),x87752),x87753))),f335(f29(x87751),f335(f335(f95(f888(x87751,a879)),x87752),x87753))),f335(f335(f75(a881),f335(f29(x87751),x87752)),f335(f29(x87751),x87753)))
% 59.73/59.67 [9966]~P26(x99661,f888(f888(x99661,a879),a879),f335(f335(f7(x99661,f888(f887(x99661,x99661),a879),f888(f888(x99661,a879),a879)),f335(f335(f8(f888(x99661,a879),f888(f888(f887(x99661,x99661),a879),f888(f888(x99661,a879),a879)),x99661),f55(x99661)),f335(f335(f7(x99661,f888(x99661,a879),f888(x99661,a879)),f312(x99661)),f188(f888(x99661,a879))))),x99663),x99662)+~P1(f335(f56(x99661),x99662))+E(f335(f29(f888(x99661,a879)),f335(f335(f55(x99661),x99662),x99663)),f335(f29(x99661),x99662))
% 59.73/59.67 [10229]~P37(f888(x102291,a879),f888(x102291,a879),x102292)+~P1(f335(f335(f242(f888(x102291,a879)),x102293),f335(x102292,f89(f888(x102291,a879),f335(f335(f7(f888(x102291,a879),f888(x102291,a879),f888(x102291,a879)),f335(f335(f8(f888(x102291,a879),f888(f888(x102291,a879),f888(x102291,a879)),f888(x102291,a879)),f104(f888(x102291,a879))),f335(f335(f7(f888(x102291,a879),f888(x102291,a879),f888(x102291,a879)),f335(f335(f8(f888(x102291,a879),f888(f888(x102291,a879),f888(x102291,a879)),f888(x102291,a879)),f104(f888(x102291,a879))),x102292)),x102293))),f90(f888(x102291,a879),x102292))))))+P1(f335(f335(f242(f888(x102291,a879)),f89(f888(x102291,a879),f335(f335(f7(f888(x102291,a879),f888(x102291,a879),f888(x102291,a879)),f335(f335(f8(f888(x102291,a879),f888(f888(x102291,a879),f888(x102291,a879)),f888(x102291,a879)),f104(f888(x102291,a879))),f335(f335(f7(f888(x102291,a879),f888(x102291,a879),f888(x102291,a879)),f335(f335(f8(f888(x102291,a879),f888(f888(x102291,a879),f888(x102291,a879)),f888(x102291,a879)),f104(f888(x102291,a879))),x102292)),x102293))),f90(f888(x102291,a879),x102292)))),f335(x102292,f89(f888(x102291,a879),f335(f335(f7(f888(x102291,a879),f888(x102291,a879),f888(x102291,a879)),f335(f335(f8(f888(x102291,a879),f888(f888(x102291,a879),f888(x102291,a879)),f888(x102291,a879)),f104(f888(x102291,a879))),f335(f335(f7(f888(x102291,a879),f888(x102291,a879),f888(x102291,a879)),f335(f335(f8(f888(x102291,a879),f888(f888(x102291,a879),f888(x102291,a879)),f888(x102291,a879)),f104(f888(x102291,a879))),x102292)),x102293))),f90(f888(x102291,a879),x102292))))))
% 59.73/59.67 [8025]~P97(x80251)+P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),x80253)))+E(f335(f335(f254(x80251),x80252),f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),x80253),x80253)),a91))),f73(x80251))
% 59.73/59.67 [8115]~P97(x81151)+P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),x81153)))+E(f335(f335(f254(x81151),f335(f97(x81151),x81152)),f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),x81153),x81153)),a91))),f73(x81151))
% 59.73/59.67 [9478]~P97(x94781)+~P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),x94783)))+E(f335(f335(f254(x94781),x94782),f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),x94783),x94783)),a91))),f335(f335(f81(x94781,x94781),f335(f335(f254(x94781),x94782),f335(f97(a881),x94783))),f335(f335(f18(x94781,x94781,x94781),f335(f335(f8(x94781,f888(x94781,x94781),x94781),f76(x94781)),f335(f76(x94781),x94782))),f5(x94781))))
% 59.73/59.67 [9545]~P97(x95451)+~P1(f335(f335(f242(a1),f2(a1)),f335(f97(a1),x95453)))+E(f335(f335(f254(x95451),f335(f97(x95451),x95452)),f335(f97(a881),f335(f335(f23(a1),f335(f335(f75(a1),x95453),x95453)),a91))),f335(f335(f81(x95451,x95451),f335(f335(f254(x95451),f335(f97(x95451),x95452)),f335(f97(a881),x95453))),f335(f335(f18(x95451,x95451,x95451),f335(f335(f8(x95451,f888(x95451,x95451),x95451),f76(x95451)),f335(f76(x95451),f335(f97(x95451),x95452)))),f5(x95451))))
% 59.73/59.67 [9879]~P1(f335(f130(x98791),x98793))+~P1(f335(f335(f337(x98791),x98792),f335(f166(x98791),x98793)))+E(f335(f335(f131(x98791),f335(f189(f882(x98791)),f171(x98791,f335(f335(f8(a879,a879,x98791),a330),f335(f335(f7(x98791,x98791,a879),a332),x98792)),f335(f162(x98791),x98793)))),f335(f162(x98791),x98793)),f335(f335(f144(x98791),x98792),f335(f162(x98791),f171(x98791,f335(f335(f8(a879,a879,x98791),a330),f335(f335(f7(x98791,x98791,a879),a332),x98792)),x98793))))
% 59.73/59.67 [9946]P1(f335(f335(f242(f888(f887(x99461,x99461),a879)),f310(x99461,x99462)),x99463))+~P1(f335(f335(f242(f888(f887(x99461,x99461),a879)),f310(x99461,f188(f888(f887(x99461,x99461),a879)))),x99463))+~P1(f335(f335(f242(f888(f887(x99461,x99461),a879)),f335(f335(f291(x99461,x99461,x99461),f335(f335(f95(f888(f887(x99461,x99461),a879)),f310(x99461,x99462)),x99463)),x99462)),x99463))
% 59.73/59.67 [9789]~P1(f335(f56(x97891),f335(f249(x97891),x97893)))+~P1(f335(f56(x97891),f335(f249(x97891),x97892)))+P1(f335(f56(x97891),f335(f249(x97891),f335(f335(f18(x97891,a879,a879),f335(f335(f8(a879,f888(a879,a879),x97891),a334),x97892)),x97893))))
% 59.73/59.67 [10080]P1(f335(f335(f242(f888(f887(x100801,x100801),a879)),f335(f335(f291(x100801,x100801,x100801),x100802),f310(x100801,x100802))),x100803))+~P1(f335(f335(f242(f888(f887(x100801,x100801),a879)),x100802),x100803))+~P1(f335(f335(f242(f888(f887(x100801,x100801),a879)),f335(f335(f291(x100801,x100801,x100801),f335(f335(f95(f888(f887(x100801,x100801),a879)),f335(f335(f291(x100801,x100801,x100801),x100802),f310(x100801,x100802))),x100803)),x100802)),x100803))
% 59.73/59.67 [10034]~P119(x100342)+E(x100341,f2(x100342))+~E(f335(f335(f75(x100342),f335(f335(f254(x100342),x100343),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f335(f335(f254(x100342),x100341),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f2(x100342))
% 59.73/59.67 [10035]~P119(x100352)+E(x100351,f2(x100352))+~E(f335(f335(f75(x100352),f335(f335(f254(x100352),x100351),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f335(f335(f254(x100352),x100353),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f2(x100352))
% 59.73/59.67 [10040]~P1(f335(f130(x100401),x100403))+~P1(f335(f335(f337(x100401),x100402),f335(f166(x100401),x100403)))+E(f335(f162(x100401),f335(f165(x100401),f335(f335(f131(x100401),f335(f189(f882(x100401)),f171(x100401,f335(f335(f8(a879,a879,x100401),a330),f335(f335(f7(x100401,x100401,a879),a332),x100402)),x100403))),x100403))),f171(x100401,f335(f335(f8(a879,a879,x100401),a330),f335(f335(f7(x100401,x100401,a879),a332),x100402)),f335(f162(x100401),x100403)))
% 59.73/59.67 [10122]~P119(x101222)+E(x101221,f2(x101222))+P1(f335(f335(f243(x101222),f2(x101222)),f335(f335(f75(x101222),f335(f335(f254(x101222),x101223),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f335(f335(f254(x101222),x101221),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))))
% 59.73/59.67 [10123]~P119(x101232)+E(x101231,f2(x101232))+P1(f335(f335(f243(x101232),f2(x101232)),f335(f335(f75(x101232),f335(f335(f254(x101232),x101231),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f335(f335(f254(x101232),x101233),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))))
% 59.73/59.67 [10167]~P119(x101671)+P1(f335(f335(f242(x101671),f2(x101671)),x101672))+~P1(f335(f335(f242(x101671),f2(x101671)),f335(f335(f254(x101671),x101672),f335(a106,f335(f335(f76(a881),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x101673)))))
% 59.73/59.67 [5517]~P16(x55171,x55174,x55173)+P16(x55171,x55172,x55173)+~P16(x55171,x55172,x55174)
% 59.73/59.67 [4987]~E(x49872,f85(x49873,x49871))+P1(f335(x49871,x49872))+~P1(f335(x49871,x49874))
% 59.73/59.67 [5235]E(f63(x52353,x52352,x52354),x52352)+E(x52351,f763(x52352,x52353,x52354))+~P1(f335(x52354,x52351))
% 59.73/59.67 [6525]E(f63(x65251,x65252,x65253),f80(x65251,x65253))+~E(f808(x65252,x65251,x65253,x65254),x65254)+~P1(f335(x65253,x65254))
% 59.73/59.67 [6739]~P36(x67392,x67394)+~P36(x67391,x67393)+P36(f887(x67391,x67392),f328(x67391,x67392,x67393,x67394))
% 59.73/59.67 [5172]~P7(x51724,x51721)+~E(f335(x51721,x51722),f335(x51721,x51723))+P1(f335(f335(x51721,x51722),x51723))
% 59.73/59.67 [5332]~P7(x53324,x53321)+E(f335(x53321,x53322),f335(x53321,x53323))+~P1(f335(f335(x53321,x53322),x53323))
% 59.73/59.67 [5424]~P20(x54243,x54244,x54241)+E(f335(x54241,x54242),f335(f58(x54243,x54244),x54242))+~P1(f335(f56(x54243),x54242))
% 59.73/59.67 [5425]~P9(x54253,x54254,x54251)+E(f335(x54251,x54252),f335(f58(x54253,x54254),x54252))+~P1(f335(f56(x54253),x54252))
% 59.73/59.67 [5550]~P7(x55504,x55501)+~P1(f335(f335(x55501,x55503),x55502))+P1(f335(f335(x55501,x55502),x55503))
% 59.73/59.67 [5619]E(x56191,x56192)+~E(f335(f263(x56193,x56194),x56191),f335(f263(x56193,x56194),x56192))+~E(f335(f267(x56193,x56194),x56191),f335(f267(x56193,x56194),x56192))
% 59.73/59.67 [5620]E(x56201,x56202)+~E(f335(f263(x56203,x56204),x56201),f335(f263(x56203,x56204),x56202))+~E(f335(f267(x56203,x56204),x56201),f335(f267(x56203,x56204),x56202))
% 59.73/59.67 [5645]E(x56451,x56452)+~P1(f335(f42(x56453,x56454),x56452))+~P1(f335(f42(x56453,x56454),x56451))
% 59.73/59.67 [5837]~P77(x58372)+E(f233(x58371,x58372,x58373,x58374),f2(x58372))+P1(f335(f56(x58371),x58374))
% 59.73/59.67 [5972]~P1(f335(f323(x59721,x59722),x59724))+P1(f335(f323(x59721,x59722),x59723))+~P1(f335(f335(x59722,x59723),x59724))
% 59.73/59.67 [5973]~P1(f335(f323(x59731,x59732),x59734))+P1(f335(f323(x59731,x59732),x59733))+~P1(f335(f335(x59732,x59733),x59734))
% 59.73/59.67 [5974]~P1(f335(f323(x59741,x59742),x59744))+P1(f335(f323(x59741,x59742),x59743))+~P1(f335(f335(x59742,x59743),x59744))
% 59.73/59.67 [6402]P50(x64021,x64022,x64023,x64024)+P1(f335(f335(x64022,x64024),x64023))+~P1(f335(f335(x64022,x64023),x64024))
% 59.73/59.67 [6775]~P29(x67751,x67753,x67754)+P1(f335(x67751,x67752))+~P1(f335(f335(f337(a1),x67752),f305(a1,x67753,x67754)))
% 59.73/59.67 [7858]E(x78581,f2(a881))+~P1(f335(x78582,x78583))+P1(f335(x78582,f801(x78582,x78583,x78581,x78584)))
% 59.73/59.67 [7941]~P106(x79412)+~P1(f335(f130(x79411),x79414))+P1(f335(f130(x79411),f143(x79411,x79412,x79413,x79414)))
% 59.73/59.67 [7991]E(f63(x79911,x79912,x79913),f80(x79911,x79913))+~P1(f335(x79913,x79914))+P1(f335(x79913,f808(x79912,x79911,x79913,x79914)))
% 59.73/59.67 [8164]~P1(f335(f56(x81642),x81644))+~P1(f335(f56(x81641),x81643))+P1(f335(f56(f889(x81641,x81642)),f321(x81641,x81642,x81643,x81644)))
% 59.73/59.67 [8165]~P1(f335(f56(x81652),x81654))+~P1(f335(f56(x81651),x81653))+P1(f335(f56(f889(x81651,x81652)),f321(x81651,x81652,x81653,x81654)))
% 59.73/59.67 [8166]~P1(f335(f130(x81662),x81664))+~P1(f335(f130(x81661),x81663))+P1(f335(f130(f887(x81661,x81662)),f54(x81661,x81662,x81663,x81664)))
% 59.73/59.67 [8170]P1(f335(f335(f337(f882(x81701)),f335(f335(f127(x81701),x81702),x81703)),f154(x81701,x81704)))+~P1(f335(f335(f337(f882(x81701)),x81703),f154(x81701,x81704)))+~P1(f335(f335(f337(f882(x81701)),x81702),f154(x81701,x81704)))
% 59.73/59.67 [8455]E(x84551,f2(a881))+P1(f335(x84552,x84553))+~P1(f335(x84552,f805(x84552,x84553,x84551,x84554)))
% 59.73/59.67 [8496]~P106(x84963)+~P1(f335(f130(x84961),f143(x84961,x84963,x84964,x84962)))+P1(f335(f130(x84961),x84962))
% 59.73/59.67 [8765]~P1(f335(f335(f337(f887(x87651,x87651)),f335(f335(f264(x87651,x87651),x87652),x87654)),f310(x87651,x87653)))+P1(f335(f335(f337(x87651),x87652),f324(x87651,x87653)))+~P1(f335(f335(f337(x87651),x87654),f324(x87651,x87653)))
% 59.73/59.67 [8766]~P1(f335(f335(f337(f887(x87661,x87661)),f335(f335(f264(x87661,x87661),x87662),x87664)),f310(x87661,x87663)))+P1(f335(f335(f337(x87661),x87662),f324(x87661,x87663)))+~P1(f335(f335(f337(x87661),x87664),f324(x87661,x87663)))
% 59.73/59.67 [5151]~P73(x51512)+E(f335(f335(f9(x51511,x51512),x51513),x51514),f73(x51512))+P1(f335(f56(x51511),x51514))
% 59.73/59.67 [5152]~P73(x51522)+E(f335(f335(f9(x51521,x51522),x51523),x51524),f73(x51522))+P1(f335(f56(x51521),x51524))
% 59.73/59.67 [5153]~P73(x51532)+E(f335(f335(f9(x51531,x51532),x51533),x51534),f73(x51532))+P1(f335(f56(x51531),x51534))
% 59.73/59.67 [5154]~P77(x51542)+E(f335(f335(f6(x51541,x51542),x51543),x51544),f2(x51542))+P1(f335(f56(x51541),x51544))
% 59.73/59.67 [5155]~P77(x51552)+E(f335(f335(f6(x51551,x51552),x51553),x51554),f2(x51552))+P1(f335(f56(x51551),x51554))
% 59.73/59.67 [5156]~P77(x51562)+E(f335(f335(f6(x51561,x51562),x51563),x51564),f2(x51562))+P1(f335(f56(x51561),x51564))
% 59.73/59.67 [5294]~P74(x52943)+E(x52941,x52942)+~E(f335(f335(f75(x52943),x52944),x52941),f335(f335(f75(x52943),x52944),x52942))
% 59.73/59.67 [5295]~P74(x52953)+E(x52951,x52952)+~E(f335(f335(f75(x52953),x52954),x52951),f335(f335(f75(x52953),x52954),x52952))
% 59.73/59.67 [5296]~P75(x52963)+E(x52961,x52962)+~E(f335(f335(f75(x52963),x52964),x52961),f335(f335(f75(x52963),x52964),x52962))
% 59.73/59.67 [5297]~P74(x52973)+E(x52971,x52972)+~E(f335(f335(f75(x52973),x52971),x52974),f335(f335(f75(x52973),x52972),x52974))
% 59.73/59.67 [5298]~P74(x52983)+E(x52981,x52982)+~E(f335(f335(f75(x52983),x52981),x52984),f335(f335(f75(x52983),x52982),x52984))
% 59.73/59.67 [5420]~P5(x54203)+E(x54201,f188(f888(x54202,a879)))+E(f335(f335(f33(x54202,x54203),x54201),f335(f16(x54203,x54202),x54204)),x54204)
% 59.73/59.67 [5421]~P5(x54213)+E(x54211,f188(f888(x54212,a879)))+E(f335(f335(f34(x54212,x54213),x54211),f335(f16(x54213,x54212),x54214)),x54214)
% 59.73/59.67 [5633]~P107(x56333)+E(x56331,x56332)+~E(f305(x56333,x56334,x56331),f335(f335(f312(x56333),x56332),f188(f888(x56333,a879))))
% 59.73/59.67 [5634]~P107(x56343)+E(x56341,x56342)+~E(f305(x56343,x56341,x56342),f335(f335(f312(x56343),x56344),f188(f888(x56343,a879))))
% 59.73/59.67 [5695]~P34(x56953,x56951,x56954)+P34(x56953,x56951,f335(f335(f144(x56953),x56952),x56954))+P1(f335(x56951,x56952))
% 59.73/59.67 [5796]~P30(x57961,x57962,x57964)+~P1(f335(x57962,x57963))+P30(x57961,x57962,f335(f335(f144(x57961),x57963),x57964))
% 59.73/59.67 [5930]P1(f335(x59301,x59302))+~P1(f335(f257(x59303,x59301),x59304))+~P1(f335(f335(f337(x59303),x59302),x59304))
% 59.73/59.67 [5939]~P30(x59391,x59392,x59394)+~P30(x59391,x59392,x59393)+P30(x59391,x59392,f335(f335(f127(x59391),x59393),x59394))
% 59.73/59.67 [5950]P32(x59501,x59502,x59503)+~P32(x59501,x59502,f335(f335(f144(x59501),x59504),x59503))+P1(f335(x59502,x59504))
% 59.73/59.67 [5951]P34(x59511,x59512,x59513)+~P34(x59511,x59512,f335(f335(f144(x59511),x59514),x59513))+P1(f335(x59512,x59514))
% 59.73/59.67 [6030]P32(x60301,x60302,x60303)+P32(x60301,x60302,x60304)+~P32(x60301,x60302,f335(f335(f127(x60301),x60304),x60303))
% 59.73/59.67 [6049]~P77(x60491)+E(f335(f335(f6(a881,x60491),x60492),f335(f304(a881,x60493),f335(a106,x60494))),f2(x60491))+~P1(f335(f335(f243(a881),x60494),x60493))
% 59.73/59.67 [6054]~P59(x60541)+~E(f39(x60541,x60542,x60543),f39(x60541,x60544,x60543))+E(f39(x60541,f335(f74(x60541),x60542),x60543),f39(x60541,f335(f74(x60541),x60544),x60543))
% 59.73/59.67 [6118]P1(f335(x61181,x61182))+~E(f335(f129(x61183,x61181),x61184),x61184)+~P1(f335(f335(f337(x61183),x61182),f335(f166(x61183),x61184)))
% 59.73/59.67 [6137]~E(f335(f335(f75(a881),x61373),x61372),f335(f335(f75(a881),x61371),x61374))+~P1(f335(f335(f243(a881),x61373),x61374))+P1(f335(f335(f243(a881),x61371),x61372))
% 59.73/59.67 [6141]P32(x61411,x61412,x61413)+~P1(f335(x61412,x61414))+~P1(f335(f335(f337(x61411),x61414),f335(f166(x61411),x61413)))
% 59.73/59.67 [6177]~P30(x61773,x61771,x61774)+P1(f335(x61771,x61772))+~P1(f335(f335(f337(x61773),x61772),f335(f166(x61773),x61774)))
% 59.73/59.67 [6178]~P30(x61783,x61781,x61784)+P1(f335(x61781,x61782))+~P1(f335(f335(f337(x61783),x61782),f335(f166(x61783),x61784)))
% 59.73/59.67 [6179]~P30(x61793,x61791,x61794)+P1(f335(x61791,x61792))+~P1(f335(f335(f337(x61793),x61792),f335(f166(x61793),x61794)))
% 59.73/59.67 [6181]~E(f335(f129(x61811,x61812),x61813),f107(x61811))+~P1(f335(x61812,x61814))+~P1(f335(f335(f337(x61811),x61814),f335(f166(x61811),x61813)))
% 59.73/59.67 [6182]~E(f171(x61823,x61821,x61824),x61824)+P1(f335(x61821,x61822))+~P1(f335(f335(f337(x61823),x61822),f335(f166(x61823),x61824)))
% 59.73/59.67 [6211]~E(x62114,f188(f888(x62112,a879)))+~E(x62113,f188(f888(x62111,a879)))+E(f321(x62111,x62112,x62113,x62114),f188(f888(f889(x62111,x62112),a879)))
% 59.73/59.67 [6358]P1(f335(x63581,x63582))+~P1(f335(f153(x63583,x63581),x63584))+~P1(f335(f335(f337(x63583),x63582),f335(f166(x63583),x63584)))
% 59.73/59.67 [6634]~P77(x66341)+E(f335(f335(f6(a881,x66341),x66342),f305(a881,x66343,f335(a106,x66344))),f2(x66341))+~P1(f335(f335(f243(a881),f335(a106,x66344)),x66343))
% 59.73/59.67 [6778]~P106(x67781)+E(f335(f335(f23(f888(x67781,a879)),f335(f304(x67781,x67782),x67783)),f335(f304(x67781,x67782),x67784)),f335(f304(x67781,x67784),x67783))+~P1(f335(f335(f242(x67781),x67782),x67784))
% 59.73/59.67 [6850]~E(x68503,x68504)+E(x68501,f2(a881))+P1(f335(f335(f337(x68502),x68503),f335(f166(x68502),f163(x68502,x68501,x68504))))
% 59.73/59.67 [7129]~P1(f335(f335(f337(f882(x71291)),x71294),f154(x71291,x71293)))+P1(f335(f335(f337(x71291),x71292),x71293))+~P1(f335(f335(f337(x71291),x71292),f335(f166(x71291),x71294)))
% 59.73/59.67 [7136]~P36(x71361,x71362)+P1(f335(f335(f337(x71361),f643(x71362,x71361,x71363)),x71363))+~P1(f335(f335(f337(x71361),x71364),x71363))
% 59.73/59.67 [7167]~P26(x71672,x71671,x71673,x71674)+E(f335(f29(x71671),f335(f313(x71672,x71671,x71673),x71674)),f335(f29(x71672),x71674))+~P1(f335(f56(x71672),x71674))
% 59.73/59.67 [7191]~P73(x71911)+E(f335(f335(f335(f60(x71911,x71912,f76(x71911)),x71913),f73(x71911)),x71914),f335(f335(f9(x71912,x71911),x71913),x71914))+~P1(f335(f56(x71912),x71914))
% 59.73/59.67 [7192]~P73(x71921)+E(f335(f335(f335(f60(x71921,x71922,f76(x71921)),x71923),f73(x71921)),x71924),f335(f335(f9(x71922,x71921),x71923),x71924))+~P1(f335(f56(x71922),x71924))
% 59.73/59.67 [7193]~P77(x71931)+E(f335(f335(f335(f60(x71931,x71932,f75(x71931)),x71933),f2(x71931)),x71934),f335(f335(f6(x71932,x71931),x71933),x71934))+~P1(f335(f56(x71932),x71934))
% 59.73/59.67 [7194]~P77(x71941)+E(f335(f335(f335(f60(x71941,x71942,f75(x71941)),x71943),f2(x71941)),x71944),f335(f335(f6(x71942,x71941),x71943),x71944))+~P1(f335(f56(x71942),x71944))
% 59.73/59.67 [7221]P26(x72211,x72212,x72213,x72214)+~E(f335(f29(x72212),f335(f313(x72211,x72212,x72213),x72214)),f335(f29(x72211),x72214))+~P1(f335(f56(x72211),x72214))
% 59.73/59.67 [7222]P26(x72221,x72222,x72223,x72224)+~E(f335(f29(x72222),f335(f313(x72221,x72222,x72223),x72224)),f335(f29(x72221),x72224))+~P1(f335(f56(x72221),x72224))
% 59.73/59.67 [7412]~P77(x74121)+E(f335(f335(f75(x74121),f335(x74122,x74123)),f335(f335(f6(a881,x74121),x74122),f307(a881,x74123,x74124))),f335(f335(f6(a881,x74121),x74122),f305(a881,x74123,x74124)))+~P1(f335(f335(f242(a881),x74123),x74124))
% 59.73/59.67 [7421]~P73(x74211)+~P26(x74212,x74211,x74213,x74214)+E(f335(f335(f9(x74211,x74211),f25(x74211)),f335(f313(x74212,x74211,x74213),x74214)),f335(f335(f9(x74212,x74211),x74213),x74214))
% 59.73/59.67 [7422]~P77(x74221)+~P26(x74222,x74221,x74223,x74224)+E(f335(f335(f6(x74221,x74221),f25(x74221)),f335(f313(x74222,x74221,x74223),x74224)),f335(f335(f6(x74222,x74221),x74223),x74224))
% 59.73/59.67 [7474]E(f335(f29(f889(x74741,x74742)),f321(x74741,x74742,x74743,x74744)),f335(f335(f75(a881),f335(f29(x74741),x74743)),f335(f29(x74742),x74744)))+~P1(f335(f56(x74742),x74744))+~P1(f335(f56(x74741),x74743))
% 59.73/59.67 [7475]E(f335(f29(f889(x74751,x74752)),f321(x74751,x74752,x74753,x74754)),f335(f335(f75(a881),f335(f29(x74751),x74753)),f335(f29(x74752),x74754)))+~P1(f335(f56(x74752),x74754))+~P1(f335(f56(x74751),x74753))
% 59.73/59.67 [7559]E(x75591,x75592)+P1(f335(f335(f337(x75593),x75591),f335(f166(x75593),f164(x75593,x75592,x75594))))+~P1(f335(f335(f337(x75593),x75591),f335(f166(x75593),x75594)))
% 59.73/59.67 [7702]~P1(f335(f335(f242(f888(x77021,a879)),x77024),f335(x77023,x77024)))+~P1(f335(f335(f337(x77021),x77022),x77024))+P1(f335(f335(f337(x77021),x77022),f90(f888(x77021,a879),x77023)))
% 59.73/59.67 [7788]~P77(x77881)+E(f335(f335(f75(x77881),f335(f335(f6(a881,x77881),x77882),f335(f304(a881,x77883),x77884))),f335(x77882,x77884)),f335(f335(f6(a881,x77881),x77882),f335(f304(a881,x77883),f335(a106,x77884))))+P1(f335(f335(f243(a881),x77884),x77883))
% 59.73/59.67 [7839]~P26(x78391,x78392,x78393,f252(f888(x78391,a879)))+~P1(f335(f56(x78392),x78394))+P1(f335(f56(x78391),f335(f314(x78391,x78392,x78393),x78394)))
% 59.73/59.67 [7956]P1(f335(f335(f337(f882(x79561)),f335(f335(f144(x79561),x79562),x79563)),f154(x79561,x79564)))+~P1(f335(f335(f337(f882(x79561)),x79563),f154(x79561,x79564)))+~P1(f335(f335(f337(x79561),x79562),x79564))
% 59.73/59.67 [8010]E(x80101,x80102)+~P1(f335(f335(f337(x80103),x80101),f335(f166(x80103),f164(x80103,x80102,x80104))))+P1(f335(f335(f337(x80103),x80101),f335(f166(x80103),x80104)))
% 59.73/59.67 [8049]~E(f335(f313(x80493,x80491,x80494),f252(f888(x80493,a879))),f252(f888(x80491,a879)))+P1(f335(f56(x80491),x80492))+~P1(f335(f56(x80493),f335(f314(x80493,x80491,x80494),x80492)))
% 59.73/59.67 [8138]~P26(x81381,x81383,x81384,x81382)+P1(f335(f56(x81381),x81382))+~P1(f335(f56(x81383),f335(f313(x81381,x81383,x81384),x81382)))
% 59.73/59.67 [8158]~E(x81582,x81583)+P1(f335(f335(f337(f887(x81581,x81581)),f335(f335(f264(x81581,x81581),x81582),x81583)),f261(x81581,x81584)))+~P1(f335(f335(f337(x81581),x81582),x81584))
% 59.73/59.67 [8159]~E(x81592,x81593)+P1(f335(f335(f337(f887(x81591,x81591)),f335(f335(f264(x81591,x81591),x81592),x81593)),f261(x81591,x81594)))+~P1(f335(f335(f337(x81591),x81592),x81594))
% 59.73/59.67 [8197]~P77(x81971)+E(f335(f335(f75(x81971),f335(f335(f6(a881,x81971),x81972),f305(a881,x81973,x81974))),f335(x81972,f335(a106,x81974))),f335(f335(f6(a881,x81971),x81972),f305(a881,x81973,f335(a106,x81974))))+P1(f335(f335(f243(a881),f335(a106,x81974)),x81973))
% 59.73/59.67 [8258]~E(x82582,x82584)+P1(f335(f335(f337(f887(x82581,x82581)),f335(f335(f264(x82581,x82581),x82582),x82584)),f310(x82581,x82583)))+P1(f335(f335(f337(x82581),x82582),f335(f262(x82581,x82581),x82583)))
% 59.73/59.67 [8260]P1(f335(x82601,x82602))+~P1(f335(x82601,f335(f335(f158(x82603),x82604),f687(x82601,x82604,x82603))))+~P1(f335(f335(f337(x82603),x82602),f335(f166(x82603),x82604)))
% 59.73/59.67 [8401]~P1(f335(f335(f337(x84011),x84012),f324(x84011,x84014)))+P1(f335(f335(f337(f882(x84011)),f335(f335(f144(x84011),x84012),x84013)),f324(f882(x84011),f150(x84011,x84014))))+~P1(f335(f335(f337(f882(x84011)),x84013),f324(f882(x84011),f150(x84011,x84014))))
% 59.73/59.67 [8416]~P26(x84162,x84163,x84164,f646(x84164,x84163,x84162,x84161))+P26(x84162,x84163,x84164,f32(f888(x84162,a879),x84161))+E(x84161,f188(f888(f888(x84162,a879),a879)))
% 59.73/59.67 [8683]E(x86831,x86832)+~P1(f335(f335(f337(f887(x86833,x86833)),f335(f335(f264(x86833,x86833),x86831),x86832)),f310(x86833,x86834)))+P1(f335(f335(f337(x86833),x86831),f335(f262(x86833,x86833),x86834)))
% 59.73/59.67 [8953]E(x89531,f2(a881))+P1(f335(x89532,x89533))+P1(f335(f335(f337(x89534),f805(x89532,x89533,x89531,x89534)),f335(f166(x89534),f163(x89534,x89531,x89533))))
% 59.73/59.67 [8963]E(x89631,f2(a881))+~P1(f335(x89633,x89634))+P1(f335(f335(f337(x89632),f801(x89633,x89634,x89631,x89632)),f335(f166(x89632),f163(x89632,x89631,x89634))))
% 59.73/59.67 [8968]P26(x89682,x89683,x89684,f32(f888(x89682,a879),x89681))+E(x89681,f188(f888(f888(x89682,a879),a879)))+P1(f335(f335(f337(f888(x89682,a879)),f646(x89684,x89683,x89682,x89681)),x89681))
% 59.73/59.67 [9099]P1(f335(f56(x90991),x90992))+~P1(f335(f56(x90994),f335(f313(x90991,x90994,x90993),x90992)))+P1(f335(f335(f337(x90991),f553(x90993,x90994,x90992,x90991)),x90992))
% 59.73/59.67 [9196]~P5(x91962)+E(f335(f335(f59(x91961,x91962,f335(f335(f8(x91962,f888(x91962,x91962),x91961),f104(x91962)),x91963)),f188(x91962)),x91964),f335(f335(f33(x91961,x91962),x91964),x91963))+~P1(f335(f56(x91961),x91964))
% 59.73/59.67 [9197]~P5(x91972)+E(f335(f335(f59(x91971,x91972,f335(f335(f8(x91972,f888(x91972,x91972),x91971),f95(x91972)),x91973)),f252(x91972)),x91974),f335(f335(f34(x91971,x91972),x91974),x91973))+~P1(f335(f56(x91971),x91974))
% 59.73/59.67 [9280]P1(f335(x92801,x92802))+~P1(f335(x92801,f335(f335(f158(x92803),x92804),f752(x92802,x92801,x92804,x92803))))+~P1(f335(f335(f337(x92803),x92802),f335(f166(x92803),x92804)))
% 59.73/59.67 [9301]E(x93011,x93012)+~P1(f335(f335(f337(f887(x93013,x93013)),f335(f335(f264(x93013,x93013),x93011),x93012)),f310(x93013,x93014)))+P1(f335(f335(f337(f887(x93013,x93013)),f335(f335(f264(x93013,x93013),x93011),x93012)),f335(f335(f291(x93013,x93013,x93013),x93014),f310(x93013,x93014))))
% 59.73/59.67 [9302]E(x93021,x93022)+~P1(f335(f335(f337(f887(x93023,x93023)),f335(f335(f264(x93023,x93023),x93021),x93022)),f310(x93023,x93024)))+P1(f335(f335(f337(f887(x93023,x93023)),f335(f335(f264(x93023,x93023),x93021),x93022)),f335(f335(f291(x93023,x93023,x93023),x93024),f310(x93023,x93024))))
% 59.73/59.67 [9347]~E(f335(f189(f882(x93471)),x93472),f335(f189(f882(x93471)),x93473))+~P1(f335(f335(f337(f887(f882(x93471),f882(x93471))),f335(f335(f264(f882(x93471),f882(x93471)),x93472),x93473)),f140(x93471,x93474)))+P1(f335(f335(f337(f887(f882(x93471),f882(x93471))),f335(f335(f264(f882(x93471),f882(x93471)),x93472),x93473)),f138(x93471,x93474)))
% 59.73/59.67 [9370]E(x93701,x93702)+P1(f335(f335(f337(f887(x93703,x93703)),f335(f335(f264(x93703,x93703),x93701),x93702)),f310(x93703,x93704)))+~P1(f335(f335(f337(f887(x93703,x93703)),f335(f335(f264(x93703,x93703),x93701),x93702)),f335(f335(f291(x93703,x93703,x93703),x93704),f310(x93703,x93704))))
% 59.73/59.67 [9580]P30(x95801,f335(f335(f18(x95801,a879,a879),f335(f335(f8(a879,f888(a879,a879),x95801),a334),f335(f335(f8(a879,a879,x95801),a330),x95802))),f335(a332,x95803)),x95804)+~P1(f335(x95802,x95803))+~P34(x95801,x95802,f335(f335(f144(x95801),x95803),x95804))
% 59.73/59.67 [9749]~P30(x97491,f335(f335(f18(x97491,a879,a879),f335(f335(f8(a879,f888(a879,a879),x97491),a334),f335(f335(f8(a879,a879,x97491),a330),x97492))),f335(a332,x97493)),x97494)+~P1(f335(x97492,x97493))+P34(x97491,x97492,f335(f335(f144(x97491),x97493),x97494))
% 59.73/59.67 [9753]~P34(x97531,x97532,x97534)+~P30(x97531,f335(f335(f18(x97531,a879,a879),f335(f335(f8(a879,f888(a879,a879),x97531),a334),f335(f335(f8(a879,a879,x97531),a330),x97532))),f335(a332,x97533)),x97534)+P34(x97531,x97532,f335(f335(f144(x97531),x97533),x97534))
% 59.73/59.67 [9792]~P64(x97921)+E(f335(f335(f6(a881,x97921),f335(f335(f18(a881,x97921,x97921),f335(f335(f8(x97921,f888(x97921,x97921),a881),f23(x97921)),x97922)),f335(f335(f8(a881,x97921,a881),x97922),f335(f335(f7(a881,a881,a881),f75(a881)),f73(a881))))),f305(a881,x97923,x97924)),f2(x97921))+P1(f335(f335(f242(a881),x97923),x97924))
% 59.73/59.67 [10033]~P36(x100332,x100334)+~P26(x100332,x100331,x100333,f252(f888(x100332,a879)))+P36(x100331,f335(f313(f887(x100332,x100332),f887(x100331,x100331),f269(x100332,x100331,x100332,x100331,x100333,x100333)),x100334))
% 59.73/59.67 [10195]~E(f335(f189(f882(x101951)),x101953),f335(f189(f882(x101951)),x101952))+P1(f335(f335(f337(f887(f882(x101951),f882(x101951))),f335(f335(f264(f882(x101951),f882(x101951)),x101952),x101953)),f151(x101951,x101954)))+~P1(f335(f335(f268(x101951,x101951,a879),f335(f335(f7(x101951,f888(f887(x101951,x101951),a879),f888(x101951,a879)),f335(f335(f8(f888(x101951,f888(f888(f887(x101951,x101951),a879),a879)),f888(f888(f887(x101951,x101951),a879),f888(x101951,a879)),x101951),f7(x101951,f888(f887(x101951,x101951),a879),a879)),f335(f335(f8(f888(x101951,f887(x101951,x101951)),f888(x101951,f888(f888(f887(x101951,x101951),a879),a879)),x101951),f335(f8(f887(x101951,x101951),f888(f888(f887(x101951,x101951),a879),a879),x101951),f337(f887(x101951,x101951)))),f264(x101951,x101951)))),x101954)),f677(x101954,x101953,x101952,x101951)))
% 59.73/59.67 [6102]~P58(x61021)+~E(x61022,f2(x61021))+E(f335(f335(f30(x61021),f335(f335(f76(x61021),x61022),x61023)),f335(f335(f76(x61021),x61022),x61024)),f2(x61021))
% 59.73/59.67 [6140]E(x61401,f107(x61402))+E(x61403,f335(f335(f23(a881),f335(f189(f882(x61402)),x61401)),f73(a881)))+E(f137(x61402,f335(f335(f152(x61402,x61401),x61403),x61404)),f137(x61402,x61401))
% 59.73/59.67 [6170]E(x61701,x61702)+P1(f335(x61703,x61702))+~P1(f335(f335(f335(f312(x61704),x61701),x61703),x61702))
% 59.73/59.67 [6186]~P77(x61861)+~P1(f335(f130(x61862),x61864))+E(f335(f159(x61861),f335(f335(f147(x61862,x61861),x61863),x61864)),f335(f335(f6(x61862,x61861),x61863),f335(f166(x61862),x61864)))
% 59.73/59.67 [6204]~P73(x62042)+~P1(f335(f56(x62041),x62044))+E(f335(f335(f9(x62041,x62042),f335(f16(x62042,x62041),x62043)),x62044),f335(f335(f254(x62042),x62043),f335(f29(x62041),x62044)))
% 59.73/59.67 [6260]~P58(x62602)+E(x62601,f2(x62602))+E(f335(f335(f30(x62602),f335(f335(f76(x62602),x62603),x62601)),f335(f335(f76(x62602),x62604),x62601)),f335(f335(f30(x62602),x62603),x62604))
% 59.73/59.67 [6261]~P58(x62612)+E(x62611,f2(x62612))+E(f335(f335(f30(x62612),f335(f335(f76(x62612),x62611),x62613)),f335(f335(f76(x62612),x62611),x62614)),f335(f335(f30(x62612),x62613),x62614))
% 59.73/59.67 [6262]~P66(x62622)+E(x62621,f2(x62622))+E(f335(f335(f292(x62622),f335(f335(f76(x62622),x62623),x62621)),f335(f335(f76(x62622),x62624),x62621)),f335(f335(f292(x62622),x62623),x62624))
% 59.73/59.67 [6263]~P66(x62632)+E(x62631,f2(x62632))+E(f335(f335(f292(x62632),f335(f335(f76(x62632),x62631),x62633)),f335(f335(f76(x62632),x62631),x62634)),f335(f335(f292(x62632),x62633),x62634))
% 59.73/59.67 [6264]~P58(x62642)+E(x62641,f2(x62642))+E(f335(f335(f30(x62642),f335(f335(f76(x62642),x62641),x62643)),f335(f335(f76(x62642),x62641),x62644)),f335(f335(f30(x62642),x62643),x62644))
% 59.73/59.67 [6325]P1(f335(x63251,x63252))+~E(x63253,f335(f335(f75(a881),x63254),x63252))+~P1(f335(x63251,f335(f335(f23(a881),x63253),x63254)))
% 59.73/59.67 [6326]P1(f335(x63261,x63262))+~E(x63263,f335(f335(f75(a881),x63264),x63262))+~P1(f335(x63261,f335(f335(f23(a881),x63263),x63264)))
% 59.73/59.67 [6413]~P1(f335(x64132,x64133))+~P1(f335(f153(x64131,x64132),x64134))+P1(f335(f153(x64131,x64132),f335(f335(f144(x64131),x64133),x64134)))
% 59.73/59.67 [6454]E(x64541,f107(x64542))+~E(x64543,f335(f335(f23(a881),f335(f189(f882(x64542)),x64541)),f73(a881)))+E(f137(x64542,f335(f335(f152(x64542,x64541),x64543),x64544)),x64544)
% 59.73/59.67 [6477]~P60(x64771)+~P1(f335(f335(f242(x64771),x64772),x64774))+P1(f335(f335(f242(x64771),x64772),f335(f335(f104(x64771),x64773),x64774)))
% 59.73/59.67 [6478]~P60(x64781)+~P1(f335(f335(f242(x64781),x64782),x64783))+P1(f335(f335(f242(x64781),x64782),f335(f335(f104(x64781),x64783),x64784)))
% 59.73/59.67 [6479]~P106(x64791)+~P1(f335(f335(f242(x64791),x64792),x64794))+P1(f335(f335(f242(x64791),x64792),f335(f335(f241(x64791),x64793),x64794)))
% 59.73/59.67 [6480]~P106(x64801)+~P1(f335(f335(f242(x64801),x64802),x64804))+P1(f335(f335(f242(x64801),x64802),f335(f335(f241(x64801),x64803),x64804)))
% 59.73/59.67 [6481]~P106(x64811)+~P1(f335(f335(f242(x64811),x64812),x64813))+P1(f335(f335(f242(x64811),x64812),f335(f335(f241(x64811),x64813),x64814)))
% 59.73/59.67 [6482]~P106(x64821)+~P1(f335(f335(f242(x64821),x64822),x64823))+P1(f335(f335(f242(x64821),x64822),f335(f335(f241(x64821),x64823),x64824)))
% 59.73/59.67 [6483]~P60(x64831)+~P1(f335(f335(f243(x64831),x64832),x64834))+P1(f335(f335(f243(x64831),x64832),f335(f335(f104(x64831),x64833),x64834)))
% 59.73/59.67 [6484]~P60(x64841)+~P1(f335(f335(f243(x64841),x64842),x64843))+P1(f335(f335(f243(x64841),x64842),f335(f335(f104(x64841),x64843),x64844)))
% 59.73/59.67 [6485]~P106(x64851)+~P1(f335(f335(f243(x64851),x64852),x64854))+P1(f335(f335(f243(x64851),x64852),f335(f335(f241(x64851),x64853),x64854)))
% 59.73/59.67 [6486]~P106(x64861)+~P1(f335(f335(f243(x64861),x64862),x64864))+P1(f335(f335(f243(x64861),x64862),f335(f335(f241(x64861),x64863),x64864)))
% 59.73/59.67 [6487]~P106(x64871)+~P1(f335(f335(f243(x64871),x64872),x64873))+P1(f335(f335(f243(x64871),x64872),f335(f335(f241(x64871),x64873),x64874)))
% 59.73/59.67 [6488]~P106(x64881)+~P1(f335(f335(f243(x64881),x64882),x64883))+P1(f335(f335(f243(x64881),x64882),f335(f335(f241(x64881),x64883),x64884)))
% 59.73/59.67 [6576]~E(f335(f335(f158(x65761),x65762),x65763),x65764)+E(f335(f335(f152(x65761,x65762),x65763),x65764),x65762)+~P1(f335(f335(f243(a881),x65763),f335(f189(f882(x65761)),x65762)))
% 59.73/59.67 [6619]P1(f335(x66191,x66192))+~P1(f335(x66193,x66192))+~P1(f335(f335(f242(f888(x66194,a879)),x66193),x66191))
% 59.73/59.67 [6620]P1(f335(x66201,x66202))+~P1(f335(x66203,x66202))+~P1(f335(f335(f242(f888(x66204,a879)),x66203),x66201))
% 59.73/59.67 [6651]~E(f335(f335(f152(x66511,x66512),x66513),x66514),x66512)+E(f335(f335(f158(x66511),x66512),x66513),x66514)+~P1(f335(f335(f243(a881),x66513),f335(f189(f882(x66511)),x66512)))
% 59.73/59.67 [6666]~P1(f335(f153(x66661,x66662),x66664))+~P1(f335(f153(x66661,x66662),x66663))+P1(f335(f153(x66661,x66662),f335(f335(f127(x66661),x66663),x66664)))
% 59.73/59.67 [6774]E(x67741,f188(f888(x67742,a879)))+E(x67743,f188(f888(x67744,a879)))+~E(f335(f335(f266(x67744,x67742),x67743),f335(f16(f888(x67742,a879),x67744),x67741)),f188(f888(f887(x67744,x67742),a879)))
% 59.73/59.67 [6793]E(x67931,x67932)+P1(f335(f335(f337(x67933),x67931),x67934))+~P1(f335(f335(f337(x67933),x67931),f335(f335(f312(x67933),x67932),x67934)))
% 59.73/59.67 [6794]E(x67941,x67942)+P1(f335(f335(f337(x67943),x67941),x67944))+~P1(f335(f335(f337(x67943),x67941),f335(f335(f312(x67943),x67942),x67944)))
% 59.73/59.67 [6810]~P106(x68101)+P1(f335(f335(f242(x68101),x68102),x68103))+~P1(f335(f335(f242(x68101),x68102),f335(f335(f240(x68101),x68104),x68103)))
% 59.73/59.67 [6811]~P106(x68111)+P1(f335(f335(f242(x68111),x68112),x68113))+~P1(f335(f335(f242(x68111),x68112),f335(f335(f240(x68111),x68114),x68113)))
% 59.73/59.67 [6812]~P106(x68121)+P1(f335(f335(f242(x68121),x68122),x68123))+~P1(f335(f335(f242(x68121),x68122),f335(f335(f240(x68121),x68123),x68124)))
% 59.73/59.67 [6813]~P106(x68131)+P1(f335(f335(f242(x68131),x68132),x68133))+~P1(f335(f335(f242(x68131),x68132),f335(f335(f240(x68131),x68133),x68134)))
% 59.73/59.67 [6814]~P102(x68141)+P1(f335(f335(f242(x68141),x68142),x68143))+~P1(f335(f335(f242(x68141),x68142),f335(f335(f95(x68141),x68144),x68143)))
% 59.73/59.67 [6815]~P102(x68151)+P1(f335(f335(f242(x68151),x68152),x68153))+~P1(f335(f335(f242(x68151),x68152),f335(f335(f95(x68151),x68154),x68153)))
% 59.73/59.67 [6816]~P102(x68161)+P1(f335(f335(f242(x68161),x68162),x68163))+~P1(f335(f335(f242(x68161),x68162),f335(f335(f95(x68161),x68163),x68164)))
% 59.73/59.67 [6817]~P102(x68171)+P1(f335(f335(f242(x68171),x68172),x68173))+~P1(f335(f335(f242(x68171),x68172),f335(f335(f95(x68171),x68173),x68174)))
% 59.73/59.67 [6818]~P106(x68181)+P1(f335(f335(f243(x68181),x68182),x68183))+~P1(f335(f335(f243(x68181),x68182),f335(f335(f240(x68181),x68184),x68183)))
% 59.73/59.67 [6819]~P106(x68191)+P1(f335(f335(f243(x68191),x68192),x68193))+~P1(f335(f335(f243(x68191),x68192),f335(f335(f240(x68191),x68193),x68194)))
% 59.73/59.67 [6841]~E(f335(f335(f158(x68411),x68413),x68414),x68412)+P1(f335(f335(f337(x68411),x68412),f335(f166(x68411),x68413)))+~P1(f335(f335(f243(a881),x68414),f335(f189(f882(x68411)),x68413)))
% 59.73/59.67 [6853]~P106(x68531)+~P15(x68531,f335(f335(f144(x68531),x68532),f335(f335(f144(x68531),x68533),x68534)))+P1(f335(f335(f242(x68531),x68532),x68533))
% 59.73/59.67 [6906]~P106(x69061)+P15(x69061,f335(f335(f144(x69061),x69062),x69063))+~P15(x69061,f335(f335(f144(x69061),x69064),f335(f335(f144(x69061),x69062),x69063)))
% 59.73/59.67 [6994]~P30(x69942,x69941,x69943)+P1(f335(x69941,f335(f335(f158(x69942),x69943),x69944)))+~P1(f335(f335(f243(a881),x69944),f335(f189(f882(x69942)),x69943)))
% 59.73/59.67 [7013]E(x70131,f2(a1))+E(f335(f335(f30(a1),x70132),x70131),x70133)+~P1(f335(f43(x70132,x70131),f335(f335(f264(a1,a1),x70133),x70134)))
% 59.73/59.67 [7034]E(f39(a1,x70342,x70341),x70343)+E(x70341,f2(a1))+~P1(f335(f43(x70342,x70341),f335(f335(f264(a1,a1),x70344),x70343)))
% 59.73/59.67 [7150]P1(f335(f335(f337(x71501),x71502),x71503))+~P1(f335(f335(f337(x71501),x71502),x71504))+~P1(f335(f335(f242(f888(x71501,a879)),x71504),x71503))
% 59.73/59.67 [7151]P1(f335(f335(f337(x71511),x71512),x71513))+~P1(f335(f335(f337(x71511),x71512),x71514))+~P1(f335(f335(f242(f888(x71511,a879)),x71514),x71513))
% 59.73/59.67 [7152]P1(f335(f335(f337(x71521),x71522),x71523))+~P1(f335(f335(f337(x71521),x71522),x71524))+~P1(f335(f335(f242(f888(x71521,a879)),x71524),x71523))
% 59.73/59.67 [7153]P1(f335(f335(f337(x71531),x71532),x71533))+~P1(f335(f335(f337(x71531),x71532),x71534))+~P1(f335(f335(f243(f888(x71531,a879)),x71534),x71533))
% 59.73/59.67 [7154]P1(f335(f335(f337(x71541),x71542),x71543))+~P1(f335(f335(f337(x71541),x71542),x71544))+~P1(f335(f335(f242(f888(x71541,a879)),x71544),x71543))
% 59.73/59.67 [7263]P32(x72631,x72632,x72633)+~P1(f335(x72632,f335(f335(f158(x72631),x72633),x72634)))+~P1(f335(f335(f243(a881),x72634),f335(f189(f882(x72631)),x72633)))
% 59.73/59.67 [7377]~P108(x73772)+~P1(f335(f335(f243(f888(x73771,x73772)),x73773),x73774))+P1(f335(f335(f242(f888(x73771,x73772)),x73773),x73774))
% 59.73/59.67 [7463]~P16(x74631,x74632,x74634)+P16(x74631,x74632,f335(f335(f312(f880(x74631)),x74633),x74634))+~P16(x74631,x74632,f335(f335(f312(f880(x74631)),x74633),f188(f888(f880(x74631),a879))))
% 59.73/59.67 [7507]~P1(f335(f335(f337(x75071),x75072),x75074))+P1(f335(f335(f337(x75071),x75072),f31(f888(x75071,a879),x75073)))+~P1(f335(f335(f337(f888(x75071,a879)),x75074),x75073))
% 59.73/59.67 [7537]~P86(x75371)+~P1(f335(f335(f242(x75371),x75373),x75374))+P1(f335(f335(f242(x75371),f335(f335(f75(x75371),x75372),x75373)),f335(f335(f75(x75371),x75372),x75374)))
% 59.73/59.67 [7538]~P87(x75381)+~P1(f335(f335(f242(x75381),x75383),x75384))+P1(f335(f335(f242(x75381),f335(f335(f75(x75381),x75382),x75383)),f335(f335(f75(x75381),x75382),x75384)))
% 59.73/59.67 [7539]~P86(x75391)+~P1(f335(f335(f242(x75391),x75392),x75394))+P1(f335(f335(f242(x75391),f335(f335(f75(x75391),x75392),x75393)),f335(f335(f75(x75391),x75394),x75393)))
% 59.73/59.67 [7540]~P87(x75401)+~P1(f335(f335(f242(x75401),x75402),x75404))+P1(f335(f335(f242(x75401),f335(f335(f75(x75401),x75402),x75403)),f335(f335(f75(x75401),x75404),x75403)))
% 59.73/59.67 [7541]~P86(x75411)+~P1(f335(f335(f243(x75411),x75413),x75414))+P1(f335(f335(f243(x75411),f335(f335(f75(x75411),x75412),x75413)),f335(f335(f75(x75411),x75412),x75414)))
% 59.73/59.67 [7542]~P89(x75421)+~P1(f335(f335(f243(x75421),x75423),x75424))+P1(f335(f335(f243(x75421),f335(f335(f75(x75421),x75422),x75423)),f335(f335(f75(x75421),x75422),x75424)))
% 59.73/59.67 [7543]~P86(x75431)+~P1(f335(f335(f243(x75431),x75432),x75434))+P1(f335(f335(f243(x75431),f335(f335(f75(x75431),x75432),x75433)),f335(f335(f75(x75431),x75434),x75433)))
% 59.73/59.67 [7544]~P89(x75441)+~P1(f335(f335(f243(x75441),x75442),x75444))+P1(f335(f335(f243(x75441),f335(f335(f75(x75441),x75442),x75443)),f335(f335(f75(x75441),x75444),x75443)))
% 59.73/59.67 [7553]~P118(x75531)+~P95(x75531)+E(f335(f335(f23(x75531),f335(f335(f76(x75531),x75532),f335(f97(x75531),x75533))),f335(f335(f76(x75531),x75534),f335(f97(x75531),x75533))),f335(f335(f76(x75531),f335(f335(f23(x75531),x75532),x75534)),f335(f97(x75531),x75533)))
% 59.73/59.67 [7554]~P139(x75541)+~P95(x75541)+E(f335(f335(f75(x75541),f335(f335(f76(x75541),x75542),f335(f97(x75541),x75543))),f335(f335(f76(x75541),x75544),f335(f97(x75541),x75543))),f335(f335(f76(x75541),f335(f335(f75(x75541),x75542),x75544)),f335(f97(x75541),x75543)))
% 59.73/59.67 [7591]~P77(x75911)+E(f335(f335(f75(x75911),f335(x75912,x75913)),f335(f335(f6(a881,x75911),x75912),f305(a881,f335(a106,x75913),x75914))),f335(f335(f6(a881,x75911),x75912),f305(a881,x75913,x75914)))+~P1(f335(f335(f242(a881),x75913),x75914))
% 59.73/59.67 [7603]~P26(x76032,x76031,x76033,f335(f166(x76032),x76034))+~P1(f335(f130(x76032),x76034))+P1(f335(f130(x76031),f335(f335(f147(x76032,x76031),x76033),x76034)))
% 59.73/59.67 [7650]~P1(f335(f335(f242(a881),x76502),x76504))+~P1(f335(f335(f242(a881),x76501),x76503))+P1(f335(f335(f242(a881),f335(f335(f76(a881),x76501),x76502)),f335(f335(f76(a881),x76503),x76504)))
% 59.73/59.67 [7651]~P1(f335(f335(f242(a881),x76512),x76514))+~P1(f335(f335(f242(a881),x76511),x76513))+P1(f335(f335(f242(a881),f335(f335(f75(a881),x76511),x76512)),f335(f335(f75(a881),x76513),x76514)))
% 59.73/59.67 [7654]~P1(f335(f335(f243(a881),x76542),x76544))+~P1(f335(f335(f243(a881),x76541),x76543))+P1(f335(f335(f243(a881),f335(f335(f75(a881),x76541),x76542)),f335(f335(f75(a881),x76543),x76544)))
% 59.73/59.67 [7655]~P1(f335(f335(f242(a1),x76552),x76554))+~P1(f335(f335(f243(a1),x76551),x76553))+P1(f335(f335(f243(a1),f335(f335(f75(a1),x76551),x76552)),f335(f335(f75(a1),x76553),x76554)))
% 59.73/59.67 [7703]P1(f335(f335(f337(x77031),x77032),x77033))+~P1(f335(f335(f337(x77031),x77032),f32(f888(x77031,a879),x77034)))+~P1(f335(f335(f337(f888(x77031,a879)),x77033),x77034))
% 59.73/59.67 [7704]P1(f335(f335(f337(x77041),x77042),x77043))+~P1(f335(f335(f337(x77041),x77042),f32(f888(x77041,a879),x77044)))+~P1(f335(f335(f337(f888(x77041,a879)),x77043),x77044))
% 59.73/59.67 [7720]~P1(f335(x77201,f686(x77201,x77203,x77202)))+P1(f335(x77201,f335(f335(f158(x77202),x77203),x77204)))+~P1(f335(f335(f243(a881),x77204),f335(f189(f882(x77202)),x77203)))
% 59.73/59.67 [7725]P1(f335(x77251,x77252))+~P1(f335(f335(f337(x77254),x77252),f335(f166(x77254),x77253)))+P1(f335(f335(f243(a881),f687(x77251,x77253,x77254)),f335(f189(f882(x77254)),x77253)))
% 59.73/59.67 [7773]~P108(x77731)+~P1(f335(f335(f243(f888(x77732,x77731)),x77734),x77733))+~P1(f335(f335(f242(f888(x77732,x77731)),x77733),x77734))
% 59.73/59.67 [7818]~P1(f335(x78184,x78182))+~P1(f335(f335(f337(x78181),x78182),x78183))+P1(f335(f335(f337(x78181),x78182),f335(f335(f95(f888(x78181,a879)),x78183),f335(f249(x78181),x78184))))
% 59.73/59.67 [7831]P1(f335(f335(f337(x78311),x78312),x78313))+~P1(f335(f335(f242(f888(x78311,a879)),x78313),x78314))+P1(f335(f335(f242(f888(x78311,a879)),x78313),f335(f335(f312(x78311),x78312),x78314)))
% 59.73/59.67 [7832]P1(f335(f335(f337(x78321),x78322),x78323))+~P1(f335(f335(f242(f888(x78321,a879)),x78323),x78324))+P1(f335(f335(f242(f888(x78321,a879)),x78323),f335(f335(f312(x78321),x78322),x78324)))
% 59.73/59.67 [7966]~P1(f335(f335(f337(x79661),x79663),x79664))+~P1(f335(f335(f243(f888(x79661,a879)),x79662),x79664))+P1(f335(f335(f243(f888(x79661,a879)),x79662),f335(f335(f312(x79661),x79663),x79664)))
% 59.73/59.67 [7968]E(f335(f335(f95(f888(x79681,a879)),x79682),x79683),f188(f888(x79681,a879)))+~E(f335(f335(f95(f888(x79681,a879)),f31(f888(x79681,a879),x79684)),x79683),f188(f888(x79681,a879)))+~P1(f335(f335(f337(f888(x79681,a879)),x79682),x79684))
% 59.73/59.67 [8044]P1(f335(f335(f337(x80441),x80442),x80443))+~P1(f335(f335(f242(f888(x80441,a879)),x80443),f335(f335(f312(x80441),x80442),x80444)))+P1(f335(f335(f242(f888(x80441,a879)),x80443),x80444))
% 59.73/59.67 [8045]P1(f335(f335(f337(x80451),x80452),x80453))+~P1(f335(f335(f242(f888(x80451,a879)),x80453),f335(f335(f312(x80451),x80452),x80454)))+P1(f335(f335(f242(f888(x80451,a879)),x80453),x80454))
% 59.73/59.67 [8062]P1(f335(f335(f337(x80622),f686(x80621,x80623,x80622)),f335(f166(x80622),x80623)))+P1(f335(x80621,f335(f335(f158(x80622),x80623),x80624)))+~P1(f335(f335(f243(a881),x80624),f335(f189(f882(x80622)),x80623)))
% 59.73/59.67 [8070]~P1(f335(f335(f242(f888(x80701,a879)),x80702),x80704))+P1(f335(f335(f242(f888(x80701,a879)),x80702),x80703))+~P1(f335(f335(f242(f888(x80701,a879)),x80704),x80703))
% 59.73/59.67 [8071]~P1(f335(f335(f243(f888(x80711,a879)),x80712),x80714))+~P1(f335(f335(f242(f888(x80711,a879)),x80714),x80713))+P1(f335(f335(f243(f888(x80711,a879)),x80712),x80713))
% 59.73/59.67 [8072]~P1(f335(f335(f242(f888(x80721,a879)),x80722),x80724))+~P1(f335(f335(f243(f888(x80721,a879)),x80724),x80723))+P1(f335(f335(f243(f888(x80721,a879)),x80722),x80723))
% 59.73/59.67 [8073]~P1(f335(f335(f243(f888(x80731,a879)),x80732),x80734))+P1(f335(f335(f243(f888(x80731,a879)),x80732),x80733))+~P1(f335(f335(f243(f888(x80731,a879)),x80734),x80733))
% 59.73/59.67 [8113]~P1(f335(f335(f337(x81131),x81134),x81133))+~P1(f335(f335(f243(f888(x81131,a879)),x81132),f335(f335(f312(x81131),x81134),x81133)))+P1(f335(f335(f243(f888(x81131,a879)),x81132),x81133))
% 59.73/59.67 [8123]~P86(x81231)+P1(f335(f335(f242(x81231),x81232),x81233))+~P1(f335(f335(f242(x81231),f335(f335(f75(x81231),x81234),x81232)),f335(f335(f75(x81231),x81234),x81233)))
% 59.73/59.67 [8124]~P86(x81241)+P1(f335(f335(f242(x81241),x81242),x81243))+~P1(f335(f335(f242(x81241),f335(f335(f75(x81241),x81244),x81242)),f335(f335(f75(x81241),x81244),x81243)))
% 59.73/59.67 [8125]~P86(x81251)+P1(f335(f335(f242(x81251),x81252),x81253))+~P1(f335(f335(f242(x81251),f335(f335(f75(x81251),x81252),x81254)),f335(f335(f75(x81251),x81253),x81254)))
% 59.73/59.67 [8126]~P86(x81261)+P1(f335(f335(f242(x81261),x81262),x81263))+~P1(f335(f335(f242(x81261),f335(f335(f75(x81261),x81262),x81264)),f335(f335(f75(x81261),x81263),x81264)))
% 59.73/59.67 [8127]~P86(x81271)+P1(f335(f335(f243(x81271),x81272),x81273))+~P1(f335(f335(f243(x81271),f335(f335(f75(x81271),x81274),x81272)),f335(f335(f75(x81271),x81274),x81273)))
% 59.73/59.67 [8128]~P86(x81281)+P1(f335(f335(f243(x81281),x81282),x81283))+~P1(f335(f335(f243(x81281),f335(f335(f75(x81281),x81284),x81282)),f335(f335(f75(x81281),x81284),x81283)))
% 59.73/59.67 [8129]~P86(x81291)+P1(f335(f335(f243(x81291),x81292),x81293))+~P1(f335(f335(f243(x81291),f335(f335(f75(x81291),x81292),x81294)),f335(f335(f75(x81291),x81293),x81294)))
% 59.73/59.67 [8130]~P86(x81301)+P1(f335(f335(f243(x81301),x81302),x81303))+~P1(f335(f335(f243(x81301),f335(f335(f75(x81301),x81302),x81304)),f335(f335(f75(x81301),x81303),x81304)))
% 59.73/59.67 [8178]P1(f335(x81781,x81782))+~E(f335(f335(f131(x81783),f335(f189(f882(x81783)),f171(x81783,x81781,x81784))),x81784),f107(x81783))+~P1(f335(f335(f337(x81783),x81782),f335(f166(x81783),x81784)))
% 59.73/59.67 [8303]P1(f335(x83031,x83032))+~P1(f335(f335(f337(x83033),x83032),f335(f166(x83033),x83034)))+P1(f335(f335(f243(a881),f335(f189(f882(x83033)),f335(f129(x83033,x83031),x83034))),f335(f189(f882(x83033)),x83034)))
% 59.73/59.67 [8779]~P1(f335(x87791,f769(x87791,x87793,x87792,x87794)))+P1(f335(x87791,f335(f335(f158(x87792),x87793),x87794)))+~P1(f335(f335(f243(a881),x87794),f335(f189(f882(x87792)),x87793)))
% 59.73/59.67 [8804]~P26(x88044,x88043,x88041,f252(f888(x88044,a879)))+E(f335(x88041,f685(x88042,x88041,x88043,x88044)),x88042)+~P1(f335(f335(f337(x88043),x88042),f335(f313(x88044,x88043,x88041),f252(f888(x88044,a879)))))
% 59.73/59.67 [8869]E(f171(x88691,x88692,x88693),f335(f335(f169(x88691),x88694),x88693))+P1(f335(f335(f243(a881),f745(x88692,x88693,x88691,x88694)),x88694))+P1(f335(f335(f243(a881),x88694),f335(f189(f882(x88691)),x88693)))
% 59.73/59.67 [8872]E(f171(x88721,x88722,x88723),f335(f335(f169(x88721),x88724),x88723))+P1(f335(f335(f243(a881),f745(x88722,x88723,x88721,x88724)),x88724))+P1(f335(x88722,f335(f335(f158(x88721),x88723),x88724)))
% 59.73/59.67 [8902]P1(f335(x89021,x89022))+~P1(f335(f335(f337(x89024),x89022),f335(f166(x89024),x89023)))+P1(f335(f335(f243(a881),f752(x89022,x89021,x89023,x89024)),f335(f189(f882(x89024)),x89023)))
% 59.73/59.67 [8904]E(f171(x89041,x89042,x89043),f335(f335(f169(x89041),x89044),x89043))+P1(f335(f335(f243(a881),x89044),f335(f189(f882(x89041)),x89043)))+P1(f335(f335(f243(a881),f745(x89042,x89043,x89041,x89044)),f335(f189(f882(x89041)),x89043)))
% 59.73/59.67 [8911]E(f171(x89111,x89112,x89113),f335(f335(f169(x89111),x89114),x89113))+P1(f335(x89112,f335(f335(f158(x89111),x89113),x89114)))+P1(f335(f335(f243(a881),f745(x89112,x89113,x89111,x89114)),f335(f189(f882(x89111)),x89113)))
% 59.73/59.67 [8939]~P122(x89394)+P1(f335(f335(f337(x89391),f789(x89392,x89393,x89391,x89394)),x89393))+P1(f335(f335(f243(x89394),f2(x89394)),f335(f335(f9(x89391,x89394),x89392),x89393)))
% 59.73/59.67 [8940]~P122(x89404)+P1(f335(f335(f337(x89401),f798(x89402,x89403,x89401,x89404)),x89403))+P1(f335(f335(f242(x89404),f2(x89404)),f335(f335(f9(x89401,x89404),x89402),x89403)))
% 59.73/59.67 [8970]~P1(f335(f56(x89701),x89704))+P1(f335(f335(f337(x89701),f534(x89702,x89703,x89704,x89701)),x89704))+P1(f335(f56(f887(x89701,x89703)),f335(f335(f266(x89701,x89703),x89704),x89702)))
% 59.73/59.67 [8999]P1(f335(f335(f337(x89992),f769(x89991,x89993,x89992,x89994)),f335(f166(x89992),x89993)))+P1(f335(x89991,f335(f335(f158(x89992),x89993),x89994)))+~P1(f335(f335(f243(a881),x89994),f335(f189(f882(x89992)),x89993)))
% 59.73/59.67 [9131]P1(f335(f335(f242(a881),x91314),f335(f189(f882(x91312)),f171(x91312,x91313,x91311))))+P1(f335(f335(f243(a881),f746(x91311,x91312,x91313,x91314)),x91314))+~P1(f335(f335(f242(a881),x91314),f335(f189(f882(x91312)),x91311)))
% 59.73/59.67 [9239]~E(f335(f335(f179(x92391,x92392),x92393),f758(x92394,x92393,x92392,x92391)),f335(f335(f179(x92391,x92392),x92394),f758(x92394,x92393,x92392,x92391)))+E(f335(f179(x92391,x92392),x92393),f335(f179(x92391,x92392),x92394))+~E(f335(f166(x92391),f335(f335(f147(f887(x92391,x92392),x92391),f263(x92391,x92392)),x92393)),f335(f166(x92391),f335(f335(f147(f887(x92391,x92392),x92391),f263(x92391,x92392)),x92394)))
% 59.73/59.67 [9284]E(f171(x92841,x92842,x92843),f335(f335(f169(x92841),x92844),x92843))+~P1(f335(x92842,f335(f335(f158(x92841),x92843),f745(x92842,x92843,x92841,x92844))))+P1(f335(f335(f243(a881),x92844),f335(f189(f882(x92841)),x92843)))
% 59.73/59.67 [9289]E(f171(x92891,x92892,x92893),f335(f335(f169(x92891),x92894),x92893))+~P1(f335(x92892,f335(f335(f158(x92891),x92893),f745(x92892,x92893,x92891,x92894))))+P1(f335(x92892,f335(f335(f158(x92891),x92893),x92894)))
% 59.73/59.67 [9296]~P1(f335(f56(x92961),x92963))+~P1(f335(f56(x92962),f335(x92964,f534(x92964,x92962,x92963,x92961))))+P1(f335(f56(f887(x92961,x92962)),f335(f335(f266(x92961,x92962),x92963),x92964)))
% 59.73/59.67 [9304]~P122(x93041)+~P1(f335(f335(f242(x93041),f2(x93041)),f335(x93043,f798(x93043,x93044,x93042,x93041))))+P1(f335(f335(f242(x93041),f2(x93041)),f335(f335(f9(x93042,x93041),x93043),x93044)))
% 59.73/59.67 [9305]~P122(x93051)+~P1(f335(f335(f243(x93051),f2(x93051)),f335(x93053,f789(x93053,x93054,x93052,x93051))))+P1(f335(f335(f243(x93051),f2(x93051)),f335(f335(f9(x93052,x93051),x93053),x93054)))
% 59.73/59.67 [9311]~E(f335(f189(f882(x93114)),x93112),f335(f189(f882(x93114)),x93113))+P1(f335(f335(f337(f887(f882(x93114),f882(x93114))),f335(f335(f264(f882(x93114),f882(x93114)),x93113),x93112)),f151(x93114,x93111)))+P1(f335(f335(f243(a881),f694(x93111,x93112,x93113,x93114)),f335(f189(f882(x93114)),x93113)))
% 59.73/59.67 [9361]~P1(f335(x93613,f335(f335(f158(x93612),x93614),f746(x93614,x93612,x93613,x93611))))+P1(f335(f335(f242(a881),x93611),f335(f189(f882(x93612)),f171(x93612,x93613,x93614))))+~P1(f335(f335(f242(a881),x93611),f335(f189(f882(x93612)),x93614)))
% 59.73/59.67 [9438]E(f335(f335(f169(x94381),f696(x94382,x94383,x94384,x94381)),x94383),f335(f335(f169(x94381),f696(x94382,x94383,x94384,x94381)),x94384))+~P1(f335(f335(f337(f887(f882(x94381),f882(x94381))),f335(f335(f264(f882(x94381),f882(x94381)),x94384),x94383)),f140(x94381,x94382)))+P1(f335(f335(f243(a881),f335(f189(f882(x94381)),x94384)),f335(f189(f882(x94381)),x94383)))
% 59.73/59.67 [9496]~P1(f335(f335(f243(a881),f2(a881)),x94963))+~P1(f335(f335(f243(a881),x94964),x94961))+P1(f335(f335(f243(a881),f335(f335(f75(a881),f335(f335(f76(a881),x94961),f39(a881,x94962,x94963))),x94964)),f335(f335(f76(a881),x94961),x94963)))
% 59.73/59.67 [9688]~P108(x96882)+~P1(f335(f335(f242(x96882),f335(x96883,f564(x96884,x96883,x96881,x96882))),f335(x96884,f564(x96884,x96883,x96881,x96882))))+P1(f335(f335(f242(f888(x96881,x96882)),x96883),x96884))
% 59.73/59.67 [9689]~P108(x96892)+~P1(f335(f335(f242(x96892),f335(x96893,f671(x96891,x96894,x96893,x96892))),f335(x96894,f671(x96891,x96894,x96893,x96892))))+P1(f335(f335(f242(f888(x96891,x96892)),x96893),x96894))
% 59.73/59.67 [9799]~P64(x97991)+E(f335(f335(f6(a881,x97991),f335(f335(f18(a881,x97991,x97991),f335(f335(f8(x97991,f888(x97991,x97991),a881),f23(x97991)),x97992)),f335(f335(f8(a881,x97991,a881),x97992),f335(f335(f7(a881,a881,a881),f75(a881)),f73(a881))))),f305(a881,x97993,x97994)),f335(f335(f23(x97991),f335(x97992,x97993)),f335(x97992,f335(f335(f75(a881),x97994),f73(a881)))))+~P1(f335(f335(f242(a881),x97993),x97994))
% 59.73/59.67 [6845]E(f335(f335(f127(x68451),x68452),x68453),x68454)+~E(x68453,f335(f335(f131(x68451),f335(f189(f882(x68451)),x68452)),x68454))+~E(f335(f335(f169(x68451),f335(f189(f882(x68451)),x68452)),x68454),x68452)
% 59.73/59.67 [6903]~P67(x69032)+E(x69031,f2(x69032))+E(f335(f335(f292(x69032),f335(f335(f254(x69032),x69033),x69034)),f335(f335(f254(x69032),x69031),x69034)),f335(f335(f254(x69032),f335(f335(f292(x69032),x69033),x69031)),x69034))
% 59.73/59.67 [7036]~E(f335(f189(f882(x70361)),x70363),f335(f189(f882(x70362)),x70364))+~P1(f335(f130(x70361),x70363))+E(f177(x70361,x70362,f335(f179(x70361,x70362),f335(f335(f175(x70361,x70362),x70363),x70364))),f335(f166(x70361),x70363))
% 59.73/59.67 [7052]~P102(x70521)+~P1(f335(f335(f242(x70521),x70523),x70524))+P1(f335(f335(f242(x70521),f335(f335(f95(x70521),x70522),x70523)),x70524))
% 59.73/59.67 [7053]~P102(x70531)+~P1(f335(f335(f242(x70531),x70532),x70534))+P1(f335(f335(f242(x70531),f335(f335(f95(x70531),x70532),x70533)),x70534))
% 59.73/59.67 [7054]~P106(x70541)+~P1(f335(f335(f242(x70541),x70543),x70544))+P1(f335(f335(f242(x70541),f335(f335(f240(x70541),x70542),x70543)),x70544))
% 59.73/59.67 [7055]~P106(x70551)+~P1(f335(f335(f242(x70551),x70553),x70554))+P1(f335(f335(f242(x70551),f335(f335(f240(x70551),x70552),x70553)),x70554))
% 59.73/59.67 [7056]~P106(x70561)+~P1(f335(f335(f242(x70561),x70562),x70564))+P1(f335(f335(f242(x70561),f335(f335(f240(x70561),x70562),x70563)),x70564))
% 59.73/59.67 [7057]~P106(x70571)+~P1(f335(f335(f242(x70571),x70572),x70574))+P1(f335(f335(f242(x70571),f335(f335(f240(x70571),x70572),x70573)),x70574))
% 59.73/59.67 [7058]~P102(x70581)+~P1(f335(f335(f243(x70581),x70583),x70584))+P1(f335(f335(f243(x70581),f335(f335(f95(x70581),x70582),x70583)),x70584))
% 59.73/59.67 [7059]~P102(x70591)+~P1(f335(f335(f243(x70591),x70592),x70594))+P1(f335(f335(f243(x70591),f335(f335(f95(x70591),x70592),x70593)),x70594))
% 59.73/59.67 [7060]~P106(x70601)+~P1(f335(f335(f243(x70601),x70603),x70604))+P1(f335(f335(f243(x70601),f335(f335(f240(x70601),x70602),x70603)),x70604))
% 59.73/59.67 [7061]~P106(x70611)+~P1(f335(f335(f243(x70611),x70613),x70614))+P1(f335(f335(f243(x70611),f335(f335(f240(x70611),x70612),x70613)),x70614))
% 59.73/59.67 [7062]~P106(x70621)+~P1(f335(f335(f243(x70621),x70622),x70624))+P1(f335(f335(f243(x70621),f335(f335(f240(x70621),x70622),x70623)),x70624))
% 59.73/59.67 [7063]~P106(x70631)+~P1(f335(f335(f243(x70631),x70632),x70634))+P1(f335(f335(f243(x70631),f335(f335(f240(x70631),x70632),x70633)),x70634))
% 59.73/59.67 [7084]~P1(f335(x70843,x70844))+~P1(f335(x70842,x70844))+P1(f335(f335(f335(f95(f888(x70841,a879)),x70842),x70843),x70844))
% 59.73/59.67 [7209]P16(x72091,x72092,x72093)+~P16(x72091,x72092,x72094)+~P1(f335(f335(f242(f888(f880(x72091),a879)),x72093),x72094))
% 59.73/59.67 [7581]~P77(x75811)+E(f335(f335(f75(x75811),f335(x75812,x75813)),f335(f335(f6(a881,x75811),x75812),f335(f304(a881,f335(a106,x75813)),x75814))),f335(f335(f6(a881,x75811),x75812),f335(f304(a881,x75813),x75814)))+~P1(f335(f335(f243(a881),x75813),x75814))
% 59.73/59.67 [7599]E(x75991,x75992)+P1(f335(f335(f166(x75993),x75994),x75992))+~P1(f335(f335(f166(x75993),f335(f335(f144(x75993),x75991),x75994)),x75992))
% 59.73/59.67 [7610]~P106(x76101)+P1(f335(f335(f242(x76101),x76102),x76103))+~P1(f335(f335(f242(x76101),f335(f335(f241(x76101),x76104),x76102)),x76103))
% 59.73/59.67 [7611]~P106(x76111)+P1(f335(f335(f242(x76111),x76112),x76113))+~P1(f335(f335(f242(x76111),f335(f335(f241(x76111),x76114),x76112)),x76113))
% 59.73/59.67 [7612]~P106(x76121)+P1(f335(f335(f242(x76121),x76122),x76123))+~P1(f335(f335(f242(x76121),f335(f335(f241(x76121),x76122),x76124)),x76123))
% 59.73/59.67 [7613]~P106(x76131)+P1(f335(f335(f242(x76131),x76132),x76133))+~P1(f335(f335(f242(x76131),f335(f335(f241(x76131),x76132),x76134)),x76133))
% 59.73/59.67 [7614]~P60(x76141)+P1(f335(f335(f242(x76141),x76142),x76143))+~P1(f335(f335(f242(x76141),f335(f335(f104(x76141),x76144),x76142)),x76143))
% 59.73/59.67 [7615]~P60(x76151)+P1(f335(f335(f242(x76151),x76152),x76153))+~P1(f335(f335(f242(x76151),f335(f335(f104(x76151),x76154),x76152)),x76153))
% 59.73/59.67 [7616]~P60(x76161)+P1(f335(f335(f242(x76161),x76162),x76163))+~P1(f335(f335(f242(x76161),f335(f335(f104(x76161),x76162),x76164)),x76163))
% 59.73/59.67 [7617]~P60(x76171)+P1(f335(f335(f242(x76171),x76172),x76173))+~P1(f335(f335(f242(x76171),f335(f335(f104(x76171),x76172),x76174)),x76173))
% 59.73/59.67 [7618]~P106(x76181)+P1(f335(f335(f243(x76181),x76182),x76183))+~P1(f335(f335(f243(x76181),f335(f335(f241(x76181),x76184),x76182)),x76183))
% 59.73/59.67 [7619]~P106(x76191)+P1(f335(f335(f243(x76191),x76192),x76193))+~P1(f335(f335(f243(x76191),f335(f335(f241(x76191),x76192),x76194)),x76193))
% 59.73/59.67 [7694]~P1(f335(f335(f337(x76941),x76942),x76944))+P1(f335(f335(f337(x76941),x76942),x76943))+P1(f335(f335(f337(x76941),x76942),f335(f335(f23(f888(x76941,a879)),x76944),x76943)))
% 59.73/59.67 [7695]~P1(f335(f335(f337(x76951),x76952),x76954))+P1(f335(f335(f337(x76951),x76952),x76953))+P1(f335(f335(f337(x76951),x76952),f335(f335(f23(f888(x76951,a879)),x76954),x76953)))
% 59.73/59.67 [7780]P1(f335(x77801,x77802))+P1(f335(x77803,x77802))+~P1(f335(f335(f335(f104(f888(x77804,a879)),x77803),x77801),x77802))
% 59.73/59.67 [7790]~P1(f335(f335(f337(x77901),x77902),x77904))+~P1(f335(f335(f337(x77901),x77902),x77903))+P1(f335(f335(f337(x77901),x77902),f335(f335(f95(f888(x77901,a879)),x77903),x77904)))
% 59.73/59.67 [7791]~P1(f335(f335(f337(x77911),x77912),x77914))+~P1(f335(f335(f337(x77911),x77912),x77913))+P1(f335(f335(f337(x77911),x77912),f335(f335(f95(f888(x77911,a879)),x77913),x77914)))
% 59.73/59.67 [7840]~P60(x78401)+~P1(f335(f56(x78401),x78404))+E(f335(f335(f59(x78401,x78401,f104(x78401)),x78402),f335(f335(f312(x78401),x78403),x78404)),f335(f335(f104(x78401),x78403),f335(f335(f59(x78401,x78401,f104(x78401)),x78402),x78404)))
% 59.73/59.67 [7841]~P102(x78411)+~P1(f335(f56(x78411),x78414))+E(f335(f335(f59(x78411,x78411,f95(x78411)),x78412),f335(f335(f312(x78411),x78413),x78414)),f335(f335(f95(x78411),x78413),f335(f335(f59(x78411,x78411,f95(x78411)),x78412),x78414)))
% 59.73/59.67 [7842]~P106(x78421)+~P1(f335(f56(x78421),x78424))+E(f335(f335(f59(x78421,x78421,f240(x78421)),x78422),f335(f335(f312(x78421),x78423),x78424)),f335(f335(f240(x78421),x78423),f335(f335(f59(x78421,x78421,f240(x78421)),x78422),x78424)))
% 59.73/59.67 [7843]~P106(x78431)+~P1(f335(f56(x78431),x78434))+E(f335(f335(f59(x78431,x78431,f241(x78431)),x78432),f335(f335(f312(x78431),x78433),x78434)),f335(f335(f241(x78431),x78433),f335(f335(f59(x78431,x78431,f241(x78431)),x78432),x78434)))
% 59.73/59.67 [7844]~P118(x78441)+~P95(x78441)+E(f335(f335(f23(x78441),f335(f335(f76(x78441),f335(f97(x78441),x78442)),x78443)),f335(f335(f76(x78441),f335(f97(x78441),x78442)),x78444)),f335(f335(f76(x78441),f335(f97(x78441),x78442)),f335(f335(f23(x78441),x78443),x78444)))
% 59.73/59.67 [7845]~P139(x78451)+~P95(x78451)+E(f335(f335(f75(x78451),f335(f335(f76(x78451),f335(f97(x78451),x78452)),x78453)),f335(f335(f76(x78451),f335(f97(x78451),x78452)),x78454)),f335(f335(f76(x78451),f335(f97(x78451),x78452)),f335(f335(f75(x78451),x78453),x78454)))
% 59.73/59.67 [7963]E(x79631,x79632)+P1(f335(f335(f337(x79633),x79631),f335(f166(x79633),x79634)))+~P1(f335(f335(f337(x79633),x79631),f335(f166(x79633),f335(f335(f144(x79633),x79632),x79634))))
% 59.73/59.67 [7992]~P4(x79921)+~E(f335(f189(f882(x79922)),x79923),f335(f189(f882(x79921)),f50(x79921)))+E(f335(f335(f179(x79921,x79922),f335(f335(f175(x79921,x79922),f50(x79921)),x79923)),x79924),f335(f235(x79922),f711(x79924,x79923,x79922,x79921)))
% 59.73/59.67 [8136]P52(x81361,x81362,x81363)+~P52(x81361,x81362,x81364)+~P1(f335(f335(f242(f888(f887(x81361,x81362),a879)),x81363),x81364))
% 59.73/59.67 [8180]P1(f335(f335(f337(x81801),x81802),x81803))+P1(f335(f335(f337(x81801),x81802),x81804))+~P1(f335(f335(f337(x81801),x81802),f335(f335(f104(f888(x81801,a879)),x81804),x81803)))
% 59.73/59.67 [8181]P1(f335(f335(f337(x81811),x81812),x81813))+P1(f335(f335(f337(x81811),x81812),x81814))+~P1(f335(f335(f337(x81811),x81812),f335(f335(f104(f888(x81811,a879)),x81814),x81813)))
% 59.73/59.67 [8189]~P46(x81891,x81894,x81893)+~P1(f335(f335(f337(x81891),x81892),x81894))+P1(f335(f335(f337(f887(x81891,x81891)),f335(f335(f264(x81891,x81891),x81892),x81892)),x81893))
% 59.73/59.67 [8190]~P46(x81901,x81904,x81903)+~P1(f335(f335(f337(x81901),x81902),x81904))+P1(f335(f335(f337(f887(x81901,x81901)),f335(f335(f264(x81901,x81901),x81902),x81902)),x81903))
% 59.73/59.67 [8191]~P46(x81911,x81914,x81913)+~P1(f335(f335(f337(x81911),x81912),x81914))+P1(f335(f335(f337(f887(x81911,x81911)),f335(f335(f264(x81911,x81911),x81912),x81912)),x81913))
% 59.73/59.67 [8206]~P1(f335(f56(x82062),x82064))+~P1(f335(f56(x82061),x82063))+P1(f335(f56(f887(x82061,x82062)),f335(f335(f266(x82061,x82062),x82063),f335(f16(f888(x82062,a879),x82061),x82064))))
% 59.73/59.67 [8207]~P1(f335(f335(f337(x82071),x82072),x82074))+~P1(f335(f335(f242(f888(x82071,a879)),x82073),x82074))+P1(f335(f335(f242(f888(x82071,a879)),f335(f335(f312(x82071),x82072),x82073)),x82074))
% 59.73/59.67 [8215]~P73(x82152)+~P137(x82152)+E(f335(f335(f9(x82151,x82152),f335(f335(f8(a1,x82152,x82151),f96(x82152)),x82153)),x82154),f335(f96(x82152),f335(f335(f9(x82151,a1),x82153),x82154)))
% 59.73/59.67 [8216]~P73(x82162)+~P143(x82162)+E(f335(f335(f9(x82161,x82162),f335(f335(f8(a881,x82162,x82161),f94(x82162)),x82163)),x82164),f335(f94(x82162),f335(f335(f9(x82161,a881),x82163),x82164)))
% 59.73/59.67 [8241]E(f335(f335(f23(f888(x82411,a879)),x82412),f335(f335(f23(f888(x82411,a879)),x82413),x82414)),x82414)+~P1(f335(f335(f242(f888(x82411,a879)),x82412),x82413))+~P1(f335(f335(f242(f888(x82411,a879)),x82414),x82412))
% 59.73/59.67 [8337]~P1(f335(f56(x83371),x83374))+E(f335(f335(f23(a881),f335(f335(f6(x83371,a881),x83372),x83373)),f335(f335(f6(x83371,a881),x83372),x83374)),f335(f335(f6(x83371,a881),x83372),f335(f335(f23(f888(x83371,a879)),x83373),x83374)))+~P1(f335(f335(f242(f888(x83371,a879)),x83374),x83373))
% 59.73/59.67 [8492]~P8(x84921,x84924,x84923)+~P1(f335(f335(f337(x84921),x84922),x84924))+P1(f335(f335(f337(x84921),x84922),f335(f288(x84921,x84921,x84923),f335(f335(f312(x84921),x84922),f188(f888(x84921,a879))))))
% 59.73/59.67 [8551]~P1(f335(f335(f242(f888(x85511,a879)),x85512),x85513))+~P1(f335(f335(f242(f888(x85511,a879)),x85512),x85514))+P1(f335(f335(f242(f888(x85511,a879)),x85512),f335(f335(f95(f888(x85511,a879)),x85513),x85514)))
% 59.73/59.67 [8649]E(x86491,f188(f888(x86492,a879)))+P1(f335(f56(x86493),x86494))+~P1(f335(f56(f887(x86493,x86492)),f335(f335(f266(x86493,x86492),x86494),f335(f16(f888(x86492,a879),x86493),x86491))))
% 59.73/59.67 [8650]E(x86501,f188(f888(x86502,a879)))+P1(f335(f56(x86503),x86504))+~P1(f335(f56(f887(x86502,x86503)),f335(f335(f266(x86502,x86503),x86501),f335(f16(f888(x86503,a879),x86502),x86504))))
% 59.73/59.67 [8719]P1(f335(f335(f337(x87191),x87192),f324(x87191,x87193)))+~P1(f335(f335(f337(x87191),x87194),f324(x87191,x87193)))+~P1(f335(f335(f337(f887(x87191,x87191)),f335(f335(f264(x87191,x87191),x87192),x87194)),x87193))
% 59.73/59.67 [8720]P1(f335(f335(f337(x87201),x87202),f324(x87201,x87203)))+~P1(f335(f335(f337(x87201),x87204),f324(x87201,x87203)))+~P1(f335(f335(f337(f887(x87201,x87201)),f335(f335(f264(x87201,x87201),x87202),x87204)),x87203))
% 59.73/59.67 [8772]~P36(x87721,x87724)+P1(f335(f335(f337(f887(x87721,x87721)),f335(f335(f264(x87721,x87721),x87723),x87722)),f310(x87721,x87724)))+P36(x87721,f335(f335(f312(f887(x87721,x87721)),f335(f335(f264(x87721,x87721),x87722),x87723)),x87724))
% 59.73/59.67 [8773]~P55(x87731,x87734)+P1(f335(f335(f337(f887(x87731,x87731)),f335(f335(f264(x87731,x87731),x87733),x87732)),f310(x87731,x87734)))+P55(x87731,f335(f335(f312(f887(x87731,x87731)),f335(f335(f264(x87731,x87731),x87732),x87733)),x87734))
% 59.73/59.67 [8854]~E(x88542,x88543)+~P1(f335(f335(f337(x88541),x88542),f335(f166(x88541),x88544)))+P1(f335(f335(f337(f887(x88541,x88541)),f335(f335(f264(x88541,x88541),x88542),x88543)),f335(f166(f887(x88541,x88541)),f335(f335(f175(x88541,x88541),x88544),x88544))))
% 59.73/59.67 [8877]~P37(f888(x88771,a879),f888(x88771,a879),x88773)+~P1(f335(f335(f337(x88771),x88772),f90(f888(x88771,a879),x88773)))+P1(f335(f335(f337(x88771),x88772),f335(x88773,f335(f335(f104(f888(x88771,a879)),x88774),f90(f888(x88771,a879),x88773)))))
% 59.73/59.67 [8937]~E(x89373,x89374)+P1(f335(f335(f268(x89371,x89371,a879),a332),x89372))+~P1(f335(f335(f337(f887(x89371,x89371)),x89372),f335(f166(f887(x89371,x89371)),f335(f335(f175(x89371,x89371),x89373),x89374))))
% 59.73/59.67 [8985]P1(f335(f335(f337(f887(f882(x89851),f882(x89851))),f335(f335(f264(f882(x89851),f882(x89851)),x89852),x89853)),f140(x89851,x89854)))+~E(f335(f335(f169(x89851),f335(f189(f882(x89851)),x89852)),x89853),x89852)+~P1(f335(f335(f243(a881),f335(f189(f882(x89851)),x89852)),f335(f189(f882(x89851)),x89853)))
% 59.73/59.67 [9080]~P1(f335(f56(x90801),x90804))+P1(f335(f335(f337(x90801),f853(x90802,x90803,x90804,x90801)),x90804))+P1(f335(f56(x90803),f335(f335(f33(x90801,f888(x90803,a879)),x90804),x90802)))
% 59.73/59.67 [9081]~P1(f335(f56(x90811),x90814))+P1(f335(f335(f337(x90811),f561(x90812,x90813,x90814,x90811)),x90814))+P1(f335(f56(x90813),f335(f335(f33(x90811,f888(x90813,a879)),x90814),x90812)))
% 59.73/59.67 [9170]P1(f335(f335(f337(f887(x91701,x91701)),x91702),f335(f335(f291(x91701,x91701,x91701),x91703),f310(x91701,x91703))))+~P1(f335(f335(f243(a881),f2(a881)),x91704))+~P1(f335(f335(f337(f887(x91701,x91701)),x91702),f335(f335(f183(f887(x91701,x91701),a879),x91704),x91703)))
% 59.73/59.67 [9177]~P36(x91771,x91772)+~P1(f335(f335(f337(f887(x91771,x91771)),f335(f335(f264(x91771,x91771),x91774),x91773)),x91772))+~P1(f335(f335(f337(f887(x91771,x91771)),f335(f335(f264(x91771,x91771),x91773),x91774)),x91772))
% 59.73/59.67 [9178]~P36(x91781,x91782)+~P1(f335(f335(f337(f887(x91781,x91781)),f335(f335(f264(x91781,x91781),x91784),x91783)),x91782))+~P1(f335(f335(f337(f887(x91781,x91781)),f335(f335(f264(x91781,x91781),x91783),x91784)),x91782))
% 59.73/59.67 [9303]~P1(f335(f56(x93031),x93034))+E(f335(f335(f6(x93031,a881),f335(f335(f8(f888(x93032,a879),a881,x93031),f29(x93032)),x93033)),x93034),f335(f29(f887(x93031,x93032)),f335(f335(f266(x93031,x93032),x93034),x93033)))+P1(f335(f335(f337(x93031),f535(x93033,x93032,x93034,x93031)),x93034))
% 59.73/59.67 [9307]~P1(f335(f130(x93071),x93072))+P1(f335(f130(x93071),f335(f335(f152(x93071,x93072),x93073),x93074)))+P1(f335(f335(f337(x93071),x93074),f335(f335(f23(f888(x93071,a879)),f335(f166(x93071),x93072)),f335(f335(f312(x93071),f335(f335(f158(x93071),x93072),x93073)),f188(f888(x93071,a879))))))
% 59.73/59.67 [9321]~P1(f335(f56(x93212),x93213))+~P1(f335(f56(x93211),f335(x93214,f853(x93214,x93211,x93213,x93212))))+P1(f335(f56(x93211),f335(f335(f33(x93212,f888(x93211,a879)),x93213),x93214)))
% 59.73/59.67 [9322]~P1(f335(f56(x93222),x93223))+~P1(f335(f56(x93221),f335(x93224,f561(x93224,x93221,x93223,x93222))))+P1(f335(f56(x93221),f335(f335(f33(x93222,f888(x93221,a879)),x93223),x93224)))
% 59.73/59.67 [9400]~P1(f335(f335(f337(f887(x94001,x94001)),x94002),f335(f335(f291(x94001,x94001,x94001),x94004),f310(x94001,x94004))))+P1(f335(f335(f337(f887(x94001,x94001)),x94002),f335(f335(f291(x94001,x94001,x94001),x94003),f310(x94001,x94003))))+~P1(f335(f335(f242(f888(f887(x94001,x94001),a879)),x94004),x94003))
% 59.73/59.67 [9407]E(f335(f335(f169(x94071),f696(x94074,x94073,x94072,x94071)),x94073),f335(f335(f169(x94071),f696(x94074,x94073,x94072,x94071)),x94072))+~P1(f335(f335(f337(f887(f882(x94071),f882(x94071))),f335(f335(f264(f882(x94071),f882(x94071)),x94072),x94073)),f140(x94071,x94074)))+E(f335(f335(f169(x94071),f335(f189(f882(x94071)),x94072)),x94073),x94072)
% 59.73/59.67 [9423]~P1(f335(f56(x94231),x94234))+E(f335(f335(f6(x94231,a881),f335(f335(f8(f888(x94232,a879),a881,x94231),f29(x94232)),x94233)),x94234),f335(f29(f887(x94231,x94232)),f335(f335(f266(x94231,x94232),x94234),x94233)))+~P1(f335(f56(x94232),f335(x94233,f535(x94233,x94232,x94234,x94231))))
% 59.73/59.67 [9427]~E(f335(f189(f882(x94271)),x94273),f335(f189(f882(x94271)),x94272))+P1(f335(f335(f337(f887(f882(x94271),f882(x94271))),f335(f335(f264(f882(x94271),f882(x94271)),x94272),x94273)),f151(x94271,x94274)))+P1(f335(f335(f337(f887(x94271,x94271)),f677(x94274,x94273,x94272,x94271)),f335(f166(f887(x94271,x94271)),f335(f335(f175(x94271,x94271),x94272),x94273))))
% 59.73/59.67 [9507]~P1(f335(f335(f337(f887(f882(x95071),f882(x95071))),f335(f335(f264(f882(x95071),f882(x95071)),x95072),x95073)),f140(x95071,x95074)))+E(f335(f335(f169(x95071),f335(f189(f882(x95071)),x95072)),x95073),x95072)+P1(f335(f335(f243(a881),f696(x95074,x95073,x95072,x95071)),f335(f335(f240(a881),f335(f189(f882(x95071)),x95072)),f335(f189(f882(x95071)),x95073))))
% 59.73/59.67 [9508]E(f335(f179(x95081,x95082),x95083),f335(f179(x95081,x95082),x95084))+~E(f335(f166(x95081),f335(f335(f147(f887(x95081,x95082),x95081),f263(x95081,x95082)),x95083)),f335(f166(x95081),f335(f335(f147(f887(x95081,x95082),x95081),f263(x95081,x95082)),x95084)))+P1(f335(f335(f337(x95081),f758(x95083,x95084,x95082,x95081)),f335(f166(x95081),f335(f335(f147(f887(x95081,x95082),x95081),f263(x95081,x95082)),x95084))))
% 59.73/59.67 [9530]~P1(f335(f335(f337(f887(f882(x95301),f882(x95301))),f335(f335(f264(f882(x95301),f882(x95301)),x95302),x95303)),f140(x95301,x95304)))+P1(f335(f335(f243(a881),f335(f189(f882(x95301)),x95302)),f335(f189(f882(x95301)),x95303)))+P1(f335(f335(f243(a881),f696(x95304,x95303,x95302,x95301)),f335(f335(f240(a881),f335(f189(f882(x95301)),x95302)),f335(f189(f882(x95301)),x95303))))
% 59.73/59.67 [9838]~P1(f335(f335(f335(x98381,f662(x98381,x98384,x98383,x98382)),f666(x98381,x98384,x98383,x98382)),f667(x98381,x98384,x98383,x98382)))+P1(f335(f335(f335(x98381,x98382),x98383),x98384))+~P1(f335(f323(f887(f888(a1,f885(f882(a331))),f887(a1,a1)),a320),f335(f335(f264(f888(a1,f885(f882(a331))),f887(a1,a1)),x98382),f335(f335(f264(a1,a1),x98383),x98384))))
% 59.73/59.67 [9915]P1(f335(f335(f335(x99151,x99152),x99153),x99154))+P1(f335(f323(f887(f888(a1,f885(f882(a331))),f887(a1,a1)),a320),f335(f335(f264(f888(a1,f885(f882(a331))),f887(a1,a1)),f662(x99151,x99154,x99153,x99152)),f335(f335(f264(a1,a1),f666(x99151,x99154,x99153,x99152)),f667(x99151,x99154,x99153,x99152)))))+~P1(f335(f323(f887(f888(a1,f885(f882(a331))),f887(a1,a1)),a320),f335(f335(f264(f888(a1,f885(f882(a331))),f887(a1,a1)),x99152),f335(f335(f264(a1,a1),x99153),x99154))))
% 59.73/59.67 [9952]~P1(f335(f335(f337(f887(f882(x99521),f882(x99521))),f335(f335(f264(f882(x99521),f882(x99521)),x99522),x99523)),f140(x99521,x99524)))+E(f335(f335(f169(x99521),f335(f189(f882(x99521)),x99522)),x99523),x99522)+P1(f335(f335(f337(f887(x99521,x99521)),f335(f335(f264(x99521,x99521),f335(f335(f158(x99521),x99522),f696(x99524,x99523,x99522,x99521))),f335(f335(f158(x99521),x99523),f696(x99524,x99523,x99522,x99521)))),x99524))
% 59.73/59.67 [9953]~P1(f335(f335(f337(f887(f882(x99531),f882(x99531))),f335(f335(f264(f882(x99531),f882(x99531)),x99532),x99533)),f140(x99531,x99534)))+P1(f335(f335(f243(a881),f335(f189(f882(x99531)),x99532)),f335(f189(f882(x99531)),x99533)))+P1(f335(f335(f337(f887(x99531,x99531)),f335(f335(f264(x99531,x99531),f335(f335(f158(x99531),x99532),f696(x99534,x99533,x99532,x99531))),f335(f335(f158(x99531),x99533),f696(x99534,x99533,x99532,x99531)))),x99534))
% 59.73/59.67 [10011]~E(f335(f189(f882(x100111)),x100112),f335(f189(f882(x100111)),x100113))+P1(f335(f335(f337(f887(f882(x100111),f882(x100111))),f335(f335(f264(f882(x100111),f882(x100111)),x100112),x100113)),f151(x100111,x100114)))+~P1(f335(f335(f337(f887(x100111,x100111)),f335(f335(f264(x100111,x100111),f335(f335(f158(x100111),x100112),f694(x100114,x100113,x100112,x100111))),f335(f335(f158(x100111),x100113),f694(x100114,x100113,x100112,x100111)))),x100114))
% 59.73/59.67 [10143]~P77(x101431)+~P1(f335(f56(x101432),x101434))+E(f335(f159(x101431),f335(f335(f147(x101432,x101431),x101433),f85(f882(x101432),f335(f335(f18(f882(x101432),a879,a879),f335(f335(f8(a879,f888(a879,a879),f882(x101432)),a333),f335(f335(f7(f882(x101432),f888(x101432,a879),a879),f335(f335(f8(f888(x101432,a879),f888(f888(x101432,a879),a879),f882(x101432)),a332),f166(x101432))),x101434))),f130(x101432))))),f233(x101432,x101431,x101433,x101434))
% 59.73/59.67 [7423]~P66(x74232)+E(x74231,f2(x74232))+E(f335(f335(f292(x74232),f335(f335(f75(x74232),x74233),f335(f335(f76(x74232),x74234),x74231))),x74231),f335(f335(f75(x74232),x74234),f335(f335(f292(x74232),x74233),x74231)))
% 59.73/59.67 [7424]~P58(x74242)+E(x74241,f2(x74242))+E(f335(f335(f30(x74242),f335(f335(f75(x74242),x74243),f335(f335(f76(x74242),x74244),x74241))),x74241),f335(f335(f75(x74242),x74244),f335(f335(f30(x74242),x74243),x74241)))
% 59.73/59.67 [7425]~P58(x74252)+E(x74251,f2(x74252))+E(f335(f335(f30(x74252),f335(f335(f75(x74252),x74253),f335(f335(f76(x74252),x74251),x74254))),x74251),f335(f335(f75(x74252),x74254),f335(f335(f30(x74252),x74253),x74251)))
% 59.73/59.67 [7658]~P67(x76582)+E(x76581,f2(x76582))+E(f335(f335(f292(x76582),f335(f335(f23(x76582),x76583),f335(f335(f76(x76582),x76581),x76584))),x76581),f335(f335(f23(x76582),f335(f335(f292(x76582),x76583),x76581)),x76584))
% 59.73/59.67 [7659]~P66(x76592)+E(x76591,f2(x76592))+E(f335(f335(f292(x76592),f335(f335(f75(x76592),x76593),f335(f335(f76(x76592),x76594),x76591))),x76591),f335(f335(f75(x76592),f335(f335(f292(x76592),x76593),x76591)),x76594))
% 59.73/59.67 [7660]~P67(x76602)+E(x76601,f2(x76602))+E(f335(f335(f292(x76602),f335(f335(f75(x76602),x76603),f335(f335(f76(x76602),x76601),x76604))),x76601),f335(f335(f75(x76602),f335(f335(f292(x76602),x76603),x76601)),x76604))
% 59.73/59.67 [8366]~P1(f335(f153(x83661,x83663),x83664))+~P1(f335(f153(x83661,x83662),x83664))+P1(f335(f153(x83661,f335(f335(f95(f888(x83661,a879)),x83662),x83663)),x83664))
% 59.73/59.67 [8734]~E(f335(f335(f291(x87341,x87341,x87341),x87342),x87344),f188(f888(f887(x87341,x87341),a879)))+~E(f335(f335(f291(x87341,x87341,x87341),x87342),x87343),f188(f888(f887(x87341,x87341),a879)))+E(f335(f335(f291(x87341,x87341,x87341),x87342),f335(f335(f104(f888(f887(x87341,x87341),a879)),x87343),x87344)),f188(f888(f887(x87341,x87341),a879)))
% 59.73/59.67 [8855]~P1(f335(f335(f242(f888(x88551,a879)),x88553),x88554))+~P1(f335(f335(f242(f888(x88551,a879)),x88552),x88554))+P1(f335(f335(f242(f888(x88551,a879)),f335(f335(f104(f888(x88551,a879)),x88552),x88553)),x88554))
% 59.73/59.67 [9233]~P1(f335(f56(x92331),x92334))+~P1(f335(f56(x92331),x92333))+E(f335(f335(f23(a881),f335(f335(f75(a881),f335(f335(f6(x92331,a881),x92332),x92333)),f335(f335(f6(x92331,a881),x92332),x92334))),f335(f335(f6(x92331,a881),x92332),f335(f335(f95(f888(x92331,a879)),x92333),x92334))),f335(f335(f6(x92331,a881),x92332),f335(f335(f104(f888(x92331,a879)),x92333),x92334)))
% 59.73/59.67 [9317]~P1(f335(f335(f337(x93171),x93173),x93172))+~P1(f335(f335(f242(f888(x93171,a879)),x93172),f335(f335(f312(x93171),x93173),x93174)))+P1(f335(f335(f242(f888(x93171,a879)),f335(f335(f23(f888(x93171,a879)),x93172),f335(f335(f312(x93171),x93173),f188(f888(x93171,a879))))),x93174))
% 59.73/59.67 [9481]~P1(f335(f335(f337(x94811),x94813),x94812))+P1(f335(f335(f242(f888(x94811,a879)),x94812),f335(f335(f312(x94811),x94813),x94814)))+~P1(f335(f335(f242(f888(x94811,a879)),f335(f335(f23(f888(x94811,a879)),x94812),f335(f335(f312(x94811),x94813),f188(f888(x94811,a879))))),x94814))
% 59.73/59.67 [9482]~P1(f335(f335(f337(x94821),x94823),x94822))+P1(f335(f335(f242(f888(x94821,a879)),x94822),f335(f335(f312(x94821),x94823),x94824)))+~P1(f335(f335(f242(f888(x94821,a879)),f335(f335(f23(f888(x94821,a879)),x94822),f335(f335(f312(x94821),x94823),f188(f888(x94821,a879))))),x94824))
% 59.73/59.67 [9506]~P1(f335(f335(f242(f888(x95061,a879)),x95062),x95064))+P1(f335(f335(f242(f888(x95061,a879)),x95062),f335(f335(f312(x95061),x95063),x95064)))+~P1(f335(f335(f242(f888(x95061,a879)),f335(f335(f23(f888(x95061,a879)),x95062),f335(f335(f312(x95061),x95063),f188(f888(x95061,a879))))),x95064))
% 59.73/59.67 [9569]~P1(f335(f335(f242(a881),x95691),x95693))+~P1(f335(f335(f243(a881),x95692),x95694))+P1(f335(f335(f337(f887(f887(a881,a881),f887(a881,a881))),f335(f335(f264(f887(a881,a881),f887(a881,a881)),f335(f335(f264(a881,a881),x95691),x95692)),f335(f335(f264(a881,a881),x95693),x95694))),a26))
% 59.73/59.67 [9570]~P1(f335(f335(f242(a881),x95702),x95704))+~P1(f335(f335(f242(a881),x95701),x95703))+P1(f335(f335(f337(f887(f887(a881,a881),f887(a881,a881))),f335(f335(f264(f887(a881,a881),f887(a881,a881)),f335(f335(f264(a881,a881),x95701),x95702)),f335(f335(f264(a881,a881),x95703),x95704))),a65))
% 59.73/59.67 [9877]~P1(f335(f335(f337(f882(x98771)),x98774),f154(x98771,x98773)))+~P1(f335(f335(f337(f882(x98771)),x98774),f154(x98771,x98772)))+P1(f335(f153(x98771,f335(f335(f95(f888(x98771,a879)),f335(f335(f7(x98771,f888(x98771,a879),a879),f337(x98771)),x98772)),f335(f335(f7(x98771,f888(x98771,a879),a879),f337(x98771)),x98773))),x98774))
% 59.73/59.67 [9976]~P26(x99761,f888(f888(x99761,a879),a879),f335(f335(f7(x99761,f888(f887(x99761,x99761),a879),f888(f888(x99761,a879),a879)),f335(f335(f8(f888(x99761,a879),f888(f888(f887(x99761,x99761),a879),f888(f888(x99761,a879),a879)),x99761),f55(x99761)),f335(f335(f7(x99761,f888(x99761,a879),f888(x99761,a879)),f312(x99761)),f188(f888(x99761,a879))))),x99763),x99762)+~P1(f335(f335(f337(x99761),x99764),x99762))+E(f335(f335(f23(f888(f888(x99761,a879),a879)),f335(f335(f55(x99761),x99762),x99763)),f335(f335(f55(x99761),f335(f335(f312(x99761),x99764),f188(f888(x99761,a879)))),x99763)),f335(f335(f55(x99761),f335(f335(f23(f888(x99761,a879)),x99762),f335(f335(f312(x99761),x99764),f188(f888(x99761,a879))))),x99763))
% 59.73/59.67 [10109]~P46(x101091,x101092,x101094)+~P1(f335(f335(f337(f887(x101091,x101091)),x101093),x101094))+P1(f335(f335(f268(x101091,x101091,a879),f335(f335(f7(x101091,f888(x101091,a879),f888(x101091,a879)),f335(f335(f8(f888(a879,a879),f888(f888(x101091,a879),f888(x101091,a879)),x101091),f8(a879,a879,x101091)),f335(f335(f8(a879,f888(a879,a879),x101091),a333),f335(f335(f7(x101091,f888(x101091,a879),a879),f337(x101091)),x101092)))),f335(f335(f7(x101091,f888(x101091,a879),a879),f337(x101091)),x101092))),x101093))
% 59.73/59.67 [10119]P1(f335(f56(x101191),x101192))+~P1(f335(f56(x101193),f335(f313(x101191,x101193,x101194),x101192)))+~P1(f335(f56(x101191),f335(f249(x101191),f335(f335(f18(x101191,a879,a879),f335(f335(f8(a879,f888(a879,a879),x101191),a333),f335(f335(f7(x101191,f888(x101191,a879),a879),f337(x101191)),x101192))),f335(f335(f7(x101191,x101193,a879),f335(f335(f8(x101193,f888(x101193,a879),x101191),a332),x101194)),f335(x101194,f553(x101194,x101193,x101192,x101191)))))))
% 59.73/59.67 [8119]~P67(x81192)+E(x81191,f2(x81192))+E(f335(f335(f292(x81192),f335(f335(f23(x81192),f335(f335(f76(x81192),x81191),x81193)),x81194)),x81191),f335(f335(f23(x81192),x81193),f335(f335(f292(x81192),x81194),x81191)))
% 59.73/59.67 [8120]~P67(x81202)+E(x81201,f2(x81202))+E(f335(f335(f292(x81202),f335(f335(f75(x81202),f335(f335(f76(x81202),x81201),x81203)),x81204)),x81201),f335(f335(f75(x81202),x81203),f335(f335(f292(x81202),x81204),x81201)))
% 59.73/59.67 [9014]~E(f335(f335(f291(x90141,x90141,x90141),x90143),x90144),f188(f888(f887(x90141,x90141),a879)))+~E(f335(f335(f291(x90141,x90141,x90141),x90142),x90144),f188(f888(f887(x90141,x90141),a879)))+E(f335(f335(f291(x90141,x90141,x90141),f335(f335(f104(f888(f887(x90141,x90141),a879)),x90142),x90143)),x90144),f188(f888(f887(x90141,x90141),a879)))
% 59.73/59.67 [10053]~P144(x100531)+~P144(x100532)+E(f335(f335(f319(x100531),f335(f335(f7(x100531,a93,f885(f882(a331))),f335(f335(f8(f888(x100532,f885(f882(a331))),f888(a93,f885(f882(a331))),x100531),f319(x100532)),f335(f335(f8(f888(x100532,f887(x100531,x100532)),f888(x100532,f885(f882(a331))),x100531),f335(f8(f887(x100531,x100532),f885(f882(a331)),x100532),x100533)),f264(x100531,x100532)))),x100534)),x100534),f335(f335(f319(f887(x100531,x100532)),x100533),x100534))
% 59.73/59.67 [9783]~P1(f335(f153(x97831,x97833),x97834))+~P1(f335(f153(x97831,x97832),x97834))+P1(f335(f153(x97831,f335(f335(f18(x97831,a879,a879),f335(f335(f8(a879,f888(a879,a879),x97831),a333),x97832)),x97833)),x97834))
% 59.73/59.67 [10045]P1(f335(x100451,f864(x100452,x100453,x100451,x100454)))+~P1(f335(f56(x100454),f335(f249(x100454),x100451)))+P1(f335(f56(x100453),f335(f249(x100453),f335(f335(f8(f888(x100454,a879),a879,x100453),f82(x100454)),f335(f335(f8(f888(x100454,a879),f888(x100454,a879),x100453),f335(f18(x100454,a879,a879),f335(f335(f8(a879,f888(a879,a879),x100454),a333),x100451))),x100452)))))
% 59.73/59.67 [10066]~P1(f335(f56(x100662),f335(f249(x100662),x100663)))+~P1(f335(f56(x100661),f335(f249(x100661),f335(f335(f7(x100661,x100662,a879),x100664),f864(x100664,x100661,x100663,x100662)))))+P1(f335(f56(x100661),f335(f249(x100661),f335(f335(f8(f888(x100662,a879),a879,x100661),f82(x100662)),f335(f335(f8(f888(x100662,a879),f888(x100662,a879),x100661),f335(f18(x100662,a879,a879),f335(f335(f8(a879,f888(a879,a879),x100662),a333),x100663))),x100664)))))
% 59.73/59.67 [5062]~E(x50622,x50624)+E(f163(x50621,x50622,x50623),f163(x50621,x50624,x50625))+~E(x50622,f2(a881))
% 59.73/59.67 [5314]E(x53141,x53142)+~E(f163(x53144,x53143,x53141),f163(x53144,x53145,x53142))+E(x53143,f2(a881))
% 59.73/59.67 [6554]E(x65541,x65542)+~E(f335(x65543,x65541),f335(x65543,x65542))+~P26(x65544,x65545,x65543,f252(f888(x65544,a879)))
% 59.73/59.67 [6555]E(x65551,x65552)+~E(f335(x65553,x65551),f335(x65553,x65552))+~P26(x65554,x65555,x65553,f252(f888(x65554,a879)))
% 59.73/59.67 [6722]~E(f335(x67223,x67225),f200(x67222))+~E(f335(x67224,x67225),f200(x67222))+E(f335(f180(x67221,x67222,x67223,x67224),x67225),f200(x67222))
% 59.73/59.67 [7458]E(x74581,x74582)+~P26(x74583,x74584,x74585,f252(f888(x74583,a879)))+~E(f335(f313(x74583,x74584,x74585),x74581),f335(f313(x74583,x74584,x74585),x74582))
% 59.73/59.67 [7713]P26(x77132,x77133,f651(x77134,x77133,x77132,x77131),x77131)+~E(f335(f313(x77133,x77132,x77135),x77134),x77131)+E(x77131,f188(f888(x77132,a879)))
% 59.73/59.67 [8252]~P1(f335(f335(x82523,x82522),x82525))+~P1(f335(f335(x82523,x82524),x82522))+P1(f335(f335(f337(x82521),x82522),f298(x82521,x82523,x82524,x82525)))
% 59.73/59.67 [8253]~P1(f335(f335(x82533,x82532),x82535))+~P1(f335(f335(x82533,x82534),x82532))+P1(f335(f335(f337(x82531),x82532),f301(x82531,x82533,x82534,x82535)))
% 59.73/59.67 [8813]~P26(x88131,x88133,x88135,f252(f888(x88131,a879)))+~P26(x88133,x88132,x88134,f252(f888(x88133,a879)))+P26(x88131,x88132,f335(f68(x88133,x88132,x88131,x88134),x88135),f252(f888(x88131,a879)))
% 59.73/59.67 [9375]P1(f335(f335(f337(f887(x93751,x93751)),f335(f335(f264(x93751,x93751),x93752),x93753)),f310(x93751,x93754)))+~P1(f335(f335(f337(f887(x93751,x93751)),f335(f335(f264(x93751,x93751),x93752),x93755)),f310(x93751,x93754)))+~P1(f335(f335(f337(f887(x93751,x93751)),f335(f335(f264(x93751,x93751),x93755),x93753)),f310(x93751,x93754)))
% 59.73/59.67 [9414]~P106(x94142)+~P1(f335(f130(x94141),x94145))+P1(f335(f130(x94141),f142(x94141,x94142,x94143,x94144,x94145)))
% 59.73/59.67 [5386]~E(x53862,f107(x53861))+E(f335(f335(f127(x53861),x53862),x53863),f335(f335(f144(x53861),x53864),x53865))+~E(x53863,f335(f335(f144(x53861),x53864),x53865))
% 59.73/59.67 [5387]~E(x53872,f107(x53871))+E(f335(f335(f127(x53871),x53872),x53873),f335(f335(f144(x53871),x53874),x53875))+~E(f335(f335(f144(x53871),x53874),x53875),x53873)
% 59.73/59.67 [6511]~E(f335(f189(f882(x65111)),x65115),f335(f189(f882(x65112)),x65114))+E(f335(f335(f147(f887(x65111,x65112),x65112),f267(x65111,x65112)),x65113),x65114)+~E(f335(f335(f175(x65111,x65112),x65115),x65114),x65113)
% 59.73/59.67 [6512]~E(f335(f189(f882(x65121)),x65124),f335(f189(f882(x65122)),x65125))+E(f335(f335(f147(f887(x65121,x65122),x65121),f263(x65121,x65122)),x65123),x65124)+~E(f335(f335(f175(x65121,x65122),x65124),x65125),x65123)
% 59.73/59.67 [6995]~P106(x69951)+~P15(x69951,f335(f335(f147(x69952,x69951),x69953),x69955))+P15(x69951,f335(f335(f147(x69952,x69951),x69953),f335(f129(x69952,x69954),x69955)))
% 59.73/59.67 [7137]~P106(x71371)+P15(x71371,f335(f335(f147(x71372,x71371),x71373),f164(x71372,x71374,x71375)))+~P15(x71371,f335(f335(f147(x71372,x71371),x71373),x71375))
% 59.73/59.67 [7160]~P52(x71603,x71602,x71605)+~P52(x71601,x71603,x71604)+P52(x71601,x71602,f335(f335(f291(x71601,x71603,x71602),x71604),x71605))
% 59.73/59.67 [7251]E(x72511,x72512)+~P26(x72513,x72514,x72515,f252(f888(x72513,a879)))+~E(f335(f335(f147(x72513,x72514),x72515),x72511),f335(f335(f147(x72513,x72514),x72515),x72512))
% 59.73/59.67 [7252]E(x72521,x72522)+~P26(x72523,x72524,x72525,f252(f888(x72523,a879)))+~E(f335(f335(f147(x72523,x72524),x72525),x72521),f335(f335(f147(x72523,x72524),x72525),x72522))
% 59.73/59.67 [7410]~P1(f335(f335(f242(a881),x74101),f335(x74103,x74105)))+P1(f335(f335(f242(a881),x74101),f148(x74102,x74103,x74104)))+~P1(f335(f335(f337(x74102),x74105),f335(f166(x74102),x74104)))
% 59.73/59.67 [7411]~P1(f335(f335(f243(a881),x74111),f335(x74113,x74115)))+P1(f335(f335(f243(a881),x74111),f148(x74112,x74113,x74114)))+~P1(f335(f335(f337(x74112),x74115),f335(f166(x74112),x74114)))
% 59.73/59.67 [7774]~E(x77743,f2(a881))+P1(f335(x77741,x77742))+~P1(f335(f335(f337(x77744),x77742),f335(f166(x77744),f163(x77744,x77743,x77745))))
% 59.73/59.67 [7789]~E(x77891,f2(a881))+~P1(f335(x77892,x77893))+~P1(f335(f335(f337(x77894),x77893),f335(f166(x77894),f163(x77894,x77891,x77895))))
% 59.73/59.67 [7812]P1(f335(x78121,x78122))+~P1(f335(x78121,x78123))+~P1(f335(f335(f337(x78124),x78122),f335(f166(x78124),f163(x78124,x78125,x78123))))
% 59.73/59.67 [7813]P1(f335(x78131,x78132))+~P1(f335(x78131,x78133))+~P1(f335(f335(f337(x78134),x78133),f335(f166(x78134),f163(x78134,x78135,x78132))))
% 59.73/59.67 [7817]~P107(x78171)+P1(f335(f335(f242(f888(x78171,a879)),f305(x78171,x78172,x78173)),f305(x78171,x78174,x78175)))+P1(f335(f335(f242(x78171),x78172),x78173))
% 59.73/59.67 [7838]~P5(x78381)+P1(f335(f335(f242(x78381),f335(f335(f34(x78382,x78381),x78383),x78384)),f335(x78384,x78385)))+~P1(f335(f335(f337(x78382),x78385),x78383))
% 59.73/59.67 [7907]~P26(x79071,x79072,x79074,x79073)+E(f335(f72(x79071,x79072,x79073,x79074),f335(x79074,x79075)),x79075)+~P1(f335(f335(f337(x79071),x79075),x79073))
% 59.73/59.67 [7908]~P26(x79081,x79082,x79084,x79083)+E(f335(f87(x79081,x79082,x79083,x79084),f335(x79084,x79085)),x79085)+~P1(f335(f335(f337(x79081),x79085),x79083))
% 59.73/59.67 [8108]~P1(f335(x81081,x81085))+P1(f335(x81081,f408(x81081,x81082,x81083,x81084)))+~P1(f335(f335(f337(x81084),x81085),x81083))
% 59.73/59.67 [8109]~P1(f335(x81091,x81095))+P1(f335(x81091,f408(x81091,x81092,x81093,x81094)))+~P1(f335(f335(f337(x81094),x81095),x81092))
% 59.73/59.67 [8204]P1(f335(f56(x82041),x82042))+~P1(f335(f56(x82043),x82044))+~P1(f335(f335(f242(f888(x82041,a879)),x82042),f335(f313(x82043,x82041,x82045),x82044)))
% 59.73/59.67 [8214]~P26(x82144,x82141,x82142,f252(f888(x82144,a879)))+~P1(f335(f335(f337(x82144),x82143),x82145))+P1(f335(f335(f337(x82141),f335(x82142,x82143)),f335(f313(x82144,x82141,x82142),x82145)))
% 59.73/59.67 [8369]E(x83691,x83692)+~P26(x83693,x83694,x83695,f335(f335(f104(f888(x83693,a879)),f335(f166(x83693),x83691)),f335(f166(x83693),x83692)))+~E(f335(f335(f147(x83693,x83694),x83695),x83691),f335(f335(f147(x83693,x83694),x83695),x83692))
% 59.73/59.67 [8370]E(x83701,x83702)+~P26(x83703,x83704,x83705,f335(f335(f104(f888(x83703,a879)),f335(f166(x83703),x83701)),f335(f166(x83703),x83702)))+~E(f335(f335(f147(x83703,x83704),x83705),x83701),f335(f335(f147(x83703,x83704),x83705),x83702))
% 59.73/59.67 [8427]~P107(x84271)+~P1(f335(f335(f243(f888(x84271,a879)),f305(x84271,x84274,x84275)),f305(x84271,x84272,x84273)))+P1(f335(f335(f242(x84271),x84272),x84273))
% 59.73/59.67 [8491]~P26(x84911,x84914,x84915,f252(f888(x84911,a879)))+~P1(f335(f335(f337(x84914),f335(x84915,x84912)),f335(f313(x84911,x84914,x84915),x84913)))+P1(f335(f335(f337(x84911),x84912),x84913))
% 59.73/59.67 [8564]P1(f335(x85641,x85642))+~P1(f335(x85641,f355(x85641,x85643,x85644,x85645)))+~P1(f335(f335(f337(x85645),x85642),x85644))
% 59.73/59.67 [8565]P1(f335(x85651,x85652))+~P1(f335(x85651,f355(x85651,x85653,x85654,x85655)))+~P1(f335(f335(f337(x85655),x85652),x85653))
% 59.73/59.67 [8852]~P26(x88522,x88523,x88521,x88524)+E(f335(x88521,f335(f72(x88522,x88523,x88524,x88521),x88525)),x88525)+~P1(f335(f335(f337(x88523),x88525),f335(f313(x88522,x88523,x88521),x88524)))
% 59.73/59.67 [8958]E(x89581,f107(x89582))+E(f335(f335(f144(x89582),x89583),f700(x89584,x89583,x89585,x89581,x89582)),x89581)+~E(f335(f335(f127(x89582),x89581),x89585),f335(f335(f144(x89582),x89583),x89584))
% 59.73/59.67 [8959]E(x89591,f107(x89592))+E(f335(f335(f144(x89592),x89593),f701(x89594,x89591,x89595,x89593,x89592)),x89591)+~E(f335(f335(f127(x89592),x89591),x89594),f335(f335(f144(x89592),x89593),x89595))
% 59.73/59.67 [8974]E(f335(f335(f144(x89742),x89743),f700(x89744,x89743,x89741,x89745,x89742)),x89745)+~E(f335(f335(f127(x89742),x89745),x89741),f335(f335(f144(x89742),x89743),x89744))+E(x89741,f335(f335(f144(x89742),x89743),x89744))
% 59.73/59.67 [8975]E(f335(f335(f144(x89751),x89752),f701(x89754,x89755,x89753,x89752,x89751)),x89755)+~E(f335(f335(f127(x89751),x89755),x89754),f335(f335(f144(x89751),x89752),x89753))+E(f335(f335(f144(x89751),x89752),x89753),x89754)
% 59.73/59.67 [9051]~E(f335(f313(x90513,x90512,x90514),f252(f888(x90513,a879))),f252(f888(x90512,a879)))+~E(f335(f313(x90511,x90513,x90515),f252(f888(x90511,a879))),f252(f888(x90513,a879)))+E(f335(f313(x90511,x90512,f335(f68(x90513,x90512,x90511,x90514),x90515)),f252(f888(x90511,a879))),f252(f888(x90512,a879)))
% 59.73/59.67 [9420]E(x94201,f107(x94202))+~E(f335(f335(f127(x94202),x94201),x94203),f335(f335(f144(x94202),x94205),x94204))+E(f335(f335(f127(x94202),f701(x94203,x94201,x94204,x94205,x94202)),x94203),x94204)
% 59.73/59.67 [9421]E(x94211,f107(x94212))+~E(f335(f335(f127(x94212),x94211),x94215),f335(f335(f144(x94212),x94214),x94213))+E(f335(f335(f127(x94212),f700(x94213,x94214,x94215,x94211,x94212)),x94215),x94213)
% 59.73/59.67 [9428]E(f335(f335(f127(x94282),f700(x94284,x94283,x94281,x94285,x94282)),x94281),x94284)+~E(f335(f335(f127(x94282),x94285),x94281),f335(f335(f144(x94282),x94283),x94284))+E(x94281,f335(f335(f144(x94282),x94283),x94284))
% 59.73/59.67 [9429]~E(f335(f335(f127(x94291),x94295),x94294),f335(f335(f144(x94291),x94292),x94293))+E(f335(f335(f127(x94291),f701(x94294,x94295,x94293,x94292,x94291)),x94294),x94293)+E(f335(f335(f144(x94291),x94292),x94293),x94294)
% 59.73/59.67 [9430]E(f335(f335(f127(x94301),x94305),f704(x94303,x94302,x94304,x94305,x94301)),x94302)+E(f335(f335(f127(x94301),x94302),f703(x94303,x94302,x94304,x94305,x94301)),x94305)+~E(f335(f335(f127(x94301),x94305),x94304),f335(f335(f127(x94301),x94302),x94303))
% 59.73/59.67 [9465]~P106(x94651)+P15(x94651,f335(f335(f147(x94652,x94651),x94653),f142(x94652,x94651,x94653,x94654,x94655)))+~P15(x94651,f335(f335(f147(x94652,x94651),x94653),x94655))
% 59.73/59.67 [9479]~P56(x94795,x94791,x94794,x94793)+P1(f335(f335(x94791,x94792),f514(x94793,x94794,x94791,x94795,x94792)))+~P1(f335(f335(f337(x94795),x94792),x94794))
% 59.73/59.67 [9581]~P1(f335(f335(f337(f887(x95811,x95811)),f335(f335(f264(x95811,x95811),x95815),x95813)),f310(x95811,x95814)))+P1(f335(f335(f337(f887(x95811,x95811)),f335(f335(f264(x95811,x95811),x95812),x95813)),f335(f335(f291(x95811,x95811,x95811),x95814),f310(x95811,x95814))))+~P1(f335(f335(f337(f887(x95811,x95811)),f335(f335(f264(x95811,x95811),x95812),x95815)),f335(f335(f291(x95811,x95811,x95811),x95814),f310(x95811,x95814))))
% 59.73/59.67 [9582]~P1(f335(f335(f337(f887(x95821,x95821)),f335(f335(f264(x95821,x95821),x95822),x95825)),f310(x95821,x95824)))+P1(f335(f335(f337(f887(x95821,x95821)),f335(f335(f264(x95821,x95821),x95822),x95823)),f335(f335(f291(x95821,x95821,x95821),x95824),f310(x95821,x95824))))+~P1(f335(f335(f337(f887(x95821,x95821)),f335(f335(f264(x95821,x95821),x95825),x95823)),f335(f335(f291(x95821,x95821,x95821),x95824),f310(x95821,x95824))))
% 59.73/59.67 [9585]P1(f335(f335(f337(f887(f882(x95851),f882(x95851))),f335(f335(f264(f882(x95851),f882(x95851)),x95852),x95853)),f151(x95851,f310(x95851,x95854))))+~P1(f335(f335(f337(f887(f882(x95851),f882(x95851))),f335(f335(f264(f882(x95851),f882(x95851)),x95852),x95855)),f151(x95851,f310(x95851,x95854))))+~P1(f335(f335(f337(f887(f882(x95851),f882(x95851))),f335(f335(f264(f882(x95851),f882(x95851)),x95855),x95853)),f151(x95851,f310(x95851,x95854))))
% 59.73/59.67 [9589]E(f335(f335(f127(x95891),x95892),f703(x95893,x95892,x95894,x95895,x95891)),x95895)+E(f335(f335(f127(x95891),f704(x95893,x95892,x95894,x95895,x95891)),x95893),x95894)+~E(f335(f335(f127(x95891),x95892),x95893),f335(f335(f127(x95891),x95895),x95894))
% 59.73/59.67 [9590]E(f335(f335(f127(x95901),x95902),f704(x95903,x95904,x95905,x95902,x95901)),x95904)+E(f335(f335(f127(x95901),f703(x95903,x95904,x95905,x95902,x95901)),x95905),x95903)+~E(f335(f335(f127(x95901),x95902),x95905),f335(f335(f127(x95901),x95904),x95903))
% 59.73/59.67 [9644]P1(f335(f335(f337(f887(x96441,x96441)),f335(f335(f264(x96441,x96441),x96442),x96443)),f335(f335(f291(x96441,x96441,x96441),x96444),f310(x96441,x96444))))+~P1(f335(f335(f337(f887(x96441,x96441)),f335(f335(f264(x96441,x96441),x96442),x96445)),f335(f335(f291(x96441,x96441,x96441),x96444),f310(x96441,x96444))))+~P1(f335(f335(f337(f887(x96441,x96441)),f335(f335(f264(x96441,x96441),x96445),x96443)),f335(f335(f291(x96441,x96441,x96441),x96444),f310(x96441,x96444))))
% 59.73/59.67 [9673]P33(x96731,x96732,x96733,x96734,x96735)+~E(f335(f189(f882(x96731)),x96734),f335(f189(f882(x96732)),x96735))+~P1(f335(f335(f268(x96731,x96732,a879),x96733),f747(x96735,x96734,x96733,x96732,x96731)))
% 59.73/59.67 [9674]P33(x96741,x96742,x96743,x96744,x96745)+~E(f335(f189(f882(x96741)),x96744),f335(f189(f882(x96742)),x96745))+~P1(f335(f335(f268(x96741,x96742,a879),x96743),f753(x96743,x96745,x96744,x96742,x96741)))
% 59.73/59.67 [9679]E(f335(f335(f127(x96791),f703(x96792,x96793,x96794,x96795,x96791)),x96794),x96792)+~E(f335(f335(f127(x96791),x96793),x96792),f335(f335(f127(x96791),x96795),x96794))+E(f335(f335(f127(x96791),f704(x96792,x96793,x96794,x96795,x96791)),x96792),x96794)
% 59.73/59.67 [9695]~P106(x96952)+E(f335(f335(f141(x96951,x96952,x96953),x96954),x96955),f335(f335(f144(x96951),x96954),x96955))+P1(f335(f335(f337(x96951),f772(x96954,x96953,x96955,x96951,x96952)),f335(f166(x96951),x96955)))
% 59.73/59.67 [9700]~P56(x97001,x97004,x97003,x97002)+~P1(f335(f335(f337(x97001),x97005),x97003))+P1(f335(f335(f337(x97001),f514(x97002,x97003,x97004,x97001,x97005)),x97002))
% 59.73/59.67 [9829]~P1(f335(f335(f337(f887(f888(x98291,a879),f888(x98291,a879))),f335(f335(f264(f888(x98291,a879),f888(x98291,a879)),x98294),x98293)),f327(x98291,x98292)))+~P1(f335(f335(f337(x98291),x98295),x98294))+P1(f335(f335(f337(x98291),f584(x98292,x98293,x98294,x98291,x98295)),x98293))
% 59.73/59.67 [9840]~P106(x98402)+E(f335(f335(f141(x98401,x98402,x98403),x98404),x98405),f335(f335(f144(x98401),x98404),x98405))+~P1(f335(f335(f242(x98402),f335(x98403,x98404)),f335(x98403,f772(x98404,x98403,x98405,x98401,x98402))))
% 59.73/59.67 [9886]~P26(x98863,x98864,x98865,f252(f888(x98863,a879)))+P1(f335(x98861,x98862))+~P1(f335(x98861,f335(f87(x98863,x98864,f252(f888(x98863,a879)),x98865),f717(x98862,x98861,x98865,x98864,x98863))))
% 59.73/59.67 [10028]P33(x100281,x100282,x100283,x100284,x100285)+~E(f335(f189(f882(x100281)),x100284),f335(f189(f882(x100282)),x100285))+~P1(f335(f335(x100283,f335(f335(f158(x100281),x100284),f754(x100285,x100284,x100283,x100282,x100281))),f335(f335(f158(x100282),x100285),f754(x100285,x100284,x100283,x100282,x100281))))
% 59.73/59.67 [10029]P33(x100291,x100292,x100293,x100294,x100295)+~E(f335(f189(f882(x100291)),x100294),f335(f189(f882(x100292)),x100295))+~P1(f335(f335(x100293,f335(f335(f158(x100291),x100294),f762(x100293,x100295,x100292,x100294,x100291))),f335(f335(f158(x100292),x100295),f762(x100293,x100295,x100292,x100294,x100291))))
% 59.73/59.67 [6585]~P19(x65852,x65855,x65851)+~P1(f335(f56(x65852),x65854))+E(f335(x65851,f335(f335(f312(x65852),x65853),x65854)),f335(f335(f59(x65852,x65852,x65855),x65853),x65854))
% 59.73/59.67 [6586]~E(x65863,x65864)+~E(x65862,x65865)+E(f335(f335(f312(x65861),x65862),f335(f335(f312(x65861),x65863),f188(f888(x65861,a879)))),f335(f335(f312(x65861),x65864),f335(f335(f312(x65861),x65865),f188(f888(x65861,a879)))))
% 59.73/59.67 [6596]P1(f335(x65962,x65965))+E(f171(x65961,x65962,f335(f335(f127(x65961),x65963),x65964)),f171(x65961,x65962,x65963))+~P1(f335(f335(f337(x65961),x65965),f335(f166(x65961),x65963)))
% 59.73/59.67 [6635]E(f335(x66351,x66352),f188(f888(x66353,a879)))+~E(f335(f335(f33(x66354,f888(x66353,a879)),x66355),x66351),f188(f888(x66353,a879)))+~P1(f335(f335(f337(x66354),x66352),x66355))
% 59.73/59.67 [6636]E(f335(x66361,x66362),f252(f888(x66363,a879)))+~E(f335(f335(f34(x66364,f888(x66363,a879)),x66365),x66361),f252(f888(x66363,a879)))+~P1(f335(f335(f337(x66364),x66362),x66365))
% 59.73/59.67 [6637]E(f335(x66371,x66372),f188(f888(x66373,a879)))+~E(f335(f335(f33(x66374,f888(x66373,a879)),x66375),x66371),f188(f888(x66373,a879)))+~P1(f335(f335(f337(x66374),x66372),x66375))
% 59.73/59.67 [6638]E(f335(x66381,x66382),f252(f888(x66383,a879)))+~E(f335(f335(f34(x66384,f888(x66383,a879)),x66385),x66381),f252(f888(x66383,a879)))+~P1(f335(f335(f337(x66384),x66382),x66385))
% 59.73/59.67 [6837]~E(x68374,f335(f335(f127(x68371),x68375),f335(f335(f144(x68371),x68372),x68373)))+P1(f335(f335(f337(x68371),x68372),f335(f166(x68371),x68373)))+P1(f335(f335(f337(x68371),x68372),f335(f166(x68371),x68374)))
% 59.73/59.67 [6838]~E(x68384,f335(f335(f127(x68381),x68383),f335(f335(f144(x68381),x68382),x68385)))+P1(f335(f335(f337(x68381),x68382),f335(f166(x68381),x68383)))+P1(f335(f335(f337(x68381),x68382),f335(f166(x68381),x68384)))
% 59.73/59.67 [7146]~E(x71462,x71464)+~P138(x71461)+E(f335(f335(f75(x71461),f335(f335(f76(x71461),x71462),x71463)),f335(f335(f76(x71461),x71464),x71465)),f335(f335(f75(x71461),f335(f335(f76(x71461),x71462),x71465)),f335(f335(f76(x71461),x71464),x71463)))
% 59.73/59.67 [7147]~E(x71472,x71474)+~P138(x71471)+E(f335(f335(f75(x71471),f335(f335(f76(x71471),x71472),x71473)),f335(f335(f76(x71471),x71474),x71475)),f335(f335(f75(x71471),f335(f335(f76(x71471),x71472),x71475)),f335(f335(f76(x71471),x71474),x71473)))
% 59.73/59.67 [7208]~P5(x72081)+~P1(f335(f335(f337(x72084),x72083),x72085))+P1(f335(f335(f242(x72081),f335(x72082,x72083)),f335(f335(f33(x72084,x72081),x72085),x72082)))
% 59.73/59.67 [7256]~P108(x72561)+P1(f335(f335(f242(x72561),f335(x72562,x72563)),f335(x72564,x72563)))+~P1(f335(f335(f242(f888(x72565,x72561)),x72562),x72564))
% 59.73/59.67 [7257]~P108(x72571)+P1(f335(f335(f242(x72571),f335(x72572,x72573)),f335(x72574,x72573)))+~P1(f335(f335(f242(f888(x72575,x72571)),x72572),x72574))
% 59.73/59.67 [7258]~P108(x72581)+P1(f335(f335(f242(x72581),f335(x72582,x72583)),f335(x72584,x72583)))+~P1(f335(f335(f242(f888(x72585,x72581)),x72582),x72584))
% 59.73/59.67 [7378]E(x73781,x73782)+E(x73783,x73781)+~E(f335(f335(f312(x73784),x73781),f335(f335(f312(x73784),x73785),f188(f888(x73784,a879)))),f335(f335(f312(x73784),x73782),f335(f335(f312(x73784),x73783),f188(f888(x73784,a879)))))
% 59.73/59.67 [7379]E(x73791,x73792)+E(x73793,x73791)+~E(f335(f335(f312(x73794),x73793),f335(f335(f312(x73794),x73792),f188(f888(x73794,a879)))),f335(f335(f312(x73794),x73795),f335(f335(f312(x73794),x73791),f188(f888(x73794,a879)))))
% 59.73/59.67 [7380]E(x73801,x73802)+E(x73801,x73803)+~E(f335(f335(f312(x73804),x73803),f335(f335(f312(x73804),x73802),f188(f888(x73804,a879)))),f335(f335(f312(x73804),x73805),f335(f335(f312(x73804),x73801),f188(f888(x73804,a879)))))
% 59.73/59.67 [7381]E(x73811,x73812)+E(x73811,x73813)+~E(f335(f335(f312(x73814),x73811),f335(f335(f312(x73814),x73815),f188(f888(x73814,a879)))),f335(f335(f312(x73814),x73812),f335(f335(f312(x73814),x73813),f188(f888(x73814,a879)))))
% 59.73/59.67 [7918]P26(x79181,x79182,x79183,x79184)+~P26(x79181,x79182,x79183,x79185)+~P1(f335(f335(f242(f888(x79181,a879)),x79184),x79185))
% 59.73/59.67 [7947]~E(f335(x79473,x79475),x79474)+~P26(x79471,x79472,x79473,f252(f888(x79471,a879)))+E(f335(f87(x79471,x79472,f252(f888(x79471,a879)),x79473),x79474),x79475)
% 59.73/59.67 [8099]E(x80991,x80992)+~E(f335(f313(x80993,x80994,x80995),x80991),f335(f313(x80993,x80994,x80995),x80992))+~P26(x80993,x80994,x80995,f335(f335(f104(f888(x80993,a879)),x80991),x80992))
% 59.73/59.67 [8169]P1(f335(x81692,x81694))+E(f335(f335(f131(x81691),f335(f189(f882(x81691)),f171(x81691,x81692,x81693))),x81693),f335(f335(f144(x81691),x81694),x81695))+~E(f335(f335(f127(x81691),f171(x81691,x81692,x81693)),f335(f335(f144(x81691),x81694),x81695)),x81693)
% 59.73/59.67 [8201]~P26(x82011,x82012,x82013,x82015)+~P26(x82011,x82012,x82013,x82014)+P26(x82011,x82012,x82013,f335(f335(f95(f888(x82011,a879)),x82014),x82015))
% 59.73/59.67 [8312]~P77(x83121)+E(f335(f335(f75(x83121),f335(x83122,x83123)),f335(f159(x83121),f335(f335(f147(x83124,x83121),x83122),f164(x83124,x83123,x83125)))),f335(f159(x83121),f335(f335(f147(x83124,x83121),x83122),x83125)))+~P1(f335(f335(f337(x83124),x83123),f335(f166(x83124),x83125)))
% 59.73/59.67 [8400]~P106(x84001)+~P15(x84001,f335(f335(f147(x84002,x84001),x84003),x84005))+P15(x84001,f335(f335(f147(x84002,x84001),x84003),f335(f335(f141(x84002,x84001,x84003),x84004),x84005)))
% 59.73/59.67 [8487]~P5(x84871)+P1(f335(f335(f242(x84871),f335(f335(f33(x84872,x84871),x84873),x84874)),f335(f335(f33(x84872,x84871),x84875),x84874)))+~P1(f335(f335(f242(f888(x84872,a879)),x84873),x84875))
% 59.73/59.67 [8488]~P5(x84881)+P1(f335(f335(f242(x84881),f335(f335(f34(x84882,x84881),x84883),x84884)),f335(f335(f34(x84882,x84881),x84885),x84884)))+~P1(f335(f335(f242(f888(x84882,a879)),x84885),x84883))
% 59.73/59.67 [8520]~P106(x85203)+P1(f335(f130(x85201),x85202))+~P1(f335(f130(x85201),f335(f335(f141(x85201,x85203,x85204),x85205),x85202)))
% 59.73/59.67 [8661]~P106(x86611)+~P1(f335(f335(f337(x86612),x86613),f335(f166(x86612),x86614)))+~P1(f335(f130(x86612),f335(f335(f141(x86612,x86611,x86615),x86613),x86614)))
% 59.73/59.67 [8744]~P106(x87441)+P15(x87441,f335(f335(f147(x87442,x87441),x87443),x87444))+~P15(x87441,f335(f335(f147(x87442,x87441),x87443),f335(f335(f141(x87442,x87441,x87443),x87445),x87444)))
% 59.73/59.67 [8789]~P26(x87892,x87891,x87894,x87893)+E(f335(f313(x87891,x87892,f87(x87892,x87891,x87893,x87894)),f335(f313(x87892,x87891,x87894),x87895)),x87895)+~P1(f335(f335(f242(f888(x87892,a879)),x87895),x87893))
% 59.73/59.67 [8840]~P106(x88402)+E(f335(f335(f141(x88401,x88402,x88403),x88404),x88405),f142(x88401,x88402,x88403,x88404,x88405))+P1(f335(f335(f337(x88402),f335(x88403,x88404)),f335(f313(x88401,x88402,x88403),f335(f166(x88401),x88405))))
% 59.73/59.67 [8914]~P106(x89142)+E(f142(x89141,x89142,x89143,x89144,x89145),x89145)+~P1(f335(f335(f337(x89142),f335(x89143,x89144)),f335(f313(x89141,x89142,x89143),f335(f166(x89141),x89145))))
% 59.73/59.67 [8930]~P26(x89302,x89301,x89303,x89305)+P1(f335(f335(f243(f888(x89301,a879)),f335(f313(x89302,x89301,x89303),x89304)),f335(f313(x89302,x89301,x89303),x89305)))+~P1(f335(f335(f243(f888(x89302,a879)),x89304),x89305))
% 59.73/59.67 [8967]~P26(x89672,x89671,x89673,f252(f888(x89672,a879)))+P1(f335(f335(f242(f888(x89671,a879)),f335(f313(x89672,x89671,x89673),x89674)),f335(f313(x89672,x89671,x89673),x89675)))+~P1(f335(f335(f242(f888(x89672,a879)),x89674),x89675))
% 59.73/59.67 [9092]~P26(x90921,x90922,x90923,f252(f888(x90921,a879)))+~P1(f335(f335(f242(f888(x90922,a879)),x90924),f335(f313(x90921,x90922,x90923),x90925)))+P1(f335(f335(f242(f888(x90921,a879)),f335(f314(x90921,x90922,x90923),x90924)),x90925))
% 59.73/59.67 [9115]~E(f335(f313(x91153,x91151,x91154),f252(f888(x91153,a879))),f252(f888(x91151,a879)))+P1(f335(f335(f242(f888(x91151,a879)),x91152),f335(f313(x91153,x91151,x91154),x91155)))+~P1(f335(f335(f242(f888(x91153,a879)),f335(f314(x91153,x91151,x91154),x91152)),x91155))
% 59.73/59.67 [9142]~E(f335(f235(x91422),x91424),f335(f335(f179(x91421,x91422),x91425),x91423))+~P1(f335(f130(x91421),f335(f335(f147(f887(x91421,x91422),x91421),f263(x91421,x91422)),x91425)))+P1(f335(f335(f337(f887(x91421,x91422)),f335(f335(f264(x91421,x91422),x91423),x91424)),f335(f166(f887(x91421,x91422)),x91425)))
% 59.73/59.67 [9143]~E(f335(f335(f179(x91431,x91432),x91435),x91433),f335(f235(x91432),x91434))+~P1(f335(f130(x91431),f335(f335(f147(f887(x91431,x91432),x91431),f263(x91431,x91432)),x91435)))+P1(f335(f335(f337(f887(x91431,x91432)),f335(f335(f264(x91431,x91432),x91433),x91434)),f335(f166(f887(x91431,x91432)),x91435)))
% 59.73/59.67 [9225]~P26(x92251,x92254,x92255,f252(f888(x92251,a879)))+~P1(f335(f335(f242(f888(x92254,a879)),f335(f313(x92251,x92254,x92255),x92252)),f335(f313(x92251,x92254,x92255),x92253)))+P1(f335(f335(f242(f888(x92251,a879)),x92252),x92253))
% 59.73/59.67 [9290]E(f335(f235(x92901),x92902),f335(f335(f179(x92903,x92901),x92904),x92905))+~P1(f335(f130(x92903),f335(f335(f147(f887(x92903,x92901),x92903),f263(x92903,x92901)),x92904)))+~P1(f335(f335(f337(f887(x92903,x92901)),f335(f335(f264(x92903,x92901),x92905),x92902)),f335(f166(f887(x92903,x92901)),x92904)))
% 59.73/59.67 [9291]E(f335(f335(f179(x92911,x92912),x92913),x92914),f335(f235(x92912),x92915))+~P1(f335(f130(x92911),f335(f335(f147(f887(x92911,x92912),x92911),f263(x92911,x92912)),x92913)))+~P1(f335(f335(f337(f887(x92911,x92912)),f335(f335(f264(x92911,x92912),x92914),x92915)),f335(f166(f887(x92911,x92912)),x92913)))
% 59.73/59.67 [9292]E(f335(f335(f179(x92921,x92922),x92923),x92924),f335(f235(x92922),x92925))+~P1(f335(f130(x92921),f335(f335(f147(f887(x92921,x92922),x92921),f263(x92921,x92922)),x92923)))+~P1(f335(f335(f337(f887(x92921,x92922)),f335(f335(f264(x92921,x92922),x92924),x92925)),f335(f166(f887(x92921,x92922)),x92923)))
% 59.73/59.67 [9343]~P83(x93431)+~E(f335(x93433,f730(x93433,x93434,x93435,x93432,x93431)),f2(x93431))+E(f335(f159(x93431),f335(f335(f147(x93432,x93431),x93433),f335(f129(x93432,x93434),x93435))),f335(f159(x93431),f335(f335(f147(x93432,x93431),x93433),x93435)))
% 59.73/59.67 [9523]~P18(x95231,x95232,x95233)+~P1(f335(f56(x95231),x95235))+P1(f335(f61(x95231,x95232,x95233,x95234,x95235),f335(f335(f59(x95231,x95232,x95233),x95234),x95235)))
% 59.73/59.67 [9602]P1(f335(x96021,f528(x96022,x96021,x96023,x96024,x96025)))+~P1(f335(f335(f242(f888(x96025,a879)),x96024),x96023))+P1(f335(f335(f242(f888(x96025,a879)),f335(f335(f95(f888(x96025,a879)),x96024),f335(f249(x96025),x96021))),f335(f335(f95(f888(x96025,a879)),x96023),f335(f249(x96025),x96022))))
% 59.73/59.67 [9616]~P83(x96161)+~P1(f335(x96164,f730(x96163,x96164,x96165,x96162,x96161)))+E(f335(f159(x96161),f335(f335(f147(x96162,x96161),x96163),f335(f129(x96162,x96164),x96165))),f335(f159(x96161),f335(f335(f147(x96162,x96161),x96163),x96165)))
% 59.73/59.67 [9698]~P5(x96985)+P1(f335(f335(f337(x96981),f623(x96982,x96983,x96981,x96984,x96985)),x96983))+P1(f335(f335(f242(x96985),x96984),f335(f335(f34(x96981,x96985),x96983),x96982)))
% 59.73/59.67 [9701]~P83(x97011)+E(f335(f159(x97011),f335(f335(f147(x97012,x97011),x97013),f335(f129(x97012,x97014),x97015))),f335(f159(x97011),f335(f335(f147(x97012,x97011),x97013),x97015)))+P1(f335(f335(f337(x97012),f730(x97013,x97014,x97015,x97012,x97011)),f335(f166(x97012),x97015)))
% 59.73/59.67 [9711]~P1(f335(x97115,f528(x97115,x97113,x97114,x97112,x97111)))+~P1(f335(f335(f242(f888(x97111,a879)),x97112),x97114))+P1(f335(f335(f242(f888(x97111,a879)),f335(f335(f95(f888(x97111,a879)),x97112),f335(f249(x97111),x97113))),f335(f335(f95(f888(x97111,a879)),x97114),f335(f249(x97111),x97115))))
% 59.73/59.67 [9727]~P26(x97275,x97273,x97274,f252(f888(x97275,a879)))+P1(f335(x97271,x97272))+P1(f335(f335(f337(x97273),f717(x97272,x97271,x97274,x97273,x97275)),f335(f313(x97275,x97273,x97274),f252(f888(x97275,a879)))))
% 59.73/59.67 [9750]P33(x97501,x97502,x97503,x97504,x97505)+~E(f335(f189(f882(x97502)),x97505),f335(f189(f882(x97501)),x97504))+P1(f335(f335(f243(a881),f754(x97505,x97504,x97503,x97502,x97501)),f335(f189(f882(x97501)),x97504)))
% 59.73/59.67 [9751]P33(x97511,x97512,x97513,x97514,x97515)+~E(f335(f189(f882(x97512)),x97515),f335(f189(f882(x97511)),x97514))+P1(f335(f335(f243(a881),f762(x97513,x97515,x97512,x97514,x97511)),f335(f189(f882(x97511)),x97514)))
% 59.73/59.67 [9786]P1(f335(f335(f337(x97861),f528(x97862,x97863,x97864,x97865,x97861)),x97865))+~P1(f335(f335(f242(f888(x97861,a879)),x97865),x97864))+P1(f335(f335(f242(f888(x97861,a879)),f335(f335(f95(f888(x97861,a879)),x97865),f335(f249(x97861),x97863))),f335(f335(f95(f888(x97861,a879)),x97864),f335(f249(x97861),x97862))))
% 59.73/59.67 [9841]~P5(x98411)+~P1(f335(f335(f242(x98411),x98412),f335(x98415,f623(x98415,x98414,x98413,x98412,x98411))))+P1(f335(f335(f242(x98411),x98412),f335(f335(f34(x98413,x98411),x98414),x98415)))
% 59.73/59.67 [9875]~P73(x98751)+~P1(f335(f56(x98752),x98755))+E(f335(f335(f335(f60(x98751,x98752,f76(x98751)),f335(f335(f18(x98752,x98751,x98751),f335(f335(f8(x98751,f888(x98751,x98751),x98752),f76(x98751)),x98753)),x98754)),f73(x98751)),x98755),f335(f335(f76(x98751),f335(f335(f335(f60(x98751,x98752,f76(x98751)),x98753),f73(x98751)),x98755)),f335(f335(f335(f60(x98751,x98752,f76(x98751)),x98754),f73(x98751)),x98755)))
% 59.73/59.67 [9936]~P1(f335(f335(f337(f887(f888(x99361,a879),f888(x99361,a879))),f335(f335(f264(f888(x99361,a879),f888(x99361,a879)),x99365),x99364)),f327(x99361,x99363)))+~P1(f335(f335(f337(x99361),x99362),x99365))+P1(f335(f335(f337(f887(x99361,x99361)),f335(f335(f264(x99361,x99361),x99362),f584(x99363,x99364,x99365,x99361,x99362))),x99363))
% 59.73/59.67 [10063]~P1(f335(f335(f337(f887(f882(x100631),f882(x100631))),f335(f335(f264(f882(x100631),f882(x100631)),f335(f335(f127(x100631),x100635),x100632)),f335(f335(f127(x100631),x100635),x100633))),f140(x100631,x100634)))+P1(f335(f335(f337(f887(f882(x100631),f882(x100631))),f335(f335(f264(f882(x100631),f882(x100631)),x100632),x100633)),f140(x100631,x100634)))+P1(f335(f335(f337(f887(x100631,x100631)),f335(f335(f264(x100631,x100631),f709(x100634,x100633,x100632,x100635,x100631)),f709(x100634,x100633,x100632,x100635,x100631))),x100634))
% 59.73/59.67 [7187]~E(f335(f189(f882(x71871)),x71873),f335(f189(f882(x71872)),x71874))+E(f335(f335(f179(x71871,x71872),f335(f335(f175(x71871,x71872),x71873),x71874)),x71875),f200(x71872))+P1(f335(f335(f337(x71871),x71875),f335(f166(x71871),x71873)))
% 59.73/59.67 [7261]~E(x72613,x72615)+E(f335(f335(f158(x72611),f335(f335(f152(x72611,x72612),x72613),x72614)),x72615),x72614)+~P1(f335(f335(f243(a881),x72613),f335(f189(f882(x72611)),x72612)))
% 59.73/59.67 [7375]~E(f335(f335(f127(x73751),x73752),x73754),f335(f335(f127(x73751),x73753),x73755))+E(f335(f335(f169(x73751),f335(f189(f882(x73751)),x73752)),x73753),x73752)+P1(f335(f335(f242(a881),f335(f189(f882(x73751)),x73753)),f335(f189(f882(x73751)),x73752)))
% 59.73/59.67 [7376]E(x73761,x73762)+E(f335(f335(f158(x73763),f335(f335(f152(x73763,x73764),x73761),x73765)),x73762),f335(f335(f158(x73763),x73764),x73762))+~P1(f335(f335(f243(a881),x73761),f335(f189(f882(x73763)),x73764)))
% 59.73/59.67 [7877]~E(f335(f335(f127(x78771),x78772),x78774),f335(f335(f127(x78771),x78773),x78775))+E(f335(f335(f169(x78771),f335(f189(f882(x78771)),x78772)),x78773),x78772)+~P1(f335(f335(f242(a881),f335(f189(f882(x78771)),x78772)),f335(f189(f882(x78771)),x78773)))
% 59.73/59.67 [7901]~P1(f335(f56(x79011),f335(x79014,x79015)))+~P1(f335(f335(f337(x79012),x79015),x79013))+P1(f335(f56(x79011),f335(f335(f34(x79012,f888(x79011,a879)),x79013),x79014)))
% 59.73/59.67 [7957]~E(f335(f189(f882(x79571)),x79572),f335(f189(f882(x79573)),x79574))+~E(f335(f335(f179(x79571,x79573),f335(f335(f175(x79571,x79573),x79572),x79574)),x79575),f200(x79573))+~P1(f335(f335(f337(x79571),x79575),f335(f166(x79571),x79572)))
% 59.73/59.67 [8084]~P46(x80841,x80843,x80845)+~P46(x80841,x80842,x80844)+P46(x80841,f335(f335(f104(f888(x80841,a879)),x80842),x80843),f335(f335(f104(f888(f887(x80841,x80841),a879)),x80844),x80845))
% 59.73/59.67 [8085]~P46(x80851,x80853,x80855)+~P46(x80851,x80852,x80854)+P46(x80851,f335(f335(f95(f888(x80851,a879)),x80852),x80853),f335(f335(f95(f888(f887(x80851,x80851),a879)),x80854),x80855))
% 59.73/59.67 [8439]E(f335(f335(f264(x84391,x84392),f335(f335(f158(x84391),x84393),x84394)),f335(f335(f158(x84392),x84395),x84394)),f335(f335(f158(f887(x84391,x84392)),f335(f335(f175(x84391,x84392),x84393),x84395)),x84394))+~P1(f335(f335(f243(a881),x84394),f335(f189(f882(x84391)),x84393)))+~P1(f335(f335(f243(a881),x84394),f335(f189(f882(x84392)),x84395)))
% 59.73/59.67 [8592]~P46(x85921,x85923,x85924)+P1(f335(f335(f337(x85921),x85922),x85923))+~P1(f335(f335(f337(f887(x85921,x85921)),f335(f335(f264(x85921,x85921),x85925),x85922)),x85924))
% 59.73/59.67 [8593]~P46(x85931,x85933,x85934)+P1(f335(f335(f337(x85931),x85932),x85933))+~P1(f335(f335(f337(f887(x85931,x85931)),f335(f335(f264(x85931,x85931),x85932),x85935)),x85934))
% 59.73/59.67 [8594]~P8(x85941,x85943,x85944)+P1(f335(f335(f337(x85941),x85942),x85943))+~P1(f335(f335(f337(f887(x85941,x85941)),f335(f335(f264(x85941,x85941),x85945),x85942)),x85944))
% 59.73/59.67 [8595]~P8(x85951,x85953,x85954)+P1(f335(f335(f337(x85951),x85952),x85953))+~P1(f335(f335(f337(f887(x85951,x85951)),f335(f335(f264(x85951,x85951),x85952),x85955)),x85954))
% 59.73/59.67 [8861]~P8(x88611,x88615,x88612)+E(f335(f288(x88611,x88611,x88612),f335(f335(f312(x88611),x88613),f188(f888(x88611,a879)))),f335(f288(x88611,x88611,x88612),f335(f335(f312(x88611),x88614),f188(f888(x88611,a879)))))+~P1(f335(f335(f337(f887(x88611,x88611)),f335(f335(f264(x88611,x88611),x88613),x88614)),x88612))
% 59.73/59.67 [8862]~P8(x88621,x88625,x88622)+E(f335(f288(x88621,x88621,x88622),f335(f335(f312(x88621),x88623),f188(f888(x88621,a879)))),f335(f288(x88621,x88621,x88622),f335(f335(f312(x88621),x88624),f188(f888(x88621,a879)))))+~P1(f335(f335(f337(f887(x88621,x88621)),f335(f335(f264(x88621,x88621),x88623),x88624)),x88622))
% 59.73/59.67 [9048]P1(f335(x90481,x90482))+~P1(f335(f335(f337(x90483),x90482),x90485))+P1(f335(f335(f337(x90483),f355(x90481,x90484,x90485,x90483)),f335(f335(f104(f888(x90483,a879)),x90485),x90484)))
% 59.73/59.67 [9049]P1(f335(x90491,x90492))+~P1(f335(f335(f337(x90493),x90492),x90494))+P1(f335(f335(f337(x90493),f355(x90491,x90494,x90495,x90493)),f335(f335(f104(f888(x90493,a879)),x90495),x90494)))
% 59.73/59.67 [9057]~P1(f335(x90572,x90575))+~P1(f335(f335(f337(x90571),x90575),x90574))+P1(f335(f335(f337(x90571),f408(x90572,x90573,x90574,x90571)),f335(f335(f104(f888(x90571,a879)),x90574),x90573)))
% 59.73/59.67 [9058]~P1(f335(x90582,x90585))+~P1(f335(f335(f337(x90581),x90585),x90583))+P1(f335(f335(f337(x90581),f408(x90582,x90583,x90584,x90581)),f335(f335(f104(f888(x90581,a879)),x90584),x90583)))
% 59.73/59.67 [9073]~P1(f335(f335(f242(f888(x90731,a879)),x90733),x90735))+~P1(f335(f335(f242(f888(x90731,a879)),x90732),x90734))+P1(f335(f335(f242(f888(x90731,a879)),f335(f335(f104(f888(x90731,a879)),x90732),x90733)),f335(f335(f104(f888(x90731,a879)),x90734),x90735)))
% 59.73/59.67 [9074]~P1(f335(f335(f242(f888(x90741,a879)),x90745),x90743))+~P1(f335(f335(f242(f888(x90741,a879)),x90742),x90744))+P1(f335(f335(f242(f888(x90741,a879)),f335(f335(f23(f888(x90741,a879)),x90742),x90743)),f335(f335(f23(f888(x90741,a879)),x90744),x90745)))
% 59.73/59.67 [9075]~P1(f335(f335(f242(f888(x90751,a879)),x90753),x90755))+~P1(f335(f335(f242(f888(x90751,a879)),x90752),x90754))+P1(f335(f335(f242(f888(x90751,a879)),f335(f335(f95(f888(x90751,a879)),x90752),x90753)),f335(f335(f95(f888(x90751,a879)),x90754),x90755)))
% 59.73/59.67 [9169]~E(f335(f189(f882(x91691)),x91693),f335(f189(f882(x91692)),x91694))+E(f335(f335(f179(x91691,x91692),f335(f335(f175(x91691,x91692),x91693),x91694)),x91695),f335(f235(x91692),f680(x91695,x91694,x91692,x91693,x91691)))+~P1(f335(f335(f337(x91691),x91695),f335(f166(x91691),x91693)))
% 59.73/59.67 [9173]P1(f335(f335(f337(f887(x91731,x91731)),f335(f335(f264(x91731,x91731),x91732),x91733)),f329(x91731,x91734,x91735)))+~P1(f335(f335(f242(a881),f335(x91734,x91732)),f335(x91734,x91733)))+~P1(f335(f335(f337(f887(x91731,x91731)),f335(f335(f264(x91731,x91731),x91732),x91733)),x91735))
% 59.73/59.67 [9353]P1(f335(f335(f337(f887(x93531,x93531)),f335(f335(f264(x93531,x93531),x93532),x93533)),f310(x93531,x93534)))+~P1(f335(f335(f337(f887(x93531,x93531)),f335(f335(f264(x93531,x93531),x93532),x93535)),f310(x93531,x93534)))+~P1(f335(f335(f337(f887(x93531,x93531)),f335(f335(f264(x93531,x93531),x93535),x93533)),x93534))
% 59.73/59.67 [9354]P1(f335(f335(f337(f887(x93541,x93541)),f335(f335(f264(x93541,x93541),x93542),x93543)),f310(x93541,x93544)))+~P1(f335(f335(f337(f887(x93541,x93541)),f335(f335(f264(x93541,x93541),x93545),x93543)),f310(x93541,x93544)))+~P1(f335(f335(f337(f887(x93541,x93541)),f335(f335(f264(x93541,x93541),x93542),x93545)),x93544))
% 59.73/59.67 [9451]E(x94511,x94512)+E(f335(a106,f602(x94513,x94514,x94511,x94512,x94515)),x94514)+~P1(f335(f335(f337(f887(x94515,x94515)),f335(f335(f264(x94515,x94515),x94512),x94511)),f335(f335(f183(f887(x94515,x94515),a879),x94514),x94513)))
% 59.73/59.67 [9452]E(x94521,x94522)+E(f335(a106,f604(x94523,x94524,x94521,x94522,x94525)),x94524)+~P1(f335(f335(f337(f887(x94525,x94525)),f335(f335(f264(x94525,x94525),x94522),x94521)),f335(f335(f183(f887(x94525,x94525),a879),x94524),x94523)))
% 59.73/59.67 [9453]E(x94531,f2(a881))+E(f335(a106,f602(x94532,x94531,x94533,x94534,x94535)),x94531)+~P1(f335(f335(f337(f887(x94535,x94535)),f335(f335(f264(x94535,x94535),x94534),x94533)),f335(f335(f183(f887(x94535,x94535),a879),x94531),x94532)))
% 59.73/59.67 [9454]E(x94541,f2(a881))+E(f335(a106,f604(x94542,x94541,x94543,x94544,x94545)),x94541)+~P1(f335(f335(f337(f887(x94545,x94545)),f335(f335(f264(x94545,x94545),x94544),x94543)),f335(f335(f183(f887(x94545,x94545),a879),x94541),x94542)))
% 59.73/59.67 [9476]P1(f335(f335(f337(f887(x94761,x94761)),f335(f335(f264(x94761,x94761),x94762),x94763)),f335(f335(f291(x94761,x94761,x94761),x94764),f310(x94761,x94764))))+~P1(f335(f335(f337(f887(x94761,x94761)),f335(f335(f264(x94761,x94761),x94762),x94765)),x94764))+~P1(f335(f335(f337(f887(x94761,x94761)),f335(f335(f264(x94761,x94761),x94765),x94763)),x94764))
% 59.73/59.67 [9483]~P1(f335(f335(f337(f887(x94831,x94831)),f335(f335(f264(x94831,x94831),x94832),x94835)),f310(x94831,x94834)))+P1(f335(f335(f337(f887(x94831,x94831)),f335(f335(f264(x94831,x94831),x94832),x94833)),f335(f335(f291(x94831,x94831,x94831),x94834),f310(x94831,x94834))))+~P1(f335(f335(f337(f887(x94831,x94831)),f335(f335(f264(x94831,x94831),x94835),x94833)),x94834))
% 59.73/59.67 [9484]~P1(f335(f335(f337(f887(x94841,x94841)),f335(f335(f264(x94841,x94841),x94845),x94843)),f310(x94841,x94844)))+P1(f335(f335(f337(f887(x94841,x94841)),f335(f335(f264(x94841,x94841),x94842),x94843)),f335(f335(f291(x94841,x94841,x94841),x94844),f310(x94841,x94844))))+~P1(f335(f335(f337(f887(x94841,x94841)),f335(f335(f264(x94841,x94841),x94842),x94845)),x94844))
% 59.73/59.67 [9519]~P8(x95191,x95195,x95192)+~P1(f335(f335(f337(f887(x95191,x95191)),f335(f335(f264(x95191,x95191),x95193),x95194)),x95192))+P1(f335(f335(f242(f888(x95191,a879)),f335(f288(x95191,x95191,x95192),f335(f335(f312(x95191),x95193),f188(f888(x95191,a879))))),f335(f288(x95191,x95191,x95192),f335(f335(f312(x95191),x95194),f188(f888(x95191,a879))))))
% 59.73/59.67 [9574]P1(f335(f335(f337(f887(x95741,x95741)),f335(f335(f264(x95741,x95741),x95742),x95743)),f335(f335(f291(x95741,x95741,x95741),x95744),f310(x95741,x95744))))+~P1(f335(f335(f337(f887(x95741,x95741)),f335(f335(f264(x95741,x95741),x95742),x95745)),f335(f335(f291(x95741,x95741,x95741),x95744),f310(x95741,x95744))))+~P1(f335(f335(f337(f887(x95741,x95741)),f335(f335(f264(x95741,x95741),x95745),x95743)),x95744))
% 59.73/59.67 [9575]P1(f335(f335(f337(f887(x95751,x95751)),f335(f335(f264(x95751,x95751),x95752),x95753)),f335(f335(f291(x95751,x95751,x95751),x95754),f310(x95751,x95754))))+~P1(f335(f335(f337(f887(x95751,x95751)),f335(f335(f264(x95751,x95751),x95755),x95753)),f335(f335(f291(x95751,x95751,x95751),x95754),f310(x95751,x95754))))+~P1(f335(f335(f337(f887(x95751,x95751)),f335(f335(f264(x95751,x95751),x95752),x95755)),x95754))
% 59.73/59.67 [9625]~P1(f335(f61(x96251,x96251,x96254,x96252,x96253),x96255))+P1(f335(f335(f337(x96251),x96252),x96253))+P1(f335(f57(x96251,x96254,f335(f335(f312(x96251),x96252),x96253)),x96255))
% 59.73/59.67 [9664]~E(f335(f313(x96643,x96642,x96645),x96644),x96641)+E(x96641,f188(f888(x96642,a879)))+P1(f335(f335(f242(f888(x96643,a879)),f335(f313(x96642,x96643,f651(x96644,x96643,x96642,x96641)),x96641)),x96644))
% 59.73/59.67 [9714]~P5(x97145)+P1(f335(f335(f337(x97141),f776(x97142,x97143,x97144,x97141,x97145)),x97144))+P1(f335(f335(f242(x97145),f335(f335(f33(x97141,x97145),x97144),x97143)),x97142))
% 59.73/59.67 [9771]P33(x97711,x97712,x97713,x97714,x97715)+~E(f335(f189(f882(x97711)),x97714),f335(f189(f882(x97712)),x97715))+P1(f335(f335(f337(f887(x97711,x97712)),f747(x97715,x97714,x97713,x97712,x97711)),f335(f166(f887(x97711,x97712)),f335(f335(f175(x97711,x97712),x97714),x97715))))
% 59.73/59.67 [9772]P33(x97721,x97722,x97723,x97724,x97725)+~E(f335(f189(f882(x97721)),x97724),f335(f189(f882(x97722)),x97725))+P1(f335(f335(f337(f887(x97721,x97722)),f753(x97723,x97725,x97724,x97722,x97721)),f335(f166(f887(x97721,x97722)),f335(f335(f175(x97721,x97722),x97724),x97725))))
% 59.73/59.67 [9913]E(x99131,x99132)+P1(f335(f335(f337(f887(x99133,x99133)),f335(f335(f264(x99133,x99133),x99131),f605(x99134,x99135,x99132,x99131,x99133))),x99134))+~P1(f335(f335(f337(f887(x99133,x99133)),f335(f335(f264(x99133,x99133),x99131),x99132)),f335(f335(f183(f887(x99133,x99133),a879),x99135),x99134)))
% 59.73/59.67 [9914]E(x99141,f2(a881))+P1(f335(f335(f337(f887(x99142,x99142)),f335(f335(f264(x99142,x99142),x99143),f605(x99144,x99141,x99145,x99143,x99142))),x99144))+~P1(f335(f335(f337(f887(x99142,x99142)),f335(f335(f264(x99142,x99142),x99143),x99145)),f335(f335(f183(f887(x99142,x99142),a879),x99141),x99144)))
% 59.73/59.67 [9955]~P5(x99551)+~P1(f335(f335(f242(x99551),f335(x99554,f776(x99555,x99554,x99553,x99552,x99551))),x99555))+P1(f335(f335(f242(x99551),f335(f335(f33(x99552,x99551),x99553),x99554)),x99555))
% 59.73/59.67 [9998]E(x99981,x99982)+P1(f335(f335(f337(f887(x99983,x99983)),f335(f335(f264(x99983,x99983),f603(x99984,x99985,x99981,x99982,x99983)),x99981)),x99984))+~P1(f335(f335(f337(f887(x99983,x99983)),f335(f335(f264(x99983,x99983),x99982),x99981)),f335(f335(f183(f887(x99983,x99983),a879),x99985),x99984)))
% 59.73/59.67 [9999]E(x99991,f2(a881))+P1(f335(f335(f337(f887(x99992,x99992)),f335(f335(f264(x99992,x99992),f603(x99993,x99991,x99994,x99995,x99992)),x99994)),x99993))+~P1(f335(f335(f337(f887(x99992,x99992)),f335(f335(f264(x99992,x99992),x99995),x99994)),f335(f335(f183(f887(x99992,x99992),a879),x99991),x99993)))
% 59.73/59.67 [10003]E(x100031,x100032)+P1(f335(f335(f337(f887(x100033,x100033)),f335(f335(f264(x100033,x100033),x100031),f603(x100034,x100035,x100032,x100031,x100033))),f335(f335(f183(f887(x100033,x100033),a879),f602(x100034,x100035,x100032,x100031,x100033)),x100034)))+~P1(f335(f335(f337(f887(x100033,x100033)),f335(f335(f264(x100033,x100033),x100031),x100032)),f335(f335(f183(f887(x100033,x100033),a879),x100035),x100034)))
% 59.73/59.67 [10004]E(x100041,f2(a881))+P1(f335(f335(f337(f887(x100042,x100042)),f335(f335(f264(x100042,x100042),x100043),f603(x100044,x100041,x100045,x100043,x100042))),f335(f335(f183(f887(x100042,x100042),a879),f602(x100044,x100041,x100045,x100043,x100042)),x100044)))+~P1(f335(f335(f337(f887(x100042,x100042)),f335(f335(f264(x100042,x100042),x100043),x100045)),f335(f335(f183(f887(x100042,x100042),a879),x100041),x100044)))
% 59.73/59.67 [10054]E(x100541,x100542)+P1(f335(f335(f337(f887(x100543,x100543)),f335(f335(f264(x100543,x100543),f605(x100544,x100545,x100541,x100542,x100543)),x100541)),f335(f335(f183(f887(x100543,x100543),a879),f604(x100544,x100545,x100541,x100542,x100543)),x100544)))+~P1(f335(f335(f337(f887(x100543,x100543)),f335(f335(f264(x100543,x100543),x100542),x100541)),f335(f335(f183(f887(x100543,x100543),a879),x100545),x100544)))
% 59.73/59.67 [10055]E(x100551,f2(a881))+P1(f335(f335(f337(f887(x100552,x100552)),f335(f335(f264(x100552,x100552),f605(x100553,x100551,x100554,x100555,x100552)),x100554)),f335(f335(f183(f887(x100552,x100552),a879),f604(x100553,x100551,x100554,x100555,x100552)),x100553)))+~P1(f335(f335(f337(f887(x100552,x100552)),f335(f335(f264(x100552,x100552),x100555),x100554)),f335(f335(f183(f887(x100552,x100552),a879),x100551),x100553)))
% 59.73/59.67 [10088]~P77(x100882)+~P1(f335(f56(x100881),x100885))+E(f335(f335(f6(x100881,x100882),f335(f335(f7(x100881,x100882,x100882),f335(f335(f18(x100881,x100882,f888(x100882,x100882)),f335(f335(f8(a879,f888(x100882,f888(x100882,x100882)),x100881),f88(x100882)),f335(f335(f7(x100881,f888(x100881,a879),a879),f337(x100881)),x100883))),x100884)),f2(x100882))),x100885),f335(f335(f6(x100881,x100882),x100884),f335(f335(f95(f888(x100881,a879)),x100885),x100883)))
% 59.73/59.67 [8657]~P73(x86571)+~P1(f335(f56(x86574),x86575))+E(f335(f335(f76(x86571),f335(x86572,x86573)),f335(f335(f9(x86574,x86571),x86572),f335(f335(f23(f888(x86574,a879)),x86575),f335(f335(f312(x86574),x86573),f188(f888(x86574,a879)))))),f335(f335(f9(x86574,x86571),x86572),f335(f335(f312(x86574),x86573),x86575)))
% 59.73/59.67 [8658]~P77(x86581)+~P1(f335(f56(x86584),x86585))+E(f335(f335(f75(x86581),f335(x86582,x86583)),f335(f335(f6(x86584,x86581),x86582),f335(f335(f23(f888(x86584,a879)),x86585),f335(f335(f312(x86584),x86583),f188(f888(x86584,a879)))))),f335(f335(f6(x86584,x86581),x86582),f335(f335(f312(x86584),x86583),x86585)))
% 59.73/59.67 [8980]~P106(x89802)+~P15(x89802,f335(f162(x89802),f335(f335(f147(x89801,x89802),x89804),x89805)))+E(f335(f129(x89801,f335(f335(f8(x89802,a879,x89801),f335(f243(x89802),x89803)),x89804)),x89805),f171(x89801,f335(f335(f8(x89802,a879,x89801),f335(f243(x89802),x89803)),x89804),x89805))
% 59.73/59.67 [9003]~P77(x90031)+E(f335(f335(f75(x90031),f335(f335(f6(a881,x90031),x90032),f305(a881,x90033,x90034))),f335(f335(f6(a881,x90031),x90032),f305(a881,f335(f335(f75(a881),x90034),f73(a881)),f335(f335(f75(a881),x90034),x90035)))),f335(f335(f6(a881,x90031),x90032),f305(a881,x90033,f335(f335(f75(a881),x90034),x90035))))+~P1(f335(f335(f242(a881),x90033),f335(f335(f75(a881),x90034),f73(a881))))
% 59.73/59.67 [9004]~P1(f335(f335(f337(x90041),x90044),x90045))+~P1(f335(f335(f242(f888(x90041,a879)),f335(f166(x90041),x90042)),x90045))+P1(f335(f335(f242(f888(x90041,a879)),f335(f166(x90041),f335(f335(f152(x90041,x90042),x90043),x90044))),x90045))
% 59.73/59.67 [9235]~P5(x92352)+~P1(f335(f56(x92351),x92355))+E(f335(f335(f59(x92351,x92352,f335(f335(f8(x92352,f888(x92352,x92352),x92351),f104(x92352)),x92353)),x92354),x92355),f335(f335(f104(x92352),x92354),f335(f335(f33(x92351,x92352),x92355),x92353)))
% 59.73/59.67 [9236]~P5(x92362)+~P1(f335(f56(x92361),x92365))+E(f335(f335(f59(x92361,x92362,f335(f335(f8(x92362,f888(x92362,x92362),x92361),f95(x92362)),x92363)),x92364),x92365),f335(f335(f95(x92362),x92364),f335(f335(f34(x92361,x92362),x92365),x92363)))
% 59.73/59.67 [9282]E(f335(x92821,x92822),f335(x92821,x92823))+P1(f335(f335(f243(a881),f335(x92821,x92822)),f335(x92821,x92823)))+~P1(f335(f335(f337(f887(x92824,x92824)),f335(f335(f264(x92824,x92824),x92822),x92823)),f146(x92824,f335(f335(f144(f888(x92824,a881)),x92821),x92825))))
% 59.73/59.67 [9314]~E(f335(x93144,x93142),f335(x93144,x93143))+~P1(f335(f335(f337(f887(x93141,x93141)),f335(f335(f264(x93141,x93141),x93142),x93143)),f146(x93141,x93145)))+P1(f335(f335(f337(f887(x93141,x93141)),f335(f335(f264(x93141,x93141),x93142),x93143)),f146(x93141,f335(f335(f144(f888(x93141,a881)),x93144),x93145))))
% 59.73/59.67 [9333]~P26(x93331,x93332,x93333,x93335)+P26(x93331,x93332,x93333,f335(f335(f312(x93331),x93334),x93335))+P1(f335(f335(f337(x93332),f335(x93333,x93334)),f335(f313(x93331,x93332,x93333),f335(f335(f23(f888(x93331,a879)),x93335),f335(f335(f312(x93331),x93334),f188(f888(x93331,a879)))))))
% 59.73/59.67 [9336]P1(f335(x93362,x93365))+~P1(f335(f335(f337(x93361),x93365),f335(f166(x93361),x93363)))+E(f335(f335(f131(x93361),f335(f189(f882(x93361)),f171(x93361,x93362,f335(f335(f127(x93361),x93363),x93364)))),f335(f335(f127(x93361),x93363),x93364)),f335(f335(f127(x93361),f335(f335(f131(x93361),f335(f189(f882(x93361)),f171(x93361,x93362,x93363))),x93363)),x93364))
% 59.73/59.67 [9339]~P1(f335(f335(f337(f887(x93391,x93391)),f335(f335(f264(x93391,x93391),x93392),x93393)),f146(x93391,x93395)))+~P1(f335(f335(f242(a881),f335(x93394,x93392)),f335(x93394,x93393)))+P1(f335(f335(f337(f887(x93391,x93391)),f335(f335(f264(x93391,x93391),x93392),x93393)),f146(x93391,f335(f335(f144(f888(x93391,a881)),x93394),x93395))))
% 59.73/59.67 [9405]P1(f335(f335(f337(f887(x94054,x94054)),f335(f335(f264(x94054,x94054),x94052),x94053)),f146(x94054,x94055)))+P1(f335(f335(f243(a881),f335(x94051,x94052)),f335(x94051,x94053)))+~P1(f335(f335(f337(f887(x94054,x94054)),f335(f335(f264(x94054,x94054),x94052),x94053)),f146(x94054,f335(f335(f144(f888(x94054,a881)),x94051),x94055))))
% 59.73/59.67 [9548]~P1(f335(f335(f337(f887(f882(x95481),f882(x95481))),f335(f335(f264(f882(x95481),f882(x95481)),x95482),x95484)),f151(x95481,x95485)))+~P1(f335(f335(f243(a881),x95483),f335(f189(f882(x95481)),x95482)))+P1(f335(f335(f337(f887(x95481,x95481)),f335(f335(f264(x95481,x95481),f335(f335(f158(x95481),x95482),x95483)),f335(f335(f158(x95481),x95484),x95483))),x95485))
% 59.73/59.67 [9800]E(x98001,f2(a1))+~P1(f335(f43(x98003,x98001),f335(f335(f264(a1,a1),x98004),x98005)))+P1(f335(f43(f335(f335(f76(a1),x98002),x98003),x98001),f335(f335(f264(a1,a1),f335(f335(f75(a1),f335(f335(f76(a1),x98002),x98004)),f335(f335(f30(a1),f335(f335(f76(a1),x98002),x98005)),x98001))),f39(a1,f335(f335(f76(a1),x98002),x98005),x98001))))
% 59.73/59.67 [9803]~P1(f335(f335(f243(a881),f2(a881)),x98033))+~P1(f335(f42(x98032,x98033),f335(f335(f264(a881,a881),x98034),x98035)))+P1(f335(f42(f335(f335(f76(a881),x98031),x98032),x98033),f335(f335(f264(a881,a881),f335(f335(f75(a881),f335(f335(f76(a881),x98031),x98034)),f335(f335(f30(a881),f335(f335(f76(a881),x98031),x98035)),x98033))),f39(a881,f335(f335(f76(a881),x98031),x98035),x98033))))
% 59.73/59.67 [10110]~P77(x101102)+~P1(f335(f56(x101101),x101104))+E(f335(f335(f6(x101101,x101102),x101103),f335(f249(x101101),f335(f335(f18(x101101,a879,a879),f335(f335(f8(a879,f888(a879,a879),x101101),a333),f335(f335(f7(x101101,f888(x101101,a879),a879),f337(x101101)),x101104))),f335(f335(f7(x101101,f888(x101101,a879),a879),f337(x101101)),x101105)))),f335(f335(f6(x101101,x101102),f335(f335(f7(x101101,x101102,x101102),f335(f335(f18(x101101,x101102,f888(x101102,x101102)),f335(f335(f8(a879,f888(x101102,f888(x101102,x101102)),x101101),f88(x101102)),f335(f335(f7(x101101,f888(x101101,a879),a879),f337(x101101)),x101105))),x101103)),f2(x101102))),x101104))
% 59.73/59.67 [8291]~E(f335(f335(f127(x82911),x82912),x82915),f335(f335(f127(x82911),x82913),x82914))+E(f335(f335(f127(x82911),f335(f335(f131(x82911),f335(f189(f882(x82911)),x82912)),x82913)),x82914),x82915)+P1(f335(f335(f242(a881),f335(f189(f882(x82911)),x82913)),f335(f189(f882(x82911)),x82912)))
% 59.73/59.67 [8490]~E(f335(f335(f127(x84902),x84903),x84901),f335(f335(f127(x84902),x84904),x84905))+E(x84901,f335(f335(f127(x84902),f335(f335(f131(x84902),f335(f189(f882(x84902)),x84903)),x84904)),x84905))+~P1(f335(f335(f242(a881),f335(f189(f882(x84902)),x84903)),f335(f189(f882(x84902)),x84904)))
% 59.73/59.67 [8575]~E(f335(f335(f75(a881),f335(f335(f76(a881),x85753),x85754)),x85751),f335(f335(f75(a881),f335(f335(f76(a881),x85752),x85754)),x85755))+~P1(f335(f335(f242(a881),x85753),x85752))+E(x85751,f335(f335(f75(a881),f335(f335(f76(a881),f335(f335(f23(a881),x85752),x85753)),x85754)),x85755))
% 59.73/59.67 [8576]~E(f335(f335(f75(a881),f335(f335(f76(a881),x85761),x85763)),x85764),f335(f335(f75(a881),f335(f335(f76(a881),x85762),x85763)),x85765))+~P1(f335(f335(f242(a881),x85762),x85761))+E(f335(f335(f75(a881),f335(f335(f76(a881),f335(f335(f23(a881),x85761),x85762)),x85763)),x85764),x85765)
% 59.73/59.67 [8737]E(f335(f335(f75(a881),f335(f335(f76(a881),x87371),x87372)),x87373),f335(f335(f75(a881),f335(f335(f76(a881),x87374),x87372)),x87375))+~P1(f335(f335(f242(a881),x87374),x87371))+~E(x87375,f335(f335(f75(a881),f335(f335(f76(a881),f335(f335(f23(a881),x87371),x87374)),x87372)),x87373))
% 59.73/59.67 [8738]E(f335(f335(f75(a881),f335(f335(f76(a881),x87381),x87382)),x87383),f335(f335(f75(a881),f335(f335(f76(a881),x87384),x87382)),x87385))+~P1(f335(f335(f242(a881),x87384),x87381))+~E(f335(f335(f75(a881),f335(f335(f76(a881),f335(f335(f23(a881),x87381),x87384)),x87382)),x87383),x87385)
% 59.73/59.67 [9599]~P73(x95992)+~P1(f335(f56(x95991),x95995))+E(f335(f335(f9(x95991,x95992),f335(f335(f18(x95991,x95992,x95992),f335(f335(f8(x95992,f888(x95992,x95992),x95991),f76(x95992)),x95993)),x95994)),x95995),f335(f335(f76(x95992),f335(f335(f9(x95991,x95992),x95993),x95995)),f335(f335(f9(x95991,x95992),x95994),x95995)))
% 59.73/59.67 [9600]~P66(x96002)+~P1(f335(f56(x96001),x96005))+E(f335(f335(f9(x96001,x96002),f335(f335(f18(x96001,x96002,x96002),f335(f335(f8(x96002,f888(x96002,x96002),x96001),f292(x96002)),x96003)),x96004)),x96005),f335(f335(f292(x96002),f335(f335(f9(x96001,x96002),x96003),x96005)),f335(f335(f9(x96001,x96002),x96004),x96005)))
% 59.73/59.67 [9601]~P77(x96012)+~P1(f335(f56(x96011),x96015))+E(f335(f335(f6(x96011,x96012),f335(f335(f18(x96011,x96012,x96012),f335(f335(f8(x96012,f888(x96012,x96012),x96011),f75(x96012)),x96013)),x96014)),x96015),f335(f335(f75(x96012),f335(f335(f6(x96011,x96012),x96013),x96015)),f335(f335(f6(x96011,x96012),x96014),x96015)))
% 59.73/59.67 [9733]~E(f608(x97335,x97334,x97333,x97332,x97331),f609(x97335,x97334,x97333,x97332,x97331))+P1(f335(f335(f337(f887(x97331,x97331)),f335(f335(f264(x97331,x97331),x97332),x97333)),f310(x97331,x97334)))+~P1(f335(f335(f337(f887(x97331,x97331)),f335(f335(f264(x97331,x97331),x97332),x97333)),f310(x97331,f335(f335(f104(f888(f887(x97331,x97331),a879)),x97334),x97335))))
% 59.73/59.67 [9734]~E(f610(x97345,x97344,x97343,x97342,x97341),f611(x97345,x97344,x97343,x97342,x97341))+P1(f335(f335(f337(f887(x97341,x97341)),f335(f335(f264(x97341,x97341),x97342),x97343)),f310(x97341,x97344)))+~P1(f335(f335(f337(f887(x97341,x97341)),f335(f335(f264(x97341,x97341),x97342),x97343)),f310(x97341,f335(f335(f104(f888(f887(x97341,x97341),a879)),x97344),x97345))))
% 59.73/59.67 [9945]P1(f335(f335(f337(f887(x99451,x99451)),f335(f335(f264(x99451,x99451),x99452),f611(x99455,x99454,x99453,x99452,x99451))),f310(x99451,x99454)))+P1(f335(f335(f337(f887(x99451,x99451)),f335(f335(f264(x99451,x99451),x99452),x99453)),f310(x99451,x99454)))+~P1(f335(f335(f337(f887(x99451,x99451)),f335(f335(f264(x99451,x99451),x99452),x99453)),f310(x99451,f335(f335(f104(f888(f887(x99451,x99451),a879)),x99454),x99455))))
% 59.73/59.67 [10025]P1(f335(f335(f337(f887(x100251,x100251)),f335(f335(f264(x100251,x100251),f609(x100255,x100254,x100253,x100252,x100251)),x100253)),f310(x100251,x100254)))+P1(f335(f335(f337(f887(x100251,x100251)),f335(f335(f264(x100251,x100251),x100252),x100253)),f310(x100251,x100254)))+~P1(f335(f335(f337(f887(x100251,x100251)),f335(f335(f264(x100251,x100251),x100252),x100253)),f310(x100251,f335(f335(f104(f888(f887(x100251,x100251),a879)),x100254),x100255))))
% 59.73/59.67 [10061]P1(f335(f335(f337(f887(x100611,x100611)),f335(f335(f264(x100611,x100611),x100612),x100613)),f310(x100611,x100614)))+P1(f335(f335(f337(f887(x100611,x100611)),f335(f335(f264(x100611,x100611),f608(x100615,x100614,x100613,x100612,x100611)),f609(x100615,x100614,x100613,x100612,x100611))),x100615))+~P1(f335(f335(f337(f887(x100611,x100611)),f335(f335(f264(x100611,x100611),x100612),x100613)),f310(x100611,f335(f335(f104(f888(f887(x100611,x100611),a879)),x100614),x100615))))
% 59.73/59.67 [10062]P1(f335(f335(f337(f887(x100621,x100621)),f335(f335(f264(x100621,x100621),x100622),x100623)),f310(x100621,x100624)))+P1(f335(f335(f337(f887(x100621,x100621)),f335(f335(f264(x100621,x100621),f611(x100625,x100624,x100623,x100622,x100621)),f610(x100625,x100624,x100623,x100622,x100621))),x100625))+~P1(f335(f335(f337(f887(x100621,x100621)),f335(f335(f264(x100621,x100621),x100622),x100623)),f310(x100621,f335(f335(f104(f888(f887(x100621,x100621),a879)),x100624),x100625))))
% 59.73/59.67 [10182]~P1(f335(f335(f337(f887(f882(x101821),f882(x101821))),f335(f335(f264(f882(x101821),f882(x101821)),x101824),x101825)),f151(x101821,x101822)))+~P1(f335(f335(f337(f887(x101821,x101821)),x101823),f335(f166(f887(x101821,x101821)),f335(f335(f175(x101821,x101821),x101824),x101825))))+P1(f335(f335(f268(x101821,x101821,a879),f335(f335(f7(x101821,f888(f887(x101821,x101821),a879),f888(x101821,a879)),f335(f335(f8(f888(x101821,f888(f888(f887(x101821,x101821),a879),a879)),f888(f888(f887(x101821,x101821),a879),f888(x101821,a879)),x101821),f7(x101821,f888(f887(x101821,x101821),a879),a879)),f335(f335(f8(f888(x101821,f887(x101821,x101821)),f888(x101821,f888(f888(f887(x101821,x101821),a879),a879)),x101821),f335(f8(f887(x101821,x101821),f888(f888(f887(x101821,x101821),a879),a879),x101821),f337(f887(x101821,x101821)))),f264(x101821,x101821)))),x101822)),x101823))
% 59.73/59.67 [9629]~P1(f335(f335(f242(a881),x96293),x96292))+~P1(f335(f335(f242(a881),f335(f335(f75(a881),f335(f335(f76(a881),x96293),x96294)),x96291)),f335(f335(f75(a881),f335(f335(f76(a881),x96292),x96294)),x96295)))+P1(f335(f335(f242(a881),x96291),f335(f335(f75(a881),f335(f335(f76(a881),f335(f335(f23(a881),x96292),x96293)),x96294)),x96295)))
% 59.73/59.67 [9630]~P1(f335(f335(f242(a881),x96303),x96302))+~P1(f335(f335(f243(a881),f335(f335(f75(a881),f335(f335(f76(a881),x96303),x96304)),x96301)),f335(f335(f75(a881),f335(f335(f76(a881),x96302),x96304)),x96305)))+P1(f335(f335(f243(a881),x96301),f335(f335(f75(a881),f335(f335(f76(a881),f335(f335(f23(a881),x96302),x96303)),x96304)),x96305)))
% 59.73/59.67 [9648]~P1(f335(f335(f242(a881),x96481),x96484))+P1(f335(f335(f242(a881),f335(f335(f75(a881),f335(f335(f76(a881),x96481),x96482)),x96483)),f335(f335(f75(a881),f335(f335(f76(a881),x96484),x96482)),x96485)))+~P1(f335(f335(f242(a881),x96483),f335(f335(f75(a881),f335(f335(f76(a881),f335(f335(f23(a881),x96484),x96481)),x96482)),x96485)))
% 59.73/59.67 [9649]~P1(f335(f335(f242(a881),x96491),x96494))+P1(f335(f335(f243(a881),f335(f335(f75(a881),f335(f335(f76(a881),x96491),x96492)),x96493)),f335(f335(f75(a881),f335(f335(f76(a881),x96494),x96492)),x96495)))+~P1(f335(f335(f243(a881),x96493),f335(f335(f75(a881),f335(f335(f76(a881),f335(f335(f23(a881),x96494),x96491)),x96492)),x96495)))
% 59.73/59.67 [9769]~P1(f335(f335(f242(a881),x97692),x97691))+~P1(f335(f335(f242(a881),f335(f335(f75(a881),f335(f335(f76(a881),x97691),x97693)),x97694)),f335(f335(f75(a881),f335(f335(f76(a881),x97692),x97693)),x97695)))+P1(f335(f335(f242(a881),f335(f335(f75(a881),f335(f335(f76(a881),f335(f335(f23(a881),x97691),x97692)),x97693)),x97694)),x97695))
% 59.73/59.67 [9770]~P1(f335(f335(f242(a881),x97702),x97701))+~P1(f335(f335(f243(a881),f335(f335(f75(a881),f335(f335(f76(a881),x97701),x97703)),x97704)),f335(f335(f75(a881),f335(f335(f76(a881),x97702),x97703)),x97705)))+P1(f335(f335(f243(a881),f335(f335(f75(a881),f335(f335(f76(a881),f335(f335(f23(a881),x97701),x97702)),x97703)),x97704)),x97705))
% 59.73/59.67 [9826]~P1(f335(f335(f242(a881),x98264),x98261))+P1(f335(f335(f242(a881),f335(f335(f75(a881),f335(f335(f76(a881),x98261),x98262)),x98263)),f335(f335(f75(a881),f335(f335(f76(a881),x98264),x98262)),x98265)))+~P1(f335(f335(f242(a881),f335(f335(f75(a881),f335(f335(f76(a881),f335(f335(f23(a881),x98261),x98264)),x98262)),x98263)),x98265))
% 59.73/59.67 [9827]~P1(f335(f335(f242(a881),x98274),x98271))+P1(f335(f335(f243(a881),f335(f335(f75(a881),f335(f335(f76(a881),x98271),x98272)),x98273)),f335(f335(f75(a881),f335(f335(f76(a881),x98274),x98272)),x98275)))+~P1(f335(f335(f243(a881),f335(f335(f75(a881),f335(f335(f76(a881),f335(f335(f23(a881),x98271),x98274)),x98272)),x98273)),x98275))
% 59.73/59.67 [10046]~P13(x100461,x100462,x100465,x100463)+~P1(f335(f335(f337(f887(x100461,x100461)),x100464),x100465))+P1(f335(f335(f268(x100461,x100461,a879),f335(f335(f7(x100461,f888(x100461,x100462),f888(x100461,a879)),f335(f335(f8(f888(x100462,a879),f888(f888(x100461,x100462),f888(x100461,a879)),x100461),f8(x100462,a879,x100461)),f335(f335(f8(x100462,f888(x100462,a879),x100461),a332),x100463))),x100463)),x100464))
% 59.73/59.67 [10070]~P107(x100701)+~P37(x100701,f888(x100702,a879),x100703)+P37(x100701,f888(x100702,a879),f335(f335(f7(x100701,f888(x100702,a879),f888(x100702,a879)),f335(f335(f8(f888(x100702,a879),f888(f888(x100702,a879),f888(x100702,a879)),x100701),f104(f888(x100702,a879))),f335(f335(f7(x100701,f888(x100702,a879),f888(x100702,a879)),f335(f335(f8(f888(x100702,a879),f888(f888(x100702,a879),f888(x100702,a879)),x100701),f104(f888(x100702,a879))),x100703)),x100704))),x100705))
% 59.73/59.67 [6833]~E(f335(x68334,x68335),f200(x68332))+E(f335(f180(x68331,x68332,x68333,x68334),x68335),f335(f235(x68332),x68336))+~E(f335(x68333,x68335),f335(f235(x68332),x68336))
% 59.73/59.67 [6935]~E(f335(x69353,x69356),f200(x69351))+E(f335(f237(f885(x69351),x69352,f200(x69351),x69353),f335(x69354,x69355)),f200(x69351))+~E(f335(x69354,x69355),f335(f235(x69352),x69356))
% 59.73/59.67 [7517]E(f335(x75171,x75172),f200(x75173))+~E(f335(f180(x75175,x75173,x75176,x75171),x75172),f335(f235(x75173),x75174))+E(f335(x75171,x75172),f335(f235(x75173),x75174))
% 59.73/59.67 [7518]E(f335(x75181,x75182),f200(x75183))+~E(f335(f180(x75185,x75183,x75186,x75181),x75182),f335(f235(x75183),x75184))+E(f335(x75181,x75182),f335(f235(x75183),x75184))
% 59.73/59.67 [7551]~E(f335(f180(x75516,x75513,x75515,x75511),x75512),f335(f235(x75513),x75514))+E(f335(x75511,x75512),f335(f235(x75513),x75514))+E(f335(x75515,x75512),f335(f235(x75513),x75514))
% 59.73/59.67 [7552]~E(f335(f180(x75526,x75523,x75525,x75521),x75522),f335(f235(x75523),x75524))+E(f335(x75521,x75522),f335(f235(x75523),x75524))+E(f335(x75525,x75522),f335(f235(x75523),x75524))
% 59.73/59.67 [8451]~P21(x84516,x84511,x84512,x84514)+E(f335(f68(x84511,x84511,x84511,f335(x84512,x84513)),f335(x84514,x84515)),f335(f68(x84511,x84511,x84511,f335(x84514,x84515)),f335(x84512,x84513)))+~P1(f335(f56(x84516),x84515))
% 59.73/59.67 [8873]~P26(x88731,x88733,x88735,x88736)+~P26(x88733,x88732,x88734,f335(f313(x88731,x88733,x88735),x88736))+P26(x88731,x88732,f335(f68(x88733,x88732,x88731,x88734),x88735),x88736)
% 59.73/59.67 [8874]~P26(x88741,x88743,x88745,x88746)+~P26(x88743,x88742,x88744,f335(f313(x88741,x88743,x88745),x88746))+P26(x88741,x88742,f335(f68(x88743,x88742,x88741,x88744),x88745),x88746)
% 59.73/59.67 [9053]~P26(x90534,x90531,x90535,x90536)+~P26(x90534,x90532,f335(f68(x90531,x90532,x90534,x90533),x90535),x90536)+P26(x90531,x90532,x90533,f335(f313(x90534,x90531,x90535),x90536))
% 59.73/59.67 [9436]~P1(f335(f335(x94363,x94362),x94366))+~P1(f335(f335(x94364,x94365),x94362))+P1(f335(f335(f337(x94361),x94362),f302(x94361,x94363,x94364,x94365,x94366)))
% 59.73/59.67 [9437]~P1(f335(f335(x94374,x94372),x94376))+~P1(f335(f335(x94373,x94375),x94372))+P1(f335(f335(f337(x94371),x94372),f299(x94371,x94373,x94374,x94375,x94376)))
% 59.73/59.67 [9549]E(x95491,x95492)+E(x95493,x95494)+~P1(f335(f335(f337(f887(f882(x95495),f882(x95495))),f335(f335(f264(f882(x95495),f882(x95495)),f335(f335(f144(x95495),x95493),x95491)),f335(f335(f144(x95495),x95494),x95492))),f150(x95495,x95496)))
% 59.73/59.67 [9558]~E(x95582,x95584)+P1(f335(f335(f337(f887(f882(x95581),f882(x95581))),f335(f335(f264(f882(x95581),f882(x95581)),f335(f335(f144(x95581),x95582),x95583)),f335(f335(f144(x95581),x95584),x95585))),f138(x95581,x95586)))+~P1(f335(f335(f337(f887(f882(x95581),f882(x95581))),f335(f335(f264(f882(x95581),f882(x95581)),x95583),x95585)),f138(x95581,x95586)))
% 59.73/59.67 [9559]~E(x95592,x95594)+P1(f335(f335(f337(f887(f882(x95591),f882(x95591))),f335(f335(f264(f882(x95591),f882(x95591)),f335(f335(f144(x95591),x95592),x95593)),f335(f335(f144(x95591),x95594),x95595))),f140(x95591,x95596)))+~P1(f335(f335(f337(f887(f882(x95591),f882(x95591))),f335(f335(f264(f882(x95591),f882(x95591)),x95593),x95595)),f140(x95591,x95596)))
% 59.73/59.67 [9560]~E(x95602,x95604)+P1(f335(f335(f337(f887(f882(x95601),f882(x95601))),f335(f335(f264(f882(x95601),f882(x95601)),f335(f335(f144(x95601),x95602),x95603)),f335(f335(f144(x95601),x95604),x95605))),f150(x95601,x95606)))+~P1(f335(f335(f337(f887(f882(x95601),f882(x95601))),f335(f335(f264(f882(x95601),f882(x95601)),x95603),x95605)),f150(x95601,x95606)))
% 59.73/59.67 [9561]~E(x95612,x95614)+P1(f335(f335(f337(f887(f882(x95611),f882(x95611))),f335(f335(f264(f882(x95611),f882(x95611)),f335(f335(f127(x95611),x95612),x95613)),f335(f335(f127(x95611),x95614),x95615))),f150(x95611,x95616)))+~P1(f335(f335(f337(f887(f882(x95611),f882(x95611))),f335(f335(f264(f882(x95611),f882(x95611)),x95613),x95615)),f150(x95611,x95616)))
% 59.73/59.67 [9562]~E(x95623,x95625)+P1(f335(f335(f337(f887(f882(x95621),f882(x95621))),f335(f335(f264(f882(x95621),f882(x95621)),f335(f335(f127(x95621),x95622),x95623)),f335(f335(f127(x95621),x95624),x95625))),f150(x95621,x95626)))+~P1(f335(f335(f337(f887(f882(x95621),f882(x95621))),f335(f335(f264(f882(x95621),f882(x95621)),x95622),x95624)),f150(x95621,x95626)))
% 59.73/59.67 [9617]E(x96171,x96172)+P1(f335(f335(f337(f887(f882(x96173),f882(x96173))),f335(f335(f264(f882(x96173),f882(x96173)),x96171),x96172)),f150(x96173,x96174)))+~P1(f335(f335(f337(f887(f882(x96173),f882(x96173))),f335(f335(f264(f882(x96173),f882(x96173)),f335(f335(f144(x96173),x96175),x96171)),f335(f335(f144(x96173),x96176),x96172))),f150(x96173,x96174)))
% 59.73/59.67 [9773]~E(x97733,x97735)+P1(f335(f335(f337(f887(f882(x97731),f882(x97731))),f335(f335(f264(f882(x97731),f882(x97731)),f335(f335(f127(x97731),x97732),f335(f335(f144(x97731),x97733),f107(x97731)))),f335(f335(f127(x97731),x97734),f335(f335(f144(x97731),x97735),f107(x97731))))),f150(x97731,x97736)))+~P1(f335(f335(f337(f887(f882(x97731),f882(x97731))),f335(f335(f264(f882(x97731),f882(x97731)),x97732),x97734)),f150(x97731,x97736)))
% 59.73/59.67 [9790]E(f335(x97901,x97902),f200(x97903))+~E(f335(f237(f885(x97906),x97903,f200(x97906),x97904),f335(x97901,x97902)),f200(x97906))+E(f335(x97904,f669(x97902,x97901,x97904,x97905,x97906,x97903)),f200(x97906))
% 59.73/59.67 [9791]E(f335(x97911,x97912),f200(x97913))+~E(f335(f237(f885(x97916),x97913,f200(x97916),x97914),f335(x97911,x97912)),f200(x97916))+E(f335(f235(x97913),f669(x97912,x97911,x97914,x97915,x97916,x97913)),f335(x97911,x97912))
% 59.73/59.67 [9830]E(x98301,x98302)+E(x98303,x98304)+~P1(f335(f335(f337(f887(f882(x98305),f882(x98305))),f335(f335(f264(f882(x98305),f882(x98305)),f335(f335(f127(x98305),x98303),f335(f335(f144(x98305),x98301),f107(x98305)))),f335(f335(f127(x98305),x98304),f335(f335(f144(x98305),x98302),f107(x98305))))),f150(x98305,x98306)))
% 59.73/59.67 [9855]E(x98551,x98552)+~P1(f335(f335(f337(f887(f882(x98553),f882(x98553))),f335(f335(f264(f882(x98553),f882(x98553)),f335(f335(f127(x98553),x98551),f335(f335(f144(x98553),x98555),f107(x98553)))),f335(f335(f127(x98553),x98552),f335(f335(f144(x98553),x98556),f107(x98553))))),f150(x98553,x98554)))+P1(f335(f335(f337(f887(f882(x98553),f882(x98553))),f335(f335(f264(f882(x98553),f882(x98553)),x98551),x98552)),f150(x98553,x98554)))
% 59.73/59.67 [9892]~P1(f335(f335(f337(f887(f888(x98921,a879),f888(x98921,a879))),f335(f335(f264(f888(x98921,a879),f888(x98921,a879)),x98922),x98924)),f327(x98921,x98926)))+~P1(f335(f335(f337(f887(f888(x98921,a879),f888(x98921,a879))),f335(f335(f264(f888(x98921,a879),f888(x98921,a879)),x98923),x98925)),f327(x98921,x98926)))+P1(f335(f335(f337(f887(f888(x98921,a879),f888(x98921,a879))),f335(f335(f264(f888(x98921,a879),f888(x98921,a879)),f335(f335(f104(f888(x98921,a879)),x98922),x98923)),f335(f335(f104(f888(x98921,a879)),x98924),x98925))),f327(x98921,x98926)))
% 59.73/59.67 [5277]~E(f335(x52773,x52776),x52775)+~E(x52774,f335(f235(x52771),x52776))+E(f335(f335(f201(x52771,x52772),x52773),x52774),f335(f235(x52772),x52775))
% 59.73/59.67 [5687]~E(f335(f335(f127(x56871),x56876),x56873),x56875)+E(f335(f335(f127(x56871),x56872),x56873),f335(f335(f144(x56871),x56874),x56875))+~E(x56872,f335(f335(f144(x56871),x56874),x56876))
% 59.73/59.67 [5688]~E(f335(f335(f127(x56881),x56886),x56883),x56885)+E(f335(f335(f127(x56881),x56882),x56883),f335(f335(f127(x56881),x56884),x56885))+~E(x56882,f335(f335(f127(x56881),x56884),x56886))
% 59.73/59.67 [5689]E(f335(f335(f127(x56891),x56892),x56893),f335(f335(f144(x56891),x56894),x56895))+~E(f335(f335(f144(x56891),x56894),x56896),x56892)+~E(x56895,f335(f335(f127(x56891),x56896),x56893))
% 59.73/59.67 [5690]E(f335(f335(f127(x56901),x56902),x56903),f335(f335(f144(x56901),x56904),x56905))+~E(f335(f335(f144(x56901),x56904),x56906),x56902)+~E(x56905,f335(f335(f127(x56901),x56906),x56903))
% 59.73/59.67 [5691]~E(f335(f335(f127(x56911),x56912),x56916),x56914)+E(f335(f335(f127(x56911),x56912),x56913),f335(f335(f127(x56911),x56914),x56915))+~E(x56913,f335(f335(f127(x56911),x56916),x56915))
% 59.73/59.67 [5692]~E(f335(f335(f127(x56921),x56922),x56926),x56924)+E(f335(f335(f127(x56921),x56922),x56923),f335(f335(f127(x56921),x56924),x56925))+~E(x56923,f335(f335(f127(x56921),x56926),x56925))
% 59.73/59.67 [6827]E(f335(x68271,x68272),f335(x68273,x68272))+~E(f335(f335(f147(x68274,x68275),x68271),x68276),f335(f335(f147(x68274,x68275),x68273),x68276))+~P1(f335(f335(f337(x68274),x68272),f335(f166(x68274),x68276)))
% 59.73/59.67 [7210]~P21(x72104,x72105,x72106,x72101)+E(f335(f335(x72101,x72102),x72103),f335(f335(f59(x72104,x72105,x72106),x72103),x72102))+~P1(f335(f56(x72104),x72102))
% 59.73/59.67 [7276]~E(x72762,f335(x72764,x72766))+~P1(f335(f335(f337(x72763),x72766),x72765))+P1(f335(f335(f337(x72761),x72762),f335(f313(x72763,x72761,x72764),x72765)))
% 59.73/59.67 [7277]~E(x72772,f335(x72774,x72776))+~P1(f335(f335(f337(x72773),x72776),x72775))+P1(f335(f335(f337(x72771),x72772),f335(f313(x72773,x72771,x72774),x72775)))
% 59.73/59.67 [7278]~E(x72782,f335(x72784,x72786))+~P1(f335(f335(f337(x72783),x72786),x72785))+P1(f335(f335(f337(x72781),x72782),f335(f313(x72783,x72781,x72784),x72785)))
% 59.73/59.67 [7279]~E(f335(x72794,x72792),x72796)+~P1(f335(f335(f337(x72793),x72796),x72795))+P1(f335(f335(f337(x72791),x72792),f335(f314(x72791,x72793,x72794),x72795)))
% 59.73/59.67 [7734]~P31(x77341,x77342,x77344,x77346)+P31(x77341,x77342,f335(f335(f144(x77341),x77343),x77344),f335(f335(f144(x77341),x77345),x77346))+~P1(f335(f335(x77342,x77343),x77345))
% 59.73/59.67 [7735]~P31(x77351,x77352,x77354,x77356)+P31(x77351,x77352,f335(f335(f144(x77351),x77353),x77354),f335(f335(f144(x77351),x77355),x77356))+~P1(f335(f335(x77352,x77353),x77355))
% 59.73/59.67 [8745]~P54(x87454,x87455,x87451,x87452,x87456)+E(f335(x87451,f335(x87452,x87453)),x87453)+~P1(f335(f335(f337(x87455),x87453),x87456))
% 59.73/59.67 [9551]E(x95511,x95512)+E(f335(f189(f882(x95513)),x95514),f335(f189(f882(x95513)),x95515))+~P1(f335(f335(f337(f887(f882(x95513),f882(x95513))),f335(f335(f264(f882(x95513),f882(x95513)),f335(f335(f144(x95513),x95511),x95514)),f335(f335(f144(x95513),x95512),x95515))),f138(x95513,x95516)))
% 59.73/59.67 [9612]~P18(x96121,x96122,x96123)+E(f335(f335(f59(x96121,x96122,x96123),x96124),x96125),x96126)+~P1(f335(f61(x96121,x96122,x96123,x96124,x96125),x96126))
% 59.73/59.67 [9620]E(f335(f189(f882(x96201)),x96202),f335(f189(f882(x96201)),x96203))+P1(f335(f335(f337(f887(f882(x96201),f882(x96201))),f335(f335(f264(f882(x96201),f882(x96201)),x96202),x96203)),f138(x96201,x96204)))+~P1(f335(f335(f337(f887(f882(x96201),f882(x96201))),f335(f335(f264(f882(x96201),f882(x96201)),f335(f335(f144(x96201),x96205),x96202)),f335(f335(f144(x96201),x96206),x96203))),f138(x96201,x96204)))
% 59.73/59.67 [9642]~P1(f335(f335(f337(f887(x96421,x96421)),f335(f335(f264(x96421,x96421),x96422),x96424)),f310(x96421,x96426)))+P1(f335(f335(f337(f887(f882(x96421),f882(x96421))),f335(f335(f264(f882(x96421),f882(x96421)),f335(f335(f144(x96421),x96422),x96423)),f335(f335(f144(x96421),x96424),x96425))),f310(f882(x96421),f150(x96421,x96426))))+~P1(f335(f335(f337(f887(f882(x96421),f882(x96421))),f335(f335(f264(f882(x96421),f882(x96421)),x96423),x96425)),f310(f882(x96421),f150(x96421,x96426))))
% 59.73/59.67 [9836]~P1(f335(x98362,x98366))+~E(f335(f129(x98361,x98362),x98363),f335(f335(f144(x98361),x98364),x98365))+~P1(f335(f335(f337(x98361),x98366),f335(f166(x98361),f771(x98365,x98364,x98363,x98362,x98361))))
% 59.73/59.67 [9837]~P1(f335(x98374,x98376))+~E(f335(f335(f144(x98371),x98372),x98373),f335(f129(x98371,x98374),x98375))+~P1(f335(f335(f337(x98371),x98376),f335(f166(x98371),f774(x98375,x98374,x98373,x98372,x98371))))
% 59.73/59.67 [10136]~P77(x101362)+E(f335(f335(f6(x101361,x101362),f335(f335(f8(f888(x101363,a879),x101362,x101361),f335(f6(x101363,x101362),x101364)),f335(f335(f8(f888(x101363,a879),f888(x101363,a879),x101361),f249(x101363)),f335(f335(f8(f888(x101363,a879),f888(x101363,a879),x101361),f335(f18(x101363,a879,a879),f335(f335(f8(a879,f888(a879,a879),x101363),a333),f335(f335(f7(x101363,f888(x101363,a879),a879),f337(x101363)),x101365)))),f335(f7(x101363,x101361,a879),f335(f335(f8(x101361,f888(x101361,a879),x101363),a332),x101366)))))),f335(f313(x101363,x101361,x101366),x101365)),f335(f335(f6(x101363,x101362),x101364),x101365))+~P1(f335(f56(x101363),x101365))
% 59.73/59.67 [6887]~P106(x68873)+P1(f335(x68872,x68875))+E(f335(f129(x68871,x68872),f335(f335(f141(x68871,x68873,x68874),x68875),x68876)),f335(f129(x68871,x68872),x68876))
% 59.73/59.67 [6889]P1(f335(x68891,x68892))+~E(f160(x68893,x68891,x68894),f335(f335(f264(f882(x68893),f882(x68893)),x68895),x68896))+~P1(f335(f335(f337(x68893),x68892),f335(f166(x68893),x68895)))
% 59.73/59.67 [6932]~P1(f335(x69322,x69326))+~E(f160(x69321,x69322,x69323),f335(f335(f264(f882(x69321),f882(x69321)),x69324),x69325))+~P1(f335(f335(f337(x69321),x69326),f335(f166(x69321),x69325)))
% 59.73/59.67 [7598]~P17(x75981,x75982,x75983)+~P1(f335(f56(x75981),x75986))+E(f335(f335(f59(x75981,x75982,x75983),x75984),f335(f335(f312(x75981),x75985),x75986)),f335(f335(f59(x75981,x75982,x75983),f335(f335(x75983,x75985),x75984)),x75986))
% 59.73/59.67 [7649]~P106(x76492)+~P1(f335(f335(f242(x76492),f335(x76493,x76494)),f335(x76493,x76495)))+E(f335(f335(f141(x76491,x76492,x76493),x76494),f335(f335(f144(x76491),x76495),x76496)),f335(f335(f144(x76491),x76494),f335(f335(f144(x76491),x76495),x76496)))
% 59.73/59.67 [7765]E(x77651,x77652)+~E(f335(f335(f266(x77653,x77654),x77651),f335(f16(f888(x77654,a879),x77653),x77655)),f335(f335(f266(x77653,x77654),x77652),f335(f16(f888(x77654,a879),x77653),x77655)))+~P1(f335(f335(f337(x77654),x77656),x77655))
% 59.73/59.67 [7830]~P17(x78301,x78302,x78303)+~P1(f335(f56(x78301),x78306))+E(f335(f335(f59(x78301,x78302,x78303),x78304),f335(f335(f312(x78301),x78305),x78306)),f335(f335(x78303,x78305),f335(f335(f59(x78301,x78302,x78303),x78304),x78306)))
% 59.73/59.67 [7948]~P18(x79481,x79482,x79483)+~P1(f335(f56(x79481),x79486))+E(f335(f335(f59(x79481,x79482,x79483),f335(f335(x79483,x79484),x79485)),x79486),f335(f335(x79483,x79484),f335(f335(f59(x79481,x79482,x79483),x79485),x79486)))
% 59.73/59.67 [8023]~P22(x80232,x80235,x80236,x80231)+~P1(f335(f56(x80232),x80234))+E(f335(x80231,f335(f335(f312(x80232),x80233),x80234)),f335(f68(x80235,x80235,x80235,f335(x80231,x80234)),f335(x80236,x80233)))
% 59.73/59.67 [8055]~P106(x80552)+P1(f335(f335(f242(x80552),f335(x80553,x80554)),f335(x80553,x80555)))+E(f335(f335(f141(x80551,x80552,x80553),x80554),f335(f335(f144(x80551),x80555),x80556)),f335(f335(f144(x80551),x80555),f335(f335(f141(x80551,x80552,x80553),x80554),x80556)))
% 59.73/59.67 [8193]~E(f335(f189(f882(x81931)),x81935),f335(f189(f882(x81932)),x81936))+~E(f335(f189(f882(x81931)),x81933),f335(f189(f882(x81932)),x81934))+E(f335(f335(f127(f887(x81931,x81932)),f335(f335(f175(x81931,x81932),x81933),x81934)),f335(f335(f175(x81931,x81932),x81935),x81936)),f335(f335(f175(x81931,x81932),f335(f335(f127(x81931),x81933),x81935)),f335(f335(f127(x81932),x81934),x81936)))
% 59.73/59.67 [8307]~E(x83072,f335(f313(x83073,x83071,x83074),x83076))+P1(f335(f335(f242(f888(x83071,a879)),x83072),f335(f313(x83073,x83071,x83074),x83075)))+~P1(f335(f335(f242(f888(x83073,a879)),x83076),x83075))
% 59.73/59.67 [8411]~P106(x84115)+E(f335(x84111,x84112),f335(x84111,x84113))+E(f335(f335(f141(x84114,x84115,x84111),x84112),f335(f335(f141(x84114,x84115,x84111),x84113),x84116)),f335(f335(f141(x84114,x84115,x84111),x84113),f335(f335(f141(x84114,x84115,x84111),x84112),x84116)))
% 59.73/59.67 [8445]~P26(x84453,x84451,x84454,x84455)+P26(x84453,x84451,f335(f335(f335(f67(x84453,x84451),x84454),x84456),x84452),x84455)+P1(f335(f335(f337(x84451),x84452),f335(f313(x84453,x84451,x84454),x84455)))
% 59.73/59.67 [8583]~P1(f335(f335(f337(x85832),x85834),f335(x85836,x85833)))+~P1(f335(f335(f337(x85831),x85833),x85835))+P1(f335(f335(f337(f887(x85831,x85832)),f335(f335(f264(x85831,x85832),x85833),x85834)),f335(f335(f266(x85831,x85832),x85835),x85836)))
% 59.73/59.67 [8584]~P1(f335(f335(f337(x85842),x85844),f335(x85846,x85843)))+~P1(f335(f335(f337(x85841),x85843),x85845))+P1(f335(f335(f337(f887(x85841,x85842)),f335(f335(f264(x85841,x85842),x85843),x85844)),f335(f335(f266(x85841,x85842),x85845),x85846)))
% 59.73/59.67 [9046]~P73(x90462)+~P26(x90464,x90461,x90465,x90466)+E(f335(f335(f9(x90461,x90462),x90463),f335(f313(x90464,x90461,x90465),x90466)),f335(f335(f9(x90464,x90462),f335(f68(x90461,x90462,x90464,x90463),x90465)),x90466))
% 59.73/59.67 [9047]~P77(x90472)+~P26(x90474,x90471,x90475,x90476)+E(f335(f335(f6(x90471,x90472),x90473),f335(f313(x90474,x90471,x90475),x90476)),f335(f335(f6(x90474,x90472),f335(f68(x90471,x90472,x90474,x90473),x90475)),x90476))
% 59.73/59.67 [9093]~P33(x90932,x90935,x90931,x90933,x90936)+P1(f335(f335(x90931,f335(f335(f158(x90932),x90933),x90934)),f335(f335(f158(x90935),x90936),x90934)))+~P1(f335(f335(f243(a881),x90934),f335(f189(f882(x90932)),x90933)))
% 59.73/59.67 [9094]~P33(x90942,x90945,x90941,x90943,x90946)+P1(f335(f335(x90941,f335(f335(f158(x90942),x90943),x90944)),f335(f335(f158(x90945),x90946),x90944)))+~P1(f335(f335(f243(a881),x90944),f335(f189(f882(x90945)),x90946)))
% 59.73/59.67 [9095]~P33(x90952,x90955,x90951,x90953,x90956)+P1(f335(f335(x90951,f335(f335(f158(x90952),x90953),x90954)),f335(f335(f158(x90955),x90956),x90954)))+~P1(f335(f335(f243(a881),x90954),f335(f189(f882(x90952)),x90953)))
% 59.73/59.67 [9105]~E(f335(f313(x91051,x91052,x91053),x91054),x91056)+E(f335(f313(x91051,x91052,x91053),f335(f313(x91052,x91051,f87(x91051,x91052,x91054,x91053)),x91055)),x91055)+~P1(f335(f335(f242(f888(x91052,a879)),x91055),x91056))
% 59.73/59.67 [9310]~P21(x93103,x93101,x93106,x93102)+~P1(f335(f56(x93103),x93104))+E(f335(f68(x93101,x93101,x93101,f335(x93102,f335(f335(f23(f888(x93103,a879)),x93104),f335(f335(f312(x93103),x93105),f188(f888(x93103,a879)))))),f335(x93106,x93105)),f335(x93102,f335(f335(f312(x93103),x93105),x93104)))
% 59.73/59.67 [9320]~P1(f335(f335(f337(x93205),x93203),x93206))+P1(f335(f335(f337(x93201),f335(x93202,x93203)),f90(f888(x93201,a879),x93204)))+~P1(f335(f335(f242(f888(x93201,a879)),f335(f313(x93205,x93201,x93202),x93206)),f335(x93204,f335(f313(x93205,x93201,x93202),x93206))))
% 59.73/59.67 [9927]~E(f335(f313(x99272,x99274,x99276),f252(f888(x99272,a879))),f252(f888(x99274,a879)))+~E(f335(f313(x99271,x99273,x99275),f252(f888(x99271,a879))),f252(f888(x99273,a879)))+E(f335(f313(f887(x99271,x99272),f887(x99273,x99274),f269(x99271,x99273,x99272,x99274,x99275,x99276)),f252(f888(f887(x99271,x99272),a879))),f252(f888(f887(x99273,x99274),a879)))
% 59.73/59.67 [9974]~P26(x99743,x99744,x99745,f335(x99746,f649(x99746,x99745,x99744,x99743,x99742,x99741)))+P26(x99743,x99744,x99745,f335(f335(f34(x99742,f888(x99743,a879)),x99741),x99746))+E(x99741,f188(f888(x99742,a879)))
% 59.73/59.67 [10032]P26(x100326,x100325,x100324,f335(f335(f34(x100322,f888(x100326,a879)),x100321),x100323))+E(x100321,f188(f888(x100322,a879)))+P1(f335(f335(f337(x100322),f649(x100323,x100324,x100325,x100326,x100322,x100321)),x100321))
% 59.73/59.67 [10037]P1(f335(f335(f337(x100371),f579(x100372,x100373,x100374,x100375,x100376,x100371)),x100376))+P1(f335(f335(f242(f888(f887(x100371,x100374),a879)),f335(f335(f266(x100371,x100374),x100376),x100373)),f335(f335(f266(x100371,x100374),x100375),x100372)))+~P1(f335(f335(f242(f888(x100371,a879)),x100376),x100375))
% 59.73/59.67 [10147]~P1(f335(f335(f242(f888(x101472,a879)),f335(x101474,f579(x101476,x101474,x101472,x101475,x101473,x101471))),f335(x101476,f579(x101476,x101474,x101472,x101475,x101473,x101471))))+~P1(f335(f335(f242(f888(x101471,a879)),x101473),x101475))+P1(f335(f335(f242(f888(f887(x101471,x101472),a879)),f335(f335(f266(x101471,x101472),x101473),x101474)),f335(f335(f266(x101471,x101472),x101475),x101476)))
% 59.73/59.67 [7785]~P1(f335(x77851,x77855))+~P1(f335(x77856,x77854))+P1(f335(x77851,f335(f267(x77852,x77853),f335(f335(f264(x77852,x77853),x77854),x77855))))
% 59.73/59.67 [7786]~P1(f335(x77861,x77864))+~P1(f335(x77866,x77865))+P1(f335(x77861,f335(f263(x77862,x77863),f335(f335(f264(x77862,x77863),x77864),x77865))))
% 59.73/59.67 [7807]~E(f335(f189(f882(x78071)),x78073),f335(f189(f882(x78074)),x78075))+~E(f335(f335(f179(x78071,x78074),f335(f335(f175(x78071,x78074),x78073),x78075)),x78072),f335(f235(x78074),x78076))+P1(f335(f335(f337(x78071),x78072),f335(f166(x78071),x78073)))
% 59.73/59.67 [7834]~P1(f335(f335(x78344,x78346),x78345))+~P1(f335(f335(f337(x78341),x78346),x78343))+P1(f335(f335(f335(f33(x78341,f888(x78342,a879)),x78343),x78344),x78345))
% 59.73/59.67 [7835]~P1(f335(f335(x78354,x78356),x78355))+~P1(f335(f335(f337(x78351),x78356),x78353))+P1(f335(f335(f335(f33(x78351,f888(x78352,a879)),x78353),x78354),x78355))
% 59.73/59.67 [8141]~P1(f335(f335(f337(x81411),x81412),f335(x81415,x81416)))+~P1(f335(f335(f337(x81413),x81416),x81414))+P1(f335(f335(f337(x81411),x81412),f335(f335(f33(x81413,f888(x81411,a879)),x81414),x81415)))
% 59.73/59.67 [8142]~P1(f335(f335(f337(x81421),x81422),f335(x81425,x81426)))+~P1(f335(f335(f337(x81423),x81426),x81424))+P1(f335(f335(f337(x81421),x81422),f335(f335(f33(x81423,f888(x81421,a879)),x81424),x81425)))
% 59.73/59.67 [8185]P1(f335(f335(x81851,x81852),x81853))+~P1(f335(f335(x81854,x81852),x81853))+~P1(f335(f335(f242(f888(x81855,f888(x81856,a879))),x81854),x81851))
% 59.73/59.67 [8186]P1(f335(f335(x81861,x81862),x81863))+~P1(f335(f335(x81864,x81862),x81863))+~P1(f335(f335(f242(f888(x81865,f888(x81866,a879))),x81864),x81861))
% 59.73/59.67 [8329]P1(f335(f335(x83291,x83292),x83293))+~P1(f335(f335(f337(x83294),x83292),x83295))+~P1(f335(f335(f335(f34(x83294,f888(x83296,a879)),x83295),x83291),x83293))
% 59.73/59.67 [8330]P1(f335(f335(x83301,x83302),x83303))+~P1(f335(f335(f337(x83304),x83302),x83305))+~P1(f335(f335(f335(f34(x83304,f888(x83306,a879)),x83305),x83301),x83303))
% 59.73/59.67 [8331]P1(f335(f335(x83311,x83312),x83313))+~P1(f335(f335(f337(x83314),x83312),x83315))+~P1(f335(f335(f335(f34(x83314,f888(x83316,a879)),x83315),x83311),x83313))
% 59.73/59.67 [8465]P1(f335(f335(f337(x84651),x84652),f335(x84653,x84654)))+~P1(f335(f335(f337(x84655),x84654),x84656))+~P1(f335(f335(f337(x84651),x84652),f335(f335(f34(x84655,f888(x84651,a879)),x84656),x84653)))
% 59.73/59.67 [8466]P1(f335(f335(f337(x84661),x84662),f335(x84663,x84664)))+~P1(f335(f335(f337(x84665),x84664),x84666))+~P1(f335(f335(f337(x84661),x84662),f335(f335(f34(x84665,f888(x84661,a879)),x84666),x84663)))
% 59.73/59.67 [8467]P1(f335(f335(f337(x84671),x84672),f335(x84673,x84674)))+~P1(f335(f335(f337(x84675),x84674),x84676))+~P1(f335(f335(f337(x84671),x84672),f335(f335(f34(x84675,f888(x84671,a879)),x84676),x84673)))
% 59.73/59.67 [8727]~P13(x87274,x87275,x87276,x87271)+E(f335(x87271,x87272),f335(x87271,x87273))+~P1(f335(f335(f337(f887(x87274,x87274)),f335(f335(f264(x87274,x87274),x87272),x87273)),x87276))
% 59.73/59.67 [8758]P1(f335(f335(f242(f888(x87581,a879)),x87582),f335(x87583,x87584)))+~P1(f335(f335(f337(x87585),x87584),x87586))+~P1(f335(f335(f242(f888(x87581,a879)),x87582),f335(f335(f34(x87585,f888(x87581,a879)),x87586),x87583)))
% 59.73/59.67 [8790]~P52(x87903,x87904,f335(f289(x87904,x87903),x87905))+E(x87901,f188(f888(x87902,a879)))+E(f335(f335(f34(x87902,f888(x87903,a879)),x87901),f335(f335(f8(f888(x87904,a879),f888(x87903,a879),x87902),f288(x87904,x87903,x87905)),x87906)),f335(f288(x87904,x87903,x87905),f335(f335(f34(x87902,f888(x87904,a879)),x87901),x87906)))
% 59.73/59.67 [8864]P1(f335(f335(f337(x88641),x88642),f335(f288(x88643,x88641,x88644),x88645)))+~P1(f335(f335(f337(x88643),x88646),x88645))+~P1(f335(f335(f337(f887(x88643,x88641)),f335(f335(f264(x88643,x88641),x88646),x88642)),x88644))
% 59.73/59.67 [8865]P1(f335(f335(f337(x88651),x88652),f335(f288(x88653,x88651,x88654),x88655)))+~P1(f335(f335(f337(x88653),x88656),x88655))+~P1(f335(f335(f337(f887(x88653,x88651)),f335(f335(f264(x88653,x88651),x88656),x88652)),x88654))
% 59.73/59.67 [9175]P1(f335(f335(f242(f888(x91751,a879)),f335(f288(x91752,x91751,x91753),x91754)),f335(f288(x91752,x91751,x91755),x91756)))+~P1(f335(f335(f242(f888(x91752,a879)),x91754),x91756))+~P1(f335(f335(f242(f888(f887(x91752,x91751),a879)),x91753),x91755))
% 59.73/59.67 [9355]~P1(f335(f335(f337(x93552),x93556),x93554))+~P1(f335(f335(f242(f888(x93551,a879)),x93553),x93555))+P1(f335(f335(f242(f888(f887(x93551,x93552),a879)),f335(f335(f266(x93551,x93552),x93553),f335(f16(f888(x93552,a879),x93551),x93554))),f335(f335(f266(x93551,x93552),x93555),f335(f16(f888(x93552,a879),x93551),x93554))))
% 59.73/59.67 [9368]~P33(x93681,x93682,x93683,x93685,x93686)+P1(f335(f335(f268(x93681,x93682,a879),x93683),x93684))+~P1(f335(f335(f337(f887(x93681,x93682)),x93684),f335(f166(f887(x93681,x93682)),f335(f335(f175(x93681,x93682),x93685),x93686))))
% 59.73/59.67 [9505]~E(x95053,x95055)+P1(f335(f335(f337(f887(f882(x95051),f882(x95051))),f335(f335(f264(f882(x95051),f882(x95051)),f335(f335(f144(x95051),x95052),x95053)),f335(f335(f144(x95051),x95054),x95055))),f150(x95051,x95056)))+~P1(f335(f335(f337(f887(x95051,x95051)),f335(f335(f264(x95051,x95051),x95052),x95054)),x95056))
% 59.73/59.67 [9511]~E(f335(f189(f882(x95111)),x95115),f335(f189(f882(x95112)),x95116))+E(f181(x95111,x95112,f182(x95111,x95112,x95113,f335(f335(f23(f888(x95111,a879)),x95114),f335(f166(x95111),x95115))),x95115,x95116),f182(x95111,x95112,f181(x95111,x95112,x95113,x95115,x95116),x95114))+~P1(f335(f335(f242(f888(x95111,a879)),f335(f166(x95111),x95115)),x95114))
% 59.73/59.67 [9512]~E(f335(f189(f882(x95121)),x95123),f335(f189(f882(x95121)),x95125))+P1(f335(f335(f337(f887(f882(x95121),f882(x95121))),f335(f335(f264(f882(x95121),f882(x95121)),f335(f335(f144(x95121),x95122),x95123)),f335(f335(f144(x95121),x95124),x95125))),f138(x95121,x95126)))+~P1(f335(f335(f337(f887(x95121,x95121)),f335(f335(f264(x95121,x95121),x95122),x95124)),x95126))
% 59.73/59.67 [9543]P1(f335(f335(f337(f887(x95431,x95431)),f335(f335(f264(x95431,x95431),x95432),x95433)),f335(f335(f183(f887(x95431,x95431),a879),f335(a106,x95434)),x95435)))+~P1(f335(f335(f337(f887(x95431,x95431)),f335(f335(f264(x95431,x95431),x95436),x95433)),x95435))+~P1(f335(f335(f337(f887(x95431,x95431)),f335(f335(f264(x95431,x95431),x95432),x95436)),f335(f335(f183(f887(x95431,x95431),a879),x95434),x95435)))
% 59.73/59.67 [9544]P1(f335(f335(f337(f887(x95441,x95441)),f335(f335(f264(x95441,x95441),x95442),x95443)),f335(f335(f183(f887(x95441,x95441),a879),f335(a106,x95444)),x95445)))+~P1(f335(f335(f337(f887(x95441,x95441)),f335(f335(f264(x95441,x95441),x95442),x95446)),x95445))+~P1(f335(f335(f337(f887(x95441,x95441)),f335(f335(f264(x95441,x95441),x95446),x95443)),f335(f335(f183(f887(x95441,x95441),a879),x95444),x95445)))
% 59.73/59.67 [9547]~P1(f335(f335(f337(x95474),x95475),x95476))+P1(f335(f335(f242(f888(x95471,a879)),x95472),x95473))+~P1(f335(f335(f242(f888(f887(x95471,x95474),a879)),f335(f335(f266(x95471,x95474),x95472),f335(f16(f888(x95474,a879),x95471),x95476))),f335(f335(f266(x95471,x95474),x95473),f335(f16(f888(x95474,a879),x95471),x95476))))
% 59.73/59.67 [9591]E(x95911,x95912)+~P1(f335(f335(f337(f887(f882(x95913),f882(x95913))),f335(f335(f264(f882(x95913),f882(x95913)),f335(f335(f144(x95913),x95911),x95915)),f335(f335(f144(x95913),x95912),x95916))),f138(x95913,x95914)))+P1(f335(f335(f337(f887(x95913,x95913)),f335(f335(f264(x95913,x95913),x95911),x95912)),x95914))
% 59.73/59.67 [9592]E(x95921,x95922)+~P1(f335(f335(f337(f887(f882(x95923),f882(x95923))),f335(f335(f264(f882(x95923),f882(x95923)),f335(f335(f144(x95923),x95921),x95925)),f335(f335(f144(x95923),x95922),x95926))),f140(x95923,x95924)))+P1(f335(f335(f337(f887(x95923,x95923)),f335(f335(f264(x95923,x95923),x95921),x95922)),x95924))
% 59.73/59.67 [9593]E(x95931,x95932)+~P1(f335(f335(f337(f887(f882(x95933),f882(x95933))),f335(f335(f264(f882(x95933),f882(x95933)),f335(f335(f144(x95933),x95931),x95935)),f335(f335(f144(x95933),x95932),x95936))),f150(x95933,x95934)))+P1(f335(f335(f337(f887(x95933,x95933)),f335(f335(f264(x95933,x95933),x95931),x95932)),x95934))
% 59.73/59.67 [9628]P1(f335(f335(f337(f887(f882(x96281),f882(x96281))),f335(f335(f264(f882(x96281),f882(x96281)),f335(f335(f144(x96281),x96282),x96283)),f335(f335(f144(x96281),x96284),x96285))),f151(x96281,x96286)))+~P1(f335(f335(f337(f887(f882(x96281),f882(x96281))),f335(f335(f264(f882(x96281),f882(x96281)),x96283),x96285)),f151(x96281,x96286)))+~P1(f335(f335(f337(f887(x96281,x96281)),f335(f335(f264(x96281,x96281),x96282),x96284)),x96286))
% 59.73/59.67 [9646]P1(f335(x96461,x96462))+~P1(f335(x96461,f761(x96461,x96463,x96464,x96465,x96466)))+~P1(f335(f335(f337(x96466),x96462),f335(f335(f33(x96465,f888(x96466,a879)),x96464),x96463)))
% 59.73/59.67 [9651]~P1(f335(f335(f337(f887(f882(x96511),f882(x96511))),f335(f335(f264(f882(x96511),f882(x96511)),f335(f335(f144(x96511),x96512),x96515)),f335(f335(f144(x96511),x96513),x96516))),f138(x96511,x96514)))+P1(f335(f335(f337(f887(f882(x96511),f882(x96511))),f335(f335(f264(f882(x96511),f882(x96511)),x96515),x96516)),f138(x96511,x96514)))+P1(f335(f335(f337(f887(x96511,x96511)),f335(f335(f264(x96511,x96511),x96512),x96513)),x96514))
% 59.73/59.67 [9652]~P1(f335(f335(f337(f887(f882(x96521),f882(x96521))),f335(f335(f264(f882(x96521),f882(x96521)),f335(f335(f144(x96521),x96522),x96525)),f335(f335(f144(x96521),x96523),x96526))),f140(x96521,x96524)))+P1(f335(f335(f337(f887(f882(x96521),f882(x96521))),f335(f335(f264(f882(x96521),f882(x96521)),x96525),x96526)),f140(x96521,x96524)))+P1(f335(f335(f337(f887(x96521,x96521)),f335(f335(f264(x96521,x96521),x96522),x96523)),x96524))
% 59.73/59.67 [9653]~P1(f335(f335(f337(f887(f882(x96531),f882(x96531))),f335(f335(f264(f882(x96531),f882(x96531)),f335(f335(f144(x96531),x96532),x96535)),f335(f335(f144(x96531),x96533),x96536))),f150(x96531,x96534)))+P1(f335(f335(f337(f887(f882(x96531),f882(x96531))),f335(f335(f264(f882(x96531),f882(x96531)),x96535),x96536)),f150(x96531,x96534)))+P1(f335(f335(f337(f887(x96531,x96531)),f335(f335(f264(x96531,x96531),x96532),x96533)),x96534))
% 59.73/59.67 [9744]P1(f335(x97441,x97442))+P1(f335(f335(f337(x97443),f750(x97441,x97444,x97445,x97443,x97446)),x97445))+~P1(f335(f335(f337(x97446),x97442),f335(f335(f33(x97443,f888(x97446,a879)),x97445),x97444)))
% 59.73/59.67 [9755]~E(x97552,x97554)+P1(f335(f335(f337(f887(f882(x97551),f882(x97551))),f335(f335(f264(f882(x97551),f882(x97551)),f335(f335(f127(x97551),x97552),f335(f335(f144(x97551),x97553),f107(x97551)))),f335(f335(f127(x97551),x97554),f335(f335(f144(x97551),x97555),f107(x97551))))),f150(x97551,x97556)))+~P1(f335(f335(f337(f887(x97551,x97551)),f335(f335(f264(x97551,x97551),x97553),x97555)),x97556))
% 59.73/59.67 [9845]E(x98451,x98452)+~P1(f335(f335(f337(f887(f882(x98453),f882(x98453))),f335(f335(f264(f882(x98453),f882(x98453)),f335(f335(f127(x98453),x98455),f335(f335(f144(x98453),x98451),f107(x98453)))),f335(f335(f127(x98453),x98456),f335(f335(f144(x98453),x98452),f107(x98453))))),f150(x98453,x98454)))+P1(f335(f335(f337(f887(x98453,x98453)),f335(f335(f264(x98453,x98453),x98451),x98452)),x98454))
% 59.73/59.67 [9874]~P1(f335(f335(f337(f887(f882(x98741),f882(x98741))),f335(f335(f264(f882(x98741),f882(x98741)),f335(f335(f127(x98741),x98745),f335(f335(f144(x98741),x98742),f107(x98741)))),f335(f335(f127(x98741),x98746),f335(f335(f144(x98741),x98743),f107(x98741))))),f150(x98741,x98744)))+P1(f335(f335(f337(f887(f882(x98741),f882(x98741))),f335(f335(f264(f882(x98741),f882(x98741)),x98745),x98746)),f150(x98741,x98744)))+P1(f335(f335(f337(f887(x98741,x98741)),f335(f335(f264(x98741,x98741),x98742),x98743)),x98744))
% 59.73/59.67 [9893]P1(f335(x98931,x98932))+P1(f335(f335(f337(x98933),f761(x98931,x98934,x98935,x98936,x98933)),f335(x98934,f750(x98931,x98934,x98935,x98936,x98933))))+~P1(f335(f335(f337(x98933),x98932),f335(f335(f33(x98936,f888(x98933,a879)),x98935),x98934)))
% 59.73/59.67 [8881]~P18(x88813,x88814,x88811)+~P1(f335(f56(x88813),x88816))+E(f335(f335(x88811,x88812),f335(f335(f59(x88813,x88814,x88811),x88815),f335(f335(f23(f888(x88813,a879)),x88816),f335(f335(f312(x88813),x88812),f188(f888(x88813,a879)))))),f335(f335(f59(x88813,x88814,x88811),x88815),f335(f335(f312(x88813),x88812),x88816)))
% 59.73/59.67 [8965]~E(f335(f335(f179(x89651,x89652),x89654),x89655),f335(f235(x89652),x89656))+~P1(f335(f335(x89653,x89655),x89656))+E(f335(f335(f179(x89651,x89652),f335(f129(f887(x89651,x89652),f335(f268(x89651,x89652,a879),x89653)),x89654)),x89655),f335(f235(x89652),x89656))
% 59.73/59.67 [9182]~P1(f335(f335(f337(x91825),x91823),x91826))+P1(f335(f335(f242(f888(x91821,a879)),f335(x91822,x91823)),x91824))+~P1(f335(f335(f242(f888(x91821,a879)),f335(f335(f33(x91825,f888(x91821,a879)),x91826),x91822)),x91824))
% 59.73/59.67 [9819]~P8(x98191,x98195,x98194)+P1(f335(f335(f337(f887(x98191,x98191)),f335(f335(f264(x98191,x98191),x98192),x98193)),x98194))+~P1(f335(f335(f337(x98191),x98196),f335(f335(f95(f888(x98191,a879)),f335(f288(x98191,x98191,x98194),f335(f335(f312(x98191),x98192),f188(f888(x98191,a879))))),f335(f288(x98191,x98191,x98194),f335(f335(f312(x98191),x98193),f188(f888(x98191,a879)))))))
% 59.73/59.67 [8621]~P118(x86212)+~E(f335(f335(f75(x86212),f335(f335(f76(x86212),x86214),x86215)),x86211),f335(f335(f75(x86212),f335(f335(f76(x86212),x86213),x86215)),x86216))+E(x86211,f335(f335(f75(x86212),f335(f335(f76(x86212),f335(f335(f23(x86212),x86213),x86214)),x86215)),x86216))
% 59.73/59.67 [8622]~P118(x86221)+~E(f335(f335(f75(x86221),f335(f335(f76(x86221),x86222),x86224)),x86225),f335(f335(f75(x86221),f335(f335(f76(x86221),x86223),x86224)),x86226))+E(f335(f335(f75(x86221),f335(f335(f76(x86221),f335(f335(f23(x86221),x86222),x86223)),x86224)),x86225),x86226)
% 59.73/59.67 [8793]~P118(x87931)+E(f335(f335(f75(x87931),f335(f335(f76(x87931),x87932),x87933)),x87934),f335(f335(f75(x87931),f335(f335(f76(x87931),x87935),x87933)),x87936))+~E(x87936,f335(f335(f75(x87931),f335(f335(f76(x87931),f335(f335(f23(x87931),x87932),x87935)),x87933)),x87934))
% 59.73/59.67 [8794]~P118(x87941)+E(f335(f335(f75(x87941),f335(f335(f76(x87941),x87942),x87943)),x87944),f335(f335(f75(x87941),f335(f335(f76(x87941),x87945),x87943)),x87946))+~E(f335(f335(f75(x87941),f335(f335(f76(x87941),f335(f335(f23(x87941),x87942),x87945)),x87943)),x87944),x87946)
% 59.73/59.67 [9117]~P1(f335(f335(x91174,x91175),x91176))+~P1(f335(f335(x91173,x91175),x91176))+P1(f335(f335(f335(f335(f95(f888(x91171,f888(x91172,a879))),x91173),x91174),x91175),x91176))
% 59.73/59.67 [9376]P1(f335(f335(x93761,x93762),x93763))+P1(f335(f335(x93764,x93762),x93763))+~P1(f335(f335(f335(f335(f104(f888(x93765,f888(x93766,a879))),x93764),x93761),x93762),x93763))
% 59.73/59.67 [9666]~P125(x96661)+~P1(f335(f335(f242(x96661),f335(f335(f75(x96661),f335(f335(f76(x96661),x96664),x96665)),x96662)),f335(f335(f75(x96661),f335(f335(f76(x96661),x96663),x96665)),x96666)))+P1(f335(f335(f242(x96661),x96662),f335(f335(f75(x96661),f335(f335(f76(x96661),f335(f335(f23(x96661),x96663),x96664)),x96665)),x96666)))
% 59.73/59.67 [9667]~P125(x96671)+~P1(f335(f335(f243(x96671),f335(f335(f75(x96671),f335(f335(f76(x96671),x96674),x96675)),x96672)),f335(f335(f75(x96671),f335(f335(f76(x96671),x96673),x96675)),x96676)))+P1(f335(f335(f243(x96671),x96672),f335(f335(f75(x96671),f335(f335(f76(x96671),f335(f335(f23(x96671),x96673),x96674)),x96675)),x96676)))
% 59.73/59.67 [9693]~P125(x96931)+P1(f335(f335(f242(x96931),f335(f335(f75(x96931),f335(f335(f76(x96931),x96932),x96933)),x96934)),f335(f335(f75(x96931),f335(f335(f76(x96931),x96935),x96933)),x96936)))+~P1(f335(f335(f242(x96931),x96934),f335(f335(f75(x96931),f335(f335(f76(x96931),f335(f335(f23(x96931),x96935),x96932)),x96933)),x96936)))
% 59.73/59.67 [9694]~P125(x96941)+P1(f335(f335(f243(x96941),f335(f335(f75(x96941),f335(f335(f76(x96941),x96942),x96943)),x96944)),f335(f335(f75(x96941),f335(f335(f76(x96941),x96945),x96943)),x96946)))+~P1(f335(f335(f243(x96941),x96944),f335(f335(f75(x96941),f335(f335(f76(x96941),f335(f335(f23(x96941),x96945),x96942)),x96943)),x96946)))
% 59.73/59.67 [9807]~P125(x98071)+~P1(f335(f335(f242(x98071),f335(f335(f75(x98071),f335(f335(f76(x98071),x98072),x98074)),x98075)),f335(f335(f75(x98071),f335(f335(f76(x98071),x98073),x98074)),x98076)))+P1(f335(f335(f242(x98071),f335(f335(f75(x98071),f335(f335(f76(x98071),f335(f335(f23(x98071),x98072),x98073)),x98074)),x98075)),x98076))
% 59.73/59.67 [9808]~P125(x98081)+~P1(f335(f335(f243(x98081),f335(f335(f75(x98081),f335(f335(f76(x98081),x98082),x98084)),x98085)),f335(f335(f75(x98081),f335(f335(f76(x98081),x98083),x98084)),x98086)))+P1(f335(f335(f243(x98081),f335(f335(f75(x98081),f335(f335(f76(x98081),f335(f335(f23(x98081),x98082),x98083)),x98084)),x98085)),x98086))
% 59.73/59.67 [9857]~P125(x98571)+P1(f335(f335(f242(x98571),f335(f335(f75(x98571),f335(f335(f76(x98571),x98572),x98573)),x98574)),f335(f335(f75(x98571),f335(f335(f76(x98571),x98575),x98573)),x98576)))+~P1(f335(f335(f242(x98571),f335(f335(f75(x98571),f335(f335(f76(x98571),f335(f335(f23(x98571),x98572),x98575)),x98573)),x98574)),x98576))
% 59.73/59.67 [9858]~P125(x98581)+P1(f335(f335(f243(x98581),f335(f335(f75(x98581),f335(f335(f76(x98581),x98582),x98583)),x98584)),f335(f335(f75(x98581),f335(f335(f76(x98581),x98585),x98583)),x98586)))+~P1(f335(f335(f243(x98581),f335(f335(f75(x98581),f335(f335(f76(x98581),f335(f335(f23(x98581),x98582),x98585)),x98583)),x98584)),x98586))
% 59.73/59.67 [10026]~P77(x100262)+~P1(f335(f56(x100261),x100266))+E(f335(f335(f6(x100261,x100262),f335(f335(f18(x100261,x100262,x100262),f335(f335(f18(x100261,x100262,f888(x100262,x100262)),f335(f335(f8(a879,f888(x100262,f888(x100262,x100262)),x100261),f88(x100262)),x100263)),x100264)),x100265)),x100266),f335(f335(f75(x100262),f335(f335(f6(x100261,x100262),x100264),f335(f335(f95(f888(x100261,a879)),x100266),f335(f249(x100261),x100263)))),f335(f335(f6(x100261,x100262),x100265),f335(f335(f95(f888(x100261,a879)),x100266),f335(f74(f888(x100261,a879)),f335(f249(x100261),x100263))))))
% 59.73/59.67 [10084]P1(f335(f335(f337(x100842),x100844),x100846))+P1(f335(f335(f337(x100842),x100845),x100846))+E(f335(f314(x100841,x100842,f335(f335(f7(x100841,x100842,x100842),f335(f335(f7(x100841,x100842,f888(x100842,x100842)),f335(f335(f8(a879,f888(x100842,f888(x100842,x100842)),x100841),f88(x100842)),f335(f335(f7(x100841,f888(x100841,a879),a879),f337(x100841)),x100843))),x100844)),x100845)),x100846),f188(f888(x100841,a879)))
% 59.73/59.67 [10085]P1(f335(f335(f337(x100852),x100855),x100856))+~P1(f335(f335(f337(x100852),x100854),x100856))+E(f335(f314(x100851,x100852,f335(f335(f7(x100851,x100852,x100852),f335(f335(f7(x100851,x100852,f888(x100852,x100852)),f335(f335(f8(a879,f888(x100852,f888(x100852,x100852)),x100851),f88(x100852)),f335(f335(f7(x100851,f888(x100851,a879),a879),f337(x100851)),x100853))),x100854)),x100855)),x100856),x100853)
% 59.73/59.67 [10086]P1(f335(f335(f337(x100862),x100864),x100866))+~P1(f335(f335(f337(x100862),x100865),x100866))+E(f335(f314(x100861,x100862,f335(f335(f7(x100861,x100862,x100862),f335(f335(f7(x100861,x100862,f888(x100862,x100862)),f335(f335(f8(a879,f888(x100862,f888(x100862,x100862)),x100861),f88(x100862)),f335(f335(f7(x100861,f888(x100861,a879),a879),f337(x100861)),x100863))),x100864)),x100865)),x100866),f335(f74(f888(x100861,a879)),x100863))
% 59.73/59.67 [10087]~P1(f335(f335(f337(x100872),x100874),x100876))+~P1(f335(f335(f337(x100872),x100875),x100876))+E(f335(f314(x100871,x100872,f335(f335(f7(x100871,x100872,x100872),f335(f335(f7(x100871,x100872,f888(x100872,x100872)),f335(f335(f8(a879,f888(x100872,f888(x100872,x100872)),x100871),f88(x100872)),f335(f335(f7(x100871,f888(x100871,a879),a879),f337(x100871)),x100873))),x100874)),x100875)),x100876),f252(f888(x100871,a879)))
% 59.73/59.67 [8651]E(x86511,x86512)+~P54(x86514,x86515,x86513,x86516,x86517)+~E(f335(x86513,x86511),f335(x86513,x86512))
% 59.73/59.67 [7038]E(f335(f237(f885(x70381),x70382,f200(x70381),x70383),f335(x70384,x70385)),f335(f235(x70381),x70386))+~E(f335(x70384,x70385),f335(f235(x70382),x70387))+~E(f335(x70383,x70387),f335(f235(x70381),x70386))
% 59.73/59.67 [8680]~P10(x86806,x86805,x86807,x86804,x86801)+E(f335(f335(x86801,x86802),x86803),x86804)+P1(f335(f56(x86805),x86803))
% 59.73/59.67 [8681]~P10(x86816,x86815,x86817,x86814,x86811)+E(f335(f335(x86811,x86812),x86813),x86814)+P1(f335(f56(x86815),x86813))
% 59.73/59.67 [9533]P40(x95331,x95332,x95333,x95334,x95335,f335(f335(x95333,x95336),x95337))+~E(f335(f335(x95333,x95336),x95337),x95334)+~E(x95335,f188(f888(x95331,a879)))
% 59.73/59.67 [9716]~P1(f335(x97166,x97163))+~P1(f335(f335(f337(f887(x97162,x97162)),f335(f335(f264(x97162,x97162),x97164),x97165)),f335(x97167,x97163)))+P1(f335(f335(f337(f887(f887(x97161,x97162),f887(x97161,x97162))),f335(f335(f264(f887(x97161,x97162),f887(x97161,x97162)),f335(f335(f264(x97161,x97162),x97163),x97164)),f335(f335(f264(x97161,x97162),x97163),x97165))),f286(x97161,x97162,x97166,x97167)))
% 59.73/59.67 [10138]~P40(x101382,x101387,x101383,x101386,x101381,f335(f335(x101383,x101385),x101384))+E(f335(f335(x101383,f565(x101384,x101385,x101381,x101386,x101383,x101387,x101382)),f573(x101384,x101385,x101381,x101386,x101383,x101387,x101382)),f335(f335(x101383,x101385),x101384))+E(x101381,f188(f888(x101382,a879)))
% 59.73/59.67 [10139]~P40(x101397,x101396,x101391,x101394,x101395,f335(f335(x101391,x101392),x101393))+E(f335(f335(x101391,f565(x101393,x101392,x101395,x101394,x101391,x101396,x101397)),f573(x101393,x101392,x101395,x101394,x101391,x101396,x101397)),f335(f335(x101391,x101392),x101393))+E(f335(f335(x101391,x101392),x101393),x101394)
% 59.73/59.67 [9218]~P33(x92181,x92182,x92183,x92185,x92187)+P33(x92181,x92182,x92183,f335(f335(f144(x92181),x92184),x92185),f335(f335(f144(x92182),x92186),x92187))+~P1(f335(f335(x92183,x92184),x92186))
% 59.73/59.67 [9237]P33(x92371,x92372,x92373,x92374,x92375)+~P33(x92371,x92372,x92373,f335(f335(f127(x92371),x92376),x92374),f335(f335(f127(x92372),x92377),x92375))+~E(f335(f189(f882(x92371)),x92376),f335(f189(f882(x92372)),x92377))
% 59.73/59.67 [9238]P33(x92381,x92382,x92383,x92384,x92385)+~P33(x92381,x92382,x92383,f335(f335(f127(x92381),x92384),x92386),f335(f335(f127(x92382),x92385),x92387))+~E(f335(f189(f882(x92381)),x92384),f335(f189(f882(x92382)),x92385))
% 59.73/59.67 [9439]~P33(x94391,x94392,x94393,x94395,x94397)+~P33(x94391,x94392,x94393,x94394,x94396)+P33(x94391,x94392,x94393,f335(f335(f127(x94391),x94394),x94395),f335(f335(f127(x94392),x94396),x94397))
% 59.73/59.67 [9794]~P1(f335(f61(x97941,x97944,x97945,x97946,x97943),x97947))+P1(f335(f61(x97941,x97944,x97945,x97946,f335(f335(f312(x97941),x97942),x97943)),f335(f335(x97945,x97942),x97947)))+P1(f335(f335(f337(x97941),x97942),x97943))
% 59.73/59.67 [9925]~P26(x99253,x99251,x99254,f252(f888(x99253,a879)))+E(f335(f335(f179(x99251,x99252),f335(f335(f147(f887(x99253,x99252),f887(x99251,x99252)),f335(f268(x99253,x99252,f887(x99251,x99252)),f335(f335(f8(x99251,f888(x99252,f887(x99251,x99252)),x99253),f264(x99251,x99252)),x99254))),x99255)),f335(x99254,x99256)),f335(f235(x99252),x99257))+~E(f335(f335(f179(x99253,x99252),x99255),x99256),f335(f235(x99252),x99257))
% 59.73/59.67 [10161]~P40(x101612,x101617,x101616,x101615,x101611,f335(f335(x101616,x101614),x101613))+E(x101611,f188(f888(x101612,a879)))+P1(f335(f335(f337(x101612),f565(x101613,x101614,x101611,x101615,x101616,x101617,x101612)),x101611))
% 59.73/59.67 [10162]~P40(x101625,x101627,x101621,x101624,x101626,f335(f335(x101621,x101622),x101623))+E(f335(f335(x101621,x101622),x101623),x101624)+P1(f335(f335(f337(x101625),f565(x101623,x101622,x101626,x101624,x101621,x101627,x101625)),x101626))
% 59.73/59.67 [6826]~E(x68265,x68267)+~E(x68266,x68264)+E(f335(f335(f335(f335(f67(x68261,f885(x68262)),x68263),x68264),f335(f235(x68262),x68265)),x68266),f335(f235(x68262),x68267))
% 59.73/59.67 [6954]E(x69541,x69542)+~E(f335(x69545,x69541),f335(f235(x69544),x69547))+E(f335(f335(f335(f335(f67(x69543,f885(x69544)),x69545),x69542),f335(f235(x69544),x69546)),x69541),f335(f235(x69544),x69547))
% 59.73/59.67 [7674]E(x76741,x76742)+~E(x76743,x76744)+~E(f335(f335(f335(f335(f67(x76745,f885(x76746)),x76747),x76744),f335(f235(x76746),x76741)),x76743),f335(f235(x76746),x76742))
% 59.73/59.67 [7741]E(x77411,x77412)+E(f335(x77413,x77414),f335(f235(x77415),x77411))+~E(f335(f335(f335(f335(f67(x77416,f885(x77415)),x77413),x77417),f335(f235(x77415),x77412)),x77414),f335(f235(x77415),x77411))
% 59.73/59.67 [7742]E(x77421,x77422)+E(f335(x77423,x77421),f335(f235(x77424),x77425))+~E(f335(f335(f335(f335(f67(x77426,f885(x77424)),x77423),x77422),f335(f235(x77424),x77427)),x77421),f335(f235(x77424),x77425))
% 59.73/59.67 [8905]~P23(x89054,x89055,x89056,x89057,x89051)+~P1(f335(f56(x89055),x89053))+E(f335(f335(x89051,x89052),x89053),f335(f335(f335(f60(x89054,x89055,x89056),x89052),x89057),x89053))
% 59.73/59.67 [8906]~P10(x89064,x89065,x89066,x89067,x89061)+~P1(f335(f56(x89065),x89063))+E(f335(f335(x89061,x89062),x89063),f335(f335(f335(f60(x89064,x89065,x89066),x89062),x89067),x89063))
% 59.73/59.67 [9687]~P25(x96873,x96874,x96875,x96877,x96876,x96871)+~P1(f335(f56(x96874),x96872))+E(f335(x96871,x96872),f335(f335(f335(f60(x96873,x96874,x96875),x96876),x96877),x96872))
% 59.73/59.67 [9852]P40(x98521,x98522,x98523,x98524,x98525,f335(f335(x98523,x98526),x98527))+~P40(x98521,x98522,x98523,x98524,f335(f335(f23(f888(x98521,a879)),x98525),f335(f335(f312(x98521),x98526),f188(f888(x98521,a879)))),x98527)+~P1(f335(f335(f337(x98521),x98526),x98525))
% 59.73/59.67 [10188]~P40(x101882,x101883,x101884,x101885,x101881,f335(f335(x101884,x101887),x101886))+P40(x101882,x101883,x101884,x101885,f335(f335(f23(f888(x101882,a879)),x101881),f335(f335(f312(x101882),f565(x101886,x101887,x101881,x101885,x101884,x101883,x101882)),f188(f888(x101882,a879)))),f573(x101886,x101887,x101881,x101885,x101884,x101883,x101882))+E(x101881,f188(f888(x101882,a879)))
% 59.73/59.67 [10189]~P40(x101895,x101896,x101891,x101894,x101897,f335(f335(x101891,x101892),x101893))+P40(x101895,x101896,x101891,x101894,f335(f335(f23(f888(x101895,a879)),x101897),f335(f335(f312(x101895),f565(x101893,x101892,x101897,x101894,x101891,x101896,x101895)),f188(f888(x101895,a879)))),f573(x101893,x101892,x101897,x101894,x101891,x101896,x101895))+E(f335(f335(x101891,x101892),x101893),x101894)
% 59.73/59.67 [9226]E(f181(x92261,x92262,x92263,x92264,f335(f335(f152(x92262,x92265),x92266),x92267)),f181(x92261,x92262,x92263,x92264,x92265))+~P1(f335(f335(f243(a881),x92266),f335(f189(f882(x92262)),x92265)))+~P1(f335(f335(f242(a881),f335(f189(f882(x92261)),x92264)),x92266))
% 59.73/59.67 [9520]P1(f335(f335(f242(f888(f887(x95201,x95202),a879)),f335(f335(f291(x95201,x95203,x95202),x95204),x95205)),f335(f335(f291(x95201,x95203,x95202),x95206),x95207)))+~P1(f335(f335(f242(f888(f887(x95203,x95202),a879)),x95205),x95207))+~P1(f335(f335(f242(f888(f887(x95201,x95203),a879)),x95204),x95206))
% 59.73/59.67 [9863]~P1(f335(f335(f337(x98631),x98636),x98635))+P1(f335(f61(x98631,x98632,x98633,x98634,x98635),f335(f335(x98633,x98636),x98637)))+~P1(f335(f61(x98631,x98632,x98633,x98634,f335(f335(f23(f888(x98631,a879)),x98635),f335(f335(f312(x98631),x98636),f188(f888(x98631,a879))))),x98637))
% 59.73/59.67 [10245]~P142(x102451)+~P26(f887(x102452,x102453),x102451,f335(f268(x102452,x102453,x102451),f335(f335(f7(x102452,f888(x102453,x102451),f888(x102453,x102451)),f335(f335(f8(f888(x102451,x102451),f888(f888(x102453,x102451),f888(x102453,x102451)),x102452),f8(x102451,x102451,x102453)),f335(f335(f8(x102451,f888(x102451,x102451),x102452),f76(x102451)),x102454))),x102455)),f335(f335(f266(x102452,x102453),x102456),f335(f16(f888(x102453,a879),x102452),x102457)))+E(f335(f335(f6(x102451,x102451),f25(x102451)),f335(f249(x102451),f335(f335(f8(f888(x102452,a879),a879,x102451),f82(x102452)),f335(f335(f8(f888(x102452,f888(x102453,a879)),f888(x102452,a879),x102451),f335(f8(f888(x102453,a879),a879,x102452),f82(x102453))),f335(f335(f7(x102451,f888(x102452,f888(x102453,a879)),f888(x102452,f888(x102453,a879))),f335(f335(f8(f888(x102452,f888(f888(x102453,a879),f888(x102453,a879))),f888(f888(x102452,f888(x102453,a879)),f888(x102452,f888(x102453,a879))),x102451),f18(x102452,f888(x102453,a879),f888(x102453,a879))),f335(f335(f8(f888(x102452,f888(x102453,f888(a879,a879))),f888(x102452,f888(f888(x102453,a879),f888(x102453,a879))),x102451),f335(f8(f888(x102453,f888(a879,a879)),f888(f888(x102453,a879),f888(x102453,a879)),x102452),f18(x102453,a879,a879))),f335(f335(f8(f888(x102452,f888(x102453,a879)),f888(x102452,f888(x102453,f888(a879,a879))),x102451),f335(f8(f888(x102453,a879),f888(x102453,f888(a879,a879)),x102452),f335(f8(a879,f888(a879,a879),x102453),a333))),f335(f335(f7(x102451,f888(x102452,f888(x102453,x102451)),f888(x102452,f888(x102453,a879))),f335(f335(f8(f888(f888(x102453,x102451),f888(x102453,a879)),f888(f888(x102452,f888(x102453,x102451)),f888(x102452,f888(x102453,a879))),x102451),f8(f888(x102453,x102451),f888(x102453,a879),x102452)),f335(f335(f8(f888(x102451,a879),f888(f888(x102453,x102451),f888(x102453,a879)),x102451),f8(x102451,a879,x102453)),a332))),f335(f335(f7(x102452,f888(x102453,x102451),f888(x102453,x102451)),f335(f335(f8(f888(x102451,x102451),f888(f888(x102453,x102451),f888(x102453,x102451)),x102452),f8(x102451,x102451,x102453)),f335(f335(f8(x102451,f888(x102451,x102451),x102452),f76(x102451)),x102454))),x102455)))))),f335(f335(f7(x102452,f888(x102453,a879),f888(x102453,a879)),f335(f335(f8(f888(a879,a879),f888(f888(x102453,a879),f888(x102453,a879)),x102452),f8(a879,a879,x102453)),f335(f335(f8(a879,f888(a879,a879),x102452),a333),f335(f335(f7(x102452,f888(x102452,a879),a879),f337(x102452)),x102456)))),f335(f335(f7(x102453,f888(x102453,a879),a879),f337(x102453)),x102457))))))),f335(f335(f76(x102451),f335(f335(f6(x102452,x102451),x102454),x102456)),f335(f335(f6(x102453,x102451),x102455),x102457)))
% 59.73/59.67 [9684]~P1(f335(f335(x96844,x96846),x96848))+~P1(f335(f335(x96845,x96848),x96847))+P1(f335(f335(f265(x96841,x96842,x96843,x96844,x96845),x96846),x96847))
% 59.73/59.67 [9685]~P1(f335(f335(x96854,x96856),x96858))+~P1(f335(f335(x96855,x96858),x96857))+P1(f335(f335(f265(x96851,x96852,x96853,x96854,x96855),x96856),x96857))
% 59.73/59.67 [9286]~P21(x92868,x92861,x92863,x92865)+~P1(f335(f56(x92868),x92866))+E(f335(f68(x92861,x92861,x92862,f335(x92863,x92864)),f335(f68(x92861,x92861,x92862,f335(x92865,x92866)),x92867)),f335(f68(x92861,x92861,x92862,f335(x92865,x92866)),f335(f68(x92861,x92861,x92862,f335(x92863,x92864)),x92867)))
% 59.73/59.67 [9675]~P24(x96757,x96752,x96755,x96758,x96756,x96751)+~P1(f335(f56(x96752),x96754))+E(f335(x96751,f335(f335(f312(x96752),x96753),x96754)),f335(f335(x96755,f335(x96756,x96753)),f335(x96751,x96754)))
% 59.73/59.67 [9804]~P26(x98042,x98044,x98046,x98048)+~P26(x98041,x98043,x98045,x98047)+P26(f887(x98041,x98042),f887(x98043,x98044),f269(x98041,x98043,x98042,x98044,x98045,x98046),f335(f335(f266(x98041,x98042),x98047),f335(f16(f888(x98042,a879),x98041),x98048)))
% 59.73/59.67 [9466]P1(f335(f335(f337(f887(x94661,x94662)),f335(f335(f264(x94661,x94662),x94663),x94664)),f335(f335(f291(x94661,x94665,x94662),x94666),x94667)))+~P1(f335(f335(f337(f887(x94661,x94665)),f335(f335(f264(x94661,x94665),x94663),x94668)),x94666))+~P1(f335(f335(f337(f887(x94665,x94662)),f335(f335(f264(x94665,x94662),x94668),x94664)),x94667))
% 59.73/59.67 [9654]~P1(f335(f335(f242(f888(f887(x96543,x96542),a879)),x96545),f335(f335(f266(x96543,x96542),x96548),f335(f16(f888(x96542,a879),x96543),x96547))))+~P1(f335(f335(f242(f888(f887(x96541,x96543),a879)),x96544),f335(f335(f266(x96541,x96543),x96546),f335(f16(f888(x96543,a879),x96541),x96548))))+P1(f335(f335(f242(f888(f887(x96541,x96542),a879)),f335(f335(f291(x96541,x96543,x96542),x96544),x96545)),f335(f335(f266(x96541,x96542),x96546),f335(f16(f888(x96542,a879),x96541),x96547))))
% 59.73/59.67 [9710]~E(x97103,x97105)+P1(f335(f335(f337(f887(f887(x97101,x97102),f887(x97101,x97102))),f335(f335(f264(f887(x97101,x97102),f887(x97101,x97102)),f335(f335(f264(x97101,x97102),x97103),x97104)),f335(f335(f264(x97101,x97102),x97105),x97106))),f328(x97101,x97102,x97107,x97108)))+~P1(f335(f335(f337(f887(x97102,x97102)),f335(f335(f264(x97102,x97102),x97104),x97106)),x97108))
% 59.73/59.67 [9828]E(x98281,x98282)+~P1(f335(f335(f337(f887(f887(x98283,x98285),f887(x98283,x98285))),f335(f335(f264(f887(x98283,x98285),f887(x98283,x98285)),f335(f335(f264(x98283,x98285),x98281),x98286)),f335(f335(f264(x98283,x98285),x98282),x98287))),f328(x98283,x98285,x98284,x98288)))+P1(f335(f335(f337(f887(x98283,x98283)),f335(f335(f264(x98283,x98283),x98281),x98282)),x98284))
% 59.73/59.67 [9844]~P1(f335(f335(f337(f887(f887(x98441,x98445),f887(x98441,x98445))),f335(f335(f264(f887(x98441,x98445),f887(x98441,x98445)),f335(f335(f264(x98441,x98445),x98442),x98446)),f335(f335(f264(x98441,x98445),x98443),x98447))),f328(x98441,x98445,x98444,x98448)))+P1(f335(f335(f337(f887(x98441,x98441)),f335(f335(f264(x98441,x98441),x98442),x98443)),x98444))+P1(f335(f335(f337(f887(x98445,x98445)),f335(f335(f264(x98445,x98445),x98446),x98447)),x98448))
% 59.73/59.67 [9745]~P25(x97457,x97455,x97451,x97458,x97452,x97454)+~P1(f335(f56(x97455),x97456))+E(f335(f335(x97451,f335(x97452,x97453)),f335(x97454,f335(f335(f23(f888(x97455,a879)),x97456),f335(f335(f312(x97455),x97453),f188(f888(x97455,a879)))))),f335(x97454,f335(f335(f312(x97455),x97453),x97456)))
% 59.73/59.67 [9244]~P1(f335(f335(f335(x92445,x92448),x92446),x92447))+~P1(f335(f335(f337(x92441),x92448),x92444))+P1(f335(f335(f335(f335(f33(x92441,f888(x92442,f888(x92443,a879))),x92444),x92445),x92446),x92447))
% 59.73/59.67 [9245]~P1(f335(f335(f335(x92455,x92458),x92456),x92457))+~P1(f335(f335(f337(x92451),x92458),x92454))+P1(f335(f335(f335(f335(f33(x92451,f888(x92452,f888(x92453,a879))),x92454),x92455),x92456),x92457))
% 59.73/59.67 [9448]P1(f335(f335(f335(x94481,x94482),x94483),x94484))+~P1(f335(f335(f337(x94485),x94482),x94486))+~P1(f335(f335(f335(f335(f34(x94485,f888(x94487,f888(x94488,a879))),x94486),x94481),x94483),x94484))
% 59.73/59.67 [9449]P1(f335(f335(f335(x94491,x94492),x94493),x94494))+~P1(f335(f335(f337(x94495),x94492),x94496))+~P1(f335(f335(f335(f335(f34(x94495,f888(x94497,f888(x94498,a879))),x94496),x94491),x94493),x94494))
% 59.73/59.67 [9450]P1(f335(f335(f335(x94501,x94502),x94503),x94504))+~P1(f335(f335(f337(x94505),x94502),x94506))+~P1(f335(f335(f335(f335(f34(x94505,f888(x94507,f888(x94508,a879))),x94506),x94501),x94503),x94504))
% 59.73/59.67 [9647]~P23(x96473,x96472,x96474,x96478,x96471)+~P1(f335(f56(x96472),x96477))+E(f335(f335(x96471,f335(f335(f18(x96472,x96473,x96473),f335(f335(f8(x96473,f888(x96473,x96473),x96472),x96474),x96475)),x96476)),x96477),f335(f335(x96474,f335(f335(x96471,x96475),x96477)),f335(f335(x96471,x96476),x96477)))
% 59.73/59.67 [9933]~E(f335(f313(x99332,x99334,x99336),x99338),x993310)+~E(f335(f313(x99331,x99333,x99335),x99337),x99339)+E(f335(f313(f887(x99331,x99332),f887(x99333,x99334),f269(x99331,x99333,x99332,x99334,x99335,x99336)),f335(f335(f266(x99331,x99332),x99337),f335(f16(f888(x99332,a879),x99331),x99338))),f335(f335(f266(x99333,x99334),x99339),f335(f16(f888(x99334,a879),x99333),x993310)))
% 59.73/59.67 [4871]~P106(x48712)+~P15(x48712,x48711)+P15(x48712,f108(x48712,x48711))+E(x48711,f107(x48712))
% 59.73/59.67 [4872]~P106(x48722)+~P15(x48722,x48721)+P15(x48722,f722(x48721,x48722))+E(x48721,f107(x48722))
% 59.73/59.67 [5104]~P5(x51042)+E(f10(x51042,x51041),f32(x51042,x51041))+E(x51041,f188(f888(x51042,a879)))+~P1(f335(f56(x51042),x51041))
% 59.73/59.67 [5105]~P5(x51052)+E(f13(x51052,x51051),f31(x51052,x51051))+E(x51051,f188(f888(x51052,a879)))+~P1(f335(f56(x51052),x51051))
% 59.73/59.67 [5265]~P106(x52652)+~P15(x52652,x52651)+E(x52651,f107(x52652))+E(f335(f335(f144(x52652),f749(x52651,x52652)),f722(x52651,x52652)),x52651)
% 59.73/59.67 [6058]~P61(x60582)+E(x60581,f188(f888(x60582,a879)))+P1(f335(f335(f242(x60582),f10(x60582,x60581)),f13(x60582,x60581)))+~P1(f335(f56(x60582),x60581))
% 59.73/59.67 [6067]~P38(x60672)+~P38(x60671)+E(x60671,x60672)+~E(f335(f313(a1,a881,a98),x60671),f335(f313(a1,a881,a98),x60672))
% 59.73/59.67 [9096]~P119(x90961)+~P1(f335(f335(f337(x90961),x90962),f103(x90961)))+P1(f335(f335(f243(x90961),f335(f335(f75(x90961),f335(f335(f75(x90961),f73(x90961)),x90962)),x90962)),f2(x90961)))+~P1(f335(f335(f243(x90961),x90962),f2(x90961)))
% 59.73/59.67 [9338]~P119(x93381)+~P1(f335(f335(f337(x93381),x93382),f103(x93381)))+~P1(f335(f335(f243(x93381),f335(f335(f75(x93381),f335(f335(f75(x93381),f73(x93381)),x93382)),x93382)),f2(x93381)))+P1(f335(f335(f243(x93381),x93382),f2(x93381)))
% 59.73/59.67 [4927]~P113(x49272)+~P142(x49272)+E(x49271,f2(a881))+E(f335(f335(f254(x49272),f2(x49272)),x49271),f2(x49272))
% 59.73/59.67 [4930]~P113(x49301)+~P142(x49301)+~E(x49302,f2(a881))+E(f335(f335(f254(x49301),f2(x49301)),x49302),f73(x49301))
% 59.73/59.67 [5091]~P136(x50912)+E(x50911,f73(x50912))+E(x50911,f335(f74(x50912),f73(x50912)))+~E(f335(f335(f76(x50912),x50911),x50911),f73(x50912))
% 59.73/59.67 [5342]~P91(x53422)+E(x53421,f2(x53422))+E(f77(x53422,x53421),f335(f74(x53422),f73(x53422)))+P1(f335(f335(f243(x53422),f2(x53422)),x53421))
% 59.73/59.67 [5537]~E(x55372,f73(a1))+~E(x55371,f73(a1))+E(f335(f335(f76(a1),x55371),x55372),f73(a1))+~P1(f335(f335(f243(a1),f2(a1)),x55371))
% 59.73/59.67 [5577]~P91(x55772)+E(f77(x55772,x55771),f73(x55772))+E(x55771,f2(x55772))+~P1(f335(f335(f243(x55772),f2(x55772)),x55771))
% 59.73/59.67 [5586]E(x55861,x55862)+~E(f335(f97(a881),x55861),f335(f97(a881),x55862))+P1(f335(a193,f335(f97(a1),x55862)))+P1(f335(a193,f335(f97(a1),x55861)))
% 59.73/59.67 [5636]~P94(x56361)+~E(x56362,f2(x56361))+E(f335(f335(f75(x56361),x56362),x56362),f2(x56361))+~P1(f335(f335(f337(x56361),x56362),f103(x56361)))
% 59.73/59.67 [5675]E(x56751,f2(a1))+~E(f335(f335(f30(a1),x56752),x56751),f2(a1))+P1(f335(f335(f243(a1),x56751),x56752))+P1(f335(f335(f243(a1),x56752),x56751))
% 59.73/59.67 [5706]E(x57061,f2(a1))+~E(f335(f335(f30(a1),x57062),x57061),f2(a1))+P1(f335(f335(f242(a1),x57062),f2(a1)))+P1(f335(f335(f243(a1),x57062),x57061))
% 59.73/59.67 [5740]E(x57401,f2(a1))+~E(f335(f335(f30(a1),x57402),x57401),f2(a1))+P1(f335(f335(f242(a1),f2(a1)),x57402))+P1(f335(f335(f243(a1),x57401),x57402))
% 59.73/59.67 [5773]E(x57731,f2(a1))+~E(f335(f335(f30(a1),x57732),x57731),f2(a1))+P1(f335(f335(f242(a1),x57732),f2(a1)))+P1(f335(f335(f242(a1),f2(a1)),x57732))
% 59.73/59.67 [5774]~P94(x57742)+E(x57741,f2(x57742))+~E(f335(f335(f75(x57742),x57741),x57741),f2(x57742))+~P1(f335(f335(f337(x57742),x57741),f103(x57742)))
% 59.73/59.67 [5835]E(f335(f97(a881),x58351),f335(f97(a881),x58352))+~E(f335(f97(a1),x58352),f2(a1))+P1(f335(a193,f335(f97(a1),x58352)))+~P1(f335(a193,f335(f97(a1),x58351)))
% 59.73/59.67 [5863]~E(f335(f97(a881),x58632),f335(f97(a881),x58631))+E(f335(f97(a1),x58631),f2(a1))+P1(f335(a193,f335(f97(a1),x58631)))+~P1(f335(a193,f335(f97(a1),x58632)))
% 59.73/59.67 [5872]~P106(x58722)+E(x58721,f188(f888(x58722,a879)))+~P1(f335(f56(x58722),x58721))+P1(f335(f335(f337(x58722),f14(x58722,x58721)),x58721))
% 59.73/59.67 [5873]~P106(x58732)+E(x58731,f188(f888(x58732,a879)))+~P1(f335(f56(x58732),x58731))+P1(f335(f335(f337(x58732),f15(x58732,x58731)),x58731))
% 59.73/59.67 [6038]~P119(x60381)+~P97(x60381)+P1(f335(f335(f242(x60381),f2(x60381)),f335(f97(x60381),x60382)))+~P1(f335(f335(f242(a1),a78),x60382))
% 59.73/59.67 [6039]~P119(x60391)+~P97(x60391)+P1(f335(f335(f243(x60391),f2(x60391)),f335(f97(x60391),x60392)))+~P1(f335(f335(f243(a1),a78),x60392))
% 59.73/59.67 [6057]~P119(x60571)+~P97(x60571)+E(f335(f70(x60571),f335(f97(x60571),x60572)),f335(f97(x60571),x60572))+P1(f335(f335(f243(x60571),f335(f97(x60571),x60572)),f2(x60571)))
% 59.73/59.67 [6093]E(x60931,x60932)+~E(f335(a98,x60931),f335(a98,x60932))+~P1(f335(f335(f242(a1),f2(a1)),x60932))+~P1(f335(f335(f242(a1),f2(a1)),x60931))
% 59.73/59.67 [6094]E(x60941,x60942)+~E(f335(a98,x60941),f335(a98,x60942))+~P1(f335(f335(f242(a1),f2(a1)),x60942))+~P1(f335(f335(f242(a1),f2(a1)),x60941))
% 59.73/59.67 [6121]~E(x61211,f2(a1))+E(f40(x61211,x61212),f335(f335(f264(a1,a1),f2(a1)),f2(a1)))+P1(f335(f335(f242(a1),f2(a1)),x61212))+~P1(f335(f335(f242(a1),f2(a1)),x61211))
% 59.73/59.67 [6286]~P97(x62862)+~P119(x62862)+~P1(f335(f335(f242(x62862),f2(x62862)),f335(f97(x62862),x62861)))+P1(f335(f335(f242(a1),a78),x62861))
% 59.73/59.67 [6287]~P97(x62872)+~P119(x62872)+~P1(f335(f335(f243(x62872),f2(x62872)),f335(f97(x62872),x62871)))+P1(f335(f335(f243(a1),a78),x62871))
% 59.73/59.67 [6292]~P119(x62921)+~P97(x62921)+P1(f335(f335(f242(x62921),f335(f97(x62921),x62922)),f2(x62921)))+~P1(f335(f335(f242(a1),x62922),a78))
% 59.73/59.67 [6293]~P119(x62931)+~P97(x62931)+P1(f335(f335(f243(x62931),f335(f97(x62931),x62932)),f2(x62931)))+~P1(f335(f335(f243(a1),x62932),a78))
% 59.73/59.67 [6611]~P97(x66112)+~P119(x66112)+~P1(f335(f335(f242(x66112),f335(f97(x66112),x66111)),f2(x66112)))+P1(f335(f335(f242(a1),x66111),a78))
% 59.73/59.67 [6612]~P97(x66122)+~P119(x66122)+~P1(f335(f335(f243(x66122),f335(f97(x66122),x66121)),f2(x66122)))+P1(f335(f335(f243(a1),x66121),a78))
% 59.73/59.67 [6703]~P119(x67031)+~P97(x67031)+E(f335(f70(x67031),f335(f97(x67031),x67032)),f335(f74(x67031),f335(f97(x67031),x67032)))+~P1(f335(f335(f243(x67031),f335(f97(x67031),x67032)),f2(x67031)))
% 59.73/59.67 [6723]E(f335(f97(a881),x67231),f335(f97(a881),x67232))+~E(f335(f97(a1),x67232),f2(a1))+~P1(f335(f335(f242(a1),f335(f97(a1),x67231)),f2(a1)))+~P1(f335(a193,f335(f97(a1),x67231)))
% 59.73/59.67 [6896]E(x68961,x68962)+~E(f335(a3,x68961),f335(a3,x68962))+~P1(f335(f335(f337(a881),x68962),f252(f888(a881,a879))))+~P1(f335(f335(f337(a881),x68961),f252(f888(a881,a879))))
% 59.73/59.67 [7118]P1(f335(f335(f242(a881),f335(a98,x71181)),f335(a98,x71182)))+~P1(f335(f335(f242(a1),f2(a1)),x71182))+~P1(f335(f335(f242(a1),f2(a1)),x71181))+~P1(f335(f335(f242(a1),x71181),x71182))
% 59.73/59.67 [7119]P1(f335(f335(f243(a881),f335(a98,x71191)),f335(a98,x71192)))+~P1(f335(f335(f242(a1),f2(a1)),x71192))+~P1(f335(f335(f242(a1),f2(a1)),x71191))+~P1(f335(f335(f243(a1),x71191),x71192))
% 59.73/59.67 [7344]~P38(x73442)+~P6(x73441)+~P1(f335(f335(f337(a1),x73441),x73442))+P1(f335(f335(f337(a881),f335(a98,x73441)),f335(f313(a1,a881,a98),x73442)))
% 59.73/59.67 [7349]~P1(f335(f335(f242(a881),f335(a98,x73491)),f335(a98,x73492)))+~P1(f335(f335(f242(a1),f2(a1)),x73492))+~P1(f335(f335(f242(a1),f2(a1)),x73491))+P1(f335(f335(f242(a1),x73491),x73492))
% 59.73/59.67 [7350]~P1(f335(f335(f243(a881),f335(a98,x73501)),f335(a98,x73502)))+~P1(f335(f335(f242(a1),f2(a1)),x73502))+~P1(f335(f335(f242(a1),f2(a1)),x73501))+P1(f335(f335(f243(a1),x73501),x73502))
% 59.73/59.67 [7605]~P106(x76052)+E(x76051,f188(f888(x76052,a879)))+~P1(f335(f56(x76052),x76051))+P1(f335(f335(f242(x76052),f11(x76052,f240(x76052),x76051)),f12(x76052,f241(x76052),x76051)))
% 59.73/59.67 [7924]~P38(x79242)+~P6(x79241)+P1(f335(f335(f337(a1),x79241),x79242))+~P1(f335(f335(f337(a881),f335(a98,x79241)),f335(f313(a1,a881,a98),x79242)))
% 59.73/59.67 [8196]~P4(x81962)+P1(f335(x81961,f200(x81962)))+~P1(f335(f52(f885(x81962)),x81961))+P1(f335(f52(x81962),f335(f335(f8(f885(x81962),a879,x81962),x81961),f235(x81962))))
% 59.73/59.67 [8660]~P4(x86601)+~P1(f335(x86602,f200(x86601)))+P1(f335(f53(f885(x86601)),x86602))+~P1(f335(f53(x86601),f335(f335(f8(f885(x86601),a879,x86601),x86602),f235(x86601))))
% 59.73/59.67 [9797]~P4(x97971)+~P4(x97972)+~P96(x97972)+E(f335(f335(f147(f882(x97971),f888(x97972,x97971)),f335(f335(f8(f888(x97972,f885(x97971)),f888(x97972,x97971),f882(x97971)),f68(f885(x97971),x97971,x97972,f239(x97971))),f335(f335(f8(f882(f887(x97972,x97971)),f888(x97972,f885(x97971)),f882(x97971)),f179(x97972,x97971)),f335(f175(x97972,x97971),f50(x97972))))),f49(x97971,f335(f189(f882(x97972)),f50(x97972)),f50(x97971))),f50(f888(x97972,x97971)))
% 59.73/59.67 [5869]~P137(x58692)+E(x58691,f2(a1))+E(f335(f74(x58692),f335(f96(x58692),f335(f74(a1),x58691))),f335(f96(x58692),x58691))+~P1(f335(f335(f243(a1),x58691),f2(a1)))
% 59.73/59.67 [5941]~P94(x59411)+~P97(x59411)+~P28(x59411,f335(f97(x59411),x59412))+P28(x59411,f335(f97(x59411),f335(f335(f75(a1),x59412),x59412)))
% 59.73/59.67 [6275]~P79(x62752)+E(x62751,f188(f888(x62752,a879)))+E(f15(x62752,f335(f313(x62752,x62752,f74(x62752)),x62751)),f335(f74(x62752),f14(x62752,x62751)))+~P1(f335(f56(x62752),x62751))
% 59.73/59.67 [6276]~P79(x62762)+E(x62761,f188(f888(x62762,a879)))+E(f14(x62762,f335(f313(x62762,x62762,f74(x62762)),x62761)),f335(f74(x62762),f15(x62762,x62761)))+~P1(f335(f56(x62762),x62761))
% 59.73/59.67 [6307]~P94(x63071)+~P97(x63071)+P28(x63071,f335(f97(x63071),x63072))+~P28(x63071,f335(f97(x63071),f335(f335(f75(a1),x63072),x63072)))
% 59.73/59.67 [6398]E(x63981,f2(a1))+E(f335(a45,f44(f335(f74(a1),x63981),f335(f74(a1),x63982))),f40(x63981,x63982))+P1(f335(f335(f242(a1),f2(a1)),x63982))+~P1(f335(f335(f242(a1),f2(a1)),x63981))
% 59.73/59.67 [7264]~P1(f335(f335(f242(a1),f2(a1)),x72641))+~P1(f335(f335(f243(a1),f2(a1)),x72642))+~P1(f335(f335(f242(a1),x72642),x72641))+P1(f335(f335(f243(a1),f2(a1)),f335(f335(f30(a1),x72641),x72642)))
% 59.73/59.67 [7679]~E(x76792,f2(a1))+E(f218(x76791,x76792),f335(f335(f264(a1,a1),f2(a1)),f73(a1)))+P1(f335(f335(f243(a1),x76792),f2(a1)))+~P1(f335(f323(f887(a1,a1),a224),f335(f335(f264(a1,a1),x76791),x76792)))
% 59.73/59.67 [7680]~E(x76801,f2(a1))+E(f218(x76801,x76802),f335(f335(f264(a1,a1),f2(a1)),f73(a1)))+P1(f335(f335(f243(a1),x76802),f2(a1)))+~P1(f335(f323(f887(a1,a1),a224),f335(f335(f264(a1,a1),x76801),x76802)))
% 59.73/59.67 [8704]~P38(x87042)+~P38(x87041)+P1(f335(f335(f242(f888(a881,a879)),f335(f313(a1,a881,a98),x87041)),f335(f313(a1,a881,a98),x87042)))+~P1(f335(f335(f242(f888(a1,a879)),x87041),x87042))
% 59.73/59.67 [8705]~P38(x87052)+~P38(x87051)+P1(f335(f335(f243(f888(a881,a879)),f335(f313(a1,a881,a98),x87051)),f335(f313(a1,a881,a98),x87052)))+~P1(f335(f335(f243(f888(a1,a879)),x87051),x87052))
% 59.73/59.67 [8925]~E(f755(x89252,x89251),f756(x89252,x89251))+~P1(f335(f130(x89251),f757(x89252,x89251)))+~P1(f335(f130(f882(x89251)),x89252))+P1(f335(f130(x89251),f335(f135(f882(x89251),f882(x89251),f127(x89251),f107(x89251)),x89252)))
% 59.73/59.67 [9015]~P38(x90152)+~P38(x90151)+~P1(f335(f335(f242(f888(a881,a879)),f335(f313(a1,a881,a98),x90151)),f335(f313(a1,a881,a98),x90152)))+P1(f335(f335(f242(f888(a1,a879)),x90151),x90152))
% 59.73/59.67 [9016]~P38(x90162)+~P38(x90161)+~P1(f335(f335(f243(f888(a881,a879)),f335(f313(a1,a881,a98),x90161)),f335(f313(a1,a881,a98),x90162)))+P1(f335(f335(f243(f888(a1,a879)),x90161),x90162))
% 59.73/59.67 [9022]~E(f755(x90222,x90221),f756(x90222,x90221))+~P1(f335(f130(f882(x90221)),x90222))+P1(f335(f130(x90221),f335(f135(f882(x90221),f882(x90221),f127(x90221),f107(x90221)),x90222)))+P1(f335(f335(f337(f882(x90221)),f757(x90222,x90221)),f335(f166(f882(x90221)),x90222)))
% 59.73/59.67 [9064]~P1(f335(f130(x90641),f757(x90642,x90641)))+~P1(f335(f130(f882(x90641)),x90642))+P1(f335(f130(x90641),f335(f135(f882(x90641),f882(x90641),f127(x90641),f107(x90641)),x90642)))+P1(f335(f335(f337(f882(x90641)),f756(x90642,x90641)),f335(f166(f882(x90641)),x90642)))
% 59.73/59.67 [9065]~P1(f335(f130(x90651),f757(x90652,x90651)))+~P1(f335(f130(f882(x90651)),x90652))+P1(f335(f130(x90651),f335(f135(f882(x90651),f882(x90651),f127(x90651),f107(x90651)),x90652)))+P1(f335(f335(f337(f882(x90651)),f755(x90652,x90651)),f335(f166(f882(x90651)),x90652)))
% 59.73/59.67 [9145]~P1(f335(f130(f882(x91451)),x91452))+P1(f335(f130(x91451),f335(f135(f882(x91451),f882(x91451),f127(x91451),f107(x91451)),x91452)))+P1(f335(f335(f337(f882(x91451)),f756(x91452,x91451)),f335(f166(f882(x91451)),x91452)))+P1(f335(f335(f337(f882(x91451)),f757(x91452,x91451)),f335(f166(f882(x91451)),x91452)))
% 59.73/59.67 [9146]~P1(f335(f130(f882(x91461)),x91462))+P1(f335(f130(x91461),f335(f135(f882(x91461),f882(x91461),f127(x91461),f107(x91461)),x91462)))+P1(f335(f335(f337(f882(x91461)),f755(x91462,x91461)),f335(f166(f882(x91461)),x91462)))+P1(f335(f335(f337(f882(x91461)),f757(x91462,x91461)),f335(f166(f882(x91461)),x91462)))
% 59.73/59.67 [9160]~E(f335(f335(f95(f888(x91601,a879)),f335(f166(x91601),f756(x91602,x91601))),f335(f166(x91601),f755(x91602,x91601))),f188(f888(x91601,a879)))+~P1(f335(f130(x91601),f757(x91602,x91601)))+~P1(f335(f130(f882(x91601)),x91602))+P1(f335(f130(x91601),f335(f135(f882(x91601),f882(x91601),f127(x91601),f107(x91601)),x91602)))
% 59.73/59.67 [9222]~E(f335(f335(f95(f888(x92221,a879)),f335(f166(x92221),f756(x92222,x92221))),f335(f166(x92221),f755(x92222,x92221))),f188(f888(x92221,a879)))+~P1(f335(f130(f882(x92221)),x92222))+P1(f335(f130(x92221),f335(f135(f882(x92221),f882(x92221),f127(x92221),f107(x92221)),x92222)))+P1(f335(f335(f337(f882(x92221)),f757(x92222,x92221)),f335(f166(f882(x92221)),x92222)))
% 59.73/59.67 [9491]E(x94911,f2(a1))+E(x94912,f2(a1))+E(f335(f335(f81(a1,f887(a1,a1)),f335(f335(a220,x94912),x94911)),f335(f335(f18(a1,a1,f887(a1,a1)),f335(f335(f8(a1,f888(a1,f887(a1,a1)),a1),f264(a1,a1)),f335(f30(a1),x94912))),f335(f30(a1),x94911))),f218(x94912,x94911))+P1(f335(f335(f243(a1),x94911),f2(a1)))
% 59.73/59.67 [8256]~P97(x82562)+~P119(x82562)+~P1(f335(f335(f242(x82562),f335(f97(x82562),x82561)),f73(x82562)))+P1(f335(f335(f242(a1),x82561),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))
% 59.73/59.67 [8257]~P97(x82572)+~P119(x82572)+~P1(f335(f335(f243(x82572),f335(f97(x82572),x82571)),f73(x82572)))+P1(f335(f335(f243(a1),x82571),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))
% 59.73/59.67 [8529]~P119(x85291)+~P97(x85291)+P1(f335(f335(f242(x85291),f335(f97(x85291),x85292)),f73(x85291)))+~P1(f335(f335(f242(a1),x85292),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))
% 59.73/59.67 [8530]~P119(x85301)+~P97(x85301)+P1(f335(f335(f243(x85301),f335(f97(x85301),x85302)),f73(x85301)))+~P1(f335(f335(f243(a1),x85302),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))
% 59.73/59.67 [8732]~P97(x87322)+~P119(x87322)+~P1(f335(f335(f242(x87322),f73(x87322)),f335(f97(x87322),x87321)))+P1(f335(f335(f242(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),x87321))
% 59.73/59.67 [8733]~P97(x87332)+~P119(x87332)+~P1(f335(f335(f243(x87332),f73(x87332)),f335(f97(x87332),x87331)))+P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),x87331))
% 59.73/59.67 [9102]~P119(x91021)+~P97(x91021)+P1(f335(f335(f242(x91021),f73(x91021)),f335(f97(x91021),x91022)))+~P1(f335(f335(f242(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),x91022))
% 59.73/59.67 [9103]~P119(x91031)+~P97(x91031)+P1(f335(f335(f243(x91031),f73(x91031)),f335(f97(x91031),x91032)))+~P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),x91032))
% 59.73/59.67 [9619]~P136(x96192)+E(x96191,f73(x96192))+E(x96191,f335(f74(x96192),f73(x96192)))+~E(f335(f335(f254(x96192),x96191),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f73(x96192))
% 59.73/59.67 [9902]~P97(x99021)+~P68(x99021)+~P1(f335(f335(f243(x99021),f2(x99021)),x99022))+P1(f335(f335(f243(x99021),f2(x99021)),f335(f335(f292(x99021),x99022),f335(f97(x99021),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))))
% 59.73/59.67 [9903]~P97(x99031)+~P68(x99031)+~P1(f335(f335(f243(x99031),f2(x99031)),x99032))+P1(f335(f335(f243(x99031),f2(x99031)),f335(f335(f292(x99031),x99032),f335(f97(x99031),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))))
% 59.73/59.67 [9962]~P97(x99621)+~P68(x99621)+P1(f335(f335(f243(x99621),f2(x99621)),x99622))+~P1(f335(f335(f243(x99621),f2(x99621)),f335(f335(f292(x99621),x99622),f335(f97(x99621),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))))
% 59.73/59.67 [10218]~P137(x102182)+E(x102181,f2(a1))+P1(f335(f335(f243(a1),x102181),f2(a1)))+E(f335(f335(f268(a1,a1,x102182),f335(f335(f7(a1,f888(a1,f888(x102182,x102182)),f888(a1,x102182)),f335(f335(f8(f888(f888(x102182,x102182),x102182),f888(f888(a1,f888(x102182,x102182)),f888(a1,x102182)),a1),f8(f888(x102182,x102182),x102182,a1)),f335(f335(f8(x102182,f888(f888(x102182,x102182),x102182),a1),f81(x102182,x102182)),f96(x102182)))),f335(f335(f7(a1,f888(x102182,x102182),f888(x102182,x102182)),f335(f335(f8(f888(x102182,f888(x102182,x102182)),f888(f888(x102182,x102182),f888(x102182,x102182)),a1),f18(x102182,x102182,x102182)),f335(f335(f7(a1,f888(x102182,x102182),f888(x102182,f888(x102182,x102182))),f335(f335(f8(f888(x102182,f888(x102182,x102182)),f888(f888(x102182,x102182),f888(x102182,f888(x102182,x102182))),a1),f8(x102182,f888(x102182,x102182),x102182)),f335(f335(f8(a879,f888(x102182,f888(x102182,x102182)),a1),f88(x102182)),f335(f335(f7(a1,a1,a879),a332),f2(a1))))),f335(f335(f18(x102182,x102182,x102182),f75(x102182)),f5(x102182))))),f335(f335(f7(x102182,x102182,x102182),f335(f335(f8(x102182,f888(x102182,x102182),x102182),f75(x102182)),f335(f335(f18(x102182,x102182,x102182),f75(x102182)),f5(x102182)))),f73(x102182))))),f40(x102181,f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f335(f96(x102182),x102181))
% 59.73/59.67 [9996]P1(f335(f335(f242(a1),x99961),f2(a1)))+P1(f335(f335(f243(a1),x99962),x99961))+~P1(f335(f323(f887(a1,a1),a51),f335(f335(f264(a1,a1),x99962),x99961)))+E(f335(f37(x99961),f41(x99962,f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x99961))),f41(x99962,x99961))
% 59.73/59.67 [10000]P1(f335(f335(f242(a1),x100001),f2(a1)))+~P1(f335(f323(f887(a1,a1),a46),f335(f335(f264(a1,a1),x100002),x100001)))+P1(f335(f335(f242(a1),f2(a1)),f335(f335(f75(a1),x100002),x100001)))+E(f335(f37(x100001),f44(x100002,f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),x100001))),f44(x100002,x100001))
% 59.73/59.67 [5222]~P107(x52221)+~P107(x52222)+~P49(x52221,x52222,x52223)+P37(x52221,x52222,x52223)
% 59.73/59.67 [5115]~P5(x51153)+~P37(x51153,x51153,x51151)+E(f335(x51151,x51152),x51152)+~E(x51152,f90(x51153,x51151))
% 59.73/59.67 [5116]~P5(x51163)+~P37(x51163,x51163,x51161)+E(f335(x51161,x51162),x51162)+~E(x51162,f89(x51163,x51161))
% 59.73/59.67 [5260]~P4(x52603)+~P34(x52603,x52602,f50(x52603))+E(x52601,f764(x52602,x52603))+~P1(f335(x52602,x52601))
% 59.73/59.67 [5412]~P4(x54121)+P34(x54121,x54122,f50(x54121))+~E(f785(x54122,x54121,x54123),x54123)+~P1(f335(x54122,x54123))
% 59.73/59.67 [4898]~P94(x48983)+~P97(x48983)+E(x48981,x48982)+~E(f335(f97(x48983),x48981),f335(f97(x48983),x48982))
% 59.73/59.67 [5879]~P107(x58791)+E(f246(x58791,x58792),x58793)+~P1(f335(x58792,x58793))+P1(f335(x58792,f856(x58793,x58792,x58791)))
% 59.73/59.67 [6037]~P4(x60371)+P34(x60371,x60372,f50(x60371))+~P1(f335(x60372,x60373))+P1(f335(x60372,f785(x60372,x60371,x60373)))
% 59.73/59.67 [6047]~P1(f335(x60471,x60472))+~P1(f335(x60471,x60473))+~P1(f335(f335(f242(a881),x60473),f364(x60472,x60471)))+P1(f335(x60471,f2(a881)))
% 59.73/59.67 [6464]P146(x64642,x64641,x64643)+E(x64641,f2(a1))+P1(f335(f335(f242(a1),f2(a1)),f821(x64643,x64641,x64642)))+P1(f335(f335(f243(a1),x64641),f2(a1)))
% 59.73/59.67 [6465]P145(x64652,x64651,x64653)+E(x64651,f2(a1))+P1(f335(f335(f242(a1),f2(a1)),f825(x64653,x64651,x64652)))+P1(f335(f335(f243(a1),x64651),f2(a1)))
% 59.73/59.67 [6587]P145(x65871,x65872,x65873)+~P1(f335(x65871,x65873))+P1(f335(f335(f242(a1),f2(a1)),f825(x65873,x65872,x65871)))+P1(f335(f335(f243(a1),x65872),f2(a1)))
% 59.73/59.67 [6617]P146(x66171,x66172,x66173)+P1(f335(f335(f242(a1),f2(a1)),f821(x66173,x66172,x66171)))+~P1(f335(x66171,f2(a1)))+P1(f335(f335(f243(a1),x66172),f2(a1)))
% 59.73/59.67 [6645]P146(x66452,x66451,x66453)+E(x66451,f2(a1))+~P1(f335(x66452,f822(x66453,x66451,x66452)))+P1(f335(f335(f243(a1),x66451),f2(a1)))
% 59.73/59.67 [6646]P145(x66462,x66461,x66463)+E(x66461,f2(a1))+~P1(f335(x66462,f825(x66463,x66461,x66462)))+P1(f335(f335(f243(a1),x66461),f2(a1)))
% 59.73/59.67 [6730]~P107(x67301)+E(f246(x67301,x67302),x67303)+~P1(f335(x67302,x67303))+~P1(f335(f335(f242(x67301),x67303),f856(x67303,x67302,x67301)))
% 59.73/59.67 [6749]~P106(x67491)+~P5(x67491)+~P1(f335(f335(f243(x67491),x67492),f31(x67491,x67493)))+P1(f335(f335(f243(x67491),x67492),f630(x67493,x67492,x67491)))
% 59.73/59.67 [6758]P145(x67581,x67582,x67583)+~P1(f335(x67581,x67583))+~P1(f335(x67581,f825(x67583,x67582,x67581)))+P1(f335(f335(f243(a1),x67582),f2(a1)))
% 59.73/59.67 [6790]P146(x67901,x67902,x67903)+~P1(f335(x67901,f822(x67903,x67902,x67901)))+~P1(f335(x67901,f2(a1)))+P1(f335(f335(f243(a1),x67902),f2(a1)))
% 59.73/59.67 [7040]P146(x70402,x70401,x70403)+E(x70401,f2(a1))+P1(f335(f335(f242(a1),f2(a1)),f821(x70403,x70401,x70402)))+P1(f335(f335(f243(a1),x70401),f820(x70403,x70401,x70402)))
% 59.73/59.67 [7041]P145(x70412,x70411,x70413)+E(x70411,f2(a1))+P1(f335(f335(f242(a1),f2(a1)),f825(x70413,x70411,x70412)))+P1(f335(f335(f243(a1),x70411),f824(x70413,x70411,x70412)))
% 59.73/59.67 [7159]P145(x71591,x71592,x71593)+~P1(f335(x71591,x71593))+P1(f335(f335(f242(a1),f2(a1)),f825(x71593,x71592,x71591)))+P1(f335(f335(f243(a1),x71592),f824(x71593,x71592,x71591)))
% 59.73/59.67 [7178]P146(x71781,x71782,x71783)+P1(f335(f335(f242(a1),f2(a1)),f821(x71783,x71782,x71781)))+P1(f335(f335(f243(a1),x71782),f820(x71783,x71782,x71781)))+~P1(f335(x71781,f2(a1)))
% 59.73/59.67 [7211]P146(x72112,x72111,x72113)+E(x72111,f2(a1))+~P1(f335(x72112,f822(x72113,x72111,x72112)))+P1(f335(f335(f243(a1),x72111),f820(x72113,x72111,x72112)))
% 59.73/59.67 [7212]P145(x72122,x72121,x72123)+E(x72121,f2(a1))+~P1(f335(x72122,f825(x72123,x72121,x72122)))+P1(f335(f335(f243(a1),x72121),f824(x72123,x72121,x72122)))
% 59.73/59.67 [7253]P146(x72532,x72531,x72533)+E(x72531,f2(a1))+P1(f335(f335(f242(a1),f2(a1)),f821(x72533,x72531,x72532)))+~P1(f335(x72532,f823(x72533,x72531,x72532)))
% 59.73/59.67 [7254]P145(x72542,x72541,x72543)+E(x72541,f2(a1))+P1(f335(f335(f242(a1),f2(a1)),f825(x72543,x72541,x72542)))+~P1(f335(x72542,f824(x72543,x72541,x72542)))
% 59.73/59.67 [7348]P145(x73481,x73482,x73483)+~P1(f335(x73481,x73483))+~P1(f335(x73481,f825(x73483,x73482,x73481)))+P1(f335(f335(f243(a1),x73482),f824(x73483,x73482,x73481)))
% 59.73/59.67 [7364]P146(x73641,x73642,x73643)+~P1(f335(x73641,f822(x73643,x73642,x73641)))+P1(f335(f335(f243(a1),x73642),f820(x73643,x73642,x73641)))+~P1(f335(x73641,f2(a1)))
% 59.73/59.67 [7368]P145(x73681,x73682,x73683)+~P1(f335(x73681,x73683))+P1(f335(f335(f242(a1),f2(a1)),f825(x73683,x73682,x73681)))+~P1(f335(x73681,f824(x73683,x73682,x73681)))
% 59.73/59.67 [7384]P146(x73841,x73842,x73843)+P1(f335(f335(f242(a1),f2(a1)),f821(x73843,x73842,x73841)))+~P1(f335(x73841,f823(x73843,x73842,x73841)))+~P1(f335(x73841,f2(a1)))
% 59.73/59.67 [7408]P146(x74082,x74081,x74083)+E(x74081,f2(a1))+~P1(f335(x74082,f822(x74083,x74081,x74082)))+~P1(f335(x74082,f823(x74083,x74081,x74082)))
% 59.73/59.67 [7409]P145(x74092,x74091,x74093)+E(x74091,f2(a1))+~P1(f335(x74092,f825(x74093,x74091,x74092)))+~P1(f335(x74092,f824(x74093,x74091,x74092)))
% 59.73/59.67 [7499]P145(x74991,x74992,x74993)+~P1(f335(x74991,x74993))+~P1(f335(x74991,f825(x74993,x74992,x74991)))+~P1(f335(x74991,f824(x74993,x74992,x74991)))
% 59.73/59.67 [7516]P146(x75161,x75162,x75163)+~P1(f335(x75161,f822(x75163,x75162,x75161)))+~P1(f335(x75161,f823(x75163,x75162,x75161)))+~P1(f335(x75161,f2(a1)))
% 59.73/59.67 [7564]P146(x75642,x75641,x75643)+E(x75641,f2(a1))+P1(f335(f335(f242(a1),f2(a1)),f821(x75643,x75641,x75642)))+P1(f335(f335(f242(a1),f820(x75643,x75641,x75642)),f2(a1)))
% 59.73/59.67 [7565]P145(x75652,x75651,x75653)+E(x75651,f2(a1))+P1(f335(f335(f242(a1),f2(a1)),f825(x75653,x75651,x75652)))+P1(f335(f335(f242(a1),f824(x75653,x75651,x75652)),f2(a1)))
% 59.73/59.67 [7566]~P90(x75661)+~P1(f335(f335(f242(x75661),x75663),f2(x75661)))+~P1(f335(f335(f242(x75661),x75662),f2(x75661)))+P1(f335(f335(f242(x75661),f335(f335(f75(x75661),x75662),x75663)),f2(x75661)))
% 59.73/59.67 [7567]~P137(x75671)+~P1(f335(f335(f337(x75671),x75673),f103(x75671)))+~P1(f335(f335(f337(x75671),x75672),f103(x75671)))+P1(f335(f335(f337(x75671),f335(f335(f23(x75671),x75672),x75673)),f103(x75671)))
% 59.73/59.67 [7568]~P137(x75681)+~P1(f335(f335(f337(x75681),x75683),f103(x75681)))+~P1(f335(f335(f337(x75681),x75682),f103(x75681)))+P1(f335(f335(f337(x75681),f335(f335(f76(x75681),x75682),x75683)),f103(x75681)))
% 59.73/59.67 [7569]~P143(x75691)+~P1(f335(f335(f337(x75691),x75693),f186(x75691)))+~P1(f335(f335(f337(x75691),x75692),f186(x75691)))+P1(f335(f335(f337(x75691),f335(f335(f76(x75691),x75692),x75693)),f186(x75691)))
% 59.73/59.67 [7570]~P137(x75701)+~P1(f335(f335(f337(x75701),x75703),f103(x75701)))+~P1(f335(f335(f337(x75701),x75702),f103(x75701)))+P1(f335(f335(f337(x75701),f335(f335(f75(x75701),x75702),x75703)),f103(x75701)))
% 59.73/59.67 [7571]~P143(x75711)+~P1(f335(f335(f337(x75711),x75713),f186(x75711)))+~P1(f335(f335(f337(x75711),x75712),f186(x75711)))+P1(f335(f335(f337(x75711),f335(f335(f75(x75711),x75712),x75713)),f186(x75711)))
% 59.73/59.67 [7572]~P90(x75721)+~P1(f335(f335(f242(x75721),x75723),f2(x75721)))+~P1(f335(f335(f243(x75721),x75722),f2(x75721)))+P1(f335(f335(f243(x75721),f335(f335(f75(x75721),x75722),x75723)),f2(x75721)))
% 59.73/59.67 [7573]~P90(x75731)+~P1(f335(f335(f242(x75731),x75732),f2(x75731)))+~P1(f335(f335(f243(x75731),x75733),f2(x75731)))+P1(f335(f335(f243(x75731),f335(f335(f75(x75731),x75732),x75733)),f2(x75731)))
% 59.73/59.67 [7574]~P90(x75741)+~P1(f335(f335(f243(x75741),x75743),f2(x75741)))+~P1(f335(f335(f243(x75741),x75742),f2(x75741)))+P1(f335(f335(f243(x75741),f335(f335(f75(x75741),x75742),x75743)),f2(x75741)))
% 59.73/59.67 [7601]P146(x76013,x76011,x76012)+E(x76011,f2(a1))+E(f335(f335(f75(a1),f335(f335(f76(a1),x76011),f822(x76012,x76011,x76013))),f821(x76012,x76011,x76013)),x76012)+P1(f335(f335(f243(a1),x76011),f2(a1)))
% 59.73/59.67 [7602]P145(x76023,x76021,x76022)+E(x76021,f2(a1))+E(f335(f335(f75(a1),f335(f335(f76(a1),x76021),f826(x76022,x76021,x76023))),f825(x76022,x76021,x76023)),x76022)+P1(f335(f335(f243(a1),x76021),f2(a1)))
% 59.73/59.67 [7684]P145(x76841,x76842,x76843)+~P1(f335(x76841,x76843))+P1(f335(f335(f242(a1),f2(a1)),f825(x76843,x76842,x76841)))+P1(f335(f335(f242(a1),f824(x76843,x76842,x76841)),f2(a1)))
% 59.73/59.67 [7714]P146(x77141,x77142,x77143)+P1(f335(f335(f242(a1),f2(a1)),f821(x77143,x77142,x77141)))+~P1(f335(x77141,f2(a1)))+P1(f335(f335(f242(a1),f820(x77143,x77142,x77141)),f2(a1)))
% 59.73/59.67 [7723]P145(x77233,x77231,x77232)+~P1(f335(x77233,x77232))+E(f335(f335(f75(a1),f335(f335(f76(a1),x77231),f826(x77232,x77231,x77233))),f825(x77232,x77231,x77233)),x77232)+P1(f335(f335(f243(a1),x77231),f2(a1)))
% 59.73/59.67 [7730]P146(x77302,x77301,x77303)+E(x77301,f2(a1))+~P1(f335(x77302,f822(x77303,x77301,x77302)))+P1(f335(f335(f242(a1),f820(x77303,x77301,x77302)),f2(a1)))
% 59.73/59.67 [7731]P145(x77312,x77311,x77313)+E(x77311,f2(a1))+~P1(f335(x77312,f825(x77313,x77311,x77312)))+P1(f335(f335(f242(a1),f824(x77313,x77311,x77312)),f2(a1)))
% 59.73/59.67 [7736]P146(x77363,x77361,x77362)+E(f335(f335(f75(a1),f335(f335(f76(a1),x77361),f822(x77362,x77361,x77363))),f821(x77362,x77361,x77363)),x77362)+~P1(f335(x77363,f2(a1)))+P1(f335(f335(f243(a1),x77361),f2(a1)))
% 59.73/59.67 [7792]P145(x77921,x77922,x77923)+~P1(f335(x77921,x77923))+~P1(f335(x77921,f825(x77923,x77922,x77921)))+P1(f335(f335(f242(a1),f824(x77923,x77922,x77921)),f2(a1)))
% 59.73/59.67 [7796]P146(x77961,x77962,x77963)+~P1(f335(x77961,f822(x77963,x77962,x77961)))+~P1(f335(x77961,f2(a1)))+P1(f335(f335(f242(a1),f820(x77963,x77962,x77961)),f2(a1)))
% 59.73/59.67 [7864]~P123(x78641)+~P1(f335(f335(f242(x78641),f335(f335(f76(x78641),x78643),x78642)),f2(x78641)))+P1(f335(f335(f242(x78641),x78642),f2(x78641)))+P1(f335(f335(f242(x78641),x78643),f2(x78641)))
% 59.73/59.67 [7865]~P68(x78651)+~P1(f335(f335(f242(x78651),f335(f335(f292(x78651),x78653),x78652)),f2(x78651)))+P1(f335(f335(f242(x78651),x78652),f2(x78651)))+P1(f335(f335(f242(x78651),x78653),f2(x78651)))
% 59.73/59.67 [7866]~P68(x78661)+~P1(f335(f335(f243(x78661),f335(f335(f292(x78661),x78663),x78662)),f2(x78661)))+P1(f335(f335(f243(x78661),x78662),f2(x78661)))+P1(f335(f335(f243(x78661),x78663),f2(x78661)))
% 59.73/59.67 [7985]P146(x79853,x79851,x79852)+E(x79851,f2(a1))+E(f335(f335(f75(a1),f335(f335(f76(a1),x79851),f822(x79852,x79851,x79853))),f821(x79852,x79851,x79853)),x79852)+P1(f335(f335(f243(a1),x79851),f820(x79852,x79851,x79853)))
% 59.73/59.67 [7986]P145(x79863,x79861,x79862)+E(x79861,f2(a1))+E(f335(f335(f75(a1),f335(f335(f76(a1),x79861),f826(x79862,x79861,x79863))),f825(x79862,x79861,x79863)),x79862)+P1(f335(f335(f243(a1),x79861),f824(x79862,x79861,x79863)))
% 59.73/59.67 [8000]P146(x80003,x80001,x80002)+E(x80001,f2(a1))+E(f335(f335(f75(a1),f335(f335(f76(a1),x80001),f823(x80002,x80001,x80003))),f820(x80002,x80001,x80003)),x80002)+P1(f335(f335(f242(a1),f2(a1)),f821(x80002,x80001,x80003)))
% 59.73/59.67 [8001]P145(x80013,x80011,x80012)+E(x80011,f2(a1))+E(f335(f335(f75(a1),f335(f335(f76(a1),x80011),f827(x80012,x80011,x80013))),f824(x80012,x80011,x80013)),x80012)+P1(f335(f335(f242(a1),f2(a1)),f825(x80012,x80011,x80013)))
% 59.73/59.67 [8043]P145(x80433,x80431,x80432)+~P1(f335(x80433,x80432))+E(f335(f335(f75(a1),f335(f335(f76(a1),x80431),f826(x80432,x80431,x80433))),f825(x80432,x80431,x80433)),x80432)+P1(f335(f335(f243(a1),x80431),f824(x80432,x80431,x80433)))
% 59.73/59.67 [8052]P146(x80523,x80521,x80522)+E(f335(f335(f75(a1),f335(f335(f76(a1),x80521),f822(x80522,x80521,x80523))),f821(x80522,x80521,x80523)),x80522)+P1(f335(f335(f243(a1),x80521),f820(x80522,x80521,x80523)))+~P1(f335(x80523,f2(a1)))
% 59.73/59.67 [8058]P145(x80583,x80581,x80582)+~P1(f335(x80583,x80582))+E(f335(f335(f75(a1),f335(f335(f76(a1),x80581),f827(x80582,x80581,x80583))),f824(x80582,x80581,x80583)),x80582)+P1(f335(f335(f242(a1),f2(a1)),f825(x80582,x80581,x80583)))
% 59.73/59.67 [8064]P146(x80643,x80641,x80642)+E(f335(f335(f75(a1),f335(f335(f76(a1),x80641),f823(x80642,x80641,x80643))),f820(x80642,x80641,x80643)),x80642)+P1(f335(f335(f242(a1),f2(a1)),f821(x80642,x80641,x80643)))+~P1(f335(x80643,f2(a1)))
% 59.73/59.67 [8075]P146(x80753,x80751,x80752)+E(x80751,f2(a1))+E(f335(f335(f75(a1),f335(f335(f76(a1),x80751),f822(x80752,x80751,x80753))),f821(x80752,x80751,x80753)),x80752)+~P1(f335(x80753,f823(x80752,x80751,x80753)))
% 59.73/59.67 [8076]P145(x80763,x80761,x80762)+E(x80761,f2(a1))+E(f335(f335(f75(a1),f335(f335(f76(a1),x80761),f826(x80762,x80761,x80763))),f825(x80762,x80761,x80763)),x80762)+~P1(f335(x80763,f824(x80762,x80761,x80763)))
% 59.73/59.67 [8077]P146(x80773,x80771,x80772)+E(x80771,f2(a1))+E(f335(f335(f75(a1),f335(f335(f76(a1),x80771),f823(x80772,x80771,x80773))),f820(x80772,x80771,x80773)),x80772)+~P1(f335(x80773,f822(x80772,x80771,x80773)))
% 59.73/59.67 [8078]P145(x80783,x80781,x80782)+E(x80781,f2(a1))+E(f335(f335(f75(a1),f335(f335(f76(a1),x80781),f827(x80782,x80781,x80783))),f824(x80782,x80781,x80783)),x80782)+~P1(f335(x80783,f825(x80782,x80781,x80783)))
% 59.73/59.67 [8134]P145(x81343,x81341,x81342)+~P1(f335(x81343,x81342))+E(f335(f335(f75(a1),f335(f335(f76(a1),x81341),f826(x81342,x81341,x81343))),f825(x81342,x81341,x81343)),x81342)+~P1(f335(x81343,f824(x81342,x81341,x81343)))
% 59.73/59.67 [8135]P145(x81353,x81351,x81352)+~P1(f335(x81353,x81352))+E(f335(f335(f75(a1),f335(f335(f76(a1),x81351),f827(x81352,x81351,x81353))),f824(x81352,x81351,x81353)),x81352)+~P1(f335(x81353,f825(x81352,x81351,x81353)))
% 59.73/59.67 [8145]P146(x81453,x81451,x81452)+E(f335(f335(f75(a1),f335(f335(f76(a1),x81451),f822(x81452,x81451,x81453))),f821(x81452,x81451,x81453)),x81452)+~P1(f335(x81453,f823(x81452,x81451,x81453)))+~P1(f335(x81453,f2(a1)))
% 59.73/59.67 [8146]P146(x81463,x81461,x81462)+E(f335(f335(f75(a1),f335(f335(f76(a1),x81461),f823(x81462,x81461,x81463))),f820(x81462,x81461,x81463)),x81462)+~P1(f335(x81463,f822(x81462,x81461,x81463)))+~P1(f335(x81463,f2(a1)))
% 59.73/59.67 [8249]P146(x82493,x82491,x82492)+E(x82491,f2(a1))+E(f335(f335(f75(a1),f335(f335(f76(a1),x82491),f822(x82492,x82491,x82493))),f821(x82492,x82491,x82493)),x82492)+P1(f335(f335(f242(a1),f820(x82492,x82491,x82493)),f2(a1)))
% 59.73/59.67 [8250]P145(x82503,x82501,x82502)+E(x82501,f2(a1))+E(f335(f335(f75(a1),f335(f335(f76(a1),x82501),f826(x82502,x82501,x82503))),f825(x82502,x82501,x82503)),x82502)+P1(f335(f335(f242(a1),f824(x82502,x82501,x82503)),f2(a1)))
% 59.73/59.67 [8290]P145(x82903,x82901,x82902)+~P1(f335(x82903,x82902))+E(f335(f335(f75(a1),f335(f335(f76(a1),x82901),f826(x82902,x82901,x82903))),f825(x82902,x82901,x82903)),x82902)+P1(f335(f335(f242(a1),f824(x82902,x82901,x82903)),f2(a1)))
% 59.73/59.67 [8295]P146(x82953,x82951,x82952)+E(f335(f335(f75(a1),f335(f335(f76(a1),x82951),f822(x82952,x82951,x82953))),f821(x82952,x82951,x82953)),x82952)+~P1(f335(x82953,f2(a1)))+P1(f335(f335(f242(a1),f820(x82952,x82951,x82953)),f2(a1)))
% 59.73/59.67 [8429]P146(x84293,x84291,x84292)+E(x84291,f2(a1))+E(f335(f335(f75(a1),f335(f335(f76(a1),x84291),f823(x84292,x84291,x84293))),f820(x84292,x84291,x84293)),x84292)+E(f335(f335(f75(a1),f335(f335(f76(a1),x84291),f822(x84292,x84291,x84293))),f821(x84292,x84291,x84293)),x84292)
% 59.73/59.67 [8430]P145(x84303,x84301,x84302)+E(x84301,f2(a1))+E(f335(f335(f75(a1),f335(f335(f76(a1),x84301),f827(x84302,x84301,x84303))),f824(x84302,x84301,x84303)),x84302)+E(f335(f335(f75(a1),f335(f335(f76(a1),x84301),f826(x84302,x84301,x84303))),f825(x84302,x84301,x84303)),x84302)
% 59.73/59.67 [8450]P145(x84503,x84501,x84502)+~P1(f335(x84503,x84502))+E(f335(f335(f75(a1),f335(f335(f76(a1),x84501),f827(x84502,x84501,x84503))),f824(x84502,x84501,x84503)),x84502)+E(f335(f335(f75(a1),f335(f335(f76(a1),x84501),f826(x84502,x84501,x84503))),f825(x84502,x84501,x84503)),x84502)
% 59.73/59.67 [8462]P146(x84623,x84621,x84622)+E(f335(f335(f75(a1),f335(f335(f76(a1),x84621),f823(x84622,x84621,x84623))),f820(x84622,x84621,x84623)),x84622)+E(f335(f335(f75(a1),f335(f335(f76(a1),x84621),f822(x84622,x84621,x84623))),f821(x84622,x84621,x84623)),x84622)+~P1(f335(x84623,f2(a1)))
% 59.73/59.67 [9110]~P123(x91101)+~E(x91103,f2(x91101))+~E(x91102,f2(x91101))+P1(f335(f335(f242(x91101),f335(f335(f75(x91101),f335(f335(f76(x91101),x91102),x91102)),f335(f335(f76(x91101),x91103),x91103))),f2(x91101)))
% 59.73/59.67 [10164]~P119(x101641)+~E(x101643,f2(x101641))+~E(x101642,f2(x101641))+P1(f335(f335(f242(x101641),f335(f335(f75(x101641),f335(f335(f254(x101641),x101642),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f335(f335(f254(x101641),x101643),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))),f2(x101641)))
% 59.73/59.67 [4847]~E(x48473,x48471)+~P116(x48472)+E(x48471,f2(x48472))+E(f335(f335(f292(x48472),x48473),x48471),f73(x48472))
% 59.73/59.67 [4899]~P62(x48991)+~E(x48993,f188(x48991))+~E(x48992,f188(x48991))+E(f335(f335(f104(x48991),x48992),x48993),f188(x48991))
% 59.73/59.67 [4900]~P101(x49001)+~E(x49003,f252(x49001))+~E(x49002,f252(x49001))+E(f335(f335(f95(x49001),x49002),x49003),f252(x49001))
% 59.73/59.67 [4988]~P116(x49883)+E(x49881,x49882)+E(x49882,f2(x49883))+~E(f335(f335(f292(x49883),x49881),x49882),f73(x49883))
% 59.73/59.67 [5006]~P140(x50062)+E(x50061,f2(x50062))+E(x50063,f2(x50062))+~E(f335(f335(f76(x50062),x50063),x50061),f2(x50062))
% 59.73/59.67 [5007]~P131(x50072)+E(x50071,f2(x50072))+E(x50073,f2(x50072))+~E(f335(f335(f76(x50072),x50073),x50071),f2(x50072))
% 59.73/59.67 [5008]~P131(x50082)+E(x50081,f2(x50082))+E(x50083,f2(x50082))+~E(f335(f335(f76(x50082),x50083),x50081),f2(x50082))
% 59.73/59.67 [5379]~P111(x53793)+E(x53791,x53792)+E(x53791,f335(f74(x53793),x53792))+~E(f335(f335(f76(x53793),x53791),x53791),f335(f335(f76(x53793),x53792),x53792))
% 59.73/59.67 [5419]~P84(x54191)+E(f335(f74(x54191),x54192),x54193)+~E(f335(f335(f104(x54191),x54192),x54193),f252(x54191))+~E(f335(f335(f95(x54191),x54192),x54193),f188(x54191))
% 59.73/59.67 [5493]~P106(x54933)+E(x54931,x54932)+P1(f335(f335(f243(x54933),x54932),x54931))+P1(f335(f335(f243(x54933),x54931),x54932))
% 59.73/59.67 [5494]~P106(x54943)+E(x54941,x54942)+P1(f335(f335(f243(x54943),x54942),x54941))+P1(f335(f335(f243(x54943),x54941),x54942))
% 59.73/59.67 [5495]~P106(x54953)+E(x54951,x54952)+P1(f335(f335(f243(x54953),x54952),x54951))+P1(f335(f335(f243(x54953),x54951),x54952))
% 59.73/59.67 [5496]~P106(x54963)+E(x54961,x54962)+P1(f335(f335(f243(x54963),x54962),x54961))+P1(f335(f335(f243(x54963),x54961),x54962))
% 59.73/59.67 [5497]~P106(x54973)+E(x54971,x54972)+P1(f335(f335(f243(x54973),x54972),x54971))+P1(f335(f335(f243(x54973),x54971),x54972))
% 59.73/59.67 [5498]~P119(x54983)+E(x54981,x54982)+P1(f335(f335(f243(x54983),x54982),x54981))+P1(f335(f335(f243(x54983),x54981),x54982))
% 59.73/59.67 [5499]~P106(x54993)+E(x54991,x54992)+P1(f335(f335(f243(x54993),x54992),x54991))+P1(f335(f335(f243(x54993),x54991),x54992))
% 59.73/59.67 [5500]~E(x55002,x55003)+~P106(x55001)+P1(f335(f335(f243(x55001),x55002),x55003))+P1(f335(f335(f242(x55001),x55002),x55003))
% 59.73/59.67 [5666]P146(x56662,x56661,x56663)+E(x56661,f2(a1))+P1(f335(f335(f243(a1),x56661),f2(a1)))+P1(f335(f335(f243(a1),f2(a1)),x56661))
% 59.73/59.67 [5667]P145(x56672,x56671,x56673)+E(x56671,f2(a1))+P1(f335(f335(f243(a1),x56671),f2(a1)))+P1(f335(f335(f243(a1),f2(a1)),x56671))
% 59.73/59.67 [5694]E(x56941,x56942)+P1(f335(f335(x56943,x56941),x56942))+P1(f335(f335(f243(a881),x56942),x56941))+P1(f335(f335(f243(a881),x56941),x56942))
% 59.73/59.67 [5756]~P107(x57563)+E(x57561,x57562)+~P1(f335(f335(f242(x57563),x57562),x57561))+P1(f335(f335(f243(x57563),x57562),x57561))
% 59.73/59.67 [5757]~P106(x57573)+E(x57571,x57572)+~P1(f335(f335(f242(x57573),x57571),x57572))+P1(f335(f335(f243(x57573),x57571),x57572))
% 59.73/59.67 [5758]~P106(x57583)+E(x57581,x57582)+~P1(f335(f335(f242(x57583),x57581),x57582))+P1(f335(f335(f243(x57583),x57581),x57582))
% 59.73/59.67 [5759]~P107(x57593)+E(x57591,x57592)+~P1(f335(f335(f242(x57593),x57591),x57592))+P1(f335(f335(f243(x57593),x57591),x57592))
% 59.73/59.67 [5760]~P107(x57603)+E(x57601,x57602)+~P1(f335(f335(f242(x57603),x57601),x57602))+P1(f335(f335(f243(x57603),x57601),x57602))
% 59.73/59.67 [5761]~P107(x57613)+E(x57611,x57612)+~P1(f335(f335(f242(x57613),x57611),x57612))+P1(f335(f335(f243(x57613),x57611),x57612))
% 59.73/59.67 [5762]~P107(x57623)+E(x57621,x57622)+~P1(f335(f335(f242(x57623),x57621),x57622))+P1(f335(f335(f243(x57623),x57621),x57622))
% 59.73/59.67 [5763]~P107(x57633)+E(x57631,x57632)+~P1(f335(f335(f242(x57633),x57631),x57632))+P1(f335(f335(f243(x57633),x57631),x57632))
% 59.73/59.67 [5764]~P107(x57643)+E(x57641,x57642)+~P1(f335(f335(f242(x57643),x57641),x57642))+P1(f335(f335(f243(x57643),x57641),x57642))
% 59.73/59.67 [5866]P145(x58661,x58662,x58663)+~P1(f335(x58661,x58663))+P1(f335(f335(f243(a1),x58662),f2(a1)))+P1(f335(f335(f243(a1),f2(a1)),x58662))
% 59.73/59.67 [5914]P146(x59141,x59142,x59143)+~P1(f335(x59141,f2(a1)))+P1(f335(f335(f243(a1),x59142),f2(a1)))+P1(f335(f335(f243(a1),f2(a1)),x59142))
% 59.73/59.67 [5918]~P61(x59181)+E(f335(f335(f104(x59181),x59182),f10(x59181,x59183)),x59182)+~P1(f335(f56(x59181),x59183))+~P1(f335(f335(f337(x59181),x59182),x59183))
% 59.73/59.67 [5919]~P61(x59191)+E(f335(f335(f95(x59191),x59192),f13(x59191,x59193)),x59192)+~P1(f335(f56(x59191),x59193))+~P1(f335(f335(f337(x59191),x59192),x59193))
% 59.73/59.67 [5954]~P61(x59541)+E(f335(f335(f104(x59541),x59542),f13(x59541,x59543)),f13(x59541,x59543))+~P1(f335(f56(x59541),x59543))+~P1(f335(f335(f337(x59541),x59542),x59543))
% 59.73/59.67 [5955]~P61(x59551)+E(f335(f335(f95(x59551),x59552),f10(x59551,x59553)),f10(x59551,x59553))+~P1(f335(f56(x59551),x59553))+~P1(f335(f335(f337(x59551),x59552),x59553))
% 59.73/59.67 [5956]~P106(x59561)+E(f335(f335(f240(x59561),x59562),f15(x59561,x59563)),f15(x59561,x59563))+~P1(f335(f56(x59561),x59563))+~P1(f335(f335(f337(x59561),x59562),x59563))
% 59.73/59.67 [5957]~P106(x59571)+E(f335(f335(f241(x59571),x59572),f14(x59571,x59573)),f14(x59571,x59573))+~P1(f335(f56(x59571),x59573))+~P1(f335(f335(f337(x59571),x59572),x59573))
% 59.73/59.67 [5995]E(x59951,x59952)+~P107(x59953)+~P1(f335(f335(f242(x59953),x59952),x59951))+~P1(f335(f335(f242(x59953),x59951),x59952))
% 59.73/59.67 [5996]E(x59961,x59962)+~P107(x59963)+~P1(f335(f335(f242(x59963),x59962),x59961))+~P1(f335(f335(f242(x59963),x59961),x59962))
% 59.73/59.67 [5997]E(x59971,x59972)+~P107(x59973)+~P1(f335(f335(f242(x59973),x59972),x59971))+~P1(f335(f335(f242(x59973),x59971),x59972))
% 59.73/59.67 [5998]E(x59981,x59982)+~P107(x59983)+~P1(f335(f335(f242(x59983),x59982),x59981))+~P1(f335(f335(f242(x59983),x59981),x59982))
% 59.73/59.67 [6000]~E(x60001,x60002)+~P106(x60003)+~P1(f335(f335(f242(x60003),x60001),x60002))+~P1(f335(f335(f243(x60003),x60001),x60002))
% 59.73/59.67 [6138]~P2(x61381)+P1(f335(f335(f243(x61381),x61383),x61382))+~P1(f335(f335(f242(x61381),x61383),x61382))+P1(f335(f335(f242(x61381),x61382),x61383))
% 59.73/59.67 [6161]~P106(x61611)+~P1(f335(f56(x61611),x61613))+P1(f335(f335(f242(x61611),x61612),f14(x61611,x61613)))+~P1(f335(f335(f337(x61611),x61612),x61613))
% 59.73/59.67 [6209]~P106(x62091)+E(f335(f335(f240(x62091),x62092),f12(x62091,f241(x62091),x62093)),x62092)+~P1(f335(f56(x62091),x62093))+~P1(f335(f335(f337(x62091),x62092),x62093))
% 59.73/59.67 [6210]~P106(x62101)+E(f335(f335(f241(x62101),x62102),f11(x62101,f240(x62101),x62103)),x62102)+~P1(f335(f56(x62101),x62103))+~P1(f335(f335(f337(x62101),x62102),x62103))
% 59.73/59.67 [6349]E(x63491,x63492)+~E(f335(f335(f23(a881),x63491),x63493),f335(f335(f23(a881),x63492),x63493))+~P1(f335(f335(f242(a881),x63493),x63491))+~P1(f335(f335(f242(a881),x63493),x63492))
% 59.73/59.67 [6377]~P106(x63771)+~P1(f335(f56(x63771),x63772))+~P1(f335(f335(f337(x63771),x63773),x63772))+P1(f335(f335(f242(x63771),f15(x63771,x63772)),x63773))
% 59.73/59.67 [6418]E(x64181,f2(a881))+~P1(f335(f42(x64183,x64181),x64182))+P1(f335(f335(f243(a881),f2(a881)),x64181))+P1(f335(f335(f243(a881),x64181),f335(f267(a881,a881),x64182)))
% 59.73/59.67 [6443]P146(x64432,x64431,x64433)+E(x64431,f2(a1))+P1(f335(f335(f243(a1),x64431),f820(x64433,x64431,x64432)))+P1(f335(f335(f243(a1),f2(a1)),x64431))
% 59.73/59.67 [6444]P145(x64442,x64441,x64443)+E(x64441,f2(a1))+P1(f335(f335(f243(a1),x64441),f824(x64443,x64441,x64442)))+P1(f335(f335(f243(a1),f2(a1)),x64441))
% 59.73/59.67 [6445]~P106(x64451)+E(f335(f335(f240(x64451),x64452),f11(x64451,f240(x64451),x64453)),f11(x64451,f240(x64451),x64453))+~P1(f335(f56(x64451),x64453))+~P1(f335(f335(f337(x64451),x64452),x64453))
% 59.73/59.67 [6446]~P106(x64461)+E(f335(f335(f241(x64461),x64462),f12(x64461,f241(x64461),x64463)),f12(x64461,f241(x64461),x64463))+~P1(f335(f56(x64461),x64463))+~P1(f335(f335(f337(x64461),x64462),x64463))
% 59.73/59.67 [6451]~P1(f335(x64511,x64512))+P1(f335(x64511,f582(x64512,x64511,x64513)))+P1(f335(x64511,f2(a881)))+~P1(f335(f335(f243(a881),x64512),x64513))
% 59.73/59.67 [6506]~P1(f335(x65061,x65062))+~P1(f335(f56(x65063),x65062))+P1(f335(x65061,f867(x65061,x65062,x65063)))+P1(f335(x65061,f188(f888(x65063,a879))))
% 59.73/59.67 [6519]~P119(x65191)+~P97(x65191)+P1(f335(f335(f242(x65191),f335(f97(x65191),x65192)),f335(f97(x65191),x65193)))+~P1(f335(f335(f242(a1),x65192),x65193))
% 59.73/59.67 [6520]~P119(x65201)+~P97(x65201)+P1(f335(f335(f243(x65201),f335(f97(x65201),x65202)),f335(f97(x65201),x65203)))+~P1(f335(f335(f243(a1),x65202),x65203))
% 59.73/59.67 [6523]~P1(f335(x65231,x65233))+~P1(f335(f56(x65232),x65233))+P1(f335(f56(x65232),f867(x65231,x65233,x65232)))+P1(f335(x65231,f188(f888(x65232,a879))))
% 59.73/59.67 [6557]P145(x65571,x65572,x65573)+~P1(f335(x65571,x65573))+P1(f335(f335(f243(a1),x65572),f824(x65573,x65572,x65571)))+P1(f335(f335(f243(a1),f2(a1)),x65572))
% 59.73/59.67 [6593]P146(x65931,x65932,x65933)+P1(f335(f335(f243(a1),x65932),f820(x65933,x65932,x65931)))+~P1(f335(x65931,f2(a1)))+P1(f335(f335(f243(a1),f2(a1)),x65932))
% 59.73/59.67 [6628]~P108(x66281)+~P95(x66281)+E(f335(f335(f240(x66281),f335(f97(x66281),x66282)),f335(f97(x66281),x66283)),f335(f97(x66281),x66283))+P1(f335(f335(f242(x66281),f335(f97(x66281),x66282)),f335(f97(x66281),x66283)))
% 59.73/59.67 [6629]~P108(x66291)+~P95(x66291)+E(f335(f335(f241(x66291),f335(f97(x66291),x66292)),f335(f97(x66291),x66293)),f335(f97(x66291),x66292))+P1(f335(f335(f242(x66291),f335(f97(x66291),x66292)),f335(f97(x66291),x66293)))
% 59.73/59.67 [6633]E(x66331,f2(a881))+~P1(f335(f42(x66333,x66331),x66332))+~P1(f335(f335(f243(a881),f2(a881)),x66331))+P1(f335(f335(f242(a881),f2(a881)),f335(f267(a881,a881),x66332)))
% 59.73/59.67 [6687]P146(x66872,x66871,x66873)+E(x66871,f2(a1))+~P1(f335(x66872,f823(x66873,x66871,x66872)))+P1(f335(f335(f243(a1),f2(a1)),x66871))
% 59.73/59.67 [6688]P145(x66882,x66881,x66883)+E(x66881,f2(a1))+~P1(f335(x66882,f824(x66883,x66881,x66882)))+P1(f335(f335(f243(a1),f2(a1)),x66881))
% 59.73/59.67 [6692]P1(f335(x66921,x66922))+~P1(f335(f56(x66923),x66922))+P1(f335(x66921,f795(x66921,x66922,x66923)))+~P1(f335(x66921,f188(f888(x66923,a879))))
% 59.73/59.67 [6713]P1(f335(x67131,x67132))+P1(f335(f56(x67133),f795(x67131,x67132,x67133)))+~P1(f335(f56(x67133),x67132))+~P1(f335(x67131,f188(f888(x67133,a879))))
% 59.73/59.67 [6779]P145(x67791,x67792,x67793)+~P1(f335(x67791,x67793))+~P1(f335(x67791,f824(x67793,x67792,x67791)))+P1(f335(f335(f243(a1),f2(a1)),x67792))
% 59.73/59.67 [6809]P146(x68091,x68092,x68093)+~P1(f335(x68091,f823(x68093,x68092,x68091)))+~P1(f335(x68091,f2(a1)))+P1(f335(f335(f243(a1),f2(a1)),x68092))
% 59.73/59.67 [6820]E(x68201,f2(a881))+~P1(f335(f42(x68203,x68201),x68202))+P1(f335(f335(f242(a881),f335(f267(a881,a881),x68202)),f2(a881)))+P1(f335(f335(f243(a881),f2(a881)),x68201))
% 59.73/59.67 [6919]~P97(x69193)+~P119(x69193)+~P1(f335(f335(f242(x69193),f335(f97(x69193),x69191)),f335(f97(x69193),x69192)))+P1(f335(f335(f242(a1),x69191),x69192))
% 59.73/59.67 [6920]~P97(x69203)+~P119(x69203)+~P1(f335(f335(f243(x69203),f335(f97(x69203),x69201)),f335(f97(x69203),x69202)))+P1(f335(f335(f243(a1),x69201),x69202))
% 59.73/59.67 [6946]~P106(x69461)+~P15(x69461,x69463)+P15(x69461,f335(f335(f144(x69461),x69462),x69463))+~P1(f335(f335(f242(x69461),x69462),f729(x69463,x69462,x69461)))
% 59.73/59.67 [6947]~P106(x69471)+~P15(x69471,x69473)+P15(x69471,f335(f335(f144(x69471),x69472),x69473))+~P1(f335(f335(f242(x69471),x69472),f735(x69473,x69472,x69471)))
% 59.73/59.67 [6948]~P106(x69481)+~P15(x69481,x69483)+P15(x69481,f335(f335(f144(x69481),x69482),x69483))+~P1(f335(f335(f242(x69481),x69482),f767(x69482,x69483,x69481)))
% 59.73/59.67 [7032]P146(x70322,x70321,x70323)+E(x70321,f2(a1))+P1(f335(f335(f243(a1),x70321),f2(a1)))+P1(f335(f335(f243(a1),f821(x70323,x70321,x70322)),x70321))
% 59.73/59.67 [7033]P145(x70332,x70331,x70333)+E(x70331,f2(a1))+P1(f335(f335(f243(a1),x70331),f2(a1)))+P1(f335(f335(f243(a1),f825(x70333,x70331,x70332)),x70331))
% 59.73/59.67 [7039]~P106(x70391)+~P95(x70391)+P1(f335(f335(f242(x70391),f335(f97(x70391),x70392)),f335(f97(x70391),x70393)))+P1(f335(f335(f243(x70391),f335(f97(x70391),x70393)),f335(f97(x70391),x70392)))
% 59.73/59.67 [7071]P146(x70712,x70711,x70713)+E(x70711,f2(a1))+P1(f335(f335(f242(a1),f820(x70713,x70711,x70712)),f2(a1)))+P1(f335(f335(f243(a1),f2(a1)),x70711))
% 59.73/59.67 [7072]P145(x70722,x70721,x70723)+E(x70721,f2(a1))+P1(f335(f335(f242(a1),f824(x70723,x70721,x70722)),f2(a1)))+P1(f335(f335(f243(a1),f2(a1)),x70721))
% 59.73/59.67 [7095]~P106(x70951)+~P15(x70951,x70953)+E(f335(f335(f141(x70951,x70951,f5(x70951)),x70952),f164(x70951,x70952,x70953)),x70953)+~P1(f335(f335(f337(x70951),x70952),f335(f166(x70951),x70953)))
% 59.73/59.67 [7142]P145(x71421,x71422,x71423)+~P1(f335(x71421,x71423))+P1(f335(f335(f243(a1),x71422),f2(a1)))+P1(f335(f335(f243(a1),f825(x71423,x71422,x71421)),x71422))
% 59.73/59.67 [7148]~P108(x71481)+~P95(x71481)+E(f335(f335(f240(x71481),f335(f97(x71481),x71482)),f335(f97(x71481),x71483)),f335(f97(x71481),x71482))+~P1(f335(f335(f242(x71481),f335(f97(x71481),x71482)),f335(f97(x71481),x71483)))
% 59.73/59.67 [7149]~P108(x71491)+~P95(x71491)+E(f335(f335(f241(x71491),f335(f97(x71491),x71492)),f335(f97(x71491),x71493)),f335(f97(x71491),x71493))+~P1(f335(f335(f242(x71491),f335(f97(x71491),x71492)),f335(f97(x71491),x71493)))
% 59.73/59.67 [7163]P146(x71631,x71632,x71633)+~P1(f335(x71631,f2(a1)))+P1(f335(f335(f243(a1),x71632),f2(a1)))+P1(f335(f335(f243(a1),f821(x71633,x71632,x71631)),x71632))
% 59.73/59.67 [7171]P145(x71711,x71712,x71713)+~P1(f335(x71711,x71713))+P1(f335(f335(f242(a1),f824(x71713,x71712,x71711)),f2(a1)))+P1(f335(f335(f243(a1),f2(a1)),x71712))
% 59.73/59.67 [7196]P146(x71961,x71962,x71963)+~P1(f335(x71961,f2(a1)))+P1(f335(f335(f242(a1),f820(x71963,x71962,x71961)),f2(a1)))+P1(f335(f335(f243(a1),f2(a1)),x71962))
% 59.73/59.67 [7223]~P1(f335(x72231,x72232))+P1(f335(x72231,f2(a881)))+~P1(f335(f335(f243(a881),x72232),x72233))+P1(f335(f335(f243(a881),f582(x72232,x72231,x72233)),x72233))
% 59.73/59.67 [7240]~P106(x72401)+~P15(x72401,x72403)+P15(x72401,f335(f335(f144(x72401),x72402),x72403))+P1(f335(f335(f337(x72401),f729(x72403,x72402,x72401)),f335(f166(x72401),x72403)))
% 59.73/59.67 [7241]~P106(x72411)+~P15(x72411,x72413)+P15(x72411,f335(f335(f144(x72411),x72412),x72413))+P1(f335(f335(f337(x72411),f735(x72413,x72412,x72411)),f335(f166(x72411),x72413)))
% 59.73/59.67 [7242]~P106(x72421)+~P15(x72421,x72423)+P15(x72421,f335(f335(f144(x72421),x72422),x72423))+P1(f335(f335(f337(x72421),f767(x72422,x72423,x72421)),f335(f166(x72421),x72423)))
% 59.73/59.67 [7352]~P106(x73521)+~P5(x73521)+~P1(f335(f335(f243(x73521),x73523),f31(x73521,x73522)))+P1(f335(f335(f337(x73521),f630(x73522,x73523,x73521)),x73522))
% 59.73/59.67 [7514]~P106(x75141)+~P5(x75141)+~P1(f335(f335(f243(x75141),f32(x75141,x75143)),x75142))+P1(f335(f335(f337(x75141),f634(x75142,x75143,x75141)),x75143))
% 59.73/59.67 [7515]~P106(x75151)+~P5(x75151)+~P1(f335(f335(f243(x75151),f32(x75151,x75153)),x75152))+P1(f335(f335(f243(x75151),f634(x75152,x75153,x75151)),x75152))
% 59.73/59.67 [7528]P146(x75282,x75281,x75283)+E(x75281,f2(a1))+P1(f335(f335(f243(a1),x75281),f820(x75283,x75281,x75282)))+P1(f335(f335(f243(a1),f821(x75283,x75281,x75282)),x75281))
% 59.73/59.67 [7529]P145(x75292,x75291,x75293)+E(x75291,f2(a1))+P1(f335(f335(f243(a1),x75291),f824(x75293,x75291,x75292)))+P1(f335(f335(f243(a1),f825(x75293,x75291,x75292)),x75291))
% 59.73/59.67 [7622]P146(x76223,x76221,x76222)+E(x76221,f2(a1))+E(f335(f335(f75(a1),f335(f335(f76(a1),x76221),f823(x76222,x76221,x76223))),f820(x76222,x76221,x76223)),x76222)+P1(f335(f335(f243(a1),f2(a1)),x76221))
% 59.73/59.67 [7623]P145(x76233,x76231,x76232)+E(x76231,f2(a1))+E(f335(f335(f75(a1),f335(f335(f76(a1),x76231),f827(x76232,x76231,x76233))),f824(x76232,x76231,x76233)),x76232)+P1(f335(f335(f243(a1),f2(a1)),x76231))
% 59.73/59.67 [7624]~P132(x76241)+~P1(f335(f335(f242(x76241),x76242),f2(x76241)))+P1(f335(f335(f242(x76241),f335(f335(f76(x76241),x76242),x76243)),f2(x76241)))+~P1(f335(f335(f242(x76241),f2(x76241)),x76243))
% 59.73/59.67 [7625]~P123(x76251)+~P1(f335(f335(f242(x76251),x76253),f2(x76251)))+P1(f335(f335(f242(x76251),f335(f335(f76(x76251),x76252),x76253)),f2(x76251)))+~P1(f335(f335(f242(x76251),f2(x76251)),x76252))
% 59.73/59.67 [7626]~P123(x76261)+~P1(f335(f335(f242(x76261),x76262),f2(x76261)))+P1(f335(f335(f242(x76261),f335(f335(f76(x76261),x76262),x76263)),f2(x76261)))+~P1(f335(f335(f242(x76261),f2(x76261)),x76263))
% 59.73/59.67 [7627]~P132(x76271)+~P1(f335(f335(f242(x76271),x76273),f2(x76271)))+P1(f335(f335(f242(x76271),f335(f335(f76(x76271),x76272),x76273)),f2(x76271)))+~P1(f335(f335(f242(x76271),f2(x76271)),x76272))
% 59.73/59.67 [7628]~P132(x76281)+~P1(f335(f335(f242(x76281),x76283),f2(x76281)))+P1(f335(f335(f242(x76281),f335(f335(f76(x76281),x76282),x76283)),f2(x76281)))+~P1(f335(f335(f242(x76281),f2(x76281)),x76282))
% 59.73/59.67 [7629]~P132(x76291)+~P1(f335(f335(f242(x76291),x76292),f2(x76291)))+P1(f335(f335(f242(x76291),f335(f335(f76(x76291),x76292),x76293)),f2(x76291)))+~P1(f335(f335(f242(x76291),f2(x76291)),x76293))
% 59.73/59.67 [7630]~P132(x76301)+~P1(f335(f335(f242(x76301),x76302),f2(x76301)))+P1(f335(f335(f242(x76301),f335(f335(f76(x76301),x76302),x76303)),f2(x76301)))+~P1(f335(f335(f242(x76301),f2(x76301)),x76303))
% 59.73/59.67 [7631]~P68(x76311)+~P1(f335(f335(f242(x76311),x76313),f2(x76311)))+P1(f335(f335(f242(x76311),f335(f335(f292(x76311),x76312),x76313)),f2(x76311)))+~P1(f335(f335(f242(x76311),f2(x76311)),x76312))
% 59.73/59.67 [7632]~P68(x76321)+~P1(f335(f335(f242(x76321),x76322),f2(x76321)))+P1(f335(f335(f242(x76321),f335(f335(f292(x76321),x76322),x76323)),f2(x76321)))+~P1(f335(f335(f242(x76321),f2(x76321)),x76323))
% 59.73/59.67 [7633]~P69(x76331)+~P1(f335(f335(f242(x76331),x76332),f2(x76331)))+P1(f335(f335(f242(x76331),f335(f335(f292(x76331),x76332),x76333)),f2(x76331)))+~P1(f335(f335(f243(x76331),f2(x76331)),x76333))
% 59.73/59.67 [7634]~P69(x76341)+~P1(f335(f335(f243(x76341),x76343),f2(x76341)))+P1(f335(f335(f242(x76341),f335(f335(f292(x76341),x76342),x76343)),f2(x76341)))+~P1(f335(f335(f242(x76341),f2(x76341)),x76342))
% 59.73/59.67 [7635]~P127(x76351)+~P1(f335(f335(f243(x76351),x76352),f2(x76351)))+P1(f335(f335(f243(x76351),f335(f335(f76(x76351),x76352),x76353)),f2(x76351)))+~P1(f335(f335(f243(x76351),f2(x76351)),x76353))
% 59.73/59.67 [7636]~P127(x76361)+~P1(f335(f335(f243(x76361),x76363),f2(x76361)))+P1(f335(f335(f243(x76361),f335(f335(f76(x76361),x76362),x76363)),f2(x76361)))+~P1(f335(f335(f243(x76361),f2(x76361)),x76362))
% 59.73/59.67 [7637]~P127(x76371)+~P1(f335(f335(f243(x76371),x76372),f2(x76371)))+P1(f335(f335(f243(x76371),f335(f335(f76(x76371),x76372),x76373)),f2(x76371)))+~P1(f335(f335(f243(x76371),f2(x76371)),x76373))
% 59.73/59.67 [7638]~P68(x76381)+~P1(f335(f335(f243(x76381),x76383),f2(x76381)))+P1(f335(f335(f243(x76381),f335(f335(f292(x76381),x76382),x76383)),f2(x76381)))+~P1(f335(f335(f243(x76381),f2(x76381)),x76382))
% 59.73/59.67 [7639]~P68(x76391)+~P1(f335(f335(f243(x76391),x76392),f2(x76391)))+P1(f335(f335(f243(x76391),f335(f335(f292(x76391),x76392),x76393)),f2(x76391)))+~P1(f335(f335(f243(x76391),f2(x76391)),x76393))
% 59.73/59.67 [7640]~P69(x76401)+~P1(f335(f335(f243(x76401),x76403),f2(x76401)))+P1(f335(f335(f243(x76401),f335(f335(f292(x76401),x76402),x76403)),f2(x76401)))+~P1(f335(f335(f243(x76401),f2(x76401)),x76402))
% 59.73/59.67 [7641]~P69(x76411)+~P1(f335(f335(f243(x76411),x76412),f2(x76411)))+P1(f335(f335(f243(x76411),f335(f335(f292(x76411),x76412),x76413)),f2(x76411)))+~P1(f335(f335(f243(x76411),f2(x76411)),x76413))
% 59.73/59.67 [7656]P145(x76561,x76562,x76563)+~P1(f335(x76561,x76563))+P1(f335(f335(f243(a1),x76562),f824(x76563,x76562,x76561)))+P1(f335(f335(f243(a1),f825(x76563,x76562,x76561)),x76562))
% 59.73/59.67 [7669]P146(x76691,x76692,x76693)+P1(f335(f335(f243(a1),x76692),f820(x76693,x76692,x76691)))+~P1(f335(x76691,f2(a1)))+P1(f335(f335(f243(a1),f821(x76693,x76692,x76691)),x76692))
% 59.73/59.67 [7721]P146(x77212,x77211,x77213)+E(x77211,f2(a1))+~P1(f335(x77212,f823(x77213,x77211,x77212)))+P1(f335(f335(f243(a1),f821(x77213,x77211,x77212)),x77211))
% 59.73/59.67 [7722]P145(x77222,x77221,x77223)+E(x77221,f2(a1))+~P1(f335(x77222,f824(x77223,x77221,x77222)))+P1(f335(f335(f243(a1),f825(x77223,x77221,x77222)),x77221))
% 59.73/59.67 [7733]P145(x77333,x77331,x77332)+~P1(f335(x77333,x77332))+E(f335(f335(f75(a1),f335(f335(f76(a1),x77331),f827(x77332,x77331,x77333))),f824(x77332,x77331,x77333)),x77332)+P1(f335(f335(f243(a1),f2(a1)),x77331))
% 59.73/59.67 [7750]P146(x77503,x77501,x77502)+E(f335(f335(f75(a1),f335(f335(f76(a1),x77501),f823(x77502,x77501,x77503))),f820(x77502,x77501,x77503)),x77502)+~P1(f335(x77503,f2(a1)))+P1(f335(f335(f243(a1),f2(a1)),x77501))
% 59.73/59.67 [7776]~P1(f335(x77761,x77763))+~P1(f335(f56(x77762),x77763))+P1(f335(f335(f337(x77762),f868(x77761,x77763,x77762)),f867(x77761,x77763,x77762)))+P1(f335(x77761,f188(f888(x77762,a879))))
% 59.73/59.67 [7787]P145(x77871,x77872,x77873)+~P1(f335(x77871,x77873))+~P1(f335(x77871,f824(x77873,x77872,x77871)))+P1(f335(f335(f243(a1),f825(x77873,x77872,x77871)),x77872))
% 59.73/59.67 [7793]P146(x77931,x77932,x77933)+~P1(f335(x77931,f823(x77933,x77932,x77931)))+~P1(f335(x77931,f2(a1)))+P1(f335(f335(f243(a1),f821(x77933,x77932,x77931)),x77932))
% 59.73/59.67 [7859]~P95(x78591)+~P106(x78591)+~P1(f335(f335(f242(x78591),f335(f97(x78591),x78592)),f335(f97(x78591),x78593)))+~P1(f335(f335(f243(x78591),f335(f97(x78591),x78593)),f335(f97(x78591),x78592)))
% 59.73/59.67 [7895]~P123(x78951)+~P1(f335(f335(f242(x78951),f335(f335(f76(x78951),x78953),x78952)),f2(x78951)))+P1(f335(f335(f242(x78951),x78952),f2(x78951)))+P1(f335(f335(f242(x78951),f2(x78951)),x78952))
% 59.73/59.67 [7896]~P123(x78961)+~P1(f335(f335(f242(x78961),f335(f335(f76(x78961),x78962),x78963)),f2(x78961)))+P1(f335(f335(f242(x78961),x78962),f2(x78961)))+P1(f335(f335(f242(x78961),f2(x78961)),x78962))
% 59.73/59.67 [7897]~P68(x78971)+~P1(f335(f335(f242(x78971),f335(f335(f292(x78971),x78973),x78972)),f2(x78971)))+P1(f335(f335(f242(x78971),x78972),f2(x78971)))+P1(f335(f335(f242(x78971),f2(x78971)),x78972))
% 59.73/59.67 [7898]~P68(x78981)+~P1(f335(f335(f242(x78981),f335(f335(f292(x78981),x78982),x78983)),f2(x78981)))+P1(f335(f335(f242(x78981),x78982),f2(x78981)))+P1(f335(f335(f242(x78981),f2(x78981)),x78982))
% 59.73/59.67 [7899]~P68(x78991)+~P1(f335(f335(f243(x78991),f335(f335(f292(x78991),x78993),x78992)),f2(x78991)))+P1(f335(f335(f243(x78991),x78992),f2(x78991)))+P1(f335(f335(f243(x78991),f2(x78991)),x78992))
% 59.73/59.67 [7900]~P68(x79001)+~P1(f335(f335(f243(x79001),f335(f335(f292(x79001),x79002),x79003)),f2(x79001)))+P1(f335(f335(f243(x79001),x79002),f2(x79001)))+P1(f335(f335(f243(x79001),f2(x79001)),x79002))
% 59.73/59.67 [7925]~P123(x79251)+~P1(f335(f335(f242(x79251),f335(f335(f76(x79251),x79252),x79253)),f2(x79251)))+P1(f335(f335(f242(x79251),f2(x79251)),x79252))+P1(f335(f335(f242(x79251),f2(x79251)),x79253))
% 59.73/59.67 [7926]~P68(x79261)+~P1(f335(f335(f242(x79261),f335(f335(f292(x79261),x79262),x79263)),f2(x79261)))+P1(f335(f335(f242(x79261),f2(x79261)),x79262))+P1(f335(f335(f242(x79261),f2(x79261)),x79263))
% 59.73/59.67 [7927]~P68(x79271)+~P1(f335(f335(f243(x79271),f335(f335(f292(x79271),x79272),x79273)),f2(x79271)))+P1(f335(f335(f243(x79271),f2(x79271)),x79272))+P1(f335(f335(f243(x79271),f2(x79271)),x79273))
% 59.73/59.67 [7949]P146(x79492,x79491,x79493)+E(x79491,f2(a1))+P1(f335(f335(f242(a1),f820(x79493,x79491,x79492)),f2(a1)))+P1(f335(f335(f243(a1),f821(x79493,x79491,x79492)),x79491))
% 59.73/59.67 [7950]P145(x79502,x79501,x79503)+E(x79501,f2(a1))+P1(f335(f335(f242(a1),f824(x79503,x79501,x79502)),f2(a1)))+P1(f335(f335(f243(a1),f825(x79503,x79501,x79502)),x79501))
% 59.73/59.67 [7958]~P122(x79581)+~P1(f335(f335(f243(x79581),x79582),f73(x79581)))+P1(f335(f335(f243(x79581),f335(f335(f254(x79581),x79582),f335(a106,x79583))),f73(x79581)))+~P1(f335(f335(f243(x79581),f2(x79581)),x79582))
% 59.73/59.67 [8017]~P106(x80171)+~E(x80173,f107(x80171))+~P15(x80171,f335(f162(x80171),x80173))+E(f335(f135(x80171,x80171,f335(f7(x80171,x80171,x80171),f241(x80171)),x80172),f335(f162(x80171),x80173)),x80172)
% 59.73/59.67 [8020]P145(x80201,x80202,x80203)+~P1(f335(x80201,x80203))+P1(f335(f335(f242(a1),f824(x80203,x80202,x80201)),f2(a1)))+P1(f335(f335(f243(a1),f825(x80203,x80202,x80201)),x80202))
% 59.73/59.67 [8027]P146(x80271,x80272,x80273)+~P1(f335(x80271,f2(a1)))+P1(f335(f335(f242(a1),f820(x80273,x80272,x80271)),f2(a1)))+P1(f335(f335(f243(a1),f821(x80273,x80272,x80271)),x80272))
% 59.73/59.67 [8244]P146(x82443,x82441,x82442)+E(x82441,f2(a1))+E(f335(f335(f75(a1),f335(f335(f76(a1),x82441),f823(x82442,x82441,x82443))),f820(x82442,x82441,x82443)),x82442)+P1(f335(f335(f243(a1),f821(x82442,x82441,x82443)),x82441))
% 59.73/59.67 [8245]P145(x82453,x82451,x82452)+E(x82451,f2(a1))+E(f335(f335(f75(a1),f335(f335(f76(a1),x82451),f827(x82452,x82451,x82453))),f824(x82452,x82451,x82453)),x82452)+P1(f335(f335(f243(a1),f825(x82452,x82451,x82453)),x82451))
% 59.73/59.67 [8281]P145(x82813,x82811,x82812)+~P1(f335(x82813,x82812))+E(f335(f335(f75(a1),f335(f335(f76(a1),x82811),f827(x82812,x82811,x82813))),f824(x82812,x82811,x82813)),x82812)+P1(f335(f335(f243(a1),f825(x82812,x82811,x82813)),x82811))
% 59.73/59.67 [8282]~P73(x82821)+~P77(x82821)+~P38(x82823)+E(f335(f335(f9(a881,x82821),f335(f335(f8(a1,x82821,a881),x82822),f94(a1))),f335(f313(a1,a881,a98),x82823)),f335(f335(f9(a1,x82821),x82822),x82823))
% 59.73/59.67 [8283]~P73(x82831)+~P77(x82831)+~P38(x82833)+E(f335(f335(f6(a881,x82831),f335(f335(f8(a1,x82831,a881),x82832),f94(a1))),f335(f313(a1,a881,a98),x82833)),f335(f335(f6(a1,x82831),x82832),x82833))
% 59.73/59.67 [8292]P146(x82923,x82921,x82922)+E(f335(f335(f75(a1),f335(f335(f76(a1),x82921),f823(x82922,x82921,x82923))),f820(x82922,x82921,x82923)),x82922)+~P1(f335(x82923,f2(a1)))+P1(f335(f335(f243(a1),f821(x82922,x82921,x82923)),x82921))
% 59.73/59.67 [8314]~E(x83142,f2(a881))+~E(f335(f263(a881,a881),x83143),f2(a881))+~E(x83141,f335(f335(f75(a881),f335(f335(f76(a881),f335(f263(a881,a881),x83143)),x83142)),f335(f267(a881,a881),x83143)))+P1(f335(f42(x83141,x83142),x83143))
% 59.73/59.67 [8367]P1(f335(x83671,x83672))+~P1(f335(f335(f337(x83673),f797(x83671,x83672,x83673)),f795(x83671,x83672,x83673)))+~P1(f335(f56(x83673),x83672))+~P1(f335(x83671,f188(f888(x83673,a879))))
% 59.73/59.67 [8981]P1(f335(x89811,x89812))+~P1(f335(f56(x89813),x89812))+~P1(f335(x89811,f335(f335(f312(x89813),f797(x89811,x89812,x89813)),f795(x89811,x89812,x89813))))+~P1(f335(x89811,f188(f888(x89813,a879))))
% 59.73/59.67 [9217]P1(f335(f335(f242(a1),x92171),f2(a1)))+~P1(f335(f335(f243(a1),f335(f335(f75(a1),f335(f335(f76(a1),x92173),x92171)),x92172)),f2(a1)))+~P1(f335(f335(f242(a1),f2(a1)),x92172))+~P1(f335(f335(f243(a1),f2(a1)),x92173))
% 59.73/59.67 [5825]~P61(x58252)+E(x58251,f188(f888(x58252,a879)))+~P1(f335(f56(x58252),x58251))+E(f10(x58252,f335(f335(f312(x58252),x58253),x58251)),f335(f335(f95(x58252),x58253),f10(x58252,x58251)))
% 59.73/59.67 [5826]~P61(x58262)+E(x58261,f188(f888(x58262,a879)))+~P1(f335(f56(x58262),x58261))+E(f13(x58262,f335(f335(f312(x58262),x58263),x58261)),f335(f335(f104(x58262),x58263),f13(x58262,x58261)))
% 59.73/59.67 [5827]~P106(x58272)+E(x58271,f188(f888(x58272,a879)))+~P1(f335(f56(x58272),x58271))+E(f14(x58272,f335(f335(f312(x58272),x58273),x58271)),f335(f335(f241(x58272),x58273),f14(x58272,x58271)))
% 59.73/59.67 [5828]~P106(x58282)+E(x58281,f188(f888(x58282,a879)))+~P1(f335(f56(x58282),x58281))+E(f15(x58282,f335(f335(f312(x58282),x58283),x58281)),f335(f335(f240(x58282),x58283),f15(x58282,x58281)))
% 59.73/59.67 [6135]~P123(x61351)+~E(x61353,f2(x61351))+~E(x61352,f2(x61351))+E(f335(f335(f75(x61351),f335(f335(f76(x61351),x61352),x61352)),f335(f335(f76(x61351),x61353),x61353)),f2(x61351))
% 59.73/59.67 [6202]~P98(x62022)+E(x62021,f188(f888(x62022,a879)))+~P1(f335(f56(x62022),x62021))+E(f335(f58(x62022,f76(x62022)),f335(f335(f312(x62022),x62023),x62021)),f335(f335(f76(x62022),x62023),f335(f58(x62022,f76(x62022)),x62021)))
% 59.73/59.67 [6327]~P106(x63272)+E(x63271,f188(f888(x63272,a879)))+~P1(f335(f56(x63272),x63271))+E(f11(x63272,f240(x63272),f335(f335(f312(x63272),x63273),x63271)),f335(f335(f240(x63272),x63273),f11(x63272,f240(x63272),x63271)))
% 59.73/59.67 [6328]~P106(x63282)+E(x63281,f188(f888(x63282,a879)))+~P1(f335(f56(x63282),x63281))+E(f12(x63282,f241(x63282),f335(f335(f312(x63282),x63283),x63281)),f335(f335(f241(x63282),x63283),f12(x63282,f241(x63282),x63281)))
% 59.73/59.67 [6732]~P61(x67321)+~P1(f335(f56(x67321),x67323))+E(f335(f335(f59(x67321,x67321,f95(x67321)),x67322),x67323),f10(x67321,f335(f335(f312(x67321),x67322),x67323)))+P1(f335(f335(f337(x67321),x67322),x67323))
% 59.73/59.67 [6733]~P61(x67331)+~P1(f335(f56(x67331),x67333))+E(f335(f335(f59(x67331,x67331,f104(x67331)),x67332),x67333),f13(x67331,f335(f335(f312(x67331),x67332),x67333)))+P1(f335(f335(f337(x67331),x67332),x67333))
% 59.73/59.67 [6734]~P106(x67341)+~P1(f335(f56(x67341),x67343))+E(f335(f335(f59(x67341,x67341,f241(x67341)),x67342),x67343),f14(x67341,f335(f335(f312(x67341),x67342),x67343)))+P1(f335(f335(f337(x67341),x67342),x67343))
% 59.73/59.67 [6735]~P106(x67351)+~P1(f335(f56(x67351),x67353))+E(f335(f335(f59(x67351,x67351,f240(x67351)),x67352),x67353),f15(x67351,f335(f335(f312(x67351),x67352),x67353)))+P1(f335(f335(f337(x67351),x67352),x67353))
% 59.73/59.67 [6844]~P70(x68441)+~P1(f335(f56(x68441),x68443))+E(f335(f58(x68441,f76(x68441)),f335(f335(f312(x68441),x68442),x68443)),f335(f335(f59(x68441,x68441,f76(x68441)),x68442),x68443))+P1(f335(f335(f337(x68441),x68442),x68443))
% 59.73/59.67 [6863]~P106(x68631)+~P1(f335(f56(x68631),x68633))+E(f11(x68631,f240(x68631),f335(f335(f312(x68631),x68632),x68633)),f335(f335(f59(x68631,x68631,f240(x68631)),x68632),x68633))+P1(f335(f335(f337(x68631),x68632),x68633))
% 59.73/59.67 [6864]~P106(x68641)+~P1(f335(f56(x68641),x68643))+E(f12(x68641,f241(x68641),f335(f335(f312(x68641),x68642),x68643)),f335(f335(f59(x68641,x68641,f241(x68641)),x68642),x68643))+P1(f335(f335(f337(x68641),x68642),x68643))
% 59.73/59.67 [6926]~E(f335(f335(f75(a1),x69262),f335(f335(f76(a1),x69263),x69261)),x69263)+~P1(f335(f335(f243(a1),f2(a1)),x69263))+P1(f335(f335(f242(a1),f73(a1)),x69261))+~P1(f335(f335(f243(a1),x69262),x69263))
% 59.73/59.67 [6953]~E(f335(f335(f75(a1),x69532),f335(f335(f76(a1),x69533),x69531)),x69533)+P1(f335(f335(f242(a1),x69531),f73(a1)))+~P1(f335(f335(f242(a1),f2(a1)),x69532))+~P1(f335(f335(f243(a1),f2(a1)),x69533))
% 59.73/59.67 [6969]E(x69691,f2(a881))+~P1(f335(f42(x69693,x69691),x69692))+~P1(f335(f335(f243(a881),f2(a881)),x69691))+P1(f335(f335(f243(a881),f335(f267(a881,a881),x69692)),x69691))
% 59.73/59.67 [6999]~P135(x69991)+~P1(f335(f335(f242(x69991),x69992),f2(x69991)))+~P1(f335(f335(f242(x69991),x69993),f2(x69991)))+E(f335(f335(f76(x69991),f335(f70(x69991),x69992)),f335(f70(x69991),x69993)),f335(f70(x69991),f335(f335(f76(x69991),x69992),x69993)))
% 59.73/59.67 [7048]~P135(x70481)+~P1(f335(f335(f242(x70481),x70482),f2(x70481)))+E(f335(f335(f76(x70481),f335(f70(x70481),x70482)),f335(f70(x70481),x70483)),f335(f70(x70481),f335(f335(f76(x70481),x70482),x70483)))+~P1(f335(f335(f242(x70481),f2(x70481)),x70483))
% 59.73/59.67 [7049]~P135(x70491)+~P1(f335(f335(f242(x70491),x70493),f2(x70491)))+E(f335(f335(f76(x70491),f335(f70(x70491),x70492)),f335(f70(x70491),x70493)),f335(f70(x70491),f335(f335(f76(x70491),x70492),x70493)))+~P1(f335(f335(f242(x70491),f2(x70491)),x70492))
% 59.73/59.67 [7104]~P135(x71041)+E(f335(f335(f76(x71041),f335(f70(x71041),x71042)),f335(f70(x71041),x71043)),f335(f70(x71041),f335(f335(f76(x71041),x71042),x71043)))+~P1(f335(f335(f242(x71041),f2(x71041)),x71042))+~P1(f335(f335(f242(x71041),f2(x71041)),x71043))
% 59.73/59.67 [7120]~P125(x71201)+~P1(f335(f335(f242(x71201),x71203),f2(x71201)))+~P1(f335(f335(f242(x71201),x71202),f2(x71201)))+P1(f335(f335(f242(x71201),f2(x71201)),f335(f335(f76(x71201),x71202),x71203)))
% 59.73/59.67 [7121]~P125(x71211)+~P1(f335(f335(f242(x71211),x71213),f2(x71211)))+~P1(f335(f335(f242(x71211),x71212),f2(x71211)))+P1(f335(f335(f242(x71211),f2(x71211)),f335(f335(f76(x71211),x71212),x71213)))
% 59.73/59.67 [7122]~P123(x71221)+~P1(f335(f335(f242(x71221),x71223),f2(x71221)))+~P1(f335(f335(f242(x71221),x71222),f2(x71221)))+P1(f335(f335(f242(x71221),f2(x71221)),f335(f335(f76(x71221),x71222),x71223)))
% 59.73/59.67 [7123]~P68(x71231)+~P1(f335(f335(f242(x71231),x71233),f2(x71231)))+~P1(f335(f335(f242(x71231),x71232),f2(x71231)))+P1(f335(f335(f242(x71231),f2(x71231)),f335(f335(f292(x71231),x71232),x71233)))
% 59.73/59.67 [7124]~P69(x71241)+~P1(f335(f335(f243(x71241),x71243),f2(x71241)))+~P1(f335(f335(f242(x71241),x71242),f2(x71241)))+P1(f335(f335(f242(x71241),f2(x71241)),f335(f335(f292(x71241),x71242),x71243)))
% 59.73/59.67 [7125]~P123(x71251)+~P1(f335(f335(f243(x71251),x71253),f2(x71251)))+~P1(f335(f335(f243(x71251),x71252),f2(x71251)))+P1(f335(f335(f243(x71251),f2(x71251)),f335(f335(f76(x71251),x71252),x71253)))
% 59.73/59.67 [7126]~P68(x71261)+~P1(f335(f335(f243(x71261),x71263),f2(x71261)))+~P1(f335(f335(f243(x71261),x71262),f2(x71261)))+P1(f335(f335(f243(x71261),f2(x71261)),f335(f335(f292(x71261),x71262),x71263)))
% 59.73/59.67 [7127]~P69(x71271)+~P1(f335(f335(f243(x71271),x71273),f2(x71271)))+~P1(f335(f335(f243(x71271),x71272),f2(x71271)))+P1(f335(f335(f243(x71271),f2(x71271)),f335(f335(f292(x71271),x71272),x71273)))
% 59.73/59.67 [7128]~P122(x71281)+~P1(f335(f335(f243(a881),f2(a881)),x71283))+~P1(f335(f335(f243(x71281),f73(x71281)),x71282))+P1(f335(f335(f243(x71281),f73(x71281)),f335(f335(f254(x71281),x71282),x71283)))
% 59.73/59.67 [7224]~P125(x72241)+~P1(f335(f335(f242(x72241),f2(x72241)),x72243))+~P1(f335(f335(f242(x72241),f2(x72241)),x72242))+P1(f335(f335(f242(x72241),f2(x72241)),f335(f335(f76(x72241),x72242),x72243)))
% 59.73/59.67 [7225]~P123(x72251)+~P1(f335(f335(f242(x72251),f2(x72251)),x72253))+~P1(f335(f335(f242(x72251),f2(x72251)),x72252))+P1(f335(f335(f242(x72251),f2(x72251)),f335(f335(f76(x72251),x72252),x72253)))
% 59.73/59.67 [7226]~P132(x72261)+~P1(f335(f335(f242(x72261),f2(x72261)),x72263))+~P1(f335(f335(f242(x72261),f2(x72261)),x72262))+P1(f335(f335(f242(x72261),f2(x72261)),f335(f335(f76(x72261),x72262),x72263)))
% 59.73/59.67 [7227]~P90(x72271)+~P1(f335(f335(f242(x72271),f2(x72271)),x72273))+~P1(f335(f335(f242(x72271),f2(x72271)),x72272))+P1(f335(f335(f242(x72271),f2(x72271)),f335(f335(f75(x72271),x72272),x72273)))
% 59.73/59.67 [7228]~P68(x72281)+~P1(f335(f335(f242(x72281),f2(x72281)),x72283))+~P1(f335(f335(f242(x72281),f2(x72281)),x72282))+P1(f335(f335(f242(x72281),f2(x72281)),f335(f335(f292(x72281),x72282),x72283)))
% 59.73/59.67 [7229]~P69(x72291)+~P1(f335(f335(f243(x72291),f2(x72291)),x72293))+~P1(f335(f335(f242(x72291),f2(x72291)),x72292))+P1(f335(f335(f242(x72291),f2(x72291)),f335(f335(f292(x72291),x72292),x72293)))
% 59.73/59.67 [7230]~P122(x72301)+~P1(f335(f335(f243(x72301),f73(x72301)),x72303))+~P1(f335(f335(f243(x72301),f73(x72301)),x72302))+P1(f335(f335(f243(x72301),f73(x72301)),f335(f335(f76(x72301),x72302),x72303)))
% 59.73/59.67 [7231]~P127(x72311)+~P1(f335(f335(f243(x72311),f2(x72311)),x72313))+~P1(f335(f335(f243(x72311),f2(x72311)),x72312))+P1(f335(f335(f243(x72311),f2(x72311)),f335(f335(f76(x72311),x72312),x72313)))
% 59.73/59.67 [7232]~P90(x72321)+~P1(f335(f335(f242(x72321),f2(x72321)),x72323))+~P1(f335(f335(f243(x72321),f2(x72321)),x72322))+P1(f335(f335(f243(x72321),f2(x72321)),f335(f335(f75(x72321),x72322),x72323)))
% 59.73/59.67 [7233]~P90(x72331)+~P1(f335(f335(f242(x72331),f2(x72331)),x72332))+~P1(f335(f335(f243(x72331),f2(x72331)),x72333))+P1(f335(f335(f243(x72331),f2(x72331)),f335(f335(f75(x72331),x72332),x72333)))
% 59.73/59.67 [7234]~P90(x72341)+~P1(f335(f335(f243(x72341),f2(x72341)),x72343))+~P1(f335(f335(f243(x72341),f2(x72341)),x72342))+P1(f335(f335(f243(x72341),f2(x72341)),f335(f335(f75(x72341),x72342),x72343)))
% 59.73/59.67 [7235]~P68(x72351)+~P1(f335(f335(f243(x72351),f2(x72351)),x72353))+~P1(f335(f335(f243(x72351),f2(x72351)),x72352))+P1(f335(f335(f243(x72351),f2(x72351)),f335(f335(f292(x72351),x72352),x72353)))
% 59.73/59.67 [7236]~P69(x72361)+~P1(f335(f335(f243(x72361),f2(x72361)),x72363))+~P1(f335(f335(f243(x72361),f2(x72361)),x72362))+P1(f335(f335(f243(x72361),f2(x72361)),f335(f335(f292(x72361),x72362),x72363)))
% 59.73/59.67 [7312]~P61(x73121)+~P1(f335(f56(x73121),x73123))+E(f10(x73121,f335(f335(f312(x73121),x73122),x73123)),x73122)+~E(f335(f335(f23(f888(x73121,a879)),x73123),f335(f335(f312(x73121),x73122),f188(f888(x73121,a879)))),f188(f888(x73121,a879)))
% 59.73/59.67 [7313]~P61(x73131)+~P1(f335(f56(x73131),x73133))+E(f13(x73131,f335(f335(f312(x73131),x73132),x73133)),x73132)+~E(f335(f335(f23(f888(x73131,a879)),x73133),f335(f335(f312(x73131),x73132),f188(f888(x73131,a879)))),f188(f888(x73131,a879)))
% 59.73/59.67 [7314]~P106(x73141)+~P1(f335(f56(x73141),x73143))+E(f14(x73141,f335(f335(f312(x73141),x73142),x73143)),x73142)+~E(f335(f335(f23(f888(x73141,a879)),x73143),f335(f335(f312(x73141),x73142),f188(f888(x73141,a879)))),f188(f888(x73141,a879)))
% 59.73/59.67 [7315]~P106(x73151)+~P1(f335(f56(x73151),x73153))+E(f15(x73151,f335(f335(f312(x73151),x73152),x73153)),x73152)+~E(f335(f335(f23(f888(x73151,a879)),x73153),f335(f335(f312(x73151),x73152),f188(f888(x73151,a879)))),f188(f888(x73151,a879)))
% 59.73/59.67 [7317]~P123(x73171)+P1(f335(f335(f242(x73171),x73172),f2(x73171)))+P1(f335(f335(f242(x73171),f2(x73171)),x73173))+~P1(f335(f335(f242(x73171),f2(x73171)),f335(f335(f76(x73171),x73173),x73172)))
% 59.73/59.67 [7318]~P123(x73181)+P1(f335(f335(f242(x73181),x73182),f2(x73181)))+P1(f335(f335(f242(x73181),f2(x73181)),x73183))+~P1(f335(f335(f242(x73181),f2(x73181)),f335(f335(f76(x73181),x73182),x73183)))
% 59.73/59.67 [7319]~P68(x73191)+P1(f335(f335(f242(x73191),x73192),f2(x73191)))+P1(f335(f335(f242(x73191),f2(x73191)),x73193))+~P1(f335(f335(f242(x73191),f2(x73191)),f335(f335(f292(x73191),x73193),x73192)))
% 59.73/59.67 [7320]~P68(x73201)+P1(f335(f335(f242(x73201),x73202),f2(x73201)))+P1(f335(f335(f242(x73201),f2(x73201)),x73203))+~P1(f335(f335(f242(x73201),f2(x73201)),f335(f335(f292(x73201),x73202),x73203)))
% 59.73/59.67 [7321]~P123(x73211)+P1(f335(f335(f242(x73211),x73212),f2(x73211)))+P1(f335(f335(f242(x73211),f2(x73211)),x73212))+~P1(f335(f335(f242(x73211),f2(x73211)),f335(f335(f76(x73211),x73213),x73212)))
% 59.73/59.67 [7322]~P123(x73221)+P1(f335(f335(f242(x73221),x73222),f2(x73221)))+P1(f335(f335(f242(x73221),f2(x73221)),x73222))+~P1(f335(f335(f242(x73221),f2(x73221)),f335(f335(f76(x73221),x73222),x73223)))
% 59.73/59.67 [7323]~P68(x73231)+P1(f335(f335(f242(x73231),x73232),f2(x73231)))+P1(f335(f335(f242(x73231),f2(x73231)),x73232))+~P1(f335(f335(f242(x73231),f2(x73231)),f335(f335(f292(x73231),x73233),x73232)))
% 59.73/59.67 [7324]~P68(x73241)+P1(f335(f335(f242(x73241),x73242),f2(x73241)))+P1(f335(f335(f242(x73241),f2(x73241)),x73242))+~P1(f335(f335(f242(x73241),f2(x73241)),f335(f335(f292(x73241),x73242),x73243)))
% 59.73/59.67 [7325]~P68(x73251)+P1(f335(f335(f243(x73251),x73252),f2(x73251)))+P1(f335(f335(f243(x73251),f2(x73251)),x73253))+~P1(f335(f335(f243(x73251),f2(x73251)),f335(f335(f292(x73251),x73253),x73252)))
% 59.73/59.67 [7326]~P68(x73261)+P1(f335(f335(f243(x73261),x73262),f2(x73261)))+P1(f335(f335(f243(x73261),f2(x73261)),x73263))+~P1(f335(f335(f243(x73261),f2(x73261)),f335(f335(f292(x73261),x73262),x73263)))
% 59.73/59.67 [7327]~P68(x73271)+P1(f335(f335(f243(x73271),x73272),f2(x73271)))+P1(f335(f335(f243(x73271),f2(x73271)),x73272))+~P1(f335(f335(f243(x73271),f2(x73271)),f335(f335(f292(x73271),x73273),x73272)))
% 59.73/59.67 [7328]~P68(x73281)+P1(f335(f335(f243(x73281),x73282),f2(x73281)))+P1(f335(f335(f243(x73281),f2(x73281)),x73282))+~P1(f335(f335(f243(x73281),f2(x73281)),f335(f335(f292(x73281),x73282),x73283)))
% 59.73/59.67 [7416]~E(f335(f335(f95(f888(x74161,a879)),f335(f166(x74161),x74162)),f335(f166(x74161),x74163)),f188(f888(x74161,a879)))+~P1(f335(f130(x74161),x74163))+~P1(f335(f130(x74161),x74162))+P1(f335(f130(x74161),f335(f335(f127(x74161),x74162),x74163)))
% 59.73/59.67 [7417]~P106(x74171)+~P1(f335(f56(x74171),x74173))+E(f11(x74171,f240(x74171),f335(f335(f312(x74171),x74172),x74173)),x74172)+~E(f335(f335(f23(f888(x74171,a879)),x74173),f335(f335(f312(x74171),x74172),f188(f888(x74171,a879)))),f188(f888(x74171,a879)))
% 59.73/59.67 [7418]~P106(x74181)+~P1(f335(f56(x74181),x74183))+E(f12(x74181,f241(x74181),f335(f335(f312(x74181),x74182),x74183)),x74182)+~E(f335(f335(f23(f888(x74181,a879)),x74183),f335(f335(f312(x74181),x74182),f188(f888(x74181,a879)))),f188(f888(x74181,a879)))
% 59.73/59.67 [7432]~P88(x74321)+~P1(f335(f335(f242(x74321),x74322),x74323))+~P1(f335(f335(f242(x74321),f335(f74(x74321),x74322)),x74323))+P1(f335(f335(f242(x74321),f335(f70(x74321),x74322)),x74323))
% 59.73/59.67 [7433]~P88(x74331)+~P1(f335(f335(f242(x74331),x74332),x74333))+~P1(f335(f335(f242(x74331),f335(f74(x74331),x74332)),x74333))+P1(f335(f335(f242(x74331),f335(f70(x74331),x74332)),x74333))
% 59.73/59.67 [7434]~P119(x74341)+~P1(f335(f335(f243(x74341),x74342),x74343))+~P1(f335(f335(f243(x74341),f335(f74(x74341),x74342)),x74343))+P1(f335(f335(f243(x74341),f335(f70(x74341),x74342)),x74343))
% 59.73/59.67 [7504]~P127(x75041)+P1(f335(f335(f243(x75041),f2(x75041)),x75042))+~P1(f335(f335(f243(x75041),f2(x75041)),x75043))+~P1(f335(f335(f243(x75041),f2(x75041)),f335(f335(f76(x75041),x75043),x75042)))
% 59.73/59.67 [7505]~P127(x75051)+P1(f335(f335(f243(x75051),f2(x75051)),x75052))+~P1(f335(f335(f243(x75051),f2(x75051)),x75053))+~P1(f335(f335(f243(x75051),f2(x75051)),f335(f335(f76(x75051),x75052),x75053)))
% 59.73/59.67 [7809]E(x78091,x78092)+~P1(f335(f56(x78093),x78091))+~P1(f335(f335(f242(a881),f335(f29(x78093),x78091)),f335(f29(x78093),x78092)))+~P1(f335(f335(f242(f888(x78093,a879)),x78092),x78091))
% 59.73/59.67 [7875]~P1(f335(f335(f242(a881),x78752),x78751))+~P1(f335(f335(f242(a881),x78752),x78753))+~P1(f335(f335(f242(a881),x78751),x78753))+P1(f335(f335(f242(a881),f335(f335(f23(a881),x78751),x78752)),f335(f335(f23(a881),x78753),x78752)))
% 59.73/59.67 [7876]~P1(f335(f335(f242(a881),x78762),x78761))+~P1(f335(f335(f242(a881),x78762),x78763))+~P1(f335(f335(f243(a881),x78761),x78763))+P1(f335(f335(f243(a881),f335(f335(f23(a881),x78761),x78762)),f335(f335(f23(a881),x78763),x78762)))
% 59.73/59.67 [7954]~P1(f335(f335(f243(a1),x79541),f2(a1)))+~P1(f335(f335(f243(a1),f2(a1)),x79542))+~P1(f335(f335(f242(a1),x79542),x79543))+P1(f335(f335(f242(a1),f335(f335(f30(a1),x79541),x79542)),f335(f335(f30(a1),x79541),x79543)))
% 59.73/59.67 [7967]~P1(f335(f335(f242(a1),f2(a1)),x79671))+~P1(f335(f335(f243(a1),f2(a1)),x79673))+~P1(f335(f335(f242(a1),x79673),x79672))+P1(f335(f335(f242(a1),f335(f335(f30(a1),x79671),x79672)),f335(f335(f30(a1),x79671),x79673)))
% 59.73/59.67 [8104]E(f335(x81041,f531(x81042,x81041,x81043)),x81042)+~P1(f335(f335(f242(a1),x81042),f335(x81041,x81043)))+P1(f335(f335(f243(a881),f532(x81042,x81041,x81043)),x81043))+~P1(f335(f335(f242(a1),f335(x81041,f2(a881))),x81042))
% 59.73/59.67 [8105]E(f335(x81051,f544(x81052,x81051,x81053)),x81052)+~P1(f335(f335(f242(a1),x81052),f335(x81051,x81053)))+P1(f335(f335(f243(a881),f545(x81052,x81051,x81053)),x81053))+~P1(f335(f335(f242(a1),f335(x81051,f2(a881))),x81052))
% 59.73/59.67 [8205]~P1(f335(f56(x82051),x82053))+~P1(f335(f335(f243(a881),f335(f29(x82051),x82052)),f335(f29(x82051),x82053)))+~P1(f335(f335(f242(f888(x82051,a879)),x82052),x82053))+P1(f335(f335(f243(f888(x82051,a879)),x82052),x82053))
% 59.73/59.67 [8234]E(f335(f335(f75(a1),f441(x82343,x82341,x82342)),f442(x82343,x82341,x82342)),x82341)+E(f335(f335(f23(a1),x82341),x82342),x82341)+~P1(f335(f335(f243(a1),f2(a1)),x82342))+~P1(f335(f335(f337(a1),f335(f335(f23(a1),x82341),f73(a1))),x82343))
% 59.73/59.67 [8235]E(f335(f335(f23(a1),f456(x82353,x82351,x82352)),f457(x82353,x82351,x82352)),x82351)+E(f335(f335(f75(a1),x82351),x82352),x82351)+~P1(f335(f335(f243(a1),f2(a1)),x82352))+~P1(f335(f335(f337(a1),f335(f335(f75(a1),x82351),f73(a1))),x82353))
% 59.73/59.67 [8287]~P1(f335(f335(f242(a881),x82873),x82871))+P1(f335(f335(f242(a881),x82871),x82872))+~P1(f335(f335(f242(a881),x82873),x82872))+~P1(f335(f335(f242(a881),f335(f335(f23(a881),x82871),x82873)),f335(f335(f23(a881),x82872),x82873)))
% 59.73/59.67 [8288]~P1(f335(f335(f242(a881),x82883),x82881))+P1(f335(f335(f243(a881),x82881),x82882))+~P1(f335(f335(f242(a881),x82883),x82882))+~P1(f335(f335(f243(a881),f335(f335(f23(a881),x82881),x82883)),f335(f335(f23(a881),x82882),x82883)))
% 59.73/59.67 [8305]~P106(x83052)+E(x83051,f107(x83052))+~P15(x83052,f335(f162(x83052),x83051))+E(f335(f135(x83052,x83052,f335(f7(x83052,x83052,x83052),f241(x83052)),x83053),f335(f162(x83052),x83051)),f335(f335(f241(x83052),f335(f335(f158(x83052),x83051),f2(a881))),x83053))
% 59.73/59.67 [8351]~P5(x83511)+~P37(x83511,x83511,x83513)+P1(f335(f335(f242(x83511),x83512),f90(x83511,x83513)))+~P1(f335(f335(f242(x83511),x83512),f335(x83513,f335(f335(f104(x83511),x83512),f90(x83511,x83513)))))
% 59.73/59.67 [8372]E(f335(f335(f23(a1),x83721),x83722),x83721)+~P1(f335(f335(f243(a1),f2(a1)),x83722))+P1(f335(f335(f337(a1),f441(x83723,x83721,x83722)),x83723))+~P1(f335(f335(f337(a1),f335(f335(f23(a1),x83721),f73(a1))),x83723))
% 59.73/59.67 [8373]E(f335(f335(f75(a1),x83731),x83732),x83731)+~P1(f335(f335(f243(a1),f2(a1)),x83732))+P1(f335(f335(f337(a1),f456(x83733,x83731,x83732)),x83733))+~P1(f335(f335(f337(a1),f335(f335(f75(a1),x83731),f73(a1))),x83733))
% 59.73/59.67 [8448]~P1(f335(f335(f242(a1),x84481),f335(x84482,x84483)))+P1(f335(f335(f243(a881),f532(x84481,x84482,x84483)),x84483))+P1(f335(f335(f242(a881),f531(x84481,x84482,x84483)),x84483))+~P1(f335(f335(f242(a1),f335(x84482,f2(a881))),x84481))
% 59.73/59.67 [8449]~P1(f335(f335(f242(a1),x84491),f335(x84492,x84493)))+P1(f335(f335(f243(a881),f545(x84491,x84492,x84493)),x84493))+P1(f335(f335(f242(a881),f544(x84491,x84492,x84493)),x84493))+~P1(f335(f335(f242(a1),f335(x84492,f2(a881))),x84491))
% 59.73/59.67 [8523]E(f335(f335(f23(a1),x85231),x85232),x85231)+~P1(f335(f335(f243(a1),f2(a1)),x85232))+P1(f335(f335(f337(a1),f442(x85233,x85231,x85232)),f305(a1,f73(a1),x85232)))+~P1(f335(f335(f337(a1),f335(f335(f23(a1),x85231),f73(a1))),x85233))
% 59.73/59.67 [8524]E(f335(f335(f75(a1),x85241),x85242),x85241)+~P1(f335(f335(f243(a1),f2(a1)),x85242))+P1(f335(f335(f337(a1),f457(x85243,x85241,x85242)),f305(a1,f73(a1),x85242)))+~P1(f335(f335(f337(a1),f335(f335(f75(a1),x85241),f73(a1))),x85243))
% 59.73/59.67 [8652]~P122(x86521)+~P1(f335(f335(f243(x86521),x86522),f73(x86521)))+~P1(f335(f335(f243(x86521),f2(x86521)),x86522))+P1(f335(f335(f243(x86521),f335(f335(f76(x86521),x86522),f335(f335(f254(x86521),x86522),x86523))),f335(f335(f254(x86521),x86522),x86523)))
% 59.73/59.67 [8739]~P1(f335(x87391,x87392))+P1(f335(x87391,f2(a881)))+~P1(f335(f335(f243(a881),x87392),x87393))+~P1(f335(x87391,f39(a881,f335(a106,f582(x87392,x87391,x87393)),x87393)))
% 59.73/59.67 [8882]E(f511(x88821,x88822,x88823),f2(a881))+P1(f335(f335(x88821,x88823),x88822))+P1(f335(f335(x88821,f511(x88821,x88822,x88823)),f39(a881,f509(x88821,x88822,x88823),f511(x88821,x88822,x88823))))+~P1(f335(f323(f887(a881,a881),a222),f335(f335(f264(a881,a881),x88823),x88822)))
% 59.73/59.67 [8919]~P26(x89191,x89191,x89192,x89193)+E(f335(f313(x89191,x89191,x89192),x89193),x89193)+~P1(f335(f56(x89191),x89193))+~P1(f335(f335(f242(f888(x89191,a879)),f335(f313(x89191,x89191,x89192),x89193)),x89193))
% 59.73/59.67 [8992]~P5(x89921)+~P37(x89921,x89921,x89923)+P1(f335(f335(f242(x89921),f335(f335(f104(x89921),x89922),f90(x89921,x89923))),f335(x89923,f335(f335(f104(x89921),x89922),f90(x89921,x89923)))))+~P1(f335(f335(f242(x89921),x89922),f335(x89923,f335(f335(f104(x89921),x89922),f90(x89921,x89923)))))
% 59.73/59.67 [9140]P1(f335(f335(x91401,x91402),x91403))+P1(f335(f335(f243(a1),f803(x91401,x91403,x91402)),f804(x91401,x91403,x91402)))+P1(f335(f335(x91401,f803(x91401,x91403,x91402)),f335(f335(f75(a1),f804(x91401,x91403,x91402)),f73(a1))))+~P1(f335(f323(f887(a1,a1),a126),f335(f335(f264(a1,a1),x91402),x91403)))
% 59.73/59.67 [9159]P1(f335(f335(x91591,x91592),x91593))+~P1(f335(f335(f243(a1),f386(x91591,x91593,x91592)),f2(a1)))+P1(f335(f335(x91591,f335(f74(a1),f385(x91591,x91593,x91592))),f335(f74(a1),f386(x91591,x91593,x91592))))+~P1(f335(f323(f887(a1,a1),a224),f335(f335(f264(a1,a1),x91592),x91593)))
% 59.73/59.67 [9342]P1(f335(f335(x93421,x93422),x93423))+P1(f335(f335(x93421,f335(f335(f75(a1),f692(x93421,x93423,x93422)),f73(a1))),f699(x93421,x93423,x93422)))+~P1(f335(f335(f242(a1),f692(x93421,x93423,x93422)),f699(x93421,x93423,x93422)))+~P1(f335(f323(f887(a1,a1),a176),f335(f335(f264(a1,a1),x93422),x93423)))
% 59.73/59.67 [9778]~P4(x97782)+~P4(x97781)+~P1(f335(f53(f887(x97781,x97782)),x97783))+P1(f335(f53(x97781),f335(f335(f8(f888(x97782,a879),a879,x97781),f53(x97782)),f335(f335(f8(f888(x97782,f887(x97781,x97782)),f888(x97782,a879),x97781),f335(f8(f887(x97781,x97782),a879,x97782),x97783)),f264(x97781,x97782)))))
% 59.73/59.67 [9779]~P4(x97792)+~P4(x97791)+~P1(f335(f52(f887(x97791,x97792)),x97793))+P1(f335(f52(x97791),f335(f335(f8(f888(x97792,a879),a879,x97791),f52(x97792)),f335(f335(f8(f888(x97792,f887(x97791,x97792)),f888(x97792,a879),x97791),f335(f8(f887(x97791,x97792),a879,x97792),x97793)),f264(x97791,x97792)))))
% 59.73/59.67 [9884]~P4(x98842)+~P4(x98841)+P1(f335(f53(f887(x98841,x98842)),x98843))+~P1(f335(f53(x98841),f335(f335(f8(f888(x98842,a879),a879,x98841),f53(x98842)),f335(f335(f8(f888(x98842,f887(x98841,x98842)),f888(x98842,a879),x98841),f335(f8(f887(x98841,x98842),a879,x98842),x98843)),f264(x98841,x98842)))))
% 59.73/59.67 [9885]~P4(x98852)+~P4(x98851)+P1(f335(f52(f887(x98851,x98852)),x98853))+~P1(f335(f52(x98851),f335(f335(f8(f888(x98852,a879),a879,x98851),f52(x98852)),f335(f335(f8(f888(x98852,f887(x98851,x98852)),f888(x98852,a879),x98851),f335(f8(f887(x98851,x98852),a879,x98852),x98853)),f264(x98851,x98852)))))
% 59.73/59.67 [10051]E(f335(x100511,f531(x100512,x100511,x100513)),x100512)+~P1(f335(f335(f242(a1),x100512),f335(x100511,x100513)))+~P1(f335(f335(f242(a1),f335(f70(a1),f335(f335(f23(a1),f335(x100511,f335(f335(f75(a881),f532(x100512,x100511,x100513)),f73(a881)))),f335(x100511,f532(x100512,x100511,x100513))))),f73(a1)))+~P1(f335(f335(f242(a1),f335(x100511,f2(a881))),x100512))
% 59.73/59.67 [10052]E(f335(x100521,f544(x100522,x100521,x100523)),x100522)+~P1(f335(f335(f242(a1),x100522),f335(x100521,x100523)))+~P1(f335(f335(f242(a1),f335(f70(a1),f335(f335(f23(a1),f335(x100521,f335(f335(f75(a881),f545(x100522,x100521,x100523)),f73(a881)))),f335(x100521,f545(x100522,x100521,x100523))))),f73(a1)))+~P1(f335(f335(f242(a1),f335(x100521,f2(a881))),x100522))
% 59.73/59.67 [10056]~P1(f335(f335(f242(a1),x100561),f335(x100562,x100563)))+~P1(f335(f335(f242(a1),f335(f70(a1),f335(f335(f23(a1),f335(x100562,f335(f335(f75(a881),f532(x100561,x100562,x100563)),f73(a881)))),f335(x100562,f532(x100561,x100562,x100563))))),f73(a1)))+P1(f335(f335(f242(a881),f531(x100561,x100562,x100563)),x100563))+~P1(f335(f335(f242(a1),f335(x100562,f2(a881))),x100561))
% 59.73/59.67 [10057]~P1(f335(f335(f242(a1),x100571),f335(x100572,x100573)))+~P1(f335(f335(f242(a1),f335(f70(a1),f335(f335(f23(a1),f335(x100572,f335(f335(f75(a881),f545(x100571,x100572,x100573)),f73(a881)))),f335(x100572,f545(x100571,x100572,x100573))))),f73(a1)))+P1(f335(f335(f242(a881),f544(x100571,x100572,x100573)),x100573))+~P1(f335(f335(f242(a1),f335(x100572,f2(a881))),x100571))
% 59.73/59.67 [10111]E(x101111,x101112)+~E(f335(f135(f882(x101113),f882(x101113),f127(x101113),f107(x101113)),x101111),f335(f135(f882(x101113),f882(x101113),f127(x101113),f107(x101113)),x101112))+~E(f335(f189(f882(f882(x101113))),x101111),f335(f189(f882(f882(x101113))),x101112))+~P1(f335(f335(f268(f882(x101113),f882(x101113),a879),f335(f335(f7(f882(x101113),f888(f882(x101113),a881),f888(f882(x101113),a879)),f335(f335(f8(f888(a881,a879),f888(f888(f882(x101113),a881),f888(f882(x101113),a879)),f882(x101113)),f8(a881,a879,f882(x101113))),f335(f335(f8(a881,f888(a881,a879),f882(x101113)),a332),f189(f882(x101113))))),f189(f882(x101113)))),f731(x101111,x101112,x101113)))
% 59.73/59.67 [10112]E(x101121,x101122)+~E(f335(f135(f882(x101123),f882(x101123),f127(x101123),f107(x101123)),x101121),f335(f135(f882(x101123),f882(x101123),f127(x101123),f107(x101123)),x101122))+~E(f335(f189(f882(f882(x101123))),x101121),f335(f189(f882(f882(x101123))),x101122))+~P1(f335(f335(f268(f882(x101123),f882(x101123),a879),f335(f335(f7(f882(x101123),f888(f882(x101123),a881),f888(f882(x101123),a879)),f335(f335(f8(f888(a881,a879),f888(f888(f882(x101123),a881),f888(f882(x101123),a879)),f882(x101123)),f8(a881,a879,f882(x101123))),f335(f335(f8(a881,f888(a881,a879),f882(x101123)),a332),f189(f882(x101123))))),f189(f882(x101123)))),f733(x101122,x101121,x101123)))
% 59.73/59.67 [6831]~E(f73(a881),f2(a881))+~P1(f335(f56(x68311),x68313))+~P1(f335(f56(x68311),x68312))+E(f335(f335(f75(a881),f335(f29(x68311),x68312)),f335(f29(x68311),x68313)),f335(f29(x68311),f335(f335(f104(f888(x68311,a879)),x68312),x68313)))
% 59.73/59.67 [7243]~P102(x72431)+~P1(f335(f56(x72431),x72432))+~P1(f335(f335(f337(x72431),x72433),x72432))+P1(f335(f335(f242(x72431),f335(f58(x72431,f95(x72431)),x72432)),x72433))
% 59.73/59.67 [7244]~P106(x72441)+~P1(f335(f56(x72441),x72442))+~P1(f335(f335(f337(x72441),x72443),x72442))+P1(f335(f335(f242(x72441),f335(f58(x72441,f240(x72441)),x72442)),x72443))
% 59.73/59.67 [7498]~P1(f335(f56(x74981),x74983))+~P1(f335(f56(x74981),x74982))+~E(f335(f335(f95(f888(x74981,a879)),x74982),x74983),f188(f888(x74981,a879)))+E(f335(f335(f75(a881),f335(f29(x74981),x74982)),f335(f29(x74981),x74983)),f335(f29(x74981),f335(f335(f104(f888(x74981,a879)),x74982),x74983)))
% 59.73/59.67 [8293]~P36(x82931,x82933)+~P36(x82931,x82932)+~E(f335(f335(f95(f888(x82931,a879)),f335(f262(x82931,x82931),x82932)),f335(f260(x82931,x82931),x82933)),f188(f888(x82931,a879)))+P36(x82931,f335(f335(f104(f888(f887(x82931,x82931),a879)),x82932),x82933))
% 59.73/59.67 [8387]E(x83871,f335(f335(f30(a881),x83872),x83873))+~P1(f335(f335(f243(a881),f2(a881)),x83873))+~P1(f335(f335(f243(a881),x83872),f335(f335(f76(a881),x83873),f335(a106,x83871))))+~P1(f335(f335(f242(a881),f335(f335(f76(a881),x83873),x83871)),x83872))
% 59.73/59.67 [8521]~P1(f335(f56(x85211),x85212))+~P1(f335(f56(x85211),x85213))+E(f335(f335(f75(a881),f335(f29(x85211),x85212)),f335(f29(x85211),x85213)),f335(f29(x85211),f335(f335(f104(f888(x85211,a879)),x85212),x85213)))+P1(f335(f335(f337(x85211),f359(x85213,x85212,x85211)),f335(f335(f95(f888(x85211,a879)),x85212),x85213)))
% 59.73/59.67 [8894]~P123(x88942)+~E(x88941,f2(x88942))+~E(x88943,f2(x88942))+~P1(f335(f335(f243(x88942),f2(x88942)),f335(f335(f75(x88942),f335(f335(f76(x88942),x88943),x88943)),f335(f335(f76(x88942),x88941),x88941))))
% 59.73/59.67 [9422]~P36(x94221,x94223)+~P36(x94221,x94222)+P36(x94221,f335(f335(f104(f888(f887(x94221,x94221),a879)),x94222),x94223))+~P1(f335(f335(f242(f888(f887(x94221,x94221),a879)),f335(f335(f291(x94221,x94221,x94221),x94222),x94223)),x94222))
% 59.73/59.67 [9550]~P1(f335(x95501,x95503))+~P1(f335(f56(x95502),x95503))+P1(f335(x95501,f188(f888(x95502,a879))))+~P1(f335(x95501,f335(f335(f23(f888(x95502,a879)),f867(x95501,x95503,x95502)),f335(f335(f312(x95502),f868(x95501,x95503,x95502)),f188(f888(x95502,a879))))))
% 59.73/59.67 [9811]~P4(x98111)+~P4(x98112)+P11(x98111,f335(f335(f8(f888(x98112,x98111),a879,f882(x98111)),x98113),f335(f335(f8(f888(x98112,f885(x98111)),f888(x98112,x98111),f882(x98111)),f68(f885(x98111),x98111,x98112,f239(x98111))),f335(f335(f8(f882(f887(x98112,x98111)),f888(x98112,f885(x98111)),f882(x98111)),f179(x98112,x98111)),f335(f175(x98112,x98111),f50(x98112))))),f335(f189(f882(x98112)),f50(x98112)))+~P1(f335(f52(f888(x98112,x98111)),x98113))
% 59.73/59.67 [9812]~P4(x98121)+~P4(x98122)+P12(x98121,f335(f335(f8(f888(x98122,x98121),a879,f882(x98121)),x98123),f335(f335(f8(f888(x98122,f885(x98121)),f888(x98122,x98121),f882(x98121)),f68(f885(x98121),x98121,x98122,f239(x98121))),f335(f335(f8(f882(f887(x98122,x98121)),f888(x98122,f885(x98121)),f882(x98121)),f179(x98122,x98121)),f335(f175(x98122,x98121),f50(x98122))))),f335(f189(f882(x98122)),f50(x98122)))+~P1(f335(f53(f888(x98122,x98121)),x98123))
% 59.73/59.67 [9906]~P4(x99061)+~P4(x99062)+~P12(x99062,f335(f335(f8(f888(x99061,x99062),a879,f882(x99062)),x99063),f335(f335(f8(f888(x99061,f885(x99062)),f888(x99061,x99062),f882(x99062)),f68(f885(x99062),x99062,x99061,f239(x99062))),f335(f335(f8(f882(f887(x99061,x99062)),f888(x99061,f885(x99062)),f882(x99062)),f179(x99061,x99062)),f335(f175(x99061,x99062),f50(x99061))))),f335(f189(f882(x99061)),f50(x99061)))+P1(f335(f53(f888(x99061,x99062)),x99063))
% 59.73/59.67 [9907]~P4(x99071)+~P4(x99072)+~P11(x99072,f335(f335(f8(f888(x99071,x99072),a879,f882(x99072)),x99073),f335(f335(f8(f888(x99071,f885(x99072)),f888(x99071,x99072),f882(x99072)),f68(f885(x99072),x99072,x99071,f239(x99072))),f335(f335(f8(f882(f887(x99071,x99072)),f888(x99071,f885(x99072)),f882(x99072)),f179(x99071,x99072)),f335(f175(x99071,x99072),f50(x99071))))),f335(f189(f882(x99071)),f50(x99071)))+P1(f335(f52(f888(x99071,x99072)),x99073))
% 59.73/59.67 [8689]~P1(f335(f335(f243(a1),f2(a1)),x86893))+P1(f335(f335(f242(a1),f2(a1)),x86891))+~P1(f335(f335(f243(a1),x86892),x86893))+~P1(f335(f335(f242(a1),f2(a1)),f335(f335(f75(a1),f335(f335(f76(a1),x86893),x86891)),x86892)))
% 59.73/59.67 [8713]~P61(x87131)+~P1(f335(f56(x87131),x87132))+E(f335(f335(f23(f888(x87131,a879)),x87132),f335(f335(f312(x87131),x87133),f188(f888(x87131,a879)))),f188(f888(x87131,a879)))+E(f335(f335(f95(x87131),x87133),f10(x87131,f335(f335(f23(f888(x87131,a879)),x87132),f335(f335(f312(x87131),x87133),f188(f888(x87131,a879)))))),f10(x87131,f335(f335(f312(x87131),x87133),x87132)))
% 59.73/59.67 [8714]~P61(x87141)+~P1(f335(f56(x87141),x87142))+E(f335(f335(f23(f888(x87141,a879)),x87142),f335(f335(f312(x87141),x87143),f188(f888(x87141,a879)))),f188(f888(x87141,a879)))+E(f335(f335(f104(x87141),x87143),f13(x87141,f335(f335(f23(f888(x87141,a879)),x87142),f335(f335(f312(x87141),x87143),f188(f888(x87141,a879)))))),f13(x87141,f335(f335(f312(x87141),x87143),x87142)))
% 59.73/59.67 [8715]~P106(x87151)+~P1(f335(f56(x87151),x87152))+E(f335(f335(f23(f888(x87151,a879)),x87152),f335(f335(f312(x87151),x87153),f188(f888(x87151,a879)))),f188(f888(x87151,a879)))+E(f335(f335(f241(x87151),x87153),f14(x87151,f335(f335(f23(f888(x87151,a879)),x87152),f335(f335(f312(x87151),x87153),f188(f888(x87151,a879)))))),f14(x87151,f335(f335(f312(x87151),x87153),x87152)))
% 59.73/59.67 [8716]~P106(x87161)+~P1(f335(f56(x87161),x87162))+E(f335(f335(f23(f888(x87161,a879)),x87162),f335(f335(f312(x87161),x87163),f188(f888(x87161,a879)))),f188(f888(x87161,a879)))+E(f335(f335(f240(x87161),x87163),f15(x87161,f335(f335(f23(f888(x87161,a879)),x87162),f335(f335(f312(x87161),x87163),f188(f888(x87161,a879)))))),f15(x87161,f335(f335(f312(x87161),x87163),x87162)))
% 59.73/59.67 [8783]~P106(x87831)+~P1(f335(f56(x87831),x87832))+E(f335(f335(f23(f888(x87831,a879)),x87832),f335(f335(f312(x87831),x87833),f188(f888(x87831,a879)))),f188(f888(x87831,a879)))+E(f335(f335(f240(x87831),x87833),f11(x87831,f240(x87831),f335(f335(f23(f888(x87831,a879)),x87832),f335(f335(f312(x87831),x87833),f188(f888(x87831,a879)))))),f11(x87831,f240(x87831),f335(f335(f312(x87831),x87833),x87832)))
% 59.73/59.67 [8784]~P106(x87841)+~P1(f335(f56(x87841),x87842))+E(f335(f335(f23(f888(x87841,a879)),x87842),f335(f335(f312(x87841),x87843),f188(f888(x87841,a879)))),f188(f888(x87841,a879)))+E(f335(f335(f241(x87841),x87843),f12(x87841,f241(x87841),f335(f335(f23(f888(x87841,a879)),x87842),f335(f335(f312(x87841),x87843),f188(f888(x87841,a879)))))),f12(x87841,f241(x87841),f335(f335(f312(x87841),x87843),x87842)))
% 59.73/59.67 [9163]~P5(x91631)+~P37(x91631,x91631,x91632)+P1(f335(f335(f242(x91631),f89(x91631,x91632)),x91633))+~P1(f335(f335(f242(x91631),f335(x91632,f335(f335(f95(x91631),f89(x91631,x91632)),x91633))),x91633))
% 59.73/59.67 [9362]E(x93621,x93622)+~E(f335(f135(f882(x93623),f882(x93623),f127(x93623),f107(x93623)),x93621),f335(f135(f882(x93623),f882(x93623),f127(x93623),f107(x93623)),x93622))+~E(f335(f189(f882(f882(x93623))),x93621),f335(f189(f882(f882(x93623))),x93622))+P1(f335(f335(f337(f887(f882(x93623),f882(x93623))),f731(x93621,x93622,x93623)),f335(f166(f887(f882(x93623),f882(x93623))),f335(f335(f175(f882(x93623),f882(x93623)),x93622),x93621))))
% 59.73/59.67 [9363]E(x93631,x93632)+~E(f335(f135(f882(x93633),f882(x93633),f127(x93633),f107(x93633)),x93631),f335(f135(f882(x93633),f882(x93633),f127(x93633),f107(x93633)),x93632))+~E(f335(f189(f882(f882(x93633))),x93631),f335(f189(f882(f882(x93633))),x93632))+P1(f335(f335(f337(f887(f882(x93633),f882(x93633))),f733(x93632,x93631,x93633)),f335(f166(f887(f882(x93633),f882(x93633))),f335(f335(f175(f882(x93633),f882(x93633)),x93631),x93632))))
% 59.73/59.67 [10197]~P100(x101972)+E(x101971,f188(f888(x101972,a879)))+~P1(f335(f56(x101972),x101971))+E(f10(x101972,f335(f249(x101972),f335(f335(f8(f888(x101972,a879),a879,x101972),f82(x101972)),f335(f335(f7(x101972,f888(x101972,a879),f888(x101972,a879)),f335(f335(f8(f888(x101972,f888(a879,a879)),f888(f888(x101972,a879),f888(x101972,a879)),x101972),f18(x101972,a879,a879)),f335(f335(f8(f888(x101972,a879),f888(x101972,f888(a879,a879)),x101972),f335(f8(a879,f888(a879,a879),x101972),a333)),f335(f335(f7(x101972,f888(x101972,x101972),f888(x101972,a879)),f335(f335(f8(f888(x101972,a879),f888(f888(x101972,x101972),f888(x101972,a879)),x101972),f8(x101972,a879,x101972)),a332)),f335(f104(x101972),x101973))))),f335(f335(f7(x101972,f888(x101972,a879),a879),f337(x101972)),x101971))))),f335(f335(f104(x101972),x101973),f10(x101972,x101971)))
% 59.73/59.67 [10198]~P100(x101982)+E(x101981,f188(f888(x101982,a879)))+~P1(f335(f56(x101982),x101981))+E(f13(x101982,f335(f249(x101982),f335(f335(f8(f888(x101982,a879),a879,x101982),f82(x101982)),f335(f335(f7(x101982,f888(x101982,a879),f888(x101982,a879)),f335(f335(f8(f888(x101982,f888(a879,a879)),f888(f888(x101982,a879),f888(x101982,a879)),x101982),f18(x101982,a879,a879)),f335(f335(f8(f888(x101982,a879),f888(x101982,f888(a879,a879)),x101982),f335(f8(a879,f888(a879,a879),x101982),a333)),f335(f335(f7(x101982,f888(x101982,x101982),f888(x101982,a879)),f335(f335(f8(f888(x101982,a879),f888(f888(x101982,x101982),f888(x101982,a879)),x101982),f8(x101982,a879,x101982)),a332)),f335(f95(x101982),x101983))))),f335(f335(f7(x101982,f888(x101982,a879),a879),f337(x101982)),x101981))))),f335(f335(f95(x101982),x101983),f13(x101982,x101981)))
% 59.73/59.67 [10199]~P78(x101992)+E(x101991,f188(f888(x101992,a879)))+~P1(f335(f56(x101992),x101991))+E(f14(x101992,f335(f249(x101992),f335(f335(f8(f888(x101992,a879),a879,x101992),f82(x101992)),f335(f335(f7(x101992,f888(x101992,a879),f888(x101992,a879)),f335(f335(f8(f888(x101992,f888(a879,a879)),f888(f888(x101992,a879),f888(x101992,a879)),x101992),f18(x101992,a879,a879)),f335(f335(f8(f888(x101992,a879),f888(x101992,f888(a879,a879)),x101992),f335(f8(a879,f888(a879,a879),x101992),a333)),f335(f335(f7(x101992,f888(x101992,x101992),f888(x101992,a879)),f335(f335(f8(f888(x101992,a879),f888(f888(x101992,x101992),f888(x101992,a879)),x101992),f8(x101992,a879,x101992)),a332)),f335(f75(x101992),x101993))))),f335(f335(f7(x101992,f888(x101992,a879),a879),f337(x101992)),x101991))))),f335(f335(f75(x101992),x101993),f14(x101992,x101991)))
% 59.73/59.67 [10200]~P78(x102002)+E(x102001,f188(f888(x102002,a879)))+~P1(f335(f56(x102002),x102001))+E(f15(x102002,f335(f249(x102002),f335(f335(f8(f888(x102002,a879),a879,x102002),f82(x102002)),f335(f335(f7(x102002,f888(x102002,a879),f888(x102002,a879)),f335(f335(f8(f888(x102002,f888(a879,a879)),f888(f888(x102002,a879),f888(x102002,a879)),x102002),f18(x102002,a879,a879)),f335(f335(f8(f888(x102002,a879),f888(x102002,f888(a879,a879)),x102002),f335(f8(a879,f888(a879,a879),x102002),a333)),f335(f335(f7(x102002,f888(x102002,x102002),f888(x102002,a879)),f335(f335(f8(f888(x102002,a879),f888(f888(x102002,x102002),f888(x102002,a879)),x102002),f8(x102002,a879,x102002)),a332)),f335(f75(x102002),x102003))))),f335(f335(f7(x102002,f888(x102002,a879),a879),f337(x102002)),x102001))))),f335(f335(f75(x102002),x102003),f15(x102002,x102001)))
% 59.73/59.67 [10201]~P106(x102012)+E(x102011,f188(f888(x102012,a879)))+~P1(f335(f56(x102012),x102011))+E(f12(x102012,f241(x102012),f335(f249(x102012),f335(f335(f8(f888(x102012,a879),a879,x102012),f82(x102012)),f335(f335(f7(x102012,f888(x102012,a879),f888(x102012,a879)),f335(f335(f8(f888(x102012,f888(a879,a879)),f888(f888(x102012,a879),f888(x102012,a879)),x102012),f18(x102012,a879,a879)),f335(f335(f8(f888(x102012,a879),f888(x102012,f888(a879,a879)),x102012),f335(f8(a879,f888(a879,a879),x102012),a333)),f335(f335(f7(x102012,f888(x102012,x102012),f888(x102012,a879)),f335(f335(f8(f888(x102012,a879),f888(f888(x102012,x102012),f888(x102012,a879)),x102012),f8(x102012,a879,x102012)),a332)),f335(f240(x102012),x102013))))),f335(f335(f7(x102012,f888(x102012,a879),a879),f337(x102012)),x102011))))),f335(f335(f240(x102012),x102013),f12(x102012,f241(x102012),x102011)))
% 59.73/59.67 [10202]~P106(x102022)+E(x102021,f188(f888(x102022,a879)))+~P1(f335(f56(x102022),x102021))+E(f11(x102022,f240(x102022),f335(f249(x102022),f335(f335(f8(f888(x102022,a879),a879,x102022),f82(x102022)),f335(f335(f7(x102022,f888(x102022,a879),f888(x102022,a879)),f335(f335(f8(f888(x102022,f888(a879,a879)),f888(f888(x102022,a879),f888(x102022,a879)),x102022),f18(x102022,a879,a879)),f335(f335(f8(f888(x102022,a879),f888(x102022,f888(a879,a879)),x102022),f335(f8(a879,f888(a879,a879),x102022),a333)),f335(f335(f7(x102022,f888(x102022,x102022),f888(x102022,a879)),f335(f335(f8(f888(x102022,a879),f888(f888(x102022,x102022),f888(x102022,a879)),x102022),f8(x102022,a879,x102022)),a332)),f335(f241(x102022),x102023))))),f335(f335(f7(x102022,f888(x102022,a879),a879),f337(x102022)),x102021))))),f335(f335(f241(x102022),x102023),f11(x102022,f240(x102022),x102021)))
% 59.73/59.67 [9954]~P119(x99541)+~E(x99543,f2(x99541))+~E(x99542,f2(x99541))+E(f335(f335(f75(x99541),f335(f335(f254(x99541),x99542),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f335(f335(f254(x99541),x99543),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f2(x99541))
% 59.73/59.67 [10095]~P122(x100951)+~P1(f335(f335(f242(x100951),f2(x100951)),x100953))+P1(f335(f335(f242(x100951),x100952),x100953))+~P1(f335(f335(f242(x100951),f335(f335(f254(x100951),x100952),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f335(f335(f254(x100951),x100953),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))))
% 59.73/59.67 [10096]~P122(x100961)+~P1(f335(f335(f242(x100961),f2(x100961)),x100963))+P1(f335(f335(f243(x100961),x100962),x100963))+~P1(f335(f335(f243(x100961),f335(f335(f254(x100961),x100962),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f335(f335(f254(x100961),x100963),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))))
% 59.73/59.67 [10140]~P119(x101402)+~E(x101401,f2(x101402))+~E(x101403,f2(x101402))+~P1(f335(f335(f243(x101402),f2(x101402)),f335(f335(f75(x101402),f335(f335(f254(x101402),x101403),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91))))),f335(f335(f254(x101402),x101401),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))))
% 59.73/59.67 [6013]~P106(x60131)+~P107(x60132)+~P49(x60131,x60132,x60133)+P26(x60131,x60132,x60133,x60134)
% 59.73/59.67 [9326]E(x93261,x93262)+~E(f714(x93261,x93262,x93264,x93263),f716(x93261,x93262,x93264,x93263))+P1(f335(f335(f337(f887(f882(x93263),f882(x93263))),f335(f335(f264(f882(x93263),f882(x93263)),x93262),x93261)),f140(x93263,x93264)))+P1(f335(f335(f337(f887(f882(x93263),f882(x93263))),f335(f335(f264(f882(x93263),f882(x93263)),x93261),x93262)),f140(x93263,x93264)))
% 59.73/59.67 [4885]~P66(x48852)+~E(x48854,f2(x48852))+~E(x48851,f2(x48852))+E(x48851,f335(f335(f292(x48852),x48853),x48854))
% 59.73/59.67 [4886]~P66(x48861)+~E(x48863,f2(x48861))+~E(x48864,f2(x48861))+E(f335(f335(f292(x48861),x48862),x48863),x48864)
% 59.73/59.67 [4997]~P66(x49972)+E(x49971,f2(x49972))+~E(x49973,f2(x49972))+~E(x49971,f335(f335(f292(x49972),x49974),x49973))
% 59.73/59.67 [4998]~P66(x49982)+E(x49981,f2(x49982))+~E(x49983,f2(x49982))+~E(f335(f335(f292(x49982),x49984),x49983),x49981)
% 59.73/59.67 [5179]~P116(x51792)+E(x51791,f2(x51792))+~E(f335(f335(f292(x51792),x51793),x51791),x51794)+E(x51793,f335(f335(f76(x51792),x51794),x51791))
% 59.73/59.67 [5180]~P116(x51802)+E(x51801,f2(x51802))+~E(f335(f335(f76(x51802),x51803),x51801),x51804)+E(x51803,f335(f335(f292(x51802),x51804),x51801))
% 59.73/59.67 [5181]~P116(x51812)+E(x51811,f2(x51812))+~E(f335(f335(f76(x51812),x51813),x51811),x51814)+E(x51813,f335(f335(f292(x51812),x51814),x51811))
% 59.73/59.67 [5182]~P66(x51822)+E(x51821,f2(x51822))+~E(f335(f335(f292(x51822),x51823),x51821),x51824)+E(x51823,f335(f335(f76(x51822),x51824),x51821))
% 59.73/59.67 [5183]~P66(x51832)+E(x51831,f2(x51832))+~E(f335(f335(f76(x51832),x51833),x51831),x51834)+E(x51833,f335(f335(f292(x51832),x51834),x51831))
% 59.73/59.67 [5184]~P116(x51842)+E(x51841,f2(x51842))+~E(x51843,f335(f335(f292(x51842),x51844),x51841))+E(f335(f335(f76(x51842),x51843),x51841),x51844)
% 59.73/59.67 [5185]~P116(x51852)+E(x51851,f2(x51852))+~E(x51853,f335(f335(f76(x51852),x51854),x51851))+E(f335(f335(f292(x51852),x51853),x51851),x51854)
% 59.73/59.67 [5186]~P116(x51862)+E(x51861,f2(x51862))+~E(x51863,f335(f335(f76(x51862),x51864),x51861))+E(f335(f335(f292(x51862),x51863),x51861),x51864)
% 59.73/59.67 [5187]~P66(x51872)+E(x51871,f2(x51872))+~E(x51873,f335(f335(f292(x51872),x51874),x51871))+E(f335(f335(f76(x51872),x51873),x51871),x51874)
% 59.73/59.67 [5188]~P66(x51882)+E(x51881,f2(x51882))+~E(x51883,f335(f335(f76(x51882),x51884),x51881))+E(f335(f335(f292(x51882),x51883),x51881),x51884)
% 59.73/59.67 [5212]~P66(x52122)+~E(x52121,f2(x52122))+~E(f335(f335(f76(x52122),x52121),x52124),x52123)+E(x52121,f335(f335(f292(x52122),x52123),x52124))
% 59.73/59.67 [5213]~P66(x52131)+~E(x52134,f2(x52131))+~E(x52132,f335(f335(f76(x52131),x52134),x52133))+E(f335(f335(f292(x52131),x52132),x52133),x52134)
% 59.73/59.67 [5288]~E(x52883,x52884)+~E(x52882,x52883)+~P107(x52881)+E(f305(x52881,x52882,x52883),f335(f335(f312(x52881),x52884),f188(f888(x52881,a879))))
% 59.73/59.67 [5488]~E(f137(x54882,x54881),x54884)+~E(f108(x54882,x54881),x54883)+E(x54881,f107(x54882))+E(f335(f335(f127(x54882),x54883),f335(f335(f144(x54882),x54884),f107(x54882))),x54881)
% 59.73/59.67 [6103]~P122(x61033)+E(x61031,x61032)+~E(f335(f335(f254(x61033),x61034),x61031),f335(f335(f254(x61033),x61034),x61032))+~P1(f335(f335(f243(x61033),f73(x61033)),x61034))
% 59.73/59.67 [6104]E(x61041,x61042)+~E(f335(f335(f312(x61043),x61044),x61041),f335(f335(f312(x61043),x61044),x61042))+P1(f335(f335(f337(x61043),x61044),x61042))+P1(f335(f335(f337(x61043),x61044),x61041))
% 59.73/59.67 [6142]E(f335(x61421,x61422),f73(a881))+~E(f335(f335(f9(x61423,a881),x61421),x61424),f73(a881))+~P1(f335(f56(x61423),x61424))+~P1(f335(f335(f337(x61423),x61422),x61424))
% 59.73/59.67 [6143]E(f335(x61431,x61432),f2(a881))+~E(f335(f335(f6(x61433,a881),x61431),x61434),f2(a881))+~P1(f335(f56(x61433),x61434))+~P1(f335(f335(f337(x61433),x61432),x61434))
% 59.73/59.67 [6362]~P107(x63621)+~P1(f335(f335(f242(x63621),x63624),x63623))+P1(f335(f335(f242(x63621),x63622),x63623))+~P1(f335(f335(f242(x63621),x63622),x63624))
% 59.73/59.67 [6363]~P2(x63631)+~P1(f335(f335(f242(x63631),x63632),x63634))+P1(f335(f335(f242(x63631),x63632),x63633))+~P1(f335(f335(f242(x63631),x63634),x63633))
% 59.73/59.67 [6364]~P107(x63641)+~P1(f335(f335(f243(x63641),x63644),x63643))+P1(f335(f335(f243(x63641),x63642),x63643))+~P1(f335(f335(f242(x63641),x63642),x63644))
% 59.73/59.67 [6365]~P107(x63651)+~P1(f335(f335(f243(x63651),x63652),x63654))+P1(f335(f335(f243(x63651),x63652),x63653))+~P1(f335(f335(f242(x63651),x63654),x63653))
% 59.73/59.67 [6366]~P107(x63661)+~P1(f335(f335(f243(x63661),x63664),x63663))+P1(f335(f335(f243(x63661),x63662),x63663))+~P1(f335(f335(f243(x63661),x63662),x63664))
% 59.73/59.67 [6367]~P2(x63671)+~P1(f335(f335(f243(x63671),x63672),x63674))+P1(f335(f335(f243(x63671),x63672),x63673))+~P1(f335(f335(f242(x63671),x63674),x63673))
% 59.73/59.67 [6368]~P2(x63681)+~P1(f335(f335(f243(x63681),x63684),x63683))+P1(f335(f335(f243(x63681),x63682),x63683))+~P1(f335(f335(f242(x63681),x63682),x63684))
% 59.73/59.67 [6369]~P2(x63691)+~P1(f335(f335(f243(x63691),x63692),x63694))+P1(f335(f335(f243(x63691),x63692),x63693))+~P1(f335(f335(f243(x63691),x63694),x63693))
% 59.73/59.67 [6452]~P34(x64524,x64523,x64522)+E(x64521,f792(x64522,x64523,x64524))+~P1(f335(x64523,x64521))+~P1(f335(f335(f337(x64524),x64521),f335(f166(x64524),x64522)))
% 59.73/59.67 [6453]~P34(x64534,x64533,x64532)+E(x64531,f793(x64532,x64533,x64534))+~P1(f335(x64533,x64531))+~P1(f335(f335(f337(x64534),x64531),f335(f166(x64534),x64532)))
% 59.73/59.67 [6603]~P5(x66031)+~P1(f335(f335(f242(x66031),x66032),f32(x66031,x66034)))+P1(f335(f335(f242(x66031),x66032),x66033))+~P1(f335(f335(f337(x66031),x66033),x66034))
% 59.73/59.67 [6751]~P106(x67511)+~P15(x67511,f335(f335(f144(x67511),x67512),x67514))+~P1(f335(f335(f337(x67511),x67513),f335(f166(x67511),x67514)))+P1(f335(f335(f242(x67511),x67512),x67513))
% 59.73/59.67 [6752]~P106(x67521)+~P15(x67521,f335(f335(f144(x67521),x67522),x67524))+~P1(f335(f335(f337(x67521),x67523),f335(f166(x67521),x67524)))+P1(f335(f335(f242(x67521),x67522),x67523))
% 59.73/59.67 [6842]~P5(x68421)+~P1(f335(f335(f242(x68421),f31(x68421,x68424)),x68423))+P1(f335(f335(f242(x68421),x68422),x68423))+~P1(f335(f335(f337(x68421),x68422),x68424))
% 59.73/59.67 [7246]~P106(x72461)+E(f335(f335(f104(f888(x72461,a879)),f335(f304(x72461,x72462),x72463)),f335(f304(x72461,x72463),x72464)),f335(f304(x72461,x72462),x72464))+~P1(f335(f335(f242(x72461),x72463),x72464))+~P1(f335(f335(f242(x72461),x72462),x72463))
% 59.73/59.67 [7287]P34(x72871,x72872,x72873)+~E(f796(x72873,x72872,x72871,x72874),x72874)+~P1(f335(x72872,x72874))+~P1(f335(f335(f337(x72871),x72874),f335(f166(x72871),x72873)))
% 59.73/59.67 [7288]P34(x72881,x72882,x72883)+~E(f809(x72883,x72882,x72881,x72884),x72884)+~P1(f335(x72882,x72884))+~P1(f335(f335(f337(x72881),x72884),f335(f166(x72881),x72883)))
% 59.73/59.67 [7363]~P106(x73631)+E(f335(f335(f104(f888(x73631,a879)),f335(f304(x73631,x73632),x73633)),f305(x73631,x73633,x73634)),f305(x73631,x73632,x73634))+~P1(f335(f335(f242(x73631),x73633),x73634))+~P1(f335(f335(f242(x73631),x73632),x73633))
% 59.73/59.67 [7426]~P106(x74261)+E(f335(f335(f104(f888(x74261,a879)),f308(x74261,x74262,x74263)),f335(f304(x74261,x74263),x74264)),f308(x74261,x74262,x74264))+~P1(f335(f335(f242(x74261),x74263),x74264))+~P1(f335(f335(f243(x74261),x74262),x74263))
% 59.73/59.67 [7446]~P106(x74461)+E(f335(f335(f104(f888(x74461,a879)),f305(x74461,x74462,x74463)),f308(x74461,x74463,x74464)),f335(f304(x74461,x74462),x74464))+~P1(f335(f335(f242(x74461),x74462),x74463))+~P1(f335(f335(f243(x74461),x74463),x74464))
% 59.73/59.67 [7478]~P106(x74781)+E(f335(f335(f104(f888(x74781,a879)),f308(x74781,x74782,x74783)),f305(x74781,x74783,x74784)),f307(x74781,x74782,x74784))+~P1(f335(f335(f242(x74781),x74783),x74784))+~P1(f335(f335(f243(x74781),x74782),x74783))
% 59.73/59.67 [7479]~P106(x74791)+E(f335(f335(f104(f888(x74791,a879)),f307(x74791,x74792,x74793)),f308(x74791,x74793,x74794)),f308(x74791,x74792,x74794))+~P1(f335(f335(f242(x74791),x74792),x74793))+~P1(f335(f335(f243(x74791),x74793),x74794))
% 59.73/59.67 [7480]~P106(x74801)+E(f335(f335(f104(f888(x74801,a879)),f307(x74801,x74802,x74803)),f307(x74801,x74803,x74804)),f307(x74801,x74802,x74804))+~P1(f335(f335(f242(x74801),x74803),x74804))+~P1(f335(f335(f242(x74801),x74802),x74803))
% 59.73/59.67 [7481]~P106(x74811)+E(f335(f335(f104(f888(x74811,a879)),f305(x74811,x74812,x74813)),f307(x74811,x74813,x74814)),f305(x74811,x74812,x74814))+~P1(f335(f335(f242(x74811),x74813),x74814))+~P1(f335(f335(f242(x74811),x74812),x74813))
% 59.73/59.67 [8277]P26(x82771,x82772,f347(x82773,x82772,x82774,x82771),x82774)+~P1(f335(f56(x82772),x82773))+~P1(f335(f56(x82771),x82774))+~P1(f335(f335(f242(a881),f335(f29(x82771),x82774)),f335(f29(x82772),x82773)))
% 59.73/59.67 [8298]P34(x82981,x82982,x82983)+~P1(f335(x82982,x82984))+P1(f335(x82982,f796(x82983,x82982,x82981,x82984)))+~P1(f335(f335(f337(x82981),x82984),f335(f166(x82981),x82983)))
% 59.73/59.67 [8299]P34(x82991,x82992,x82993)+~P1(f335(x82992,x82994))+P1(f335(x82992,f809(x82993,x82992,x82991,x82994)))+~P1(f335(f335(f337(x82991),x82994),f335(f166(x82991),x82993)))
% 59.73/59.67 [8350]~P73(x83501)+~E(f335(x83503,f581(x83503,x83504,x83502,x83501)),f73(x83501))+E(f335(f335(f335(f60(x83501,x83502,f76(x83501)),x83503),f73(x83501)),x83504),f73(x83501))+~P1(f335(f56(x83502),x83504))
% 59.73/59.67 [8619]~P122(x86191)+~P1(f335(f335(f242(x86191),f2(x86191)),x86193))+P1(f335(f335(f242(x86191),x86192),x86193))+~P1(f335(f335(f242(x86191),f335(f335(f254(x86191),x86192),f335(a106,x86194))),f335(f335(f254(x86191),x86193),f335(a106,x86194))))
% 59.73/59.67 [8782]~P37(f888(x87824,a879),f888(x87824,a879),x87823)+P1(f335(x87821,x87822))+~P1(f335(x87821,f533(x87821,x87823,x87822,x87824)))+~P1(f335(f335(f337(x87824),x87822),f89(f888(x87824,a879),x87823)))
% 59.73/59.67 [8920]P34(x89201,x89202,x89203)+~P1(f335(x89202,x89204))+~P1(f335(f335(f337(x89201),x89204),f335(f166(x89201),x89203)))+P1(f335(f335(f337(x89201),f796(x89203,x89202,x89201,x89204)),f335(f166(x89201),x89203)))
% 59.73/59.67 [8921]P34(x89211,x89212,x89213)+~P1(f335(x89212,x89214))+~P1(f335(f335(f337(x89211),x89214),f335(f166(x89211),x89213)))+P1(f335(f335(f337(x89211),f809(x89213,x89212,x89211,x89214)),f335(f166(x89211),x89213)))
% 59.73/59.67 [9000]~P73(x90001)+E(f335(f335(f335(f60(x90001,x90002,f76(x90001)),x90003),f73(x90001)),x90004),f73(x90001))+~P1(f335(f56(x90002),x90004))+P1(f335(f335(f337(x90002),f581(x90003,x90004,x90002,x90001)),x90004))
% 59.73/59.67 [9492]~P1(f335(f335(f242(a1),x94924),f2(a1)))+P1(f335(f335(f242(a1),f335(f335(f75(a1),f335(f335(f76(a1),x94921),f39(a1,x94922,x94923))),x94924)),f2(a1)))+~P1(f335(f335(f243(a1),f2(a1)),x94923))+~P1(f335(f335(f243(a1),x94921),x94924))
% 59.73/59.67 [9947]~P1(f335(f56(x99471),x99472))+~P1(f335(f335(f337(x99471),x99474),x99472))+~P1(f335(f335(f337(x99471),x99473),x99472))+P1(f335(f335(f243(a881),f335(f29(x99471),f335(f335(f23(f888(x99471,a879)),f335(f335(f23(f888(x99471,a879)),x99472),f335(f335(f312(x99471),x99473),f188(f888(x99471,a879))))),f335(f335(f312(x99471),x99474),f188(f888(x99471,a879)))))),f335(f29(x99471),x99472)))
% 59.73/59.67 [6956]~P102(x69561)+~P1(f335(f335(f242(x69561),x69562),x69564))+~P1(f335(f335(f242(x69561),x69562),x69563))+P1(f335(f335(f242(x69561),x69562),f335(f335(f95(x69561),x69563),x69564)))
% 59.73/59.67 [6957]~P102(x69571)+~P1(f335(f335(f242(x69571),x69572),x69574))+~P1(f335(f335(f242(x69571),x69572),x69573))+P1(f335(f335(f242(x69571),x69572),f335(f335(f95(x69571),x69573),x69574)))
% 59.73/59.67 [6958]~P102(x69581)+~P1(f335(f335(f242(x69581),x69582),x69584))+~P1(f335(f335(f242(x69581),x69582),x69583))+P1(f335(f335(f242(x69581),x69582),f335(f335(f95(x69581),x69583),x69584)))
% 59.73/59.67 [6959]~P106(x69591)+~P1(f335(f335(f242(x69591),x69592),x69594))+~P1(f335(f335(f242(x69591),x69592),x69593))+P1(f335(f335(f242(x69591),x69592),f335(f335(f240(x69591),x69593),x69594)))
% 59.73/59.67 [6960]~P106(x69601)+~P1(f335(f335(f242(x69601),x69602),x69604))+~P1(f335(f335(f242(x69601),x69602),x69603))+P1(f335(f335(f242(x69601),x69602),f335(f335(f240(x69601),x69603),x69604)))
% 59.73/59.67 [6961]~P106(x69611)+~P1(f335(f335(f242(x69611),x69612),x69614))+~P1(f335(f335(f242(x69611),x69612),x69613))+P1(f335(f335(f242(x69611),x69612),f335(f335(f240(x69611),x69613),x69614)))
% 59.73/59.67 [6962]~P106(x69621)+~P1(f335(f335(f243(x69621),x69622),x69624))+~P1(f335(f335(f243(x69621),x69622),x69623))+P1(f335(f335(f243(x69621),x69622),f335(f335(f240(x69621),x69623),x69624)))
% 59.73/59.67 [6981]~P67(x69812)+E(x69811,f2(x69812))+E(f335(f335(f292(x69812),f335(f335(f254(x69812),x69811),x69813)),f335(f335(f254(x69812),x69811),x69814)),f335(f335(f254(x69812),x69811),f335(f335(f23(a881),x69813),x69814)))+~P1(f335(f335(f242(a881),x69814),x69813))
% 59.73/59.67 [7025]~P106(x70251)+~P15(x70251,f335(f335(f144(x70251),x70253),x70254))+P15(x70251,f335(f335(f144(x70251),x70252),f335(f335(f144(x70251),x70253),x70254)))+~P1(f335(f335(f242(x70251),x70252),x70253))
% 59.73/59.67 [7026]~P106(x70261)+~P15(x70261,f335(f335(f144(x70261),x70263),x70264))+P15(x70261,f335(f335(f144(x70261),x70262),f335(f335(f144(x70261),x70263),x70264)))+~P1(f335(f335(f242(x70261),x70262),x70263))
% 59.73/59.67 [7064]~P90(x70641)+~P1(f335(f335(f242(x70641),f2(x70641)),x70644))+~P1(f335(f335(f242(x70641),x70642),x70643))+P1(f335(f335(f242(x70641),x70642),f335(f335(f75(x70641),x70643),x70644)))
% 59.73/59.67 [7065]~P90(x70651)+~P1(f335(f335(f242(x70651),f2(x70651)),x70653))+~P1(f335(f335(f242(x70651),x70652),x70654))+P1(f335(f335(f242(x70651),x70652),f335(f335(f75(x70651),x70653),x70654)))
% 59.73/59.67 [7066]~P122(x70661)+~P1(f335(f335(f243(x70661),f2(x70661)),x70663))+~P1(f335(f335(f243(x70661),x70662),x70664))+P1(f335(f335(f243(x70661),x70662),f335(f335(f75(x70661),x70663),x70664)))
% 59.73/59.67 [7067]~P90(x70671)+~P1(f335(f335(f242(x70671),x70672),x70674))+~P1(f335(f335(f243(x70671),f2(x70671)),x70673))+P1(f335(f335(f243(x70671),x70672),f335(f335(f75(x70671),x70673),x70674)))
% 59.73/59.67 [7068]~P90(x70681)+~P1(f335(f335(f242(x70681),f2(x70681)),x70683))+~P1(f335(f335(f243(x70681),x70682),x70684))+P1(f335(f335(f243(x70681),x70682),f335(f335(f75(x70681),x70683),x70684)))
% 59.73/59.67 [7108]~P106(x71081)+P1(f335(f335(f242(x71081),x71082),x71083))+P1(f335(f335(f242(x71081),x71082),x71084))+~P1(f335(f335(f242(x71081),x71082),f335(f335(f241(x71081),x71084),x71083)))
% 59.73/59.67 [7109]~P106(x71091)+P1(f335(f335(f243(x71091),x71092),x71093))+P1(f335(f335(f243(x71091),x71092),x71094))+~P1(f335(f335(f243(x71091),x71092),f335(f335(f241(x71091),x71094),x71093)))
% 59.73/59.67 [7399]~P107(x73992)+~P4(x73991)+~P1(f335(f335(f243(f888(x73991,x73992)),x73993),x73994))+P1(f335(f335(f242(f888(x73991,x73992)),x73993),x73994))
% 59.73/59.67 [7769]~P69(x77691)+~P1(f335(f335(f243(x77691),x77694),f2(x77691)))+~P1(f335(f335(f242(x77691),x77693),f335(f335(f292(x77691),x77692),x77694)))+P1(f335(f335(f242(x77691),x77692),f335(f335(f76(x77691),x77693),x77694)))
% 59.73/59.67 [7770]~P69(x77701)+~P1(f335(f335(f243(x77701),x77704),f2(x77701)))+~P1(f335(f335(f242(x77701),x77703),f335(f335(f76(x77701),x77702),x77704)))+P1(f335(f335(f242(x77701),x77702),f335(f335(f292(x77701),x77703),x77704)))
% 59.73/59.67 [7771]~P69(x77711)+~P1(f335(f335(f243(x77711),x77714),f2(x77711)))+~P1(f335(f335(f243(x77711),x77713),f335(f335(f292(x77711),x77712),x77714)))+P1(f335(f335(f243(x77711),x77712),f335(f335(f76(x77711),x77713),x77714)))
% 59.73/59.67 [7772]~P69(x77721)+~P1(f335(f335(f243(x77721),x77724),f2(x77721)))+~P1(f335(f335(f243(x77721),x77723),f335(f335(f76(x77721),x77722),x77724)))+P1(f335(f335(f243(x77721),x77722),f335(f335(f292(x77721),x77723),x77724)))
% 59.73/59.67 [7878]~P125(x78781)+~P1(f335(f335(f242(x78781),x78782),f2(x78781)))+~P1(f335(f335(f242(x78781),x78784),x78783))+P1(f335(f335(f242(x78781),f335(f335(f76(x78781),x78782),x78783)),f335(f335(f76(x78781),x78782),x78784)))
% 59.73/59.67 [7879]~P123(x78791)+~P1(f335(f335(f243(x78791),x78792),f2(x78791)))+~P1(f335(f335(f242(x78791),x78794),x78793))+P1(f335(f335(f242(x78791),f335(f335(f76(x78791),x78792),x78793)),f335(f335(f76(x78791),x78792),x78794)))
% 59.73/59.67 [7880]~P125(x78801)+~P1(f335(f335(f242(x78801),x78803),f2(x78801)))+~P1(f335(f335(f242(x78801),x78804),x78802))+P1(f335(f335(f242(x78801),f335(f335(f76(x78801),x78802),x78803)),f335(f335(f76(x78801),x78804),x78803)))
% 59.73/59.67 [7881]~P68(x78811)+~P1(f335(f335(f242(x78811),x78813),f2(x78811)))+~P1(f335(f335(f242(x78811),x78814),x78812))+P1(f335(f335(f242(x78811),f335(f335(f292(x78811),x78812),x78813)),f335(f335(f292(x78811),x78814),x78813)))
% 59.73/59.67 [7882]~P123(x78821)+~P1(f335(f335(f243(x78821),x78822),f2(x78821)))+~P1(f335(f335(f243(x78821),x78824),x78823))+P1(f335(f335(f243(x78821),f335(f335(f76(x78821),x78822),x78823)),f335(f335(f76(x78821),x78822),x78824)))
% 59.73/59.67 [7883]~P123(x78831)+~P1(f335(f335(f243(x78831),x78832),f2(x78831)))+~P1(f335(f335(f243(x78831),x78834),x78833))+P1(f335(f335(f243(x78831),f335(f335(f76(x78831),x78832),x78833)),f335(f335(f76(x78831),x78832),x78834)))
% 59.73/59.67 [7884]~P123(x78841)+~P1(f335(f335(f243(x78841),x78843),f2(x78841)))+~P1(f335(f335(f243(x78841),x78844),x78842))+P1(f335(f335(f243(x78841),f335(f335(f76(x78841),x78842),x78843)),f335(f335(f76(x78841),x78844),x78843)))
% 59.73/59.67 [7885]~P123(x78851)+~P1(f335(f335(f243(x78851),x78853),f2(x78851)))+~P1(f335(f335(f243(x78851),x78854),x78852))+P1(f335(f335(f243(x78851),f335(f335(f76(x78851),x78852),x78853)),f335(f335(f76(x78851),x78854),x78853)))
% 59.73/59.67 [7886]~P123(x78861)+~P1(f335(f335(f243(x78861),x78862),f2(x78861)))+~P1(f335(f335(f243(x78861),x78864),x78863))+P1(f335(f335(f243(x78861),f335(f335(f76(x78861),x78862),x78863)),f335(f335(f76(x78861),x78862),x78864)))
% 59.73/59.67 [7887]~P69(x78871)+~P1(f335(f335(f243(x78871),x78873),f2(x78871)))+~P1(f335(f335(f243(x78871),x78874),x78872))+P1(f335(f335(f243(x78871),f335(f335(f292(x78871),x78872),x78873)),f335(f335(f292(x78871),x78874),x78873)))
% 59.73/59.67 [7888]~P122(x78881)+~P1(f335(f335(f243(x78881),f73(x78881)),x78882))+~P1(f335(f335(f242(a881),x78883),x78884))+P1(f335(f335(f242(x78881),f335(f335(f254(x78881),x78882),x78883)),f335(f335(f254(x78881),x78882),x78884)))
% 59.73/59.67 [7889]~P122(x78891)+~P1(f335(f335(f242(x78891),f73(x78891)),x78892))+~P1(f335(f335(f242(a881),x78893),x78894))+P1(f335(f335(f242(x78891),f335(f335(f254(x78891),x78892),x78893)),f335(f335(f254(x78891),x78892),x78894)))
% 59.73/59.67 [7890]~P122(x78901)+~P1(f335(f335(f243(x78901),f73(x78901)),x78902))+~P1(f335(f335(f243(a881),x78903),x78904))+P1(f335(f335(f243(x78901),f335(f335(f254(x78901),x78902),x78903)),f335(f335(f254(x78901),x78902),x78904)))
% 59.73/59.67 [7891]~P122(x78911)+~P1(f335(f335(f243(x78911),f73(x78911)),x78912))+~P1(f335(f335(f243(a881),x78913),x78914))+P1(f335(f335(f243(x78911),f335(f335(f254(x78911),x78912),x78913)),f335(f335(f254(x78911),x78912),x78914)))
% 59.73/59.67 [7920]P1(f335(f335(f243(a881),f2(a881)),f335(x79201,x79202)))+~P1(f335(f56(x79203),x79204))+~P1(f335(f335(f337(x79203),x79202),x79204))+~P1(f335(f335(f243(a881),f2(a881)),f335(f335(f9(x79203,a881),x79201),x79204)))
% 59.73/59.67 [7928]~P123(x79281)+~P1(f335(f335(f243(x79281),f2(x79281)),x79282))+~P1(f335(f335(f242(x79281),x79283),x79284))+P1(f335(f335(f242(x79281),f335(f335(f76(x79281),x79282),x79283)),f335(f335(f76(x79281),x79282),x79284)))
% 59.73/59.67 [7929]~P134(x79291)+~P1(f335(f335(f242(x79291),x79293),x79294))+~P1(f335(f335(f242(x79291),f2(x79291)),x79292))+P1(f335(f335(f242(x79291),f335(f335(f76(x79291),x79292),x79293)),f335(f335(f76(x79291),x79292),x79294)))
% 59.73/59.67 [7930]~P133(x79301)+~P1(f335(f335(f242(x79301),x79303),x79304))+~P1(f335(f335(f242(x79301),f2(x79301)),x79302))+P1(f335(f335(f242(x79301),f335(f335(f76(x79301),x79302),x79303)),f335(f335(f76(x79301),x79302),x79304)))
% 59.73/59.67 [7931]~P134(x79311)+~P1(f335(f335(f242(x79311),x79312),x79314))+~P1(f335(f335(f242(x79311),f2(x79311)),x79313))+P1(f335(f335(f242(x79311),f335(f335(f76(x79311),x79312),x79313)),f335(f335(f76(x79311),x79314),x79313)))
% 59.73/59.67 [7932]~P122(x79321)+~P1(f335(f335(f242(x79321),x79322),x79324))+~P1(f335(f335(f242(x79321),f2(x79321)),x79322))+P1(f335(f335(f242(x79321),f335(f335(f254(x79321),x79322),x79323)),f335(f335(f254(x79321),x79324),x79323)))
% 59.73/59.67 [7933]~P68(x79331)+~P1(f335(f335(f242(x79331),x79332),x79334))+~P1(f335(f335(f242(x79331),f2(x79331)),x79333))+P1(f335(f335(f242(x79331),f335(f335(f292(x79331),x79332),x79333)),f335(f335(f292(x79331),x79334),x79333)))
% 59.73/59.67 [7934]~P123(x79341)+~P1(f335(f335(f243(x79341),x79343),x79344))+~P1(f335(f335(f243(x79341),f2(x79341)),x79342))+P1(f335(f335(f243(x79341),f335(f335(f76(x79341),x79342),x79343)),f335(f335(f76(x79341),x79342),x79344)))
% 59.73/59.67 [7935]~P120(x79351)+~P1(f335(f335(f243(x79351),x79353),x79354))+~P1(f335(f335(f243(x79351),f2(x79351)),x79352))+P1(f335(f335(f243(x79351),f335(f335(f76(x79351),x79352),x79353)),f335(f335(f76(x79351),x79352),x79354)))
% 59.73/59.67 [7936]~P127(x79361)+~P1(f335(f335(f243(x79361),x79363),x79364))+~P1(f335(f335(f243(x79361),f2(x79361)),x79362))+P1(f335(f335(f243(x79361),f335(f335(f76(x79361),x79362),x79363)),f335(f335(f76(x79361),x79362),x79364)))
% 59.73/59.67 [7937]~P123(x79371)+~P1(f335(f335(f243(x79371),x79372),x79374))+~P1(f335(f335(f243(x79371),f2(x79371)),x79373))+P1(f335(f335(f243(x79371),f335(f335(f76(x79371),x79372),x79373)),f335(f335(f76(x79371),x79374),x79373)))
% 59.73/59.67 [7938]~P127(x79381)+~P1(f335(f335(f243(x79381),x79382),x79384))+~P1(f335(f335(f243(x79381),f2(x79381)),x79383))+P1(f335(f335(f243(x79381),f335(f335(f76(x79381),x79382),x79383)),f335(f335(f76(x79381),x79384),x79383)))
% 59.73/59.67 [7939]~P123(x79391)+~P1(f335(f335(f243(x79391),x79393),x79394))+~P1(f335(f335(f243(x79391),f2(x79391)),x79392))+P1(f335(f335(f243(x79391),f335(f335(f76(x79391),x79392),x79393)),f335(f335(f76(x79391),x79392),x79394)))
% 59.73/59.67 [7940]~P69(x79401)+~P1(f335(f335(f243(x79401),x79402),x79404))+~P1(f335(f335(f243(x79401),f2(x79401)),x79403))+P1(f335(f335(f243(x79401),f335(f335(f292(x79401),x79402),x79403)),f335(f335(f292(x79401),x79404),x79403)))
% 59.73/59.67 [7988]~P108(x79882)+P1(f335(f335(f243(f888(x79881,x79882)),x79884),x79883))+~P1(f335(f335(f242(f888(x79881,x79882)),x79884),x79883))+P1(f335(f335(f242(f888(x79881,x79882)),x79883),x79884))
% 59.73/59.67 [8029]P1(f335(f335(f337(x80291),x80292),x80293))+P1(f335(f335(f337(x80291),x80292),x80294))+~P1(f335(f335(f242(f888(x80291,a879)),x80294),x80293))+P1(f335(f335(f243(f888(x80291,a879)),x80294),f335(f335(f312(x80291),x80292),x80293)))
% 59.73/59.67 [8184]P1(f335(f335(f337(x81841),x81842),x81843))+P1(f335(f335(f337(x81841),x81842),x81844))+~P1(f335(f335(f243(f888(x81841,a879)),x81844),f335(f335(f312(x81841),x81842),x81843)))+P1(f335(f335(f242(f888(x81841,a879)),x81844),x81843))
% 59.73/59.67 [8192]~P4(x81921)+P11(x81921,x81922,x81923)+~P1(f335(x81922,x81924))+~P1(f335(f335(f337(f882(x81921)),x81924),f335(f166(f882(x81921)),f49(x81921,x81923,f50(x81921)))))
% 59.73/59.67 [8202]~P12(x82023,x82021,x82024)+~P4(x82023)+P1(f335(x82021,x82022))+~P1(f335(f335(f337(f882(x82023)),x82022),f335(f166(f882(x82023)),f49(x82023,x82024,f50(x82023)))))
% 59.73/59.67 [8254]~P123(x82541)+P1(f335(f335(f243(x82541),x82543),x82542))+P1(f335(f335(f243(x82541),x82542),x82543))+~P1(f335(f335(f243(x82541),f335(f335(f76(x82541),x82544),x82542)),f335(f335(f76(x82541),x82544),x82543)))
% 59.73/59.67 [8255]~P123(x82551)+P1(f335(f335(f243(x82551),x82553),x82552))+P1(f335(f335(f243(x82551),x82552),x82553))+~P1(f335(f335(f243(x82551),f335(f335(f76(x82551),x82552),x82554)),f335(f335(f76(x82551),x82553),x82554)))
% 59.73/59.67 [8266]~P123(x82661)+P1(f335(f335(f243(x82661),x82664),f2(x82661)))+P1(f335(f335(f243(x82661),x82662),x82663))+~P1(f335(f335(f243(x82661),f335(f335(f76(x82661),x82662),x82664)),f335(f335(f76(x82661),x82663),x82664)))
% 59.73/59.67 [8267]~P123(x82671)+P1(f335(f335(f243(x82671),x82674),f2(x82671)))+P1(f335(f335(f243(x82671),x82672),x82673))+~P1(f335(f335(f243(x82671),f335(f335(f76(x82671),x82674),x82672)),f335(f335(f76(x82671),x82674),x82673)))
% 59.73/59.67 [8271]~P123(x82711)+P1(f335(f335(f243(x82711),x82712),x82713))+P1(f335(f335(f243(x82711),f2(x82711)),x82714))+~P1(f335(f335(f243(x82711),f335(f335(f76(x82711),x82714),x82713)),f335(f335(f76(x82711),x82714),x82712)))
% 59.73/59.67 [8272]~P123(x82721)+P1(f335(f335(f243(x82721),x82722),x82723))+P1(f335(f335(f243(x82721),f2(x82721)),x82724))+~P1(f335(f335(f243(x82721),f335(f335(f76(x82721),x82723),x82724)),f335(f335(f76(x82721),x82722),x82724)))
% 59.73/59.67 [8285]~P123(x82851)+P1(f335(f335(f243(x82851),x82852),f2(x82851)))+P1(f335(f335(f243(x82851),f2(x82851)),x82852))+~P1(f335(f335(f243(x82851),f335(f335(f76(x82851),x82853),x82852)),f335(f335(f76(x82851),x82854),x82852)))
% 59.73/59.67 [8286]~P123(x82861)+P1(f335(f335(f243(x82861),x82862),f2(x82861)))+P1(f335(f335(f243(x82861),f2(x82861)),x82862))+~P1(f335(f335(f243(x82861),f335(f335(f76(x82861),x82862),x82863)),f335(f335(f76(x82861),x82862),x82864)))
% 59.73/59.67 [8315]~P123(x83151)+~P1(f335(f335(f243(x83151),x83154),f2(x83151)))+P1(f335(f335(f242(x83151),x83152),x83153))+~P1(f335(f335(f242(x83151),f335(f335(f76(x83151),x83154),x83153)),f335(f335(f76(x83151),x83154),x83152)))
% 59.73/59.67 [8316]~P123(x83161)+~P1(f335(f335(f243(x83161),x83164),f2(x83161)))+P1(f335(f335(f243(x83161),x83162),x83163))+~P1(f335(f335(f243(x83161),f335(f335(f76(x83161),x83164),x83163)),f335(f335(f76(x83161),x83164),x83162)))
% 59.73/59.67 [8325]~P122(x83253)+~P1(f335(f335(f243(x83253),f73(x83253)),x83254))+P1(f335(f335(f242(a881),x83251),x83252))+~P1(f335(f335(f242(x83253),f335(f335(f254(x83253),x83254),x83251)),f335(f335(f254(x83253),x83254),x83252)))
% 59.73/59.67 [8326]~P122(x83263)+~P1(f335(f335(f243(x83263),f73(x83263)),x83264))+P1(f335(f335(f242(a881),x83261),x83262))+~P1(f335(f335(f242(x83263),f335(f335(f254(x83263),x83264),x83261)),f335(f335(f254(x83263),x83264),x83262)))
% 59.73/59.67 [8327]~P122(x83273)+~P1(f335(f335(f243(x83273),f73(x83273)),x83274))+P1(f335(f335(f243(a881),x83271),x83272))+~P1(f335(f335(f243(x83273),f335(f335(f254(x83273),x83274),x83271)),f335(f335(f254(x83273),x83274),x83272)))
% 59.73/59.67 [8328]~P122(x83283)+~P1(f335(f335(f243(x83283),f73(x83283)),x83284))+P1(f335(f335(f243(a881),x83281),x83282))+~P1(f335(f335(f243(x83283),f335(f335(f254(x83283),x83284),x83281)),f335(f335(f254(x83283),x83284),x83282)))
% 59.73/59.67 [8338]~P123(x83381)+P1(f335(f335(f242(x83381),x83382),x83383))+~P1(f335(f335(f243(x83381),f2(x83381)),x83384))+~P1(f335(f335(f242(x83381),f335(f335(f76(x83381),x83384),x83382)),f335(f335(f76(x83381),x83384),x83383)))
% 59.73/59.67 [8339]~P127(x83391)+P1(f335(f335(f242(x83391),x83392),x83393))+~P1(f335(f335(f243(x83391),f2(x83391)),x83394))+~P1(f335(f335(f242(x83391),f335(f335(f76(x83391),x83394),x83392)),f335(f335(f76(x83391),x83394),x83393)))
% 59.73/59.67 [8340]~P127(x83401)+P1(f335(f335(f242(x83401),x83402),x83403))+~P1(f335(f335(f243(x83401),f2(x83401)),x83404))+~P1(f335(f335(f242(x83401),f335(f335(f76(x83401),x83402),x83404)),f335(f335(f76(x83401),x83403),x83404)))
% 59.73/59.67 [8341]~P123(x83411)+P1(f335(f335(f243(x83411),x83412),x83413))+~P1(f335(f335(f243(x83411),f2(x83411)),x83414))+~P1(f335(f335(f243(x83411),f335(f335(f76(x83411),x83414),x83412)),f335(f335(f76(x83411),x83414),x83413)))
% 59.73/59.67 [8342]~P127(x83421)+P1(f335(f335(f243(x83421),x83422),x83423))+~P1(f335(f335(f242(x83421),f2(x83421)),x83424))+~P1(f335(f335(f243(x83421),f335(f335(f76(x83421),x83424),x83422)),f335(f335(f76(x83421),x83424),x83423)))
% 59.73/59.67 [8343]~P128(x83431)+P1(f335(f335(f243(x83431),x83432),x83433))+~P1(f335(f335(f242(x83431),f2(x83431)),x83434))+~P1(f335(f335(f243(x83431),f335(f335(f76(x83431),x83434),x83432)),f335(f335(f76(x83431),x83434),x83433)))
% 59.73/59.67 [8344]~P122(x83441)+~P1(f335(f335(f242(x83441),f2(x83441)),x83443))+P1(f335(f335(f243(x83441),x83442),x83443))+~P1(f335(f335(f243(x83441),f335(f335(f254(x83441),x83442),x83444)),f335(f335(f254(x83441),x83443),x83444)))
% 59.73/59.67 [8345]~P127(x83451)+P1(f335(f335(f243(x83451),x83452),x83453))+~P1(f335(f335(f242(x83451),f2(x83451)),x83454))+~P1(f335(f335(f243(x83451),f335(f335(f76(x83451),x83452),x83454)),f335(f335(f76(x83451),x83453),x83454)))
% 59.73/59.67 [8346]~P128(x83461)+P1(f335(f335(f243(x83461),x83462),x83463))+~P1(f335(f335(f242(x83461),f2(x83461)),x83464))+~P1(f335(f335(f243(x83461),f335(f335(f76(x83461),x83462),x83464)),f335(f335(f76(x83461),x83463),x83464)))
% 59.73/59.67 [8390]P1(f335(f335(f337(x83901),x83902),x83903))+~P1(f335(f335(f242(f888(x83901,a879)),x83903),x83904))+~P1(f335(f335(f243(f888(x83901,a879)),x83903),x83904))+P1(f335(f335(f243(f888(x83901,a879)),x83903),f335(f335(f312(x83901),x83902),x83904)))
% 59.73/59.67 [8642]~P4(x86421)+~P96(x86422)+~E(f335(x86423,f802(x86424,x86423,x86421,x86422)),f335(x86424,f802(x86424,x86423,x86421,x86422)))+P1(f335(f335(f86(f888(x86421,x86422)),x86423),x86424))
% 59.73/59.67 [8760]E(f335(f335(f23(a1),f471(x87601,x87602,x87603,x87604)),f472(x87601,x87602,x87603,x87604)),x87604)+~P1(f335(f335(f243(a1),f2(a1)),x87603))+~P1(f335(f335(f242(a1),x87601),x87604))+P1(f335(f335(f242(a1),x87601),f335(f335(f75(a1),x87604),x87603)))
% 59.73/59.67 [8761]E(f335(f335(f23(a1),f479(x87611,x87612,x87613,x87614)),f480(x87611,x87612,x87613,x87614)),x87614)+~P1(f335(f335(f243(a1),f2(a1)),x87613))+~P1(f335(f335(f243(a1),x87611),x87614))+P1(f335(f335(f243(a1),x87611),f335(f335(f75(a1),x87614),x87613)))
% 59.73/59.67 [8900]~P4(x89001)+~P96(x89002)+P1(f335(f335(f337(x89001),f802(x89004,x89003,x89001,x89002)),f335(f166(x89001),f50(x89001))))+P1(f335(f335(f86(f888(x89001,x89002)),x89003),x89004))
% 59.73/59.67 [8901]~E(f335(f335(f158(x89011),x89013),f719(x89014,x89013,x89011,x89012)),f335(f335(f158(x89011),x89014),f719(x89014,x89013,x89011,x89012)))+E(f335(f335(f169(x89011),x89012),x89013),f335(f335(f169(x89011),x89012),x89014))+~P1(f335(f335(f242(a881),x89012),f335(f189(f882(x89011)),x89013)))+~P1(f335(f335(f242(a881),x89012),f335(f189(f882(x89011)),x89014)))
% 59.73/59.67 [8971]~P1(f335(f335(f243(a1),f2(a1)),x89713))+~P1(f335(f335(f242(a1),x89711),x89714))+P1(f335(f335(f337(a1),f471(x89711,x89712,x89713,x89714)),x89712))+P1(f335(f335(f242(a1),x89711),f335(f335(f75(a1),x89714),x89713)))
% 59.73/59.67 [8972]~P1(f335(f335(f243(a1),f2(a1)),x89723))+~P1(f335(f335(f243(a1),x89721),x89724))+P1(f335(f335(f337(a1),f479(x89721,x89722,x89723,x89724)),x89722))+P1(f335(f335(f243(a1),x89721),f335(f335(f75(a1),x89724),x89723)))
% 59.73/59.67 [9009]~P102(x90091)+~P1(f335(f56(x90091),x90093))+~P1(f335(f335(f337(x90091),x90094),x90093))+P1(f335(f335(f242(x90091),f335(f335(f59(x90091,x90091,f95(x90091)),x90092),x90093)),f335(f335(f95(x90091),x90094),x90092)))
% 59.73/59.67 [9010]~P106(x90101)+~P1(f335(f56(x90101),x90103))+~P1(f335(f335(f337(x90101),x90104),x90103))+P1(f335(f335(f242(x90101),f335(f335(f59(x90101,x90101,f240(x90101)),x90102),x90103)),f335(f335(f240(x90101),x90104),x90102)))
% 59.73/59.67 [9056]E(f335(f335(f169(x90561),x90562),x90563),f335(f335(f169(x90561),x90562),x90564))+P1(f335(f335(f243(a881),f719(x90563,x90564,x90561,x90562)),x90562))+~P1(f335(f335(f242(a881),x90562),f335(f189(f882(x90561)),x90563)))+~P1(f335(f335(f242(a881),x90562),f335(f189(f882(x90561)),x90564)))
% 59.73/59.67 [9061]~P1(f335(f335(f243(a1),f2(a1)),x90613))+~P1(f335(f335(f242(a1),x90611),x90612))+P1(f335(f335(f337(a1),f472(x90611,x90614,x90613,x90612)),f305(a1,f73(a1),x90613)))+P1(f335(f335(f242(a1),x90611),f335(f335(f75(a1),x90612),x90613)))
% 59.73/59.67 [9062]~P1(f335(f335(f243(a1),f2(a1)),x90623))+~P1(f335(f335(f243(a1),x90621),x90622))+P1(f335(f335(f337(a1),f480(x90621,x90624,x90623,x90622)),f305(a1,f73(a1),x90623)))+P1(f335(f335(f243(a1),x90621),f335(f335(f75(a1),x90622),x90623)))
% 59.73/59.67 [9231]~E(f335(f179(x92311,x92312),x92313),f335(f179(x92311,x92312),x92314))+E(f335(f166(f887(x92311,x92312)),x92313),f335(f166(f887(x92311,x92312)),x92314))+~P1(f335(f130(x92311),f335(f335(f147(f887(x92311,x92312),x92311),f263(x92311,x92312)),x92314)))+~P1(f335(f130(x92311),f335(f335(f147(f887(x92311,x92312),x92311),f263(x92311,x92312)),x92313)))
% 59.73/59.67 [9243]E(f335(f179(x92431,x92432),x92433),f335(f179(x92431,x92432),x92434))+~E(f335(f166(f887(x92431,x92432)),x92433),f335(f166(f887(x92431,x92432)),x92434))+~P1(f335(f130(x92431),f335(f335(f147(f887(x92431,x92432),x92431),f263(x92431,x92432)),x92434)))+~P1(f335(f130(x92431),f335(f335(f147(f887(x92431,x92432),x92431),f263(x92431,x92432)),x92433)))
% 59.73/59.67 [9384]~P106(x93841)+~P1(f335(f56(x93841),x93844))+P1(f335(f335(f337(x93841),f648(x93842,x93843,x93844,x93841)),x93844))+P1(f335(f335(f242(x93841),f335(f335(f59(x93841,x93841,f241(x93841)),x93842),x93844)),f335(f335(f241(x93841),x93843),x93842)))
% 59.73/59.67 [9385]~P60(x93851)+~P1(f335(f56(x93851),x93854))+P1(f335(f335(f337(x93851),f653(x93852,x93853,x93854,x93851)),x93854))+P1(f335(f335(f242(x93851),f335(f335(f59(x93851,x93851,f104(x93851)),x93852),x93854)),f335(f335(f104(x93851),x93853),x93852)))
% 59.73/59.67 [9509]~P60(x95091)+~P1(f335(f56(x95091),x95093))+~P1(f335(f335(f242(x95091),f653(x95092,x95094,x95093,x95091)),x95094))+P1(f335(f335(f242(x95091),f335(f335(f59(x95091,x95091,f104(x95091)),x95092),x95093)),f335(f335(f104(x95091),x95094),x95092)))
% 59.73/59.67 [9510]~P106(x95101)+~P1(f335(f56(x95101),x95103))+~P1(f335(f335(f242(x95101),f648(x95102,x95104,x95103,x95101)),x95104))+P1(f335(f335(f242(x95101),f335(f335(f59(x95101,x95101,f241(x95101)),x95102),x95103)),f335(f335(f241(x95101),x95104),x95102)))
% 59.73/59.67 [9513]~P1(f335(f335(f242(a1),f2(a1)),x95134))+~P1(f335(f335(f243(a1),f2(a1)),x95133))+~P1(f335(f335(f243(a1),x95134),x95131))+P1(f335(f335(f243(a1),f335(f335(f75(a1),f335(f335(f76(a1),x95131),f39(a1,x95132,x95133))),x95134)),f335(f335(f76(a1),x95131),x95133)))
% 59.73/59.67 [9918]E(x99181,x99182)+P1(f335(f335(f337(f887(f882(x99183),f882(x99183))),f335(f335(f264(f882(x99183),f882(x99183)),x99182),x99181)),f140(x99183,x99184)))+P1(f335(f335(f337(f887(f882(x99183),f882(x99183))),f335(f335(f264(f882(x99183),f882(x99183)),x99181),x99182)),f140(x99183,x99184)))+~P1(f335(f335(f337(f887(x99183,x99183)),f335(f335(f264(x99183,x99183),f714(x99181,x99182,x99184,x99183)),f716(x99181,x99182,x99184,x99183))),x99184))
% 59.73/59.67 [9919]E(x99191,x99192)+P1(f335(f335(f337(f887(f882(x99193),f882(x99193))),f335(f335(f264(f882(x99193),f882(x99193)),x99192),x99191)),f140(x99193,x99194)))+P1(f335(f335(f337(f887(f882(x99193),f882(x99193))),f335(f335(f264(f882(x99193),f882(x99193)),x99191),x99192)),f140(x99193,x99194)))+~P1(f335(f335(f337(f887(x99193,x99193)),f335(f335(f264(x99193,x99193),f716(x99191,x99192,x99194,x99193)),f714(x99191,x99192,x99194,x99193))),x99194))
% 59.73/59.67 [7466]~P60(x74661)+~P1(f335(f335(f242(x74661),x74663),x74664))+~P1(f335(f335(f242(x74661),x74662),x74664))+P1(f335(f335(f242(x74661),f335(f335(f104(x74661),x74662),x74663)),x74664))
% 59.73/59.67 [7467]~P60(x74671)+~P1(f335(f335(f242(x74671),x74673),x74674))+~P1(f335(f335(f242(x74671),x74672),x74674))+P1(f335(f335(f242(x74671),f335(f335(f104(x74671),x74672),x74673)),x74674))
% 59.73/59.67 [7468]~P60(x74681)+~P1(f335(f335(f242(x74681),x74683),x74684))+~P1(f335(f335(f242(x74681),x74682),x74684))+P1(f335(f335(f242(x74681),f335(f335(f104(x74681),x74682),x74683)),x74684))
% 59.73/59.67 [7469]~P106(x74691)+~P1(f335(f335(f242(x74691),x74693),x74694))+~P1(f335(f335(f242(x74691),x74692),x74694))+P1(f335(f335(f242(x74691),f335(f335(f241(x74691),x74692),x74693)),x74694))
% 59.73/59.67 [7470]~P106(x74701)+~P1(f335(f335(f242(x74701),x74703),x74704))+~P1(f335(f335(f242(x74701),x74702),x74704))+P1(f335(f335(f242(x74701),f335(f335(f241(x74701),x74702),x74703)),x74704))
% 59.73/59.67 [7471]~P106(x74711)+~P1(f335(f335(f242(x74711),x74713),x74714))+~P1(f335(f335(f242(x74711),x74712),x74714))+P1(f335(f335(f242(x74711),f335(f335(f241(x74711),x74712),x74713)),x74714))
% 59.73/59.67 [7472]~P106(x74721)+~P1(f335(f335(f243(x74721),x74723),x74724))+~P1(f335(f335(f243(x74721),x74722),x74724))+P1(f335(f335(f243(x74721),f335(f335(f241(x74721),x74722),x74723)),x74724))
% 59.73/59.67 [7794]~E(x77941,x77943)+E(f132(a881,f335(f304(a881,x77941),x77942)),f335(f335(f144(a881),x77943),x77944))+~E(f132(a881,f335(f304(a881,f335(f335(f75(a881),x77941),f73(a881))),x77942)),x77944)+~P1(f335(f335(f243(a881),x77941),x77942))
% 59.73/59.67 [7803]~P106(x78031)+P1(f335(f335(f242(x78031),x78032),x78033))+P1(f335(f335(f242(x78031),x78034),x78033))+~P1(f335(f335(f242(x78031),f335(f335(f240(x78031),x78034),x78032)),x78033))
% 59.73/59.67 [7804]~P106(x78041)+P1(f335(f335(f243(x78041),x78042),x78043))+P1(f335(f335(f243(x78041),x78044),x78043))+~P1(f335(f335(f243(x78041),f335(f335(f240(x78041),x78044),x78042)),x78043))
% 59.73/59.67 [8086]~P68(x80861)+~P1(f335(f335(f243(x80861),f2(x80861)),x80863))+~P1(f335(f335(f242(x80861),x80862),f335(f335(f292(x80861),x80864),x80863)))+P1(f335(f335(f242(x80861),f335(f335(f76(x80861),x80862),x80863)),x80864))
% 59.73/59.67 [8087]~P69(x80871)+~P1(f335(f335(f243(x80871),f2(x80871)),x80873))+~P1(f335(f335(f242(x80871),x80872),f335(f335(f292(x80871),x80874),x80873)))+P1(f335(f335(f242(x80871),f335(f335(f76(x80871),x80872),x80873)),x80874))
% 59.73/59.67 [8088]~P68(x80881)+~P1(f335(f335(f243(x80881),f2(x80881)),x80883))+~P1(f335(f335(f242(x80881),x80882),f335(f335(f76(x80881),x80884),x80883)))+P1(f335(f335(f242(x80881),f335(f335(f292(x80881),x80882),x80883)),x80884))
% 59.73/59.67 [8089]~P69(x80891)+~P1(f335(f335(f243(x80891),f2(x80891)),x80893))+~P1(f335(f335(f242(x80891),x80892),f335(f335(f76(x80891),x80894),x80893)))+P1(f335(f335(f242(x80891),f335(f335(f292(x80891),x80892),x80893)),x80894))
% 59.73/59.67 [8090]~P69(x80901)+~P1(f335(f335(f243(x80901),f2(x80901)),x80903))+~P1(f335(f335(f242(x80901),x80902),f335(f335(f76(x80901),x80904),x80903)))+P1(f335(f335(f242(x80901),f335(f335(f292(x80901),x80902),x80903)),x80904))
% 59.73/59.67 [8091]~P68(x80911)+~P1(f335(f335(f243(x80911),f2(x80911)),x80913))+~P1(f335(f335(f243(x80911),x80912),f335(f335(f292(x80911),x80914),x80913)))+P1(f335(f335(f243(x80911),f335(f335(f76(x80911),x80912),x80913)),x80914))
% 59.73/59.67 [8092]~P69(x80921)+~P1(f335(f335(f243(x80921),f2(x80921)),x80923))+~P1(f335(f335(f243(x80921),x80922),f335(f335(f292(x80921),x80924),x80923)))+P1(f335(f335(f243(x80921),f335(f335(f76(x80921),x80922),x80923)),x80924))
% 59.73/59.67 [8093]~P68(x80931)+~P1(f335(f335(f243(x80931),f2(x80931)),x80933))+~P1(f335(f335(f243(x80931),x80932),f335(f335(f76(x80931),x80934),x80933)))+P1(f335(f335(f243(x80931),f335(f335(f292(x80931),x80932),x80933)),x80934))
% 59.73/59.67 [8094]~P69(x80941)+~P1(f335(f335(f243(x80941),f2(x80941)),x80943))+~P1(f335(f335(f243(x80941),x80942),f335(f335(f76(x80941),x80944),x80943)))+P1(f335(f335(f243(x80941),f335(f335(f292(x80941),x80942),x80943)),x80944))
% 59.73/59.67 [8095]~P69(x80951)+~P1(f335(f335(f243(x80951),f2(x80951)),x80953))+~P1(f335(f335(f243(x80951),x80952),f335(f335(f76(x80951),x80954),x80953)))+P1(f335(f335(f243(x80951),f335(f335(f292(x80951),x80952),x80953)),x80954))
% 59.73/59.67 [8224]~P68(x82241)+~P1(f335(f335(f243(x82241),f2(x82241)),x82244))+P1(f335(f335(f242(x82241),x82242),f335(f335(f76(x82241),x82243),x82244)))+~P1(f335(f335(f242(x82241),f335(f335(f292(x82241),x82242),x82244)),x82243))
% 59.73/59.67 [8225]~P68(x82251)+~P1(f335(f335(f243(x82251),f2(x82251)),x82254))+P1(f335(f335(f242(x82251),x82252),f335(f335(f292(x82251),x82253),x82254)))+~P1(f335(f335(f242(x82251),f335(f335(f76(x82251),x82252),x82254)),x82253))
% 59.73/59.67 [8226]~P69(x82261)+~P1(f335(f335(f243(x82261),f2(x82261)),x82264))+P1(f335(f335(f242(x82261),x82262),f335(f335(f292(x82261),x82263),x82264)))+~P1(f335(f335(f242(x82261),f335(f335(f76(x82261),x82262),x82264)),x82263))
% 59.73/59.67 [8227]~P69(x82271)+~P1(f335(f335(f243(x82271),f2(x82271)),x82274))+P1(f335(f335(f242(x82271),x82272),f335(f335(f76(x82271),x82273),x82274)))+~P1(f335(f335(f242(x82271),f335(f335(f292(x82271),x82272),x82274)),x82273))
% 59.73/59.67 [8228]~P69(x82281)+~P1(f335(f335(f243(x82281),f2(x82281)),x82284))+P1(f335(f335(f242(x82281),x82282),f335(f335(f292(x82281),x82283),x82284)))+~P1(f335(f335(f242(x82281),f335(f335(f76(x82281),x82282),x82284)),x82283))
% 59.73/59.67 [8229]~P68(x82291)+~P1(f335(f335(f243(x82291),f2(x82291)),x82294))+P1(f335(f335(f243(x82291),x82292),f335(f335(f76(x82291),x82293),x82294)))+~P1(f335(f335(f243(x82291),f335(f335(f292(x82291),x82292),x82294)),x82293))
% 59.73/59.67 [8230]~P68(x82301)+~P1(f335(f335(f243(x82301),f2(x82301)),x82304))+P1(f335(f335(f243(x82301),x82302),f335(f335(f292(x82301),x82303),x82304)))+~P1(f335(f335(f243(x82301),f335(f335(f76(x82301),x82302),x82304)),x82303))
% 59.73/59.67 [8231]~P69(x82311)+~P1(f335(f335(f243(x82311),f2(x82311)),x82314))+P1(f335(f335(f243(x82311),x82312),f335(f335(f292(x82311),x82313),x82314)))+~P1(f335(f335(f243(x82311),f335(f335(f76(x82311),x82312),x82314)),x82313))
% 59.73/59.67 [8232]~P69(x82321)+~P1(f335(f335(f243(x82321),f2(x82321)),x82324))+P1(f335(f335(f243(x82321),x82322),f335(f335(f76(x82321),x82323),x82324)))+~P1(f335(f335(f243(x82321),f335(f335(f292(x82321),x82322),x82324)),x82323))
% 59.73/59.67 [8233]~P69(x82331)+~P1(f335(f335(f243(x82331),f2(x82331)),x82334))+P1(f335(f335(f243(x82331),x82332),f335(f335(f292(x82331),x82333),x82334)))+~P1(f335(f335(f243(x82331),f335(f335(f76(x82331),x82332),x82334)),x82333))
% 59.73/59.67 [8394]~P69(x83941)+~P1(f335(f335(f243(x83941),x83943),f2(x83941)))+~P1(f335(f335(f242(x83941),f335(f335(f292(x83941),x83944),x83943)),x83942))+P1(f335(f335(f242(x83941),f335(f335(f76(x83941),x83942),x83943)),x83944))
% 59.73/59.67 [8395]~P69(x83951)+~P1(f335(f335(f243(x83951),x83953),f2(x83951)))+~P1(f335(f335(f242(x83951),f335(f335(f76(x83951),x83954),x83953)),x83952))+P1(f335(f335(f242(x83951),f335(f335(f292(x83951),x83952),x83953)),x83954))
% 59.73/59.67 [8396]~P69(x83961)+~P1(f335(f335(f243(x83961),x83963),f2(x83961)))+~P1(f335(f335(f243(x83961),f335(f335(f292(x83961),x83964),x83963)),x83962))+P1(f335(f335(f243(x83961),f335(f335(f76(x83961),x83962),x83963)),x83964))
% 59.73/59.67 [8397]~P69(x83971)+~P1(f335(f335(f243(x83971),x83973),f2(x83971)))+~P1(f335(f335(f243(x83971),f335(f335(f76(x83971),x83974),x83973)),x83972))+P1(f335(f335(f243(x83971),f335(f335(f292(x83971),x83972),x83973)),x83974))
% 59.73/59.67 [8409]~P1(f335(x84091,x84094))+~P1(f335(f335(f243(a881),x84092),f335(f335(f76(a881),x84093),f335(a106,x84094))))+P1(f335(x84091,f335(f335(f30(a881),x84092),x84093)))+~P1(f335(f335(f242(a881),f335(f335(f76(a881),x84093),x84094)),x84092))
% 59.73/59.67 [8616]~P60(x86161)+~P1(f335(f56(x86161),x86164))+~P1(f335(f335(f337(x86161),x86162),x86164))+P1(f335(f335(f242(x86161),f335(f335(f104(x86161),x86162),x86163)),f335(f335(f59(x86161,x86161,f104(x86161)),x86163),x86164)))
% 59.73/59.67 [8617]~P106(x86171)+~P1(f335(f56(x86171),x86174))+~P1(f335(f335(f337(x86171),x86172),x86174))+P1(f335(f335(f242(x86171),f335(f335(f241(x86171),x86172),x86173)),f335(f335(f59(x86171,x86171,f241(x86171)),x86173),x86174)))
% 59.73/59.67 [8762]~P1(f335(f56(x87621),x87622))+E(f335(f29(x87621),f335(f335(f23(f888(x87621,a879)),x87622),f335(f335(f312(x87621),x87623),x87624))),f335(f335(f23(a881),f335(f29(x87621),f335(f335(f23(f888(x87621,a879)),x87622),x87624))),f73(a881)))+P1(f335(f335(f337(x87621),x87623),x87624))+~P1(f335(f335(f337(x87621),x87623),x87622))
% 59.73/59.67 [8836]E(f335(f335(f75(a1),f473(x88361,x88362,x88363,x88364)),f474(x88361,x88362,x88363,x88364)),x88364)+~P1(f335(f335(f243(a1),f2(a1)),x88363))+~P1(f335(f335(f242(a1),x88364),x88361))+P1(f335(f335(f242(a1),f335(f335(f23(a1),x88364),x88363)),x88361))
% 59.73/59.67 [8837]E(f335(f335(f75(a1),f481(x88371,x88372,x88373,x88374)),f482(x88371,x88372,x88373,x88374)),x88374)+~P1(f335(f335(f243(a1),f2(a1)),x88373))+~P1(f335(f335(f243(a1),x88374),x88371))+P1(f335(f335(f243(a1),f335(f335(f23(a1),x88374),x88373)),x88371))
% 59.73/59.67 [9041]~P1(f335(f335(f243(a1),f2(a1)),x90413))+~P1(f335(f335(f242(a1),x90414),x90411))+P1(f335(f335(f337(a1),f473(x90411,x90412,x90413,x90414)),x90412))+P1(f335(f335(f242(a1),f335(f335(f23(a1),x90414),x90413)),x90411))
% 59.73/59.67 [9042]~P1(f335(f335(f243(a1),f2(a1)),x90423))+~P1(f335(f335(f243(a1),x90424),x90421))+P1(f335(f335(f337(a1),f481(x90421,x90422,x90423,x90424)),x90422))+P1(f335(f335(f243(a1),f335(f335(f23(a1),x90424),x90423)),x90421))
% 59.73/59.67 [9129]~P1(f335(f335(f243(a1),f2(a1)),x91292))+~P1(f335(f335(f242(a1),x91291),x91293))+P1(f335(f335(f337(a1),f474(x91293,x91294,x91292,x91291)),f305(a1,f73(a1),x91292)))+P1(f335(f335(f242(a1),f335(f335(f23(a1),x91291),x91292)),x91293))
% 59.73/59.67 [9130]~P1(f335(f335(f243(a1),f2(a1)),x91302))+~P1(f335(f335(f243(a1),x91301),x91303))+P1(f335(f335(f337(a1),f482(x91303,x91304,x91302,x91301)),f305(a1,f73(a1),x91302)))+P1(f335(f335(f243(a1),f335(f335(f23(a1),x91301),x91302)),x91303))
% 59.73/59.67 [9150]~P1(f335(f335(f242(a1),f2(a1)),x91504))+~P1(f335(f335(f243(a1),f2(a1)),x91503))+~P1(f335(f335(f243(a1),x91504),x91501))+P1(f335(f335(f242(a1),f2(a1)),f335(f335(f75(a1),f335(f335(f76(a1),x91501),f39(a1,x91502,x91503))),x91504)))
% 59.73/59.67 [9213]~P102(x92131)+~P1(f335(f56(x92131),x92134))+~P1(f335(f335(f242(x92131),x92132),f652(x92133,x92132,x92134,x92131)))+P1(f335(f335(f242(x92131),f335(f335(f95(x92131),x92132),x92133)),f335(f335(f59(x92131,x92131,f95(x92131)),x92133),x92134)))
% 59.73/59.67 [9214]~P106(x92141)+~P1(f335(f56(x92141),x92144))+~P1(f335(f335(f242(x92141),x92142),f647(x92143,x92142,x92144,x92141)))+P1(f335(f335(f242(x92141),f335(f335(f240(x92141),x92142),x92143)),f335(f335(f59(x92141,x92141,f240(x92141)),x92143),x92144)))
% 59.73/59.67 [9230]~P1(f335(f335(f242(a1),x92304),f2(a1)))+~P1(f335(f335(f243(a1),f2(a1)),x92302))+~P1(f335(f335(f243(a1),x92301),x92304))+P1(f335(f335(f243(a1),f335(f335(f76(a1),x92301),x92302)),f335(f335(f75(a1),f335(f335(f76(a1),x92301),f39(a1,x92303,x92302))),x92304)))
% 59.73/59.67 [9252]P1(f335(f56(x92521),x92522))+~P1(f335(f56(x92521),x92523))+~P1(f335(f335(f337(f888(x92521,a879)),x92522),f335(f335(f55(x92521),x92523),x92524)))+~P1(f335(f335(f242(f888(f887(x92521,x92521),a879)),x92524),f335(f335(f266(x92521,x92521),x92523),f335(f16(f888(x92521,a879),x92521),x92523))))
% 59.73/59.67 [9276]~P106(x92761)+~P1(f335(f56(x92761),x92764))+P1(f335(f335(f337(x92761),f647(x92762,x92763,x92764,x92761)),x92764))+P1(f335(f335(f242(x92761),f335(f335(f240(x92761),x92763),x92762)),f335(f335(f59(x92761,x92761,f240(x92761)),x92762),x92764)))
% 59.73/59.67 [9277]~P102(x92771)+~P1(f335(f56(x92771),x92774))+P1(f335(f335(f337(x92771),f652(x92772,x92773,x92774,x92771)),x92774))+P1(f335(f335(f242(x92771),f335(f335(f95(x92771),x92773),x92772)),f335(f335(f59(x92771,x92771,f95(x92771)),x92772),x92774)))
% 59.73/59.67 [9288]~P37(f888(x92881,a879),f888(x92881,a879),x92883)+~P1(f335(f335(f337(x92881),x92882),x92884))+P1(f335(f335(f337(x92881),x92882),f90(f888(x92881,a879),x92883)))+~P1(f335(f335(f242(f888(x92881,a879)),x92884),f335(x92883,f335(f335(f104(f888(x92881,a879)),x92884),f90(f888(x92881,a879),x92883)))))
% 59.73/59.67 [9464]~P37(f888(x94643,a879),f888(x94643,a879),x94644)+P1(f335(x94641,x94642))+~P1(f335(f335(f337(x94643),x94642),f89(f888(x94643,a879),x94644)))+P1(f335(f335(f337(x94643),f533(x94641,x94644,x94642,x94643)),f335(x94644,f335(f335(f95(f888(x94643,a879)),f89(f888(x94643,a879),x94644)),f335(f249(x94643),x94641)))))
% 59.73/59.67 [9677]~P1(f335(f56(x96772),x96774))+~P1(f335(f56(x96771),x96773))+~P1(f335(f335(f242(a881),f335(f29(x96772),x96774)),f335(f29(x96771),x96773)))+P1(f335(f335(f242(f888(x96771,a879)),f335(f313(x96772,x96771,f347(x96773,x96771,x96774,x96772)),x96774)),x96773))
% 59.73/59.67 [9325]~P1(f335(f335(f337(x93251),x93252),x93254))+P1(f335(f335(f337(x93251),x93252),x93253))+~P1(f335(f335(f243(f888(x93251,a879)),x93254),f335(f335(f312(x93251),x93252),x93253)))+P1(f335(f335(f243(f888(x93251,a879)),f335(f335(f23(f888(x93251,a879)),x93254),f335(f335(f312(x93251),x93252),f188(f888(x93251,a879))))),x93253))
% 59.73/59.67 [9489]~P1(f335(f335(f337(x94891),x94892),x94894))+P1(f335(f335(f337(x94891),x94892),x94893))+P1(f335(f335(f243(f888(x94891,a879)),x94894),f335(f335(f312(x94891),x94892),x94893)))+~P1(f335(f335(f243(f888(x94891,a879)),f335(f335(f23(f888(x94891,a879)),x94894),f335(f335(f312(x94891),x94892),f188(f888(x94891,a879))))),x94893))
% 59.73/59.67 [9516]P1(f335(f335(f337(x95161),x95162),x95163))+~P1(f335(f335(f242(f888(x95161,a879)),x95164),x95163))+P1(f335(f335(f243(f888(x95161,a879)),x95164),f335(f335(f312(x95161),x95162),x95163)))+~P1(f335(f335(f243(f888(x95161,a879)),f335(f335(f23(f888(x95161,a879)),x95164),f335(f335(f312(x95161),x95162),f188(f888(x95161,a879))))),x95163))
% 59.73/59.67 [9521]~P1(f335(f335(f337(x95211),x95213),x95212))+~P1(f335(f335(f243(f888(x95211,a879)),x95212),x95214))+P1(f335(f335(f243(f888(x95211,a879)),x95212),f335(f335(f312(x95211),x95213),x95214)))+~P1(f335(f335(f243(f888(x95211,a879)),f335(f335(f23(f888(x95211,a879)),x95212),f335(f335(f312(x95211),x95213),f188(f888(x95211,a879))))),x95214))
% 59.73/59.67 [9535]~P1(f335(f335(f242(f888(x95351,a879)),x95352),x95354))+~P1(f335(f335(f243(f888(x95351,a879)),x95352),x95354))+P1(f335(f335(f243(f888(x95351,a879)),x95352),f335(f335(f312(x95351),x95353),x95354)))+~P1(f335(f335(f243(f888(x95351,a879)),f335(f335(f23(f888(x95351,a879)),x95352),f335(f335(f312(x95351),x95353),f188(f888(x95351,a879))))),x95354))
% 59.73/59.67 [9578]~P107(x95782)+~P4(x95781)+~P1(f335(f335(f242(f888(x95781,x95782)),x95783),x95784))+P1(f335(f53(x95781),f335(f335(f18(x95781,x95782,a879),f335(f335(f8(x95782,f888(x95782,a879),x95781),f242(x95782)),x95783)),x95784)))
% 59.73/59.67 [9726]~P107(x97262)+~P4(x97261)+P1(f335(f335(f242(f888(x97261,x97262)),x97263),x97264))+~P1(f335(f53(x97261),f335(f335(f18(x97261,x97262,a879),f335(f335(f8(x97262,f888(x97262,a879),x97261),f242(x97262)),x97263)),x97264)))
% 59.73/59.67 [10211]~P37(f888(x102111,a879),f888(x102111,a879),x102113)+~P1(f335(f335(f337(x102111),x102112),x102114))+P1(f335(f335(f337(x102111),x102112),f90(f888(x102111,a879),x102113)))+~P1(f335(f335(f242(f888(x102111,a879)),x102114),f335(x102113,f89(f888(x102111,a879),f335(f335(f7(f888(x102111,a879),f888(x102111,a879),f888(x102111,a879)),f335(f335(f8(f888(x102111,a879),f888(f888(x102111,a879),f888(x102111,a879)),f888(x102111,a879)),f104(f888(x102111,a879))),f335(f335(f7(f888(x102111,a879),f888(x102111,a879),f888(x102111,a879)),f335(f335(f8(f888(x102111,a879),f888(f888(x102111,a879),f888(x102111,a879)),f888(x102111,a879)),f104(f888(x102111,a879))),x102113)),x102114))),f90(f888(x102111,a879),x102113))))))
% 59.73/59.67 [9904]E(f335(f335(f158(x99041),f335(f335(f158(f882(x99041)),f173(x99041,x99042)),x99043)),x99044),f335(f335(f158(x99041),f335(f335(f158(f882(x99041)),x99042),x99044)),x99043))+~P1(f335(f335(f243(a881),x99043),f335(f189(f882(f882(x99041))),f173(x99041,x99042))))+~P15(a881,f335(f162(a881),f335(f335(f147(f882(x99041),a881),f189(f882(x99041))),x99042)))+~P1(f335(f335(f243(a881),x99044),f335(f189(f882(f882(x99041))),f335(f129(f882(x99041),f335(f335(f8(a881,a879,f882(x99041)),f335(f243(a881),x99043)),f189(f882(x99041)))),x99042))))
% 59.73/59.67 [9931]~P1(f335(f335(f337(f887(a881,a881)),x99314),x99311))+~P1(f335(f335(f337(f887(f887(a881,a881),f887(a881,a881))),f335(f335(f264(f887(a881,a881),f887(a881,a881)),x99314),x99312)),a26))+~P1(f335(f335(f337(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879))),f335(f335(f264(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),x99311),x99313)),a27))+P1(f335(f335(f337(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879))),f335(f335(f264(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),x99311),f335(f335(f312(f887(a881,a881)),x99312),x99313))),a27))
% 59.73/59.67 [9932]~P1(f335(f335(f337(f887(a881,a881)),x99324),x99321))+~P1(f335(f335(f337(f887(f887(a881,a881),f887(a881,a881))),f335(f335(f264(f887(a881,a881),f887(a881,a881)),x99324),x99322)),a65))+~P1(f335(f335(f337(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879))),f335(f335(f264(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),x99321),x99323)),a66))+P1(f335(f335(f337(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879))),f335(f335(f264(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),x99321),f335(f335(f312(f887(a881,a881)),x99322),x99323))),a66))
% 59.73/59.67 [9818]~P107(x98182)+~P4(x98181)+~P1(f335(f335(f243(f888(x98181,x98182)),x98183),x98184))+P1(f335(f52(x98181),f335(f335(f8(a879,a879,x98181),a330),f335(f335(f18(x98181,x98182,a879),f335(f335(f8(x98182,f888(x98182,a879),x98181),a332),x98183)),x98184))))
% 59.73/59.67 [9943]~P1(f335(f335(f337(f887(a881,a881)),x99434),x99433))+~P1(f335(f335(f337(f887(f887(a881,a881),f887(a881,a881))),f335(f335(f264(f887(a881,a881),f887(a881,a881)),x99431),x99434)),a26))+~P1(f335(f335(f337(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879))),f335(f335(f264(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),x99432),x99433)),a28))+P1(f335(f335(f337(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879))),f335(f335(f264(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),f335(f335(f312(f887(a881,a881)),x99431),x99432)),x99433)),a28))
% 59.73/59.67 [9944]~P1(f335(f335(f337(f887(a881,a881)),x99444),x99443))+~P1(f335(f335(f337(f887(f887(a881,a881),f887(a881,a881))),f335(f335(f264(f887(a881,a881),f887(a881,a881)),x99441),x99444)),a65))+~P1(f335(f335(f337(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879))),f335(f335(f264(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),x99442),x99443)),a64))+P1(f335(f335(f337(f887(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879))),f335(f335(f264(f888(f887(a881,a881),a879),f888(f887(a881,a881),a879)),f335(f335(f312(f887(a881,a881)),x99441),x99442)),x99443)),a64))
% 59.73/59.67 [6056]~P7(x60564,x60561)+~P1(f335(f335(x60561,x60562),x60565))+P1(f335(f335(x60561,x60562),x60563))+~P1(f335(f335(x60561,x60565),x60563))
% 59.73/59.67 [5312]~P64(x53125)+E(x53121,x53122)+~E(x53123,x53124)+~E(f335(f335(f23(x53125),x53123),x53124),f335(f335(f23(x53125),x53121),x53122))
% 59.73/59.67 [5313]~P64(x53135)+E(x53131,x53132)+~E(x53133,x53134)+~E(f335(f335(f23(x53135),x53133),x53134),f335(f335(f23(x53135),x53131),x53132))
% 59.73/59.67 [6162]~P19(x61625,x61621,x61623)+E(f335(f335(x61621,x61622),f335(x61623,x61624)),f335(x61623,x61624))+~P1(f335(f56(x61625),x61624))+~P1(f335(f335(f337(x61625),x61622),x61624))
% 59.73/59.67 [6352]~P80(x63521)+~E(f335(f335(f23(x63521),x63524),x63525),f335(f335(f23(x63521),x63522),x63523))+~P1(f335(f335(f242(x63521),x63524),x63525))+P1(f335(f335(f242(x63521),x63522),x63523))
% 59.73/59.67 [6353]~P80(x63531)+~E(f335(f335(f23(x63531),x63534),x63535),f335(f335(f23(x63531),x63532),x63533))+~P1(f335(f335(f242(x63531),x63534),x63535))+P1(f335(f335(f242(x63531),x63532),x63533))
% 59.73/59.67 [6354]~P80(x63541)+~E(f335(f335(f23(x63541),x63544),x63545),f335(f335(f23(x63541),x63542),x63543))+~P1(f335(f335(f243(x63541),x63544),x63545))+P1(f335(f335(f243(x63541),x63542),x63543))
% 59.73/59.67 [6355]~P80(x63551)+~E(f335(f335(f23(x63551),x63554),x63555),f335(f335(f23(x63551),x63552),x63553))+~P1(f335(f335(f243(x63551),x63554),x63555))+P1(f335(f335(f243(x63551),x63552),x63553))
% 59.73/59.67 [7330]~E(x73302,f335(f335(f144(x73301),x73304),x73305))+P1(f335(f335(f337(f882(x73301)),x73302),f154(x73301,x73303)))+~P1(f335(f335(f337(f882(x73301)),x73305),f154(x73301,x73303)))+~P1(f335(f335(f337(x73301),x73304),x73303))
% 59.73/59.67 [7745]~E(f335(f189(f882(x77451)),x77453),f335(f189(f882(x77452)),x77454))+~E(f335(f335(f147(f887(x77451,x77452),x77452),f267(x77451,x77452)),x77455),x77454)+~E(f335(f335(f147(f887(x77451,x77452),x77451),f263(x77451,x77452)),x77455),x77453)+E(f335(f335(f175(x77451,x77452),x77453),x77454),x77455)
% 59.73/59.67 [8083]~P107(x80831)+P1(f335(f335(f243(f888(x80831,a879)),f305(x80831,x80832,x80833)),f305(x80831,x80834,x80835)))+~P1(f335(f335(f242(x80831),x80834),x80835))+P1(f335(f335(f242(x80831),x80832),x80833))
% 59.73/59.67 [8176]~P107(x81761)+P1(f335(f335(f242(f888(x81761,a879)),f305(x81761,x81762,x81763)),f305(x81761,x81764,x81765)))+~P1(f335(f335(f242(x81761),x81763),x81765))+~P1(f335(f335(f242(x81761),x81764),x81762))
% 59.73/59.67 [8301]~P106(x83011)+P1(f335(f335(f242(x83011),x83012),x83013))+P1(f335(f335(f242(x83011),x83014),x83013))+~P1(f335(f335(f242(f888(x83011,a879)),f335(f304(x83011,x83013),x83012)),f335(f304(x83011,x83014),x83015)))
% 59.73/59.67 [8302]~P106(x83021)+P1(f335(f335(f242(x83021),x83022),x83023))+P1(f335(f335(f242(x83021),x83022),x83024))+~P1(f335(f335(f242(f888(x83021,a879)),f335(f304(x83021,x83023),x83022)),f335(f304(x83021,x83025),x83024)))
% 59.73/59.67 [8471]~P102(x84713)+~P102(x84711)+~P37(x84713,x84711,x84712)+P1(f335(f335(f242(x84711),f335(x84712,f335(f335(f95(x84713),x84714),x84715))),f335(f335(f95(x84711),f335(x84712,x84714)),f335(x84712,x84715))))
% 59.73/59.67 [8472]~P106(x84723)+~P102(x84721)+~P37(x84723,x84721,x84722)+P1(f335(f335(f242(x84721),f335(x84722,f335(f335(f240(x84723),x84724),x84725))),f335(f335(f95(x84721),f335(x84722,x84724)),f335(x84722,x84725))))
% 59.73/59.67 [8535]~P107(x85351)+~P1(f335(f335(f242(f888(x85351,a879)),f305(x85351,x85354,x85352)),f305(x85351,x85355,x85353)))+P1(f335(f335(f242(x85351),x85352),x85353))+~P1(f335(f335(f242(x85351),x85354),x85352))
% 59.73/59.67 [8536]~P107(x85361)+~P1(f335(f335(f243(f888(x85361,a879)),f305(x85361,x85364,x85362)),f305(x85361,x85365,x85363)))+P1(f335(f335(f242(x85361),x85362),x85363))+~P1(f335(f335(f242(x85361),x85364),x85362))
% 59.73/59.67 [8537]~P107(x85371)+~P1(f335(f335(f242(f888(x85371,a879)),f305(x85371,x85373,x85374)),f305(x85371,x85372,x85375)))+P1(f335(f335(f242(x85371),x85372),x85373))+~P1(f335(f335(f242(x85371),x85373),x85374))
% 59.73/59.67 [8538]~P107(x85381)+~P1(f335(f335(f243(f888(x85381,a879)),f305(x85381,x85383,x85384)),f305(x85381,x85382,x85385)))+P1(f335(f335(f242(x85381),x85382),x85383))+~P1(f335(f335(f242(x85381),x85383),x85384))
% 59.73/59.67 [6004]~P106(x60045)+~P106(x60041)+~P37(x60045,x60041,x60042)+E(f335(f335(f240(x60041),f335(x60042,x60043)),f335(x60042,x60044)),f335(x60042,f335(f335(f240(x60045),x60043),x60044)))
% 59.73/59.67 [6005]~P106(x60055)+~P106(x60051)+~P37(x60055,x60051,x60052)+E(f335(f335(f241(x60051),f335(x60052,x60053)),f335(x60052,x60054)),f335(x60052,f335(f335(f241(x60055),x60053),x60054)))
% 59.73/59.67 [6055]~P19(x60552,x60555,x60553)+E(x60551,f188(f888(x60552,a879)))+~P1(f335(f56(x60552),x60551))+E(f335(x60553,f335(f335(f312(x60552),x60554),x60551)),f335(f335(x60555,x60554),f335(x60553,x60551)))
% 59.73/59.67 [6829]~E(x68291,x68292)+~E(f335(f335(f95(f888(x68293,a879)),x68294),x68295),f188(f888(x68293,a879)))+~P1(f335(f335(f337(x68293),x68292),x68295))+~P1(f335(f335(f337(x68293),x68291),x68294))
% 59.73/59.67 [6913]~P20(x69132,x69135,x69131)+~P1(f335(f56(x69132),x69134))+E(f335(x69131,f335(f335(f312(x69132),x69133),x69134)),f335(f335(f59(x69132,x69132,x69135),x69133),x69134))+P1(f335(f335(f337(x69132),x69133),x69134))
% 59.73/59.67 [6976]~P73(x69762)+~P1(f335(f56(x69761),x69765))+E(f335(f335(f9(x69761,x69762),x69763),f335(f335(f312(x69761),x69764),x69765)),f335(f335(f76(x69762),f335(x69763,x69764)),f335(f335(f9(x69761,x69762),x69763),x69765)))+P1(f335(f335(f337(x69761),x69764),x69765))
% 59.73/59.67 [6977]~P73(x69772)+~P1(f335(f56(x69771),x69775))+E(f335(f335(f9(x69771,x69772),x69773),f335(f335(f312(x69771),x69774),x69775)),f335(f335(f76(x69772),f335(x69773,x69774)),f335(f335(f9(x69771,x69772),x69773),x69775)))+P1(f335(f335(f337(x69771),x69774),x69775))
% 59.73/59.67 [6978]~P77(x69782)+~P1(f335(f56(x69781),x69785))+E(f335(f335(f6(x69781,x69782),x69783),f335(f335(f312(x69781),x69784),x69785)),f335(f335(f75(x69782),f335(x69783,x69784)),f335(f335(f6(x69781,x69782),x69783),x69785)))+P1(f335(f335(f337(x69781),x69784),x69785))
% 59.73/59.67 [6979]~P77(x69792)+~P1(f335(f56(x69791),x69795))+E(f335(f335(f6(x69791,x69792),x69793),f335(f335(f312(x69791),x69794),x69795)),f335(f335(f75(x69792),f335(x69793,x69794)),f335(f335(f6(x69791,x69792),x69793),x69795)))+P1(f335(f335(f337(x69791),x69794),x69795))
% 59.73/59.67 [7483]~P20(x74832,x74835,x74831)+~P1(f335(f56(x74832),x74834))+E(f335(x74831,f335(f335(f312(x74832),x74833),x74834)),x74833)+~E(f335(f335(f23(f888(x74832,a879)),x74834),f335(f335(f312(x74832),x74833),f188(f888(x74832,a879)))),f188(f888(x74832,a879)))
% 59.73/59.67 [7847]~P60(x78471)+~P1(f335(f335(f242(x78471),x78473),x78475))+~P1(f335(f335(f242(x78471),x78472),x78474))+P1(f335(f335(f242(x78471),f335(f335(f104(x78471),x78472),x78473)),f335(f335(f104(x78471),x78474),x78475)))
% 59.73/59.67 [7848]~P102(x78481)+~P1(f335(f335(f242(x78481),x78483),x78485))+~P1(f335(f335(f242(x78481),x78482),x78484))+P1(f335(f335(f242(x78481),f335(f335(f95(x78481),x78482),x78483)),f335(f335(f95(x78481),x78484),x78485)))
% 59.73/59.67 [7849]~P87(x78491)+~P1(f335(f335(f242(x78491),x78493),x78495))+~P1(f335(f335(f242(x78491),x78492),x78494))+P1(f335(f335(f242(x78491),f335(f335(f75(x78491),x78492),x78493)),f335(f335(f75(x78491),x78494),x78495)))
% 59.73/59.67 [7850]~P106(x78501)+~P1(f335(f335(f242(x78501),x78503),x78505))+~P1(f335(f335(f242(x78501),x78502),x78504))+P1(f335(f335(f242(x78501),f335(f335(f240(x78501),x78502),x78503)),f335(f335(f240(x78501),x78504),x78505)))
% 59.73/59.67 [7851]~P106(x78511)+~P1(f335(f335(f242(x78511),x78513),x78515))+~P1(f335(f335(f242(x78511),x78512),x78514))+P1(f335(f335(f242(x78511),f335(f335(f241(x78511),x78512),x78513)),f335(f335(f241(x78511),x78514),x78515)))
% 59.73/59.67 [7852]~P89(x78521)+~P1(f335(f335(f242(x78521),x78523),x78525))+~P1(f335(f335(f243(x78521),x78522),x78524))+P1(f335(f335(f243(x78521),f335(f335(f75(x78521),x78522),x78523)),f335(f335(f75(x78521),x78524),x78525)))
% 59.73/59.67 [7853]~P89(x78531)+~P1(f335(f335(f242(x78531),x78532),x78534))+~P1(f335(f335(f243(x78531),x78533),x78535))+P1(f335(f335(f243(x78531),f335(f335(f75(x78531),x78532),x78533)),f335(f335(f75(x78531),x78534),x78535)))
% 59.73/59.67 [7854]~P89(x78541)+~P1(f335(f335(f243(x78541),x78543),x78545))+~P1(f335(f335(f243(x78541),x78542),x78544))+P1(f335(f335(f243(x78541),f335(f335(f75(x78541),x78542),x78543)),f335(f335(f75(x78541),x78544),x78545)))
% 59.73/59.67 [7998]~P138(x79985)+E(x79981,x79982)+E(x79983,x79984)+~E(f335(f335(f75(x79985),f335(f335(f76(x79985),x79983),x79981)),f335(f335(f76(x79985),x79984),x79982)),f335(f335(f75(x79985),f335(f335(f76(x79985),x79983),x79982)),f335(f335(f76(x79985),x79984),x79981)))
% 59.73/59.67 [7999]~P138(x79995)+E(x79991,x79992)+E(x79993,x79994)+~E(f335(f335(f75(x79995),f335(f335(f76(x79995),x79993),x79991)),f335(f335(f76(x79995),x79994),x79992)),f335(f335(f75(x79995),f335(f335(f76(x79995),x79993),x79992)),f335(f335(f76(x79995),x79994),x79991)))
% 59.73/59.67 [8199]~P106(x81994)+~P1(f335(f130(x81991),x81993))+P1(f335(f335(f337(x81991),x81992),f335(f166(x81991),x81993)))+P1(f335(f130(x81991),f335(f335(f141(x81991,x81994,x81995),x81992),x81993)))
% 59.73/59.67 [8347]~P64(x83471)+E(f335(f335(f23(x83471),f335(f335(f6(a881,x83471),x83472),f335(f304(a881,x83473),x83474))),f335(f335(f6(a881,x83471),x83472),f335(f304(a881,x83473),x83475))),f335(f335(f6(a881,x83471),x83472),f335(f304(a881,x83475),x83474)))+~P1(f335(f335(f242(a881),x83475),x83474))+~P1(f335(f335(f242(a881),x83473),x83475))
% 59.73/59.67 [8348]~P77(x83481)+E(f335(f335(f75(x83481),f335(f335(f6(a881,x83481),x83482),f335(f304(a881,x83483),x83484))),f335(f335(f6(a881,x83481),x83482),f335(f304(a881,x83484),x83485))),f335(f335(f6(a881,x83481),x83482),f335(f304(a881,x83483),x83485)))+~P1(f335(f335(f242(a881),x83484),x83485))+~P1(f335(f335(f242(a881),x83483),x83484))
% 59.73/59.67 [8675]~P67(x86752)+E(x86751,f2(x86752))+E(x86753,f2(x86752))+E(f335(f335(f292(x86752),f335(f335(f23(x86752),f335(f335(f76(x86752),x86754),x86751)),f335(f335(f76(x86752),x86755),x86753))),f335(f335(f76(x86752),x86753),x86751)),f335(f335(f23(x86752),f335(f335(f292(x86752),x86754),x86753)),f335(f335(f292(x86752),x86755),x86751)))
% 59.73/59.67 [8676]~P67(x86762)+E(x86761,f2(x86762))+E(x86763,f2(x86762))+E(f335(f335(f292(x86762),f335(f335(f75(x86762),f335(f335(f76(x86762),x86764),x86761)),f335(f335(f76(x86762),x86765),x86763))),f335(f335(f76(x86762),x86763),x86761)),f335(f335(f75(x86762),f335(f335(f292(x86762),x86764),x86763)),f335(f335(f292(x86762),x86765),x86761)))
% 59.73/59.67 [8685]~E(x86852,f335(x86853,x86851))+E(x86851,f685(x86852,x86853,x86854,x86855))+~P26(x86855,x86854,x86853,f252(f888(x86855,a879)))+~P1(f335(f335(f337(x86854),x86852),f335(f313(x86855,x86854,x86853),f252(f888(x86855,a879)))))
% 59.73/59.67 [8886]~P119(x88861)+~P1(f335(f335(f243(x88861),f335(f70(x88861),x88862)),x88864))+P1(f335(f335(f243(x88861),f335(f335(f76(x88861),f335(f70(x88861),x88862)),f335(f70(x88861),x88863))),f335(f335(f76(x88861),x88864),x88865)))+~P1(f335(f335(f243(x88861),f335(f70(x88861),x88863)),x88865))
% 59.73/59.67 [9001]~P26(x90011,x90013,x90015,x90012)+~P1(f335(f56(x90013),x90014))+P1(f335(f335(f242(a881),f335(f29(x90011),x90012)),f335(f29(x90013),x90014)))+~P1(f335(f335(f242(f888(x90013,a879)),f335(f313(x90011,x90013,x90015),x90012)),x90014))
% 59.73/59.67 [9070]~P73(x90702)+~P26(x90701,x90701,x90704,x90705)+~P1(f335(f56(x90701),x90705))+E(f335(f335(f9(x90701,x90702),f335(f68(x90701,x90702,x90701,x90703),x90704)),x90705),f335(f335(f9(x90701,x90702),x90703),f335(f313(x90701,x90701,x90704),x90705)))
% 59.73/59.67 [9071]~P77(x90712)+~P26(x90711,x90711,x90714,x90715)+~P1(f335(f56(x90711),x90715))+E(f335(f335(f6(x90711,x90712),f335(f68(x90711,x90712,x90711,x90713),x90714)),x90715),f335(f335(f6(x90711,x90712),x90713),f335(f313(x90711,x90711,x90714),x90715)))
% 59.73/59.67 [9154]~E(f693(x91542,x91544,x91541,x91543,x91545),x91545)+~E(x91542,f335(x91544,x91545))+~P26(x91543,x91541,x91544,f252(f888(x91543,a879)))+P1(f335(f335(f337(x91541),x91542),f335(f313(x91543,x91541,x91544),f252(f888(x91543,a879)))))
% 59.73/59.67 [9191]~P36(x91911,x91912)+~P1(f335(f335(f337(x91911),x91913),x91914))+~P1(f335(f335(f337(x91911),x91915),x91914))+~P1(f335(f335(f337(f887(x91911,x91911)),f335(f335(f264(x91911,x91911),x91915),f643(x91912,x91911,x91914))),x91912))
% 59.73/59.67 [9229]~P26(x92292,x92293,x92295,x92291)+E(x92291,f188(f888(x92292,a879)))+E(f335(f313(x92293,x92292,f640(x92294,x92293,x92292,x92291)),x92294),x92291)+~P1(f335(f335(f242(f888(x92293,a879)),f335(f313(x92292,x92293,x92295),x92291)),x92294))
% 59.73/59.67 [9266]~E(x92662,f335(x92661,x92665))+~P26(x92664,x92663,x92661,f252(f888(x92664,a879)))+E(f335(x92661,f693(x92662,x92661,x92663,x92664,x92665)),x92662)+P1(f335(f335(f337(x92663),x92662),f335(f313(x92664,x92663,x92661),f252(f888(x92664,a879)))))
% 59.73/59.67 [9707]~P106(x97075)+~P5(x97075)+P1(f335(f335(f337(x97071),f784(x97072,x97073,x97071,x97074,x97075)),x97073))+~P1(f335(f335(f243(x97075),x97074),f335(f335(f33(x97071,x97075),x97073),x97072)))
% 59.73/59.67 [9712]~P106(x97121)+~P5(x97121)+P1(f335(f335(f243(x97121),x97122),f335(x97123,f784(x97123,x97124,x97125,x97122,x97121))))+~P1(f335(f335(f243(x97121),x97122),f335(f335(f33(x97125,x97121),x97124),x97123)))
% 59.73/59.67 [9796]~P70(x97961)+~P1(f335(f61(x97961,x97961,f76(x97961),x97962,x97963),x97965))+P1(f335(f335(f337(x97961),x97962),x97963))+P1(f335(f61(x97961,x97961,f76(x97961),x97964,f335(f335(f312(x97961),x97962),x97963)),f335(f335(f76(x97961),x97964),x97965)))
% 59.73/59.67 [10012]~P73(x100122)+~P1(f335(f56(x100121),x100125))+E(f335(f335(f9(x100121,x100122),f335(f335(f7(x100121,x100122,x100122),f335(f335(f18(x100121,x100122,f888(x100122,x100122)),f335(f335(f8(a879,f888(x100122,f888(x100122,x100122)),x100121),f88(x100122)),f335(a332,x100123))),x100124)),f73(x100122))),x100125),f73(x100122))+P1(f335(f335(f337(x100121),x100123),x100125))
% 59.73/59.67 [10013]~P77(x100132)+~P1(f335(f56(x100131),x100135))+E(f335(f335(f6(x100131,x100132),f335(f335(f7(x100131,x100132,x100132),f335(f335(f18(x100131,x100132,f888(x100132,x100132)),f335(f335(f8(a879,f888(x100132,f888(x100132,x100132)),x100131),f88(x100132)),f335(a332,x100133))),x100134)),f2(x100132))),x100135),f2(x100132))+P1(f335(f335(f337(x100131),x100133),x100135))
% 59.73/59.67 [10014]~P73(x100142)+~P1(f335(f56(x100141),x100145))+E(f335(f335(f9(x100141,x100142),f335(f335(f7(x100141,x100142,x100142),f335(f335(f18(x100141,x100142,f888(x100142,x100142)),f335(f335(f8(a879,f888(x100142,f888(x100142,x100142)),x100141),f88(x100142)),f335(a332,x100143))),x100144)),f73(x100142))),x100145),f335(x100144,x100143))+~P1(f335(f335(f337(x100141),x100143),x100145))
% 59.73/59.67 [10015]~P77(x100152)+~P1(f335(f56(x100151),x100155))+E(f335(f335(f6(x100151,x100152),f335(f335(f7(x100151,x100152,x100152),f335(f335(f18(x100151,x100152,f888(x100152,x100152)),f335(f335(f8(a879,f888(x100152,f888(x100152,x100152)),x100151),f88(x100152)),f335(a332,x100153))),x100154)),f2(x100152))),x100155),f335(x100154,x100153))+~P1(f335(f335(f337(x100151),x100153),x100155))
% 59.73/59.67 [10071]~P73(x100712)+~P1(f335(f56(x100711),x100715))+E(f335(f335(f9(x100711,x100712),f335(f335(f7(x100711,x100712,x100712),f335(f335(f18(x100711,x100712,f888(x100712,x100712)),f335(f335(f8(a879,f888(x100712,f888(x100712,x100712)),x100711),f88(x100712)),f335(f335(f7(x100711,x100711,a879),a332),x100713))),x100714)),f73(x100712))),x100715),f73(x100712))+P1(f335(f335(f337(x100711),x100713),x100715))
% 59.73/59.67 [10072]~P77(x100722)+~P1(f335(f56(x100721),x100725))+E(f335(f335(f6(x100721,x100722),f335(f335(f7(x100721,x100722,x100722),f335(f335(f18(x100721,x100722,f888(x100722,x100722)),f335(f335(f8(a879,f888(x100722,f888(x100722,x100722)),x100721),f88(x100722)),f335(f335(f7(x100721,x100721,a879),a332),x100723))),x100724)),f2(x100722))),x100725),f2(x100722))+P1(f335(f335(f337(x100721),x100723),x100725))
% 59.73/59.67 [10074]~P73(x100742)+~P1(f335(f56(x100741),x100745))+E(f335(f335(f9(x100741,x100742),f335(f335(f7(x100741,x100742,x100742),f335(f335(f18(x100741,x100742,f888(x100742,x100742)),f335(f335(f8(a879,f888(x100742,f888(x100742,x100742)),x100741),f88(x100742)),f335(f335(f7(x100741,x100741,a879),a332),x100743))),x100744)),f73(x100742))),x100745),f335(x100744,x100743))+~P1(f335(f335(f337(x100741),x100743),x100745))
% 59.73/59.67 [10075]~P77(x100752)+~P1(f335(f56(x100751),x100755))+E(f335(f335(f6(x100751,x100752),f335(f335(f7(x100751,x100752,x100752),f335(f335(f18(x100751,x100752,f888(x100752,x100752)),f335(f335(f8(a879,f888(x100752,f888(x100752,x100752)),x100751),f88(x100752)),f335(f335(f7(x100751,x100751,a879),a332),x100753))),x100754)),f2(x100752))),x100755),f335(x100754,x100753))+~P1(f335(f335(f337(x100751),x100753),x100755))
% 59.73/59.67 [7846]~P64(x78462)+~P1(f335(f56(x78461),x78464))+E(f335(f335(f6(x78461,x78462),x78463),f335(f335(f23(f888(x78461,a879)),x78464),f335(f335(f312(x78461),x78465),f188(f888(x78461,a879))))),f335(f335(f6(x78461,x78462),x78463),x78464))+P1(f335(f335(f337(x78461),x78465),x78464))
% 59.73/59.67 [8354]~P118(x83542)+~P1(f335(f56(x83541),x83544))+E(f335(f335(f6(x83541,x83542),x83543),f335(f335(f23(f888(x83541,a879)),x83544),f335(f335(f312(x83541),x83545),f188(f888(x83541,a879))))),f335(f335(f23(x83542),f335(f335(f6(x83541,x83542),x83543),x83544)),f335(x83543,x83545)))+~P1(f335(f335(f337(x83541),x83545),x83544))
% 59.73/59.67 [8355]~P64(x83552)+~P1(f335(f56(x83551),x83554))+E(f335(f335(f6(x83551,x83552),x83553),f335(f335(f23(f888(x83551,a879)),x83554),f335(f335(f312(x83551),x83555),f188(f888(x83551,a879))))),f335(f335(f23(x83552),f335(f335(f6(x83551,x83552),x83553),x83554)),f335(x83553,x83555)))+~P1(f335(f335(f337(x83551),x83555),x83554))
% 59.73/59.67 [8386]~P64(x83861)+~P1(f335(f56(x83862),x83864))+E(f335(f335(f23(x83861),f335(f335(f6(x83862,x83861),x83863),x83864)),f335(f335(f6(x83862,x83861),x83863),x83865)),f335(f335(f6(x83862,x83861),x83863),f335(f335(f23(f888(x83862,a879)),x83864),x83865)))+~P1(f335(f335(f242(f888(x83862,a879)),x83865),x83864))
% 59.73/59.67 [8406]P1(f335(f56(x84061),f335(x84062,x84063)))+~P1(f335(f56(x84064),x84065))+~P1(f335(f335(f337(x84064),x84063),x84065))+~P1(f335(f56(x84061),f335(f335(f33(x84064,f888(x84061,a879)),x84065),x84062)))
% 59.73/59.67 [8516]~P60(x85165)+~P60(x85161)+~P37(x85165,x85161,x85162)+P1(f335(f335(f242(x85161),f335(f335(f104(x85161),f335(x85162,x85163)),f335(x85162,x85164))),f335(x85162,f335(f335(f104(x85165),x85163),x85164))))
% 59.73/59.67 [8517]~P106(x85175)+~P60(x85171)+~P37(x85175,x85171,x85172)+P1(f335(f335(f242(x85171),f335(f335(f104(x85171),f335(x85172,x85173)),f335(x85172,x85174))),f335(x85172,f335(f335(f241(x85175),x85173),x85174))))
% 59.73/59.67 [8848]~P8(x88481,x88485,x88484)+~E(f335(f288(x88481,x88481,x88484),f335(f335(f312(x88481),x88482),f188(f888(x88481,a879)))),f335(f288(x88481,x88481,x88484),f335(f335(f312(x88481),x88483),f188(f888(x88481,a879)))))+~P1(f335(f335(f337(x88481),x88483),x88485))+P1(f335(f335(f337(f887(x88481,x88481)),f335(f335(f264(x88481,x88481),x88482),x88483)),x88484))
% 59.73/59.67 [9148]~P1(f335(x91481,x91485))+P1(f335(x91481,f397(x91481,x91482,x91483,x91484)))+P1(f335(x91481,f389(x91481,x91482,x91483,x91484)))+~P1(f335(f335(f337(x91484),x91485),f335(f335(f104(f888(x91484,a879)),x91483),x91482)))
% 59.73/59.67 [9330]~P1(f335(x93301,x93305))+P1(f335(x93301,f389(x93301,x93302,x93303,x93304)))+P1(f335(f335(f337(x93304),f397(x93301,x93302,x93303,x93304)),x93302))+~P1(f335(f335(f337(x93304),x93305),f335(f335(f104(f888(x93304,a879)),x93303),x93302)))
% 59.73/59.67 [9331]~P1(f335(x93311,x93315))+P1(f335(x93311,f397(x93311,x93312,x93313,x93314)))+P1(f335(f335(f337(x93314),f389(x93311,x93312,x93313,x93314)),x93313))+~P1(f335(f335(f337(x93314),x93315),f335(f335(f104(f888(x93314,a879)),x93313),x93312)))
% 59.73/59.67 [9335]P1(f335(x93351,x93352))+~P1(f335(x93351,f379(x93351,x93353,x93354,x93355)))+~P1(f335(x93351,f368(x93351,x93353,x93354,x93355)))+~P1(f335(f335(f337(x93355),x93352),f335(f335(f104(f888(x93355,a879)),x93354),x93353)))
% 59.73/59.67 [9377]E(x93771,x93772)+~P1(f335(f335(f337(f887(x93773,x93773)),f335(f335(f264(x93773,x93773),x93771),x93772)),f310(x93773,x93775)))+P1(f335(f335(f337(x93773),x93771),x93774))+~P1(f335(f335(f242(f888(f887(x93773,x93773),a879)),x93775),f335(f335(f266(x93773,x93773),x93774),f335(f16(f888(x93773,a879),x93773),x93774))))
% 59.73/59.67 [9397]P1(f335(x93971,x93972))+~P1(f335(x93971,f368(x93971,x93974,x93975,x93973)))+P1(f335(f335(f337(x93973),f379(x93971,x93974,x93975,x93973)),x93974))+~P1(f335(f335(f337(x93973),x93972),f335(f335(f104(f888(x93973,a879)),x93975),x93974)))
% 59.73/59.67 [9398]P1(f335(x93981,x93982))+~P1(f335(x93981,f379(x93981,x93984,x93985,x93983)))+P1(f335(f335(f337(x93983),f368(x93981,x93984,x93985,x93983)),x93985))+~P1(f335(f335(f337(x93983),x93982),f335(f335(f104(f888(x93983,a879)),x93985),x93984)))
% 59.73/59.67 [9460]P1(f335(x94601,x94602))+P1(f335(f335(f337(x94603),f379(x94601,x94604,x94605,x94603)),x94604))+P1(f335(f335(f337(x94603),f368(x94601,x94604,x94605,x94603)),x94605))+~P1(f335(f335(f337(x94603),x94602),f335(f335(f104(f888(x94603,a879)),x94605),x94604)))
% 59.73/59.67 [9462]~P1(f335(x94622,x94625))+P1(f335(f335(f337(x94621),f397(x94622,x94623,x94624,x94621)),x94623))+P1(f335(f335(f337(x94621),f389(x94622,x94623,x94624,x94621)),x94624))+~P1(f335(f335(f337(x94621),x94625),f335(f335(f104(f888(x94621,a879)),x94624),x94623)))
% 59.73/59.67 [9610]~P8(x96101,x96105,x96104)+~P1(f335(f335(f337(x96101),x96103),x96105))+P1(f335(f335(f337(f887(x96101,x96101)),f335(f335(f264(x96101,x96101),x96102),x96103)),x96104))+~P1(f335(f335(f242(f888(x96101,a879)),f335(f288(x96101,x96101,x96104),f335(f335(f312(x96101),x96103),f188(f888(x96101,a879))))),f335(f288(x96101,x96101,x96104),f335(f335(f312(x96101),x96102),f188(f888(x96101,a879))))))
% 59.73/59.67 [9741]~P106(x97415)+~P5(x97415)+P1(f335(f335(f337(x97411),f624(x97412,x97413,x97414,x97411,x97415)),x97414))+~P1(f335(f335(f243(x97415),f335(f335(f34(x97411,x97415),x97414),x97413)),x97412))
% 59.73/59.67 [9775]~P87(x97755)+~P83(x97755)+P1(f335(f335(f337(x97751),f698(x97752,x97753,x97754,x97751,x97755)),f335(f166(x97751),x97754)))+P1(f335(f335(f242(x97755),f335(f159(x97755),f335(f335(f147(x97751,x97755),x97753),x97754))),f335(f159(x97755),f335(f335(f147(x97751,x97755),x97752),x97754))))
% 59.73/59.67 [9894]~P106(x98941)+~P5(x98941)+P1(f335(f335(f243(x98941),f335(x98942,f624(x98943,x98942,x98944,x98945,x98941))),x98943))+~P1(f335(f335(f243(x98941),f335(f335(f34(x98945,x98941),x98944),x98942)),x98943))
% 59.73/59.67 [10030]~P87(x100301)+~P83(x100301)+~P1(f335(f335(f242(x100301),f335(x100303,f698(x100305,x100303,x100304,x100302,x100301))),f335(x100305,f698(x100305,x100303,x100304,x100302,x100301))))+P1(f335(f335(f242(x100301),f335(f159(x100301),f335(f335(f147(x100302,x100301),x100303),x100304))),f335(f159(x100301),f335(f335(f147(x100302,x100301),x100305),x100304))))
% 59.73/59.67 [8692]~P73(x86921)+~P1(f335(f56(x86924),x86925))+~P1(f335(f335(f337(x86924),x86923),x86925))+E(f335(f335(f76(x86921),f335(x86922,x86923)),f335(f335(f9(x86924,x86921),x86922),f335(f335(f23(f888(x86924,a879)),x86925),f335(f335(f312(x86924),x86923),f188(f888(x86924,a879)))))),f335(f335(f9(x86924,x86921),x86922),x86925))
% 59.73/59.67 [8693]~P77(x86931)+~P1(f335(f56(x86934),x86935))+~P1(f335(f335(f337(x86934),x86933),x86935))+E(f335(f335(f75(x86931),f335(x86932,x86933)),f335(f335(f6(x86934,x86931),x86932),f335(f335(f23(f888(x86934,a879)),x86935),f335(f335(f312(x86934),x86933),f188(f888(x86934,a879)))))),f335(f335(f6(x86934,x86931),x86932),x86935))
% 59.73/59.67 [8694]~P77(x86941)+~P1(f335(f56(x86944),x86945))+~P1(f335(f335(f337(x86944),x86943),x86945))+E(f335(f335(f75(x86941),f335(x86942,x86943)),f335(f335(f6(x86944,x86941),x86942),f335(f335(f23(f888(x86944,a879)),x86945),f335(f335(f312(x86944),x86943),f188(f888(x86944,a879)))))),f335(f335(f6(x86944,x86941),x86942),x86945))
% 59.73/59.67 [8751]~P20(x87511,x87514,x87515)+~P1(f335(f56(x87511),x87512))+E(f335(f335(f23(f888(x87511,a879)),x87512),f335(f335(f312(x87511),x87513),f188(f888(x87511,a879)))),f188(f888(x87511,a879)))+E(f335(f335(x87514,x87513),f335(x87515,f335(f335(f23(f888(x87511,a879)),x87512),f335(f335(f312(x87511),x87513),f188(f888(x87511,a879)))))),f335(x87515,f335(f335(f312(x87511),x87513),x87512)))
% 59.73/59.67 [9124]~P73(x91241)+~P1(f335(f56(x91242),x91245))+~P1(f335(f56(x91242),x91244))+E(f335(f335(f76(x91241),f335(f335(f9(x91242,x91241),x91243),f335(f335(f104(f888(x91242,a879)),x91244),x91245))),f335(f335(f9(x91242,x91241),x91243),f335(f335(f95(f888(x91242,a879)),x91244),x91245))),f335(f335(f76(x91241),f335(f335(f9(x91242,x91241),x91243),x91244)),f335(f335(f9(x91242,x91241),x91243),x91245)))
% 59.73/59.67 [9125]~P73(x91251)+~P1(f335(f56(x91252),x91255))+~P1(f335(f56(x91252),x91254))+E(f335(f335(f76(x91251),f335(f335(f9(x91252,x91251),x91253),f335(f335(f104(f888(x91252,a879)),x91254),x91255))),f335(f335(f9(x91252,x91251),x91253),f335(f335(f95(f888(x91252,a879)),x91254),x91255))),f335(f335(f76(x91251),f335(f335(f9(x91252,x91251),x91253),x91254)),f335(f335(f9(x91252,x91251),x91253),x91255)))
% 59.73/59.67 [9126]~P77(x91261)+~P1(f335(f56(x91262),x91265))+~P1(f335(f56(x91262),x91264))+E(f335(f335(f75(x91261),f335(f335(f6(x91262,x91261),x91263),f335(f335(f104(f888(x91262,a879)),x91264),x91265))),f335(f335(f6(x91262,x91261),x91263),f335(f335(f95(f888(x91262,a879)),x91264),x91265))),f335(f335(f75(x91261),f335(f335(f6(x91262,x91261),x91263),x91264)),f335(f335(f6(x91262,x91261),x91263),x91265)))
% 59.73/59.67 [9265]~P64(x92651)+~P1(f335(f56(x92652),x92655))+~P1(f335(f56(x92652),x92654))+E(f335(f335(f23(x92651),f335(f335(f75(x92651),f335(f335(f6(x92652,x92651),x92653),x92654)),f335(f335(f6(x92652,x92651),x92653),x92655))),f335(f335(f6(x92652,x92651),x92653),f335(f335(f95(f888(x92652,a879)),x92654),x92655))),f335(f335(f6(x92652,x92651),x92653),f335(f335(f104(f888(x92652,a879)),x92654),x92655)))
% 59.73/59.67 [9473]~P26(x94731,x94732,x94733,x94735)+~P26(x94731,x94732,x94733,x94734)+P26(x94731,x94732,x94733,f335(f335(f104(f888(x94731,a879)),x94734),x94735))+~E(f335(f335(f95(f888(x94732,a879)),f335(f313(x94731,x94732,x94733),f335(f335(f23(f888(x94731,a879)),x94734),x94735))),f335(f313(x94731,x94732,x94733),f335(f335(f23(f888(x94731,a879)),x94735),x94734))),f188(f888(x94732,a879)))
% 59.73/59.67 [9586]E(x95861,f2(a1))+~P1(f335(f335(f243(a1),f2(a1)),x95863))+~P1(f335(f43(x95862,x95861),f335(f335(f264(a1,a1),x95864),x95865)))+P1(f335(f43(x95862,f335(f335(f76(a1),x95861),x95863)),f335(f335(f264(a1,a1),f335(f335(f30(a1),x95864),x95863)),f335(f335(f75(a1),f335(f335(f76(a1),x95861),f39(a1,x95864,x95863))),x95865))))
% 59.73/59.67 [9594]~P1(f335(f335(f243(a881),f2(a881)),x95943))+~P1(f335(f335(f243(a881),f2(a881)),x95942))+~P1(f335(f42(x95941,x95942),f335(f335(f264(a881,a881),x95944),x95945)))+P1(f335(f42(x95941,f335(f335(f76(a881),x95942),x95943)),f335(f335(f264(a881,a881),f335(f335(f30(a881),x95944),x95943)),f335(f335(f75(a881),f335(f335(f76(a881),x95942),f39(a881,x95944,x95943))),x95945))))
% 59.73/59.67 [9643]~P73(x96431)+~P1(f335(f56(x96432),x96435))+~P1(f335(f56(x96432),x96434))+E(f335(f335(f76(x96431),f335(f335(f335(f60(x96431,x96432,f76(x96431)),x96433),f73(x96431)),f335(f335(f104(f888(x96432,a879)),x96434),x96435))),f335(f335(f335(f60(x96431,x96432,f76(x96431)),x96433),f73(x96431)),f335(f335(f95(f888(x96432,a879)),x96434),x96435))),f335(f335(f76(x96431),f335(f335(f335(f60(x96431,x96432,f76(x96431)),x96433),f73(x96431)),x96434)),f335(f335(f335(f60(x96431,x96432,f76(x96431)),x96433),f73(x96431)),x96435)))
% 59.73/59.67 [9645]~E(f335(f335(f169(x96451),x96455),x96452),f335(f335(f169(x96451),x96455),x96453))+P1(f335(f335(f337(f887(f882(x96451),f882(x96451))),f335(f335(f264(f882(x96451),f882(x96451)),x96452),x96453)),f140(x96451,x96454)))+~P1(f335(f335(f243(a881),x96455),f335(f335(f240(a881),f335(f189(f882(x96451)),x96452)),f335(f189(f882(x96451)),x96453))))+~P1(f335(f335(f337(f887(x96451,x96451)),f335(f335(f264(x96451,x96451),f335(f335(f158(x96451),x96452),x96455)),f335(f335(f158(x96451),x96453),x96455))),x96454))
% 59.73/59.67 [9763]~P87(x97635)+~P143(x97635)+P1(f335(f335(f337(x97631),f488(x97632,x97633,x97634,x97631,x97635)),x97634))+P1(f335(f335(f242(x97635),f335(f335(f6(x97631,x97635),x97633),x97634)),f335(f335(f76(x97635),f335(f94(x97635),f335(f29(x97631),x97634))),x97632)))
% 59.73/59.67 [9958]~P87(x99581)+~P143(x99581)+~P1(f335(f335(f242(x99581),f335(x99583,f488(x99585,x99583,x99584,x99582,x99581))),x99585))+P1(f335(f335(f242(x99581),f335(f335(f6(x99582,x99581),x99583),x99584)),f335(f335(f76(x99581),f335(f94(x99581),f335(f29(x99582),x99584))),x99585)))
% 59.73/59.67 [8723]E(f335(f335(f127(x87231),x87232),x87233),f335(f335(f127(x87231),x87234),x87235))+~E(f335(f335(f169(x87231),f335(f189(f882(x87231)),x87232)),x87234),x87232)+~E(f335(f335(f127(x87231),f335(f335(f131(x87231),f335(f189(f882(x87231)),x87232)),x87234)),x87235),x87233)+P1(f335(f335(f242(a881),f335(f189(f882(x87231)),x87234)),f335(f189(f882(x87231)),x87232)))
% 59.73/59.67 [8847]E(f335(f335(f127(x88471),x88472),x88473),f335(f335(f127(x88471),x88474),x88475))+~E(f335(f335(f169(x88471),f335(f189(f882(x88471)),x88472)),x88474),x88472)+~E(x88473,f335(f335(f127(x88471),f335(f335(f131(x88471),f335(f189(f882(x88471)),x88472)),x88474)),x88475))+~P1(f335(f335(f242(a881),f335(f189(f882(x88471)),x88472)),f335(f189(f882(x88471)),x88474)))
% 59.73/59.67 [10091]~P1(f335(x100915,x100914))+~P1(f335(f56(x100912),f335(f249(x100912),x100915)))+P1(f335(f56(x100911),f335(f249(x100911),f335(f335(f7(x100911,x100912,a879),x100913),x100914))))+~P1(f335(f56(x100911),f335(f249(x100911),f335(f335(f8(f888(x100912,a879),a879,x100911),f82(x100912)),f335(f335(f8(f888(x100912,a879),f888(x100912,a879),x100911),f335(f18(x100912,a879,a879),f335(f335(f8(a879,f888(a879,a879),x100912),a333),x100915))),x100913)))))
% 59.73/59.67 [8514]~P21(x85145,x85141,x85146,x85142)+E(f335(f68(x85141,x85141,x85141,f335(x85142,x85143)),f335(x85142,x85144)),f335(f68(x85141,x85141,x85141,f335(x85142,x85144)),f335(x85142,x85143)))+~P1(f335(f56(x85145),x85144))+~P1(f335(f56(x85145),x85143))
% 59.73/59.67 [7903]~P26(x79031,x79032,x79034,x79033)+~E(f335(x79034,x79036),x79035)+E(f335(f72(x79031,x79032,x79033,x79034),x79035),x79036)+~P1(f335(f335(f337(x79031),x79036),x79033))
% 59.73/59.67 [7904]~P26(x79041,x79042,x79044,x79043)+~E(f335(x79044,x79046),x79045)+E(f335(f87(x79041,x79042,x79043,x79044),x79045),x79046)+~P1(f335(f335(f337(x79041),x79046),x79043))
% 59.73/59.67 [8103]~P22(x81036,x81031,x81034,x81032)+E(f335(f68(x81031,x81031,x81031,f335(x81032,x81033)),f335(x81034,x81035)),f335(x81032,x81033))+~P1(f335(f56(x81036),x81033))+~P1(f335(f335(f337(x81036),x81035),x81033))
% 59.73/59.67 [9219]E(x92191,x92192)+~E(f335(f87(x92193,x92194,x92195,x92196),x92191),f335(f87(x92193,x92194,x92195,x92196),x92192))+~P1(f335(f335(f337(x92194),x92192),f335(f313(x92193,x92194,x92196),x92195)))+~P1(f335(f335(f337(x92194),x92191),f335(f313(x92193,x92194,x92196),x92195)))
% 59.73/59.67 [9315]~P21(x93153,x93151,x93156,x93152)+E(f335(f68(x93151,x93151,x93151,f335(x93152,f335(f335(f23(f888(x93153,a879)),x93154),f335(f335(f312(x93153),x93155),f188(f888(x93153,a879)))))),f335(x93156,x93155)),f335(x93152,x93154))+~P1(f335(f56(x93153),x93154))+~P1(f335(f335(f337(x93153),x93155),x93154))
% 59.73/59.67 [6982]~P59(x69821)+~E(f39(x69821,x69823,x69824),f39(x69821,x69826,x69824))+~E(f39(x69821,x69822,x69824),f39(x69821,x69825,x69824))+E(f39(x69821,f335(f335(f23(x69821),x69822),x69823),x69824),f39(x69821,f335(f335(f23(x69821),x69825),x69826),x69824))
% 59.73/59.67 [6983]~P58(x69831)+~E(f39(x69831,x69833,x69834),f39(x69831,x69836,x69834))+~E(f39(x69831,x69832,x69834),f39(x69831,x69835,x69834))+E(f39(x69831,f335(f335(f76(x69831),x69832),x69833),x69834),f39(x69831,f335(f335(f76(x69831),x69835),x69836),x69834))
% 59.73/59.67 [6984]~P58(x69841)+~E(f39(x69841,x69843,x69844),f39(x69841,x69846,x69844))+~E(f39(x69841,x69842,x69844),f39(x69841,x69845,x69844))+E(f39(x69841,f335(f335(f75(x69841),x69842),x69843),x69844),f39(x69841,f335(f335(f75(x69841),x69845),x69846),x69844))
% 59.73/59.67 [7798]~P18(x77981,x77982,x77983)+~P1(f335(f56(x77981),x77986))+E(f335(f335(f59(x77981,x77982,x77983),x77984),f335(f335(f312(x77981),x77985),x77986)),f335(f335(f59(x77981,x77982,x77983),f335(f335(x77983,x77985),x77984)),x77986))+P1(f335(f335(f337(x77981),x77985),x77986))
% 59.73/59.67 [7861]~P5(x78611)+P1(f335(f335(f242(x78611),x78612),f335(x78613,x78614)))+~P1(f335(f335(f337(x78615),x78614),x78616))+~P1(f335(f335(f242(x78611),x78612),f335(f335(f34(x78615,x78611),x78616),x78613)))
% 59.73/59.67 [8026]~P18(x80261,x80262,x80263)+~P1(f335(f56(x80261),x80266))+E(f335(f335(f59(x80261,x80262,x80263),x80264),f335(f335(f312(x80261),x80265),x80266)),f335(f335(x80263,x80265),f335(f335(f59(x80261,x80262,x80263),x80264),x80266)))+P1(f335(f335(f337(x80261),x80265),x80266))
% 59.73/59.67 [8118]~P106(x81183)+~P1(f335(x81182,x81185))+~P15(x81183,f335(f335(f147(x81181,x81183),x81184),x81186))+E(f335(f129(x81181,x81182),f335(f335(f141(x81181,x81183,x81184),x81185),x81186)),f335(f335(f141(x81181,x81183,x81184),x81185),f335(f129(x81181,x81182),x81186)))
% 59.73/59.67 [8139]E(x81391,x81392)+E(x81393,f2(a1))+~P1(f335(f43(x81394,x81393),f335(f335(f264(a1,a1),x81395),x81392)))+~P1(f335(f43(x81394,x81393),f335(f335(f264(a1,a1),x81396),x81391)))
% 59.73/59.67 [8140]E(x81401,x81402)+E(x81403,f2(a1))+~P1(f335(f43(x81404,x81403),f335(f335(f264(a1,a1),x81402),x81405)))+~P1(f335(f43(x81404,x81403),f335(f335(f264(a1,a1),x81401),x81406)))
% 59.73/59.67 [8160]~P21(x81602,x81605,x81606,x81601)+~P1(f335(f56(x81602),x81604))+E(f335(x81601,f335(f335(f312(x81602),x81603),x81604)),f335(f68(x81605,x81605,x81605,f335(x81601,x81604)),f335(x81606,x81603)))+P1(f335(f335(f337(x81602),x81603),x81604))
% 59.73/59.67 [8389]~P22(x83895,x83891,x83896,x83892)+E(f335(f68(x83891,x83891,x83891,f335(x83892,x83893)),f335(x83892,x83894)),f335(x83892,x83893))+~P1(f335(f56(x83895),x83893))+~P1(f335(f335(f242(f888(x83895,a879)),x83894),x83893))
% 59.73/59.67 [9518]~P26(x95181,x95182,x95184,x95183)+~P1(f335(f335(f337(x95182),x95185),f335(f313(x95181,x95182,x95184),x95183)))+P1(f335(f335(f337(x95181),f335(f72(x95181,x95182,x95183,x95184),x95185)),x95186))+~P1(f335(f335(f242(f888(x95181,a879)),x95183),x95186))
% 59.73/59.67 [9905]~P77(x99052)+~E(f500(x99051,x99053,x99055,x99056,x99054,x99052),f501(x99051,x99053,x99055,x99056,x99054,x99052))+~P1(f335(f56(x99054),x99056))+E(f335(f335(f6(x99051,x99052),x99053),f335(f313(x99054,x99051,x99055),x99056)),f335(f335(f6(x99054,x99052),f335(f68(x99051,x99052,x99054,x99053),x99055)),x99056))
% 59.73/59.67 [9939]~P77(x99396)+E(f335(x99391,f500(x99392,x99393,x99391,x99394,x99395,x99396)),f335(x99391,f501(x99392,x99393,x99391,x99394,x99395,x99396)))+E(f335(f335(f6(x99392,x99396),x99393),f335(f313(x99395,x99392,x99391),x99394)),f335(f335(f6(x99395,x99396),f335(f68(x99392,x99396,x99395,x99393),x99391)),x99394))+~P1(f335(f56(x99395),x99394))
% 59.73/59.67 [9980]~P77(x99802)+~E(f335(x99803,f335(x99805,f501(x99801,x99803,x99805,x99806,x99804,x99802))),f2(x99802))+~P1(f335(f56(x99804),x99806))+E(f335(f335(f6(x99801,x99802),x99803),f335(f313(x99804,x99801,x99805),x99806)),f335(f335(f6(x99804,x99802),f335(f68(x99801,x99802,x99804,x99803),x99805)),x99806))
% 59.73/59.67 [10038]~P77(x100382)+~P1(f335(f56(x100384),x100386))+E(f335(f335(f6(x100381,x100382),x100383),f335(f313(x100384,x100381,x100385),x100386)),f335(f335(f6(x100384,x100382),f335(f68(x100381,x100382,x100384,x100383),x100385)),x100386))+P1(f335(f335(f337(x100384),f501(x100381,x100383,x100385,x100386,x100384,x100382)),x100386))
% 59.73/59.67 [10039]~P77(x100392)+~P1(f335(f56(x100394),x100396))+E(f335(f335(f6(x100391,x100392),x100393),f335(f313(x100394,x100391,x100395),x100396)),f335(f335(f6(x100394,x100392),f335(f68(x100391,x100392,x100394,x100393),x100395)),x100396))+P1(f335(f335(f337(x100394),f500(x100391,x100393,x100395,x100396,x100394,x100392)),x100396))
% 59.73/59.67 [10113]~P37(f888(f887(x101134,x101135),a879),f888(f887(x101134,x101135),a879),x101136)+~P1(f335(f335(x101131,f391(x101131,x101136,x101133,x101132,x101135,x101134)),f392(x101131,x101136,x101133,x101132,x101135,x101134)))+P1(f335(f335(x101131,x101132),x101133))+~P1(f335(f335(f337(f887(x101134,x101135)),f335(f335(f264(x101134,x101135),x101132),x101133)),f89(f888(f887(x101134,x101135),a879),x101136)))
% 59.73/59.67 [10148]~P73(x101481)+~P1(f335(f56(x101482),x101486))+E(f335(f335(f335(f60(x101481,x101482,f76(x101481)),f335(f335(f18(x101482,f888(x101483,a879),x101481),f335(f335(f7(x101482,x101481,f888(f888(x101483,a879),x101481)),f335(f335(f8(f888(x101483,x101481),f888(x101481,f888(f888(x101483,a879),x101481)),x101482),f60(x101481,x101483,f76(x101481))),x101484)),f73(x101481))),x101485)),f73(x101481)),x101486),f335(f335(f335(f60(x101481,f887(x101482,x101483),f76(x101481)),f335(f268(x101482,x101483,x101481),x101484)),f73(x101481)),f335(f335(f266(x101482,x101483),x101486),x101485)))+P1(f335(f335(f337(x101482),f537(x101484,x101485,x101483,x101486,x101482,x101481)),x101486))
% 59.73/59.67 [10168]~P73(x101681)+~P1(f335(f56(x101682),x101686))+E(f335(f335(f335(f60(x101681,x101682,f76(x101681)),f335(f335(f18(x101682,f888(x101683,a879),x101681),f335(f335(f7(x101682,x101681,f888(f888(x101683,a879),x101681)),f335(f335(f8(f888(x101683,x101681),f888(x101681,f888(f888(x101683,a879),x101681)),x101682),f60(x101681,x101683,f76(x101681))),x101684)),f73(x101681))),x101685)),f73(x101681)),x101686),f335(f335(f335(f60(x101681,f887(x101682,x101683),f76(x101681)),f335(f268(x101682,x101683,x101681),x101684)),f73(x101681)),f335(f335(f266(x101682,x101683),x101686),x101685)))+~P1(f335(f56(x101683),f335(x101685,f537(x101684,x101685,x101683,x101686,x101682,x101681))))
% 59.73/59.67 [8300]~P22(x83002,x83005,x83006,x83001)+~P1(f335(f56(x83002),x83004))+~P1(f335(f56(x83002),x83003))+E(f335(x83001,f335(f335(f104(f888(x83002,a879)),x83003),x83004)),f335(f68(x83005,x83005,x83005,f335(x83001,x83003)),f335(x83001,x83004)))
% 59.73/59.67 [8515]~P5(x85151)+P1(f335(f335(f242(x85151),f335(x85152,x85153)),x85154))+~P1(f335(f335(f337(x85155),x85153),x85156))+~P1(f335(f335(f242(x85151),f335(f335(f33(x85155,x85151),x85156),x85152)),x85154))
% 59.73/59.67 [8928]~P26(x89282,x89281,x89283,x89286)+E(f335(f335(f23(f888(x89281,a879)),f335(f313(x89282,x89281,x89283),x89284)),f335(f313(x89282,x89281,x89283),x89285)),f335(f313(x89282,x89281,x89283),f335(f335(f23(f888(x89282,a879)),x89284),x89285)))+~P1(f335(f335(f242(f888(x89282,a879)),x89285),x89286))+~P1(f335(f335(f242(f888(x89282,a879)),x89284),x89286))
% 59.73/59.67 [8929]~P26(x89292,x89291,x89293,x89296)+E(f335(f335(f95(f888(x89291,a879)),f335(f313(x89292,x89291,x89293),x89294)),f335(f313(x89292,x89291,x89293),x89295)),f335(f313(x89292,x89291,x89293),f335(f335(f95(f888(x89292,a879)),x89294),x89295)))+~P1(f335(f335(f242(f888(x89292,a879)),x89295),x89296))+~P1(f335(f335(f242(f888(x89292,a879)),x89294),x89296))
% 59.73/59.67 [9192]E(x91921,x91922)+~P52(x91923,x91924,x91925)+~P1(f335(f335(f337(f887(x91923,x91924)),f335(f335(f264(x91923,x91924),x91926),x91922)),x91925))+~P1(f335(f335(f337(f887(x91923,x91924)),f335(f335(f264(x91923,x91924),x91926),x91921)),x91925))
% 59.73/59.67 [9193]E(x91931,x91932)+~P52(x91933,x91934,x91935)+~P1(f335(f335(f337(f887(x91933,x91934)),f335(f335(f264(x91933,x91934),x91936),x91932)),x91935))+~P1(f335(f335(f337(f887(x91933,x91934)),f335(f335(f264(x91933,x91934),x91936),x91931)),x91935))
% 59.73/59.67 [9975]~P70(x99751)+~E(f335(x99753,f587(x99754,x99756,x99753,x99755,x99752,x99751)),f335(x99756,f587(x99754,x99756,x99753,x99755,x99752,x99751)))+~P1(f335(f56(x99752),x99755))+E(f335(f335(f335(f60(x99751,x99752,f76(x99751)),x99753),x99754),x99755),f335(f335(f335(f60(x99751,x99752,f76(x99751)),x99756),x99754),x99755))
% 59.73/59.67 [10036]~P70(x100361)+~P1(f335(f56(x100362),x100365))+E(f335(f335(f335(f60(x100361,x100362,f76(x100361)),x100363),x100364),x100365),f335(f335(f335(f60(x100361,x100362,f76(x100361)),x100366),x100364),x100365))+P1(f335(f335(f337(x100362),f587(x100364,x100363,x100366,x100365,x100362,x100361)),x100365))
% 59.73/59.67 [8736]~P70(x87361)+~P1(f335(f56(x87362),x87366))+P1(f335(f335(f337(x87362),x87365),x87366))+E(f335(f335(f335(f60(x87361,x87362,f76(x87361)),x87363),x87364),f335(f335(f312(x87362),x87365),x87366)),f335(f335(f76(x87361),f335(x87363,x87365)),f335(f335(f335(f60(x87361,x87362,f76(x87361)),x87363),x87364),x87366)))
% 59.73/59.67 [8785]~P8(x87851,x87856,x87853)+~P13(x87851,f888(x87852,a879),x87853,x87855)+~P1(f335(f335(f337(x87851),x87854),x87856))+E(f335(f335(f33(x87851,f888(x87852,a879)),f335(f288(x87851,x87851,x87853),f335(f335(f312(x87851),x87854),f188(f888(x87851,a879))))),x87855),f335(x87855,x87854))
% 59.73/59.67 [8903]~P18(x89033,x89034,x89031)+~P1(f335(f56(x89033),x89036))+~P1(f335(f335(f337(x89033),x89032),x89036))+E(f335(f335(x89031,x89032),f335(f335(f59(x89033,x89034,x89031),x89035),f335(f335(f23(f888(x89033,a879)),x89036),f335(f335(f312(x89033),x89032),f188(f888(x89033,a879)))))),f335(f335(f59(x89033,x89034,x89031),x89035),x89036))
% 59.73/59.67 [9205]~P21(x92053,x92051,x92056,x92052)+~P1(f335(f56(x92053),x92055))+~P1(f335(f56(x92053),x92054))+E(f335(f68(x92051,x92051,x92051,f335(x92052,f335(f335(f104(f888(x92053,a879)),x92054),x92055))),f335(x92052,f335(f335(f95(f888(x92053,a879)),x92054),x92055))),f335(f68(x92051,x92051,x92051,f335(x92052,x92054)),f335(x92052,x92055)))
% 59.73/59.67 [10172]~P37(f888(f887(x101724,x101725),a879),f888(f887(x101724,x101725),a879),x101726)+P1(f335(f335(x101721,x101722),x101723))+~P1(f335(f335(f337(f887(x101724,x101725)),f335(f335(f264(x101724,x101725),x101722),x101723)),f89(f888(f887(x101724,x101725),a879),x101726)))+P1(f335(f335(f337(f887(x101724,x101725)),f335(f335(f264(x101724,x101725),f391(x101721,x101726,x101723,x101722,x101725,x101724)),f392(x101721,x101726,x101723,x101722,x101725,x101724))),f335(x101726,f335(f335(f95(f888(f887(x101724,x101725),a879)),f89(f888(f887(x101724,x101725),a879),x101726)),f335(f249(f887(x101724,x101725)),f335(f268(x101724,x101725,a879),x101721))))))
% 59.73/59.67 [9541]~E(x95413,f335(f335(f152(x95411,x95412),x95415),x95416))+P1(f335(f335(f337(f887(f882(x95411),f882(x95411))),f335(f335(f264(f882(x95411),f882(x95411)),x95412),x95413)),f150(x95411,x95414)))+~P1(f335(f335(f243(a881),x95415),f335(f189(f882(x95411)),x95412)))+~P1(f335(f335(f337(f887(x95411,x95411)),f335(f335(f264(x95411,x95411),f335(f335(f158(x95411),x95412),x95415)),x95416)),x95414))
% 59.73/59.67 [10049]~P73(x100492)+~P1(f335(f56(x100491),x100496))+P1(f335(f335(f337(x100491),f536(x100494,x100495,x100493,x100496,x100491,x100492)),x100496))+E(f335(f335(f9(x100491,x100492),f335(f335(f18(x100491,f888(x100493,a879),x100492),f335(f335(f8(f888(x100493,x100492),f888(f888(x100493,a879),x100492),x100491),f9(x100493,x100492)),x100494)),x100495)),x100496),f335(f335(f9(f887(x100491,x100493),x100492),f335(f268(x100491,x100493,x100492),x100494)),f335(f335(f266(x100491,x100493),x100496),x100495)))
% 59.73/59.67 [10050]~P77(x100502)+~P1(f335(f56(x100501),x100506))+P1(f335(f335(f337(x100501),f538(x100504,x100505,x100503,x100506,x100501,x100502)),x100506))+E(f335(f335(f6(x100501,x100502),f335(f335(f18(x100501,f888(x100503,a879),x100502),f335(f335(f8(f888(x100503,x100502),f888(f888(x100503,a879),x100502),x100501),f6(x100503,x100502)),x100504)),x100505)),x100506),f335(f335(f6(f887(x100501,x100503),x100502),f335(f268(x100501,x100503,x100502),x100504)),f335(f335(f266(x100501,x100503),x100506),x100505)))
% 59.73/59.67 [10089]~P73(x100892)+~P1(f335(f56(x100891),x100896))+~P1(f335(f56(x100893),f335(x100895,f536(x100894,x100895,x100893,x100896,x100891,x100892))))+E(f335(f335(f9(x100891,x100892),f335(f335(f18(x100891,f888(x100893,a879),x100892),f335(f335(f8(f888(x100893,x100892),f888(f888(x100893,a879),x100892),x100891),f9(x100893,x100892)),x100894)),x100895)),x100896),f335(f335(f9(f887(x100891,x100893),x100892),f335(f268(x100891,x100893,x100892),x100894)),f335(f335(f266(x100891,x100893),x100896),x100895)))
% 59.73/59.67 [10090]~P77(x100902)+~P1(f335(f56(x100901),x100906))+~P1(f335(f56(x100903),f335(x100905,f538(x100904,x100905,x100903,x100906,x100901,x100902))))+E(f335(f335(f6(x100901,x100902),f335(f335(f18(x100901,f888(x100903,a879),x100902),f335(f335(f8(f888(x100903,x100902),f888(f888(x100903,a879),x100902),x100901),f6(x100903,x100902)),x100904)),x100905)),x100906),f335(f335(f6(f887(x100901,x100903),x100902),f335(f268(x100901,x100903,x100902),x100904)),f335(f335(f266(x100901,x100903),x100906),x100905)))
% 59.73/59.67 [10073]~P73(x100732)+~P1(f335(f56(x100731),x100736))+P1(f335(f335(f337(x100731),x100733),x100736))+E(f335(f335(f9(x100731,x100732),f335(f335(f7(x100731,x100732,x100732),f335(f335(f18(x100731,x100732,f888(x100732,x100732)),f335(f335(f8(a879,f888(x100732,f888(x100732,x100732)),x100731),f88(x100732)),f335(f335(f7(x100731,x100731,a879),a332),x100733))),x100734)),x100735)),x100736),f335(f335(f254(x100732),x100735),f335(f29(x100731),x100736)))
% 59.73/59.67 [10076]~P73(x100762)+~P1(f335(f56(x100761),x100766))+~P1(f335(f335(f337(x100761),x100763),x100766))+E(f335(f335(f9(x100761,x100762),f335(f335(f7(x100761,x100762,x100762),f335(f335(f18(x100761,x100762,f888(x100762,x100762)),f335(f335(f8(a879,f888(x100762,f888(x100762,x100762)),x100761),f88(x100762)),f335(f335(f7(x100761,x100761,a879),a332),x100763))),x100764)),x100765)),x100766),f335(f335(f76(x100762),f335(x100764,x100763)),f335(f335(f254(x100762),x100765),f335(f335(f23(a881),f335(f29(x100761),x100766)),f73(a881)))))
% 59.73/59.67 [10141]~P1(f335(f56(x101411),x101415))+~P1(f335(f56(x101412),x101413))+P1(f335(f335(f337(x101412),f494(x101416,x101414,x101413,x101412,x101415,x101411)),x101413))+E(f335(f335(f6(x101411,a881),f335(f335(f8(f888(x101412,a879),a881,x101411),f29(x101412)),f335(f335(f8(f888(x101412,a879),f888(x101412,a879),x101411),f249(x101412)),f335(f335(f8(f888(x101412,a879),f888(x101412,a879),x101411),f335(f18(x101412,a879,a879),f335(f335(f8(a879,f888(a879,a879),x101412),a333),f335(f335(f7(x101412,f888(x101412,a879),a879),f337(x101412)),x101413)))),x101414)))),x101415),f335(f335(f76(a881),x101416),f335(f29(x101412),x101413)))
% 59.73/59.67 [10142]~P1(f335(f56(x101421),x101425))+~P1(f335(f56(x101422),x101423))+P1(f335(f335(f337(x101422),f502(x101426,x101424,x101423,x101422,x101425,x101421)),x101423))+E(f335(f335(f6(x101421,a881),f335(f335(f8(f888(x101422,a879),a881,x101421),f29(x101422)),f335(f335(f8(f888(x101422,a879),f888(x101422,a879),x101421),f249(x101422)),f335(f335(f8(f888(x101422,a879),f888(x101422,a879),x101421),f335(f18(x101422,a879,a879),f335(f335(f8(a879,f888(a879,a879),x101422),a333),f335(f335(f7(x101422,f888(x101422,a879),a879),f337(x101422)),x101423)))),x101424)))),x101425),f335(f335(f6(x101422,a881),x101426),x101423))
% 59.73/59.67 [10175]~P1(f335(f56(x101752),x101753))+~P1(f335(f56(x101751),x101755))+~E(f335(f29(x101751),f335(f249(x101751),f335(f335(f18(x101751,a879,a879),f335(f335(f8(a879,f888(a879,a879),x101751),a333),f335(f335(f7(x101751,f888(x101751,a879),a879),f337(x101751)),x101755))),f335(f335(f7(x101751,x101752,a879),x101754),f494(x101756,x101754,x101753,x101752,x101755,x101751))))),x101756)+E(f335(f335(f6(x101751,a881),f335(f335(f8(f888(x101752,a879),a881,x101751),f29(x101752)),f335(f335(f8(f888(x101752,a879),f888(x101752,a879),x101751),f249(x101752)),f335(f335(f8(f888(x101752,a879),f888(x101752,a879),x101751),f335(f18(x101752,a879,a879),f335(f335(f8(a879,f888(a879,a879),x101752),a333),f335(f335(f7(x101752,f888(x101752,a879),a879),f337(x101752)),x101753)))),x101754)))),x101755),f335(f335(f76(a881),x101756),f335(f29(x101752),x101753)))
% 59.73/59.67 [10177]~P1(f335(f56(x101772),x101773))+~P1(f335(f56(x101771),x101775))+~E(f335(f29(x101771),f335(f249(x101771),f335(f335(f18(x101771,a879,a879),f335(f335(f8(a879,f888(a879,a879),x101771),a333),f335(f335(f7(x101771,f888(x101771,a879),a879),f337(x101771)),x101775))),f335(f335(f7(x101771,x101772,a879),x101774),f502(x101776,x101774,x101773,x101772,x101775,x101771))))),f335(x101776,f502(x101776,x101774,x101773,x101772,x101775,x101771)))+E(f335(f335(f6(x101771,a881),f335(f335(f8(f888(x101772,a879),a881,x101771),f29(x101772)),f335(f335(f8(f888(x101772,a879),f888(x101772,a879),x101771),f249(x101772)),f335(f335(f8(f888(x101772,a879),f888(x101772,a879),x101771),f335(f18(x101772,a879,a879),f335(f335(f8(a879,f888(a879,a879),x101772),a333),f335(f335(f7(x101772,f888(x101772,a879),a879),f337(x101772)),x101773)))),x101774)))),x101775),f335(f335(f6(x101772,a881),x101776),x101773))
% 59.73/59.67 [9833]E(x98331,x98332)+~P18(x98333,x98334,x98335)+~P1(f335(f61(x98333,x98334,x98335,x98336,x98337),x98332))+~P1(f335(f61(x98333,x98334,x98335,x98336,x98337),x98331))
% 59.73/59.67 [9463]~P33(x94631,x94632,x94633,x94635,x94637)+~P33(x94631,x94632,x94633,x94634,x94636)+P33(x94631,x94632,x94633,f335(f335(f127(x94631),x94634),x94635),f335(f335(f127(x94632),x94636),x94637))+~E(f335(f189(f882(x94631)),x94634),f335(f189(f882(x94632)),x94636))
% 59.73/59.67 [9614]P1(f335(x96141,x96142))+~P1(f335(f335(f337(x96147),x96142),f335(x96146,x96144)))+~P1(f335(x96141,f739(x96141,x96146,x96145,x96143,x96147)))+~P1(f335(f335(f337(x96143),x96144),x96145))
% 59.73/59.67 [10064]~P18(x100647,x100646,x100641)+E(f335(f335(x100641,x100642),f621(x100642,x100643,x100644,x100645,x100641,x100646,x100647)),x100643)+~P1(f335(f61(x100647,x100646,x100641,x100645,x100644),x100643))+~P1(f335(f335(f337(x100647),x100642),x100644))
% 59.73/59.67 [10126]~P18(x101261,x101262,x101263)+~P1(f335(f61(x101261,x101262,x101263,x101264,x101265),x101267))+P1(f335(f61(x101261,x101262,x101263,x101264,f335(f335(f23(f888(x101261,a879)),x101265),f335(f335(f312(x101261),x101266),f188(f888(x101261,a879))))),f621(x101266,x101267,x101265,x101264,x101263,x101262,x101261)))+~P1(f335(f335(f337(x101261),x101266),x101265))
% 59.73/59.67 [9514]~P70(x95141)+~P26(x95145,x95142,x95146,x95147)+~P1(f335(f56(x95145),x95147))+E(f335(f335(f335(f60(x95141,x95142,f76(x95141)),x95143),x95144),f335(f313(x95145,x95142,x95146),x95147)),f335(f335(f335(f60(x95141,x95145,f76(x95141)),f335(f68(x95142,x95141,x95145,x95143),x95146)),x95144),x95147))
% 59.73/59.67 [9638]~E(f335(f335(f312(x96381),x96385),x96386),f335(f335(f312(x96381),x96382),x96383))+~P1(f335(f61(x96381,x96381,x96384,x96382,x96383),x96387))+P1(f335(f335(f337(x96381),x96382),x96383))+P1(f335(f57(x96381,x96384,f335(f335(f312(x96381),x96385),x96386)),x96387))
% 59.73/59.67 [9725]P1(f335(x97251,x97252))+~P1(f335(f335(f337(x97253),x97252),f335(x97254,x97257)))+~P1(f335(f335(f337(x97256),x97257),x97255))+P1(f335(f335(f337(x97253),f739(x97251,x97254,x97255,x97256,x97253)),f335(f335(f33(x97256,f888(x97253,a879)),x97255),x97254)))
% 59.73/59.67 [9742]~P26(x97422,x97421,x97425,x97424)+~P26(x97421,x97423,x97426,f335(f313(x97422,x97421,x97425),x97424))+E(f335(f335(f68(x97421,x97422,x97423,f72(x97422,x97421,x97424,x97425)),f72(x97421,x97423,f335(f313(x97422,x97421,x97425),x97424),x97426)),x97427),f335(f72(x97422,x97423,x97424,f335(f68(x97421,x97423,x97422,x97426),x97425)),x97427))+~P1(f335(f335(f337(x97423),x97427),f335(f313(x97421,x97423,x97426),f335(f313(x97422,x97421,x97425),x97424))))
% 59.73/59.67 [9743]~P26(x97432,x97431,x97435,x97434)+~P26(x97431,x97433,x97436,f335(f313(x97432,x97431,x97435),x97434))+E(f335(f335(f68(x97431,x97432,x97433,f87(x97432,x97431,x97434,x97435)),f87(x97431,x97433,f335(f313(x97432,x97431,x97435),x97434),x97436)),x97437),f335(f87(x97432,x97433,x97434,f335(f68(x97431,x97433,x97432,x97436),x97435)),x97437))+~P1(f335(f335(f337(x97433),x97437),f335(f313(x97431,x97433,x97436),f335(f313(x97432,x97431,x97435),x97434))))
% 59.73/59.67 [10065]~P18(x100657,x100656,x100651)+E(f335(f335(x100651,x100652),f650(x100653,x100654,x100652,x100655,x100651,x100656,x100657)),x100653)+P1(f335(f335(f337(x100657),x100652),x100654))+~P1(f335(f61(x100657,x100656,x100651,x100655,f335(f335(f312(x100657),x100652),x100654)),x100653))
% 59.73/59.67 [10125]~P18(x101251,x101254,x101255)+P1(f335(f61(x101251,x101254,x101255,x101256,x101253),f650(x101257,x101253,x101252,x101256,x101255,x101254,x101251)))+P1(f335(f335(f337(x101251),x101252),x101253))+~P1(f335(f61(x101251,x101254,x101255,x101256,f335(f335(f312(x101251),x101252),x101253)),x101257))
% 59.73/59.67 [9815]E(x98151,f2(a1))+~P1(f335(f43(x98153,x98151),f335(f335(f264(a1,a1),x98155),x98157)))+~P1(f335(f43(x98152,x98151),f335(f335(f264(a1,a1),x98154),x98156)))+P1(f335(f43(f335(f335(f75(a1),x98152),x98153),x98151),f335(f335(f264(a1,a1),f335(f335(f75(a1),f335(f335(f75(a1),x98154),x98155)),f335(f335(f30(a1),f335(f335(f75(a1),x98156),x98157)),x98151))),f39(a1,f335(f335(f75(a1),x98156),x98157),x98151))))
% 59.73/59.67 [9817]~P1(f335(f335(f243(a881),f2(a881)),x98173))+~P1(f335(f42(x98172,x98173),f335(f335(f264(a881,a881),x98175),x98177)))+~P1(f335(f42(x98171,x98173),f335(f335(f264(a881,a881),x98174),x98176)))+P1(f335(f42(f335(f335(f75(a881),x98171),x98172),x98173),f335(f335(f264(a881,a881),f335(f335(f75(a881),f335(f335(f75(a881),x98174),x98175)),f335(f335(f30(a881),f335(f335(f75(a881),x98176),x98177)),x98173))),f39(a881,f335(f335(f75(a881),x98176),x98177),x98173))))
% 59.73/59.67 [10174]~P77(x101742)+~P1(f335(f56(x101743),x101745))+~P1(f335(f56(x101741),x101747))+E(f335(f335(f6(x101741,x101742),f335(f335(f18(x101741,f888(x101743,a879),x101742),f335(f335(f8(f888(x101743,x101742),f888(f888(x101743,a879),x101742),x101741),f6(x101743,x101742)),x101744)),f335(f335(f8(f888(x101743,a879),f888(x101743,a879),x101741),f249(x101743)),f335(f335(f8(f888(x101743,a879),f888(x101743,a879),x101741),f335(f18(x101743,a879,a879),f335(f335(f8(a879,f888(a879,a879),x101743),a333),f335(f335(f7(x101743,f888(x101743,a879),a879),f337(x101743)),x101745)))),x101746)))),x101747),f335(f335(f6(x101743,x101742),f335(f335(f18(x101743,f888(x101741,a879),x101742),f335(f335(f8(f888(x101741,x101742),f888(f888(x101741,a879),x101742),x101743),f6(x101741,x101742)),f335(f7(x101741,x101743,x101742),x101744))),f335(f335(f8(f888(x101741,a879),f888(x101741,a879),x101743),f249(x101741)),f335(f335(f8(f888(x101741,a879),f888(x101741,a879),x101743),f335(f18(x101741,a879,a879),f335(f335(f8(a879,f888(a879,a879),x101741),a333),f335(f335(f7(x101741,f888(x101741,a879),a879),f337(x101741)),x101747)))),f335(f7(x101741,x101743,a879),x101746))))),x101745))
% 59.73/59.67 [9676]~P24(x96767,x96766,x96761,x96768,x96762,x96764)+E(f335(f335(x96761,f335(x96762,x96763)),f335(x96764,x96765)),f335(x96764,x96765))+~P1(f335(f56(x96766),x96765))+~P1(f335(f335(f337(x96766),x96763),x96765))
% 59.73/59.67 [9680]~P14(x96806,x96801,x96802,x96808,x96803,x96804)+~P8(x96806,x96807,x96808)+P13(x96801,x96802,x96803,f335(x96804,x96805))+~P1(f335(f335(f337(x96806),x96805),x96807))
% 59.73/59.67 [9300]~P21(x93007,x93001,x93008,x93003)+~P1(f335(f56(x93007),x93005))+~P1(f335(f56(x93007),x93004))+E(f335(f68(x93001,x93001,x93002,f335(x93003,x93004)),f335(f68(x93001,x93001,x93002,f335(x93003,x93005)),x93006)),f335(f68(x93001,x93001,x93002,f335(x93003,x93005)),f335(f68(x93001,x93001,x93002,f335(x93003,x93004)),x93006)))
% 59.73/59.67 [9308]~P33(x93081,x93082,x93083,x93084,x93087)+P33(x93081,x93082,x93083,f335(f335(f152(x93081,x93084),x93085),x93086),f335(f335(f152(x93082,x93087),x93085),x93088))+~P1(f335(f335(x93083,x93086),x93088))+~P1(f335(f335(f243(a881),x93085),f335(f189(f882(x93081)),x93084)))
% 59.73/59.67 [9309]~P33(x93091,x93092,x93093,x93094,x93097)+P33(x93091,x93092,x93093,f335(f335(f152(x93091,x93094),x93095),x93096),f335(f335(f152(x93092,x93097),x93095),x93098))+~P1(f335(f335(x93093,x93096),x93098))+~P1(f335(f335(f243(a881),x93095),f335(f189(f882(x93092)),x93097)))
% 59.73/59.67 [9386]~P26(x93862,x93862,x93865,x93866)+~P23(x93863,x93862,x93867,x93868,x93861)+~P1(f335(f56(x93862),x93866))+E(f335(f335(x93861,f335(f68(x93862,x93863,x93862,x93864),x93865)),x93866),f335(f335(x93861,x93864),f335(f313(x93862,x93862,x93865),x93866)))
% 59.73/59.67 [9678]~P25(x96787,x96782,x96785,x96788,x96786,x96781)+~P1(f335(f56(x96782),x96784))+E(f335(x96781,f335(f335(f312(x96782),x96783),x96784)),f335(f335(x96785,f335(x96786,x96783)),f335(x96781,x96784)))+P1(f335(f335(f337(x96782),x96783),x96784))
% 59.73/59.67 [9690]~P24(x96906,x96905,x96901,x96907,x96908,x96902)+E(f335(f335(x96901,f335(x96902,x96903)),f335(x96902,x96904)),f335(x96902,x96904))+~P1(f335(f56(x96905),x96904))+~P1(f335(f335(f242(f888(x96905,a879)),x96903),x96904))
% 59.73/59.67 [9285]P1(f335(f335(f337(f887(f882(x92851),f882(x92851))),f335(f335(f264(f882(x92851),f882(x92851)),x92852),x92853)),f150(x92851,x92854)))+~E(x92853,f335(f335(f127(x92851),x92855),f335(f335(f144(x92851),x92856),x92857)))+~E(x92852,f335(f335(f127(x92851),x92855),f335(f335(f144(x92851),x92858),x92857)))+~P1(f335(f335(f337(f887(x92851,x92851)),f335(f335(f264(x92851,x92851),x92858),x92856)),x92854))
% 59.73/59.67 [9683]~P24(x96836,x96832,x96835,x96837,x96838,x96831)+~P1(f335(f56(x96832),x96834))+~P1(f335(f56(x96832),x96833))+E(f335(x96831,f335(f335(f104(f888(x96832,a879)),x96833),x96834)),f335(f335(x96835,f335(x96831,x96833)),f335(x96831,x96834)))
% 59.73/59.67 [10215]~P26(x102154,x102152,x102155,x102158)+E(f335(f335(f34(x102151,f888(x102152,a879)),x102153),f335(f335(f8(f888(x102154,a879),f888(x102152,a879),x102151),f313(x102154,x102152,x102155)),x102156)),f335(f313(x102154,x102152,x102155),f335(f335(f34(x102151,f888(x102154,a879)),x102153),x102156)))+~P1(f335(f335(f337(x102151),x102157),x102153))+P1(f335(f335(f337(x102151),f639(x102157,x102156,x102153,x102151,x102158,x102155,x102152,x102154)),x102153))
% 59.73/59.67 [10237]~P26(x102374,x102372,x102375,x102377)+E(f335(f335(f34(x102371,f888(x102372,a879)),x102373),f335(f335(f8(f888(x102374,a879),f888(x102372,a879),x102371),f313(x102374,x102372,x102375)),x102376)),f335(f313(x102374,x102372,x102375),f335(f335(f34(x102371,f888(x102374,a879)),x102373),x102376)))+~P1(f335(f335(f337(x102371),x102378),x102373))+~P1(f335(f335(f242(f888(x102374,a879)),f335(x102376,f639(x102378,x102376,x102373,x102371,x102377,x102375,x102372,x102374))),x102377))
% 59.73/59.67 [9752]~P25(x97527,x97525,x97521,x97528,x97522,x97524)+~P1(f335(f56(x97525),x97526))+~P1(f335(f335(f337(x97525),x97523),x97526))+E(f335(f335(x97521,f335(x97522,x97523)),f335(x97524,f335(f335(f23(f888(x97525,a879)),x97526),f335(f335(f312(x97525),x97523),f188(f888(x97525,a879)))))),f335(x97524,x97526))
% 59.73/59.67 [9760]~P25(x97606,x97603,x97601,x97607,x97608,x97602)+~P1(f335(f56(x97603),x97605))+~P1(f335(f56(x97603),x97604))+E(f335(f335(x97601,f335(x97602,f335(f335(f104(f888(x97603,a879)),x97604),x97605))),f335(x97602,f335(f335(f95(f888(x97603,a879)),x97604),x97605))),f335(f335(x97601,f335(x97602,x97604)),f335(x97602,x97605)))
% 59.73/59.67 [9856]P40(x98561,x98562,x98563,x98564,x98565,f335(f335(x98563,x98566),x98567))+~P40(x98561,x98562,x98563,x98564,f335(f335(f23(f888(x98561,a879)),x98565),f335(f335(f312(x98561),x98568),f188(f888(x98561,a879)))),x98569)+~E(f335(f335(x98563,x98566),x98567),f335(f335(x98563,x98568),x98569))+~P1(f335(f335(f337(x98561),x98568),x98565))
% 59.73/59.67 [9788]~P14(x97886,x97887,x97888,x97889,x978810,x97881)+E(f335(f335(x97881,x97882),x97883),f335(f335(x97881,x97884),x97885))+~P1(f335(f335(f337(f887(x97887,x97887)),f335(f335(f264(x97887,x97887),x97883),x97885)),x978810))+~P1(f335(f335(f337(f887(x97886,x97886)),f335(f335(f264(x97886,x97886),x97882),x97884)),x97889))
% 59.73/59.67 [9540]E(x95401,f2(a1))+E(x95402,f2(a1))+E(f335(f335(f81(a1,f887(a1,a1)),f335(f335(a220,x95402),x95401)),f335(f335(f18(a1,a1,f887(a1,a1)),f335(f335(f8(a1,f888(a1,f887(a1,a1)),a1),f264(a1,a1)),f335(f30(a1),x95402))),f335(f30(a1),x95401))),f218(x95402,x95401))+P1(f335(f335(f243(a1),x95401),f2(a1)))+~P1(f335(f323(f887(a1,a1),a224),f335(f335(f264(a1,a1),x95402),x95401)))
% 59.73/59.67 [9388]~P61(x93882)+E(x93881,f188(f888(x93882,a879)))+~P1(f335(f56(x93882),x93881))+P1(f335(f335(f337(x93882),f10(x93882,x93881)),x93881))+~P1(f335(f335(f337(x93882),f335(f335(f95(x93882),f858(x93881,x93882)),f859(x93881,x93882))),f335(f335(f312(x93882),f858(x93881,x93882)),f335(f335(f312(x93882),f859(x93881,x93882)),f188(f888(x93882,a879))))))
% 59.73/59.67 [9389]~P61(x93892)+E(x93891,f188(f888(x93892,a879)))+~P1(f335(f56(x93892),x93891))+P1(f335(f335(f337(x93892),f13(x93892,x93891)),x93891))+~P1(f335(f335(f337(x93892),f335(f335(f104(x93892),f860(x93891,x93892)),f861(x93891,x93892))),f335(f335(f312(x93892),f860(x93891,x93892)),f335(f335(f312(x93892),f861(x93891,x93892)),f188(f888(x93892,a879))))))
% 59.73/59.67 [9390]~P106(x93902)+E(x93901,f188(f888(x93902,a879)))+~P1(f335(f56(x93902),x93901))+P1(f335(f335(f337(x93902),f14(x93902,x93901)),x93901))+~P1(f335(f335(f337(x93902),f335(f335(f241(x93902),f424(x93901,x93902)),f428(x93901,x93902))),f335(f335(f312(x93902),f424(x93901,x93902)),f335(f335(f312(x93902),f428(x93901,x93902)),f188(f888(x93902,a879))))))
% 59.73/59.67 [9391]~P106(x93912)+E(x93911,f188(f888(x93912,a879)))+~P1(f335(f56(x93912),x93911))+P1(f335(f335(f337(x93912),f15(x93912,x93911)),x93911))+~P1(f335(f335(f337(x93912),f335(f335(f240(x93912),f412(x93911,x93912)),f413(x93911,x93912))),f335(f335(f312(x93912),f412(x93911,x93912)),f335(f335(f312(x93912),f413(x93911,x93912)),f188(f888(x93912,a879))))))
% 59.73/59.67 [9419]~P70(x94192)+E(x94191,f188(f888(x94192,a879)))+~P1(f335(f56(x94192),x94191))+P1(f335(f335(f337(x94192),f335(f58(x94192,f76(x94192)),x94191)),x94191))+~P1(f335(f335(f337(x94192),f335(f335(f76(x94192),f349(x94191,x94192)),f350(x94191,x94192))),f335(f335(f312(x94192),f349(x94191,x94192)),f335(f335(f312(x94192),f350(x94191,x94192)),f188(f888(x94192,a879))))))
% 59.73/59.67 [9424]~P106(x94242)+E(x94241,f188(f888(x94242,a879)))+~P1(f335(f56(x94242),x94241))+P1(f335(f335(f337(x94242),f11(x94242,f240(x94242),x94241)),x94241))+~P1(f335(f335(f337(x94242),f335(f335(f240(x94242),f420(x94241,x94242)),f425(x94241,x94242))),f335(f335(f312(x94242),f420(x94241,x94242)),f335(f335(f312(x94242),f425(x94241,x94242)),f188(f888(x94242,a879))))))
% 59.73/59.67 [9425]~P106(x94252)+E(x94251,f188(f888(x94252,a879)))+~P1(f335(f56(x94252),x94251))+P1(f335(f335(f337(x94252),f12(x94252,f241(x94252),x94251)),x94251))+~P1(f335(f335(f337(x94252),f335(f335(f241(x94252),f426(x94251,x94252)),f427(x94251,x94252))),f335(f335(f312(x94252),f426(x94251,x94252)),f335(f335(f312(x94252),f427(x94251,x94252)),f188(f888(x94252,a879))))))
% 59.73/59.67 [6543]~P90(x65432)+E(x65431,f2(x65432))+~E(f335(f335(f75(x65432),x65433),x65431),f2(x65432))+~P1(f335(f335(f242(x65432),f2(x65432)),x65433))+~P1(f335(f335(f242(x65432),f2(x65432)),x65431))
% 59.73/59.67 [6544]~P90(x65442)+E(x65441,f2(x65442))+~E(f335(f335(f75(x65442),x65441),x65443),f2(x65442))+~P1(f335(f335(f242(x65442),f2(x65442)),x65443))+~P1(f335(f335(f242(x65442),f2(x65442)),x65441))
% 59.73/59.67 [7082]~P106(x70822)+~P15(x70822,x70821)+E(x70821,f107(x70822))+~P1(f335(f335(f337(x70822),x70823),f335(f166(x70822),f722(x70821,x70822))))+P1(f335(f335(f242(x70822),f749(x70821,x70822)),x70823))
% 59.73/59.67 [7248]~P106(x72481)+E(f15(x72481,x72482),x72483)+~P1(f335(f56(x72481),x72482))+~P1(f335(f335(f242(x72481),x72483),f585(x72483,x72482,x72481)))+~P1(f335(f335(f337(x72481),x72483),x72482))
% 59.73/59.67 [7281]~P106(x72811)+~P15(x72811,x72812)+~P15(x72811,x72813)+P15(x72811,f335(f335(f127(x72811),x72812),x72813))+P1(f335(f335(f337(x72811),f736(x72813,x72812,x72811)),f335(f166(x72811),x72812)))
% 59.73/59.67 [7282]~P106(x72821)+~P15(x72821,x72822)+~P15(x72821,x72823)+P15(x72821,f335(f335(f127(x72821),x72822),x72823))+P1(f335(f335(f337(x72821),f737(x72823,x72822,x72821)),f335(f166(x72821),x72823)))
% 59.73/59.67 [7342]~P106(x73421)+E(f14(x73421,x73422),x73423)+~P1(f335(f56(x73421),x73422))+P1(f335(f335(f337(x73421),f588(x73423,x73422,x73421)),x73422))+~P1(f335(f335(f337(x73421),x73423),x73422))
% 59.73/59.67 [7343]~P106(x73431)+E(f15(x73431,x73432),x73433)+~P1(f335(f56(x73431),x73432))+P1(f335(f335(f337(x73431),f585(x73433,x73432,x73431)),x73432))+~P1(f335(f335(f337(x73431),x73433),x73432))
% 59.73/59.67 [7923]~P106(x79231)+E(f14(x79231,x79232),x79233)+~P1(f335(f56(x79231),x79232))+~P1(f335(f335(f337(x79231),x79233),x79232))+~P1(f335(f335(f242(x79231),f588(x79233,x79232,x79231)),x79233))
% 59.73/59.67 [8247]~P106(x82471)+~P15(x82471,x82472)+~P15(x82471,x82473)+P15(x82471,f335(f335(f127(x82471),x82472),x82473))+~P1(f335(f335(f242(x82471),f736(x82473,x82472,x82471)),f737(x82473,x82472,x82471)))
% 59.73/59.67 [9025]~P61(x90252)+E(x90251,f188(f888(x90252,a879)))+~E(f335(f335(f95(x90252),f335(x90253,f857(x90251,x90253,x90252))),f335(x90253,f865(x90251,x90253,x90252))),f335(x90253,f335(f335(f95(x90252),f857(x90251,x90253,x90252)),f865(x90251,x90253,x90252))))+E(f10(x90252,f335(f313(x90252,x90252,x90253),x90251)),f335(x90253,f10(x90252,x90251)))+~P1(f335(f56(x90252),x90251))
% 59.73/59.67 [9026]~P61(x90262)+E(x90261,f188(f888(x90262,a879)))+~E(f335(f335(f104(x90262),f335(x90263,f866(x90261,x90263,x90262))),f335(x90263,f869(x90261,x90263,x90262))),f335(x90263,f335(f335(f104(x90262),f866(x90261,x90263,x90262)),f869(x90261,x90263,x90262))))+E(f13(x90262,f335(f313(x90262,x90262,x90263),x90261)),f335(x90263,f13(x90262,x90261)))+~P1(f335(f56(x90262),x90261))
% 59.73/59.67 [9027]~P106(x90272)+E(x90271,f188(f888(x90272,a879)))+~E(f335(f335(f241(x90272),f335(x90273,f421(x90271,x90273,x90272))),f335(x90273,f431(x90271,x90273,x90272))),f335(x90273,f335(f335(f241(x90272),f421(x90271,x90273,x90272)),f431(x90271,x90273,x90272))))+E(f14(x90272,f335(f313(x90272,x90272,x90273),x90271)),f335(x90273,f14(x90272,x90271)))+~P1(f335(f56(x90272),x90271))
% 59.73/59.67 [9028]~P106(x90282)+E(x90281,f188(f888(x90282,a879)))+~E(f335(f335(f240(x90282),f335(x90283,f433(x90281,x90283,x90282))),f335(x90283,f434(x90281,x90283,x90282))),f335(x90283,f335(f335(f240(x90282),f433(x90281,x90283,x90282)),f434(x90281,x90283,x90282))))+E(f15(x90282,f335(f313(x90282,x90282,x90283),x90281)),f335(x90283,f15(x90282,x90281)))+~P1(f335(f56(x90282),x90281))
% 59.73/59.67 [9097]~P106(x90972)+E(x90971,f188(f888(x90972,a879)))+~E(f335(f335(f240(x90972),f335(x90973,f422(x90971,x90973,x90972))),f335(x90973,f430(x90971,x90973,x90972))),f335(x90973,f335(f335(f240(x90972),f422(x90971,x90973,x90972)),f430(x90971,x90973,x90972))))+E(f11(x90972,f240(x90972),f335(f313(x90972,x90972,x90973),x90971)),f335(x90973,f11(x90972,f240(x90972),x90971)))+~P1(f335(f56(x90972),x90971))
% 59.73/59.67 [9098]~P106(x90982)+E(x90981,f188(f888(x90982,a879)))+~E(f335(f335(f241(x90982),f335(x90983,f423(x90981,x90983,x90982))),f335(x90983,f429(x90981,x90983,x90982))),f335(x90983,f335(f335(f241(x90982),f423(x90981,x90983,x90982)),f429(x90981,x90983,x90982))))+E(f12(x90982,f241(x90982),f335(f313(x90982,x90982,x90983),x90981)),f335(x90983,f12(x90982,f241(x90982),x90981)))+~P1(f335(f56(x90982),x90981))
% 59.73/59.67 [6173]~P61(x61732)+E(x61731,f188(f888(x61732,a879)))+~P1(f335(f56(x61732),x61731))+E(f10(x61732,f335(f335(f312(x61732),x61733),x61731)),f335(f335(f95(x61732),x61733),f10(x61732,x61731)))+P1(f335(f335(f337(x61732),x61733),x61731))
% 59.73/59.67 [6174]~P61(x61742)+E(x61741,f188(f888(x61742,a879)))+~P1(f335(f56(x61742),x61741))+E(f13(x61742,f335(f335(f312(x61742),x61743),x61741)),f335(f335(f104(x61742),x61743),f13(x61742,x61741)))+P1(f335(f335(f337(x61742),x61743),x61741))
% 59.73/59.67 [6175]~P106(x61752)+E(x61751,f188(f888(x61752,a879)))+~P1(f335(f56(x61752),x61751))+E(f14(x61752,f335(f335(f312(x61752),x61753),x61751)),f335(f335(f241(x61752),x61753),f14(x61752,x61751)))+P1(f335(f335(f337(x61752),x61753),x61751))
% 59.73/59.67 [6176]~P106(x61762)+E(x61761,f188(f888(x61762,a879)))+~P1(f335(f56(x61762),x61761))+E(f15(x61762,f335(f335(f312(x61762),x61763),x61761)),f335(f335(f240(x61762),x61763),f15(x61762,x61761)))+P1(f335(f335(f337(x61762),x61763),x61761))
% 59.73/59.67 [6559]~P70(x65592)+E(x65591,f188(f888(x65592,a879)))+~P1(f335(f56(x65592),x65591))+E(f335(f58(x65592,f76(x65592)),f335(f335(f312(x65592),x65593),x65591)),f335(f335(f76(x65592),x65593),f335(f58(x65592,f76(x65592)),x65591)))+P1(f335(f335(f337(x65592),x65593),x65591))
% 59.73/59.67 [6647]~P106(x66472)+E(x66471,f188(f888(x66472,a879)))+~P1(f335(f56(x66472),x66471))+E(f11(x66472,f240(x66472),f335(f335(f312(x66472),x66473),x66471)),f335(f335(f240(x66472),x66473),f11(x66472,f240(x66472),x66471)))+P1(f335(f335(f337(x66472),x66473),x66471))
% 59.73/59.67 [6648]~P106(x66482)+E(x66481,f188(f888(x66482,a879)))+~P1(f335(f56(x66482),x66481))+E(f12(x66482,f241(x66482),f335(f335(f312(x66482),x66483),x66481)),f335(f335(f241(x66482),x66483),f12(x66482,f241(x66482),x66481)))+P1(f335(f335(f337(x66482),x66483),x66481))
% 59.73/59.67 [7088]~P61(x70882)+E(f335(f335(f104(x70882),f13(x70882,x70881)),f13(x70882,x70883)),f13(x70882,x70883))+E(x70881,f188(f888(x70882,a879)))+~P1(f335(f56(x70882),x70883))+~P1(f335(f335(f242(f888(x70882,a879)),x70881),x70883))
% 59.73/59.67 [7089]~P61(x70892)+E(f335(f335(f95(x70892),f10(x70892,x70891)),f10(x70892,x70893)),f10(x70892,x70893))+E(x70891,f188(f888(x70892,a879)))+~P1(f335(f56(x70892),x70893))+~P1(f335(f335(f242(f888(x70892,a879)),x70891),x70893))
% 59.73/59.67 [7090]~P106(x70902)+E(f335(f335(f240(x70902),f15(x70902,x70901)),f15(x70902,x70903)),f15(x70902,x70903))+E(x70901,f188(f888(x70902,a879)))+~P1(f335(f56(x70902),x70903))+~P1(f335(f335(f242(f888(x70902,a879)),x70901),x70903))
% 59.73/59.67 [7091]~P106(x70912)+E(f335(f335(f241(x70912),f14(x70912,x70911)),f14(x70912,x70913)),f14(x70912,x70913))+E(x70911,f188(f888(x70912,a879)))+~P1(f335(f56(x70912),x70913))+~P1(f335(f335(f242(f888(x70912,a879)),x70911),x70913))
% 59.73/59.67 [7391]~P106(x73912)+E(x73911,f188(f888(x73912,a879)))+~P1(f335(f56(x73912),x73913))+P1(f335(f335(f242(x73912),f14(x73912,x73911)),f14(x73912,x73913)))+~P1(f335(f335(f242(f888(x73912,a879)),x73911),x73913))
% 59.73/59.67 [7392]~P106(x73922)+E(x73921,f188(f888(x73922,a879)))+~P1(f335(f56(x73922),x73923))+P1(f335(f335(f242(x73922),f15(x73922,x73923)),f15(x73922,x73921)))+~P1(f335(f335(f242(f888(x73922,a879)),x73921),x73923))
% 59.73/59.67 [7450]~P61(x74501)+E(f10(x74501,x74502),x74503)+~P1(f335(f56(x74501),x74502))+~E(f335(f335(f23(f888(x74501,a879)),x74502),f335(f335(f312(x74501),x74503),f188(f888(x74501,a879)))),f188(f888(x74501,a879)))+~P1(f335(f335(f337(x74501),x74503),x74502))
% 59.73/59.67 [7451]~P61(x74511)+E(f13(x74511,x74512),x74513)+~P1(f335(f56(x74511),x74512))+~E(f335(f335(f23(f888(x74511,a879)),x74512),f335(f335(f312(x74511),x74513),f188(f888(x74511,a879)))),f188(f888(x74511,a879)))+~P1(f335(f335(f337(x74511),x74513),x74512))
% 59.73/59.67 [7452]~P106(x74521)+E(f14(x74521,x74522),x74523)+~P1(f335(f56(x74521),x74522))+~E(f335(f335(f23(f888(x74521,a879)),x74522),f335(f335(f312(x74521),x74523),f188(f888(x74521,a879)))),f188(f888(x74521,a879)))+~P1(f335(f335(f337(x74521),x74523),x74522))
% 59.73/59.67 [7453]~P106(x74531)+E(f15(x74531,x74532),x74533)+~P1(f335(f56(x74531),x74532))+~E(f335(f335(f23(f888(x74531,a879)),x74532),f335(f335(f312(x74531),x74533),f188(f888(x74531,a879)))),f188(f888(x74531,a879)))+~P1(f335(f335(f337(x74531),x74533),x74532))
% 59.73/59.67 [7549]~P106(x75491)+E(f11(x75491,f240(x75491),x75492),x75493)+~P1(f335(f56(x75491),x75492))+~E(f335(f335(f23(f888(x75491,a879)),x75492),f335(f335(f312(x75491),x75493),f188(f888(x75491,a879)))),f188(f888(x75491,a879)))+~P1(f335(f335(f337(x75491),x75493),x75492))
% 59.73/59.67 [7550]~P106(x75501)+E(f12(x75501,f241(x75501),x75502),x75503)+~P1(f335(f56(x75501),x75502))+~E(f335(f335(f23(f888(x75501,a879)),x75502),f335(f335(f312(x75501),x75503),f188(f888(x75501,a879)))),f188(f888(x75501,a879)))+~P1(f335(f335(f337(x75501),x75503),x75502))
% 59.73/59.67 [7588]~P102(x75882)+E(x75881,f188(f888(x75882,a879)))+~P1(f335(f56(x75882),x75881))+~P1(f335(f335(f242(x75882),x75883),f346(x75883,x75881,x75882)))+P1(f335(f335(f242(x75882),x75883),f335(f58(x75882,f95(x75882)),x75881)))
% 59.73/59.67 [7589]~P106(x75892)+E(x75891,f188(f888(x75892,a879)))+~P1(f335(f56(x75892),x75891))+~P1(f335(f335(f242(x75892),x75893),f404(x75893,x75891,x75892)))+P1(f335(f335(f242(x75892),x75893),f335(f58(x75892,f240(x75892)),x75891)))
% 59.73/59.67 [7590]~P106(x75902)+E(x75901,f188(f888(x75902,a879)))+~P1(f335(f56(x75902),x75901))+~P1(f335(f335(f243(x75902),x75903),f407(x75903,x75901,x75902)))+P1(f335(f335(f243(x75902),x75903),f335(f58(x75902,f240(x75902)),x75901)))
% 59.73/59.67 [7676]~P102(x76762)+E(x76761,f188(f888(x76762,a879)))+~P1(f335(f56(x76762),x76761))+P1(f335(f335(f337(x76762),f346(x76763,x76761,x76762)),x76761))+P1(f335(f335(f242(x76762),x76763),f335(f58(x76762,f95(x76762)),x76761)))
% 59.73/59.67 [7677]~P106(x76772)+E(x76771,f188(f888(x76772,a879)))+~P1(f335(f56(x76772),x76771))+P1(f335(f335(f337(x76772),f404(x76773,x76771,x76772)),x76771))+P1(f335(f335(f242(x76772),x76773),f335(f58(x76772,f240(x76772)),x76771)))
% 59.73/59.67 [7678]~P106(x76782)+E(x76781,f188(f888(x76782,a879)))+~P1(f335(f56(x76782),x76781))+P1(f335(f335(f337(x76782),f407(x76783,x76781,x76782)),x76781))+P1(f335(f335(f243(x76782),x76783),f335(f58(x76782,f240(x76782)),x76781)))
% 59.73/59.67 [7800]~P106(x78002)+E(x78001,f188(f888(x78002,a879)))+E(f335(f335(f240(x78002),f11(x78002,f240(x78002),x78001)),f11(x78002,f240(x78002),x78003)),f11(x78002,f240(x78002),x78003))+~P1(f335(f56(x78002),x78003))+~P1(f335(f335(f242(f888(x78002,a879)),x78001),x78003))
% 59.73/59.67 [7801]~P106(x78012)+E(x78011,f188(f888(x78012,a879)))+E(f335(f335(f241(x78012),f12(x78012,f241(x78012),x78011)),f12(x78012,f241(x78012),x78013)),f12(x78012,f241(x78012),x78013))+~P1(f335(f56(x78012),x78013))+~P1(f335(f335(f242(f888(x78012,a879)),x78011),x78013))
% 59.73/59.67 [8007]~E(f636(x80071,x80073,x80072),f637(x80071,x80073,x80072))+~E(f335(f29(x80072),f638(x80071,x80073,x80072)),x80071)+E(f335(f335(f76(a881),x80071),f335(f29(f888(x80072,a879)),x80073)),f335(f29(x80072),f31(f888(x80072,a879),x80073)))+~P1(f335(f56(x80072),f31(f888(x80072,a879),x80073)))+~P1(f335(f56(f888(x80072,a879)),x80073))
% 59.73/59.67 [8182]~P106(x81822)+E(x81821,f188(f888(x81822,a879)))+~P1(f335(f56(x81822),x81823))+P1(f335(f335(f242(x81822),f335(f58(x81822,f240(x81822)),x81823)),f335(f58(x81822,f240(x81822)),x81821)))+~P1(f335(f335(f242(f888(x81822,a879)),x81821),x81823))
% 59.73/59.67 [8489]~E(f636(x84891,x84893,x84892),f637(x84891,x84893,x84892))+E(f335(f335(f76(a881),x84891),f335(f29(f888(x84892,a879)),x84893)),f335(f29(x84892),f31(f888(x84892,a879),x84893)))+P1(f335(f335(f337(f888(x84892,a879)),f638(x84891,x84893,x84892)),x84893))+~P1(f335(f56(x84892),f31(f888(x84892,a879),x84893)))+~P1(f335(f56(f888(x84892,a879)),x84893))
% 59.73/59.67 [8511]~E(f335(f29(x85112),f638(x85111,x85113,x85112)),x85111)+E(f335(f335(f76(a881),x85111),f335(f29(f888(x85112,a879)),x85113)),f335(f29(x85112),f31(f888(x85112,a879),x85113)))+P1(f335(f335(f337(f888(x85112,a879)),f637(x85111,x85113,x85112)),x85113))+~P1(f335(f56(x85112),f31(f888(x85112,a879),x85113)))+~P1(f335(f56(f888(x85112,a879)),x85113))
% 59.73/59.67 [8512]~E(f335(f29(x85122),f638(x85121,x85123,x85122)),x85121)+E(f335(f335(f76(a881),x85121),f335(f29(f888(x85122,a879)),x85123)),f335(f29(x85122),f31(f888(x85122,a879),x85123)))+P1(f335(f335(f337(f888(x85122,a879)),f636(x85121,x85123,x85122)),x85123))+~P1(f335(f56(x85122),f31(f888(x85122,a879),x85123)))+~P1(f335(f56(f888(x85122,a879)),x85123))
% 59.73/59.67 [8539]~E(f335(f29(x85392),f638(x85391,x85393,x85392)),x85391)+~E(f335(f335(f95(f888(x85392,a879)),f637(x85391,x85393,x85392)),f636(x85391,x85393,x85392)),f188(f888(x85392,a879)))+E(f335(f335(f76(a881),x85391),f335(f29(f888(x85392,a879)),x85393)),f335(f29(x85392),f31(f888(x85392,a879),x85393)))+~P1(f335(f56(f888(x85392,a879)),x85393))+~P1(f335(f56(x85392),f31(f888(x85392,a879),x85393)))
% 59.73/59.67 [8791]E(f335(f335(f76(a881),x87911),f335(f29(f888(x87912,a879)),x87913)),f335(f29(x87912),f31(f888(x87912,a879),x87913)))+P1(f335(f335(f337(f888(x87912,a879)),f638(x87911,x87913,x87912)),x87913))+P1(f335(f335(f337(f888(x87912,a879)),f637(x87911,x87913,x87912)),x87913))+~P1(f335(f56(f888(x87912,a879)),x87913))+~P1(f335(f56(x87912),f31(f888(x87912,a879),x87913)))
% 59.73/59.67 [8792]E(f335(f335(f76(a881),x87921),f335(f29(f888(x87922,a879)),x87923)),f335(f29(x87922),f31(f888(x87922,a879),x87923)))+P1(f335(f335(f337(f888(x87922,a879)),f638(x87921,x87923,x87922)),x87923))+P1(f335(f335(f337(f888(x87922,a879)),f636(x87921,x87923,x87922)),x87923))+~P1(f335(f56(f888(x87922,a879)),x87923))+~P1(f335(f56(x87922),f31(f888(x87922,a879),x87923)))
% 59.73/59.67 [8817]~E(f335(f335(f95(f888(x88172,a879)),f637(x88171,x88173,x88172)),f636(x88171,x88173,x88172)),f188(f888(x88172,a879)))+E(f335(f335(f76(a881),x88171),f335(f29(f888(x88172,a879)),x88173)),f335(f29(x88172),f31(f888(x88172,a879),x88173)))+~P1(f335(f56(f888(x88172,a879)),x88173))+P1(f335(f335(f337(f888(x88172,a879)),f638(x88171,x88173,x88172)),x88173))+~P1(f335(f56(x88172),f31(f888(x88172,a879),x88173)))
% 59.73/59.67 [9072]~P98(x90722)+E(x90721,f188(f888(x90722,a879)))+~E(f335(f335(f76(x90722),f335(x90723,f348(x90721,x90723,x90722))),f335(x90723,f351(x90721,x90723,x90722))),f335(x90723,f335(f335(f76(x90722),f348(x90721,x90723,x90722)),f351(x90721,x90723,x90722))))+~P1(f335(f56(x90722),x90721))+E(f335(f58(x90722,f76(x90722)),f335(f313(x90722,x90722,x90723),x90721)),f335(x90723,f335(f58(x90722,f76(x90722)),x90721)))
% 59.73/59.67 [10010]P1(f335(f335(x100101,x100102),x100103))+P1(f335(f335(f243(a1),f395(x100101,x100103,x100102)),f396(x100101,x100103,x100102)))+P1(f335(f335(f242(a1),f396(x100101,x100103,x100102)),f2(a1)))+P1(f335(f335(x100101,f395(x100101,x100103,x100102)),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f396(x100101,x100103,x100102))))+~P1(f335(f323(f887(a1,a1),a51),f335(f335(f264(a1,a1),x100102),x100103)))
% 59.73/59.67 [10016]P1(f335(f335(x100161,x100162),x100163))+P1(f335(f335(f242(a1),f406(x100161,x100163,x100162)),f2(a1)))+P1(f335(f335(x100161,f405(x100161,x100163,x100162)),f335(f335(f76(a1),f335(f97(a1),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f406(x100161,x100163,x100162))))+P1(f335(f335(f242(a1),f2(a1)),f335(f335(f75(a1),f405(x100161,x100163,x100162)),f406(x100161,x100163,x100162))))+~P1(f335(f323(f887(a1,a1),a46),f335(f335(f264(a1,a1),x100162),x100163)))
% 59.73/59.67 [7976]~P119(x79761)+~P1(f335(f335(f242(x79761),x79762),f73(x79761)))+~P1(f335(f335(f242(x79761),f2(x79761)),x79762))+~P1(f335(f335(f242(x79761),f2(x79761)),x79763))+P1(f335(f335(f242(x79761),f335(f335(f76(x79761),x79762),x79763)),x79763))
% 59.73/59.67 [7977]~P119(x79771)+~P1(f335(f335(f242(x79771),x79773),f73(x79771)))+~P1(f335(f335(f242(x79771),f2(x79771)),x79773))+~P1(f335(f335(f242(x79771),f2(x79771)),x79772))+P1(f335(f335(f242(x79771),f335(f335(f76(x79771),x79772),x79773)),x79772))
% 59.73/59.67 [8332]~P106(x83322)+E(x83321,f188(f888(x83322,a879)))+~P1(f335(f56(x83322),x83321))+P1(f335(f335(f242(x83322),f409(x83323,x83321,x83322)),x83323))+~P1(f335(f335(f242(x83322),f335(f58(x83322,f240(x83322)),x83321)),x83323))
% 59.73/59.67 [8333]~P106(x83332)+E(x83331,f188(f888(x83332,a879)))+~P1(f335(f56(x83332),x83331))+P1(f335(f335(f337(x83332),f409(x83333,x83331,x83332)),x83331))+~P1(f335(f335(f242(x83332),f335(f58(x83332,f240(x83332)),x83331)),x83333))
% 59.73/59.67 [8334]~P106(x83342)+E(x83341,f188(f888(x83342,a879)))+~P1(f335(f56(x83342),x83341))+P1(f335(f335(f337(x83342),f410(x83343,x83341,x83342)),x83341))+~P1(f335(f335(f243(x83342),f335(f58(x83342,f240(x83342)),x83341)),x83343))
% 59.73/59.67 [8335]~P106(x83352)+E(x83351,f188(f888(x83352,a879)))+~P1(f335(f56(x83352),x83351))+P1(f335(f335(f243(x83352),f410(x83353,x83351,x83352)),x83353))+~P1(f335(f335(f243(x83352),f335(f58(x83352,f240(x83352)),x83351)),x83353))
% 59.73/59.67 [8423]~P1(f335(x84231,x84233))+P1(f335(x84231,f476(x84231,x84232)))+P1(f335(x84231,f466(x84231,x84232)))+~P1(f335(f335(f243(a1),f2(a1)),x84232))+P1(f335(x84231,f335(f335(f23(a1),f466(x84231,x84232)),f335(f335(f76(a1),f477(x84231,x84232)),x84232))))
% 59.73/59.67 [8636]~P1(f335(x86361,x86363))+P1(f335(x86361,f466(x86361,x86362)))+~P1(f335(f335(f243(a1),f2(a1)),x86362))+P1(f335(f335(f337(a1),f476(x86361,x86362)),f305(a1,f73(a1),x86362)))+P1(f335(x86361,f335(f335(f23(a1),f466(x86361,x86362)),f335(f335(f76(a1),f477(x86361,x86362)),x86362))))
% 59.73/59.67 [8839]~P1(f335(x88391,x88393))+~P1(f335(x88391,f466(x88391,x88392)))+P1(f335(x88391,f476(x88391,x88392)))+~P1(f335(f335(f243(a1),f2(a1)),x88392))+~P1(f335(x88391,f335(f335(f23(a1),f466(x88391,x88392)),f335(f335(f76(a1),f477(x88391,x88392)),x88392))))
% 59.73/59.67 [8964]~P1(f335(x89641,x89643))+~P1(f335(x89641,f466(x89641,x89642)))+~P1(f335(f335(f243(a1),f2(a1)),x89642))+P1(f335(f335(f337(a1),f476(x89641,x89642)),f305(a1,f73(a1),x89642)))+~P1(f335(x89641,f335(f335(f23(a1),f466(x89641,x89642)),f335(f335(f76(a1),f477(x89641,x89642)),x89642))))
% 59.73/59.67 [9813]~P4(x98131)+~P4(x98132)+~P96(x98132)+P11(x98131,f335(f335(f8(f888(x98132,x98131),a879,f882(x98131)),x98133),f335(f335(f8(f888(x98132,f885(x98131)),f888(x98132,x98131),f882(x98131)),f68(f885(x98131),x98131,x98132,f239(x98131))),f335(f335(f8(f882(f887(x98132,x98131)),f888(x98132,f885(x98131)),f882(x98131)),f179(x98132,x98131)),f335(f175(x98132,x98131),f50(x98132))))),f335(f189(f882(x98132)),f50(x98132)))+~P1(f335(f52(f888(x98132,x98131)),x98133))
% 59.73/59.67 [9814]~P4(x98141)+~P4(x98142)+~P96(x98142)+P12(x98141,f335(f335(f8(f888(x98142,x98141),a879,f882(x98141)),x98143),f335(f335(f8(f888(x98142,f885(x98141)),f888(x98142,x98141),f882(x98141)),f68(f885(x98141),x98141,x98142,f239(x98141))),f335(f335(f8(f882(f887(x98142,x98141)),f888(x98142,f885(x98141)),f882(x98141)),f179(x98142,x98141)),f335(f175(x98142,x98141),f50(x98142))))),f335(f189(f882(x98142)),f50(x98142)))+~P1(f335(f53(f888(x98142,x98141)),x98143))
% 59.73/59.67 [9908]~P4(x99081)+~P4(x99082)+~P96(x99081)+~P12(x99082,f335(f335(f8(f888(x99081,x99082),a879,f882(x99082)),x99083),f335(f335(f8(f888(x99081,f885(x99082)),f888(x99081,x99082),f882(x99082)),f68(f885(x99082),x99082,x99081,f239(x99082))),f335(f335(f8(f882(f887(x99081,x99082)),f888(x99081,f885(x99082)),f882(x99082)),f179(x99081,x99082)),f335(f175(x99081,x99082),f50(x99081))))),f335(f189(f882(x99081)),f50(x99081)))+P1(f335(f53(f888(x99081,x99082)),x99083))
% 59.73/59.67 [9909]~P4(x99091)+~P4(x99092)+~P96(x99091)+~P11(x99092,f335(f335(f8(f888(x99091,x99092),a879,f882(x99092)),x99093),f335(f335(f8(f888(x99091,f885(x99092)),f888(x99091,x99092),f882(x99092)),f68(f885(x99092),x99092,x99091,f239(x99092))),f335(f335(f8(f882(f887(x99091,x99092)),f888(x99091,f885(x99092)),f882(x99092)),f179(x99091,x99092)),f335(f175(x99091,x99092),f50(x99091))))),f335(f189(f882(x99091)),f50(x99091)))+P1(f335(f52(f888(x99091,x99092)),x99093))
% 59.73/59.67 [8747]~P61(x87471)+~P1(f335(f56(x87471),x87472))+E(f335(f335(f23(f888(x87471,a879)),x87472),f335(f335(f312(x87471),x87473),f188(f888(x87471,a879)))),f188(f888(x87471,a879)))+~P1(f335(f335(f337(x87471),x87473),x87472))+E(f335(f335(f95(x87471),x87473),f10(x87471,f335(f335(f23(f888(x87471,a879)),x87472),f335(f335(f312(x87471),x87473),f188(f888(x87471,a879)))))),f10(x87471,x87472))
% 59.73/59.67 [8748]~P61(x87481)+~P1(f335(f56(x87481),x87482))+E(f335(f335(f23(f888(x87481,a879)),x87482),f335(f335(f312(x87481),x87483),f188(f888(x87481,a879)))),f188(f888(x87481,a879)))+~P1(f335(f335(f337(x87481),x87483),x87482))+E(f335(f335(f104(x87481),x87483),f13(x87481,f335(f335(f23(f888(x87481,a879)),x87482),f335(f335(f312(x87481),x87483),f188(f888(x87481,a879)))))),f13(x87481,x87482))
% 59.73/59.67 [8749]~P106(x87491)+~P1(f335(f56(x87491),x87492))+E(f335(f335(f23(f888(x87491,a879)),x87492),f335(f335(f312(x87491),x87493),f188(f888(x87491,a879)))),f188(f888(x87491,a879)))+~P1(f335(f335(f337(x87491),x87493),x87492))+E(f335(f335(f241(x87491),x87493),f14(x87491,f335(f335(f23(f888(x87491,a879)),x87492),f335(f335(f312(x87491),x87493),f188(f888(x87491,a879)))))),f14(x87491,x87492))
% 59.73/59.67 [8750]~P106(x87501)+~P1(f335(f56(x87501),x87502))+E(f335(f335(f23(f888(x87501,a879)),x87502),f335(f335(f312(x87501),x87503),f188(f888(x87501,a879)))),f188(f888(x87501,a879)))+~P1(f335(f335(f337(x87501),x87503),x87502))+E(f335(f335(f240(x87501),x87503),f15(x87501,f335(f335(f23(f888(x87501,a879)),x87502),f335(f335(f312(x87501),x87503),f188(f888(x87501,a879)))))),f15(x87501,x87502))
% 59.73/59.67 [8811]~P106(x88111)+~P1(f335(f56(x88111),x88112))+E(f335(f335(f23(f888(x88111,a879)),x88112),f335(f335(f312(x88111),x88113),f188(f888(x88111,a879)))),f188(f888(x88111,a879)))+~P1(f335(f335(f337(x88111),x88113),x88112))+E(f335(f335(f240(x88111),x88113),f11(x88111,f240(x88111),f335(f335(f23(f888(x88111,a879)),x88112),f335(f335(f312(x88111),x88113),f188(f888(x88111,a879)))))),f11(x88111,f240(x88111),x88112))
% 59.73/59.67 [8812]~P106(x88121)+~P1(f335(f56(x88121),x88122))+E(f335(f335(f23(f888(x88121,a879)),x88122),f335(f335(f312(x88121),x88123),f188(f888(x88121,a879)))),f188(f888(x88121,a879)))+~P1(f335(f335(f337(x88121),x88123),x88122))+E(f335(f335(f241(x88121),x88123),f12(x88121,f241(x88121),f335(f335(f23(f888(x88121,a879)),x88122),f335(f335(f312(x88121),x88123),f188(f888(x88121,a879)))))),f12(x88121,f241(x88121),x88122))
% 59.73/59.67 [8826]~P61(x88261)+~P1(f335(f56(x88261),x88263))+~P1(f335(f56(x88261),x88262))+E(f335(f335(f95(f888(x88261,a879)),x88262),x88263),f188(f888(x88261,a879)))+E(f335(f335(f104(x88261),f13(x88261,f335(f335(f104(f888(x88261,a879)),x88262),x88263))),f13(x88261,f335(f335(f95(f888(x88261,a879)),x88262),x88263))),f335(f335(f104(x88261),f13(x88261,x88262)),f13(x88261,x88263)))
% 59.73/59.67 [8827]~P61(x88271)+~P1(f335(f56(x88271),x88273))+~P1(f335(f56(x88271),x88272))+E(f335(f335(f95(f888(x88271,a879)),x88272),x88273),f188(f888(x88271,a879)))+E(f335(f335(f95(x88271),f10(x88271,f335(f335(f104(f888(x88271,a879)),x88272),x88273))),f10(x88271,f335(f335(f95(f888(x88271,a879)),x88272),x88273))),f335(f335(f95(x88271),f10(x88271,x88272)),f10(x88271,x88273)))
% 59.73/59.67 [8828]~P106(x88281)+~P1(f335(f56(x88281),x88283))+~P1(f335(f56(x88281),x88282))+E(f335(f335(f95(f888(x88281,a879)),x88282),x88283),f188(f888(x88281,a879)))+E(f335(f335(f240(x88281),f15(x88281,f335(f335(f104(f888(x88281,a879)),x88282),x88283))),f15(x88281,f335(f335(f95(f888(x88281,a879)),x88282),x88283))),f335(f335(f240(x88281),f15(x88281,x88282)),f15(x88281,x88283)))
% 59.73/59.67 [8829]~P106(x88291)+~P1(f335(f56(x88291),x88293))+~P1(f335(f56(x88291),x88292))+E(f335(f335(f95(f888(x88291,a879)),x88292),x88293),f188(f888(x88291,a879)))+E(f335(f335(f241(x88291),f14(x88291,f335(f335(f104(f888(x88291,a879)),x88292),x88293))),f14(x88291,f335(f335(f95(f888(x88291,a879)),x88292),x88293))),f335(f335(f241(x88291),f14(x88291,x88292)),f14(x88291,x88293)))
% 59.73/59.67 [9044]~P106(x90441)+~P1(f335(f56(x90441),x90443))+~P1(f335(f56(x90441),x90442))+E(f335(f335(f95(f888(x90441,a879)),x90442),x90443),f188(f888(x90441,a879)))+E(f335(f335(f240(x90441),f11(x90441,f240(x90441),f335(f335(f104(f888(x90441,a879)),x90442),x90443))),f11(x90441,f240(x90441),f335(f335(f95(f888(x90441,a879)),x90442),x90443))),f335(f335(f240(x90441),f11(x90441,f240(x90441),x90442)),f11(x90441,f240(x90441),x90443)))
% 59.73/59.67 [9045]~P106(x90451)+~P1(f335(f56(x90451),x90453))+~P1(f335(f56(x90451),x90452))+E(f335(f335(f95(f888(x90451,a879)),x90452),x90453),f188(f888(x90451,a879)))+E(f335(f335(f241(x90451),f12(x90451,f241(x90451),f335(f335(f104(f888(x90451,a879)),x90452),x90453))),f12(x90451,f241(x90451),f335(f335(f95(f888(x90451,a879)),x90452),x90453))),f335(f335(f241(x90451),f12(x90451,f241(x90451),x90452)),f12(x90451,f241(x90451),x90453)))
% 59.73/59.67 [9853]~P122(x98533)+E(x98531,x98532)+~P1(f335(f335(f242(x98533),f2(x98533)),x98532))+~P1(f335(f335(f242(x98533),f2(x98533)),x98531))+~E(f335(f335(f254(x98533),x98531),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))),f335(f335(f254(x98533),x98532),f335(f97(a881),f335(f335(f75(a1),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)),f335(f335(f23(a1),f335(f335(f75(a1),a78),a78)),a91)))))
% 59.73/59.67 [5117]~P95(x51171)+~P66(x51171)+~E(x51174,f2(x51171))+~E(f335(f97(x51171),x51172),f2(x51171))+E(f335(f97(x51171),x51172),f335(f335(f292(x51171),x51173),x51174))
% 59.73/59.67 [5118]~P95(x51181)+~P66(x51181)+~E(x51183,f2(x51181))+~E(f335(f97(x51181),x51184),f2(x51181))+E(f335(f335(f292(x51181),x51182),x51183),f335(f97(x51181),x51184))
% 59.73/59.67 [5209]~P95(x52092)+~P66(x52092)+~E(x52091,f2(x52092))+~E(f335(f97(x52092),x52094),f2(x52092))+E(x52091,f335(f335(f292(x52092),x52093),f335(f97(x52092),x52094)))
% 59.73/59.67 [5210]~P95(x52101)+~P66(x52101)+~E(x52104,f2(x52101))+~E(f335(f97(x52101),x52103),f2(x52101))+E(f335(f335(f292(x52101),x52102),f335(f97(x52101),x52103)),x52104)
% 59.73/59.67 [5241]~P95(x52411)+~P66(x52411)+~E(x52413,f2(x52411))+E(f335(f97(x52411),x52412),f2(x52411))+~E(f335(f97(x52411),x52412),f335(f335(f292(x52411),x52414),x52413))
% 59.73/59.68 [5242]~P95(x52421)+~P66(x52421)+~E(x52423,f2(x52421))+E(f335(f97(x52421),x52422),f2(x52421))+~E(f335(f335(f292(x52421),x52424),x52423),f335(f97(x52421),x52422))
% 59.73/59.68 [5406]~P95(x54062)+~P66(x54062)+E(x54061,f2(x54062))+~E(f335(f97(x54062),x54063),f2(x54062))+~E(x54061,f335(f335(f292(x54062),x54064),f335(f97(x54062),x54063)))
% 59.73/59.68 [5407]~P95(x54072)+~P66(x54072)+E(x54071,f2(x54072))+~E(f335(f97(x54072),x54073),f2(x54072))+~E(f335(f335(f292(x54072),x54074),f335(f97(x54072),x54073)),x54071)
% 59.73/59.68 [5631]~P95(x56312)+~P66(x56312)+~E(x56311,f2(x56312))+E(x56311,f335(f335(f292(x56312),x56313),f335(f97(x56312),x56314)))+~E(f335(f335(f76(x56312),x56311),f335(f97(x56312),x56314)),x56313)
% 59.73/59.68 [5632]~P95(x56321)+~P66(x56321)+~E(x56324,f2(x56321))+~E(x56322,f335(f335(f76(x56321),x56324),f335(f97(x56321),x56323)))+E(f335(f335(f292(x56321),x56322),f335(f97(x56321),x56323)),x56324)
% 59.73/59.68 [5698]~P95(x56981)+~P66(x56981)+E(f335(f97(x56981),x56982),f2(x56981))+~E(f335(f335(f292(x56981),x56983),f335(f97(x56981),x56982)),x56984)+E(x56983,f335(f335(f76(x56981),x56984),f335(f97(x56981),x56982)))
% 59.73/59.68 [5699]~P95(x56991)+~P66(x56991)+E(f335(f97(x56991),x56992),f2(x56991))+~E(f335(f335(f76(x56991),x56993),f335(f97(x56991),x56992)),x56994)+E(x56993,f335(f335(f292(x56991),x56994),f335(f97(x56991),x56992)))
% 59.73/59.68 [5700]~P95(x57001)+~P66(x57001)+E(f335(f97(x57001),x57002),f2(x57001))+~E(x57003,f335(f335(f292(x57001),x57004),f335(f97(x57001),x57002)))+E(f335(f335(f76(x57001),x57003),f335(f97(x57001),x57002)),x57004)
% 59.73/59.68 [5701]~P95(x57011)+~P66(x57011)+E(f335(f97(x57011),x57012),f2(x57011))+~E(x57013,f335(f335(f76(x57011),x57014),f335(f97(x57011),x57012)))+E(f335(f335(f292(x57011),x57013),f335(f97(x57011),x57012)),x57014)
% 59.73/59.68 [6357]E(f463(x63571,x63572,x63573),x63574)+E(f335(x63571,x63574),f2(a881))+~E(f335(f335(f6(x63573,a881),x63571),x63572),f73(a881))+~P1(f335(f56(x63573),x63572))+~P1(f335(f335(f337(x63573),x63574),x63572))
% 59.73/59.68 [6421]E(f489(x64211,x64212,x64213),x64214)+E(f335(x64211,x64214),f2(a881))+~E(f335(f335(f6(x64213,a881),x64211),x64212),f335(a106,f2(a881)))+~P1(f335(f56(x64213),x64212))+~P1(f335(f335(f337(x64213),x64214),x64212))
% 59.73/59.68 [6528]~P106(x65281)+~P5(x65281)+P1(f335(f335(f243(x65281),x65282),f31(x65281,x65283)))+~P1(f335(f335(f243(x65281),x65282),x65284))+~P1(f335(f335(f337(x65281),x65284),x65283))
% 59.73/59.68 [6706]~P106(x67061)+~P5(x67061)+~P1(f335(f335(f243(x67061),x67064),x67063))+P1(f335(f335(f243(x67061),f32(x67061,x67062)),x67063))+~P1(f335(f335(f337(x67061),x67064),x67062))
% 59.73/59.68 [6968]~P122(x69683)+E(x69681,x69682)+~E(f335(f335(f254(x69683),x69681),f335(a106,x69684)),f335(f335(f254(x69683),x69682),f335(a106,x69684)))+~P1(f335(f335(f242(x69683),f2(x69683)),x69682))+~P1(f335(f335(f242(x69683),f2(x69683)),x69681))
% 59.73/59.68 [7177]~E(f491(x71772,x71773,x71771,x71774),x71774)+~E(f335(x71772,x71774),f73(a881))+E(f335(f335(f6(x71771,a881),x71772),x71773),f73(a881))+~P1(f335(f56(x71771),x71773))+~P1(f335(f335(f337(x71771),x71774),x71773))
% 59.73/59.68 [7184]~P114(x71844)+~P131(x71844)+E(f335(x71841,f366(x71841,x71842,x71843,x71844)),f2(x71844))+~E(f335(f335(f9(x71843,x71844),x71841),x71842),f2(x71844))+~P1(f335(f56(x71843),x71842))
% 59.73/59.68 [7271]~E(f490(x72712,x72713,x72711,x72714),x72714)+~E(f335(x72712,x72714),f335(a106,f2(a881)))+E(f335(f335(f6(x72711,a881),x72712),x72713),f335(a106,f2(a881)))+~P1(f335(f56(x72711),x72713))+~P1(f335(f335(f337(x72711),x72714),x72713))
% 59.73/59.68 [8019]~E(f335(x80192,x80194),f73(a881))+~E(f335(x80192,f491(x80192,x80193,x80191,x80194)),f2(a881))+E(f335(f335(f6(x80191,a881),x80192),x80193),f73(a881))+~P1(f335(f56(x80191),x80193))+~P1(f335(f335(f337(x80191),x80194),x80193))
% 59.73/59.68 [8057]~E(f335(x80572,x80574),f335(a106,f2(a881)))+~E(f335(x80572,f490(x80572,x80573,x80571,x80574)),f2(a881))+E(f335(f335(f6(x80571,a881),x80572),x80573),f335(a106,f2(a881)))+~P1(f335(f56(x80571),x80573))+~P1(f335(f335(f337(x80571),x80574),x80573))
% 59.73/59.68 [8605]~P106(x86051)+~P15(x86051,x86054)+P15(x86051,x86052)+~E(x86052,f335(f335(f144(x86051),x86053),x86054))+~P1(f335(f335(f242(x86051),x86053),f751(x86052,x86051,x86054,x86053)))
% 59.73/59.68 [8640]E(x86401,x86402)+E(f335(f335(f23(a1),f467(x86403,x86402,x86404,x86401)),f468(x86403,x86402,x86404,x86401)),x86401)+~E(f335(f335(f75(a1),x86401),x86404),x86402)+~P1(f335(f335(f243(a1),f2(a1)),x86404))+~P1(f335(f335(f337(a1),x86402),x86403))
% 59.73/59.68 [8641]E(x86411,x86412)+E(f335(f335(f75(a1),f469(x86413,x86412,x86414,x86411)),f470(x86413,x86412,x86414,x86411)),x86411)+~E(f335(f335(f23(a1),x86411),x86414),x86412)+~P1(f335(f335(f243(a1),f2(a1)),x86414))+~P1(f335(f335(f337(a1),x86412),x86413))
% 59.73/59.68 [8824]E(f335(x88241,f618(x88242,x88241,x88243,x88244)),x88242)+P1(f335(f335(f242(a881),x88244),f619(x88242,x88241,x88243,x88244)))+~P1(f335(f335(f242(a1),x88242),f335(x88241,x88243)))+~P1(f335(f335(f243(a881),x88244),x88243))+~P1(f335(f335(f242(a1),f335(x88241,x88244)),x88242))
% 59.73/59.68 [8825]~P106(x88251)+~P15(x88251,x88253)+P15(x88251,x88252)+~E(x88252,f335(f335(f144(x88251),x88254),x88253))+P1(f335(f335(f337(x88251),f751(x88252,x88251,x88253,x88254)),f335(f166(x88251),x88253)))
% 59.73/59.68 [8843]~P114(x88434)+~P131(x88434)+~E(f335(f335(f9(x88431,x88434),x88432),x88433),f2(x88434))+~P1(f335(f56(x88431),x88433))+P1(f335(f335(f337(x88431),f366(x88432,x88433,x88431,x88434)),x88433))
% 59.73/59.68 [8878]~E(f335(x88782,x88784),f73(a881))+E(f335(f335(f6(x88781,a881),x88782),x88783),f73(a881))+~P1(f335(f56(x88781),x88783))+~P1(f335(f335(f337(x88781),x88784),x88783))+P1(f335(f335(f337(x88781),f491(x88782,x88783,x88781,x88784)),x88783))
% 59.73/59.68 [8887]E(x88871,x88872)+~E(f335(f335(f75(a1),x88872),x88874),x88871)+~P1(f335(f335(f243(a1),f2(a1)),x88874))+~P1(f335(f335(f337(a1),x88871),x88873))+P1(f335(f335(f337(a1),f467(x88873,x88871,x88874,x88872)),x88873))
% 59.73/59.68 [8888]E(x88881,x88882)+~E(f335(f335(f23(a1),x88882),x88884),x88881)+~P1(f335(f335(f243(a1),f2(a1)),x88884))+~P1(f335(f335(f337(a1),x88881),x88883))+P1(f335(f335(f337(a1),f469(x88883,x88881,x88884,x88882)),x88883))
% 59.73/59.68 [8890]~E(f335(x88902,x88904),f335(a106,f2(a881)))+E(f335(f335(f6(x88901,a881),x88902),x88903),f335(a106,f2(a881)))+~P1(f335(f56(x88901),x88903))+~P1(f335(f335(f337(x88901),x88904),x88903))+P1(f335(f335(f337(x88901),f490(x88902,x88903,x88901,x88904)),x88903))
% 59.73/59.68 [8895]P56(x88952,x88953,x88954,x88951)+E(x88951,f188(f888(x88952,a879)))+~P1(f335(f56(x88952),x88954))+~P1(f335(f56(x88952),x88951))+P1(f335(f335(f337(x88952),f513(x88951,x88954,x88953,x88952)),x88954))
% 59.73/59.68 [8976]E(x89761,x89762)+~E(f335(f335(f75(a1),x89762),x89764),x89761)+~P1(f335(f335(f243(a1),f2(a1)),x89764))+~P1(f335(f335(f337(a1),x89761),x89763))+P1(f335(f335(f337(a1),f468(x89763,x89761,x89764,x89762)),f305(a1,f73(a1),x89764)))
% 59.73/59.68 [8977]E(x89771,x89772)+~E(f335(f335(f23(a1),x89772),x89774),x89771)+~P1(f335(f335(f243(a1),f2(a1)),x89774))+~P1(f335(f335(f337(a1),x89771),x89773))+P1(f335(f335(f337(a1),f470(x89773,x89771,x89774,x89772)),f305(a1,f73(a1),x89774)))
% 59.73/59.68 [9050]P1(f335(f335(f242(a881),x90501),f618(x90502,x90503,x90504,x90501)))+~P1(f335(f335(f242(a1),x90502),f335(x90503,x90504)))+P1(f335(f335(f242(a881),x90501),f619(x90502,x90503,x90504,x90501)))+~P1(f335(f335(f243(a881),x90501),x90504))+~P1(f335(f335(f242(a1),f335(x90503,x90501)),x90502))
% 59.73/59.68 [9167]E(f335(x91671,f618(x91672,x91671,x91673,x91674)),x91672)+~P1(f335(f335(f242(a1),x91672),f335(x91671,x91673)))+P1(f335(f335(f243(a881),f619(x91672,x91671,x91673,x91674)),x91673))+~P1(f335(f335(f243(a881),x91674),x91673))+~P1(f335(f335(f242(a1),f335(x91671,x91674)),x91672))
% 59.73/59.68 [9297]~P1(f335(f335(f242(a1),x92972),f335(x92973,x92974)))+P1(f335(f335(f242(a881),x92971),f619(x92972,x92973,x92974,x92971)))+P1(f335(f335(f242(a881),f618(x92972,x92973,x92974,x92971)),x92974))+~P1(f335(f335(f243(a881),x92971),x92974))+~P1(f335(f335(f242(a1),f335(x92973,x92971)),x92972))
% 59.73/59.68 [9298]~P1(f335(f335(f242(a1),x92982),f335(x92983,x92984)))+P1(f335(f335(f242(a881),x92981),f618(x92982,x92983,x92984,x92981)))+P1(f335(f335(f243(a881),f619(x92982,x92983,x92984,x92981)),x92984))+~P1(f335(f335(f243(a881),x92981),x92984))+~P1(f335(f335(f242(a1),f335(x92983,x92981)),x92982))
% 59.73/59.68 [9402]~P1(f335(f335(f242(a1),x94021),f335(x94022,x94023)))+P1(f335(f335(f243(a881),f619(x94021,x94022,x94023,x94024)),x94023))+~P1(f335(f335(f243(a881),x94024),x94023))+~P1(f335(f335(f242(a1),f335(x94022,x94024)),x94021))+P1(f335(f335(f242(a881),f618(x94021,x94022,x94023,x94024)),x94023))
% 59.73/59.68 [9485]E(x94851,f188(f888(x94852,a879)))+~P1(f335(f56(x94852),x94854))+~P1(f335(f56(x94852),x94851))+P1(f335(f335(f337(f887(f888(x94852,a879),f888(x94852,a879))),f335(f335(f264(f888(x94852,a879),f888(x94852,a879)),x94854),x94851)),f327(x94852,x94853)))+P1(f335(f335(f337(x94852),f522(x94853,x94851,x94854,x94852)),x94854))
% 59.73/59.68 [9486]E(x94861,f188(f888(x94862,a879)))+~P1(f335(f56(x94862),x94864))+~P1(f335(f56(x94862),x94861))+P1(f335(f335(f337(f887(f888(x94862,a879),f888(x94862,a879))),f335(f335(f264(f888(x94862,a879),f888(x94862,a879)),x94864),x94861)),f327(x94862,x94863)))+P1(f335(f335(f337(x94862),f583(x94863,x94861,x94864,x94862)),x94864))
% 59.73/59.68 [10149]E(f335(x101491,f618(x101492,x101491,x101493,x101494)),x101492)+~P1(f335(f335(f242(a1),x101492),f335(x101491,x101493)))+~P1(f335(f335(f242(a1),f335(f70(a1),f335(f335(f23(a1),f335(x101491,f335(f335(f75(a881),f619(x101492,x101491,x101493,x101494)),f73(a881)))),f335(x101491,f619(x101492,x101491,x101493,x101494))))),f73(a1)))+~P1(f335(f335(f243(a881),x101494),x101493))+~P1(f335(f335(f242(a1),f335(x101491,x101494)),x101492))
% 59.73/59.68 [10150]~P1(f335(f335(f242(a1),x101502),f335(x101503,x101504)))+P1(f335(f335(f242(a881),x101501),f618(x101502,x101503,x101504,x101501)))+~P1(f335(f335(f242(a1),f335(f70(a1),f335(f335(f23(a1),f335(x101503,f335(f335(f75(a881),f619(x101502,x101503,x101504,x101501)),f73(a881)))),f335(x101503,f619(x101502,x101503,x101504,x101501))))),f73(a1)))+~P1(f335(f335(f243(a881),x101501),x101504))+~P1(f335(f335(f242(a1),f335(x101503,x101501)),x101502))
% 59.73/59.68 [10151]~P1(f335(f335(f242(a1),x101511),f335(x101512,x101513)))+~P1(f335(f335(f242(a1),f335(f70(a1),f335(f335(f23(a1),f335(x101512,f335(f335(f75(a881),f619(x101511,x101512,x101513,x101514)),f73(a881)))),f335(x101512,f619(x101511,x101512,x101513,x101514))))),f73(a1)))+~P1(f335(f335(f243(a881),x101514),x101513))+~P1(f335(f335(f242(a1),f335(x101512,x101514)),x101511))+P1(f335(f335(f242(a881),f618(x101511,x101512,x101513,x101514)),x101513))
% 59.73/59.68 [5653]~P95(x56532)+~P66(x56532)+E(x56531,f2(x56532))+~E(f335(f335(f292(x56532),x56533),x56531),f335(f97(x56532),x56534))+E(x56533,f335(f335(f76(x56532),f335(f97(x56532),x56534)),x56531))
% 59.73/59.68 [5654]~P95(x56542)+~P66(x56542)+E(x56541,f2(x56542))+~E(f335(f97(x56542),x56543),f335(f335(f292(x56542),x56544),x56541))+E(f335(f335(f76(x56542),f335(f97(x56542),x56543)),x56541),x56544)
% 59.73/59.68 [5811]~P95(x58112)+~P66(x58112)+E(x58111,f2(x58112))+E(f335(f97(x58112),x58113),f335(f335(f292(x58112),x58114),x58111))+~E(f335(f335(f76(x58112),f335(f97(x58112),x58113)),x58111),x58114)
% 59.73/59.68 [5812]~P95(x58122)+~P66(x58122)+E(x58121,f2(x58122))+E(f335(f335(f292(x58122),x58123),x58121),f335(f97(x58122),x58124))+~E(x58123,f335(f335(f76(x58122),f335(f97(x58122),x58124)),x58121))
% 59.73/59.68 [5934]~P95(x59341)+~P66(x59341)+~E(f335(f97(x59341),x59342),f2(x59341))+E(f335(f97(x59341),x59342),f335(f335(f292(x59341),x59343),x59344))+~E(f335(f335(f76(x59341),f335(f97(x59341),x59342)),x59344),x59343)
% 59.73/59.68 [5935]~P95(x59351)+~P66(x59351)+~E(f335(f97(x59351),x59354),f2(x59351))+E(f335(f335(f292(x59351),x59352),x59353),f335(f97(x59351),x59354))+~E(x59352,f335(f335(f76(x59351),f335(f97(x59351),x59354)),x59353))
% 59.73/59.68 [7237]~P68(x72371)+P1(f335(f335(f243(x72371),x72372),f2(x72371)))+~P1(f335(f335(f242(x72371),x72373),f2(x72371)))+P1(f335(f335(f243(x72371),f2(x72371)),x72372))+P1(f335(f335(f242(x72371),x72373),f335(f335(f292(x72371),x72374),x72372)))
% 59.73/59.68 [7238]~P68(x72381)+P1(f335(f335(f243(x72381),x72382),f2(x72381)))+~P1(f335(f335(f243(x72381),x72383),f2(x72381)))+P1(f335(f335(f243(x72381),f2(x72381)),x72382))+P1(f335(f335(f243(x72381),x72383),f335(f335(f292(x72381),x72384),x72382)))
% 59.73/59.68 [7489]~P68(x74891)+P1(f335(f335(f242(x74891),x74892),f2(x74891)))+P1(f335(f335(f243(x74891),x74893),f2(x74891)))+P1(f335(f335(f243(x74891),f2(x74891)),x74893))+~P1(f335(f335(f242(x74891),x74892),f335(f335(f292(x74891),x74894),x74893)))
% 59.73/59.68 [7490]~P68(x74901)+P1(f335(f335(f243(x74901),x74902),f2(x74901)))+P1(f335(f335(f243(x74901),x74903),f2(x74901)))+P1(f335(f335(f243(x74901),f2(x74901)),x74903))+~P1(f335(f335(f243(x74901),x74902),f335(f335(f292(x74901),x74904),x74903)))
% 59.73/59.68 [7608]E(x76081,x76082)+~E(f335(f335(f158(x76083),x76084),x76081),f335(f335(f158(x76083),x76084),x76082))+~P1(f335(f130(x76083),x76084))+~P1(f335(f335(f243(a881),x76082),f335(f189(f882(x76083)),x76084)))+~P1(f335(f335(f243(a881),x76081),f335(f189(f882(x76083)),x76084)))
% 59.73/59.68 [7609]E(x76091,x76092)+~E(f335(f335(f158(x76093),x76094),x76091),f335(f335(f158(x76093),x76094),x76092))+~P1(f335(f130(x76093),x76094))+~P1(f335(f335(f243(a881),x76092),f335(f189(f882(x76093)),x76094)))+~P1(f335(f335(f243(a881),x76091),f335(f189(f882(x76093)),x76094)))
% 59.73/59.68 [7978]~P68(x79781)+~P1(f335(f335(f242(x79781),x79783),f2(x79781)))+P1(f335(f335(f243(x79781),f2(x79781)),x79782))+~P1(f335(f335(f242(x79781),x79784),f335(f335(f76(x79781),x79783),x79782)))+P1(f335(f335(f242(x79781),x79783),f335(f335(f292(x79781),x79784),x79782)))
% 59.73/59.68 [7979]~P68(x79791)+~P1(f335(f335(f243(x79791),x79793),f2(x79791)))+P1(f335(f335(f243(x79791),f2(x79791)),x79792))+~P1(f335(f335(f243(x79791),x79794),f335(f335(f76(x79791),x79793),x79792)))+P1(f335(f335(f243(x79791),x79793),f335(f335(f292(x79791),x79794),x79792)))
% 59.73/59.68 [7980]~P68(x79801)+~P1(f335(f335(f243(x79801),x79802),f2(x79801)))+P1(f335(f335(f243(x79801),f2(x79801)),x79802))+~P1(f335(f335(f242(x79801),x79804),f335(f335(f76(x79801),x79803),x79802)))+P1(f335(f335(f242(x79801),x79803),f335(f335(f292(x79801),x79804),x79802)))
% 59.73/59.68 [7981]~P68(x79811)+~P1(f335(f335(f243(x79811),x79812),f2(x79811)))+P1(f335(f335(f243(x79811),f2(x79811)),x79812))+~P1(f335(f335(f242(x79811),x79814),f335(f335(f292(x79811),x79813),x79812)))+P1(f335(f335(f242(x79811),x79813),f335(f335(f76(x79811),x79814),x79812)))
% 59.73/59.68 [7982]~P68(x79821)+~P1(f335(f335(f243(x79821),x79822),f2(x79821)))+P1(f335(f335(f243(x79821),f2(x79821)),x79822))+~P1(f335(f335(f243(x79821),x79824),f335(f335(f76(x79821),x79823),x79822)))+P1(f335(f335(f243(x79821),x79823),f335(f335(f292(x79821),x79824),x79822)))
% 59.73/59.68 [7983]~P68(x79831)+~P1(f335(f335(f243(x79831),x79832),f2(x79831)))+P1(f335(f335(f243(x79831),f2(x79831)),x79832))+~P1(f335(f335(f243(x79831),x79834),f335(f335(f292(x79831),x79833),x79832)))+P1(f335(f335(f243(x79831),x79833),f335(f335(f76(x79831),x79834),x79832)))
% 59.73/59.68 [8121]~P106(x81211)+~P15(x81211,x81212)+~P1(f335(f335(f242(a881),x81213),x81214))+P1(f335(f335(f242(x81211),f335(f335(f158(x81211),x81212),x81213)),f335(f335(f158(x81211),x81212),x81214)))+~P1(f335(f335(f243(a881),x81214),f335(f189(f882(x81211)),x81212)))
% 59.73/59.68 [8122]~P106(x81221)+~P15(x81221,x81222)+~P1(f335(f335(f242(a881),x81223),x81224))+P1(f335(f335(f242(x81221),f335(f335(f158(x81221),x81222),x81223)),f335(f335(f158(x81221),x81222),x81224)))+~P1(f335(f335(f243(a881),x81224),f335(f189(f882(x81221)),x81222)))
% 59.73/59.68 [8172]~P122(x81721)+~P1(f335(f335(f242(x81721),x81722),f73(x81721)))+~P1(f335(f335(f242(x81721),f2(x81721)),x81722))+~P1(f335(f335(f242(a881),x81724),x81723))+P1(f335(f335(f242(x81721),f335(f335(f254(x81721),x81722),x81723)),f335(f335(f254(x81721),x81722),x81724)))
% 59.73/59.68 [8173]~P122(x81731)+~P1(f335(f335(f243(x81731),x81732),f73(x81731)))+~P1(f335(f335(f243(x81731),f2(x81731)),x81732))+~P1(f335(f335(f243(a881),x81734),x81733))+P1(f335(f335(f243(x81731),f335(f335(f254(x81731),x81732),x81733)),f335(f335(f254(x81731),x81732),x81734)))
% 59.73/59.68 [8174]~P122(x81741)+~P1(f335(f335(f242(x81741),f2(x81741)),x81742))+~P1(f335(f335(f243(a881),f2(a881)),x81743))+~P1(f335(f335(f243(x81741),x81742),x81744))+P1(f335(f335(f243(x81741),f335(f335(f254(x81741),x81742),x81743)),f335(f335(f254(x81741),x81744),x81743)))
% 59.73/59.68 [8194]~P106(x81941)+~P15(x81941,f335(f162(x81941),x81942))+~P1(f335(f335(f242(a881),x81944),x81943))+P1(f335(f335(f242(x81941),f335(f335(f158(x81941),x81942),x81943)),f335(f335(f158(x81941),x81942),x81944)))+~P1(f335(f335(f243(a881),x81943),f335(f189(f882(x81941)),x81942)))
% 59.73/59.68 [8443]~P68(x84431)+~P1(f335(f335(f242(x84431),x84432),f2(x84431)))+~P1(f335(f335(f242(x84431),x84433),x84434))+~P1(f335(f335(f243(x84431),f2(x84431)),f335(f335(f76(x84431),x84433),x84434)))+P1(f335(f335(f242(x84431),f335(f335(f292(x84431),x84432),x84433)),f335(f335(f292(x84431),x84432),x84434)))
% 59.73/59.68 [8444]~P69(x84441)+~P1(f335(f335(f243(x84441),x84442),f2(x84441)))+~P1(f335(f335(f243(x84441),x84443),x84444))+~P1(f335(f335(f243(x84441),f2(x84441)),f335(f335(f76(x84441),x84443),x84444)))+P1(f335(f335(f243(x84441),f335(f335(f292(x84441),x84442),x84443)),f335(f335(f292(x84441),x84442),x84444)))
% 59.73/59.68 [8453]~P69(x84531)+~P1(f335(f335(f242(x84531),x84534),x84533))+~P1(f335(f335(f242(x84531),f2(x84531)),x84532))+~P1(f335(f335(f243(x84531),f2(x84531)),f335(f335(f76(x84531),x84533),x84534)))+P1(f335(f335(f242(x84531),f335(f335(f292(x84531),x84532),x84533)),f335(f335(f292(x84531),x84532),x84534)))
% 59.73/59.68 [8454]~P69(x84541)+~P1(f335(f335(f243(x84541),x84544),x84543))+~P1(f335(f335(f243(x84541),f2(x84541)),x84542))+~P1(f335(f335(f243(x84541),f2(x84541)),f335(f335(f76(x84541),x84543),x84544)))+P1(f335(f335(f243(x84541),f335(f335(f292(x84541),x84542),x84543)),f335(f335(f292(x84541),x84542),x84544)))
% 59.73/59.68 [8555]P1(f335(x85551,x85552))+~P1(f335(f56(x85554),x85552))+P1(f335(x85551,f873(x85551,x85553,x85552,x85554)))+~P1(f335(x85551,f188(f888(x85554,a879))))+~P1(f335(f335(f242(f888(x85554,a879)),x85552),x85553))
% 59.73/59.68 [8563]P1(f335(x85631,x85632))+P1(f335(f56(x85633),f873(x85631,x85634,x85632,x85633)))+~P1(f335(f56(x85633),x85632))+~P1(f335(x85631,f188(f888(x85633,a879))))+~P1(f335(f335(f242(f888(x85633,a879)),x85632),x85634))
% 59.73/59.68 [8819]E(f335(f335(f75(a1),f458(x88191,x88192,x88193,x88194)),f459(x88191,x88192,x88193,x88194)),x88194)+~P1(f335(f335(f243(a1),f2(a1)),x88193))+~P1(f335(f335(f243(a1),x88192),x88194))+~P1(f335(f335(f337(a1),x88192),x88191))+P1(f335(f335(f243(a1),x88192),f335(f335(f23(a1),x88194),x88193)))
% 59.73/59.68 [9031]~P1(f335(f335(f243(a1),f2(a1)),x90313))+~P1(f335(f335(f243(a1),x90312),x90314))+~P1(f335(f335(f337(a1),x90312),x90311))+P1(f335(f335(f337(a1),f458(x90311,x90312,x90313,x90314)),x90311))+P1(f335(f335(f243(a1),x90312),f335(f335(f23(a1),x90314),x90313)))
% 59.73/59.68 [9043]P1(f335(x90431,x90432))+~P1(f335(f56(x90433),x90432))+P1(f335(f335(f337(x90433),f874(x90431,x90434,x90432,x90433)),x90434))+~P1(f335(x90431,f188(f888(x90433,a879))))+~P1(f335(f335(f242(f888(x90433,a879)),x90432),x90434))
% 59.73/59.68 [9060]E(f335(f335(f75(a1),f443(x90601,x90602,x90603,x90604)),f444(x90601,x90602,x90603,x90604)),x90604)+~P1(f335(f335(f243(a1),f2(a1)),x90603))+~P1(f335(f335(f242(a1),x90602),x90604))+P1(f335(f335(f242(a1),x90602),f335(f335(f23(a1),x90604),x90603)))+~P1(f335(f335(f337(a1),f335(f335(f23(a1),x90602),f73(a1))),x90601))
% 59.73/59.68 [9114]~P1(f335(f335(f243(a1),f2(a1)),x91143))+~P1(f335(f335(f243(a1),x91141),x91142))+~P1(f335(f335(f337(a1),x91141),x91144))+P1(f335(f335(f337(a1),f459(x91144,x91141,x91143,x91142)),f305(a1,f73(a1),x91143)))+P1(f335(f335(f243(a1),x91141),f335(f335(f23(a1),x91142),x91143)))
% 59.73/59.68 [9141]~P77(x91412)+~E(f814(x91413,x91414,x91411,x91412),f815(x91413,x91414,x91411,x91412))+~P1(f335(f56(x91411),f816(x91413,x91414,x91411,x91412)))+E(f335(f335(f6(f888(x91411,a879),x91412),f335(f6(x91411,x91412),x91413)),x91414),f335(f335(f6(x91411,x91412),x91413),f31(f888(x91411,a879),x91414)))+~P1(f335(f56(f888(x91411,a879)),x91414))
% 59.73/59.68 [9147]~P77(x91472)+~E(f335(x91473,f817(x91473,x91474,x91471,x91472)),f2(x91472))+~P1(f335(f56(x91471),f816(x91473,x91474,x91471,x91472)))+E(f335(f335(f6(f888(x91471,a879),x91472),f335(f6(x91471,x91472),x91473)),x91474),f335(f335(f6(x91471,x91472),x91473),f31(f888(x91471,a879),x91474)))+~P1(f335(f56(f888(x91471,a879)),x91474))
% 59.73/59.68 [9212]~P1(f335(f335(f243(a1),f2(a1)),x92123))+~P1(f335(f335(f242(a1),x92122),x92124))+P1(f335(f335(f337(a1),f443(x92121,x92122,x92123,x92124)),x92121))+P1(f335(f335(f242(a1),x92122),f335(f335(f23(a1),x92124),x92123)))+~P1(f335(f335(f337(a1),f335(f335(f23(a1),x92122),f73(a1))),x92121))
% 59.73/59.68 [9253]~P1(f335(f335(f243(a1),f2(a1)),x92533))+~P1(f335(f335(f242(a1),x92531),x92532))+P1(f335(f335(f337(a1),f444(x92534,x92531,x92533,x92532)),f305(a1,f73(a1),x92533)))+P1(f335(f335(f242(a1),x92531),f335(f335(f23(a1),x92532),x92533)))+~P1(f335(f335(f337(a1),f335(f335(f23(a1),x92531),f73(a1))),x92534))
% 59.73/59.68 [9274]~P77(x92742)+~E(f814(x92743,x92744,x92741,x92742),f815(x92743,x92744,x92741,x92742))+E(f335(f335(f6(f888(x92741,a879),x92742),f335(f6(x92741,x92742),x92743)),x92744),f335(f335(f6(x92741,x92742),x92743),f31(f888(x92741,a879),x92744)))+P1(f335(f335(f337(f888(x92741,a879)),f816(x92743,x92744,x92741,x92742)),x92744))+~P1(f335(f56(f888(x92741,a879)),x92744))
% 59.73/59.68 [9281]~P77(x92812)+~E(f335(x92813,f817(x92813,x92814,x92811,x92812)),f2(x92812))+E(f335(f335(f6(f888(x92811,a879),x92812),f335(f6(x92811,x92812),x92813)),x92814),f335(f335(f6(x92811,x92812),x92813),f31(f888(x92811,a879),x92814)))+P1(f335(f335(f337(f888(x92811,a879)),f816(x92813,x92814,x92811,x92812)),x92814))+~P1(f335(f56(f888(x92811,a879)),x92814))
% 59.73/59.68 [9380]~P77(x93802)+~P1(f335(f56(x93801),f816(x93803,x93804,x93801,x93802)))+E(f335(f335(f6(f888(x93801,a879),x93802),f335(f6(x93801,x93802),x93803)),x93804),f335(f335(f6(x93801,x93802),x93803),f31(f888(x93801,a879),x93804)))+P1(f335(f335(f337(f888(x93801,a879)),f815(x93803,x93804,x93801,x93802)),x93804))+~P1(f335(f56(f888(x93801,a879)),x93804))
% 59.73/59.68 [9381]~P77(x93812)+~P1(f335(f56(x93811),f816(x93813,x93814,x93811,x93812)))+E(f335(f335(f6(f888(x93811,a879),x93812),f335(f6(x93811,x93812),x93813)),x93814),f335(f335(f6(x93811,x93812),x93813),f31(f888(x93811,a879),x93814)))+P1(f335(f335(f337(f888(x93811,a879)),f814(x93813,x93814,x93811,x93812)),x93814))+~P1(f335(f56(f888(x93811,a879)),x93814))
% 59.73/59.68 [9455]~P77(x94552)+E(f335(f335(f6(f888(x94551,a879),x94552),f335(f6(x94551,x94552),x94553)),x94554),f335(f335(f6(x94551,x94552),x94553),f31(f888(x94551,a879),x94554)))+P1(f335(f335(f337(f888(x94551,a879)),f816(x94553,x94554,x94551,x94552)),x94554))+P1(f335(f335(f337(f888(x94551,a879)),f815(x94553,x94554,x94551,x94552)),x94554))+~P1(f335(f56(f888(x94551,a879)),x94554))
% 59.73/59.68 [9456]~P77(x94562)+E(f335(f335(f6(f888(x94561,a879),x94562),f335(f6(x94561,x94562),x94563)),x94564),f335(f335(f6(x94561,x94562),x94563),f31(f888(x94561,a879),x94564)))+P1(f335(f335(f337(f888(x94561,a879)),f816(x94563,x94564,x94561,x94562)),x94564))+P1(f335(f335(f337(f888(x94561,a879)),f814(x94563,x94564,x94561,x94562)),x94564))+~P1(f335(f56(f888(x94561,a879)),x94564))
% 59.73/59.68 [9474]~P77(x94742)+P1(f335(f335(f337(x94741),f817(x94743,x94744,x94741,x94742)),f815(x94743,x94744,x94741,x94742)))+~P1(f335(f56(x94741),f816(x94743,x94744,x94741,x94742)))+E(f335(f335(f6(f888(x94741,a879),x94742),f335(f6(x94741,x94742),x94743)),x94744),f335(f335(f6(x94741,x94742),x94743),f31(f888(x94741,a879),x94744)))+~P1(f335(f56(f888(x94741,a879)),x94744))
% 59.73/59.68 [9475]~P77(x94752)+P1(f335(f335(f337(x94751),f817(x94753,x94754,x94751,x94752)),f814(x94753,x94754,x94751,x94752)))+~P1(f335(f56(x94751),f816(x94753,x94754,x94751,x94752)))+E(f335(f335(f6(f888(x94751,a879),x94752),f335(f6(x94751,x94752),x94753)),x94754),f335(f335(f6(x94751,x94752),x94753),f31(f888(x94751,a879),x94754)))+~P1(f335(f56(f888(x94751,a879)),x94754))
% 59.73/59.68 [9488]P1(f335(x94881,x94882))+~P1(f335(f335(f337(x94883),f874(x94881,x94884,x94882,x94883)),f873(x94881,x94884,x94882,x94883)))+~P1(f335(f56(x94883),x94882))+~P1(f335(x94881,f188(f888(x94883,a879))))+~P1(f335(f335(f242(f888(x94883,a879)),x94882),x94884))
% 59.73/59.68 [9526]~P77(x95262)+P1(f335(f335(f337(x95261),f817(x95263,x95264,x95261,x95262)),f815(x95263,x95264,x95261,x95262)))+E(f335(f335(f6(f888(x95261,a879),x95262),f335(f6(x95261,x95262),x95263)),x95264),f335(f335(f6(x95261,x95262),x95263),f31(f888(x95261,a879),x95264)))+P1(f335(f335(f337(f888(x95261,a879)),f816(x95263,x95264,x95261,x95262)),x95264))+~P1(f335(f56(f888(x95261,a879)),x95264))
% 59.73/59.68 [9527]~P77(x95272)+P1(f335(f335(f337(x95271),f817(x95273,x95274,x95271,x95272)),f814(x95273,x95274,x95271,x95272)))+E(f335(f335(f6(f888(x95271,a879),x95272),f335(f6(x95271,x95272),x95273)),x95274),f335(f335(f6(x95271,x95272),x95273),f31(f888(x95271,a879),x95274)))+P1(f335(f335(f337(f888(x95271,a879)),f816(x95273,x95274,x95271,x95272)),x95274))+~P1(f335(f56(f888(x95271,a879)),x95274))
% 59.73/59.68 [9704]P1(f335(x97041,x97042))+~P1(f335(f56(x97043),x97042))+~P1(f335(x97041,f335(f335(f312(x97043),f874(x97041,x97044,x97042,x97043)),f873(x97041,x97044,x97042,x97043))))+~P1(f335(x97041,f188(f888(x97043,a879))))+~P1(f335(f335(f242(f888(x97043,a879)),x97042),x97044))
% 59.73/59.68 [7746]~P68(x77461)+P1(f335(f335(f243(x77461),x77462),f2(x77461)))+~P1(f335(f335(f242(x77461),f2(x77461)),x77464))+P1(f335(f335(f243(x77461),f2(x77461)),x77462))+P1(f335(f335(f242(x77461),f335(f335(f292(x77461),x77463),x77462)),x77464))
% 59.73/59.68 [7747]~P68(x77471)+P1(f335(f335(f243(x77471),x77472),f2(x77471)))+P1(f335(f335(f243(x77471),f2(x77471)),x77472))+~P1(f335(f335(f243(x77471),f2(x77471)),x77474))+P1(f335(f335(f243(x77471),f335(f335(f292(x77471),x77473),x77472)),x77474))
% 59.73/59.68 [7964]~P5(x79641)+~P37(x79641,x79641,x79644)+~E(x79643,f90(x79641,x79644))+P1(f335(f335(f242(x79641),x79642),x79643))+~P1(f335(f335(f242(x79641),x79642),f335(x79644,f335(f335(f104(x79641),x79642),x79643))))
% 59.73/59.68 [8032]~P1(f335(f335(f242(a1),x80324),f2(a1)))+~E(x80322,f335(f335(f75(a1),f335(f335(f76(a1),x80321),x80323)),x80324))+P1(f335(f335(f243(a1),f2(a1)),x80321))+~P1(f335(f335(f243(a1),x80321),x80324))+P1(f335(f43(x80322,x80321),f335(f335(f264(a1,a1),x80323),x80324)))
% 59.73/59.68 [8066]~P1(f335(x80661,x80664))+P1(f335(x80661,f418(x80662,x80661,x80663)))+~P1(f335(f335(f242(a1),f2(a1)),x80662))+~P1(f335(f335(f243(a1),f2(a1)),x80663))+P1(f335(x80661,f335(f335(f23(a1),x80664),f335(f335(f76(a1),x80662),x80663))))
% 59.73/59.68 [8067]~P1(f335(x80671,x80674))+P1(f335(x80671,f435(x80672,x80671,x80673)))+~P1(f335(f335(f242(a1),f2(a1)),x80672))+~P1(f335(f335(f243(a1),f2(a1)),x80673))+P1(f335(x80671,f335(f335(f75(a1),x80674),f335(f335(f76(a1),x80672),x80673))))
% 59.73/59.68 [8068]~P68(x80681)+P1(f335(f335(f243(x80681),x80682),f2(x80681)))+P1(f335(f335(f243(x80681),f2(x80681)),x80682))+P1(f335(f335(f242(x80681),f2(x80681)),x80683))+~P1(f335(f335(f242(x80681),f335(f335(f292(x80681),x80684),x80682)),x80683))
% 59.73/59.68 [8069]~P68(x80691)+P1(f335(f335(f243(x80691),x80692),f2(x80691)))+P1(f335(f335(f243(x80691),f2(x80691)),x80692))+P1(f335(f335(f243(x80691),f2(x80691)),x80693))+~P1(f335(f335(f243(x80691),f335(f335(f292(x80691),x80694),x80692)),x80693))
% 59.73/59.68 [8117]~E(x81171,f335(f335(f75(a1),f335(f335(f76(a1),x81172),x81173)),x81174))+~P1(f335(f335(f242(a1),f2(a1)),x81174))+~P1(f335(f335(f243(a1),f2(a1)),x81172))+~P1(f335(f335(f243(a1),x81174),x81172))+P1(f335(f43(x81171,x81172),f335(f335(f264(a1,a1),x81173),x81174)))
% 59.73/59.68 [8237]~P68(x82371)+P1(f335(f335(f243(x82371),x82372),f2(x82371)))+~P1(f335(f335(f242(x82371),f2(x82371)),x82374))+~P1(f335(f335(f242(x82371),x82373),f335(f335(f76(x82371),x82374),x82372)))+P1(f335(f335(f242(x82371),f335(f335(f292(x82371),x82373),x82372)),x82374))
% 59.73/59.68 [8238]~P68(x82381)+P1(f335(f335(f243(x82381),x82382),f2(x82381)))+~P1(f335(f335(f243(x82381),f2(x82381)),x82384))+~P1(f335(f335(f243(x82381),x82383),f335(f335(f76(x82381),x82384),x82382)))+P1(f335(f335(f243(x82381),f335(f335(f292(x82381),x82383),x82382)),x82384))
% 59.73/59.68 [8322]~P68(x83221)+P1(f335(f335(f243(x83221),x83222),f2(x83221)))+~P1(f335(f335(f242(x83221),x83223),f2(x83221)))+P1(f335(f335(f242(x83221),x83223),f335(f335(f292(x83221),x83224),x83222)))+~P1(f335(f335(f242(x83221),f335(f335(f76(x83221),x83223),x83222)),x83224))
% 59.73/59.68 [8323]~P68(x83231)+P1(f335(f335(f243(x83231),x83232),f2(x83231)))+~P1(f335(f335(f243(x83231),x83233),f2(x83231)))+P1(f335(f335(f243(x83231),x83233),f335(f335(f292(x83231),x83234),x83232)))+~P1(f335(f335(f243(x83231),f335(f335(f76(x83231),x83233),x83232)),x83234))
% 59.73/59.68 [8478]~P68(x84781)+~P1(f335(f335(f243(x84781),x84782),f2(x84781)))+P1(f335(f335(f243(x84781),f2(x84781)),x84782))+~P1(f335(f335(f242(x84781),f335(f335(f292(x84781),x84784),x84782)),x84783))+P1(f335(f335(f242(x84781),f335(f335(f76(x84781),x84783),x84782)),x84784))
% 59.73/59.68 [8479]~P68(x84791)+~P1(f335(f335(f243(x84791),x84792),f2(x84791)))+P1(f335(f335(f243(x84791),f2(x84791)),x84792))+~P1(f335(f335(f242(x84791),f335(f335(f76(x84791),x84794),x84792)),x84793))+P1(f335(f335(f242(x84791),f335(f335(f292(x84791),x84793),x84792)),x84794))
% 59.73/59.68 [8480]~P68(x84801)+~P1(f335(f335(f243(x84801),x84802),f2(x84801)))+P1(f335(f335(f243(x84801),f2(x84801)),x84802))+~P1(f335(f335(f243(x84801),f335(f335(f292(x84801),x84804),x84802)),x84803))+P1(f335(f335(f243(x84801),f335(f335(f76(x84801),x84803),x84802)),x84804))
% 59.73/59.68 [8481]~P68(x84811)+~P1(f335(f335(f243(x84811),x84812),f2(x84811)))+P1(f335(f335(f243(x84811),f2(x84811)),x84812))+~P1(f335(f335(f243(x84811),f335(f335(f76(x84811),x84814),x84812)),x84813))+P1(f335(f335(f243(x84811),f335(f335(f292(x84811),x84813),x84812)),x84814))
% 59.73/59.68 [8498]~P68(x84981)+~P1(f335(f335(f242(x84981),f2(x84981)),x84984))+P1(f335(f335(f243(x84981),f2(x84981)),x84982))+~P1(f335(f335(f242(x84981),f335(f335(f76(x84981),x84984),x84982)),x84983))+P1(f335(f335(f242(x84981),f335(f335(f292(x84981),x84983),x84982)),x84984))
% 59.73/59.68 [8499]~P68(x84991)+~P1(f335(f335(f243(x84991),f2(x84991)),x84994))+P1(f335(f335(f243(x84991),f2(x84991)),x84992))+~P1(f335(f335(f243(x84991),f335(f335(f76(x84991),x84994),x84992)),x84993))+P1(f335(f335(f243(x84991),f335(f335(f292(x84991),x84993),x84992)),x84994))
% 59.73/59.68 [8549]~P95(x85491)+~P68(x85491)+~P1(f335(f335(f243(x85491),f2(x85491)),x85494))+~P1(f335(f335(f242(x85491),f335(f335(f292(x85491),x85492),x85494)),f335(f97(x85491),x85493)))+P1(f335(f335(f242(x85491),x85492),f335(f335(f76(x85491),f335(f97(x85491),x85493)),x85494)))
% 59.73/59.68 [8550]~P95(x85501)+~P68(x85501)+~P1(f335(f335(f243(x85501),f2(x85501)),x85504))+~P1(f335(f335(f243(x85501),f335(f335(f292(x85501),x85502),x85504)),f335(f97(x85501),x85503)))+P1(f335(f335(f243(x85501),x85502),f335(f335(f76(x85501),f335(f97(x85501),x85503)),x85504)))
% 59.73/59.68 [8556]~P95(x85561)+~P68(x85561)+~P1(f335(f335(f243(x85561),f2(x85561)),x85563))+P1(f335(f335(f242(x85561),f335(f335(f292(x85561),x85562),x85563)),f335(f97(x85561),x85564)))+~P1(f335(f335(f242(x85561),x85562),f335(f335(f76(x85561),f335(f97(x85561),x85564)),x85563)))
% 59.73/59.68 [8557]~P95(x85571)+~P68(x85571)+~P1(f335(f335(f243(x85571),f2(x85571)),x85573))+P1(f335(f335(f243(x85571),f335(f335(f292(x85571),x85572),x85573)),f335(f97(x85571),x85574)))+~P1(f335(f335(f243(x85571),x85572),f335(f335(f76(x85571),f335(f97(x85571),x85574)),x85573)))
% 59.73/59.68 [8571]~P68(x85711)+~P1(f335(f335(f243(x85711),x85714),f2(x85711)))+~P1(f335(f335(f242(x85711),x85713),f335(f335(f76(x85711),x85712),x85714)))+P1(f335(f335(f242(x85711),x85712),f335(f335(f292(x85711),x85713),x85714)))+~P1(f335(f335(f242(x85711),f335(f335(f76(x85711),x85712),x85714)),x85713))
% 59.73/59.68 [8572]~P68(x85721)+~P1(f335(f335(f242(x85721),x85722),f2(x85721)))+~P1(f335(f335(f242(x85721),x85723),f335(f335(f76(x85721),x85722),x85724)))+P1(f335(f335(f242(x85721),x85722),f335(f335(f292(x85721),x85723),x85724)))+~P1(f335(f335(f242(x85721),f335(f335(f76(x85721),x85722),x85724)),x85723))
% 59.73/59.68 [8573]~P68(x85731)+~P1(f335(f335(f243(x85731),x85734),f2(x85731)))+~P1(f335(f335(f243(x85731),x85733),f335(f335(f76(x85731),x85732),x85734)))+P1(f335(f335(f243(x85731),x85732),f335(f335(f292(x85731),x85733),x85734)))+~P1(f335(f335(f243(x85731),f335(f335(f76(x85731),x85732),x85734)),x85733))
% 59.73/59.68 [8574]~P68(x85741)+~P1(f335(f335(f243(x85741),x85742),f2(x85741)))+~P1(f335(f335(f243(x85741),x85743),f335(f335(f76(x85741),x85742),x85744)))+P1(f335(f335(f243(x85741),x85742),f335(f335(f292(x85741),x85743),x85744)))+~P1(f335(f335(f243(x85741),f335(f335(f76(x85741),x85742),x85744)),x85743))
% 59.73/59.68 [8623]~P95(x86231)+~P68(x86231)+~P1(f335(f335(f243(x86231),f2(x86231)),f335(f97(x86231),x86233)))+~P1(f335(f335(f242(x86231),x86232),f335(f335(f292(x86231),x86234),f335(f97(x86231),x86233))))+P1(f335(f335(f242(x86231),f335(f335(f76(x86231),x86232),f335(f97(x86231),x86233))),x86234))
% 59.73/59.68 [8624]~P95(x86241)+~P68(x86241)+~P1(f335(f335(f243(x86241),f2(x86241)),f335(f97(x86241),x86243)))+~P1(f335(f335(f242(x86241),x86242),f335(f335(f76(x86241),x86244),f335(f97(x86241),x86243))))+P1(f335(f335(f242(x86241),f335(f335(f292(x86241),x86242),f335(f97(x86241),x86243))),x86244))
% 59.73/59.68 [8625]~P95(x86251)+~P68(x86251)+~P1(f335(f335(f243(x86251),f2(x86251)),f335(f97(x86251),x86253)))+~P1(f335(f335(f243(x86251),x86252),f335(f335(f292(x86251),x86254),f335(f97(x86251),x86253))))+P1(f335(f335(f243(x86251),f335(f335(f76(x86251),x86252),f335(f97(x86251),x86253))),x86254))
% 59.73/59.68 [8626]~P95(x86261)+~P68(x86261)+~P1(f335(f335(f243(x86261),f2(x86261)),f335(f97(x86261),x86263)))+~P1(f335(f335(f243(x86261),x86262),f335(f335(f76(x86261),x86264),f335(f97(x86261),x86263))))+P1(f335(f335(f243(x86261),f335(f335(f292(x86261),x86262),f335(f97(x86261),x86263))),x86264))
% 59.73/59.68 [8690]~P68(x86901)+~P1(f335(f335(f243(x86901),x86903),f2(x86901)))+~P1(f335(f335(f242(x86901),x86902),f335(f335(f76(x86901),x86904),x86903)))+~P1(f335(f335(f242(x86901),f335(f335(f76(x86901),x86904),x86903)),x86902))+P1(f335(f335(f242(x86901),f335(f335(f292(x86901),x86902),x86903)),x86904))
% 59.73/59.68 [8691]~P68(x86911)+~P1(f335(f335(f243(x86911),x86913),f2(x86911)))+~P1(f335(f335(f243(x86911),x86912),f335(f335(f76(x86911),x86914),x86913)))+~P1(f335(f335(f243(x86911),f335(f335(f76(x86911),x86914),x86913)),x86912))+P1(f335(f335(f243(x86911),f335(f335(f292(x86911),x86912),x86913)),x86914))
% 59.73/59.68 [8708]~P68(x87081)+~P1(f335(f335(f242(x87081),f2(x87081)),x87084))+~P1(f335(f335(f242(x87081),x87082),f335(f335(f76(x87081),x87084),x87083)))+~P1(f335(f335(f242(x87081),f335(f335(f76(x87081),x87084),x87083)),x87082))+P1(f335(f335(f242(x87081),f335(f335(f292(x87081),x87082),x87083)),x87084))
% 59.73/59.68 [8709]~P68(x87091)+~P1(f335(f335(f243(x87091),f2(x87091)),x87094))+~P1(f335(f335(f243(x87091),x87092),f335(f335(f76(x87091),x87094),x87093)))+~P1(f335(f335(f243(x87091),f335(f335(f76(x87091),x87094),x87093)),x87092))+P1(f335(f335(f243(x87091),f335(f335(f292(x87091),x87092),x87093)),x87094))
% 59.73/59.68 [8740]~P95(x87401)+~P68(x87401)+~P1(f335(f335(f243(x87401),f2(x87401)),f335(f97(x87401),x87404)))+P1(f335(f335(f242(x87401),x87402),f335(f335(f76(x87401),x87403),f335(f97(x87401),x87404))))+~P1(f335(f335(f242(x87401),f335(f335(f292(x87401),x87402),f335(f97(x87401),x87404))),x87403))
% 59.73/59.68 [8741]~P95(x87411)+~P68(x87411)+~P1(f335(f335(f243(x87411),f2(x87411)),f335(f97(x87411),x87414)))+P1(f335(f335(f242(x87411),x87412),f335(f335(f292(x87411),x87413),f335(f97(x87411),x87414))))+~P1(f335(f335(f242(x87411),f335(f335(f76(x87411),x87412),f335(f97(x87411),x87414))),x87413))
% 59.73/59.68 [8742]~P95(x87421)+~P68(x87421)+~P1(f335(f335(f243(x87421),f2(x87421)),f335(f97(x87421),x87424)))+P1(f335(f335(f243(x87421),x87422),f335(f335(f76(x87421),x87423),f335(f97(x87421),x87424))))+~P1(f335(f335(f243(x87421),f335(f335(f292(x87421),x87422),f335(f97(x87421),x87424))),x87423))
% 59.73/59.68 [8743]~P95(x87431)+~P68(x87431)+~P1(f335(f335(f243(x87431),f2(x87431)),f335(f97(x87431),x87434)))+P1(f335(f335(f243(x87431),x87432),f335(f335(f292(x87431),x87433),f335(f97(x87431),x87434))))+~P1(f335(f335(f243(x87431),f335(f335(f76(x87431),x87432),f335(f97(x87431),x87434))),x87433))
% 59.73/59.68 [8880]E(f335(f335(f23(a1),f460(x88801,x88802,x88803,x88804)),f461(x88801,x88802,x88803,x88804)),x88804)+~P1(f335(f335(f243(a1),f2(a1)),x88803))+~P1(f335(f335(f337(a1),x88802),x88801))+~P1(f335(f335(f243(a1),x88804),x88802))+P1(f335(f335(f243(a1),f335(f335(f75(a1),x88804),x88803)),x88802))
% 59.73/59.68 [8960]~P1(f335(x89601,x89602))+~P1(f335(f335(f242(a1),f2(a1)),x89603))+~P1(f335(f335(f243(a1),f2(a1)),x89604))+~P1(f335(x89601,f335(f335(f23(a1),f418(x89603,x89601,x89604)),x89604)))+P1(f335(x89601,f335(f335(f23(a1),x89602),f335(f335(f76(a1),x89603),x89604))))
% 59.73/59.68 [8961]~P1(f335(x89611,x89612))+~P1(f335(f335(f242(a1),f2(a1)),x89613))+~P1(f335(f335(f243(a1),f2(a1)),x89614))+~P1(f335(x89611,f335(f335(f75(a1),f435(x89613,x89611,x89614)),x89614)))+P1(f335(x89611,f335(f335(f75(a1),x89612),f335(f335(f76(a1),x89613),x89614))))
% 59.73/59.68 [9107]~P1(f335(f335(f243(a1),f2(a1)),x91073))+~P1(f335(f335(f337(a1),x91072),x91071))+~P1(f335(f335(f243(a1),x91074),x91072))+P1(f335(f335(f337(a1),f460(x91071,x91072,x91073,x91074)),x91071))+P1(f335(f335(f243(a1),f335(f335(f75(a1),x91074),x91073)),x91072))
% 59.73/59.68 [9128]E(f335(f335(f23(a1),f446(x91281,x91282,x91283,x91284)),f447(x91281,x91282,x91283,x91284)),x91284)+~P1(f335(f335(f243(a1),f2(a1)),x91283))+~P1(f335(f335(f242(a1),x91284),x91282))+~P1(f335(f335(f337(a1),f335(f335(f75(a1),x91282),f73(a1))),x91281))+P1(f335(f335(f242(a1),f335(f335(f75(a1),x91284),x91283)),x91282))
% 59.73/59.68 [9158]~P1(f335(f335(f243(a1),f2(a1)),x91582))+~P1(f335(f335(f337(a1),x91583),x91584))+~P1(f335(f335(f243(a1),x91581),x91583))+P1(f335(f335(f337(a1),f461(x91584,x91583,x91582,x91581)),f305(a1,f73(a1),x91582)))+P1(f335(f335(f243(a1),f335(f335(f75(a1),x91581),x91582)),x91583))
% 59.73/59.68 [9248]~P1(f335(f335(f243(a1),f2(a1)),x92483))+~P1(f335(f335(f242(a1),x92484),x92482))+P1(f335(f335(f337(a1),f446(x92481,x92482,x92483,x92484)),x92481))+~P1(f335(f335(f337(a1),f335(f335(f75(a1),x92482),f73(a1))),x92481))+P1(f335(f335(f242(a1),f335(f335(f75(a1),x92484),x92483)),x92482))
% 59.73/59.68 [9293]~P1(f335(f335(f243(a1),f2(a1)),x92932))+~P1(f335(f335(f242(a1),x92931),x92933))+P1(f335(f335(f337(a1),f447(x92934,x92933,x92932,x92931)),f305(a1,f73(a1),x92932)))+~P1(f335(f335(f337(a1),f335(f335(f75(a1),x92933),f73(a1))),x92934))+P1(f335(f335(f242(a1),f335(f335(f75(a1),x92931),x92932)),x92933))
% 59.73/59.68 [9577]~P36(x95771,x95773)+~P27(x95771,x95774)+P36(x95771,f335(f335(f104(f888(f887(x95771,x95771),a879)),x95772),x95773))+~P1(f335(f335(f242(f888(f887(x95771,x95771),a879)),x95772),f335(f263(f888(f887(x95771,x95771),a879),f888(f887(x95771,x95771),a879)),x95774)))+~P1(f335(f335(f242(f888(f887(x95771,x95771),a879)),x95773),f335(f267(f888(f887(x95771,x95771),a879),f888(f887(x95771,x95771),a879)),x95774)))
% 59.73/59.68 [9881]~E(f335(f662(x98811,x98814,x98813,x98812),f667(x98811,x98814,x98813,x98812)),f200(f882(a331)))+P1(f335(f335(f243(a1),f666(x98811,x98814,x98813,x98812)),f667(x98811,x98814,x98813,x98812)))+P1(f335(f335(f335(x98811,x98812),x98813),x98814))+P1(f335(f335(f335(x98811,f662(x98811,x98814,x98813,x98812)),f666(x98811,x98814,x98813,x98812)),f335(f335(f75(a1),f667(x98811,x98814,x98813,x98812)),f73(a1))))+~P1(f335(f323(f887(f888(a1,f885(f882(a331))),f887(a1,a1)),a320),f335(f335(f264(f888(a1,f885(f882(a331))),f887(a1,a1)),x98812),f335(f335(f264(a1,a1),x98813),x98814))))
% 59.73/59.68 [9979]~P20(x99792,x99794,x99793)+E(x99791,f188(f888(x99792,a879)))+~P1(f335(f56(x99792),x99791))+P1(f335(f335(f337(x99792),f335(x99793,x99791)),x99791))+~P1(f335(f335(f337(x99792),f335(f335(x99794,f862(x99791,x99793,x99794,x99792)),f863(x99791,x99793,x99794,x99792))),f335(f335(f312(x99792),f862(x99791,x99793,x99794,x99792)),f335(f335(f312(x99792),f863(x99791,x99793,x99794,x99792)),f188(f888(x99792,a879))))))
% 59.73/59.68 [8598]~P5(x85981)+~P37(x85981,x85981,x85984)+~E(x85982,f89(x85981,x85984))+P1(f335(f335(f242(x85981),x85982),x85983))+~P1(f335(f335(f242(x85981),f335(x85984,f335(f335(f95(x85981),x85982),x85983))),x85983))
% 59.73/59.68 [8730]~P95(x87301)+~P68(x87301)+~P1(f335(f335(f243(x87301),f2(x87301)),x87303))+~P1(f335(f335(f242(x87301),f335(f97(x87301),x87302)),f335(f335(f292(x87301),x87304),x87303)))+P1(f335(f335(f242(x87301),f335(f335(f76(x87301),f335(f97(x87301),x87302)),x87303)),x87304))
% 59.73/59.68 [8731]~P95(x87311)+~P68(x87311)+~P1(f335(f335(f243(x87311),f2(x87311)),x87313))+~P1(f335(f335(f243(x87311),f335(f97(x87311),x87312)),f335(f335(f292(x87311),x87314),x87313)))+P1(f335(f335(f243(x87311),f335(f335(f76(x87311),f335(f97(x87311),x87312)),x87313)),x87314))
% 59.73/59.68 [8883]~P95(x88831)+~P68(x88831)+~P1(f335(f335(f243(x88831),f2(x88831)),x88834))+P1(f335(f335(f242(x88831),f335(f97(x88831),x88832)),f335(f335(f292(x88831),x88833),x88834)))+~P1(f335(f335(f242(x88831),f335(f335(f76(x88831),f335(f97(x88831),x88832)),x88834)),x88833))
% 59.73/59.68 [8884]~P95(x88841)+~P68(x88841)+~P1(f335(f335(f243(x88841),f2(x88841)),x88844))+P1(f335(f335(f243(x88841),f335(f97(x88841),x88842)),f335(f335(f292(x88841),x88843),x88844)))+~P1(f335(f335(f243(x88841),f335(f335(f76(x88841),f335(f97(x88841),x88842)),x88844)),x88843))
% 59.73/59.68 [9911]~P107(x99112)+~P4(x99111)+~P1(f335(f335(f242(f888(x99111,x99112)),x99113),x99114))+P1(f335(f335(f243(f888(x99111,x99112)),x99113),x99114))+~P1(f335(f52(x99111),f335(f335(f8(a879,a879,x99111),a330),f335(f335(f18(x99111,x99112,a879),f335(f335(f8(x99112,f888(x99112,a879),x99111),a332),x99113)),x99114))))
% 59.73/59.68 [5163]~P49(x51634,x51635,x51633)+E(x51631,x51632)+~P106(x51634)+~P107(x51635)+~E(f335(x51633,x51631),f335(x51633,x51632))
% 59.73/59.68 [9494]~P52(x94941,x94941,x94944)+P1(f335(f335(f337(f887(x94941,x94941)),f335(f335(f264(x94941,x94941),x94942),x94943)),f310(x94941,x94944)))+P1(f335(f335(f337(f887(x94941,x94941)),f335(f335(f264(x94941,x94941),x94943),x94942)),f310(x94941,x94944)))+~P1(f335(f335(f337(f887(x94941,x94941)),f335(f335(f264(x94941,x94941),x94945),x94942)),f310(x94941,x94944)))+~P1(f335(f335(f337(f887(x94941,x94941)),f335(f335(f264(x94941,x94941),x94945),x94943)),f310(x94941,x94944)))
% 59.73/59.68 [5643]E(x56431,f2(a881))+~E(f335(f29(x56432),x56435),x56431)+E(f335(f29(x56432),x56433),f335(a106,x56431))+~E(x56433,f335(f335(f312(x56432),x56434),x56435))+P1(f335(f335(f337(x56432),x56434),x56435))
% 59.73/59.68 [5768]~P67(x57682)+E(x57681,f2(x57682))+E(x57683,f2(x57682))+~E(f335(f335(f292(x57682),x57684),x57683),f335(f335(f292(x57682),x57685),x57681))+E(f335(f335(f76(x57682),x57684),x57681),f335(f335(f76(x57682),x57685),x57683))
% 59.73/59.68 [5769]~P67(x57692)+E(x57691,f2(x57692))+E(x57693,f2(x57692))+~E(f335(f335(f76(x57692),x57694),x57693),f335(f335(f76(x57692),x57695),x57691))+E(f335(f335(f292(x57692),x57694),x57691),f335(f335(f292(x57692),x57695),x57693))
% 59.73/59.68 [5836]~E(f335(f29(x58361),x58365),x58363)+~E(x58365,f188(f888(x58361,a879)))+E(f335(f29(x58361),x58362),f335(a106,x58363))+~E(x58362,f335(f335(f312(x58361),x58364),x58365))+P1(f335(f335(f337(x58361),x58364),x58365))
% 59.73/59.68 [6065]~P114(x60652)+~E(f335(x60653,x60655),f2(x60652))+E(f335(f335(f9(x60651,x60652),x60653),x60654),f2(x60652))+~P1(f335(f56(x60651),x60654))+~P1(f335(f335(f337(x60651),x60655),x60654))
% 59.73/59.68 [6432]~P106(x64323)+E(x64321,x64322)+~E(f335(f304(x64323,x64324),x64321),f335(f304(x64323,x64325),x64322))+~P1(f335(f335(f243(x64323),x64325),x64322))+~P1(f335(f335(f243(x64323),x64324),x64321))
% 59.73/59.68 [6433]~P106(x64333)+E(x64331,x64332)+~E(f335(f304(x64333,x64331),x64334),f335(f304(x64333,x64332),x64335))+~P1(f335(f335(f243(x64333),x64332),x64335))+~P1(f335(f335(f243(x64333),x64331),x64334))
% 59.73/59.68 [6434]~P106(x64343)+E(x64341,x64342)+~E(f335(f304(x64343,x64344),x64341),f335(f304(x64343,x64345),x64342))+~P1(f335(f335(f243(x64343),x64345),x64342))+~P1(f335(f335(f243(x64343),x64344),x64341))
% 59.73/59.68 [6435]~P106(x64353)+E(x64351,x64352)+~E(f335(f304(x64353,x64351),x64354),f335(f304(x64353,x64352),x64355))+~P1(f335(f335(f243(x64353),x64352),x64355))+~P1(f335(f335(f243(x64353),x64351),x64354))
% 59.73/59.68 [6599]~P107(x65991)+~P49(x65995,x65991,x65992)+~P106(x65995)+P1(f335(f335(f242(x65991),f335(x65992,x65993)),f335(x65992,x65994)))+~P1(f335(f335(f242(x65995),x65993),x65994))
% 59.73/59.68 [6600]~P107(x66001)+~P37(x66005,x66001,x66002)+~P107(x66005)+P1(f335(f335(f242(x66001),f335(x66002,x66003)),f335(x66002,x66004)))+~P1(f335(f335(f242(x66005),x66003),x66004))
% 59.73/59.68 [6601]~P107(x66011)+~P49(x66015,x66011,x66012)+~P106(x66015)+P1(f335(f335(f243(x66011),f335(x66012,x66013)),f335(x66012,x66014)))+~P1(f335(f335(f243(x66015),x66013),x66014))
% 59.73/59.68 [6602]~P107(x66021)+~P49(x66025,x66021,x66022)+~P107(x66025)+P1(f335(f335(f243(x66021),f335(x66022,x66023)),f335(x66022,x66024)))+~P1(f335(f335(f243(x66025),x66023),x66024))
% 59.73/59.68 [6857]~P106(x68571)+~P49(x68571,x68574,x68575)+~P107(x68574)+~P1(f335(f335(f242(x68574),f335(x68575,x68572)),f335(x68575,x68573)))+P1(f335(f335(f242(x68571),x68572),x68573))
% 59.73/59.68 [6858]~P106(x68581)+~P49(x68581,x68584,x68585)+~P107(x68584)+~P1(f335(f335(f243(x68584),f335(x68585,x68582)),f335(x68585,x68583)))+P1(f335(f335(f243(x68581),x68582),x68583))
% 59.73/59.68 [7506]~P106(x75061)+~P15(x75061,f335(f335(f127(x75061),x75064),x75065))+~P1(f335(f335(f337(x75061),x75063),f335(f166(x75061),x75065)))+~P1(f335(f335(f337(x75061),x75062),f335(f166(x75061),x75064)))+P1(f335(f335(f242(x75061),x75062),x75063))
% 59.73/59.68 [8607]~P107(x86071)+~P1(f335(f335(f243(f888(x86071,a879)),f305(x86071,x86075,x86072)),f305(x86071,x86074,x86073)))+~P1(f335(f335(f242(x86071),x86075),x86072))+P1(f335(f335(f243(x86071),x86072),x86073))+P1(f335(f335(f243(x86071),x86074),x86075))
% 59.73/59.68 [9613]~P37(f888(x96134,a879),f888(x96134,a879),x96135)+P1(f335(x96131,x96132))+~E(x96133,f89(f888(x96134,a879),x96135))+~P1(f335(x96131,f550(x96131,x96132,x96135,x96134,x96133)))+~P1(f335(f335(f337(x96134),x96132),x96133))
% 59.73/59.68 [10022]~P19(x100222,x100225,x100223)+E(x100221,f188(f888(x100222,a879)))+~E(f335(f335(x100225,f335(x100224,f875(x100221,x100224,x100223,x100225,x100222))),f335(x100224,f876(x100221,x100224,x100223,x100225,x100222))),f335(x100224,f335(f335(x100225,f875(x100221,x100224,x100223,x100225,x100222)),f876(x100221,x100224,x100223,x100225,x100222))))+E(f335(x100223,f335(f313(x100222,x100222,x100224),x100221)),f335(x100224,f335(x100223,x100221)))+~P1(f335(f56(x100222),x100221))
% 59.73/59.68 [6431]~P20(x64312,x64315,x64313)+E(x64311,f188(f888(x64312,a879)))+~P1(f335(f56(x64312),x64311))+E(f335(x64313,f335(f335(f312(x64312),x64314),x64311)),f335(f335(x64315,x64314),f335(x64313,x64311)))+P1(f335(f335(f337(x64312),x64314),x64311))
% 59.73/59.68 [7262]~P19(x72622,x72623,x72624)+E(f335(f335(x72623,f335(x72624,x72621)),f335(x72624,x72625)),f335(x72624,x72625))+E(x72621,f188(f888(x72622,a879)))+~P1(f335(f56(x72622),x72625))+~P1(f335(f335(f242(f888(x72622,a879)),x72621),x72625))
% 59.73/59.68 [7482]~P4(x74824)+~P96(x74825)+E(f335(x74821,x74822),f335(x74823,x74822))+~P1(f335(f335(f337(x74824),x74822),f335(f166(x74824),f50(x74824))))+~P1(f335(f335(f86(f888(x74824,x74825)),x74821),x74823))
% 59.73/59.68 [7642]~P20(x76424,x76425,x76421)+E(f335(x76421,x76422),x76423)+~P1(f335(f56(x76424),x76422))+~E(f335(f335(f23(f888(x76424,a879)),x76422),f335(f335(f312(x76424),x76423),f188(f888(x76424,a879)))),f188(f888(x76424,a879)))+~P1(f335(f335(f337(x76424),x76423),x76422))
% 59.73/59.68 [7729]E(x77291,x77292)+~E(f335(f189(f882(x77293)),x77292),f335(f189(f882(x77294)),x77295))+~E(f335(f189(f882(x77293)),x77291),f335(f189(f882(x77294)),x77295))+~E(f335(f179(x77294,x77293),f335(f335(f175(x77294,x77293),x77295),x77291)),f335(f179(x77294,x77293),f335(f335(f175(x77294,x77293),x77295),x77292)))+~P1(f335(f130(x77294),x77295))
% 59.73/59.68 [8578]E(x85781,x85782)+~P8(x85783,x85784,x85785)+E(f335(f335(f95(f888(x85783,a879)),x85781),x85782),f188(f888(x85783,a879)))+~P1(f335(f335(f337(f888(x85783,a879)),x85782),f335(f335(f55(x85783),x85784),x85785)))+~P1(f335(f335(f337(f888(x85783,a879)),x85781),f335(f335(f55(x85783),x85784),x85785)))
% 59.73/59.68 [9033]~P26(x90331,x90333,x90335,x90332)+~P1(f335(f56(x90333),x90334))+~P1(f335(f56(x90331),x90332))+P1(f335(f335(f242(a881),f335(f29(x90331),x90332)),f335(f29(x90333),x90334)))+~P1(f335(f335(f242(f888(x90333,a879)),f335(f313(x90331,x90333,x90335),x90332)),x90334))
% 59.73/59.68 [9371]~P73(x93712)+~E(f335(x93713,f436(x93713,x93714,x93715,x93711,x93712)),f73(x93712))+E(f335(f335(f9(x93711,x93712),x93713),x93714),f335(f335(f9(x93711,x93712),x93713),x93715))+~P1(f335(f56(x93711),x93715))+~P1(f335(f335(f242(f888(x93711,a879)),x93714),x93715))
% 59.73/59.68 [9372]~P73(x93722)+~E(f335(x93723,f438(x93723,x93724,x93725,x93721,x93722)),f73(x93722))+E(f335(f335(f9(x93721,x93722),x93723),x93724),f335(f335(f9(x93721,x93722),x93723),x93725))+~P1(f335(f56(x93721),x93725))+~P1(f335(f335(f242(f888(x93721,a879)),x93724),x93725))
% 59.73/59.68 [9373]~P77(x93732)+~E(f335(x93733,f496(x93733,x93734,x93735,x93731,x93732)),f2(x93732))+E(f335(f335(f6(x93731,x93732),x93733),x93734),f335(f335(f6(x93731,x93732),x93733),x93735))+~P1(f335(f56(x93731),x93735))+~P1(f335(f335(f242(f888(x93731,a879)),x93734),x93735))
% 59.73/59.68 [9374]~P77(x93742)+~E(f335(x93743,f504(x93743,x93744,x93745,x93741,x93742)),f2(x93742))+E(f335(f335(f6(x93741,x93742),x93743),x93744),f335(f335(f6(x93741,x93742),x93743),x93745))+~P1(f335(f56(x93741),x93745))+~P1(f335(f335(f242(f888(x93741,a879)),x93744),x93745))
% 59.73/59.68 [9802]~P37(f888(x98021,a879),f888(x98021,a879),f335(f335(f8(f888(x98021,a879),f888(x98021,a879),f888(x98021,a879)),f249(x98021)),x98024))+~P1(f335(f335(x98024,f335(f335(f104(f888(x98021,a879)),x98025),x98023)),f520(x98025,x98022,x98024,x98021,x98023)))+~E(x98023,f90(f888(x98021,a879),f335(f335(f8(f888(x98021,a879),f888(x98021,a879),f888(x98021,a879)),f249(x98021)),x98024)))+P1(f335(f335(f337(x98021),x98022),x98023))+~P1(f335(f335(f337(x98021),x98022),x98025))
% 59.73/59.68 [9806]~P37(f888(x98061,a879),f888(x98061,a879),f335(f335(f8(f888(x98061,a879),f888(x98061,a879),f888(x98061,a879)),f249(x98061)),x98065))+~E(x98063,f90(f888(x98061,a879),f335(f335(f8(f888(x98061,a879),f888(x98061,a879),f888(x98061,a879)),f249(x98061)),x98065)))+~P1(f335(f335(f337(x98061),x98062),x98064))+P1(f335(f335(f337(x98061),f520(x98064,x98062,x98065,x98061,x98063)),x98064))+P1(f335(f335(f337(x98061),x98062),x98063))
% 59.73/59.68 [9861]~P90(x98611)+~P1(f335(f56(x98612),x98615))+~P1(f335(f335(f242(x98611),f2(x98611)),f335(x98613,f485(x98613,x98614,x98615,x98612,x98611))))+P1(f335(f335(f242(x98611),f335(f335(f6(x98612,x98611),x98613),x98614)),f335(f335(f6(x98612,x98611),x98613),x98615)))+~P1(f335(f335(f242(f888(x98612,a879)),x98614),x98615))
% 59.73/59.68 [7503]E(x75031,f2(a881))+P1(f335(x75032,x75033))+~E(x75034,f335(f335(f75(a881),f335(f335(f76(a881),x75031),x75033)),x75035))+~P1(f335(f335(f243(a881),x75035),x75031))+~P1(f335(x75032,f335(f335(f30(a881),x75034),x75031)))
% 59.73/59.68 [7582]E(x75821,f2(a881))+P1(f335(x75822,x75823))+~P1(f335(x75822,f39(a881,x75824,x75821)))+~E(x75824,f335(f335(f75(a881),f335(f335(f76(a881),x75821),x75825)),x75823))+~P1(f335(f335(f243(a881),x75823),x75821))
% 59.73/59.68 [7874]~P67(x78743)+E(f335(x78741,x78742),f2(x78743))+~P1(f335(f56(x78744),x78745))+E(f335(f335(f9(x78744,x78743),x78741),f335(f335(f23(f888(x78744,a879)),x78745),f335(f335(f312(x78744),x78742),f188(f888(x78744,a879))))),f335(f335(f9(x78744,x78743),x78741),x78745))+P1(f335(f335(f337(x78744),x78742),x78745))
% 59.73/59.68 [8278]~P73(x82781)+~P1(f335(f56(x82782),x82785))+~P1(f335(f56(x82782),x82784))+~E(f335(f335(f95(f888(x82782,a879)),x82784),x82785),f188(f888(x82782,a879)))+E(f335(f335(f76(x82781),f335(f335(f9(x82782,x82781),x82783),x82784)),f335(f335(f9(x82782,x82781),x82783),x82785)),f335(f335(f9(x82782,x82781),x82783),f335(f335(f104(f888(x82782,a879)),x82784),x82785)))
% 59.73/59.68 [8279]~P73(x82791)+~P1(f335(f56(x82792),x82795))+~P1(f335(f56(x82792),x82794))+~E(f335(f335(f95(f888(x82792,a879)),x82794),x82795),f188(f888(x82792,a879)))+E(f335(f335(f76(x82791),f335(f335(f9(x82792,x82791),x82793),x82794)),f335(f335(f9(x82792,x82791),x82793),x82795)),f335(f335(f9(x82792,x82791),x82793),f335(f335(f104(f888(x82792,a879)),x82794),x82795)))
% 59.73/59.68 [8280]~P77(x82801)+~P1(f335(f56(x82802),x82805))+~P1(f335(f56(x82802),x82804))+~E(f335(f335(f95(f888(x82802,a879)),x82804),x82805),f188(f888(x82802,a879)))+E(f335(f335(f75(x82801),f335(f335(f6(x82802,x82801),x82803),x82804)),f335(f335(f6(x82802,x82801),x82803),x82805)),f335(f335(f6(x82802,x82801),x82803),f335(f335(f104(f888(x82802,a879)),x82804),x82805)))
% 59.73/59.68 [8375]~P67(x83753)+E(f335(x83751,x83752),f2(x83753))+~P1(f335(f56(x83754),x83755))+E(f335(f335(f9(x83754,x83753),x83751),f335(f335(f23(f888(x83754,a879)),x83755),f335(f335(f312(x83754),x83752),f188(f888(x83754,a879))))),f335(f335(f292(x83753),f335(f335(f9(x83754,x83753),x83751),x83755)),f335(x83751,x83752)))+~P1(f335(f335(f337(x83754),x83752),x83755))
% 59.73/59.68 [8896]~P8(x88961,x88965,x88964)+~E(f335(f288(x88961,x88961,x88964),f335(f335(f312(x88961),x88962),f188(f888(x88961,a879)))),f335(f288(x88961,x88961,x88964),f335(f335(f312(x88961),x88963),f188(f888(x88961,a879)))))+~P1(f335(f335(f337(x88961),x88963),x88965))+~P1(f335(f335(f337(x88961),x88962),x88965))+P1(f335(f335(f337(f887(x88961,x88961)),f335(f335(f264(x88961,x88961),x88962),x88963)),x88964))
% 59.73/59.68 [8897]~P8(x88971,x88975,x88974)+~E(f335(f288(x88971,x88971,x88974),f335(f335(f312(x88971),x88972),f188(f888(x88971,a879)))),f335(f288(x88971,x88971,x88974),f335(f335(f312(x88971),x88973),f188(f888(x88971,a879)))))+~P1(f335(f335(f337(x88971),x88973),x88975))+~P1(f335(f335(f337(x88971),x88972),x88975))+P1(f335(f335(f337(f887(x88971,x88971)),f335(f335(f264(x88971,x88971),x88972),x88973)),x88974))
% 59.73/59.68 [8995]~P8(x89951,x89955,x89952)+E(f335(f288(x89951,x89951,x89952),f335(f335(f312(x89951),x89953),f188(f888(x89951,a879)))),f335(f288(x89951,x89951,x89952),f335(f335(f312(x89951),x89954),f188(f888(x89951,a879)))))+~P1(f335(f335(f337(x89951),x89954),x89955))+~P1(f335(f335(f337(x89951),x89953),x89955))+~P1(f335(f335(f337(f887(x89951,x89951)),f335(f335(f264(x89951,x89951),x89953),x89954)),x89952))
% 59.73/59.68 [9084]~P8(x90841,x90845,x90844)+~E(f335(f335(f55(x90841),f335(f335(f312(x90841),x90842),f188(f888(x90841,a879)))),x90844),f335(f335(f55(x90841),f335(f335(f312(x90841),x90843),f188(f888(x90841,a879)))),x90844))+~P1(f335(f335(f337(x90841),x90843),x90845))+~P1(f335(f335(f337(x90841),x90842),x90845))+P1(f335(f335(f337(f887(x90841,x90841)),f335(f335(f264(x90841,x90841),x90842),x90843)),x90844))
% 59.73/59.68 [9106]~P8(x91061,x91065,x91063)+E(f335(f335(f55(x91061),f335(f335(f312(x91061),x91062),f188(f888(x91061,a879)))),x91063),f335(f335(f55(x91061),f335(f335(f312(x91061),x91064),f188(f888(x91061,a879)))),x91063))+~P1(f335(f335(f337(x91061),x91064),x91065))+~P1(f335(f335(f337(x91061),x91062),x91065))+~P1(f335(f335(f337(f887(x91061,x91061)),f335(f335(f264(x91061,x91061),x91062),x91064)),x91063))
% 59.73/59.68 [9401]~P73(x94011)+~P1(f335(f56(x94012),x94015))+~P1(f335(f56(x94012),x94014))+~E(f335(f335(f95(f888(x94012,a879)),x94014),x94015),f188(f888(x94012,a879)))+E(f335(f335(f76(x94011),f335(f335(f335(f60(x94011,x94012,f76(x94011)),x94013),f73(x94011)),x94014)),f335(f335(f335(f60(x94011,x94012,f76(x94011)),x94013),f73(x94011)),x94015)),f335(f335(f335(f60(x94011,x94012,f76(x94011)),x94013),f73(x94011)),f335(f335(f104(f888(x94012,a879)),x94014),x94015)))
% 59.73/59.68 [9410]~P73(x94101)+~E(f335(x94103,f369(x94103,x94105,x94104,x94102,x94101)),f73(x94101))+~P1(f335(f56(x94102),x94104))+~P1(f335(f56(x94102),x94105))+E(f335(f335(f76(x94101),f335(f335(f9(x94102,x94101),x94103),x94104)),f335(f335(f9(x94102,x94101),x94103),x94105)),f335(f335(f9(x94102,x94101),x94103),f335(f335(f104(f888(x94102,a879)),x94104),x94105)))
% 59.73/59.68 [9411]~P73(x94111)+~E(f335(x94113,f370(x94113,x94115,x94114,x94112,x94111)),f73(x94111))+~P1(f335(f56(x94112),x94114))+~P1(f335(f56(x94112),x94115))+E(f335(f335(f76(x94111),f335(f335(f9(x94112,x94111),x94113),x94114)),f335(f335(f9(x94112,x94111),x94113),x94115)),f335(f335(f9(x94112,x94111),x94113),f335(f335(f104(f888(x94112,a879)),x94114),x94115)))
% 59.73/59.68 [9412]~P77(x94121)+~E(f335(x94123,f483(x94123,x94125,x94124,x94122,x94121)),f2(x94121))+~P1(f335(f56(x94122),x94124))+~P1(f335(f56(x94122),x94125))+E(f335(f335(f75(x94121),f335(f335(f6(x94122,x94121),x94123),x94124)),f335(f335(f6(x94122,x94121),x94123),x94125)),f335(f335(f6(x94122,x94121),x94123),f335(f335(f104(f888(x94122,a879)),x94124),x94125)))
% 59.73/59.68 [9413]~P77(x94131)+~E(f335(x94133,f493(x94133,x94135,x94134,x94132,x94131)),f2(x94131))+~P1(f335(f56(x94132),x94134))+~P1(f335(f56(x94132),x94135))+E(f335(f335(f75(x94131),f335(f335(f6(x94132,x94131),x94133),x94134)),f335(f335(f6(x94132,x94131),x94133),x94135)),f335(f335(f6(x94132,x94131),x94133),f335(f335(f104(f888(x94132,a879)),x94134),x94135)))
% 59.73/59.68 [9621]~P73(x96211)+~E(f335(x96213,f352(x96213,x96215,x96214,x96212,x96211)),f73(x96211))+~P1(f335(f56(x96212),x96214))+~P1(f335(f56(x96212),x96215))+E(f335(f335(f76(x96211),f335(f335(f335(f60(x96211,x96212,f76(x96211)),x96213),f73(x96211)),x96214)),f335(f335(f335(f60(x96211,x96212,f76(x96211)),x96213),f73(x96211)),x96215)),f335(f335(f335(f60(x96211,x96212,f76(x96211)),x96213),f73(x96211)),f335(f335(f104(f888(x96212,a879)),x96214),x96215)))
% 59.73/59.68 [9735]~P73(x97352)+E(f335(f335(f9(x97351,x97352),x97353),x97354),f335(f335(f9(x97351,x97352),x97353),x97355))+~P1(f335(f56(x97351),x97355))+~P1(f335(f335(f242(f888(x97351,a879)),x97354),x97355))+P1(f335(f335(f337(x97351),f436(x97353,x97354,x97355,x97351,x97352)),f335(f335(f23(f888(x97351,a879)),x97355),x97354)))
% 59.73/59.68 [9736]~P73(x97362)+E(f335(f335(f9(x97361,x97362),x97363),x97364),f335(f335(f9(x97361,x97362),x97363),x97365))+~P1(f335(f56(x97361),x97365))+~P1(f335(f335(f242(f888(x97361,a879)),x97364),x97365))+P1(f335(f335(f337(x97361),f438(x97363,x97364,x97365,x97361,x97362)),f335(f335(f23(f888(x97361,a879)),x97365),x97364)))
% 59.73/59.68 [9737]~P77(x97372)+E(f335(f335(f6(x97371,x97372),x97373),x97374),f335(f335(f6(x97371,x97372),x97373),x97375))+~P1(f335(f56(x97371),x97375))+~P1(f335(f335(f242(f888(x97371,a879)),x97374),x97375))+P1(f335(f335(f337(x97371),f496(x97373,x97374,x97375,x97371,x97372)),f335(f335(f23(f888(x97371,a879)),x97375),x97374)))
% 59.73/59.68 [9738]~P77(x97382)+E(f335(f335(f6(x97381,x97382),x97383),x97384),f335(f335(f6(x97381,x97382),x97383),x97385))+~P1(f335(f56(x97381),x97385))+~P1(f335(f335(f242(f888(x97381,a879)),x97384),x97385))+P1(f335(f335(f337(x97381),f504(x97383,x97384,x97385,x97381,x97382)),f335(f335(f23(f888(x97381,a879)),x97385),x97384)))
% 59.73/59.68 [9756]~P73(x97561)+~P1(f335(f56(x97562),x97564))+~P1(f335(f56(x97562),x97565))+E(f335(f335(f76(x97561),f335(f335(f9(x97562,x97561),x97563),x97564)),f335(f335(f9(x97562,x97561),x97563),x97565)),f335(f335(f9(x97562,x97561),x97563),f335(f335(f104(f888(x97562,a879)),x97564),x97565)))+P1(f335(f335(f337(x97562),f369(x97563,x97565,x97564,x97562,x97561)),f335(f335(f95(f888(x97562,a879)),x97564),x97565)))
% 59.73/59.68 [9757]~P73(x97571)+~P1(f335(f56(x97572),x97574))+~P1(f335(f56(x97572),x97575))+E(f335(f335(f76(x97571),f335(f335(f9(x97572,x97571),x97573),x97574)),f335(f335(f9(x97572,x97571),x97573),x97575)),f335(f335(f9(x97572,x97571),x97573),f335(f335(f104(f888(x97572,a879)),x97574),x97575)))+P1(f335(f335(f337(x97572),f370(x97573,x97575,x97574,x97572,x97571)),f335(f335(f95(f888(x97572,a879)),x97574),x97575)))
% 59.73/59.68 [9758]~P77(x97581)+~P1(f335(f56(x97582),x97584))+~P1(f335(f56(x97582),x97585))+E(f335(f335(f75(x97581),f335(f335(f6(x97582,x97581),x97583),x97584)),f335(f335(f6(x97582,x97581),x97583),x97585)),f335(f335(f6(x97582,x97581),x97583),f335(f335(f104(f888(x97582,a879)),x97584),x97585)))+P1(f335(f335(f337(x97582),f483(x97583,x97585,x97584,x97582,x97581)),f335(f335(f95(f888(x97582,a879)),x97584),x97585)))
% 59.73/59.68 [9759]~P77(x97591)+~P1(f335(f56(x97592),x97594))+~P1(f335(f56(x97592),x97595))+E(f335(f335(f75(x97591),f335(f335(f6(x97592,x97591),x97593),x97594)),f335(f335(f6(x97592,x97591),x97593),x97595)),f335(f335(f6(x97592,x97591),x97593),f335(f335(f104(f888(x97592,a879)),x97594),x97595)))+P1(f335(f335(f337(x97592),f493(x97593,x97595,x97594,x97592,x97591)),f335(f335(f95(f888(x97592,a879)),x97594),x97595)))
% 59.73/59.68 [9762]~P37(f888(x97623,a879),f888(x97623,a879),x97624)+P1(f335(x97621,x97622))+~E(x97625,f89(f888(x97623,a879),x97624))+~P1(f335(f335(f337(x97623),x97622),x97625))+P1(f335(f335(f337(x97623),f550(x97621,x97622,x97624,x97623,x97625)),f335(x97624,f335(f335(f95(f888(x97623,a879)),x97625),f335(f249(x97623),x97621)))))
% 59.73/59.68 [9767]~P90(x97675)+~P1(f335(f56(x97671),x97674))+P1(f335(f335(f242(x97675),f335(f335(f6(x97671,x97675),x97672),x97673)),f335(f335(f6(x97671,x97675),x97672),x97674)))+~P1(f335(f335(f242(f888(x97671,a879)),x97673),x97674))+P1(f335(f335(f337(x97671),f485(x97672,x97673,x97674,x97671,x97675)),f335(f335(f23(f888(x97671,a879)),x97674),x97673)))
% 59.73/59.68 [9824]~P73(x98241)+~P1(f335(f56(x98242),x98244))+~P1(f335(f56(x98242),x98245))+E(f335(f335(f76(x98241),f335(f335(f335(f60(x98241,x98242,f76(x98241)),x98243),f73(x98241)),x98244)),f335(f335(f335(f60(x98241,x98242,f76(x98241)),x98243),f73(x98241)),x98245)),f335(f335(f335(f60(x98241,x98242,f76(x98241)),x98243),f73(x98241)),f335(f335(f104(f888(x98242,a879)),x98244),x98245)))+P1(f335(f335(f337(x98242),f352(x98243,x98245,x98244,x98242,x98241)),f335(f335(f95(f888(x98242,a879)),x98244),x98245)))
% 59.73/59.68 [8776]~P20(x87761,x87764,x87765)+~P1(f335(f56(x87761),x87762))+E(f335(f335(f23(f888(x87761,a879)),x87762),f335(f335(f312(x87761),x87763),f188(f888(x87761,a879)))),f188(f888(x87761,a879)))+~P1(f335(f335(f337(x87761),x87763),x87762))+E(f335(f335(x87764,x87763),f335(x87765,f335(f335(f23(f888(x87761,a879)),x87762),f335(f335(f312(x87761),x87763),f188(f888(x87761,a879)))))),f335(x87765,x87762))
% 59.73/59.68 [8853]~P20(x88531,x88534,x88535)+~P1(f335(f56(x88531),x88533))+~P1(f335(f56(x88531),x88532))+E(f335(f335(f95(f888(x88531,a879)),x88532),x88533),f188(f888(x88531,a879)))+E(f335(f335(x88534,f335(x88535,f335(f335(f104(f888(x88531,a879)),x88532),x88533))),f335(x88535,f335(f335(f95(f888(x88531,a879)),x88532),x88533))),f335(f335(x88534,f335(x88535,x88532)),f335(x88535,x88533)))
% 59.73/59.68 [9034]~P37(f888(x90341,a879),f888(x90341,a879),x90344)+~E(x90343,f90(f888(x90341,a879),x90344))+P1(f335(f335(f337(x90341),x90342),x90343))+~P1(f335(f335(f337(x90341),x90342),x90345))+~P1(f335(f335(f242(f888(x90341,a879)),x90345),f335(x90344,f335(f335(f104(f888(x90341,a879)),x90345),x90343))))
% 59.73/59.68 [9415]~P1(f335(f335(f242(a1),x94154),f2(a1)))+~P1(f335(f335(f243(a1),x94153),x94155))+P1(f335(f335(f242(a1),x94151),x94152))+~P1(f335(f335(f243(a1),x94153),x94154))+~P1(f335(f335(f242(a1),f335(f335(f75(a1),f335(f335(f76(a1),x94153),x94152)),x94155)),f335(f335(f75(a1),f335(f335(f76(a1),x94153),x94151)),x94154)))
% 59.73/59.68 [9417]~P1(f335(f335(f242(a1),f2(a1)),x94175))+P1(f335(f335(f242(a1),x94171),x94172))+~P1(f335(f335(f243(a1),x94173),x94174))+~P1(f335(f335(f243(a1),x94175),x94174))+~P1(f335(f335(f242(a1),f335(f335(f75(a1),f335(f335(f76(a1),x94174),x94171)),x94175)),f335(f335(f75(a1),f335(f335(f76(a1),x94174),x94172)),x94173)))
% 59.73/59.68 [9531]~P67(x95315)+E(f335(x95311,f390(x95311,x95312,x95313,x95314,x95315)),f2(x95315))+~P1(f335(f56(x95314),x95313))+~P1(f335(f56(x95314),x95312))+E(f335(f335(f292(x95315),f335(f335(f76(x95315),f335(f335(f9(x95314,x95315),x95311),x95313)),f335(f335(f9(x95314,x95315),x95311),x95312))),f335(f335(f9(x95314,x95315),x95311),f335(f335(f95(f888(x95314,a879)),x95313),x95312))),f335(f335(f9(x95314,x95315),x95311),f335(f335(f104(f888(x95314,a879)),x95313),x95312)))
% 59.73/59.68 [9816]~P67(x98161)+~P1(f335(f56(x98162),x98164))+~P1(f335(f56(x98162),x98165))+E(f335(f335(f292(x98161),f335(f335(f76(x98161),f335(f335(f9(x98162,x98161),x98163),x98164)),f335(f335(f9(x98162,x98161),x98163),x98165))),f335(f335(f9(x98162,x98161),x98163),f335(f335(f95(f888(x98162,a879)),x98164),x98165))),f335(f335(f9(x98162,x98161),x98163),f335(f335(f104(f888(x98162,a879)),x98164),x98165)))+P1(f335(f335(f337(x98162),f390(x98163,x98165,x98164,x98162,x98161)),f335(f335(f95(f888(x98162,a879)),x98164),x98165)))
% 59.73/59.68 [9127]E(f335(f335(f127(x91271),x91272),x91273),f335(f335(f127(x91271),x91274),x91275))+~E(f335(f335(f169(x91271),f335(f189(f882(x91271)),x91274)),x91272),x91274)+~E(f335(f335(f169(x91271),f335(f189(f882(x91271)),x91272)),x91274),x91272)+~E(x91275,f335(f335(f127(x91271),f335(f335(f131(x91271),f335(f189(f882(x91271)),x91274)),x91272)),x91273))+~E(f335(f335(f127(x91271),f335(f335(f131(x91271),f335(f189(f882(x91271)),x91272)),x91274)),x91275),x91273)
% 59.73/59.68 [9529]~P106(x95292)+E(f335(f335(f141(x95291,x95292,x95293),x95294),f164(x95291,x95294,x95295)),x95295)+~P15(x95292,f335(f335(f147(x95291,x95292),x95293),x95295))+~P1(f335(f335(f337(x95291),x95294),f335(f166(x95291),x95295)))+~E(f335(f134(x95291),f335(f129(x95291,f335(f335(f8(x95292,a879,x95291),f335(a332,f335(x95293,x95294))),x95293)),x95295)),x95294)
% 59.73/59.68 [9878]~P70(x98781)+~P1(f335(f61(x98781,x98781,f76(x98781),x98782,x98783),x98785))+~P1(f335(f335(f337(x98781),x98784),x98783))+P1(f335(f335(f337(x98781),x98782),x98783))+P1(f335(f61(x98781,x98781,f76(x98781),x98784,f335(f335(f312(x98781),x98782),f335(f335(f23(f888(x98781,a879)),x98783),f335(f335(f312(x98781),x98784),f188(f888(x98781,a879)))))),x98785))
% 59.73/59.68 [10210]~P37(f888(x102101,a879),f888(x102101,a879),x102104)+~E(x102103,f90(f888(x102101,a879),x102104))+P1(f335(f335(f337(x102101),x102102),x102103))+~P1(f335(f335(f337(x102101),x102102),x102105))+~P1(f335(f335(f242(f888(x102101,a879)),x102105),f335(x102104,f89(f888(x102101,a879),f335(f335(f7(f888(x102101,a879),f888(x102101,a879),f888(x102101,a879)),f335(f335(f8(f888(x102101,a879),f888(f888(x102101,a879),f888(x102101,a879)),f888(x102101,a879)),f104(f888(x102101,a879))),f335(f335(f7(f888(x102101,a879),f888(x102101,a879),f888(x102101,a879)),f335(f335(f8(f888(x102101,a879),f888(f888(x102101,a879),f888(x102101,a879)),f888(x102101,a879)),f104(f888(x102101,a879))),x102104)),x102105))),x102103)))))
% 59.73/59.68 [7267]E(x72671,x72672)+~P26(x72674,x72675,x72673,x72676)+~E(f335(x72673,x72671),f335(x72673,x72672))+~P1(f335(f335(f337(x72674),x72672),x72676))+~P1(f335(f335(f337(x72674),x72671),x72676))
% 59.73/59.68 [7268]E(x72681,x72682)+~P26(x72684,x72685,x72683,x72686)+~E(f335(x72683,x72681),f335(x72683,x72682))+~P1(f335(f335(f337(x72684),x72682),x72686))+~P1(f335(f335(f337(x72684),x72681),x72686))
% 59.73/59.68 [7269]E(x72691,x72692)+~P26(x72694,x72695,x72693,x72696)+~E(f335(x72693,x72691),f335(x72693,x72692))+~P1(f335(f335(f337(x72694),x72692),x72696))+~P1(f335(f335(f337(x72694),x72691),x72696))
% 59.73/59.68 [7270]E(x72701,x72702)+~P26(x72704,x72705,x72703,x72706)+~E(f335(x72703,x72701),f335(x72703,x72702))+~P1(f335(f335(f337(x72704),x72702),x72706))+~P1(f335(f335(f337(x72704),x72701),x72706))
% 59.73/59.68 [6522]~P138(x65224)+E(x65221,x65222)+~E(x65225,x65226)+E(x65223,f2(x65224))+~E(f335(f335(f75(x65224),x65225),f335(f335(f76(x65224),x65223),x65221)),f335(f335(f75(x65224),x65226),f335(f335(f76(x65224),x65223),x65222)))
% 59.73/59.68 [7561]~P106(x75611)+~P5(x75611)+~P1(f335(f335(f243(x75611),x75612),f335(x75615,x75616)))+~P1(f335(f335(f337(x75613),x75616),x75614))+P1(f335(f335(f243(x75611),x75612),f335(f335(f33(x75613,x75611),x75614),x75615)))
% 59.73/59.68 [8248]~P106(x82481)+~P5(x82481)+~P1(f335(f335(f243(x82481),f335(x82484,x82486)),x82485))+~P1(f335(f335(f337(x82482),x82486),x82483))+P1(f335(f335(f243(x82481),f335(f335(f34(x82482,x82481),x82483),x82484)),x82485))
% 59.73/59.68 [8505]~P21(x85052,x85055,x85056,x85051)+~P1(f335(f56(x85052),x85054))+~P1(f335(f56(x85052),x85053))+~E(f335(f335(f95(f888(x85052,a879)),x85053),x85054),f188(f888(x85052,a879)))+E(f335(x85051,f335(f335(f104(f888(x85052,a879)),x85053),x85054)),f335(f68(x85055,x85055,x85055,f335(x85051,x85053)),f335(x85051,x85054)))
% 59.73/59.68 [8823]E(x88231,x88232)+~P54(x88234,x88235,x88236,x88233,x88237)+~E(f335(x88233,x88231),f335(x88233,x88232))+~P1(f335(f335(f337(x88235),x88232),x88237))+~P1(f335(f335(f337(x88235),x88231),x88237))
% 59.73/59.68 [10117]~P1(f335(x101172,x101174))+~E(x101175,f335(f129(x101171,x101172),x101177))+E(f335(f129(x101171,x101172),x101173),f335(f335(f144(x101171),x101174),x101175))+~E(x101173,f335(f335(f127(x101171),x101176),f335(f335(f144(x101171),x101174),x101177)))+P1(f335(x101172,f775(x101175,x101174,x101173,x101172,x101171,x101176,x101177)))
% 59.73/59.68 [10118]~P1(f335(x101184,x101182))+~E(x101183,f335(f129(x101181,x101184),x101187))+E(f335(f335(f144(x101181),x101182),x101183),f335(f129(x101181,x101184),x101185))+~E(x101185,f335(f335(f127(x101181),x101186),f335(f335(f144(x101181),x101182),x101187)))+P1(f335(x101184,f777(x101185,x101184,x101183,x101182,x101181,x101186,x101187)))
% 59.73/59.68 [10152]~P1(f335(x101522,x101524))+~E(x101525,f335(f129(x101521,x101522),x101527))+E(f335(f129(x101521,x101522),x101523),f335(f335(f144(x101521),x101524),x101525))+~E(x101523,f335(f335(f127(x101521),x101526),f335(f335(f144(x101521),x101524),x101527)))+P1(f335(f335(f337(x101521),f775(x101525,x101524,x101523,x101522,x101521,x101526,x101527)),f335(f166(x101521),x101526)))
% 59.73/59.68 [10153]~P1(f335(x101534,x101532))+~E(x101533,f335(f129(x101531,x101534),x101537))+E(f335(f335(f144(x101531),x101532),x101533),f335(f129(x101531,x101534),x101535))+~E(x101535,f335(f335(f127(x101531),x101536),f335(f335(f144(x101531),x101532),x101537)))+P1(f335(f335(f337(x101531),f777(x101535,x101534,x101533,x101532,x101531,x101536,x101537)),f335(f166(x101531),x101536)))
% 59.73/59.68 [10156]~P8(x101561,x101567,x101566)+~P13(x101561,f888(x101565,a879),x101566,x101564)+P1(f335(f335(f337(x101561),f830(x101562,x101563,x101564,x101565,x101566,x101567,x101561)),x101567))+~P1(f335(f335(f337(f888(x101561,a879)),x101563),f335(f335(f55(x101561),x101567),x101566)))+P1(f335(f335(f337(f888(x101565,a879)),f335(f335(f33(x101561,f888(x101565,a879)),x101563),x101564)),x101562))
% 59.73/59.68 [10205]~P8(x102052,x102056,x102057)+~P13(x102052,f888(x102051,a879),x102057,x102054)+~P1(f335(f335(f337(f888(x102052,a879)),x102053),f335(f335(f55(x102052),x102056),x102057)))+~P1(f335(f335(f337(f888(x102051,a879)),f335(x102054,f830(x102055,x102053,x102054,x102051,x102057,x102056,x102052))),x102055))+P1(f335(f335(f337(f888(x102051,a879)),f335(f335(f33(x102052,f888(x102051,a879)),x102053),x102054)),x102055))
% 59.73/59.68 [8422]~P73(x84222)+~P26(x84221,x84225,x84228,x84224)+~E(x84223,f335(f68(x84225,x84222,x84221,x84226),x84228))+~E(x84227,f335(f313(x84221,x84225,x84228),x84224))+E(f335(f335(f9(x84221,x84222),x84223),x84224),f335(f335(f9(x84225,x84222),x84226),x84227))
% 59.73/59.68 [10209]~P73(x102092)+~P26(x102095,x102091,x102098,x102097)+~E(f335(x102096,f437(x102093,x102096,x102094,x102097,x102098,x102091,x102095,x102092)),f335(f335(f68(x102091,x102092,x102095,x102093),x102098),f437(x102093,x102096,x102094,x102097,x102098,x102091,x102095,x102092)))+~E(x102094,f335(f313(x102095,x102091,x102098),x102097))+E(f335(f335(f9(x102091,x102092),x102093),x102094),f335(f335(f9(x102095,x102092),x102096),x102097))
% 59.73/59.68 [10213]~P73(x102132)+~P26(x102131,x102135,x102138,x102134)+~E(x102137,f335(f313(x102131,x102135,x102138),x102134))+E(f335(f335(f9(x102131,x102132),x102133),x102134),f335(f335(f9(x102135,x102132),x102136),x102137))+P1(f335(f335(f337(x102131),f437(x102136,x102133,x102137,x102134,x102138,x102135,x102131,x102132)),x102134))
% 59.73/59.68 [10214]~P77(x102142)+~P26(x102141,x102145,x102148,x102144)+~E(x102147,f335(f313(x102141,x102145,x102148),x102144))+E(f335(f335(f6(x102141,x102142),x102143),x102144),f335(f335(f6(x102145,x102142),x102146),x102147))+P1(f335(f335(f337(x102141),f592(x102146,x102143,x102147,x102144,x102148,x102145,x102141,x102142)),x102144))
% 59.73/59.68 [10219]~P77(x102192)+~P26(x102195,x102191,x102198,x102197)+~E(x102194,f335(f313(x102195,x102191,x102198),x102197))+~E(f335(x102196,f592(x102193,x102196,x102194,x102197,x102198,x102191,x102195,x102192)),f335(x102193,f335(x102198,f592(x102193,x102196,x102194,x102197,x102198,x102191,x102195,x102192))))+E(f335(f335(f6(x102191,x102192),x102193),x102194),f335(f335(f6(x102195,x102192),x102196),x102197))
% 59.73/59.68 [9583]~E(f335(f189(f882(x95832)),x95835),f335(f189(f882(x95831)),x95833))+~E(f335(f189(f882(x95832)),x95834),f335(f189(f882(x95831)),x95833))+~E(f335(f335(f335(f67(x95831,f885(x95832)),f335(f179(x95831,x95832),f335(f335(f175(x95831,x95832),x95833),x95834))),x95836),f335(f235(x95832),x95837)),f335(f335(f335(f67(x95831,f885(x95832)),f335(f179(x95831,x95832),f335(f335(f175(x95831,x95832),x95833),x95835))),x95836),f335(f235(x95832),x95838)))+E(f335(f179(x95831,x95832),f335(f335(f175(x95831,x95832),x95833),x95834)),f335(f179(x95831,x95832),f335(f335(f175(x95831,x95832),x95833),x95835)))+P1(f335(f335(f337(x95831),x95836),f335(f166(x95831),x95833)))
% 59.73/59.68 [9699]~P25(x96996,x96992,x96995,x96997,x96998,x96991)+~P1(f335(f56(x96992),x96994))+~P1(f335(f56(x96992),x96993))+~E(f335(f335(f95(f888(x96992,a879)),x96993),x96994),f188(f888(x96992,a879)))+E(f335(x96991,f335(f335(f104(f888(x96992,a879)),x96993),x96994)),f335(f335(x96995,f335(x96991,x96993)),f335(x96991,x96994)))
% 59.73/59.68 [10106]~P25(x101068,x101062,x101065,x101067,x101066,x101061)+~E(f335(x101066,f877(x101064,x101063,x101061,x101066,x101067,x101065,x101062)),x101067)+~P1(f335(f56(x101062),x101063))+~P1(f335(f56(x101062),x101064))+E(f335(x101061,f335(f335(f104(f888(x101062,a879)),x101063),x101064)),f335(f335(x101065,f335(x101061,x101063)),f335(x101061,x101064)))
% 59.73/59.68 [10163]~P25(x101638,x101632,x101635,x101637,x101636,x101631)+~P1(f335(f56(x101632),x101633))+~P1(f335(f56(x101632),x101634))+E(f335(x101631,f335(f335(f104(f888(x101632,a879)),x101633),x101634)),f335(f335(x101635,f335(x101631,x101633)),f335(x101631,x101634)))+P1(f335(f335(f337(x101632),f877(x101634,x101633,x101631,x101636,x101637,x101635,x101632)),f335(f335(f95(f888(x101632,a879)),x101633),x101634)))
% 59.73/59.68 [9866]~P8(x98664,x98668,x98665)+~P8(x98661,x98669,x98663)+~P14(x98661,x98664,f888(x98662,a879),x98663,x98665,x98667)+P13(x98661,f888(x98662,a879),x98663,f335(f335(f8(f888(x98664,f888(x98662,a879)),f888(x98662,a879),x98661),f335(f33(x98664,f888(x98662,a879)),f335(f288(x98664,x98664,x98665),f335(f335(f312(x98664),x98666),f188(f888(x98664,a879)))))),x98667))+~P1(f335(f335(f337(x98664),x98666),x98668))
% 59.73/59.68 [5448]~P106(x54483)+~P15(x54483,x54481)+E(x54481,f748(x54482,x54483))+~E(f335(f166(x54483),x54481),x54482)+~P1(f335(f56(x54483),x54482))+~P1(f335(f130(x54483),x54481))
% 59.73/59.68 [5075]~P126(x50752)+~P131(x50752)+~P141(x50752)+~P113(x50752)+E(x50751,f2(x50752))+~E(f335(f335(f254(x50752),x50751),x50753),f2(x50752))
% 59.73/59.68 [5076]~P126(x50762)+~P131(x50762)+~P141(x50762)+~P113(x50762)+~E(x50761,f2(a881))+~E(f335(f335(f254(x50762),x50763),x50761),f2(x50762))
% 59.73/59.68 [6504]~P90(x65041)+~E(x65043,f2(x65041))+~E(x65042,f2(x65041))+E(f335(f335(f75(x65041),x65042),x65043),f2(x65041))+~P1(f335(f335(f242(x65041),f2(x65041)),x65043))+~P1(f335(f335(f242(x65041),f2(x65041)),x65042))
% 59.73/59.68 [8871]E(x88711,f2(a881))+~E(x88712,f335(f335(f75(a881),f335(f335(f76(a881),f335(f263(a881,a881),x88713)),x88711)),f335(f267(a881,a881),x88713)))+P1(f335(f42(x88712,x88711),x88713))+~P1(f335(f335(f242(a881),f335(f267(a881,a881),x88713)),f2(a881)))+P1(f335(f335(f243(a881),f2(a881)),x88711))+~P1(f335(f335(f243(a881),x88711),f335(f267(a881,a881),x88713)))
% 59.73/59.68 [8885]~E(f335(f263(a881,a881),x88853),f2(a881))+~E(x88851,f335(f335(f75(a881),f335(f335(f76(a881),f335(f263(a881,a881),x88853)),x88852)),f335(f267(a881,a881),x88853)))+P1(f335(f42(x88851,x88852),x88853))+~P1(f335(f335(f242(a881),f335(f267(a881,a881),x88853)),f2(a881)))+P1(f335(f335(f243(a881),f2(a881)),x88852))+~P1(f335(f335(f243(a881),x88852),f335(f267(a881,a881),x88853)))
% 59.73/59.68 [8893]E(x88931,f2(a881))+~E(x88932,f335(f335(f75(a881),f335(f335(f76(a881),f335(f263(a881,a881),x88933)),x88931)),f335(f267(a881,a881),x88933)))+P1(f335(f42(x88932,x88931),x88933))+~P1(f335(f335(f243(a881),f2(a881)),x88931))+~P1(f335(f335(f242(a881),f2(a881)),f335(f267(a881,a881),x88933)))+~P1(f335(f335(f243(a881),f335(f267(a881,a881),x88933)),x88931))
% 59.73/59.68 [8910]~E(f335(f263(a881,a881),x89103),f2(a881))+~E(x89101,f335(f335(f75(a881),f335(f335(f76(a881),f335(f263(a881,a881),x89103)),x89102)),f335(f267(a881,a881),x89103)))+P1(f335(f42(x89101,x89102),x89103))+~P1(f335(f335(f243(a881),f2(a881)),x89102))+~P1(f335(f335(f242(a881),f2(a881)),f335(f267(a881,a881),x89103)))+~P1(f335(f335(f243(a881),f335(f267(a881,a881),x89103)),x89102))
% 59.73/59.68 [6897]~P61(x68972)+E(x68971,f188(f888(x68972,a879)))+E(x68973,f188(f888(x68972,a879)))+~P1(f335(f56(x68972),x68971))+~P1(f335(f56(x68972),x68973))+E(f10(x68972,f335(f335(f104(f888(x68972,a879)),x68973),x68971)),f335(f335(f95(x68972),f10(x68972,x68973)),f10(x68972,x68971)))
% 59.73/59.68 [6898]~P61(x68982)+E(x68981,f188(f888(x68982,a879)))+E(x68983,f188(f888(x68982,a879)))+~P1(f335(f56(x68982),x68981))+~P1(f335(f56(x68982),x68983))+E(f13(x68982,f335(f335(f104(f888(x68982,a879)),x68983),x68981)),f335(f335(f104(x68982),f13(x68982,x68983)),f13(x68982,x68981)))
% 59.73/59.68 [6899]~P106(x68992)+E(x68991,f188(f888(x68992,a879)))+E(x68993,f188(f888(x68992,a879)))+~P1(f335(f56(x68992),x68991))+~P1(f335(f56(x68992),x68993))+E(f14(x68992,f335(f335(f104(f888(x68992,a879)),x68993),x68991)),f335(f335(f241(x68992),f14(x68992,x68993)),f14(x68992,x68991)))
% 59.73/59.68 [6900]~P106(x69002)+E(x69001,f188(f888(x69002,a879)))+E(x69003,f188(f888(x69002,a879)))+~P1(f335(f56(x69002),x69001))+~P1(f335(f56(x69002),x69003))+E(f15(x69002,f335(f335(f104(f888(x69002,a879)),x69003),x69001)),f335(f335(f240(x69002),f15(x69002,x69003)),f15(x69002,x69001)))
% 59.73/59.68 [7536]~P98(x75362)+E(x75361,f188(f888(x75362,a879)))+E(x75363,f188(f888(x75362,a879)))+~P1(f335(f56(x75362),x75361))+~P1(f335(f56(x75362),x75363))+E(f335(f335(f76(x75362),f335(f58(x75362,f76(x75362)),x75363)),f335(f58(x75362,f76(x75362)),x75361)),f335(f58(x75362,f76(x75362)),f335(f335(f104(f888(x75362,a879)),x75363),x75361)))
% 59.73/59.68 [7696]~P106(x76962)+E(x76961,f188(f888(x76962,a879)))+E(x76963,f188(f888(x76962,a879)))+~P1(f335(f56(x76962),x76961))+~P1(f335(f56(x76962),x76963))+E(f335(f335(f240(x76962),f11(x76962,f240(x76962),x76963)),f11(x76962,f240(x76962),x76961)),f11(x76962,f240(x76962),f335(f335(f104(f888(x76962,a879)),x76963),x76961)))
% 59.73/59.68 [7697]~P106(x76972)+E(x76971,f188(f888(x76972,a879)))+E(x76973,f188(f888(x76972,a879)))+~P1(f335(f56(x76972),x76971))+~P1(f335(f56(x76972),x76973))+E(f335(f335(f241(x76972),f12(x76972,f241(x76972),x76973)),f12(x76972,f241(x76972),x76971)),f12(x76972,f241(x76972),f335(f335(f104(f888(x76972,a879)),x76973),x76971)))
% 59.73/59.68 [8729]~P1(f335(x87291,x87293))+P1(f335(x87291,f478(x87291,x87292)))+P1(f335(x87291,f466(x87291,x87292)))+~P1(f335(f335(f243(a1),f2(a1)),x87292))+~P1(f335(f335(f337(a1),x87293),f305(a1,f73(a1),x87292)))+P1(f335(x87291,f335(f335(f23(a1),f466(x87291,x87292)),f335(f335(f76(a1),f477(x87291,x87292)),x87292))))
% 59.73/59.68 [9024]~P1(f335(x90241,x90243))+~P1(f335(x90241,f466(x90241,x90242)))+P1(f335(x90241,f478(x90241,x90242)))+~P1(f335(f335(f243(a1),f2(a1)),x90242))+~P1(f335(f335(f337(a1),x90243),f305(a1,f73(a1),x90242)))+~P1(f335(x90241,f335(f335(f23(a1),f466(x90241,x90242)),f335(f335(f76(a1),f477(x90241,x90242)),x90242))))
% 59.73/59.68 [10241]~P100(x102412)+E(x102411,f188(f888(x102412,a879)))+E(x102413,f188(f888(x102412,a879)))+~P1(f335(f56(x102412),x102411))+~P1(f335(f56(x102412),x102413))+E(f10(x102412,f335(f249(x102412),f335(f335(f8(f888(x102412,a879),a879,x102412),f82(x102412)),f335(f335(f8(f888(x102412,f888(x102412,a879)),f888(x102412,a879),x102412),f335(f8(f888(x102412,a879),a879,x102412),f82(x102412))),f335(f335(f7(x102412,f888(x102412,f888(x102412,a879)),f888(x102412,f888(x102412,a879))),f335(f335(f8(f888(x102412,f888(f888(x102412,a879),f888(x102412,a879))),f888(f888(x102412,f888(x102412,a879)),f888(x102412,f888(x102412,a879))),x102412),f18(x102412,f888(x102412,a879),f888(x102412,a879))),f335(f335(f8(f888(x102412,f888(x102412,f888(a879,a879))),f888(x102412,f888(f888(x102412,a879),f888(x102412,a879))),x102412),f335(f8(f888(x102412,f888(a879,a879)),f888(f888(x102412,a879),f888(x102412,a879)),x102412),f18(x102412,a879,a879))),f335(f335(f8(f888(x102412,f888(x102412,a879)),f888(x102412,f888(x102412,f888(a879,a879))),x102412),f335(f8(f888(x102412,a879),f888(x102412,f888(a879,a879)),x102412),f335(f8(a879,f888(a879,a879),x102412),a333))),f335(f335(f7(x102412,f888(x102412,f888(x102412,x102412)),f888(x102412,f888(x102412,a879))),f335(f335(f8(f888(f888(x102412,x102412),f888(x102412,a879)),f888(f888(x102412,f888(x102412,x102412)),f888(x102412,f888(x102412,a879))),x102412),f8(f888(x102412,x102412),f888(x102412,a879),x102412)),f335(f335(f8(f888(x102412,a879),f888(f888(x102412,x102412),f888(x102412,a879)),x102412),f8(x102412,a879,x102412)),a332))),f104(x102412)))))),f335(f335(f7(x102412,f888(x102412,a879),f888(x102412,a879)),f335(f335(f8(f888(a879,a879),f888(f888(x102412,a879),f888(x102412,a879)),x102412),f8(a879,a879,x102412)),f335(f335(f8(a879,f888(a879,a879),x102412),a333),f335(f335(f7(x102412,f888(x102412,a879),a879),f337(x102412)),x102413)))),f335(f335(f7(x102412,f888(x102412,a879),a879),f337(x102412)),x102411))))))),f335(f335(f104(x102412),f10(x102412,x102413)),f10(x102412,x102411)))
% 59.73/59.68 [10242]~P100(x102422)+E(x102421,f188(f888(x102422,a879)))+E(x102423,f188(f888(x102422,a879)))+~P1(f335(f56(x102422),x102421))+~P1(f335(f56(x102422),x102423))+E(f13(x102422,f335(f249(x102422),f335(f335(f8(f888(x102422,a879),a879,x102422),f82(x102422)),f335(f335(f8(f888(x102422,f888(x102422,a879)),f888(x102422,a879),x102422),f335(f8(f888(x102422,a879),a879,x102422),f82(x102422))),f335(f335(f7(x102422,f888(x102422,f888(x102422,a879)),f888(x102422,f888(x102422,a879))),f335(f335(f8(f888(x102422,f888(f888(x102422,a879),f888(x102422,a879))),f888(f888(x102422,f888(x102422,a879)),f888(x102422,f888(x102422,a879))),x102422),f18(x102422,f888(x102422,a879),f888(x102422,a879))),f335(f335(f8(f888(x102422,f888(x102422,f888(a879,a879))),f888(x102422,f888(f888(x102422,a879),f888(x102422,a879))),x102422),f335(f8(f888(x102422,f888(a879,a879)),f888(f888(x102422,a879),f888(x102422,a879)),x102422),f18(x102422,a879,a879))),f335(f335(f8(f888(x102422,f888(x102422,a879)),f888(x102422,f888(x102422,f888(a879,a879))),x102422),f335(f8(f888(x102422,a879),f888(x102422,f888(a879,a879)),x102422),f335(f8(a879,f888(a879,a879),x102422),a333))),f335(f335(f7(x102422,f888(x102422,f888(x102422,x102422)),f888(x102422,f888(x102422,a879))),f335(f335(f8(f888(f888(x102422,x102422),f888(x102422,a879)),f888(f888(x102422,f888(x102422,x102422)),f888(x102422,f888(x102422,a879))),x102422),f8(f888(x102422,x102422),f888(x102422,a879),x102422)),f335(f335(f8(f888(x102422,a879),f888(f888(x102422,x102422),f888(x102422,a879)),x102422),f8(x102422,a879,x102422)),a332))),f95(x102422)))))),f335(f335(f7(x102422,f888(x102422,a879),f888(x102422,a879)),f335(f335(f8(f888(a879,a879),f888(f888(x102422,a879),f888(x102422,a879)),x102422),f8(a879,a879,x102422)),f335(f335(f8(a879,f888(a879,a879),x102422),a333),f335(f335(f7(x102422,f888(x102422,a879),a879),f337(x102422)),x102423)))),f335(f335(f7(x102422,f888(x102422,a879),a879),f337(x102422)),x102421))))))),f335(f335(f95(x102422),f13(x102422,x102423)),f13(x102422,x102421)))
% 59.73/59.68 [10243]~P106(x102432)+E(x102431,f188(f888(x102432,a879)))+E(x102433,f188(f888(x102432,a879)))+~P1(f335(f56(x102432),x102431))+~P1(f335(f56(x102432),x102433))+E(f12(x102432,f241(x102432),f335(f249(x102432),f335(f335(f8(f888(x102432,a879),a879,x102432),f82(x102432)),f335(f335(f8(f888(x102432,f888(x102432,a879)),f888(x102432,a879),x102432),f335(f8(f888(x102432,a879),a879,x102432),f82(x102432))),f335(f335(f7(x102432,f888(x102432,f888(x102432,a879)),f888(x102432,f888(x102432,a879))),f335(f335(f8(f888(x102432,f888(f888(x102432,a879),f888(x102432,a879))),f888(f888(x102432,f888(x102432,a879)),f888(x102432,f888(x102432,a879))),x102432),f18(x102432,f888(x102432,a879),f888(x102432,a879))),f335(f335(f8(f888(x102432,f888(x102432,f888(a879,a879))),f888(x102432,f888(f888(x102432,a879),f888(x102432,a879))),x102432),f335(f8(f888(x102432,f888(a879,a879)),f888(f888(x102432,a879),f888(x102432,a879)),x102432),f18(x102432,a879,a879))),f335(f335(f8(f888(x102432,f888(x102432,a879)),f888(x102432,f888(x102432,f888(a879,a879))),x102432),f335(f8(f888(x102432,a879),f888(x102432,f888(a879,a879)),x102432),f335(f8(a879,f888(a879,a879),x102432),a333))),f335(f335(f7(x102432,f888(x102432,f888(x102432,x102432)),f888(x102432,f888(x102432,a879))),f335(f335(f8(f888(f888(x102432,x102432),f888(x102432,a879)),f888(f888(x102432,f888(x102432,x102432)),f888(x102432,f888(x102432,a879))),x102432),f8(f888(x102432,x102432),f888(x102432,a879),x102432)),f335(f335(f8(f888(x102432,a879),f888(f888(x102432,x102432),f888(x102432,a879)),x102432),f8(x102432,a879,x102432)),a332))),f240(x102432)))))),f335(f335(f7(x102432,f888(x102432,a879),f888(x102432,a879)),f335(f335(f8(f888(a879,a879),f888(f888(x102432,a879),f888(x102432,a879)),x102432),f8(a879,a879,x102432)),f335(f335(f8(a879,f888(a879,a879),x102432),a333),f335(f335(f7(x102432,f888(x102432,a879),a879),f337(x102432)),x102433)))),f335(f335(f7(x102432,f888(x102432,a879),a879),f337(x102432)),x102431))))))),f335(f335(f240(x102432),f12(x102432,f241(x102432),x102433)),f12(x102432,f241(x102432),x102431)))
% 59.73/59.68 [10244]~P106(x102442)+E(x102441,f188(f888(x102442,a879)))+E(x102443,f188(f888(x102442,a879)))+~P1(f335(f56(x102442),x102441))+~P1(f335(f56(x102442),x102443))+E(f11(x102442,f240(x102442),f335(f249(x102442),f335(f335(f8(f888(x102442,a879),a879,x102442),f82(x102442)),f335(f335(f8(f888(x102442,f888(x102442,a879)),f888(x102442,a879),x102442),f335(f8(f888(x102442,a879),a879,x102442),f82(x102442))),f335(f335(f7(x102442,f888(x102442,f888(x102442,a879)),f888(x102442,f888(x102442,a879))),f335(f335(f8(f888(x102442,f888(f888(x102442,a879),f888(x102442,a879))),f888(f888(x102442,f888(x102442,a879)),f888(x102442,f888(x102442,a879))),x102442),f18(x102442,f888(x102442,a879),f888(x102442,a879))),f335(f335(f8(f888(x102442,f888(x102442,f888(a879,a879))),f888(x102442,f888(f888(x102442,a879),f888(x102442,a879))),x102442),f335(f8(f888(x102442,f888(a879,a879)),f888(f888(x102442,a879),f888(x102442,a879)),x102442),f18(x102442,a879,a879))),f335(f335(f8(f888(x102442,f888(x102442,a879)),f888(x102442,f888(x102442,f888(a879,a879))),x102442),f335(f8(f888(x102442,a879),f888(x102442,f888(a879,a879)),x102442),f335(f8(a879,f888(a879,a879),x102442),a333))),f335(f335(f7(x102442,f888(x102442,f888(x102442,x102442)),f888(x102442,f888(x102442,a879))),f335(f335(f8(f888(f888(x102442,x102442),f888(x102442,a879)),f888(f888(x102442,f888(x102442,x102442)),f888(x102442,f888(x102442,a879))),x102442),f8(f888(x102442,x102442),f888(x102442,a879),x102442)),f335(f335(f8(f888(x102442,a879),f888(f888(x102442,x102442),f888(x102442,a879)),x102442),f8(x102442,a879,x102442)),a332))),f241(x102442)))))),f335(f335(f7(x102442,f888(x102442,a879),f888(x102442,a879)),f335(f335(f8(f888(a879,a879),f888(f888(x102442,a879),f888(x102442,a879)),x102442),f8(a879,a879,x102442)),f335(f335(f8(a879,f888(a879,a879),x102442),a333),f335(f335(f7(x102442,f888(x102442,a879),a879),f337(x102442)),x102443)))),f335(f335(f7(x102442,f888(x102442,a879),a879),f337(x102442)),x102441))))))),f335(f335(f241(x102442),f11(x102442,f240(x102442),x102443)),f11(x102442,f240(x102442),x102441)))
% 59.73/59.68 [7220]~P122(x72203)+E(x72201,x72202)+~E(f335(f335(f254(x72203),x72201),x72204),f335(f335(f254(x72203),x72202),x72204))+~P1(f335(f335(f242(x72203),f2(x72203)),x72202))+~P1(f335(f335(f242(x72203),f2(x72203)),x72201))+~P1(f335(f335(f243(a881),f2(a881)),x72204))
% 59.73/59.68 [8053]~P95(x80531)+~P68(x80531)+P1(f335(f335(f243(x80531),x80532),f2(x80531)))+P1(f335(f335(f243(x80531),f2(x80531)),x80532))+P1(f335(f335(f242(x80531),f335(f335(f292(x80531),x80533),x80532)),f335(f97(x80531),x80534)))+~P1(f335(f335(f242(x80531),f2(x80531)),f335(f97(x80531),x80534)))
% 59.73/59.68 [8054]~P95(x80541)+~P68(x80541)+P1(f335(f335(f243(x80541),x80542),f2(x80541)))+P1(f335(f335(f243(x80541),f2(x80541)),x80542))+P1(f335(f335(f243(x80541),f335(f335(f292(x80541),x80543),x80542)),f335(f97(x80541),x80544)))+~P1(f335(f335(f243(x80541),f2(x80541)),f335(f97(x80541),x80544)))
% 59.73/59.68 [8296]~P95(x82961)+~P68(x82961)+P1(f335(f335(f243(x82961),x82962),f2(x82961)))+P1(f335(f335(f243(x82961),f2(x82961)),x82962))+~P1(f335(f335(f242(x82961),f335(f335(f292(x82961),x82964),x82962)),f335(f97(x82961),x82963)))+P1(f335(f335(f242(x82961),f2(x82961)),f335(f97(x82961),x82963)))
% 59.73/59.68 [8297]~P95(x82971)+~P68(x82971)+P1(f335(f335(f243(x82971),x82972),f2(x82971)))+P1(f335(f335(f243(x82971),f2(x82971)),x82972))+~P1(f335(f335(f243(x82971),f335(f335(f292(x82971),x82974),x82972)),f335(f97(x82971),x82973)))+P1(f335(f335(f243(x82971),f2(x82971)),f335(f97(x82971),x82973)))
% 59.73/59.68 [7495]~P106(x74952)+E(x74951,f188(f888(x74952,a879)))+~P1(f335(f56(x74952),x74951))+~P1(f335(f335(f337(x74952),x74954),x74951))+P1(f335(f335(f242(x74952),x74953),x74954))+~P1(f335(f335(f242(x74952),x74953),f335(f58(x74952,f240(x74952)),x74951)))
% 59.73/59.68 [7496]~P102(x74962)+E(x74961,f188(f888(x74962,a879)))+~P1(f335(f56(x74962),x74961))+~P1(f335(f335(f337(x74962),x74964),x74961))+P1(f335(f335(f242(x74962),x74963),x74964))+~P1(f335(f335(f242(x74962),x74963),f335(f58(x74962,f95(x74962)),x74961)))
% 59.73/59.68 [7497]~P106(x74972)+E(x74971,f188(f888(x74972,a879)))+~P1(f335(f56(x74972),x74971))+~P1(f335(f335(f337(x74972),x74974),x74971))+P1(f335(f335(f243(x74972),x74973),x74974))+~P1(f335(f335(f243(x74972),x74973),f335(f58(x74972,f240(x74972)),x74971)))
% 59.73/59.68 [8008]~P95(x80081)+~P68(x80081)+P1(f335(f335(f243(x80081),f335(f97(x80081),x80082)),f2(x80081)))+~P1(f335(f335(f242(x80081),x80083),f2(x80081)))+P1(f335(f335(f243(x80081),f2(x80081)),f335(f97(x80081),x80082)))+P1(f335(f335(f242(x80081),x80083),f335(f335(f292(x80081),x80084),f335(f97(x80081),x80082))))
% 59.73/59.68 [8009]~P95(x80091)+~P68(x80091)+P1(f335(f335(f243(x80091),f335(f97(x80091),x80092)),f2(x80091)))+~P1(f335(f335(f243(x80091),x80093),f2(x80091)))+P1(f335(f335(f243(x80091),f2(x80091)),f335(f97(x80091),x80092)))+P1(f335(f335(f243(x80091),x80093),f335(f335(f292(x80091),x80094),f335(f97(x80091),x80092))))
% 59.73/59.68 [8021]~P95(x80211)+~P68(x80211)+P1(f335(f335(f243(x80211),x80212),f2(x80211)))+~P1(f335(f335(f242(x80211),f335(f97(x80211),x80213)),f2(x80211)))+P1(f335(f335(f243(x80211),f2(x80211)),x80212))+P1(f335(f335(f242(x80211),f335(f97(x80211),x80213)),f335(f335(f292(x80211),x80214),x80212)))
% 59.73/59.68 [8022]~P95(x80221)+~P68(x80221)+P1(f335(f335(f243(x80221),x80222),f2(x80221)))+~P1(f335(f335(f243(x80221),f335(f97(x80221),x80223)),f2(x80221)))+P1(f335(f335(f243(x80221),f2(x80221)),x80222))+P1(f335(f335(f243(x80221),f335(f97(x80221),x80223)),f335(f335(f292(x80221),x80224),x80222)))
% 59.73/59.68 [8162]~P95(x81621)+~P68(x81621)+P1(f335(f335(f243(x81621),x81622),f2(x81621)))+P1(f335(f335(f242(x81621),f335(f97(x81621),x81623)),f2(x81621)))+P1(f335(f335(f243(x81621),f2(x81621)),x81622))+~P1(f335(f335(f242(x81621),f335(f97(x81621),x81623)),f335(f335(f292(x81621),x81624),x81622)))
% 59.73/59.68 [8163]~P95(x81631)+~P68(x81631)+P1(f335(f335(f243(x81631),x81632),f2(x81631)))+P1(f335(f335(f243(x81631),f335(f97(x81631),x81633)),f2(x81631)))+P1(f335(f335(f243(x81631),f2(x81631)),x81632))+~P1(f335(f335(f243(x81631),f335(f97(x81631),x81633)),f335(f335(f292(x81631),x81634),x81632)))
% 59.73/59.68 [8242]~P95(x82421)+~P68(x82421)+P1(f335(f335(f242(x82421),x82422),f2(x82421)))+P1(f335(f335(f243(x82421),f335(f97(x82421),x82423)),f2(x82421)))+P1(f335(f335(f243(x82421),f2(x82421)),f335(f97(x82421),x82423)))+~P1(f335(f335(f242(x82421),x82422),f335(f335(f292(x82421),x82424),f335(f97(x82421),x82423))))
% 59.73/59.68 [8243]~P95(x82431)+~P68(x82431)+P1(f335(f335(f243(x82431),x82432),f2(x82431)))+P1(f335(f335(f243(x82431),f335(f97(x82431),x82433)),f2(x82431)))+P1(f335(f335(f243(x82431),f2(x82431)),f335(f97(x82431),x82433)))+~P1(f335(f335(f243(x82431),x82432),f335(f335(f292(x82431),x82434),f335(f97(x82431),x82433))))
% 59.73/59.68 [8435]~P95(x84351)+~P68(x84351)+~P1(f335(f335(f242(x84351),x84353),f2(x84351)))+P1(f335(f335(f243(x84351),f2(x84351)),f335(f97(x84351),x84352)))+~P1(f335(f335(f242(x84351),x84354),f335(f335(f76(x84351),x84353),f335(f97(x84351),x84352))))+P1(f335(f335(f242(x84351),x84353),f335(f335(f292(x84351),x84354),f335(f97(x84351),x84352))))
% 59.73/59.68 [8436]~P95(x84361)+~P68(x84361)+~P1(f335(f335(f243(x84361),x84363),f2(x84361)))+P1(f335(f335(f243(x84361),f2(x84361)),f335(f97(x84361),x84362)))+~P1(f335(f335(f243(x84361),x84364),f335(f335(f76(x84361),x84363),f335(f97(x84361),x84362))))+P1(f335(f335(f243(x84361),x84363),f335(f335(f292(x84361),x84364),f335(f97(x84361),x84362))))
% 59.73/59.68 [8600]~P95(x86001)+~P68(x86001)+~P1(f335(f335(f243(x86001),f335(f97(x86001),x86002)),f2(x86001)))+P1(f335(f335(f243(x86001),f2(x86001)),f335(f97(x86001),x86002)))+~P1(f335(f335(f242(x86001),x86004),f335(f335(f76(x86001),x86003),f335(f97(x86001),x86002))))+P1(f335(f335(f242(x86001),x86003),f335(f335(f292(x86001),x86004),f335(f97(x86001),x86002))))
% 59.73/59.68 [8601]~P95(x86011)+~P68(x86011)+~P1(f335(f335(f243(x86011),f335(f97(x86011),x86012)),f2(x86011)))+P1(f335(f335(f243(x86011),f2(x86011)),f335(f97(x86011),x86012)))+~P1(f335(f335(f242(x86011),x86014),f335(f335(f292(x86011),x86013),f335(f97(x86011),x86012))))+P1(f335(f335(f242(x86011),x86013),f335(f335(f76(x86011),x86014),f335(f97(x86011),x86012))))
% 59.73/59.68 [8602]~P95(x86021)+~P68(x86021)+~P1(f335(f335(f243(x86021),f335(f97(x86021),x86022)),f2(x86021)))+P1(f335(f335(f243(x86021),f2(x86021)),f335(f97(x86021),x86022)))+~P1(f335(f335(f243(x86021),x86024),f335(f335(f76(x86021),x86023),f335(f97(x86021),x86022))))+P1(f335(f335(f243(x86021),x86023),f335(f335(f292(x86021),x86024),f335(f97(x86021),x86022))))
% 59.73/59.68 [8603]~P95(x86031)+~P68(x86031)+~P1(f335(f335(f243(x86031),f335(f97(x86031),x86032)),f2(x86031)))+P1(f335(f335(f243(x86031),f2(x86031)),f335(f97(x86031),x86032)))+~P1(f335(f335(f243(x86031),x86034),f335(f335(f292(x86031),x86033),f335(f97(x86031),x86032))))+P1(f335(f335(f243(x86031),x86033),f335(f335(f76(x86031),x86034),f335(f97(x86031),x86032))))
% 59.73/59.68 [7397]E(x73971,f2(a1))+E(f335(f335(f30(a1),x73972),x73971),x73973)+~P1(f335(f335(f242(a1),x73974),f2(a1)))+~E(x73972,f335(f335(f75(a1),f335(f335(f76(a1),x73971),x73973)),x73974))+P1(f335(f335(f243(a1),f2(a1)),x73971))+~P1(f335(f335(f243(a1),x73971),x73974))
% 59.73/59.68 [7413]E(f39(a1,x74132,x74131),x74133)+E(x74131,f2(a1))+~P1(f335(f335(f242(a1),x74133),f2(a1)))+~E(x74132,f335(f335(f75(a1),f335(f335(f76(a1),x74131),x74134)),x74133))+P1(f335(f335(f243(a1),f2(a1)),x74131))+~P1(f335(f335(f243(a1),x74131),x74133))
% 59.73/59.68 [7535]E(x75351,f2(a1))+E(f335(f335(f30(a1),x75352),x75351),x75353)+~E(x75352,f335(f335(f75(a1),f335(f335(f76(a1),x75351),x75353)),x75354))+~P1(f335(f335(f242(a1),f2(a1)),x75354))+~P1(f335(f335(f243(a1),f2(a1)),x75351))+~P1(f335(f335(f243(a1),x75354),x75351))
% 59.73/59.68 [7557]E(f39(a1,x75572,x75571),x75573)+E(x75571,f2(a1))+~E(x75572,f335(f335(f75(a1),f335(f335(f76(a1),x75571),x75574)),x75573))+~P1(f335(f335(f242(a1),f2(a1)),x75573))+~P1(f335(f335(f243(a1),f2(a1)),x75571))+~P1(f335(f335(f243(a1),x75573),x75571))
% 59.73/59.68 [7700]~P106(x77002)+E(x77001,f188(f888(x77002,a879)))+~P1(f335(f56(x77002),x77001))+~P1(f335(f335(f337(x77002),x77004),x77001))+~P1(f335(f335(f242(x77002),x77004),x77003))+P1(f335(f335(f242(x77002),f335(f58(x77002,f240(x77002)),x77001)),x77003))
% 59.73/59.68 [7701]~P106(x77012)+E(x77011,f188(f888(x77012,a879)))+~P1(f335(f56(x77012),x77011))+~P1(f335(f335(f243(x77012),x77014),x77013))+~P1(f335(f335(f337(x77012),x77014),x77011))+P1(f335(f335(f243(x77012),f335(f58(x77012,f240(x77012)),x77011)),x77013))
% 59.73/59.68 [8273]~P1(f335(f335(f242(a1),x82734),f2(a1)))+~E(x82731,f335(f335(f75(a1),f335(f335(f76(a1),x82732),x82733)),x82734))+~P1(f335(f335(f242(a1),f2(a1)),x82734))+~P1(f335(f335(f243(a1),x82734),x82732))+~P1(f335(f335(f243(a1),x82732),x82734))+P1(f335(f43(x82731,x82732),f335(f335(f264(a1,a1),x82733),x82734)))
% 59.73/59.68 [8398]~P95(x83981)+~P68(x83981)+P1(f335(f335(f243(x83981),f335(f97(x83981),x83982)),f2(x83981)))+~P1(f335(f335(f242(x83981),f2(x83981)),x83984))+P1(f335(f335(f243(x83981),f2(x83981)),f335(f97(x83981),x83982)))+P1(f335(f335(f242(x83981),f335(f335(f292(x83981),x83983),f335(f97(x83981),x83982))),x83984))
% 59.73/59.68 [8399]~P95(x83991)+~P68(x83991)+P1(f335(f335(f243(x83991),f335(f97(x83991),x83992)),f2(x83991)))+~P1(f335(f335(f243(x83991),f2(x83991)),x83994))+P1(f335(f335(f243(x83991),f2(x83991)),f335(f97(x83991),x83992)))+P1(f335(f335(f243(x83991),f335(f335(f292(x83991),x83993),f335(f97(x83991),x83992))),x83994))
% 59.73/59.68 [8508]~P95(x85081)+~P68(x85081)+~P1(f335(f335(f243(x85081),x85082),f2(x85081)))+P1(f335(f335(f243(x85081),f2(x85081)),x85082))+~P1(f335(f335(f242(x85081),f335(f97(x85081),x85084)),f335(f335(f292(x85081),x85083),x85082)))+P1(f335(f335(f242(x85081),x85083),f335(f335(f76(x85081),f335(f97(x85081),x85084)),x85082)))
% 59.73/59.68 [8509]~P95(x85091)+~P68(x85091)+~P1(f335(f335(f243(x85091),x85092),f2(x85091)))+P1(f335(f335(f243(x85091),f2(x85091)),x85092))+~P1(f335(f335(f243(x85091),f335(f97(x85091),x85094)),f335(f335(f292(x85091),x85093),x85092)))+P1(f335(f335(f243(x85091),x85093),f335(f335(f76(x85091),f335(f97(x85091),x85094)),x85092)))
% 59.73/59.68 [8547]~P95(x85471)+~P68(x85471)+~P1(f335(f335(f243(x85471),x85472),f2(x85471)))+P1(f335(f335(f243(x85471),f2(x85471)),x85472))+P1(f335(f335(f242(x85471),f335(f97(x85471),x85473)),f335(f335(f292(x85471),x85474),x85472)))+~P1(f335(f335(f242(x85471),x85474),f335(f335(f76(x85471),f335(f97(x85471),x85473)),x85472)))
% 59.73/59.68 [8548]~P95(x85481)+~P68(x85481)+~P1(f335(f335(f243(x85481),x85482),f2(x85481)))+P1(f335(f335(f243(x85481),f2(x85481)),x85482))+P1(f335(f335(f243(x85481),f335(f97(x85481),x85483)),f335(f335(f292(x85481),x85484),x85482)))+~P1(f335(f335(f243(x85481),x85484),f335(f335(f76(x85481),f335(f97(x85481),x85483)),x85482)))
% 59.73/59.68 [8638]~P95(x86381)+~P68(x86381)+P1(f335(f335(f243(x86381),f335(f97(x86381),x86383)),f2(x86381)))+P1(f335(f335(f242(x86381),f2(x86381)),x86382))+P1(f335(f335(f243(x86381),f2(x86381)),f335(f97(x86381),x86383)))+~P1(f335(f335(f242(x86381),f335(f335(f292(x86381),x86384),f335(f97(x86381),x86383))),x86382))
% 59.73/59.68 [8639]~P95(x86391)+~P68(x86391)+P1(f335(f335(f243(x86391),f335(f97(x86391),x86393)),f2(x86391)))+P1(f335(f335(f243(x86391),f2(x86391)),x86392))+P1(f335(f335(f243(x86391),f2(x86391)),f335(f97(x86391),x86393)))+~P1(f335(f335(f243(x86391),f335(f335(f292(x86391),x86394),f335(f97(x86391),x86393))),x86392))
% 59.73/59.68 [8687]~P95(x86871)+~P68(x86871)+~P1(f335(f335(f242(x86871),f335(f97(x86871),x86873)),f2(x86871)))+P1(f335(f335(f243(x86871),f2(x86871)),x86872))+P1(f335(f335(f242(x86871),f335(f97(x86871),x86873)),f335(f335(f292(x86871),x86874),x86872)))+~P1(f335(f335(f242(x86871),x86874),f335(f335(f76(x86871),f335(f97(x86871),x86873)),x86872)))
% 59.73/59.68 [8688]~P95(x86881)+~P68(x86881)+~P1(f335(f335(f243(x86881),f335(f97(x86881),x86883)),f2(x86881)))+P1(f335(f335(f243(x86881),f2(x86881)),x86882))+P1(f335(f335(f243(x86881),f335(f97(x86881),x86883)),f335(f335(f292(x86881),x86884),x86882)))+~P1(f335(f335(f243(x86881),x86884),f335(f335(f76(x86881),f335(f97(x86881),x86883)),x86882)))
% 59.73/59.68 [8695]~P95(x86951)+~P68(x86951)+P1(f335(f335(f243(x86951),x86952),f2(x86951)))+P1(f335(f335(f242(x86951),f335(f335(f292(x86951),x86953),x86952)),f335(f97(x86951),x86954)))+~P1(f335(f335(f242(x86951),f2(x86951)),f335(f97(x86951),x86954)))+~P1(f335(f335(f242(x86951),x86953),f335(f335(f76(x86951),f335(f97(x86951),x86954)),x86952)))
% 59.73/59.68 [8696]~P95(x86961)+~P68(x86961)+P1(f335(f335(f243(x86961),x86962),f2(x86961)))+P1(f335(f335(f243(x86961),f335(f335(f292(x86961),x86963),x86962)),f335(f97(x86961),x86964)))+~P1(f335(f335(f243(x86961),f2(x86961)),f335(f97(x86961),x86964)))+~P1(f335(f335(f243(x86961),x86963),f335(f335(f76(x86961),f335(f97(x86961),x86964)),x86962)))
% 59.73/59.68 [8717]~P95(x87171)+~P68(x87171)+P1(f335(f335(f243(x87171),f335(f97(x87171),x87172)),f2(x87171)))+~P1(f335(f335(f242(x87171),f2(x87171)),x87174))+~P1(f335(f335(f242(x87171),x87173),f335(f335(f76(x87171),x87174),f335(f97(x87171),x87172))))+P1(f335(f335(f242(x87171),f335(f335(f292(x87171),x87173),f335(f97(x87171),x87172))),x87174))
% 59.73/59.68 [8718]~P95(x87181)+~P68(x87181)+P1(f335(f335(f243(x87181),f335(f97(x87181),x87182)),f2(x87181)))+~P1(f335(f335(f243(x87181),f2(x87181)),x87184))+~P1(f335(f335(f243(x87181),x87183),f335(f335(f76(x87181),x87184),f335(f97(x87181),x87182))))+P1(f335(f335(f243(x87181),f335(f335(f292(x87181),x87183),f335(f97(x87181),x87182))),x87184))
% 59.73/59.68 [8805]~P95(x88051)+~P68(x88051)+P1(f335(f335(f243(x88051),f335(f97(x88051),x88052)),f2(x88051)))+~P1(f335(f335(f242(x88051),x88053),f2(x88051)))+P1(f335(f335(f242(x88051),x88053),f335(f335(f292(x88051),x88054),f335(f97(x88051),x88052))))+~P1(f335(f335(f242(x88051),f335(f335(f76(x88051),x88053),f335(f97(x88051),x88052))),x88054))
% 59.73/59.68 [8806]~P95(x88061)+~P68(x88061)+P1(f335(f335(f243(x88061),f335(f97(x88061),x88062)),f2(x88061)))+~P1(f335(f335(f243(x88061),x88063),f2(x88061)))+P1(f335(f335(f243(x88061),x88063),f335(f335(f292(x88061),x88064),f335(f97(x88061),x88062))))+~P1(f335(f335(f243(x88061),f335(f335(f76(x88061),x88063),f335(f97(x88061),x88062))),x88064))
% 59.73/59.68 [8915]~P95(x89151)+~P68(x89151)+~P1(f335(f335(f242(x89151),f2(x89151)),x89154))+P1(f335(f335(f243(x89151),f2(x89151)),f335(f97(x89151),x89152)))+~P1(f335(f335(f242(x89151),f335(f335(f76(x89151),x89154),f335(f97(x89151),x89152))),x89153))+P1(f335(f335(f242(x89151),f335(f335(f292(x89151),x89153),f335(f97(x89151),x89152))),x89154))
% 59.73/59.68 [8916]~P95(x89161)+~P68(x89161)+~P1(f335(f335(f243(x89161),f2(x89161)),x89164))+P1(f335(f335(f243(x89161),f2(x89161)),f335(f97(x89161),x89162)))+~P1(f335(f335(f243(x89161),f335(f335(f76(x89161),x89164),f335(f97(x89161),x89162))),x89163))+P1(f335(f335(f243(x89161),f335(f335(f292(x89161),x89163),f335(f97(x89161),x89162))),x89164))
% 59.73/59.68 [8978]~P95(x89781)+~P68(x89781)+~P1(f335(f335(f242(x89781),x89782),f2(x89781)))+P1(f335(f335(f242(x89781),x89782),f335(f335(f292(x89781),x89783),f335(f97(x89781),x89784))))+~P1(f335(f335(f242(x89781),x89783),f335(f335(f76(x89781),x89782),f335(f97(x89781),x89784))))+~P1(f335(f335(f242(x89781),f335(f335(f76(x89781),x89782),f335(f97(x89781),x89784))),x89783))
% 59.73/59.68 [8979]~P95(x89791)+~P68(x89791)+~P1(f335(f335(f243(x89791),x89792),f2(x89791)))+P1(f335(f335(f243(x89791),x89792),f335(f335(f292(x89791),x89793),f335(f97(x89791),x89794))))+~P1(f335(f335(f243(x89791),x89793),f335(f335(f76(x89791),x89792),f335(f97(x89791),x89794))))+~P1(f335(f335(f243(x89791),f335(f335(f76(x89791),x89792),f335(f97(x89791),x89794))),x89793))
% 59.73/59.68 [9005]~P95(x90051)+~P68(x90051)+~P1(f335(f335(f243(x90051),f335(f97(x90051),x90052)),f2(x90051)))+P1(f335(f335(f243(x90051),f2(x90051)),f335(f97(x90051),x90052)))+~P1(f335(f335(f242(x90051),f335(f335(f292(x90051),x90054),f335(f97(x90051),x90052))),x90053))+P1(f335(f335(f242(x90051),f335(f335(f76(x90051),x90053),f335(f97(x90051),x90052))),x90054))
% 59.73/59.68 [9006]~P95(x90061)+~P68(x90061)+~P1(f335(f335(f243(x90061),f335(f97(x90061),x90062)),f2(x90061)))+P1(f335(f335(f243(x90061),f2(x90061)),f335(f97(x90061),x90062)))+~P1(f335(f335(f242(x90061),f335(f335(f76(x90061),x90064),f335(f97(x90061),x90062))),x90063))+P1(f335(f335(f242(x90061),f335(f335(f292(x90061),x90063),f335(f97(x90061),x90062))),x90064))
% 59.73/59.68 [9007]~P95(x90071)+~P68(x90071)+~P1(f335(f335(f243(x90071),f335(f97(x90071),x90072)),f2(x90071)))+P1(f335(f335(f243(x90071),f2(x90071)),f335(f97(x90071),x90072)))+~P1(f335(f335(f243(x90071),f335(f335(f292(x90071),x90074),f335(f97(x90071),x90072))),x90073))+P1(f335(f335(f243(x90071),f335(f335(f76(x90071),x90073),f335(f97(x90071),x90072))),x90074))
% 59.73/59.68 [9008]~P95(x90081)+~P68(x90081)+~P1(f335(f335(f243(x90081),f335(f97(x90081),x90082)),f2(x90081)))+P1(f335(f335(f243(x90081),f2(x90081)),f335(f97(x90081),x90082)))+~P1(f335(f335(f243(x90081),f335(f335(f76(x90081),x90084),f335(f97(x90081),x90082))),x90083))+P1(f335(f335(f243(x90081),f335(f335(f292(x90081),x90083),f335(f97(x90081),x90082))),x90084))
% 59.73/59.68 [9085]~P95(x90851)+~P68(x90851)+~P1(f335(f335(f243(x90851),f335(f97(x90851),x90854)),f2(x90851)))+P1(f335(f335(f242(x90851),x90852),f335(f335(f292(x90851),x90853),f335(f97(x90851),x90854))))+~P1(f335(f335(f242(x90851),x90853),f335(f335(f76(x90851),x90852),f335(f97(x90851),x90854))))+~P1(f335(f335(f242(x90851),f335(f335(f76(x90851),x90852),f335(f97(x90851),x90854))),x90853))
% 59.73/59.68 [9086]~P95(x90861)+~P68(x90861)+~P1(f335(f335(f243(x90861),f335(f97(x90861),x90864)),f2(x90861)))+P1(f335(f335(f243(x90861),x90862),f335(f335(f292(x90861),x90863),f335(f97(x90861),x90864))))+~P1(f335(f335(f243(x90861),x90863),f335(f335(f76(x90861),x90862),f335(f97(x90861),x90864))))+~P1(f335(f335(f243(x90861),f335(f335(f76(x90861),x90862),f335(f97(x90861),x90864))),x90863))
% 59.73/59.68 [9132]~P95(x91321)+~P68(x91321)+~P1(f335(f335(f242(x91321),f2(x91321)),x91324))+~P1(f335(f335(f242(x91321),x91322),f335(f335(f76(x91321),x91324),f335(f97(x91321),x91323))))+~P1(f335(f335(f242(x91321),f335(f335(f76(x91321),x91324),f335(f97(x91321),x91323))),x91322))+P1(f335(f335(f242(x91321),f335(f335(f292(x91321),x91322),f335(f97(x91321),x91323))),x91324))
% 59.73/59.68 [9133]~P95(x91331)+~P68(x91331)+~P1(f335(f335(f243(x91331),f2(x91331)),x91334))+~P1(f335(f335(f243(x91331),x91332),f335(f335(f76(x91331),x91334),f335(f97(x91331),x91333))))+~P1(f335(f335(f243(x91331),f335(f335(f76(x91331),x91334),f335(f97(x91331),x91333))),x91332))+P1(f335(f335(f243(x91331),f335(f335(f292(x91331),x91332),f335(f97(x91331),x91333))),x91334))
% 59.73/59.68 [9171]~P95(x91711)+~P68(x91711)+~P1(f335(f335(f243(x91711),f335(f97(x91711),x91713)),f2(x91711)))+~P1(f335(f335(f242(x91711),x91712),f335(f335(f76(x91711),x91714),f335(f97(x91711),x91713))))+~P1(f335(f335(f242(x91711),f335(f335(f76(x91711),x91714),f335(f97(x91711),x91713))),x91712))+P1(f335(f335(f242(x91711),f335(f335(f292(x91711),x91712),f335(f97(x91711),x91713))),x91714))
% 59.73/59.68 [9172]~P95(x91721)+~P68(x91721)+~P1(f335(f335(f243(x91721),f335(f97(x91721),x91723)),f2(x91721)))+~P1(f335(f335(f243(x91721),x91722),f335(f335(f76(x91721),x91724),f335(f97(x91721),x91723))))+~P1(f335(f335(f243(x91721),f335(f335(f76(x91721),x91724),f335(f97(x91721),x91723))),x91722))+P1(f335(f335(f243(x91721),f335(f335(f292(x91721),x91722),f335(f97(x91721),x91723))),x91724))
% 59.73/59.68 [9223]~P4(x92233)+~P4(x92234)+E(x92231,x92232)+~E(f335(f189(f882(x92233)),x92232),f335(f189(f882(x92234)),f50(x92234)))+~E(f335(f189(f882(x92233)),x92231),f335(f189(f882(x92234)),f50(x92234)))+~E(f335(f68(f885(x92233),x92233,x92234,f239(x92233)),f335(f179(x92234,x92233),f335(f335(f175(x92234,x92233),f50(x92234)),x92231))),f335(f68(f885(x92233),x92233,x92234,f239(x92233)),f335(f179(x92234,x92233),f335(f335(f175(x92234,x92233),f50(x92234)),x92232))))
% 59.73/59.68 [8866]~P95(x88661)+~P68(x88661)+~P1(f335(f335(f243(x88661),x88662),f2(x88661)))+~P1(f335(f335(f242(x88661),f335(f335(f292(x88661),x88664),x88662)),f335(f97(x88661),x88663)))+P1(f335(f335(f243(x88661),f2(x88661)),x88662))+P1(f335(f335(f242(x88661),f335(f335(f76(x88661),f335(f97(x88661),x88663)),x88662)),x88664))
% 59.73/59.68 [8867]~P95(x88671)+~P68(x88671)+~P1(f335(f335(f243(x88671),x88672),f2(x88671)))+~P1(f335(f335(f243(x88671),f335(f335(f292(x88671),x88674),x88672)),f335(f97(x88671),x88673)))+P1(f335(f335(f243(x88671),f2(x88671)),x88672))+P1(f335(f335(f243(x88671),f335(f335(f76(x88671),f335(f97(x88671),x88673)),x88672)),x88674))
% 59.73/59.68 [8982]~P95(x89821)+~P68(x89821)+~P1(f335(f335(f243(x89821),x89822),f2(x89821)))+P1(f335(f335(f243(x89821),f2(x89821)),x89822))+P1(f335(f335(f242(x89821),f335(f335(f292(x89821),x89823),x89822)),f335(f97(x89821),x89824)))+~P1(f335(f335(f242(x89821),f335(f335(f76(x89821),f335(f97(x89821),x89824)),x89822)),x89823))
% 59.73/59.68 [8983]~P95(x89831)+~P68(x89831)+~P1(f335(f335(f243(x89831),x89832),f2(x89831)))+P1(f335(f335(f243(x89831),f2(x89831)),x89832))+P1(f335(f335(f243(x89831),f335(f335(f292(x89831),x89833),x89832)),f335(f97(x89831),x89834)))+~P1(f335(f335(f243(x89831),f335(f335(f76(x89831),f335(f97(x89831),x89834)),x89832)),x89833))
% 59.73/59.68 [9020]~P95(x90201)+~P68(x90201)+P1(f335(f335(f243(x90201),x90202),f2(x90201)))+~P1(f335(f335(f242(x90201),f335(f97(x90201),x90203)),f2(x90201)))+P1(f335(f335(f242(x90201),f335(f97(x90201),x90203)),f335(f335(f292(x90201),x90204),x90202)))+~P1(f335(f335(f242(x90201),f335(f335(f76(x90201),f335(f97(x90201),x90203)),x90202)),x90204))
% 59.73/59.68 [9021]~P95(x90211)+~P68(x90211)+P1(f335(f335(f243(x90211),x90212),f2(x90211)))+~P1(f335(f335(f243(x90211),f335(f97(x90211),x90213)),f2(x90211)))+P1(f335(f335(f243(x90211),f335(f97(x90211),x90213)),f335(f335(f292(x90211),x90214),x90212)))+~P1(f335(f335(f243(x90211),f335(f335(f76(x90211),f335(f97(x90211),x90213)),x90212)),x90214))
% 59.73/59.68 [9037]~P95(x90371)+~P68(x90371)+P1(f335(f335(f243(x90371),f2(x90371)),x90372))+P1(f335(f335(f242(x90371),f335(f335(f292(x90371),x90373),x90372)),f335(f97(x90371),x90374)))+~P1(f335(f335(f242(x90371),f2(x90371)),f335(f97(x90371),x90374)))+~P1(f335(f335(f242(x90371),f335(f335(f76(x90371),f335(f97(x90371),x90374)),x90372)),x90373))
% 59.73/59.68 [9038]~P95(x90381)+~P68(x90381)+P1(f335(f335(f243(x90381),f2(x90381)),x90382))+P1(f335(f335(f243(x90381),f335(f335(f292(x90381),x90383),x90382)),f335(f97(x90381),x90384)))+~P1(f335(f335(f243(x90381),f2(x90381)),f335(f97(x90381),x90384)))+~P1(f335(f335(f243(x90381),f335(f335(f76(x90381),f335(f97(x90381),x90384)),x90382)),x90383))
% 59.73/59.68 [9202]~P95(x92021)+~P68(x92021)+~P1(f335(f335(f243(x92021),x92024),f2(x92021)))+P1(f335(f335(f242(x92021),f335(f97(x92021),x92022)),f335(f335(f292(x92021),x92023),x92024)))+~P1(f335(f335(f242(x92021),x92023),f335(f335(f76(x92021),f335(f97(x92021),x92022)),x92024)))+~P1(f335(f335(f242(x92021),f335(f335(f76(x92021),f335(f97(x92021),x92022)),x92024)),x92023))
% 59.73/59.68 [9203]~P95(x92031)+~P68(x92031)+~P1(f335(f335(f243(x92031),x92034),f2(x92031)))+P1(f335(f335(f243(x92031),f335(f97(x92031),x92032)),f335(f335(f292(x92031),x92033),x92034)))+~P1(f335(f335(f243(x92031),x92033),f335(f335(f76(x92031),f335(f97(x92031),x92032)),x92034)))+~P1(f335(f335(f243(x92031),f335(f335(f76(x92031),f335(f97(x92031),x92032)),x92034)),x92033))
% 59.73/59.68 [9240]~P95(x92401)+~P68(x92401)+~P1(f335(f335(f243(x92401),x92403),f2(x92401)))+P1(f335(f335(f242(x92401),f335(f335(f292(x92401),x92402),x92403)),f335(f97(x92401),x92404)))+~P1(f335(f335(f242(x92401),x92402),f335(f335(f76(x92401),f335(f97(x92401),x92404)),x92403)))+~P1(f335(f335(f242(x92401),f335(f335(f76(x92401),f335(f97(x92401),x92404)),x92403)),x92402))
% 59.73/59.68 [9241]~P95(x92411)+~P68(x92411)+~P1(f335(f335(f243(x92411),x92413),f2(x92411)))+P1(f335(f335(f243(x92411),f335(f335(f292(x92411),x92412),x92413)),f335(f97(x92411),x92414)))+~P1(f335(f335(f243(x92411),x92412),f335(f335(f76(x92411),f335(f97(x92411),x92414)),x92413)))+~P1(f335(f335(f243(x92411),f335(f335(f76(x92411),f335(f97(x92411),x92414)),x92413)),x92412))
% 59.73/59.68 [9255]~P95(x92551)+~P68(x92551)+~P1(f335(f335(f242(x92551),f335(f97(x92551),x92552)),f2(x92551)))+P1(f335(f335(f242(x92551),f335(f97(x92551),x92552)),f335(f335(f292(x92551),x92553),x92554)))+~P1(f335(f335(f242(x92551),x92553),f335(f335(f76(x92551),f335(f97(x92551),x92552)),x92554)))+~P1(f335(f335(f242(x92551),f335(f335(f76(x92551),f335(f97(x92551),x92552)),x92554)),x92553))
% 59.73/59.68 [9256]~P95(x92561)+~P68(x92561)+~P1(f335(f335(f243(x92561),f335(f97(x92561),x92562)),f2(x92561)))+P1(f335(f335(f243(x92561),f335(f97(x92561),x92562)),f335(f335(f292(x92561),x92563),x92564)))+~P1(f335(f335(f243(x92561),x92563),f335(f335(f76(x92561),f335(f97(x92561),x92562)),x92564)))+~P1(f335(f335(f243(x92561),f335(f335(f76(x92561),f335(f97(x92561),x92562)),x92564)),x92563))
% 59.73/59.68 [9260]~P95(x92601)+~P68(x92601)+P1(f335(f335(f242(x92601),f335(f335(f292(x92601),x92602),x92603)),f335(f97(x92601),x92604)))+~P1(f335(f335(f242(x92601),f2(x92601)),f335(f97(x92601),x92604)))+~P1(f335(f335(f242(x92601),x92602),f335(f335(f76(x92601),f335(f97(x92601),x92604)),x92603)))+~P1(f335(f335(f242(x92601),f335(f335(f76(x92601),f335(f97(x92601),x92604)),x92603)),x92602))
% 59.73/59.68 [9261]~P95(x92611)+~P68(x92611)+P1(f335(f335(f243(x92611),f335(f335(f292(x92611),x92612),x92613)),f335(f97(x92611),x92614)))+~P1(f335(f335(f243(x92611),f2(x92611)),f335(f97(x92611),x92614)))+~P1(f335(f335(f243(x92611),x92612),f335(f335(f76(x92611),f335(f97(x92611),x92614)),x92613)))+~P1(f335(f335(f243(x92611),f335(f335(f76(x92611),f335(f97(x92611),x92614)),x92613)),x92612))
% 59.73/59.68 [6083]~P114(x60832)+~P131(x60832)+~E(f335(x60833,x60835),f2(x60832))+E(f335(f335(f9(x60831,x60832),x60833),x60834),f2(x60832))+~P1(f335(f56(x60831),x60834))+~P1(f335(f335(f337(x60831),x60835),x60834))
% 59.73/59.68 [8440]~P107(x84401)+P1(f335(f335(f243(f888(x84401,a879)),f305(x84401,x84402,x84403)),f305(x84401,x84404,x84405)))+~P1(f335(f335(f242(x84401),x84404),x84402))+~P1(f335(f335(f242(x84401),x84404),x84405))+~P1(f335(f335(f242(x84401),x84403),x84405))+~P1(f335(f335(f243(x84401),x84403),x84405))
% 59.73/59.68 [8441]~P107(x84411)+P1(f335(f335(f243(f888(x84411,a879)),f305(x84411,x84412,x84413)),f305(x84411,x84414,x84415)))+~P1(f335(f335(f242(x84411),x84413),x84415))+~P1(f335(f335(f242(x84411),x84414),x84415))+~P1(f335(f335(f242(x84411),x84414),x84412))+~P1(f335(f335(f243(x84411),x84414),x84412))
% 59.73/59.68 [9287]P56(x92872,x92873,x92874,x92871)+E(x92871,f188(f888(x92872,a879)))+~P1(f335(f56(x92872),x92874))+~P1(f335(f56(x92872),x92871))+~P1(f335(f335(x92873,f513(x92871,x92874,x92873,x92872)),x92875))+~P1(f335(f335(f337(x92872),x92875),x92871))
% 59.73/59.68 [9433]~E(x94333,x94335)+~P73(x94331)+~P77(x94331)+~P38(x94333)+E(f335(f335(f9(a1,x94331),x94332),x94333),f335(f335(f9(a1,x94331),x94334),x94335))+P1(f335(f335(f242(a1),f2(a1)),f510(x94332,x94334,x94333,x94335,x94331)))
% 59.73/59.68 [9434]~E(x94343,x94345)+~P73(x94341)+~P77(x94341)+~P38(x94343)+E(f335(f335(f6(a1,x94341),x94342),x94343),f335(f335(f6(a1,x94341),x94344),x94345))+P1(f335(f335(f242(a1),f2(a1)),f512(x94342,x94344,x94343,x94345,x94341)))
% 59.73/59.68 [9604]~E(x96045,x96043)+~P73(x96041)+~P77(x96041)+~P38(x96045)+~E(f335(x96042,f510(x96044,x96042,x96045,x96043,x96041)),f335(x96044,f510(x96044,x96042,x96045,x96043,x96041)))+E(f335(f335(f9(a1,x96041),x96042),x96043),f335(f335(f9(a1,x96041),x96044),x96045))
% 59.73/59.68 [9605]~E(x96055,x96053)+~P73(x96051)+~P77(x96051)+~P38(x96055)+~E(f335(x96052,f512(x96054,x96052,x96055,x96053,x96051)),f335(x96054,f512(x96054,x96052,x96055,x96053,x96051)))+E(f335(f335(f6(a1,x96051),x96052),x96053),f335(f335(f6(a1,x96051),x96054),x96055))
% 59.73/59.68 [9696]~P80(x96963)+E(f335(x96961,x96962),f2(x96963))+~E(f335(f335(f6(x96964,x96963),x96961),x96965),f2(x96963))+~P1(f335(f56(x96964),x96965))+P1(f335(f335(f337(x96964),f498(x96962,x96961,x96965,x96964,x96963)),x96965))+~P1(f335(f335(f337(x96964),x96962),x96965))
% 59.73/59.68 [9839]~P80(x98393)+E(f335(x98391,x98392),f2(x98393))+~E(f335(f335(f6(x98394,x98393),x98391),x98395),f2(x98393))+~P1(f335(f56(x98394),x98395))+~P1(f335(f335(f337(x98394),x98392),x98395))+~P1(f335(f335(f242(x98393),f2(x98393)),f335(x98391,f498(x98392,x98391,x98395,x98394,x98393))))
% 59.73/59.68 [8356]~P134(x83561)+~P1(f335(f335(f242(x83561),x83563),x83565))+~P1(f335(f335(f242(x83561),x83562),x83564))+~P1(f335(f335(f242(x83561),f2(x83561)),x83563))+~P1(f335(f335(f242(x83561),f2(x83561)),x83564))+P1(f335(f335(f242(x83561),f335(f335(f76(x83561),x83562),x83563)),f335(f335(f76(x83561),x83564),x83565)))
% 59.73/59.68 [8357]~P134(x83571)+~P1(f335(f335(f242(x83571),x83573),x83575))+~P1(f335(f335(f242(x83571),x83572),x83574))+~P1(f335(f335(f242(x83571),f2(x83571)),x83573))+~P1(f335(f335(f242(x83571),f2(x83571)),x83572))+P1(f335(f335(f242(x83571),f335(f335(f76(x83571),x83572),x83573)),f335(f335(f76(x83571),x83574),x83575)))
% 59.73/59.68 [8358]~P69(x83581)+~P1(f335(f335(f243(x83581),f2(x83581)),x83585))+~P1(f335(f335(f242(x83581),x83585),x83583))+~P1(f335(f335(f242(x83581),x83582),x83584))+~P1(f335(f335(f242(x83581),f2(x83581)),x83582))+P1(f335(f335(f242(x83581),f335(f335(f292(x83581),x83582),x83583)),f335(f335(f292(x83581),x83584),x83585)))
% 59.73/59.68 [8359]~P127(x83591)+~P1(f335(f335(f242(x83591),x83593),x83595))+~P1(f335(f335(f242(x83591),f2(x83591)),x83592))+~P1(f335(f335(f243(x83591),x83592),x83594))+~P1(f335(f335(f243(x83591),f2(x83591)),x83593))+P1(f335(f335(f243(x83591),f335(f335(f76(x83591),x83592),x83593)),f335(f335(f76(x83591),x83594),x83595)))
% 59.73/59.68 [8360]~P127(x83601)+~P1(f335(f335(f242(x83601),x83602),x83604))+~P1(f335(f335(f242(x83601),f2(x83601)),x83603))+~P1(f335(f335(f243(x83601),x83603),x83605))+~P1(f335(f335(f243(x83601),f2(x83601)),x83602))+P1(f335(f335(f243(x83601),f335(f335(f76(x83601),x83602),x83603)),f335(f335(f76(x83601),x83604),x83605)))
% 59.73/59.68 [8361]~P127(x83611)+~P1(f335(f335(f242(x83611),f2(x83611)),x83613))+~P1(f335(f335(f242(x83611),f2(x83611)),x83612))+~P1(f335(f335(f243(x83611),x83613),x83615))+~P1(f335(f335(f243(x83611),x83612),x83614))+P1(f335(f335(f243(x83611),f335(f335(f76(x83611),x83612),x83613)),f335(f335(f76(x83611),x83614),x83615)))
% 59.73/59.68 [8362]~P127(x83621)+~P1(f335(f335(f242(x83621),f2(x83621)),x83623))+~P1(f335(f335(f243(x83621),x83623),x83625))+~P1(f335(f335(f243(x83621),x83622),x83624))+~P1(f335(f335(f243(x83621),f2(x83621)),x83624))+P1(f335(f335(f243(x83621),f335(f335(f76(x83621),x83622),x83623)),f335(f335(f76(x83621),x83624),x83625)))
% 59.73/59.68 [8363]~P69(x83631)+~P1(f335(f335(f242(x83631),x83635),x83633))+~P1(f335(f335(f242(x83631),f2(x83631)),x83632))+~P1(f335(f335(f243(x83631),x83632),x83634))+~P1(f335(f335(f243(x83631),f2(x83631)),x83635))+P1(f335(f335(f243(x83631),f335(f335(f292(x83631),x83632),x83633)),f335(f335(f292(x83631),x83634),x83635)))
% 59.73/59.68 [8364]~P69(x83641)+~P1(f335(f335(f242(x83641),x83642),x83644))+~P1(f335(f335(f243(x83641),x83645),x83643))+~P1(f335(f335(f243(x83641),f2(x83641)),x83645))+~P1(f335(f335(f243(x83641),f2(x83641)),x83642))+P1(f335(f335(f243(x83641),f335(f335(f292(x83641),x83642),x83643)),f335(f335(f292(x83641),x83644),x83645)))
% 59.73/59.68 [9739]~P89(x97395)+~P77(x97395)+E(x97391,f188(f888(x97392,a879)))+~P1(f335(f56(x97392),x97391))+P1(f335(f335(f337(x97392),f505(x97393,x97394,x97391,x97392,x97395)),x97391))+P1(f335(f335(f243(x97395),f335(f335(f6(x97392,x97395),x97394),x97391)),f335(f335(f6(x97392,x97395),x97393),x97391)))
% 59.73/59.68 [9862]~P87(x98621)+~P77(x98621)+~P1(f335(f56(x98622),x98625))+~P1(f335(f335(f242(x98621),f2(x98621)),f335(x98623,f499(x98623,x98624,x98625,x98622,x98621))))+P1(f335(f335(f242(x98621),f335(f335(f6(x98622,x98621),x98623),x98624)),f335(f335(f6(x98622,x98621),x98623),x98625)))+~P1(f335(f335(f242(f888(x98622,a879)),x98624),x98625))
% 59.73/59.68 [10027]~P89(x100273)+~P77(x100273)+E(x100271,f188(f888(x100272,a879)))+~P1(f335(f56(x100272),x100271))+~P1(f335(f335(f243(x100273),f335(x100274,f505(x100275,x100274,x100271,x100272,x100273))),f335(x100275,f505(x100275,x100274,x100271,x100272,x100273))))+P1(f335(f335(f243(x100273),f335(f335(f6(x100272,x100273),x100274),x100271)),f335(f335(f6(x100272,x100273),x100275),x100271)))
% 59.73/59.68 [7078]~P19(x70782,x70785,x70784)+E(x70781,f188(f888(x70782,a879)))+E(x70783,f188(f888(x70782,a879)))+~P1(f335(f56(x70782),x70781))+~P1(f335(f56(x70782),x70783))+E(f335(x70784,f335(f335(f104(f888(x70782,a879)),x70783),x70781)),f335(f335(x70785,f335(x70784,x70783)),f335(x70784,x70781)))
% 59.73/59.68 [7666]~P146(x76661,x76664,x76663)+P1(f335(x76661,x76662))+~P1(f335(f335(f243(a1),x76664),f2(a1)))+~P1(f335(f335(f242(a1),x76665),f2(a1)))+~E(x76663,f335(f335(f75(a1),f335(f335(f76(a1),x76664),x76662)),x76665))+~P1(f335(f335(f243(a1),x76664),x76665))
% 59.73/59.68 [7667]~P145(x76671,x76674,x76673)+P1(f335(x76671,x76672))+~P1(f335(f335(f243(a1),x76674),f2(a1)))+~P1(f335(f335(f242(a1),x76672),f2(a1)))+~E(x76673,f335(f335(f75(a1),f335(f335(f76(a1),x76674),x76675)),x76672))+~P1(f335(f335(f243(a1),x76674),x76672))
% 59.73/59.68 [7710]~P146(x77101,x77104,x77103)+P1(f335(x77101,x77102))+~E(x77103,f335(f335(f75(a1),f335(f335(f76(a1),x77104),x77102)),x77105))+~P1(f335(f335(f242(a1),f2(a1)),x77105))+~P1(f335(f335(f243(a1),f2(a1)),x77104))+~P1(f335(f335(f243(a1),x77105),x77104))
% 59.73/59.68 [7711]~P145(x77111,x77114,x77113)+P1(f335(x77111,x77112))+~E(x77113,f335(f335(f75(a1),f335(f335(f76(a1),x77114),x77115)),x77112))+~P1(f335(f335(f242(a1),f2(a1)),x77112))+~P1(f335(f335(f243(a1),f2(a1)),x77114))+~P1(f335(f335(f243(a1),x77112),x77114))
% 59.73/59.68 [8647]P1(f335(f335(x86471,x86472),x86473))+~P1(f335(f335(x86471,f335(f335(f30(a1),x86474),x86475)),f39(a1,x86474,x86475)))+~P1(f335(f335(f243(a1),x86475),f2(a1)))+~P1(f335(f335(f242(a1),x86473),f2(a1)))+~E(x86474,f335(f335(f75(a1),f335(f335(f76(a1),x86475),x86472)),x86473))+~P1(f335(f335(f243(a1),x86475),x86473))
% 59.73/59.68 [8655]P1(f335(f335(x86551,x86552),x86553))+~P1(f335(f335(x86551,f335(f335(f30(a1),x86554),x86555)),f39(a1,x86554,x86555)))+~E(x86554,f335(f335(f75(a1),f335(f335(f76(a1),x86555),x86552)),x86553))+~P1(f335(f335(f242(a1),f2(a1)),x86553))+~P1(f335(f335(f243(a1),f2(a1)),x86555))+~P1(f335(f335(f243(a1),x86553),x86555))
% 59.73/59.68 [8899]E(x88991,x88992)+~P53(x88993,x88995,x88994)+~P1(f335(f335(f337(x88993),x88992),x88995))+~P1(f335(f335(f337(x88993),x88991),x88995))+P1(f335(f335(f337(f887(x88993,x88993)),f335(f335(f264(x88993,x88993),x88991),x88992)),x88994))+P1(f335(f335(f337(f887(x88993,x88993)),f335(f335(f264(x88993,x88993),x88992),x88991)),x88994))
% 59.73/59.68 [9715]~P107(x97151)+~P107(x97152)+~P37(x97152,x97151,x97153)+~P1(f335(f335(f242(x97152),x97155),f432(x97154,x97153,x97152,x97151,x97155)))+E(f246(x97151,f335(f335(f7(x97151,f888(x97151,a879),a879),f337(x97151)),f335(f313(x97152,x97151,x97153),x97154))),f335(x97153,f246(x97152,f335(f335(f7(x97152,f888(x97152,a879),a879),f337(x97152)),x97154))))+~P1(f335(f335(f337(x97152),x97155),x97154))
% 59.73/59.68 [9768]~P87(x97685)+~P77(x97685)+~P1(f335(f56(x97681),x97684))+P1(f335(f335(f242(x97685),f335(f335(f6(x97681,x97685),x97682),x97683)),f335(f335(f6(x97681,x97685),x97682),x97684)))+~P1(f335(f335(f242(f888(x97681,a879)),x97683),x97684))+P1(f335(f335(f337(x97681),f499(x97682,x97683,x97684,x97681,x97685)),f335(f335(f23(f888(x97681,a879)),x97684),x97683)))
% 59.73/59.68 [9784]~P107(x97841)+~P107(x97842)+~P37(x97842,x97841,x97843)+E(f246(x97841,f335(f335(f7(x97841,f888(x97841,a879),a879),f337(x97841)),f335(f313(x97842,x97841,x97843),x97844))),f335(x97843,f246(x97842,f335(f335(f7(x97842,f888(x97842,a879),a879),f337(x97842)),x97844))))+~P1(f335(f335(f337(x97842),x97845),x97844))+P1(f335(f335(f337(x97842),f432(x97844,x97843,x97842,x97841,x97845)),x97844))
% 59.73/59.68 [9870]E(x98701,f188(f888(x98702,a879)))+~P1(f335(f56(x98702),x98703))+~P1(f335(f56(x98702),x98701))+P1(f335(f335(f337(f887(f888(x98702,a879),f888(x98702,a879))),f335(f335(f264(f888(x98702,a879),f888(x98702,a879)),x98703),x98701)),f327(x98702,x98704)))+~P1(f335(f335(f337(x98702),x98705),x98701))+~P1(f335(f335(f337(f887(x98702,x98702)),f335(f335(f264(x98702,x98702),f522(x98704,x98701,x98703,x98702)),x98705)),x98704))
% 59.73/59.68 [9871]E(x98711,f188(f888(x98712,a879)))+~P1(f335(f56(x98712),x98713))+~P1(f335(f56(x98712),x98711))+P1(f335(f335(f337(f887(f888(x98712,a879),f888(x98712,a879))),f335(f335(f264(f888(x98712,a879),f888(x98712,a879)),x98713),x98711)),f327(x98712,x98714)))+~P1(f335(f335(f337(x98712),x98715),x98711))+~P1(f335(f335(f337(f887(x98712,x98712)),f335(f335(f264(x98712,x98712),f583(x98714,x98711,x98713,x98712)),x98715)),x98714))
% 59.73/59.68 [10031]~P80(x100311)+~E(f335(f335(f6(x100315,x100311),x100312),x100316),x100314)+~P1(f335(f56(x100315),x100316))+P1(f335(f335(f337(x100315),f503(x100313,x100314,x100312,x100316,x100315,x100311)),x100316))+P1(f335(f335(f242(x100311),f335(x100312,x100313)),x100314))+~P1(f335(f335(f337(x100315),x100313),x100316))
% 59.73/59.68 [10077]~P80(x100771)+~E(f335(f335(f6(x100775,x100771),x100772),x100776),x100774)+~P1(f335(f56(x100775),x100776))+~P1(f335(f335(f337(x100775),x100773),x100776))+~P1(f335(f335(f242(x100771),f2(x100771)),f335(x100772,f503(x100773,x100774,x100772,x100776,x100775,x100771))))+P1(f335(f335(f242(x100771),f335(x100772,x100773)),x100774))
% 59.73/59.68 [10191]~E(x101915,x101918)+~E(x101914,x101917)+~P108(x101911)+~P77(x101912)+E(f335(f335(f6(x101911,x101912),x101913),f335(f304(x101911,x101914),x101915)),f335(f335(f6(x101911,x101912),x101916),f335(f304(x101911,x101917),x101918)))+P1(f335(f335(f242(x101911),x101914),f591(x101913,x101916,x101915,x101918,x101914,x101917,x101911,x101912)))
% 59.73/59.68 [10208]~E(x102087,x102084)+~E(x102088,x102085)+~P108(x102081)+~P77(x102082)+~E(f335(x102083,f591(x102086,x102083,x102088,x102085,x102087,x102084,x102081,x102082)),f335(x102086,f591(x102086,x102083,x102088,x102085,x102087,x102084,x102081,x102082)))+E(f335(f335(f6(x102081,x102082),x102083),f335(f304(x102081,x102084),x102085)),f335(f335(f6(x102081,x102082),x102086),f335(f304(x102081,x102087),x102088)))
% 59.73/59.68 [10212]~E(x102124,x102127)+~E(x102125,x102128)+~P108(x102121)+~P77(x102122)+E(f335(f335(f6(x102121,x102122),x102123),f335(f304(x102121,x102124),x102125)),f335(f335(f6(x102121,x102122),x102126),f335(f304(x102121,x102127),x102128)))+P1(f335(f335(f243(x102121),f591(x102123,x102126,x102125,x102128,x102124,x102127,x102121,x102122)),x102125))
% 59.73/59.68 [9876]~P8(x98765,x98769,x98766)+~P8(x98761,x987610,x98763)+~P14(x98761,x98765,f888(x98762,a879),x98763,x98766,x98768)+~P1(f335(f335(f337(x98765),x98767),x98769))+~P1(f335(f335(f337(x98761),x98764),x987610))+E(f335(f335(f33(x98761,f888(x98762,a879)),f335(f288(x98761,x98761,x98763),f335(f335(f312(x98761),x98764),f188(f888(x98761,a879))))),f335(f335(f8(f888(x98765,f888(x98762,a879)),f888(x98762,a879),x98761),f335(f33(x98765,f888(x98762,a879)),f335(f288(x98765,x98765,x98766),f335(f335(f312(x98765),x98767),f188(f888(x98765,a879)))))),x98768)),f335(f335(x98768,x98764),x98767))
% 59.73/59.68 [5616]~P106(x56163)+~P15(x56163,x56162)+~P15(x56163,x56161)+E(x56161,x56162)+~E(f335(f166(x56163),x56161),f335(f166(x56163),x56162))+~P1(f335(f130(x56163),x56162))+~P1(f335(f130(x56163),x56161))
% 59.73/59.68 [4959]~P126(x49592)+~P131(x49592)+~P141(x49592)+~P113(x49592)+~E(x49593,f2(x49592))+E(x49591,f2(a881))+E(f335(f335(f254(x49592),x49593),x49591),f2(x49592))
% 59.73/59.68 [9165]E(x91651,f2(a881))+~E(x91652,f335(f335(f75(a881),f335(f335(f76(a881),f335(f263(a881,a881),x91653)),x91651)),f335(f267(a881,a881),x91653)))+P1(f335(f42(x91652,x91651),x91653))+~P1(f335(f335(f242(a881),f335(f267(a881,a881),x91653)),f2(a881)))+~P1(f335(f335(f242(a881),f2(a881)),f335(f267(a881,a881),x91653)))+~P1(f335(f335(f243(a881),x91651),f335(f267(a881,a881),x91653)))+~P1(f335(f335(f243(a881),f335(f267(a881,a881),x91653)),x91651))
% 59.73/59.68 [9174]~E(f335(f263(a881,a881),x91743),f2(a881))+~E(x91741,f335(f335(f75(a881),f335(f335(f76(a881),f335(f263(a881,a881),x91743)),x91742)),f335(f267(a881,a881),x91743)))+P1(f335(f42(x91741,x91742),x91743))+~P1(f335(f335(f242(a881),f335(f267(a881,a881),x91743)),f2(a881)))+~P1(f335(f335(f242(a881),f2(a881)),f335(f267(a881,a881),x91743)))+~P1(f335(f335(f243(a881),x91742),f335(f267(a881,a881),x91743)))+~P1(f335(f335(f243(a881),f335(f267(a881,a881),x91743)),x91742))
% 59.73/59.68 [7545]~P61(x75452)+E(x75451,f188(f888(x75452,a879)))+E(x75453,f188(f888(x75452,a879)))+~P1(f335(f56(x75452),x75451))+~P1(f335(f56(x75452),x75453))+~E(f335(f335(f95(f888(x75452,a879)),x75453),x75451),f188(f888(x75452,a879)))+E(f10(x75452,f335(f335(f104(f888(x75452,a879)),x75453),x75451)),f335(f335(f95(x75452),f10(x75452,x75453)),f10(x75452,x75451)))
% 59.73/59.68 [7546]~P61(x75462)+E(x75461,f188(f888(x75462,a879)))+E(x75463,f188(f888(x75462,a879)))+~P1(f335(f56(x75462),x75461))+~P1(f335(f56(x75462),x75463))+~E(f335(f335(f95(f888(x75462,a879)),x75463),x75461),f188(f888(x75462,a879)))+E(f13(x75462,f335(f335(f104(f888(x75462,a879)),x75463),x75461)),f335(f335(f104(x75462),f13(x75462,x75463)),f13(x75462,x75461)))
% 59.73/59.68 [7547]~P106(x75472)+E(x75471,f188(f888(x75472,a879)))+E(x75473,f188(f888(x75472,a879)))+~P1(f335(f56(x75472),x75471))+~P1(f335(f56(x75472),x75473))+~E(f335(f335(f95(f888(x75472,a879)),x75473),x75471),f188(f888(x75472,a879)))+E(f14(x75472,f335(f335(f104(f888(x75472,a879)),x75473),x75471)),f335(f335(f241(x75472),f14(x75472,x75473)),f14(x75472,x75471)))
% 59.73/59.68 [7548]~P106(x75482)+E(x75481,f188(f888(x75482,a879)))+E(x75483,f188(f888(x75482,a879)))+~P1(f335(f56(x75482),x75481))+~P1(f335(f56(x75482),x75483))+~E(f335(f335(f95(f888(x75482,a879)),x75483),x75481),f188(f888(x75482,a879)))+E(f15(x75482,f335(f335(f104(f888(x75482,a879)),x75483),x75481)),f335(f335(f240(x75482),f15(x75482,x75483)),f15(x75482,x75481)))
% 59.73/59.68 [8028]~P70(x80282)+E(x80281,f188(f888(x80282,a879)))+E(x80283,f188(f888(x80282,a879)))+~P1(f335(f56(x80282),x80281))+~P1(f335(f56(x80282),x80283))+~E(f335(f335(f95(f888(x80282,a879)),x80283),x80281),f188(f888(x80282,a879)))+E(f335(f335(f76(x80282),f335(f58(x80282,f76(x80282)),x80283)),f335(f58(x80282,f76(x80282)),x80281)),f335(f58(x80282,f76(x80282)),f335(f335(f104(f888(x80282,a879)),x80283),x80281)))
% 59.73/59.68 [8100]~P106(x81002)+E(x81001,f188(f888(x81002,a879)))+E(x81003,f188(f888(x81002,a879)))+~P1(f335(f56(x81002),x81001))+~P1(f335(f56(x81002),x81003))+~E(f335(f335(f95(f888(x81002,a879)),x81003),x81001),f188(f888(x81002,a879)))+E(f335(f335(f240(x81002),f11(x81002,f240(x81002),x81003)),f11(x81002,f240(x81002),x81001)),f11(x81002,f240(x81002),f335(f335(f104(f888(x81002,a879)),x81003),x81001)))
% 59.73/59.68 [8101]~P106(x81012)+E(x81011,f188(f888(x81012,a879)))+E(x81013,f188(f888(x81012,a879)))+~P1(f335(f56(x81012),x81011))+~P1(f335(f56(x81012),x81013))+~E(f335(f335(f95(f888(x81012,a879)),x81013),x81011),f188(f888(x81012,a879)))+E(f335(f335(f241(x81012),f12(x81012,f241(x81012),x81013)),f12(x81012,f241(x81012),x81011)),f12(x81012,f241(x81012),f335(f335(f104(f888(x81012,a879)),x81013),x81011)))
% 59.73/59.68 [7806]E(x78061,f2(a1))+E(f335(f335(f30(a1),x78062),x78061),x78063)+~P1(f335(f335(f242(a1),x78064),f2(a1)))+~E(x78062,f335(f335(f75(a1),f335(f335(f76(a1),x78061),x78063)),x78064))+~P1(f335(f335(f242(a1),f2(a1)),x78064))+~P1(f335(f335(f243(a1),x78064),x78061))+~P1(f335(f335(f243(a1),x78061),x78064))
% 59.73/59.68 [7815]E(f39(a1,x78152,x78151),x78153)+E(x78151,f2(a1))+~P1(f335(f335(f242(a1),x78153),f2(a1)))+~E(x78152,f335(f335(f75(a1),f335(f335(f76(a1),x78151),x78154)),x78153))+~P1(f335(f335(f242(a1),f2(a1)),x78153))+~P1(f335(f335(f243(a1),x78153),x78151))+~P1(f335(f335(f243(a1),x78151),x78153))
% 59.73/59.68 [7719]~P20(x77192,x77195,x77194)+E(x77191,f188(f888(x77192,a879)))+E(x77193,f188(f888(x77192,a879)))+~P1(f335(f56(x77192),x77191))+~P1(f335(f56(x77192),x77193))+~E(f335(f335(f95(f888(x77192,a879)),x77193),x77191),f188(f888(x77192,a879)))+E(f335(x77194,f335(f335(f104(f888(x77192,a879)),x77193),x77191)),f335(f335(x77195,f335(x77194,x77193)),f335(x77194,x77191)))
% 59.73/59.68 [9406]~P26(x94063,x94061,x94065,x94064)+~P26(x94061,x94063,x94066,x94062)+E(f335(f29(x94061),x94062),f335(f29(x94063),x94064))+~P1(f335(f56(x94063),x94064))+~P1(f335(f56(x94061),x94062))+~P1(f335(f335(f242(f888(x94063,a879)),f335(f313(x94061,x94063,x94066),x94062)),x94064))+~P1(f335(f335(f242(f888(x94061,a879)),f335(f313(x94063,x94061,x94065),x94064)),x94062))
% 59.73/59.68 [9349]~P1(f335(f335(f243(a1),f335(f335(f75(a1),f335(f335(f76(a1),x93495),x93491)),x93496)),f2(a1)))+~E(f335(f335(f75(a1),f335(f335(f76(a1),x93493),x93492)),x93494),f335(f335(f75(a1),f335(f335(f76(a1),x93495),x93491)),x93496))+~P1(f335(f335(f242(a1),f2(a1)),x93496))+~P1(f335(f335(f243(a1),f2(a1)),x93495))+~P1(f335(f335(f242(a1),x93495),x93493))+~P1(f335(f335(f243(a1),x93494),x93493))+P1(f335(f335(f242(a1),x93491),x93492))
% 59.73/59.68 [9113]~E(f335(f335(f75(a1),f335(f335(f76(a1),x91133),x91131)),x91134),f335(f335(f75(a1),f335(f335(f76(a1),x91135),x91132)),x91136))+~P1(f335(f335(f242(a1),f2(a1)),x91134))+~P1(f335(f335(f243(a1),f2(a1)),x91135))+~P1(f335(f335(f242(a1),x91135),x91133))+~P1(f335(f335(f243(a1),x91136),x91135))+P1(f335(f335(f242(a1),x91131),x91132))+~P1(f335(f335(f242(a1),f2(a1)),f335(f335(f75(a1),f335(f335(f76(a1),x91135),x91132)),x91136)))
% 59.73/59.68 [9294]~P129(x92941)+~E(f335(f335(f75(x92941),x92942),x92944),f73(x92941))+~P1(f335(f335(f242(x92941),x92945),x92946))+~P1(f335(f335(f242(x92941),x92943),x92946))+~P1(f335(f335(f242(x92941),f2(x92941)),x92944))+~P1(f335(f335(f242(x92941),f2(x92941)),x92942))+P1(f335(f335(f242(x92941),f335(f335(f75(x92941),f335(f335(f76(x92941),x92942),x92943)),f335(f335(f76(x92941),x92944),x92945))),x92946))
% 59.73/59.68 [9295]~P130(x92951)+~E(f335(f335(f75(x92951),x92952),x92954),f73(x92951))+~P1(f335(f335(f242(x92951),f2(x92951)),x92954))+~P1(f335(f335(f242(x92951),f2(x92951)),x92952))+~P1(f335(f335(f243(x92951),x92955),x92956))+~P1(f335(f335(f243(x92951),x92953),x92956))+P1(f335(f335(f243(x92951),f335(f335(f75(x92951),f335(f335(f76(x92951),x92952),x92953)),f335(f335(f76(x92951),x92954),x92955))),x92956))
% 59.73/59.68 [10120]~P8(x101207,x101206,x101205)+E(x101201,x101202)+~P13(x101207,f888(x101204,a879),x101205,x101203)+E(f335(x101203,f840(x101201,x101202,x101203,x101204,x101205,x101206,x101207)),f335(x101203,f841(x101201,x101202,x101203,x101204,x101205,x101206,x101207)))+~E(f335(f335(f33(x101207,f888(x101204,a879)),x101201),x101203),f335(f335(f33(x101207,f888(x101204,a879)),x101202),x101203))+~P1(f335(f335(f337(f888(x101207,a879)),x101202),f335(f335(f55(x101207),x101206),x101205)))+~P1(f335(f335(f337(f888(x101207,a879)),x101201),f335(f335(f55(x101207),x101206),x101205)))
% 59.73/59.68 [10154]~P8(x101543,x101547,x101546)+E(x101541,x101542)+~P13(x101543,f888(x101545,a879),x101546,x101544)+~E(f335(f335(f33(x101543,f888(x101545,a879)),x101541),x101544),f335(f335(f33(x101543,f888(x101545,a879)),x101542),x101544))+P1(f335(f335(f337(x101543),f841(x101541,x101542,x101544,x101545,x101546,x101547,x101543)),x101547))+~P1(f335(f335(f337(f888(x101543,a879)),x101542),f335(f335(f55(x101543),x101547),x101546)))+~P1(f335(f335(f337(f888(x101543,a879)),x101541),f335(f335(f55(x101543),x101547),x101546)))
% 59.73/59.68 [10155]~P8(x101553,x101557,x101556)+E(x101551,x101552)+~P13(x101553,f888(x101555,a879),x101556,x101554)+~E(f335(f335(f33(x101553,f888(x101555,a879)),x101551),x101554),f335(f335(f33(x101553,f888(x101555,a879)),x101552),x101554))+P1(f335(f335(f337(x101553),f840(x101551,x101552,x101554,x101555,x101556,x101557,x101553)),x101557))+~P1(f335(f335(f337(f888(x101553,a879)),x101552),f335(f335(f55(x101553),x101557),x101556)))+~P1(f335(f335(f337(f888(x101553,a879)),x101551),f335(f335(f55(x101553),x101557),x101556)))
% 59.73/59.68 [10226]E(x102261,x102262)+~P8(x102263,x102266,x102267)+~P13(x102263,f888(x102264,a879),x102267,x102265)+~E(f335(f335(f33(x102263,f888(x102264,a879)),x102261),x102265),f335(f335(f33(x102263,f888(x102264,a879)),x102262),x102265))+~P1(f335(f335(f337(f887(x102263,x102263)),f335(f335(f264(x102263,x102263),f841(x102261,x102262,x102265,x102264,x102267,x102266,x102263)),f840(x102261,x102262,x102265,x102264,x102267,x102266,x102263))),x102267))+~P1(f335(f335(f337(f888(x102263,a879)),x102262),f335(f335(f55(x102263),x102266),x102267)))+~P1(f335(f335(f337(f888(x102263,a879)),x102261),f335(f335(f55(x102263),x102266),x102267)))
% 59.73/59.68 [9112]~P8(x91121,x91127,x91124)+~E(x91125,x91126)+~P1(f335(f335(f337(x91121),x91123),x91126))+~P1(f335(f335(f337(x91121),x91122),x91125))+~P1(f335(f335(f337(f888(x91121,a879)),x91126),f335(f335(f55(x91121),x91127),x91124)))+~P1(f335(f335(f337(f888(x91121,a879)),x91125),f335(f335(f55(x91121),x91127),x91124)))+P1(f335(f335(f337(f887(x91121,x91121)),f335(f335(f264(x91121,x91121),x91122),x91123)),x91124))
% 59.73/59.68 [9250]E(x92501,x92502)+~P8(x92503,x92504,x92505)+~P1(f335(f335(f337(x92503),x92506),x92502))+~P1(f335(f335(f337(x92503),x92507),x92501))+~P1(f335(f335(f337(f888(x92503,a879)),x92502),f335(f335(f55(x92503),x92504),x92505)))+~P1(f335(f335(f337(f888(x92503,a879)),x92501),f335(f335(f55(x92503),x92504),x92505)))+~P1(f335(f335(f337(f887(x92503,x92503)),f335(f335(f264(x92503,x92503),x92507),x92506)),x92505))
% 59.73/59.68 [9251]E(x92511,x92512)+~P8(x92513,x92514,x92515)+~P1(f335(f335(f337(x92513),x92516),x92512))+~P1(f335(f335(f337(x92513),x92517),x92511))+~P1(f335(f335(f337(f888(x92513,a879)),x92512),f335(f335(f55(x92513),x92514),x92515)))+~P1(f335(f335(f337(f888(x92513,a879)),x92511),f335(f335(f55(x92513),x92514),x92515)))+~P1(f335(f335(f337(f887(x92513,x92513)),f335(f335(f264(x92513,x92513),x92517),x92516)),x92515))
% 59.73/59.68 [10246]~P8(x102469,x102468,x102467)+~P8(x102461,x1024611,x1024610)+~P14(x102461,x102469,f888(x102466,a879),x1024610,x102467,x102465)+P1(f335(f335(f337(x102461),f831(x102462,x102463,x102464,x102465,x102466,x102467,x102468,x102469,x1024610,x1024611,x102461)),x1024611))+~P1(f335(f335(f337(f888(x102469,a879)),x102463),f335(f335(f55(x102469),x102468),x102467)))+~P1(f335(f335(f337(f888(x102461,a879)),x102464),f335(f335(f55(x102461),x1024611),x1024610)))+P1(f335(f335(f337(f888(x102466,a879)),f335(f335(f33(x102461,f888(x102466,a879)),x102464),f335(f335(f8(f888(x102469,f888(x102466,a879)),f888(x102466,a879),x102461),f335(f33(x102469,f888(x102466,a879)),x102463)),x102465))),x102462))
% 59.73/59.68 [10247]~P8(x1024711,x1024710,x102479)+~P8(x102471,x102478,x102477)+~P14(x1024711,x102471,f888(x102476,a879),x102479,x102477,x102475)+P1(f335(f335(f337(x102471),f832(x102472,x102473,x102474,x102475,x102476,x102477,x102478,x102471,x102479,x1024710,x1024711)),x102478))+~P1(f335(f335(f337(f888(x1024711,a879)),x102474),f335(f335(f55(x1024711),x1024710),x102479)))+~P1(f335(f335(f337(f888(x102471,a879)),x102473),f335(f335(f55(x102471),x102478),x102477)))+P1(f335(f335(f337(f888(x102476,a879)),f335(f335(f33(x1024711,f888(x102476,a879)),x102474),f335(f335(f8(f888(x102471,f888(x102476,a879)),f888(x102476,a879),x1024711),f335(f33(x102471,f888(x102476,a879)),x102473)),x102475))),x102472))
% 59.73/59.68 [10248]~P8(x102482,x102488,x102489)+~P8(x102484,x1024810,x1024811)+~P14(x102482,x102484,f888(x102481,a879),x102489,x1024811,x102486)+~P1(f335(f335(f337(f888(x102482,a879)),x102483),f335(f335(f55(x102482),x102488),x102489)))+~P1(f335(f335(f337(f888(x102484,a879)),x102485),f335(f335(f55(x102484),x1024810),x1024811)))+~P1(f335(f335(f337(f888(x102481,a879)),f335(f335(x102486,f831(x102487,x102485,x102483,x102486,x102481,x1024811,x1024810,x102484,x102489,x102488,x102482)),f832(x102487,x102485,x102483,x102486,x102481,x1024811,x1024810,x102484,x102489,x102488,x102482))),x102487))+P1(f335(f335(f337(f888(x102481,a879)),f335(f335(f33(x102482,f888(x102481,a879)),x102483),f335(f335(f8(f888(x102484,f888(x102481,a879)),f888(x102481,a879),x102482),f335(f33(x102484,f888(x102481,a879)),x102485)),x102486))),x102487))
% 59.73/59.68 [9151]E(x91511,x91512)+~P106(x91514)+~P26(x91513,x91514,x91515,f335(f335(f104(f888(x91513,a879)),f335(f166(x91513),x91511)),f335(f166(x91513),x91512)))+~E(f335(f166(x91513),x91511),f335(f166(x91513),x91512))+~P15(x91514,f335(f335(f147(x91513,x91514),x91515),x91512))+~P15(x91514,f335(f335(f147(x91513,x91514),x91515),x91511))+~P1(f335(f130(x91514),f335(f335(f147(x91513,x91514),x91515),x91512)))+~P1(f335(f130(x91514),f335(f335(f147(x91513,x91514),x91515),x91511)))
% 59.73/59.68 %EqnAxiom
% 59.73/59.68 [1]E(x11,x11)
% 59.73/59.68 [2]E(x22,x21)+~E(x21,x22)
% 59.73/59.68 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 59.73/59.68 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 59.73/59.68 [5]~E(x51,x52)+E(f94(x51),f94(x52))
% 59.73/59.68 [6]~E(x61,x62)+E(f23(x61),f23(x62))
% 59.73/59.68 [7]~E(x71,x72)+E(f188(x71),f188(x72))
% 59.73/59.68 [8]~E(x81,x82)+E(f335(x81,x83),f335(x82,x83))
% 59.73/59.68 [9]~E(x91,x92)+E(f335(x93,x91),f335(x93,x92))
% 59.73/59.68 [10]~E(x101,x102)+E(f95(x101),f95(x102))
% 59.73/59.68 [11]~E(x111,x112)+E(f240(x111),f240(x112))
% 59.73/59.68 [12]~E(x121,x122)+E(f104(x121),f104(x122))
% 59.73/59.68 [13]~E(x131,x132)+E(f241(x131),f241(x132))
% 59.73/59.68 [14]~E(x141,x142)+E(f96(x141),f96(x142))
% 59.73/59.68 [15]~E(x151,x152)+E(f25(x151),f25(x152))
% 59.73/59.68 [16]~E(x161,x162)+E(f79(x161),f79(x162))
% 59.73/59.68 [17]~E(x171,x172)+E(f618(x171,x173,x174,x175),f618(x172,x173,x174,x175))
% 59.73/59.68 [18]~E(x181,x182)+E(f618(x183,x181,x184,x185),f618(x183,x182,x184,x185))
% 59.73/59.68 [19]~E(x191,x192)+E(f618(x193,x194,x191,x195),f618(x193,x194,x192,x195))
% 59.73/59.68 [20]~E(x201,x202)+E(f618(x203,x204,x205,x201),f618(x203,x204,x205,x202))
% 59.73/59.68 [21]~E(x211,x212)+E(f242(x211),f242(x212))
% 59.73/59.68 [22]~E(x221,x222)+E(f882(x221),f882(x222))
% 59.73/59.68 [23]~E(x231,x232)+E(f73(x231),f73(x232))
% 59.73/59.68 [24]~E(x241,x242)+E(f832(x241,x243,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412),f832(x242,x243,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412))
% 59.73/59.68 [25]~E(x251,x252)+E(f832(x253,x251,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512),f832(x253,x252,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512))
% 59.73/59.68 [26]~E(x261,x262)+E(f832(x263,x264,x261,x265,x266,x267,x268,x269,x2610,x2611,x2612),f832(x263,x264,x262,x265,x266,x267,x268,x269,x2610,x2611,x2612))
% 59.73/59.68 [27]~E(x271,x272)+E(f832(x273,x274,x275,x271,x276,x277,x278,x279,x2710,x2711,x2712),f832(x273,x274,x275,x272,x276,x277,x278,x279,x2710,x2711,x2712))
% 59.73/59.68 [28]~E(x281,x282)+E(f832(x283,x284,x285,x286,x281,x287,x288,x289,x2810,x2811,x2812),f832(x283,x284,x285,x286,x282,x287,x288,x289,x2810,x2811,x2812))
% 59.73/59.68 [29]~E(x291,x292)+E(f832(x293,x294,x295,x296,x297,x291,x298,x299,x2910,x2911,x2912),f832(x293,x294,x295,x296,x297,x292,x298,x299,x2910,x2911,x2912))
% 59.73/59.68 [30]~E(x301,x302)+E(f832(x303,x304,x305,x306,x307,x308,x301,x309,x3010,x3011,x3012),f832(x303,x304,x305,x306,x307,x308,x302,x309,x3010,x3011,x3012))
% 59.73/59.68 [31]~E(x311,x312)+E(f832(x313,x314,x315,x316,x317,x318,x319,x311,x3110,x3111,x3112),f832(x313,x314,x315,x316,x317,x318,x319,x312,x3110,x3111,x3112))
% 59.73/59.68 [32]~E(x321,x322)+E(f832(x323,x324,x325,x326,x327,x328,x329,x3210,x321,x3211,x3212),f832(x323,x324,x325,x326,x327,x328,x329,x3210,x322,x3211,x3212))
% 59.73/59.68 [33]~E(x331,x332)+E(f832(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x331,x3312),f832(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x332,x3312))
% 59.73/59.68 [34]~E(x341,x342)+E(f832(x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x3412,x341),f832(x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x3412,x342))
% 59.73/59.68 [35]~E(x351,x352)+E(f243(x351),f243(x352))
% 59.73/59.68 [36]~E(x361,x362)+E(f105(x361),f105(x362))
% 59.73/59.68 [37]~E(x371,x372)+E(f831(x371,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712),f831(x372,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712))
% 59.73/59.68 [38]~E(x381,x382)+E(f831(x383,x381,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812),f831(x383,x382,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812))
% 59.73/59.68 [39]~E(x391,x392)+E(f831(x393,x394,x391,x395,x396,x397,x398,x399,x3910,x3911,x3912),f831(x393,x394,x392,x395,x396,x397,x398,x399,x3910,x3911,x3912))
% 59.73/59.68 [40]~E(x401,x402)+E(f831(x403,x404,x405,x401,x406,x407,x408,x409,x4010,x4011,x4012),f831(x403,x404,x405,x402,x406,x407,x408,x409,x4010,x4011,x4012))
% 59.73/59.68 [41]~E(x411,x412)+E(f831(x413,x414,x415,x416,x411,x417,x418,x419,x4110,x4111,x4112),f831(x413,x414,x415,x416,x412,x417,x418,x419,x4110,x4111,x4112))
% 59.73/59.68 [42]~E(x421,x422)+E(f831(x423,x424,x425,x426,x427,x421,x428,x429,x4210,x4211,x4212),f831(x423,x424,x425,x426,x427,x422,x428,x429,x4210,x4211,x4212))
% 59.73/59.68 [43]~E(x431,x432)+E(f831(x433,x434,x435,x436,x437,x438,x431,x439,x4310,x4311,x4312),f831(x433,x434,x435,x436,x437,x438,x432,x439,x4310,x4311,x4312))
% 59.73/59.68 [44]~E(x441,x442)+E(f831(x443,x444,x445,x446,x447,x448,x449,x441,x4410,x4411,x4412),f831(x443,x444,x445,x446,x447,x448,x449,x442,x4410,x4411,x4412))
% 59.73/59.68 [45]~E(x451,x452)+E(f831(x453,x454,x455,x456,x457,x458,x459,x4510,x451,x4511,x4512),f831(x453,x454,x455,x456,x457,x458,x459,x4510,x452,x4511,x4512))
% 59.73/59.68 [46]~E(x461,x462)+E(f831(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x461,x4612),f831(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x462,x4612))
% 59.73/59.68 [47]~E(x471,x472)+E(f831(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x471),f831(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x472))
% 59.73/59.68 [48]~E(x481,x482)+E(f337(x481),f337(x482))
% 59.73/59.68 [49]~E(x491,x492)+E(f4(x491),f4(x492))
% 59.73/59.68 [50]~E(x501,x502)+E(f888(x501,x503),f888(x502,x503))
% 59.73/59.68 [51]~E(x511,x512)+E(f888(x513,x511),f888(x513,x512))
% 59.73/59.68 [52]~E(x521,x522)+E(f880(x521),f880(x522))
% 59.73/59.68 [53]~E(x531,x532)+E(f885(x531),f885(x532))
% 59.73/59.68 [54]~E(x541,x542)+E(f56(x541),f56(x542))
% 59.73/59.68 [55]~E(x551,x552)+E(f883(x551),f883(x552))
% 59.73/59.68 [56]~E(x561,x562)+E(f11(x561,x563,x564),f11(x562,x563,x564))
% 59.73/59.68 [57]~E(x571,x572)+E(f11(x573,x571,x574),f11(x573,x572,x574))
% 59.73/59.68 [58]~E(x581,x582)+E(f11(x583,x584,x581),f11(x583,x584,x582))
% 59.73/59.68 [59]~E(x591,x592)+E(f30(x591),f30(x592))
% 59.73/59.68 [60]~E(x601,x602)+E(f812(x601,x603),f812(x602,x603))
% 59.73/59.68 [61]~E(x611,x612)+E(f812(x613,x611),f812(x613,x612))
% 59.73/59.68 [62]~E(x621,x622)+E(f254(x621),f254(x622))
% 59.73/59.68 [63]~E(x631,x632)+E(f74(x631),f74(x632))
% 59.73/59.68 [64]~E(x641,x642)+E(f619(x641,x643,x644,x645),f619(x642,x643,x644,x645))
% 59.73/59.68 [65]~E(x651,x652)+E(f619(x653,x651,x654,x655),f619(x653,x652,x654,x655))
% 59.73/59.68 [66]~E(x661,x662)+E(f619(x663,x664,x661,x665),f619(x663,x664,x662,x665))
% 59.73/59.68 [67]~E(x671,x672)+E(f619(x673,x674,x675,x671),f619(x673,x674,x675,x672))
% 59.73/59.68 [68]~E(x681,x682)+E(f189(x681),f189(x682))
% 59.73/59.68 [69]~E(x691,x692)+E(f152(x691,x693),f152(x692,x693))
% 59.73/59.68 [70]~E(x701,x702)+E(f152(x703,x701),f152(x703,x702))
% 59.73/59.68 [71]~E(x711,x712)+E(f97(x711),f97(x712))
% 59.73/59.68 [72]~E(x721,x722)+E(f33(x721,x723),f33(x722,x723))
% 59.73/59.68 [73]~E(x731,x732)+E(f33(x733,x731),f33(x733,x732))
% 59.73/59.68 [74]~E(x741,x742)+E(f75(x741),f75(x742))
% 59.73/59.68 [75]~E(x751,x752)+E(f107(x751),f107(x752))
% 59.73/59.68 [76]~E(x761,x762)+E(f166(x761),f166(x762))
% 59.73/59.68 [77]~E(x771,x772)+E(f76(x771),f76(x772))
% 59.73/59.68 [78]~E(x781,x782)+E(f70(x781),f70(x782))
% 59.73/59.68 [79]~E(x791,x792)+E(f887(x791,x793),f887(x792,x793))
% 59.73/59.68 [80]~E(x801,x802)+E(f887(x803,x801),f887(x803,x802))
% 59.73/59.68 [81]~E(x811,x812)+E(f144(x811),f144(x812))
% 59.73/59.68 [82]~E(x821,x822)+E(f292(x821),f292(x822))
% 59.73/59.68 [83]~E(x831,x832)+E(f733(x831,x833,x834),f733(x832,x833,x834))
% 59.73/59.68 [84]~E(x841,x842)+E(f733(x843,x841,x844),f733(x843,x842,x844))
% 59.73/59.68 [85]~E(x851,x852)+E(f733(x853,x854,x851),f733(x853,x854,x852))
% 59.73/59.68 [86]~E(x861,x862)+E(f42(x861,x863),f42(x862,x863))
% 59.73/59.68 [87]~E(x871,x872)+E(f42(x873,x871),f42(x873,x872))
% 59.73/59.68 [88]~E(x881,x882)+E(f288(x881,x883,x884),f288(x882,x883,x884))
% 59.73/59.68 [89]~E(x891,x892)+E(f288(x893,x891,x894),f288(x893,x892,x894))
% 59.73/59.68 [90]~E(x901,x902)+E(f288(x903,x904,x901),f288(x903,x904,x902))
% 59.73/59.68 [91]~E(x911,x912)+E(f129(x911,x913),f129(x912,x913))
% 59.73/59.68 [92]~E(x921,x922)+E(f129(x923,x921),f129(x923,x922))
% 59.73/59.68 [93]~E(x931,x932)+E(f55(x931),f55(x932))
% 59.73/59.68 [94]~E(x941,x942)+E(f29(x941),f29(x942))
% 59.73/59.68 [95]~E(x951,x952)+E(f6(x951,x953),f6(x952,x953))
% 59.73/59.68 [96]~E(x961,x962)+E(f6(x963,x961),f6(x963,x962))
% 59.73/59.68 [97]~E(x971,x972)+E(f313(x971,x973,x974),f313(x972,x973,x974))
% 59.73/59.68 [98]~E(x981,x982)+E(f313(x983,x981,x984),f313(x983,x982,x984))
% 59.73/59.68 [99]~E(x991,x992)+E(f313(x993,x994,x991),f313(x993,x994,x992))
% 59.73/59.68 [100]~E(x1001,x1002)+E(f537(x1001,x1003,x1004,x1005,x1006,x1007),f537(x1002,x1003,x1004,x1005,x1006,x1007))
% 59.73/59.68 [101]~E(x1011,x1012)+E(f537(x1013,x1011,x1014,x1015,x1016,x1017),f537(x1013,x1012,x1014,x1015,x1016,x1017))
% 59.73/59.68 [102]~E(x1021,x1022)+E(f537(x1023,x1024,x1021,x1025,x1026,x1027),f537(x1023,x1024,x1022,x1025,x1026,x1027))
% 59.73/59.68 [103]~E(x1031,x1032)+E(f537(x1033,x1034,x1035,x1031,x1036,x1037),f537(x1033,x1034,x1035,x1032,x1036,x1037))
% 59.73/59.68 [104]~E(x1041,x1042)+E(f537(x1043,x1044,x1045,x1046,x1041,x1047),f537(x1043,x1044,x1045,x1046,x1042,x1047))
% 59.73/59.68 [105]~E(x1051,x1052)+E(f537(x1053,x1054,x1055,x1056,x1057,x1051),f537(x1053,x1054,x1055,x1056,x1057,x1052))
% 59.73/59.68 [106]~E(x1061,x1062)+E(f18(x1061,x1063,x1064),f18(x1062,x1063,x1064))
% 59.73/59.68 [107]~E(x1071,x1072)+E(f18(x1073,x1071,x1074),f18(x1073,x1072,x1074))
% 59.73/59.68 [108]~E(x1081,x1082)+E(f18(x1083,x1084,x1081),f18(x1083,x1084,x1082))
% 59.73/59.68 [109]~E(x1091,x1092)+E(f264(x1091,x1093),f264(x1092,x1093))
% 59.73/59.68 [110]~E(x1101,x1102)+E(f264(x1103,x1101),f264(x1103,x1102))
% 59.73/59.68 [111]~E(x1111,x1112)+E(f252(x1111),f252(x1112))
% 59.73/59.68 [112]~E(x1121,x1122)+E(f312(x1121),f312(x1122))
% 59.73/59.68 [113]~E(x1131,x1132)+E(f341(x1131),f341(x1132))
% 59.73/59.68 [114]~E(x1141,x1142)+E(f266(x1141,x1143),f266(x1142,x1143))
% 59.73/59.68 [115]~E(x1151,x1152)+E(f266(x1153,x1151),f266(x1153,x1152))
% 59.73/59.68 [116]~E(x1161,x1162)+E(f127(x1161),f127(x1162))
% 59.73/59.68 [117]~E(x1171,x1172)+E(f268(x1171,x1173,x1174),f268(x1172,x1173,x1174))
% 59.73/59.68 [118]~E(x1181,x1182)+E(f268(x1183,x1181,x1184),f268(x1183,x1182,x1184))
% 59.73/59.68 [119]~E(x1191,x1192)+E(f268(x1193,x1194,x1191),f268(x1193,x1194,x1192))
% 59.73/59.68 [120]~E(x1201,x1202)+E(f60(x1201,x1203,x1204),f60(x1202,x1203,x1204))
% 59.73/59.68 [121]~E(x1211,x1212)+E(f60(x1213,x1211,x1214),f60(x1213,x1212,x1214))
% 59.73/59.68 [122]~E(x1221,x1222)+E(f60(x1223,x1224,x1221),f60(x1223,x1224,x1222))
% 59.73/59.68 [123]~E(x1231,x1232)+E(f561(x1231,x1233,x1234,x1235),f561(x1232,x1233,x1234,x1235))
% 59.73/59.68 [124]~E(x1241,x1242)+E(f561(x1243,x1241,x1244,x1245),f561(x1243,x1242,x1244,x1245))
% 59.73/59.68 [125]~E(x1251,x1252)+E(f561(x1253,x1254,x1251,x1255),f561(x1253,x1254,x1252,x1255))
% 59.73/59.68 [126]~E(x1261,x1262)+E(f561(x1263,x1264,x1265,x1261),f561(x1263,x1264,x1265,x1262))
% 59.73/59.68 [127]~E(x1271,x1272)+E(f629(x1271,x1273),f629(x1272,x1273))
% 59.73/59.68 [128]~E(x1281,x1282)+E(f629(x1283,x1281),f629(x1283,x1282))
% 59.73/59.68 [129]~E(x1291,x1292)+E(f8(x1291,x1293,x1294),f8(x1292,x1293,x1294))
% 59.73/59.68 [130]~E(x1301,x1302)+E(f8(x1303,x1301,x1304),f8(x1303,x1302,x1304))
% 59.73/59.68 [131]~E(x1311,x1312)+E(f8(x1313,x1314,x1311),f8(x1313,x1314,x1312))
% 59.73/59.68 [132]~E(x1321,x1322)+E(f743(x1321,x1323,x1324),f743(x1322,x1323,x1324))
% 59.73/59.68 [133]~E(x1331,x1332)+E(f743(x1333,x1331,x1334),f743(x1333,x1332,x1334))
% 59.73/59.68 [134]~E(x1341,x1342)+E(f743(x1343,x1344,x1341),f743(x1343,x1344,x1342))
% 59.73/59.68 [135]~E(x1351,x1352)+E(f39(x1351,x1353,x1354),f39(x1352,x1353,x1354))
% 59.73/59.68 [136]~E(x1361,x1362)+E(f39(x1363,x1361,x1364),f39(x1363,x1362,x1364))
% 59.73/59.68 [137]~E(x1371,x1372)+E(f39(x1373,x1374,x1371),f39(x1373,x1374,x1372))
% 59.73/59.68 [138]~E(x1381,x1382)+E(f169(x1381),f169(x1382))
% 59.73/59.68 [139]~E(x1391,x1392)+E(f291(x1391,x1393,x1394),f291(x1392,x1393,x1394))
% 59.73/59.68 [140]~E(x1401,x1402)+E(f291(x1403,x1401,x1404),f291(x1403,x1402,x1404))
% 59.73/59.68 [141]~E(x1411,x1412)+E(f291(x1413,x1414,x1411),f291(x1413,x1414,x1412))
% 59.73/59.68 [142]~E(x1421,x1422)+E(f158(x1421),f158(x1422))
% 59.73/59.68 [143]~E(x1431,x1432)+E(f399(x1431),f399(x1432))
% 59.73/59.68 [144]~E(x1441,x1442)+E(f147(x1441,x1443),f147(x1442,x1443))
% 59.73/59.68 [145]~E(x1451,x1452)+E(f147(x1453,x1451),f147(x1453,x1452))
% 59.73/59.68 [146]~E(x1461,x1462)+E(f99(x1461),f99(x1462))
% 59.73/59.68 [147]~E(x1471,x1472)+E(f100(x1471),f100(x1472))
% 59.73/59.68 [148]~E(x1481,x1482)+E(f336(x1481),f336(x1482))
% 59.73/59.68 [149]~E(x1491,x1492)+E(f306(x1491),f306(x1492))
% 59.73/59.68 [150]~E(x1501,x1502)+E(f239(x1501),f239(x1502))
% 59.73/59.68 [151]~E(x1511,x1512)+E(f103(x1511),f103(x1512))
% 59.73/59.68 [152]~E(x1521,x1522)+E(f34(x1521,x1523),f34(x1522,x1523))
% 59.73/59.68 [153]~E(x1531,x1532)+E(f34(x1533,x1531),f34(x1533,x1532))
% 59.73/59.68 [154]~E(x1541,x1542)+E(f249(x1541),f249(x1542))
% 59.73/59.68 [155]~E(x1551,x1552)+E(f58(x1551,x1553),f58(x1552,x1553))
% 59.73/59.68 [156]~E(x1561,x1562)+E(f58(x1563,x1561),f58(x1563,x1562))
% 59.73/59.68 [157]~E(x1571,x1572)+E(f5(x1571),f5(x1572))
% 59.73/59.68 [158]~E(x1581,x1582)+E(f90(x1581,x1583),f90(x1582,x1583))
% 59.73/59.68 [159]~E(x1591,x1592)+E(f90(x1593,x1591),f90(x1593,x1592))
% 59.73/59.68 [160]~E(x1601,x1602)+E(f151(x1601,x1603),f151(x1602,x1603))
% 59.73/59.68 [161]~E(x1611,x1612)+E(f151(x1613,x1611),f151(x1613,x1612))
% 59.73/59.68 [162]~E(x1621,x1622)+E(f183(x1621,x1623),f183(x1622,x1623))
% 59.73/59.68 [163]~E(x1631,x1632)+E(f183(x1633,x1631),f183(x1633,x1632))
% 59.73/59.68 [164]~E(x1641,x1642)+E(f7(x1641,x1643,x1644),f7(x1642,x1643,x1644))
% 59.73/59.68 [165]~E(x1651,x1652)+E(f7(x1653,x1651,x1654),f7(x1653,x1652,x1654))
% 59.73/59.68 [166]~E(x1661,x1662)+E(f7(x1663,x1664,x1661),f7(x1663,x1664,x1662))
% 59.73/59.68 [167]~E(x1671,x1672)+E(f327(x1671,x1673),f327(x1672,x1673))
% 59.73/59.68 [168]~E(x1681,x1682)+E(f327(x1683,x1681),f327(x1683,x1682))
% 59.73/59.68 [169]~E(x1691,x1692)+E(f310(x1691,x1693),f310(x1692,x1693))
% 59.73/59.68 [170]~E(x1701,x1702)+E(f310(x1703,x1701),f310(x1703,x1702))
% 59.73/59.68 [171]~E(x1711,x1712)+E(f177(x1711,x1713,x1714),f177(x1712,x1713,x1714))
% 59.73/59.68 [172]~E(x1721,x1722)+E(f177(x1723,x1721,x1724),f177(x1723,x1722,x1724))
% 59.73/59.68 [173]~E(x1731,x1732)+E(f177(x1733,x1734,x1731),f177(x1733,x1734,x1732))
% 59.73/59.68 [174]~E(x1741,x1742)+E(f13(x1741,x1743),f13(x1742,x1743))
% 59.73/59.68 [175]~E(x1751,x1752)+E(f13(x1753,x1751),f13(x1753,x1752))
% 59.73/59.68 [176]~E(x1761,x1762)+E(f150(x1761,x1763),f150(x1762,x1763))
% 59.73/59.68 [177]~E(x1771,x1772)+E(f150(x1773,x1771),f150(x1773,x1772))
% 59.73/59.68 [178]~E(x1781,x1782)+E(f307(x1781,x1783,x1784),f307(x1782,x1783,x1784))
% 59.73/59.68 [179]~E(x1791,x1792)+E(f307(x1793,x1791,x1794),f307(x1793,x1792,x1794))
% 59.73/59.68 [180]~E(x1801,x1802)+E(f307(x1803,x1804,x1801),f307(x1803,x1804,x1802))
% 59.73/59.68 [181]~E(x1811,x1812)+E(f824(x1811,x1813,x1814),f824(x1812,x1813,x1814))
% 59.73/59.68 [182]~E(x1821,x1822)+E(f824(x1823,x1821,x1824),f824(x1823,x1822,x1824))
% 59.73/59.68 [183]~E(x1831,x1832)+E(f824(x1833,x1834,x1831),f824(x1833,x1834,x1832))
% 59.73/59.68 [184]~E(x1841,x1842)+E(f61(x1841,x1843,x1844,x1845,x1846),f61(x1842,x1843,x1844,x1845,x1846))
% 59.73/59.68 [185]~E(x1851,x1852)+E(f61(x1853,x1851,x1854,x1855,x1856),f61(x1853,x1852,x1854,x1855,x1856))
% 59.73/59.68 [186]~E(x1861,x1862)+E(f61(x1863,x1864,x1861,x1865,x1866),f61(x1863,x1864,x1862,x1865,x1866))
% 59.73/59.68 [187]~E(x1871,x1872)+E(f61(x1873,x1874,x1875,x1871,x1876),f61(x1873,x1874,x1875,x1872,x1876))
% 59.73/59.68 [188]~E(x1881,x1882)+E(f61(x1883,x1884,x1885,x1886,x1881),f61(x1883,x1884,x1885,x1886,x1882))
% 59.73/59.68 [189]~E(x1891,x1892)+E(f130(x1891),f130(x1892))
% 59.73/59.68 [190]~E(x1901,x1902)+E(f68(x1901,x1903,x1904,x1905),f68(x1902,x1903,x1904,x1905))
% 59.73/59.68 [191]~E(x1911,x1912)+E(f68(x1913,x1911,x1914,x1915),f68(x1913,x1912,x1914,x1915))
% 59.73/59.68 [192]~E(x1921,x1922)+E(f68(x1923,x1924,x1921,x1925),f68(x1923,x1924,x1922,x1925))
% 59.73/59.68 [193]~E(x1931,x1932)+E(f68(x1933,x1934,x1935,x1931),f68(x1933,x1934,x1935,x1932))
% 59.73/59.68 [194]~E(x1941,x1942)+E(f182(x1941,x1943,x1944,x1945),f182(x1942,x1943,x1944,x1945))
% 59.73/59.68 [195]~E(x1951,x1952)+E(f182(x1953,x1951,x1954,x1955),f182(x1953,x1952,x1954,x1955))
% 59.73/59.68 [196]~E(x1961,x1962)+E(f182(x1963,x1964,x1961,x1965),f182(x1963,x1964,x1962,x1965))
% 59.73/59.68 [197]~E(x1971,x1972)+E(f182(x1973,x1974,x1975,x1971),f182(x1973,x1974,x1975,x1972))
% 59.73/59.68 [198]~E(x1981,x1982)+E(f12(x1981,x1983,x1984),f12(x1982,x1983,x1984))
% 59.73/59.68 [199]~E(x1991,x1992)+E(f12(x1993,x1991,x1994),f12(x1993,x1992,x1994))
% 59.73/59.68 [200]~E(x2001,x2002)+E(f12(x2003,x2004,x2001),f12(x2003,x2004,x2002))
% 59.73/59.68 [201]~E(x2011,x2012)+E(f53(x2011),f53(x2012))
% 59.73/59.68 [202]~E(x2021,x2022)+E(f269(x2021,x2023,x2024,x2025,x2026,x2027),f269(x2022,x2023,x2024,x2025,x2026,x2027))
% 59.73/59.68 [203]~E(x2031,x2032)+E(f269(x2033,x2031,x2034,x2035,x2036,x2037),f269(x2033,x2032,x2034,x2035,x2036,x2037))
% 59.73/59.68 [204]~E(x2041,x2042)+E(f269(x2043,x2044,x2041,x2045,x2046,x2047),f269(x2043,x2044,x2042,x2045,x2046,x2047))
% 59.73/59.68 [205]~E(x2051,x2052)+E(f269(x2053,x2054,x2055,x2051,x2056,x2057),f269(x2053,x2054,x2055,x2052,x2056,x2057))
% 59.73/59.68 [206]~E(x2061,x2062)+E(f269(x2063,x2064,x2065,x2066,x2061,x2067),f269(x2063,x2064,x2065,x2066,x2062,x2067))
% 59.73/59.68 [207]~E(x2071,x2072)+E(f269(x2073,x2074,x2075,x2076,x2077,x2071),f269(x2073,x2074,x2075,x2076,x2077,x2072))
% 59.73/59.68 [208]~E(x2081,x2082)+E(f565(x2081,x2083,x2084,x2085,x2086,x2087,x2088),f565(x2082,x2083,x2084,x2085,x2086,x2087,x2088))
% 59.73/59.68 [209]~E(x2091,x2092)+E(f565(x2093,x2091,x2094,x2095,x2096,x2097,x2098),f565(x2093,x2092,x2094,x2095,x2096,x2097,x2098))
% 59.73/59.68 [210]~E(x2101,x2102)+E(f565(x2103,x2104,x2101,x2105,x2106,x2107,x2108),f565(x2103,x2104,x2102,x2105,x2106,x2107,x2108))
% 59.73/59.68 [211]~E(x2111,x2112)+E(f565(x2113,x2114,x2115,x2111,x2116,x2117,x2118),f565(x2113,x2114,x2115,x2112,x2116,x2117,x2118))
% 59.73/59.68 [212]~E(x2121,x2122)+E(f565(x2123,x2124,x2125,x2126,x2121,x2127,x2128),f565(x2123,x2124,x2125,x2126,x2122,x2127,x2128))
% 59.73/59.68 [213]~E(x2131,x2132)+E(f565(x2133,x2134,x2135,x2136,x2137,x2131,x2138),f565(x2133,x2134,x2135,x2136,x2137,x2132,x2138))
% 59.73/59.68 [214]~E(x2141,x2142)+E(f565(x2143,x2144,x2145,x2146,x2147,x2148,x2141),f565(x2143,x2144,x2145,x2146,x2147,x2148,x2142))
% 59.73/59.68 [215]~E(x2151,x2152)+E(f579(x2151,x2153,x2154,x2155,x2156,x2157),f579(x2152,x2153,x2154,x2155,x2156,x2157))
% 59.73/59.68 [216]~E(x2161,x2162)+E(f579(x2163,x2161,x2164,x2165,x2166,x2167),f579(x2163,x2162,x2164,x2165,x2166,x2167))
% 59.73/59.68 [217]~E(x2171,x2172)+E(f579(x2173,x2174,x2171,x2175,x2176,x2177),f579(x2173,x2174,x2172,x2175,x2176,x2177))
% 59.73/59.68 [218]~E(x2181,x2182)+E(f579(x2183,x2184,x2185,x2181,x2186,x2187),f579(x2183,x2184,x2185,x2182,x2186,x2187))
% 59.73/59.68 [219]~E(x2191,x2192)+E(f579(x2193,x2194,x2195,x2196,x2191,x2197),f579(x2193,x2194,x2195,x2196,x2192,x2197))
% 59.73/59.68 [220]~E(x2201,x2202)+E(f579(x2203,x2204,x2205,x2206,x2207,x2201),f579(x2203,x2204,x2205,x2206,x2207,x2202))
% 59.73/59.68 [221]~E(x2211,x2212)+E(f688(x2211,x2213),f688(x2212,x2213))
% 59.73/59.68 [222]~E(x2221,x2222)+E(f688(x2223,x2221),f688(x2223,x2222))
% 59.73/59.68 [223]~E(x2231,x2232)+E(f305(x2231,x2233,x2234),f305(x2232,x2233,x2234))
% 59.73/59.68 [224]~E(x2241,x2242)+E(f305(x2243,x2241,x2244),f305(x2243,x2242,x2244))
% 59.73/59.68 [225]~E(x2251,x2252)+E(f305(x2253,x2254,x2251),f305(x2253,x2254,x2252))
% 59.73/59.68 [226]~E(x2261,x2262)+E(f634(x2261,x2263,x2264),f634(x2262,x2263,x2264))
% 59.73/59.68 [227]~E(x2271,x2272)+E(f634(x2273,x2271,x2274),f634(x2273,x2272,x2274))
% 59.73/59.68 [228]~E(x2281,x2282)+E(f634(x2283,x2284,x2281),f634(x2283,x2284,x2282))
% 59.73/59.68 [229]~E(x2291,x2292)+E(f687(x2291,x2293,x2294),f687(x2292,x2293,x2294))
% 59.73/59.68 [230]~E(x2301,x2302)+E(f687(x2303,x2301,x2304),f687(x2303,x2302,x2304))
% 59.73/59.68 [231]~E(x2311,x2312)+E(f687(x2313,x2314,x2311),f687(x2313,x2314,x2312))
% 59.73/59.68 [232]~E(x2321,x2322)+E(f31(x2321,x2323),f31(x2322,x2323))
% 59.73/59.68 [233]~E(x2331,x2332)+E(f31(x2333,x2331),f31(x2333,x2332))
% 59.73/59.68 [234]~E(x2341,x2342)+E(f113(x2341),f113(x2342))
% 59.73/59.68 [235]~E(x2351,x2352)+E(f15(x2351,x2353),f15(x2352,x2353))
% 59.73/59.68 [236]~E(x2361,x2362)+E(f15(x2363,x2361),f15(x2363,x2362))
% 59.73/59.68 [237]~E(x2371,x2372)+E(f153(x2371,x2373),f153(x2372,x2373))
% 59.73/59.68 [238]~E(x2381,x2382)+E(f153(x2383,x2381),f153(x2383,x2382))
% 59.73/59.68 [239]~E(x2391,x2392)+E(f175(x2391,x2393),f175(x2392,x2393))
% 59.73/59.68 [240]~E(x2401,x2402)+E(f175(x2403,x2401),f175(x2403,x2402))
% 59.73/59.68 [241]~E(x2411,x2412)+E(f258(x2411,x2413,x2414),f258(x2412,x2413,x2414))
% 59.73/59.68 [242]~E(x2421,x2422)+E(f258(x2423,x2421,x2424),f258(x2423,x2422,x2424))
% 59.73/59.68 [243]~E(x2431,x2432)+E(f258(x2433,x2434,x2431),f258(x2433,x2434,x2432))
% 59.73/59.68 [244]~E(x2441,x2442)+E(f171(x2441,x2443,x2444),f171(x2442,x2443,x2444))
% 59.73/59.68 [245]~E(x2451,x2452)+E(f171(x2453,x2451,x2454),f171(x2453,x2452,x2454))
% 59.73/59.68 [246]~E(x2461,x2462)+E(f171(x2463,x2464,x2461),f171(x2463,x2464,x2462))
% 59.73/59.68 [247]~E(x2471,x2472)+E(f757(x2471,x2473),f757(x2472,x2473))
% 59.73/59.68 [248]~E(x2481,x2482)+E(f757(x2483,x2481),f757(x2483,x2482))
% 59.73/59.68 [249]~E(x2491,x2492)+E(f16(x2491,x2493),f16(x2492,x2493))
% 59.73/59.68 [250]~E(x2501,x2502)+E(f16(x2503,x2501),f16(x2503,x2502))
% 59.73/59.68 [251]~E(x2511,x2512)+E(f143(x2511,x2513,x2514,x2515),f143(x2512,x2513,x2514,x2515))
% 59.73/59.68 [252]~E(x2521,x2522)+E(f143(x2523,x2521,x2524,x2525),f143(x2523,x2522,x2524,x2525))
% 59.73/59.68 [253]~E(x2531,x2532)+E(f143(x2533,x2534,x2531,x2535),f143(x2533,x2534,x2532,x2535))
% 59.73/59.68 [254]~E(x2541,x2542)+E(f143(x2543,x2544,x2545,x2541),f143(x2543,x2544,x2545,x2542))
% 59.73/59.68 [255]~E(x2551,x2552)+E(f108(x2551,x2553),f108(x2552,x2553))
% 59.73/59.68 [256]~E(x2561,x2562)+E(f108(x2563,x2561),f108(x2563,x2562))
% 59.73/59.68 [257]~E(x2571,x2572)+E(f267(x2571,x2573),f267(x2572,x2573))
% 59.73/59.68 [258]~E(x2581,x2582)+E(f267(x2583,x2581),f267(x2583,x2582))
% 59.73/59.68 [259]~E(x2591,x2592)+E(f324(x2591,x2593),f324(x2592,x2593))
% 59.73/59.68 [260]~E(x2601,x2602)+E(f324(x2603,x2601),f324(x2603,x2602))
% 59.73/59.68 [261]~E(x2611,x2612)+E(f145(x2611,x2613),f145(x2612,x2613))
% 59.73/59.68 [262]~E(x2621,x2622)+E(f145(x2623,x2621),f145(x2623,x2622))
% 59.73/59.68 [263]~E(x2631,x2632)+E(f142(x2631,x2633,x2634,x2635,x2636),f142(x2632,x2633,x2634,x2635,x2636))
% 59.73/59.68 [264]~E(x2641,x2642)+E(f142(x2643,x2641,x2644,x2645,x2646),f142(x2643,x2642,x2644,x2645,x2646))
% 59.73/59.68 [265]~E(x2651,x2652)+E(f142(x2653,x2654,x2651,x2655,x2656),f142(x2653,x2654,x2652,x2655,x2656))
% 59.73/59.68 [266]~E(x2661,x2662)+E(f142(x2663,x2664,x2665,x2661,x2666),f142(x2663,x2664,x2665,x2662,x2666))
% 59.73/59.68 [267]~E(x2671,x2672)+E(f142(x2673,x2674,x2675,x2676,x2671),f142(x2673,x2674,x2675,x2676,x2672))
% 59.73/59.68 [268]~E(x2681,x2682)+E(f191(x2681),f191(x2682))
% 59.73/59.68 [269]~E(x2691,x2692)+E(f304(x2691,x2693),f304(x2692,x2693))
% 59.73/59.68 [270]~E(x2701,x2702)+E(f304(x2703,x2701),f304(x2703,x2702))
% 59.73/59.68 [271]~E(x2711,x2712)+E(f109(x2711),f109(x2712))
% 59.73/59.68 [272]~E(x2721,x2722)+E(f368(x2721,x2723,x2724,x2725),f368(x2722,x2723,x2724,x2725))
% 59.73/59.68 [273]~E(x2731,x2732)+E(f368(x2733,x2731,x2734,x2735),f368(x2733,x2732,x2734,x2735))
% 59.73/59.68 [274]~E(x2741,x2742)+E(f368(x2743,x2744,x2741,x2745),f368(x2743,x2744,x2742,x2745))
% 59.73/59.68 [275]~E(x2751,x2752)+E(f368(x2753,x2754,x2755,x2751),f368(x2753,x2754,x2755,x2752))
% 59.73/59.68 [276]~E(x2761,x2762)+E(f889(x2761,x2763),f889(x2762,x2763))
% 59.73/59.68 [277]~E(x2771,x2772)+E(f889(x2773,x2771),f889(x2773,x2772))
% 59.73/59.68 [278]~E(x2781,x2782)+E(f886(x2781,x2783),f886(x2782,x2783))
% 59.73/59.68 [279]~E(x2791,x2792)+E(f886(x2793,x2791),f886(x2793,x2792))
% 59.73/59.68 [280]~E(x2801,x2802)+E(f88(x2801),f88(x2802))
% 59.73/59.68 [281]~E(x2811,x2812)+E(f164(x2811,x2813,x2814),f164(x2812,x2813,x2814))
% 59.73/59.68 [282]~E(x2821,x2822)+E(f164(x2823,x2821,x2824),f164(x2823,x2822,x2824))
% 59.73/59.68 [283]~E(x2831,x2832)+E(f164(x2833,x2834,x2831),f164(x2833,x2834,x2832))
% 59.73/59.68 [284]~E(x2841,x2842)+E(f582(x2841,x2843,x2844),f582(x2842,x2843,x2844))
% 59.73/59.68 [285]~E(x2851,x2852)+E(f582(x2853,x2851,x2854),f582(x2853,x2852,x2854))
% 59.73/59.68 [286]~E(x2861,x2862)+E(f582(x2863,x2864,x2861),f582(x2863,x2864,x2862))
% 59.73/59.68 [287]~E(x2871,x2872)+E(f161(x2871),f161(x2872))
% 59.73/59.68 [288]~E(x2881,x2882)+E(f49(x2881,x2883,x2884),f49(x2882,x2883,x2884))
% 59.73/59.68 [289]~E(x2891,x2892)+E(f49(x2893,x2891,x2894),f49(x2893,x2892,x2894))
% 59.73/59.68 [290]~E(x2901,x2902)+E(f49(x2903,x2904,x2901),f49(x2903,x2904,x2902))
% 59.73/59.68 [291]~E(x2911,x2912)+E(f89(x2911,x2913),f89(x2912,x2913))
% 59.73/59.68 [292]~E(x2921,x2922)+E(f89(x2923,x2921),f89(x2923,x2922))
% 59.73/59.68 [293]~E(x2931,x2932)+E(f141(x2931,x2933,x2934),f141(x2932,x2933,x2934))
% 59.73/59.68 [294]~E(x2941,x2942)+E(f141(x2943,x2941,x2944),f141(x2943,x2942,x2944))
% 59.73/59.68 [295]~E(x2951,x2952)+E(f141(x2953,x2954,x2951),f141(x2953,x2954,x2952))
% 59.73/59.68 [296]~E(x2961,x2962)+E(f165(x2961),f165(x2962))
% 59.73/59.68 [297]~E(x2971,x2972)+E(f289(x2971,x2973),f289(x2972,x2973))
% 59.73/59.68 [298]~E(x2981,x2982)+E(f289(x2983,x2981),f289(x2983,x2982))
% 59.73/59.68 [299]~E(x2991,x2992)+E(f516(x2991,x2993),f516(x2992,x2993))
% 59.73/59.68 [300]~E(x3001,x3002)+E(f516(x3003,x3001),f516(x3003,x3002))
% 59.73/59.68 [301]~E(x3011,x3012)+E(f162(x3011),f162(x3012))
% 59.73/59.68 [302]~E(x3021,x3022)+E(f184(x3021,x3023,x3024),f184(x3022,x3023,x3024))
% 59.73/59.68 [303]~E(x3031,x3032)+E(f184(x3033,x3031,x3034),f184(x3033,x3032,x3034))
% 59.73/59.68 [304]~E(x3041,x3042)+E(f184(x3043,x3044,x3041),f184(x3043,x3044,x3042))
% 59.73/59.68 [305]~E(x3051,x3052)+E(f50(x3051),f50(x3052))
% 59.73/59.68 [306]~E(x3061,x3062)+E(f778(x3061,x3063,x3064),f778(x3062,x3063,x3064))
% 59.73/59.68 [307]~E(x3071,x3072)+E(f778(x3073,x3071,x3074),f778(x3073,x3072,x3074))
% 59.73/59.68 [308]~E(x3081,x3082)+E(f778(x3083,x3084,x3081),f778(x3083,x3084,x3082))
% 59.73/59.68 [309]~E(x3091,x3092)+E(f181(x3091,x3093,x3094,x3095,x3096),f181(x3092,x3093,x3094,x3095,x3096))
% 59.73/59.68 [310]~E(x3101,x3102)+E(f181(x3103,x3101,x3104,x3105,x3106),f181(x3103,x3102,x3104,x3105,x3106))
% 59.73/59.68 [311]~E(x3111,x3112)+E(f181(x3113,x3114,x3111,x3115,x3116),f181(x3113,x3114,x3112,x3115,x3116))
% 59.73/59.68 [312]~E(x3121,x3122)+E(f181(x3123,x3124,x3125,x3121,x3126),f181(x3123,x3124,x3125,x3122,x3126))
% 59.73/59.68 [313]~E(x3131,x3132)+E(f181(x3133,x3134,x3135,x3136,x3131),f181(x3133,x3134,x3135,x3136,x3132))
% 59.73/59.68 [314]~E(x3141,x3142)+E(f116(x3141,x3143,x3144,x3145),f116(x3142,x3143,x3144,x3145))
% 59.73/59.68 [315]~E(x3151,x3152)+E(f116(x3153,x3151,x3154,x3155),f116(x3153,x3152,x3154,x3155))
% 59.73/59.68 [316]~E(x3161,x3162)+E(f116(x3163,x3164,x3161,x3165),f116(x3163,x3164,x3162,x3165))
% 59.73/59.68 [317]~E(x3171,x3172)+E(f116(x3173,x3174,x3175,x3171),f116(x3173,x3174,x3175,x3172))
% 59.73/59.68 [318]~E(x3181,x3182)+E(f569(x3181,x3183,x3184,x3185,x3186,x3187),f569(x3182,x3183,x3184,x3185,x3186,x3187))
% 59.73/59.68 [319]~E(x3191,x3192)+E(f569(x3193,x3191,x3194,x3195,x3196,x3197),f569(x3193,x3192,x3194,x3195,x3196,x3197))
% 59.73/59.68 [320]~E(x3201,x3202)+E(f569(x3203,x3204,x3201,x3205,x3206,x3207),f569(x3203,x3204,x3202,x3205,x3206,x3207))
% 59.73/59.68 [321]~E(x3211,x3212)+E(f569(x3213,x3214,x3215,x3211,x3216,x3217),f569(x3213,x3214,x3215,x3212,x3216,x3217))
% 59.73/59.68 [322]~E(x3221,x3222)+E(f569(x3223,x3224,x3225,x3226,x3221,x3227),f569(x3223,x3224,x3225,x3226,x3222,x3227))
% 59.73/59.68 [323]~E(x3231,x3232)+E(f569(x3233,x3234,x3235,x3236,x3237,x3231),f569(x3233,x3234,x3235,x3236,x3237,x3232))
% 59.73/59.68 [324]~E(x3241,x3242)+E(f323(x3241,x3243),f323(x3242,x3243))
% 59.73/59.68 [325]~E(x3251,x3252)+E(f323(x3253,x3251),f323(x3253,x3252))
% 59.73/59.68 [326]~E(x3261,x3262)+E(f568(x3261,x3263,x3264,x3265,x3266,x3267),f568(x3262,x3263,x3264,x3265,x3266,x3267))
% 59.73/59.68 [327]~E(x3271,x3272)+E(f568(x3273,x3271,x3274,x3275,x3276,x3277),f568(x3273,x3272,x3274,x3275,x3276,x3277))
% 59.73/59.68 [328]~E(x3281,x3282)+E(f568(x3283,x3284,x3281,x3285,x3286,x3287),f568(x3283,x3284,x3282,x3285,x3286,x3287))
% 59.73/59.68 [329]~E(x3291,x3292)+E(f568(x3293,x3294,x3295,x3291,x3296,x3297),f568(x3293,x3294,x3295,x3292,x3296,x3297))
% 59.73/59.68 [330]~E(x3301,x3302)+E(f568(x3303,x3304,x3305,x3306,x3301,x3307),f568(x3303,x3304,x3305,x3306,x3302,x3307))
% 59.73/59.68 [331]~E(x3311,x3312)+E(f568(x3313,x3314,x3315,x3316,x3317,x3311),f568(x3313,x3314,x3315,x3316,x3317,x3312))
% 59.73/59.68 [332]~E(x3321,x3322)+E(f179(x3321,x3323),f179(x3322,x3323))
% 59.73/59.68 [333]~E(x3331,x3332)+E(f179(x3333,x3331),f179(x3333,x3332))
% 59.73/59.68 [334]~E(x3341,x3342)+E(f326(x3341,x3343),f326(x3342,x3343))
% 59.73/59.68 [335]~E(x3351,x3352)+E(f326(x3353,x3351),f326(x3353,x3352))
% 59.73/59.68 [336]~E(x3361,x3362)+E(f154(x3361,x3363),f154(x3362,x3363))
% 59.73/59.68 [337]~E(x3371,x3372)+E(f154(x3373,x3371),f154(x3373,x3372))
% 59.73/59.68 [338]~E(x3381,x3382)+E(f43(x3381,x3383),f43(x3382,x3383))
% 59.73/59.68 [339]~E(x3391,x3392)+E(f43(x3393,x3391),f43(x3393,x3392))
% 59.73/59.68 [340]~E(x3401,x3402)+E(f163(x3401,x3403,x3404),f163(x3402,x3403,x3404))
% 59.73/59.68 [341]~E(x3411,x3412)+E(f163(x3413,x3411,x3414),f163(x3413,x3412,x3414))
% 59.73/59.68 [342]~E(x3421,x3422)+E(f163(x3423,x3424,x3421),f163(x3423,x3424,x3422))
% 59.73/59.68 [343]~E(x3431,x3432)+E(f302(x3431,x3433,x3434,x3435,x3436),f302(x3432,x3433,x3434,x3435,x3436))
% 59.73/59.68 [344]~E(x3441,x3442)+E(f302(x3443,x3441,x3444,x3445,x3446),f302(x3443,x3442,x3444,x3445,x3446))
% 59.73/59.68 [345]~E(x3451,x3452)+E(f302(x3453,x3454,x3451,x3455,x3456),f302(x3453,x3454,x3452,x3455,x3456))
% 59.73/59.68 [346]~E(x3461,x3462)+E(f302(x3463,x3464,x3465,x3461,x3466),f302(x3463,x3464,x3465,x3462,x3466))
% 59.73/59.68 [347]~E(x3471,x3472)+E(f302(x3473,x3474,x3475,x3476,x3471),f302(x3473,x3474,x3475,x3476,x3472))
% 59.73/59.68 [348]~E(x3481,x3482)+E(f132(x3481,x3483),f132(x3482,x3483))
% 59.73/59.68 [349]~E(x3491,x3492)+E(f132(x3493,x3491),f132(x3493,x3492))
% 59.73/59.68 [350]~E(x3501,x3502)+E(f9(x3501,x3503),f9(x3502,x3503))
% 59.73/59.68 [351]~E(x3511,x3512)+E(f9(x3513,x3511),f9(x3513,x3512))
% 59.73/59.68 [352]~E(x3521,x3522)+E(f119(x3521,x3523),f119(x3522,x3523))
% 59.73/59.68 [353]~E(x3531,x3532)+E(f119(x3533,x3531),f119(x3533,x3532))
% 59.73/59.68 [354]~E(x3541,x3542)+E(f873(x3541,x3543,x3544,x3545),f873(x3542,x3543,x3544,x3545))
% 59.73/59.68 [355]~E(x3551,x3552)+E(f873(x3553,x3551,x3554,x3555),f873(x3553,x3552,x3554,x3555))
% 59.73/59.68 [356]~E(x3561,x3562)+E(f873(x3563,x3564,x3561,x3565),f873(x3563,x3564,x3562,x3565))
% 59.73/59.68 [357]~E(x3571,x3572)+E(f873(x3573,x3574,x3575,x3571),f873(x3573,x3574,x3575,x3572))
% 59.73/59.68 [358]~E(x3581,x3582)+E(f806(x3581,x3583,x3584,x3585),f806(x3582,x3583,x3584,x3585))
% 59.73/59.68 [359]~E(x3591,x3592)+E(f806(x3593,x3591,x3594,x3595),f806(x3593,x3592,x3594,x3595))
% 59.73/59.68 [360]~E(x3601,x3602)+E(f806(x3603,x3604,x3601,x3605),f806(x3603,x3604,x3602,x3605))
% 59.73/59.68 [361]~E(x3611,x3612)+E(f806(x3613,x3614,x3615,x3611),f806(x3613,x3614,x3615,x3612))
% 59.73/59.68 [362]~E(x3621,x3622)+E(f185(x3621,x3623,x3624,x3625),f185(x3622,x3623,x3624,x3625))
% 59.73/59.68 [363]~E(x3631,x3632)+E(f185(x3633,x3631,x3634,x3635),f185(x3633,x3632,x3634,x3635))
% 59.73/59.68 [364]~E(x3641,x3642)+E(f185(x3643,x3644,x3641,x3645),f185(x3643,x3644,x3642,x3645))
% 59.73/59.68 [365]~E(x3651,x3652)+E(f185(x3653,x3654,x3655,x3651),f185(x3653,x3654,x3655,x3652))
% 59.73/59.68 [366]~E(x3661,x3662)+E(f825(x3661,x3663,x3664),f825(x3662,x3663,x3664))
% 59.73/59.68 [367]~E(x3671,x3672)+E(f825(x3673,x3671,x3674),f825(x3673,x3672,x3674))
% 59.73/59.68 [368]~E(x3681,x3682)+E(f825(x3683,x3684,x3681),f825(x3683,x3684,x3682))
% 59.73/59.68 [369]~E(x3691,x3692)+E(f754(x3691,x3693,x3694,x3695,x3696),f754(x3692,x3693,x3694,x3695,x3696))
% 59.73/59.68 [370]~E(x3701,x3702)+E(f754(x3703,x3701,x3704,x3705,x3706),f754(x3703,x3702,x3704,x3705,x3706))
% 59.73/59.68 [371]~E(x3711,x3712)+E(f754(x3713,x3714,x3711,x3715,x3716),f754(x3713,x3714,x3712,x3715,x3716))
% 59.73/59.68 [372]~E(x3721,x3722)+E(f754(x3723,x3724,x3725,x3721,x3726),f754(x3723,x3724,x3725,x3722,x3726))
% 59.73/59.68 [373]~E(x3731,x3732)+E(f754(x3733,x3734,x3735,x3736,x3731),f754(x3733,x3734,x3735,x3736,x3732))
% 59.73/59.68 [374]~E(x3741,x3742)+E(f820(x3741,x3743,x3744),f820(x3742,x3743,x3744))
% 59.73/59.68 [375]~E(x3751,x3752)+E(f820(x3753,x3751,x3754),f820(x3753,x3752,x3754))
% 59.73/59.68 [376]~E(x3761,x3762)+E(f820(x3763,x3764,x3761),f820(x3763,x3764,x3762))
% 59.73/59.68 [377]~E(x3771,x3772)+E(f44(x3771,x3773),f44(x3772,x3773))
% 59.73/59.68 [378]~E(x3781,x3782)+E(f44(x3783,x3781),f44(x3783,x3782))
% 59.73/59.68 [379]~E(x3791,x3792)+E(f723(x3791,x3793),f723(x3792,x3793))
% 59.73/59.68 [380]~E(x3801,x3802)+E(f723(x3803,x3801),f723(x3803,x3802))
% 59.73/59.68 [381]~E(x3811,x3812)+E(f37(x3811),f37(x3812))
% 59.73/59.68 [382]~E(x3821,x3822)+E(f263(x3821,x3823),f263(x3822,x3823))
% 59.73/59.68 [383]~E(x3831,x3832)+E(f263(x3833,x3831),f263(x3833,x3832))
% 59.73/59.68 [384]~E(x3841,x3842)+E(f149(x3841,x3843,x3844,x3845),f149(x3842,x3843,x3844,x3845))
% 59.73/59.68 [385]~E(x3851,x3852)+E(f149(x3853,x3851,x3854,x3855),f149(x3853,x3852,x3854,x3855))
% 59.73/59.68 [386]~E(x3861,x3862)+E(f149(x3863,x3864,x3861,x3865),f149(x3863,x3864,x3862,x3865))
% 59.73/59.68 [387]~E(x3871,x3872)+E(f149(x3873,x3874,x3875,x3871),f149(x3873,x3874,x3875,x3872))
% 59.73/59.68 [388]~E(x3881,x3882)+E(f80(x3881,x3883),f80(x3882,x3883))
% 59.73/59.68 [389]~E(x3891,x3892)+E(f80(x3893,x3891),f80(x3893,x3892))
% 59.73/59.68 [390]~E(x3901,x3902)+E(f769(x3901,x3903,x3904,x3905),f769(x3902,x3903,x3904,x3905))
% 59.73/59.68 [391]~E(x3911,x3912)+E(f769(x3913,x3911,x3914,x3915),f769(x3913,x3912,x3914,x3915))
% 59.73/59.68 [392]~E(x3921,x3922)+E(f769(x3923,x3924,x3921,x3925),f769(x3923,x3924,x3922,x3925))
% 59.73/59.68 [393]~E(x3931,x3932)+E(f769(x3933,x3934,x3935,x3931),f769(x3933,x3934,x3935,x3932))
% 59.73/59.68 [394]~E(x3941,x3942)+E(f85(x3941,x3943),f85(x3942,x3943))
% 59.73/59.68 [395]~E(x3951,x3952)+E(f85(x3953,x3951),f85(x3953,x3952))
% 59.73/59.68 [396]~E(x3961,x3962)+E(f172(x3961,x3963),f172(x3962,x3963))
% 59.73/59.68 [397]~E(x3971,x3972)+E(f172(x3973,x3971),f172(x3973,x3972))
% 59.73/59.68 [398]~E(x3981,x3982)+E(f146(x3981,x3983),f146(x3982,x3983))
% 59.73/59.68 [399]~E(x3991,x3992)+E(f146(x3993,x3991),f146(x3993,x3992))
% 59.73/59.68 [400]~E(x4001,x4002)+E(f200(x4001),f200(x4002))
% 59.73/59.68 [401]~E(x4011,x4012)+E(f201(x4011,x4013),f201(x4012,x4013))
% 59.73/59.68 [402]~E(x4021,x4022)+E(f201(x4023,x4021),f201(x4023,x4022))
% 59.73/59.68 [403]~E(x4031,x4032)+E(f682(x4031,x4033,x4034,x4035,x4036),f682(x4032,x4033,x4034,x4035,x4036))
% 59.73/59.68 [404]~E(x4041,x4042)+E(f682(x4043,x4041,x4044,x4045,x4046),f682(x4043,x4042,x4044,x4045,x4046))
% 59.73/59.68 [405]~E(x4051,x4052)+E(f682(x4053,x4054,x4051,x4055,x4056),f682(x4053,x4054,x4052,x4055,x4056))
% 59.73/59.68 [406]~E(x4061,x4062)+E(f682(x4063,x4064,x4065,x4061,x4066),f682(x4063,x4064,x4065,x4062,x4066))
% 59.73/59.68 [407]~E(x4071,x4072)+E(f682(x4073,x4074,x4075,x4076,x4071),f682(x4073,x4074,x4075,x4076,x4072))
% 59.73/59.68 [408]~E(x4081,x4082)+E(f821(x4081,x4083,x4084),f821(x4082,x4083,x4084))
% 59.73/59.68 [409]~E(x4091,x4092)+E(f821(x4093,x4091,x4094),f821(x4093,x4092,x4094))
% 59.73/59.68 [410]~E(x4101,x4102)+E(f821(x4103,x4104,x4101),f821(x4103,x4104,x4102))
% 59.73/59.68 [411]~E(x4111,x4112)+E(f81(x4111,x4113),f81(x4112,x4113))
% 59.73/59.68 [412]~E(x4121,x4122)+E(f81(x4123,x4121),f81(x4123,x4122))
% 59.73/59.68 [413]~E(x4131,x4132)+E(f524(x4131,x4133,x4134,x4135),f524(x4132,x4133,x4134,x4135))
% 59.73/59.68 [414]~E(x4141,x4142)+E(f524(x4143,x4141,x4144,x4145),f524(x4143,x4142,x4144,x4145))
% 59.73/59.68 [415]~E(x4151,x4152)+E(f524(x4153,x4154,x4151,x4155),f524(x4153,x4154,x4152,x4155))
% 59.73/59.68 [416]~E(x4161,x4162)+E(f524(x4163,x4164,x4165,x4161),f524(x4163,x4164,x4165,x4162))
% 59.73/59.68 [417]~E(x4171,x4172)+E(f135(x4171,x4173,x4174,x4175),f135(x4172,x4173,x4174,x4175))
% 59.73/59.68 [418]~E(x4181,x4182)+E(f135(x4183,x4181,x4184,x4185),f135(x4183,x4182,x4184,x4185))
% 59.73/59.68 [419]~E(x4191,x4192)+E(f135(x4193,x4194,x4191,x4195),f135(x4193,x4194,x4192,x4195))
% 59.73/59.68 [420]~E(x4201,x4202)+E(f135(x4203,x4204,x4205,x4201),f135(x4203,x4204,x4205,x4202))
% 59.73/59.68 [421]~E(x4211,x4212)+E(f329(x4211,x4213,x4214),f329(x4212,x4213,x4214))
% 59.73/59.68 [422]~E(x4221,x4222)+E(f329(x4223,x4221,x4224),f329(x4223,x4222,x4224))
% 59.73/59.68 [423]~E(x4231,x4232)+E(f329(x4233,x4234,x4231),f329(x4233,x4234,x4232))
% 59.73/59.68 [424]~E(x4241,x4242)+E(f235(x4241),f235(x4242))
% 59.73/59.68 [425]~E(x4251,x4252)+E(f32(x4251,x4253),f32(x4252,x4253))
% 59.73/59.68 [426]~E(x4261,x4262)+E(f32(x4263,x4261),f32(x4263,x4262))
% 59.73/59.68 [427]~E(x4271,x4272)+E(f584(x4271,x4273,x4274,x4275,x4276),f584(x4272,x4273,x4274,x4275,x4276))
% 59.73/59.68 [428]~E(x4281,x4282)+E(f584(x4283,x4281,x4284,x4285,x4286),f584(x4283,x4282,x4284,x4285,x4286))
% 59.73/59.68 [429]~E(x4291,x4292)+E(f584(x4293,x4294,x4291,x4295,x4296),f584(x4293,x4294,x4292,x4295,x4296))
% 59.73/59.68 [430]~E(x4301,x4302)+E(f584(x4303,x4304,x4305,x4301,x4306),f584(x4303,x4304,x4305,x4302,x4306))
% 59.73/59.68 [431]~E(x4311,x4312)+E(f584(x4313,x4314,x4315,x4316,x4311),f584(x4313,x4314,x4315,x4316,x4312))
% 59.73/59.68 [432]~E(x4321,x4322)+E(f287(x4321),f287(x4322))
% 59.73/59.68 [433]~E(x4331,x4332)+E(f140(x4331,x4333),f140(x4332,x4333))
% 59.73/59.68 [434]~E(x4341,x4342)+E(f140(x4343,x4341),f140(x4343,x4342))
% 59.73/59.68 [435]~E(x4351,x4352)+E(f466(x4351,x4353),f466(x4352,x4353))
% 59.73/59.68 [436]~E(x4361,x4362)+E(f466(x4363,x4361),f466(x4363,x4362))
% 59.73/59.68 [437]~E(x4371,x4372)+E(f722(x4371,x4373),f722(x4372,x4373))
% 59.73/59.68 [438]~E(x4381,x4382)+E(f722(x4383,x4381),f722(x4383,x4382))
% 59.73/59.68 [439]~E(x4391,x4392)+E(f396(x4391,x4393,x4394),f396(x4392,x4393,x4394))
% 59.73/59.68 [440]~E(x4401,x4402)+E(f396(x4403,x4401,x4404),f396(x4403,x4402,x4404))
% 59.73/59.68 [441]~E(x4411,x4412)+E(f396(x4413,x4414,x4411),f396(x4413,x4414,x4412))
% 59.73/59.68 [442]~E(x4421,x4422)+E(f59(x4421,x4423,x4424),f59(x4422,x4423,x4424))
% 59.73/59.68 [443]~E(x4431,x4432)+E(f59(x4433,x4431,x4434),f59(x4433,x4432,x4434))
% 59.73/59.68 [444]~E(x4441,x4442)+E(f59(x4443,x4444,x4441),f59(x4443,x4444,x4442))
% 59.73/59.68 [445]~E(x4451,x4452)+E(f437(x4451,x4453,x4454,x4455,x4456,x4457,x4458,x4459),f437(x4452,x4453,x4454,x4455,x4456,x4457,x4458,x4459))
% 59.73/59.68 [446]~E(x4461,x4462)+E(f437(x4463,x4461,x4464,x4465,x4466,x4467,x4468,x4469),f437(x4463,x4462,x4464,x4465,x4466,x4467,x4468,x4469))
% 59.73/59.68 [447]~E(x4471,x4472)+E(f437(x4473,x4474,x4471,x4475,x4476,x4477,x4478,x4479),f437(x4473,x4474,x4472,x4475,x4476,x4477,x4478,x4479))
% 59.73/59.68 [448]~E(x4481,x4482)+E(f437(x4483,x4484,x4485,x4481,x4486,x4487,x4488,x4489),f437(x4483,x4484,x4485,x4482,x4486,x4487,x4488,x4489))
% 59.73/59.68 [449]~E(x4491,x4492)+E(f437(x4493,x4494,x4495,x4496,x4491,x4497,x4498,x4499),f437(x4493,x4494,x4495,x4496,x4492,x4497,x4498,x4499))
% 59.73/59.68 [450]~E(x4501,x4502)+E(f437(x4503,x4504,x4505,x4506,x4507,x4501,x4508,x4509),f437(x4503,x4504,x4505,x4506,x4507,x4502,x4508,x4509))
% 59.73/59.68 [451]~E(x4511,x4512)+E(f437(x4513,x4514,x4515,x4516,x4517,x4518,x4511,x4519),f437(x4513,x4514,x4515,x4516,x4517,x4518,x4512,x4519))
% 59.73/59.68 [452]~E(x4521,x4522)+E(f437(x4523,x4524,x4525,x4526,x4527,x4528,x4529,x4521),f437(x4523,x4524,x4525,x4526,x4527,x4528,x4529,x4522))
% 59.73/59.68 [453]~E(x4531,x4532)+E(f680(x4531,x4533,x4534,x4535,x4536),f680(x4532,x4533,x4534,x4535,x4536))
% 59.73/59.68 [454]~E(x4541,x4542)+E(f680(x4543,x4541,x4544,x4545,x4546),f680(x4543,x4542,x4544,x4545,x4546))
% 59.73/59.68 [455]~E(x4551,x4552)+E(f680(x4553,x4554,x4551,x4555,x4556),f680(x4553,x4554,x4552,x4555,x4556))
% 59.73/59.68 [456]~E(x4561,x4562)+E(f680(x4563,x4564,x4565,x4561,x4566),f680(x4563,x4564,x4565,x4562,x4566))
% 59.73/59.68 [457]~E(x4571,x4572)+E(f680(x4573,x4574,x4575,x4576,x4571),f680(x4573,x4574,x4575,x4576,x4572))
% 59.73/59.68 [458]~E(x4581,x4582)+E(f822(x4581,x4583,x4584),f822(x4582,x4583,x4584))
% 59.73/59.68 [459]~E(x4591,x4592)+E(f822(x4593,x4591,x4594),f822(x4593,x4592,x4594))
% 59.73/59.68 [460]~E(x4601,x4602)+E(f822(x4603,x4604,x4601),f822(x4603,x4604,x4602))
% 59.73/59.68 [461]~E(x4611,x4612)+E(f657(x4611,x4613,x4614),f657(x4612,x4613,x4614))
% 59.73/59.68 [462]~E(x4621,x4622)+E(f657(x4623,x4621,x4624),f657(x4623,x4622,x4624))
% 59.73/59.68 [463]~E(x4631,x4632)+E(f657(x4633,x4634,x4631),f657(x4633,x4634,x4632))
% 59.73/59.68 [464]~E(x4641,x4642)+E(f541(x4641,x4643,x4644,x4645,x4646,x4647,x4648,x4649),f541(x4642,x4643,x4644,x4645,x4646,x4647,x4648,x4649))
% 59.73/59.68 [465]~E(x4651,x4652)+E(f541(x4653,x4651,x4654,x4655,x4656,x4657,x4658,x4659),f541(x4653,x4652,x4654,x4655,x4656,x4657,x4658,x4659))
% 59.73/59.68 [466]~E(x4661,x4662)+E(f541(x4663,x4664,x4661,x4665,x4666,x4667,x4668,x4669),f541(x4663,x4664,x4662,x4665,x4666,x4667,x4668,x4669))
% 59.73/59.68 [467]~E(x4671,x4672)+E(f541(x4673,x4674,x4675,x4671,x4676,x4677,x4678,x4679),f541(x4673,x4674,x4675,x4672,x4676,x4677,x4678,x4679))
% 59.73/59.68 [468]~E(x4681,x4682)+E(f541(x4683,x4684,x4685,x4686,x4681,x4687,x4688,x4689),f541(x4683,x4684,x4685,x4686,x4682,x4687,x4688,x4689))
% 59.73/59.68 [469]~E(x4691,x4692)+E(f541(x4693,x4694,x4695,x4696,x4697,x4691,x4698,x4699),f541(x4693,x4694,x4695,x4696,x4697,x4692,x4698,x4699))
% 59.73/59.68 [470]~E(x4701,x4702)+E(f541(x4703,x4704,x4705,x4706,x4707,x4708,x4701,x4709),f541(x4703,x4704,x4705,x4706,x4707,x4708,x4702,x4709))
% 59.73/59.68 [471]~E(x4711,x4712)+E(f541(x4713,x4714,x4715,x4716,x4717,x4718,x4719,x4711),f541(x4713,x4714,x4715,x4716,x4717,x4718,x4719,x4712))
% 59.73/59.68 [472]~E(x4721,x4722)+E(f704(x4721,x4723,x4724,x4725,x4726),f704(x4722,x4723,x4724,x4725,x4726))
% 59.73/59.68 [473]~E(x4731,x4732)+E(f704(x4733,x4731,x4734,x4735,x4736),f704(x4733,x4732,x4734,x4735,x4736))
% 59.73/59.68 [474]~E(x4741,x4742)+E(f704(x4743,x4744,x4741,x4745,x4746),f704(x4743,x4744,x4742,x4745,x4746))
% 59.73/59.68 [475]~E(x4751,x4752)+E(f704(x4753,x4754,x4755,x4751,x4756),f704(x4753,x4754,x4755,x4752,x4756))
% 59.73/59.68 [476]~E(x4761,x4762)+E(f704(x4763,x4764,x4765,x4766,x4761),f704(x4763,x4764,x4765,x4766,x4762))
% 59.73/59.68 [477]~E(x4771,x4772)+E(f270(x4771,x4773,x4774,x4775),f270(x4772,x4773,x4774,x4775))
% 59.73/59.68 [478]~E(x4781,x4782)+E(f270(x4783,x4781,x4784,x4785),f270(x4783,x4782,x4784,x4785))
% 59.73/59.68 [479]~E(x4791,x4792)+E(f270(x4793,x4794,x4791,x4795),f270(x4793,x4794,x4792,x4795))
% 59.73/59.68 [480]~E(x4801,x4802)+E(f270(x4803,x4804,x4805,x4801),f270(x4803,x4804,x4805,x4802))
% 59.73/59.68 [481]~E(x4811,x4812)+E(f40(x4811,x4813),f40(x4812,x4813))
% 59.73/59.68 [482]~E(x4821,x4822)+E(f40(x4823,x4821),f40(x4823,x4822))
% 59.73/59.68 [483]~E(x4831,x4832)+E(f156(x4831,x4833,x4834,x4835),f156(x4832,x4833,x4834,x4835))
% 59.73/59.68 [484]~E(x4841,x4842)+E(f156(x4843,x4841,x4844,x4845),f156(x4843,x4842,x4844,x4845))
% 59.73/59.68 [485]~E(x4851,x4852)+E(f156(x4853,x4854,x4851,x4855),f156(x4853,x4854,x4852,x4855))
% 59.73/59.68 [486]~E(x4861,x4862)+E(f156(x4863,x4864,x4865,x4861),f156(x4863,x4864,x4865,x4862))
% 59.73/59.68 [487]~E(x4871,x4872)+E(f173(x4871,x4873),f173(x4872,x4873))
% 59.73/59.68 [488]~E(x4881,x4882)+E(f173(x4883,x4881),f173(x4883,x4882))
% 59.73/59.68 [489]~E(x4891,x4892)+E(f238(x4891,x4893,x4894,x4895,x4896),f238(x4892,x4893,x4894,x4895,x4896))
% 59.73/59.68 [490]~E(x4901,x4902)+E(f238(x4903,x4901,x4904,x4905,x4906),f238(x4903,x4902,x4904,x4905,x4906))
% 59.73/59.68 [491]~E(x4911,x4912)+E(f238(x4913,x4914,x4911,x4915,x4916),f238(x4913,x4914,x4912,x4915,x4916))
% 59.73/59.68 [492]~E(x4921,x4922)+E(f238(x4923,x4924,x4925,x4921,x4926),f238(x4923,x4924,x4925,x4922,x4926))
% 59.73/59.68 [493]~E(x4931,x4932)+E(f238(x4933,x4934,x4935,x4936,x4931),f238(x4933,x4934,x4935,x4936,x4932))
% 59.73/59.68 [494]~E(x4941,x4942)+E(f10(x4941,x4943),f10(x4942,x4943))
% 59.73/59.68 [495]~E(x4951,x4952)+E(f10(x4953,x4951),f10(x4953,x4952))
% 59.73/59.68 [496]~E(x4961,x4962)+E(f308(x4961,x4963,x4964),f308(x4962,x4963,x4964))
% 59.73/59.68 [497]~E(x4971,x4972)+E(f308(x4973,x4971,x4974),f308(x4973,x4972,x4974))
% 59.73/59.68 [498]~E(x4981,x4982)+E(f308(x4983,x4984,x4981),f308(x4983,x4984,x4982))
% 59.73/59.68 [499]~E(x4991,x4992)+E(f309(x4991),f309(x4992))
% 59.73/59.68 [500]~E(x5001,x5002)+E(f511(x5001,x5003,x5004),f511(x5002,x5003,x5004))
% 59.73/59.68 [501]~E(x5011,x5012)+E(f511(x5013,x5011,x5014),f511(x5013,x5012,x5014))
% 59.73/59.68 [502]~E(x5021,x5022)+E(f511(x5023,x5024,x5021),f511(x5023,x5024,x5022))
% 59.73/59.68 [503]~E(x5031,x5032)+E(f48(x5031,x5033),f48(x5032,x5033))
% 59.73/59.68 [504]~E(x5041,x5042)+E(f48(x5043,x5041),f48(x5043,x5042))
% 59.73/59.68 [505]~E(x5051,x5052)+E(f131(x5051),f131(x5052))
% 59.73/59.68 [506]~E(x5061,x5062)+E(f86(x5061),f86(x5062))
% 59.73/59.68 [507]~E(x5071,x5072)+E(f303(x5071),f303(x5072))
% 59.73/59.68 [508]~E(x5081,x5082)+E(f342(x5081,x5083,x5084),f342(x5082,x5083,x5084))
% 59.73/59.68 [509]~E(x5091,x5092)+E(f342(x5093,x5091,x5094),f342(x5093,x5092,x5094))
% 59.73/59.68 [510]~E(x5101,x5102)+E(f342(x5103,x5104,x5101),f342(x5103,x5104,x5102))
% 59.73/59.68 [511]~E(x5111,x5112)+E(f250(x5111),f250(x5112))
% 59.73/59.68 [512]~E(x5121,x5122)+E(f776(x5121,x5123,x5124,x5125,x5126),f776(x5122,x5123,x5124,x5125,x5126))
% 59.73/59.68 [513]~E(x5131,x5132)+E(f776(x5133,x5131,x5134,x5135,x5136),f776(x5133,x5132,x5134,x5135,x5136))
% 59.73/59.68 [514]~E(x5141,x5142)+E(f776(x5143,x5144,x5141,x5145,x5146),f776(x5143,x5144,x5142,x5145,x5146))
% 59.73/59.68 [515]~E(x5151,x5152)+E(f776(x5153,x5154,x5155,x5151,x5156),f776(x5153,x5154,x5155,x5152,x5156))
% 59.73/59.68 [516]~E(x5161,x5162)+E(f776(x5163,x5164,x5165,x5166,x5161),f776(x5163,x5164,x5165,x5166,x5162))
% 59.73/59.68 [517]~E(x5171,x5172)+E(f14(x5171,x5173),f14(x5172,x5173))
% 59.73/59.68 [518]~E(x5181,x5182)+E(f14(x5183,x5181),f14(x5183,x5182))
% 59.73/59.68 [519]~E(x5191,x5192)+E(f490(x5191,x5193,x5194,x5195),f490(x5192,x5193,x5194,x5195))
% 59.73/59.68 [520]~E(x5201,x5202)+E(f490(x5203,x5201,x5204,x5205),f490(x5203,x5202,x5204,x5205))
% 59.73/59.68 [521]~E(x5211,x5212)+E(f490(x5213,x5214,x5211,x5215),f490(x5213,x5214,x5212,x5215))
% 59.73/59.68 [522]~E(x5221,x5222)+E(f490(x5223,x5224,x5225,x5221),f490(x5223,x5224,x5225,x5222))
% 59.73/59.68 [523]~E(x5231,x5232)+E(f237(x5231,x5233,x5234,x5235),f237(x5232,x5233,x5234,x5235))
% 59.73/59.68 [524]~E(x5241,x5242)+E(f237(x5243,x5241,x5244,x5245),f237(x5243,x5242,x5244,x5245))
% 59.73/59.68 [525]~E(x5251,x5252)+E(f237(x5253,x5254,x5251,x5255),f237(x5253,x5254,x5252,x5255))
% 59.73/59.68 [526]~E(x5261,x5262)+E(f237(x5263,x5264,x5265,x5261),f237(x5263,x5264,x5265,x5262))
% 59.73/59.68 [527]~E(x5271,x5272)+E(f251(x5271),f251(x5272))
% 59.73/59.68 [528]~E(x5281,x5282)+E(f262(x5281,x5283),f262(x5282,x5283))
% 59.73/59.68 [529]~E(x5291,x5292)+E(f262(x5293,x5291),f262(x5293,x5292))
% 59.73/59.68 [530]~E(x5301,x5302)+E(f656(x5301,x5303),f656(x5302,x5303))
% 59.73/59.68 [531]~E(x5311,x5312)+E(f656(x5313,x5311),f656(x5313,x5312))
% 59.73/59.68 [532]~E(x5321,x5322)+E(f734(x5321,x5323,x5324),f734(x5322,x5323,x5324))
% 59.73/59.68 [533]~E(x5331,x5332)+E(f734(x5333,x5331,x5334),f734(x5333,x5332,x5334))
% 59.73/59.68 [534]~E(x5341,x5342)+E(f734(x5343,x5344,x5341),f734(x5343,x5344,x5342))
% 59.73/59.68 [535]~E(x5351,x5352)+E(f314(x5351,x5353,x5354),f314(x5352,x5353,x5354))
% 59.73/59.68 [536]~E(x5361,x5362)+E(f314(x5363,x5361,x5364),f314(x5363,x5362,x5364))
% 59.73/59.68 [537]~E(x5371,x5372)+E(f314(x5373,x5374,x5371),f314(x5373,x5374,x5372))
% 59.73/59.68 [538]~E(x5381,x5382)+E(f311(x5381),f311(x5382))
% 59.73/59.68 [539]~E(x5391,x5392)+E(f71(x5391,x5393,x5394,x5395,x5396),f71(x5392,x5393,x5394,x5395,x5396))
% 59.73/59.68 [540]~E(x5401,x5402)+E(f71(x5403,x5401,x5404,x5405,x5406),f71(x5403,x5402,x5404,x5405,x5406))
% 59.73/59.68 [541]~E(x5411,x5412)+E(f71(x5413,x5414,x5411,x5415,x5416),f71(x5413,x5414,x5412,x5415,x5416))
% 59.73/59.68 [542]~E(x5421,x5422)+E(f71(x5423,x5424,x5425,x5421,x5426),f71(x5423,x5424,x5425,x5422,x5426))
% 59.73/59.68 [543]~E(x5431,x5432)+E(f71(x5433,x5434,x5435,x5436,x5431),f71(x5433,x5434,x5435,x5436,x5432))
% 59.73/59.68 [544]~E(x5441,x5442)+E(f321(x5441,x5443,x5444,x5445),f321(x5442,x5443,x5444,x5445))
% 59.73/59.68 [545]~E(x5451,x5452)+E(f321(x5453,x5451,x5454,x5455),f321(x5453,x5452,x5454,x5455))
% 59.73/59.68 [546]~E(x5461,x5462)+E(f321(x5463,x5464,x5461,x5465),f321(x5463,x5464,x5462,x5465))
% 59.73/59.68 [547]~E(x5471,x5472)+E(f321(x5473,x5474,x5475,x5471),f321(x5473,x5474,x5475,x5472))
% 59.73/59.68 [548]~E(x5481,x5482)+E(f740(x5481,x5483),f740(x5482,x5483))
% 59.73/59.68 [549]~E(x5491,x5492)+E(f740(x5493,x5491),f740(x5493,x5492))
% 59.73/59.68 [550]~E(x5501,x5502)+E(f464(x5501,x5503,x5504),f464(x5502,x5503,x5504))
% 59.73/59.68 [551]~E(x5511,x5512)+E(f464(x5513,x5511,x5514),f464(x5513,x5512,x5514))
% 59.73/59.68 [552]~E(x5521,x5522)+E(f464(x5523,x5524,x5521),f464(x5523,x5524,x5522))
% 59.73/59.68 [553]~E(x5531,x5532)+E(f463(x5531,x5533,x5534),f463(x5532,x5533,x5534))
% 59.73/59.68 [554]~E(x5541,x5542)+E(f463(x5543,x5541,x5544),f463(x5543,x5542,x5544))
% 59.73/59.68 [555]~E(x5551,x5552)+E(f463(x5553,x5554,x5551),f463(x5553,x5554,x5552))
% 59.73/59.68 [556]~E(x5561,x5562)+E(f453(x5561,x5563),f453(x5562,x5563))
% 59.73/59.68 [557]~E(x5571,x5572)+E(f453(x5573,x5571),f453(x5573,x5572))
% 59.73/59.68 [558]~E(x5581,x5582)+E(f668(x5581,x5583,x5584,x5585,x5586),f668(x5582,x5583,x5584,x5585,x5586))
% 59.73/59.68 [559]~E(x5591,x5592)+E(f668(x5593,x5591,x5594,x5595,x5596),f668(x5593,x5592,x5594,x5595,x5596))
% 59.73/59.68 [560]~E(x5601,x5602)+E(f668(x5603,x5604,x5601,x5605,x5606),f668(x5603,x5604,x5602,x5605,x5606))
% 59.73/59.68 [561]~E(x5611,x5612)+E(f668(x5613,x5614,x5615,x5611,x5616),f668(x5613,x5614,x5615,x5612,x5616))
% 59.73/59.68 [562]~E(x5621,x5622)+E(f668(x5623,x5624,x5625,x5626,x5621),f668(x5623,x5624,x5625,x5626,x5622))
% 59.73/59.68 [563]~E(x5631,x5632)+E(f260(x5631,x5633),f260(x5632,x5633))
% 59.73/59.68 [564]~E(x5641,x5642)+E(f260(x5643,x5641),f260(x5643,x5642))
% 59.73/59.68 [565]~E(x5651,x5652)+E(f505(x5651,x5653,x5654,x5655,x5656),f505(x5652,x5653,x5654,x5655,x5656))
% 59.73/59.68 [566]~E(x5661,x5662)+E(f505(x5663,x5661,x5664,x5665,x5666),f505(x5663,x5662,x5664,x5665,x5666))
% 59.73/59.68 [567]~E(x5671,x5672)+E(f505(x5673,x5674,x5671,x5675,x5676),f505(x5673,x5674,x5672,x5675,x5676))
% 59.73/59.68 [568]~E(x5681,x5682)+E(f505(x5683,x5684,x5685,x5681,x5686),f505(x5683,x5684,x5685,x5682,x5686))
% 59.73/59.68 [569]~E(x5691,x5692)+E(f505(x5693,x5694,x5695,x5696,x5691),f505(x5693,x5694,x5695,x5696,x5692))
% 59.73/59.68 [570]~E(x5701,x5702)+E(f234(x5701,x5703),f234(x5702,x5703))
% 59.73/59.68 [571]~E(x5711,x5712)+E(f234(x5713,x5711),f234(x5713,x5712))
% 59.73/59.68 [572]~E(x5721,x5722)+E(f457(x5721,x5723,x5724),f457(x5722,x5723,x5724))
% 59.73/59.68 [573]~E(x5731,x5732)+E(f457(x5733,x5731,x5734),f457(x5733,x5732,x5734))
% 59.73/59.68 [574]~E(x5741,x5742)+E(f457(x5743,x5744,x5741),f457(x5743,x5744,x5742))
% 59.73/59.68 [575]~E(x5751,x5752)+E(f118(x5751),f118(x5752))
% 59.73/59.68 [576]~E(x5761,x5762)+E(f491(x5761,x5763,x5764,x5765),f491(x5762,x5763,x5764,x5765))
% 59.73/59.68 [577]~E(x5771,x5772)+E(f491(x5773,x5771,x5774,x5775),f491(x5773,x5772,x5774,x5775))
% 59.73/59.68 [578]~E(x5781,x5782)+E(f491(x5783,x5784,x5781,x5785),f491(x5783,x5784,x5782,x5785))
% 59.73/59.68 [579]~E(x5791,x5792)+E(f491(x5793,x5794,x5795,x5791),f491(x5793,x5794,x5795,x5792))
% 59.73/59.68 [580]~E(x5801,x5802)+E(f652(x5801,x5803,x5804,x5805),f652(x5802,x5803,x5804,x5805))
% 59.73/59.68 [581]~E(x5811,x5812)+E(f652(x5813,x5811,x5814,x5815),f652(x5813,x5812,x5814,x5815))
% 59.73/59.68 [582]~E(x5821,x5822)+E(f652(x5823,x5824,x5821,x5825),f652(x5823,x5824,x5822,x5825))
% 59.73/59.68 [583]~E(x5831,x5832)+E(f652(x5833,x5834,x5835,x5831),f652(x5833,x5834,x5835,x5832))
% 59.73/59.68 [584]~E(x5841,x5842)+E(f137(x5841,x5843),f137(x5842,x5843))
% 59.73/59.68 [585]~E(x5851,x5852)+E(f137(x5853,x5851),f137(x5853,x5852))
% 59.73/59.68 [586]~E(x5861,x5862)+E(f196(x5861,x5863,x5864,x5865),f196(x5862,x5863,x5864,x5865))
% 59.73/59.68 [587]~E(x5871,x5872)+E(f196(x5873,x5871,x5874,x5875),f196(x5873,x5872,x5874,x5875))
% 59.73/59.68 [588]~E(x5881,x5882)+E(f196(x5883,x5884,x5881,x5885),f196(x5883,x5884,x5882,x5885))
% 59.73/59.68 [589]~E(x5891,x5892)+E(f196(x5893,x5894,x5895,x5891),f196(x5893,x5894,x5895,x5892))
% 59.73/59.68 [590]~E(x5901,x5902)+E(f667(x5901,x5903,x5904,x5905),f667(x5902,x5903,x5904,x5905))
% 59.73/59.68 [591]~E(x5911,x5912)+E(f667(x5913,x5911,x5914,x5915),f667(x5913,x5912,x5914,x5915))
% 59.73/59.68 [592]~E(x5921,x5922)+E(f667(x5923,x5924,x5921,x5925),f667(x5923,x5924,x5922,x5925))
% 59.73/59.68 [593]~E(x5931,x5932)+E(f667(x5933,x5934,x5935,x5931),f667(x5933,x5934,x5935,x5932))
% 59.73/59.68 [594]~E(x5941,x5942)+E(f673(x5941,x5943),f673(x5942,x5943))
% 59.73/59.68 [595]~E(x5951,x5952)+E(f673(x5953,x5951),f673(x5953,x5952))
% 59.73/59.68 [596]~E(x5961,x5962)+E(f554(x5961,x5963,x5964),f554(x5962,x5963,x5964))
% 59.73/59.68 [597]~E(x5971,x5972)+E(f554(x5973,x5971,x5974),f554(x5973,x5972,x5974))
% 59.73/59.68 [598]~E(x5981,x5982)+E(f554(x5983,x5984,x5981),f554(x5983,x5984,x5982))
% 59.73/59.68 [599]~E(x5991,x5992)+E(f556(x5991),f556(x5992))
% 59.73/59.68 [600]~E(x6001,x6002)+E(f261(x6001,x6003),f261(x6002,x6003))
% 59.73/59.68 [601]~E(x6011,x6012)+E(f261(x6013,x6011),f261(x6013,x6012))
% 59.73/59.68 [602]~E(x6021,x6022)+E(f83(x6021),f83(x6022))
% 59.73/59.68 [603]~E(x6031,x6032)+E(f299(x6031,x6033,x6034,x6035,x6036),f299(x6032,x6033,x6034,x6035,x6036))
% 59.73/59.68 [604]~E(x6041,x6042)+E(f299(x6043,x6041,x6044,x6045,x6046),f299(x6043,x6042,x6044,x6045,x6046))
% 59.73/59.68 [605]~E(x6051,x6052)+E(f299(x6053,x6054,x6051,x6055,x6056),f299(x6053,x6054,x6052,x6055,x6056))
% 59.73/59.68 [606]~E(x6061,x6062)+E(f299(x6063,x6064,x6065,x6061,x6066),f299(x6063,x6064,x6065,x6062,x6066))
% 59.73/59.68 [607]~E(x6071,x6072)+E(f299(x6073,x6074,x6075,x6076,x6071),f299(x6073,x6074,x6075,x6076,x6072))
% 59.73/59.68 [608]~E(x6081,x6082)+E(f67(x6081,x6083),f67(x6082,x6083))
% 59.73/59.68 [609]~E(x6091,x6092)+E(f67(x6093,x6091),f67(x6093,x6092))
% 59.73/59.68 [610]~E(x6101,x6102)+E(f199(x6101,x6103,x6104,x6105),f199(x6102,x6103,x6104,x6105))
% 59.73/59.68 [611]~E(x6111,x6112)+E(f199(x6113,x6111,x6114,x6115),f199(x6113,x6112,x6114,x6115))
% 59.73/59.68 [612]~E(x6121,x6122)+E(f199(x6123,x6124,x6121,x6125),f199(x6123,x6124,x6122,x6125))
% 59.73/59.68 [613]~E(x6131,x6132)+E(f199(x6133,x6134,x6135,x6131),f199(x6133,x6134,x6135,x6132))
% 59.73/59.68 [614]~E(x6141,x6142)+E(f567(x6141,x6143,x6144,x6145),f567(x6142,x6143,x6144,x6145))
% 59.73/59.68 [615]~E(x6151,x6152)+E(f567(x6153,x6151,x6154,x6155),f567(x6153,x6152,x6154,x6155))
% 59.73/59.68 [616]~E(x6161,x6162)+E(f567(x6163,x6164,x6161,x6165),f567(x6163,x6164,x6162,x6165))
% 59.73/59.68 [617]~E(x6171,x6172)+E(f567(x6173,x6174,x6175,x6171),f567(x6173,x6174,x6175,x6172))
% 59.73/59.68 [618]~E(x6181,x6182)+E(f846(x6181),f846(x6182))
% 59.73/59.68 [619]~E(x6191,x6192)+E(f829(x6191,x6193,x6194,x6195,x6196),f829(x6192,x6193,x6194,x6195,x6196))
% 59.73/59.68 [620]~E(x6201,x6202)+E(f829(x6203,x6201,x6204,x6205,x6206),f829(x6203,x6202,x6204,x6205,x6206))
% 59.73/59.68 [621]~E(x6211,x6212)+E(f829(x6213,x6214,x6211,x6215,x6216),f829(x6213,x6214,x6212,x6215,x6216))
% 59.73/59.68 [622]~E(x6221,x6222)+E(f829(x6223,x6224,x6225,x6221,x6226),f829(x6223,x6224,x6225,x6222,x6226))
% 59.73/59.68 [623]~E(x6231,x6232)+E(f829(x6233,x6234,x6235,x6236,x6231),f829(x6233,x6234,x6235,x6236,x6232))
% 59.73/59.68 [624]~E(x6241,x6242)+E(f727(x6241,x6243),f727(x6242,x6243))
% 59.73/59.68 [625]~E(x6251,x6252)+E(f727(x6253,x6251),f727(x6253,x6252))
% 59.73/59.68 [626]~E(x6261,x6262)+E(f578(x6261,x6263,x6264),f578(x6262,x6263,x6264))
% 59.73/59.68 [627]~E(x6271,x6272)+E(f578(x6273,x6271,x6274),f578(x6273,x6272,x6274))
% 59.73/59.68 [628]~E(x6281,x6282)+E(f578(x6283,x6284,x6281),f578(x6283,x6284,x6282))
% 59.73/59.68 [629]~E(x6291,x6292)+E(f599(x6291,x6293,x6294),f599(x6292,x6293,x6294))
% 59.73/59.68 [630]~E(x6301,x6302)+E(f599(x6303,x6301,x6304),f599(x6303,x6302,x6304))
% 59.73/59.68 [631]~E(x6311,x6312)+E(f599(x6313,x6314,x6311),f599(x6313,x6314,x6312))
% 59.73/59.68 [632]~E(x6321,x6322)+E(f590(x6321,x6323,x6324),f590(x6322,x6323,x6324))
% 59.73/59.68 [633]~E(x6331,x6332)+E(f590(x6333,x6331,x6334),f590(x6333,x6332,x6334))
% 59.73/59.68 [634]~E(x6341,x6342)+E(f590(x6343,x6344,x6341),f590(x6343,x6344,x6342))
% 59.73/59.68 [635]~E(x6351,x6352)+E(f294(x6351,x6353),f294(x6352,x6353))
% 59.73/59.68 [636]~E(x6361,x6362)+E(f294(x6363,x6361),f294(x6363,x6362))
% 59.73/59.68 [637]~E(x6371,x6372)+E(f531(x6371,x6373,x6374),f531(x6372,x6373,x6374))
% 59.73/59.68 [638]~E(x6381,x6382)+E(f531(x6383,x6381,x6384),f531(x6383,x6382,x6384))
% 59.73/59.68 [639]~E(x6391,x6392)+E(f531(x6393,x6394,x6391),f531(x6393,x6394,x6392))
% 59.73/59.68 [640]~E(x6401,x6402)+E(f801(x6401,x6403,x6404,x6405),f801(x6402,x6403,x6404,x6405))
% 59.73/59.68 [641]~E(x6411,x6412)+E(f801(x6413,x6411,x6414,x6415),f801(x6413,x6412,x6414,x6415))
% 59.73/59.68 [642]~E(x6421,x6422)+E(f801(x6423,x6424,x6421,x6425),f801(x6423,x6424,x6422,x6425))
% 59.73/59.68 [643]~E(x6431,x6432)+E(f801(x6433,x6434,x6435,x6431),f801(x6433,x6434,x6435,x6432))
% 59.73/59.68 [644]~E(x6441,x6442)+E(f315(x6441,x6443),f315(x6442,x6443))
% 59.73/59.68 [645]~E(x6451,x6452)+E(f315(x6453,x6451),f315(x6453,x6452))
% 59.73/59.68 [646]~E(x6461,x6462)+E(f379(x6461,x6463,x6464,x6465),f379(x6462,x6463,x6464,x6465))
% 59.73/59.68 [647]~E(x6471,x6472)+E(f379(x6473,x6471,x6474,x6475),f379(x6473,x6472,x6474,x6475))
% 59.73/59.68 [648]~E(x6481,x6482)+E(f379(x6483,x6484,x6481,x6485),f379(x6483,x6484,x6482,x6485))
% 59.73/59.68 [649]~E(x6491,x6492)+E(f379(x6493,x6494,x6495,x6491),f379(x6493,x6494,x6495,x6492))
% 59.73/59.68 [650]~E(x6501,x6502)+E(f611(x6501,x6503,x6504,x6505,x6506),f611(x6502,x6503,x6504,x6505,x6506))
% 59.73/59.68 [651]~E(x6511,x6512)+E(f611(x6513,x6511,x6514,x6515,x6516),f611(x6513,x6512,x6514,x6515,x6516))
% 59.73/59.68 [652]~E(x6521,x6522)+E(f611(x6523,x6524,x6521,x6525,x6526),f611(x6523,x6524,x6522,x6525,x6526))
% 59.73/59.68 [653]~E(x6531,x6532)+E(f611(x6533,x6534,x6535,x6531,x6536),f611(x6533,x6534,x6535,x6532,x6536))
% 59.73/59.68 [654]~E(x6541,x6542)+E(f611(x6543,x6544,x6545,x6546,x6541),f611(x6543,x6544,x6545,x6546,x6542))
% 59.73/59.68 [655]~E(x6551,x6552)+E(f72(x6551,x6553,x6554,x6555),f72(x6552,x6553,x6554,x6555))
% 59.73/59.68 [656]~E(x6561,x6562)+E(f72(x6563,x6561,x6564,x6565),f72(x6563,x6562,x6564,x6565))
% 59.73/59.68 [657]~E(x6571,x6572)+E(f72(x6573,x6574,x6571,x6575),f72(x6573,x6574,x6572,x6575))
% 59.73/59.68 [658]~E(x6581,x6582)+E(f72(x6583,x6584,x6585,x6581),f72(x6583,x6584,x6585,x6582))
% 59.73/59.68 [659]~E(x6591,x6592)+E(f748(x6591,x6593),f748(x6592,x6593))
% 59.73/59.68 [660]~E(x6601,x6602)+E(f748(x6603,x6601),f748(x6603,x6602))
% 59.73/59.68 [661]~E(x6611,x6612)+E(f41(x6611,x6613),f41(x6612,x6613))
% 59.73/59.68 [662]~E(x6621,x6622)+E(f41(x6623,x6621),f41(x6623,x6622))
% 59.73/59.68 [663]~E(x6631,x6632)+E(f82(x6631),f82(x6632))
% 59.73/59.68 [664]~E(x6641,x6642)+E(f691(x6641,x6643,x6644),f691(x6642,x6643,x6644))
% 59.73/59.68 [665]~E(x6651,x6652)+E(f691(x6653,x6651,x6654),f691(x6653,x6652,x6654))
% 59.73/59.68 [666]~E(x6661,x6662)+E(f691(x6663,x6664,x6661),f691(x6663,x6664,x6662))
% 59.73/59.68 [667]~E(x6671,x6672)+E(f716(x6671,x6673,x6674,x6675),f716(x6672,x6673,x6674,x6675))
% 59.73/59.68 [668]~E(x6681,x6682)+E(f716(x6683,x6681,x6684,x6685),f716(x6683,x6682,x6684,x6685))
% 59.73/59.68 [669]~E(x6691,x6692)+E(f716(x6693,x6694,x6691,x6695),f716(x6693,x6694,x6692,x6695))
% 59.73/59.68 [670]~E(x6701,x6702)+E(f716(x6703,x6704,x6705,x6701),f716(x6703,x6704,x6705,x6702))
% 59.73/59.68 [671]~E(x6711,x6712)+E(f87(x6711,x6713,x6714,x6715),f87(x6712,x6713,x6714,x6715))
% 59.73/59.68 [672]~E(x6721,x6722)+E(f87(x6723,x6721,x6724,x6725),f87(x6723,x6722,x6724,x6725))
% 59.73/59.68 [673]~E(x6731,x6732)+E(f87(x6733,x6734,x6731,x6735),f87(x6733,x6734,x6732,x6735))
% 59.73/59.68 [674]~E(x6741,x6742)+E(f87(x6743,x6744,x6745,x6741),f87(x6743,x6744,x6745,x6742))
% 59.73/59.68 [675]~E(x6751,x6752)+E(f434(x6751,x6753,x6754),f434(x6752,x6753,x6754))
% 59.73/59.68 [676]~E(x6761,x6762)+E(f434(x6763,x6761,x6764),f434(x6763,x6762,x6764))
% 59.73/59.68 [677]~E(x6771,x6772)+E(f434(x6773,x6774,x6771),f434(x6773,x6774,x6772))
% 59.73/59.68 [678]~E(x6781,x6782)+E(f774(x6781,x6783,x6784,x6785,x6786),f774(x6782,x6783,x6784,x6785,x6786))
% 59.73/59.68 [679]~E(x6791,x6792)+E(f774(x6793,x6791,x6794,x6795,x6796),f774(x6793,x6792,x6794,x6795,x6796))
% 59.73/59.68 [680]~E(x6801,x6802)+E(f774(x6803,x6804,x6801,x6805,x6806),f774(x6803,x6804,x6802,x6805,x6806))
% 59.73/59.68 [681]~E(x6811,x6812)+E(f774(x6813,x6814,x6815,x6811,x6816),f774(x6813,x6814,x6815,x6812,x6816))
% 59.73/59.68 [682]~E(x6821,x6822)+E(f774(x6823,x6824,x6825,x6826,x6821),f774(x6823,x6824,x6825,x6826,x6822))
% 59.73/59.68 [683]~E(x6831,x6832)+E(f253(x6831,x6833,x6834),f253(x6832,x6833,x6834))
% 59.73/59.68 [684]~E(x6841,x6842)+E(f253(x6843,x6841,x6844),f253(x6843,x6842,x6844))
% 59.73/59.68 [685]~E(x6851,x6852)+E(f253(x6853,x6854,x6851),f253(x6853,x6854,x6852))
% 59.73/59.68 [686]~E(x6861,x6862)+E(f219(x6861,x6863),f219(x6862,x6863))
% 59.73/59.68 [687]~E(x6871,x6872)+E(f219(x6873,x6871),f219(x6873,x6872))
% 59.73/59.68 [688]~E(x6881,x6882)+E(f148(x6881,x6883,x6884),f148(x6882,x6883,x6884))
% 59.73/59.68 [689]~E(x6891,x6892)+E(f148(x6893,x6891,x6894),f148(x6893,x6892,x6894))
% 59.73/59.68 [690]~E(x6901,x6902)+E(f148(x6903,x6904,x6901),f148(x6903,x6904,x6902))
% 59.73/59.68 [691]~E(x6911,x6912)+E(f180(x6911,x6913,x6914,x6915),f180(x6912,x6913,x6914,x6915))
% 59.73/59.68 [692]~E(x6921,x6922)+E(f180(x6923,x6921,x6924,x6925),f180(x6923,x6922,x6924,x6925))
% 59.73/59.68 [693]~E(x6931,x6932)+E(f180(x6933,x6934,x6931,x6935),f180(x6933,x6934,x6932,x6935))
% 59.73/59.68 [694]~E(x6941,x6942)+E(f180(x6943,x6944,x6945,x6941),f180(x6943,x6944,x6945,x6942))
% 59.73/59.68 [695]~E(x6951,x6952)+E(f124(x6951,x6953,x6954,x6955),f124(x6952,x6953,x6954,x6955))
% 59.73/59.68 [696]~E(x6961,x6962)+E(f124(x6963,x6961,x6964,x6965),f124(x6963,x6962,x6964,x6965))
% 59.73/59.68 [697]~E(x6971,x6972)+E(f124(x6973,x6974,x6971,x6975),f124(x6973,x6974,x6972,x6975))
% 59.73/59.68 [698]~E(x6981,x6982)+E(f124(x6983,x6984,x6985,x6981),f124(x6983,x6984,x6985,x6982))
% 59.73/59.68 [699]~E(x6991,x6992)+E(f77(x6991,x6993),f77(x6992,x6993))
% 59.73/59.68 [700]~E(x7001,x7002)+E(f77(x7003,x7001),f77(x7003,x7002))
% 59.73/59.68 [701]~E(x7011,x7012)+E(f662(x7011,x7013,x7014,x7015),f662(x7012,x7013,x7014,x7015))
% 59.73/59.68 [702]~E(x7021,x7022)+E(f662(x7023,x7021,x7024,x7025),f662(x7023,x7022,x7024,x7025))
% 59.73/59.68 [703]~E(x7031,x7032)+E(f662(x7033,x7034,x7031,x7035),f662(x7033,x7034,x7032,x7035))
% 59.73/59.68 [704]~E(x7041,x7042)+E(f662(x7043,x7044,x7045,x7041),f662(x7043,x7044,x7045,x7042))
% 59.73/59.68 [705]~E(x7051,x7052)+E(f614(x7051,x7053,x7054,x7055,x7056),f614(x7052,x7053,x7054,x7055,x7056))
% 59.73/59.68 [706]~E(x7061,x7062)+E(f614(x7063,x7061,x7064,x7065,x7066),f614(x7063,x7062,x7064,x7065,x7066))
% 59.73/59.68 [707]~E(x7071,x7072)+E(f614(x7073,x7074,x7071,x7075,x7076),f614(x7073,x7074,x7072,x7075,x7076))
% 59.73/59.68 [708]~E(x7081,x7082)+E(f614(x7083,x7084,x7085,x7081,x7086),f614(x7083,x7084,x7085,x7082,x7086))
% 59.73/59.68 [709]~E(x7091,x7092)+E(f614(x7093,x7094,x7095,x7096,x7091),f614(x7093,x7094,x7095,x7096,x7092))
% 59.73/59.68 [710]~E(x7101,x7102)+E(f215(x7101),f215(x7102))
% 59.73/59.68 [711]~E(x7111,x7112)+E(f708(x7111,x7113,x7114,x7115),f708(x7112,x7113,x7114,x7115))
% 59.73/59.68 [712]~E(x7121,x7122)+E(f708(x7123,x7121,x7124,x7125),f708(x7123,x7122,x7124,x7125))
% 59.73/59.68 [713]~E(x7131,x7132)+E(f708(x7133,x7134,x7131,x7135),f708(x7133,x7134,x7132,x7135))
% 59.73/59.68 [714]~E(x7141,x7142)+E(f708(x7143,x7144,x7145,x7141),f708(x7143,x7144,x7145,x7142))
% 59.73/59.68 [715]~E(x7151,x7152)+E(f17(x7151,x7153,x7154,x7155),f17(x7152,x7153,x7154,x7155))
% 59.73/59.68 [716]~E(x7161,x7162)+E(f17(x7163,x7161,x7164,x7165),f17(x7163,x7162,x7164,x7165))
% 59.73/59.68 [717]~E(x7171,x7172)+E(f17(x7173,x7174,x7171,x7175),f17(x7173,x7174,x7172,x7175))
% 59.73/59.68 [718]~E(x7181,x7182)+E(f17(x7183,x7184,x7185,x7181),f17(x7183,x7184,x7185,x7182))
% 59.73/59.68 [719]~E(x7191,x7192)+E(f233(x7191,x7193,x7194,x7195),f233(x7192,x7193,x7194,x7195))
% 59.73/59.68 [720]~E(x7201,x7202)+E(f233(x7203,x7201,x7204,x7205),f233(x7203,x7202,x7204,x7205))
% 59.73/59.68 [721]~E(x7211,x7212)+E(f233(x7213,x7214,x7211,x7215),f233(x7213,x7214,x7212,x7215))
% 59.73/59.68 [722]~E(x7221,x7222)+E(f233(x7223,x7224,x7225,x7221),f233(x7223,x7224,x7225,x7222))
% 59.73/59.68 [723]~E(x7231,x7232)+E(f794(x7231,x7233,x7234),f794(x7232,x7233,x7234))
% 59.73/59.68 [724]~E(x7241,x7242)+E(f794(x7243,x7241,x7244),f794(x7243,x7242,x7244))
% 59.73/59.68 [725]~E(x7251,x7252)+E(f794(x7253,x7254,x7251),f794(x7253,x7254,x7252))
% 59.73/59.68 [726]~E(x7261,x7262)+E(f638(x7261,x7263,x7264),f638(x7262,x7263,x7264))
% 59.73/59.68 [727]~E(x7271,x7272)+E(f638(x7273,x7271,x7274),f638(x7273,x7272,x7274))
% 59.73/59.68 [728]~E(x7281,x7282)+E(f638(x7283,x7284,x7281),f638(x7283,x7284,x7282))
% 59.73/59.68 [729]~E(x7291,x7292)+E(f826(x7291,x7293,x7294),f826(x7292,x7293,x7294))
% 59.73/59.68 [730]~E(x7301,x7302)+E(f826(x7303,x7301,x7304),f826(x7303,x7302,x7304))
% 59.73/59.68 [731]~E(x7311,x7312)+E(f826(x7313,x7314,x7311),f826(x7313,x7314,x7312))
% 59.73/59.68 [732]~E(x7321,x7322)+E(f807(x7321,x7323,x7324,x7325,x7326),f807(x7322,x7323,x7324,x7325,x7326))
% 59.73/59.68 [733]~E(x7331,x7332)+E(f807(x7333,x7331,x7334,x7335,x7336),f807(x7333,x7332,x7334,x7335,x7336))
% 59.73/59.68 [734]~E(x7341,x7342)+E(f807(x7343,x7344,x7341,x7345,x7346),f807(x7343,x7344,x7342,x7345,x7346))
% 59.73/59.68 [735]~E(x7351,x7352)+E(f807(x7353,x7354,x7355,x7351,x7356),f807(x7353,x7354,x7355,x7352,x7356))
% 59.73/59.68 [736]~E(x7361,x7362)+E(f807(x7363,x7364,x7365,x7366,x7361),f807(x7363,x7364,x7365,x7366,x7362))
% 59.73/59.68 [737]~E(x7371,x7372)+E(f134(x7371),f134(x7372))
% 59.73/59.68 [738]~E(x7381,x7382)+E(f620(x7381,x7383,x7384,x7385,x7386),f620(x7382,x7383,x7384,x7385,x7386))
% 59.73/59.68 [739]~E(x7391,x7392)+E(f620(x7393,x7391,x7394,x7395,x7396),f620(x7393,x7392,x7394,x7395,x7396))
% 59.73/59.68 [740]~E(x7401,x7402)+E(f620(x7403,x7404,x7401,x7405,x7406),f620(x7403,x7404,x7402,x7405,x7406))
% 59.73/59.68 [741]~E(x7411,x7412)+E(f620(x7413,x7414,x7415,x7411,x7416),f620(x7413,x7414,x7415,x7412,x7416))
% 59.73/59.68 [742]~E(x7421,x7422)+E(f620(x7423,x7424,x7425,x7426,x7421),f620(x7423,x7424,x7425,x7426,x7422))
% 59.73/59.68 [743]~E(x7431,x7432)+E(f397(x7431,x7433,x7434,x7435),f397(x7432,x7433,x7434,x7435))
% 59.73/59.68 [744]~E(x7441,x7442)+E(f397(x7443,x7441,x7444,x7445),f397(x7443,x7442,x7444,x7445))
% 59.73/59.68 [745]~E(x7451,x7452)+E(f397(x7453,x7454,x7451,x7455),f397(x7453,x7454,x7452,x7455))
% 59.73/59.68 [746]~E(x7461,x7462)+E(f397(x7463,x7464,x7465,x7461),f397(x7463,x7464,x7465,x7462))
% 59.73/59.68 [747]~E(x7471,x7472)+E(f525(x7471,x7473,x7474,x7475),f525(x7472,x7473,x7474,x7475))
% 59.73/59.68 [748]~E(x7481,x7482)+E(f525(x7483,x7481,x7484,x7485),f525(x7483,x7482,x7484,x7485))
% 59.73/59.68 [749]~E(x7491,x7492)+E(f525(x7493,x7494,x7491,x7495),f525(x7493,x7494,x7492,x7495))
% 59.73/59.68 [750]~E(x7501,x7502)+E(f525(x7503,x7504,x7505,x7501),f525(x7503,x7504,x7505,x7502))
% 59.73/59.68 [751]~E(x7511,x7512)+E(f814(x7511,x7513,x7514,x7515),f814(x7512,x7513,x7514,x7515))
% 59.73/59.68 [752]~E(x7521,x7522)+E(f814(x7523,x7521,x7524,x7525),f814(x7523,x7522,x7524,x7525))
% 59.73/59.68 [753]~E(x7531,x7532)+E(f814(x7533,x7534,x7531,x7535),f814(x7533,x7534,x7532,x7535))
% 59.73/59.68 [754]~E(x7541,x7542)+E(f814(x7543,x7544,x7545,x7541),f814(x7543,x7544,x7545,x7542))
% 59.73/59.68 [755]~E(x7551,x7552)+E(f603(x7551,x7553,x7554,x7555,x7556),f603(x7552,x7553,x7554,x7555,x7556))
% 59.73/59.68 [756]~E(x7561,x7562)+E(f603(x7563,x7561,x7564,x7565,x7566),f603(x7563,x7562,x7564,x7565,x7566))
% 59.73/59.68 [757]~E(x7571,x7572)+E(f603(x7573,x7574,x7571,x7575,x7576),f603(x7573,x7574,x7572,x7575,x7576))
% 59.73/59.68 [758]~E(x7581,x7582)+E(f603(x7583,x7584,x7585,x7581,x7586),f603(x7583,x7584,x7585,x7582,x7586))
% 59.73/59.68 [759]~E(x7591,x7592)+E(f603(x7593,x7594,x7595,x7596,x7591),f603(x7593,x7594,x7595,x7596,x7592))
% 59.73/59.68 [760]~E(x7601,x7602)+E(f758(x7601,x7603,x7604,x7605),f758(x7602,x7603,x7604,x7605))
% 59.73/59.68 [761]~E(x7611,x7612)+E(f758(x7613,x7611,x7614,x7615),f758(x7613,x7612,x7614,x7615))
% 59.73/59.68 [762]~E(x7621,x7622)+E(f758(x7623,x7624,x7621,x7625),f758(x7623,x7624,x7622,x7625))
% 59.73/59.68 [763]~E(x7631,x7632)+E(f758(x7633,x7634,x7635,x7631),f758(x7633,x7634,x7635,x7632))
% 59.73/59.68 [764]~E(x7641,x7642)+E(f787(x7641,x7643,x7644),f787(x7642,x7643,x7644))
% 59.73/59.68 [765]~E(x7651,x7652)+E(f787(x7653,x7651,x7654),f787(x7653,x7652,x7654))
% 59.73/59.68 [766]~E(x7661,x7662)+E(f787(x7663,x7664,x7661),f787(x7663,x7664,x7662))
% 59.73/59.68 [767]~E(x7671,x7672)+E(f864(x7671,x7673,x7674,x7675),f864(x7672,x7673,x7674,x7675))
% 59.73/59.68 [768]~E(x7681,x7682)+E(f864(x7683,x7681,x7684,x7685),f864(x7683,x7682,x7684,x7685))
% 59.73/59.68 [769]~E(x7691,x7692)+E(f864(x7693,x7694,x7691,x7695),f864(x7693,x7694,x7692,x7695))
% 59.73/59.68 [770]~E(x7701,x7702)+E(f864(x7703,x7704,x7705,x7701),f864(x7703,x7704,x7705,x7702))
% 59.73/59.68 [771]~E(x7711,x7712)+E(f698(x7711,x7713,x7714,x7715,x7716),f698(x7712,x7713,x7714,x7715,x7716))
% 59.73/59.68 [772]~E(x7721,x7722)+E(f698(x7723,x7721,x7724,x7725,x7726),f698(x7723,x7722,x7724,x7725,x7726))
% 59.73/59.68 [773]~E(x7731,x7732)+E(f698(x7733,x7734,x7731,x7735,x7736),f698(x7733,x7734,x7732,x7735,x7736))
% 59.73/59.68 [774]~E(x7741,x7742)+E(f698(x7743,x7744,x7745,x7741,x7746),f698(x7743,x7744,x7745,x7742,x7746))
% 59.73/59.68 [775]~E(x7751,x7752)+E(f698(x7753,x7754,x7755,x7756,x7751),f698(x7753,x7754,x7755,x7756,x7752))
% 59.73/59.68 [776]~E(x7761,x7762)+E(f712(x7761,x7763,x7764),f712(x7762,x7763,x7764))
% 59.73/59.68 [777]~E(x7771,x7772)+E(f712(x7773,x7771,x7774),f712(x7773,x7772,x7774))
% 59.73/59.68 [778]~E(x7781,x7782)+E(f712(x7783,x7784,x7781),f712(x7783,x7784,x7782))
% 59.73/59.68 [779]~E(x7791,x7792)+E(f159(x7791),f159(x7792))
% 59.73/59.68 [780]~E(x7801,x7802)+E(f609(x7801,x7803,x7804,x7805,x7806),f609(x7802,x7803,x7804,x7805,x7806))
% 59.73/59.68 [781]~E(x7811,x7812)+E(f609(x7813,x7811,x7814,x7815,x7816),f609(x7813,x7812,x7814,x7815,x7816))
% 59.73/59.68 [782]~E(x7821,x7822)+E(f609(x7823,x7824,x7821,x7825,x7826),f609(x7823,x7824,x7822,x7825,x7826))
% 59.73/59.68 [783]~E(x7831,x7832)+E(f609(x7833,x7834,x7835,x7831,x7836),f609(x7833,x7834,x7835,x7832,x7836))
% 59.73/59.68 [784]~E(x7841,x7842)+E(f609(x7843,x7844,x7845,x7846,x7841),f609(x7843,x7844,x7845,x7846,x7842))
% 59.73/59.68 [785]~E(x7851,x7852)+E(f110(x7851,x7853,x7854),f110(x7852,x7853,x7854))
% 59.73/59.68 [786]~E(x7861,x7862)+E(f110(x7863,x7861,x7864),f110(x7863,x7862,x7864))
% 59.73/59.68 [787]~E(x7871,x7872)+E(f110(x7873,x7874,x7871),f110(x7873,x7874,x7872))
% 59.73/59.68 [788]~E(x7881,x7882)+E(f257(x7881,x7883),f257(x7882,x7883))
% 59.73/59.68 [789]~E(x7891,x7892)+E(f257(x7893,x7891),f257(x7893,x7892))
% 59.73/59.68 [790]~E(x7901,x7902)+E(f167(x7901,x7903,x7904),f167(x7902,x7903,x7904))
% 59.73/59.68 [791]~E(x7911,x7912)+E(f167(x7913,x7911,x7914),f167(x7913,x7912,x7914))
% 59.73/59.68 [792]~E(x7921,x7922)+E(f167(x7923,x7924,x7921),f167(x7923,x7924,x7922))
% 59.73/59.68 [793]~E(x7931,x7932)+E(f816(x7931,x7933,x7934,x7935),f816(x7932,x7933,x7934,x7935))
% 59.73/59.68 [794]~E(x7941,x7942)+E(f816(x7943,x7941,x7944,x7945),f816(x7943,x7942,x7944,x7945))
% 59.73/59.68 [795]~E(x7951,x7952)+E(f816(x7953,x7954,x7951,x7955),f816(x7953,x7954,x7952,x7955))
% 59.73/59.68 [796]~E(x7961,x7962)+E(f816(x7963,x7964,x7965,x7961),f816(x7963,x7964,x7965,x7962))
% 59.73/59.68 [797]~E(x7971,x7972)+E(f685(x7971,x7973,x7974,x7975),f685(x7972,x7973,x7974,x7975))
% 59.73/59.68 [798]~E(x7981,x7982)+E(f685(x7983,x7981,x7984,x7985),f685(x7983,x7982,x7984,x7985))
% 59.73/59.68 [799]~E(x7991,x7992)+E(f685(x7993,x7994,x7991,x7995),f685(x7993,x7994,x7992,x7995))
% 59.73/59.68 [800]~E(x8001,x8002)+E(f685(x8003,x8004,x8005,x8001),f685(x8003,x8004,x8005,x8002))
% 59.73/59.68 [801]~E(x8011,x8012)+E(f400(x8011),f400(x8012))
% 59.73/59.68 [802]~E(x8021,x8022)+E(f866(x8021,x8023,x8024),f866(x8022,x8023,x8024))
% 59.73/59.68 [803]~E(x8031,x8032)+E(f866(x8033,x8031,x8034),f866(x8033,x8032,x8034))
% 59.73/59.68 [804]~E(x8041,x8042)+E(f866(x8043,x8044,x8041),f866(x8043,x8044,x8042))
% 59.73/59.68 [805]~E(x8051,x8052)+E(f677(x8051,x8053,x8054,x8055),f677(x8052,x8053,x8054,x8055))
% 59.73/59.68 [806]~E(x8061,x8062)+E(f677(x8063,x8061,x8064,x8065),f677(x8063,x8062,x8064,x8065))
% 59.73/59.68 [807]~E(x8071,x8072)+E(f677(x8073,x8074,x8071,x8075),f677(x8073,x8074,x8072,x8075))
% 59.73/59.68 [808]~E(x8081,x8082)+E(f677(x8083,x8084,x8085,x8081),f677(x8083,x8084,x8085,x8082))
% 59.73/59.68 [809]~E(x8091,x8092)+E(f811(x8091,x8093,x8094),f811(x8092,x8093,x8094))
% 59.73/59.68 [810]~E(x8101,x8102)+E(f811(x8103,x8101,x8104),f811(x8103,x8102,x8104))
% 59.73/59.68 [811]~E(x8111,x8112)+E(f811(x8113,x8114,x8111),f811(x8113,x8114,x8112))
% 59.73/59.68 [812]~E(x8121,x8122)+E(f358(x8121,x8123,x8124),f358(x8122,x8123,x8124))
% 59.73/59.68 [813]~E(x8131,x8132)+E(f358(x8133,x8131,x8134),f358(x8133,x8132,x8134))
% 59.73/59.68 [814]~E(x8141,x8142)+E(f358(x8143,x8144,x8141),f358(x8143,x8144,x8142))
% 59.73/59.68 [815]~E(x8151,x8152)+E(f328(x8151,x8153,x8154,x8155),f328(x8152,x8153,x8154,x8155))
% 59.73/59.68 [816]~E(x8161,x8162)+E(f328(x8163,x8161,x8164,x8165),f328(x8163,x8162,x8164,x8165))
% 59.73/59.68 [817]~E(x8171,x8172)+E(f328(x8173,x8174,x8171,x8175),f328(x8173,x8174,x8172,x8175))
% 59.73/59.68 [818]~E(x8181,x8182)+E(f328(x8183,x8184,x8185,x8181),f328(x8183,x8184,x8185,x8182))
% 59.73/59.68 [819]~E(x8191,x8192)+E(f411(x8191,x8193,x8194),f411(x8192,x8193,x8194))
% 59.73/59.68 [820]~E(x8201,x8202)+E(f411(x8203,x8201,x8204),f411(x8203,x8202,x8204))
% 59.73/59.68 [821]~E(x8211,x8212)+E(f411(x8213,x8214,x8211),f411(x8213,x8214,x8212))
% 59.73/59.68 [822]~E(x8221,x8222)+E(f265(x8221,x8223,x8224,x8225,x8226),f265(x8222,x8223,x8224,x8225,x8226))
% 59.73/59.68 [823]~E(x8231,x8232)+E(f265(x8233,x8231,x8234,x8235,x8236),f265(x8233,x8232,x8234,x8235,x8236))
% 59.73/59.68 [824]~E(x8241,x8242)+E(f265(x8243,x8244,x8241,x8245,x8246),f265(x8243,x8244,x8242,x8245,x8246))
% 59.73/59.68 [825]~E(x8251,x8252)+E(f265(x8253,x8254,x8255,x8251,x8256),f265(x8253,x8254,x8255,x8252,x8256))
% 59.73/59.68 [826]~E(x8261,x8262)+E(f265(x8263,x8264,x8265,x8266,x8261),f265(x8263,x8264,x8265,x8266,x8262))
% 59.73/59.68 [827]~E(x8271,x8272)+E(f157(x8271,x8273,x8274,x8275),f157(x8272,x8273,x8274,x8275))
% 59.73/59.68 [828]~E(x8281,x8282)+E(f157(x8283,x8281,x8284,x8285),f157(x8283,x8282,x8284,x8285))
% 59.73/59.68 [829]~E(x8291,x8292)+E(f157(x8293,x8294,x8291,x8295),f157(x8293,x8294,x8292,x8295))
% 59.73/59.68 [830]~E(x8301,x8302)+E(f157(x8303,x8304,x8305,x8301),f157(x8303,x8304,x8305,x8302))
% 59.73/59.68 [831]~E(x8311,x8312)+E(f460(x8311,x8313,x8314,x8315),f460(x8312,x8313,x8314,x8315))
% 59.73/59.68 [832]~E(x8321,x8322)+E(f460(x8323,x8321,x8324,x8325),f460(x8323,x8322,x8324,x8325))
% 59.73/59.68 [833]~E(x8331,x8332)+E(f460(x8333,x8334,x8331,x8335),f460(x8333,x8334,x8332,x8335))
% 59.73/59.68 [834]~E(x8341,x8342)+E(f460(x8343,x8344,x8345,x8341),f460(x8343,x8344,x8345,x8342))
% 59.73/59.68 [835]~E(x8351,x8352)+E(f406(x8351,x8353,x8354),f406(x8352,x8353,x8354))
% 59.73/59.68 [836]~E(x8361,x8362)+E(f406(x8363,x8361,x8364),f406(x8363,x8362,x8364))
% 59.73/59.68 [837]~E(x8371,x8372)+E(f406(x8373,x8374,x8371),f406(x8373,x8374,x8372))
% 59.73/59.68 [838]~E(x8381,x8382)+E(f692(x8381,x8383,x8384),f692(x8382,x8383,x8384))
% 59.73/59.68 [839]~E(x8391,x8392)+E(f692(x8393,x8391,x8394),f692(x8393,x8392,x8394))
% 59.73/59.68 [840]~E(x8401,x8402)+E(f692(x8403,x8404,x8401),f692(x8403,x8404,x8402))
% 59.73/59.68 [841]~E(x8411,x8412)+E(f815(x8411,x8413,x8414,x8415),f815(x8412,x8413,x8414,x8415))
% 59.73/59.68 [842]~E(x8421,x8422)+E(f815(x8423,x8421,x8424,x8425),f815(x8423,x8422,x8424,x8425))
% 59.73/59.68 [843]~E(x8431,x8432)+E(f815(x8433,x8434,x8431,x8435),f815(x8433,x8434,x8432,x8435))
% 59.73/59.68 [844]~E(x8441,x8442)+E(f815(x8443,x8444,x8445,x8441),f815(x8443,x8444,x8445,x8442))
% 59.73/59.68 [845]~E(x8451,x8452)+E(f366(x8451,x8453,x8454,x8455),f366(x8452,x8453,x8454,x8455))
% 59.73/59.68 [846]~E(x8461,x8462)+E(f366(x8463,x8461,x8464,x8465),f366(x8463,x8462,x8464,x8465))
% 59.73/59.68 [847]~E(x8471,x8472)+E(f366(x8473,x8474,x8471,x8475),f366(x8473,x8474,x8472,x8475))
% 59.73/59.68 [848]~E(x8481,x8482)+E(f366(x8483,x8484,x8485,x8481),f366(x8483,x8484,x8485,x8482))
% 59.73/59.68 [849]~E(x8491,x8492)+E(f839(x8491,x8493,x8494,x8495,x8496),f839(x8492,x8493,x8494,x8495,x8496))
% 59.73/59.68 [850]~E(x8501,x8502)+E(f839(x8503,x8501,x8504,x8505,x8506),f839(x8503,x8502,x8504,x8505,x8506))
% 59.73/59.68 [851]~E(x8511,x8512)+E(f839(x8513,x8514,x8511,x8515,x8516),f839(x8513,x8514,x8512,x8515,x8516))
% 59.73/59.68 [852]~E(x8521,x8522)+E(f839(x8523,x8524,x8525,x8521,x8526),f839(x8523,x8524,x8525,x8522,x8526))
% 59.73/59.68 [853]~E(x8531,x8532)+E(f839(x8533,x8534,x8535,x8536,x8531),f839(x8533,x8534,x8535,x8536,x8532))
% 59.73/59.68 [854]~E(x8541,x8542)+E(f653(x8541,x8543,x8544,x8545),f653(x8542,x8543,x8544,x8545))
% 59.73/59.68 [855]~E(x8551,x8552)+E(f653(x8553,x8551,x8554,x8555),f653(x8553,x8552,x8554,x8555))
% 59.73/59.68 [856]~E(x8561,x8562)+E(f653(x8563,x8564,x8561,x8565),f653(x8563,x8564,x8562,x8565))
% 59.73/59.68 [857]~E(x8571,x8572)+E(f653(x8573,x8574,x8575,x8571),f653(x8573,x8574,x8575,x8572))
% 59.73/59.68 [858]~E(x8581,x8582)+E(f502(x8581,x8583,x8584,x8585,x8586,x8587),f502(x8582,x8583,x8584,x8585,x8586,x8587))
% 59.73/59.68 [859]~E(x8591,x8592)+E(f502(x8593,x8591,x8594,x8595,x8596,x8597),f502(x8593,x8592,x8594,x8595,x8596,x8597))
% 59.73/59.68 [860]~E(x8601,x8602)+E(f502(x8603,x8604,x8601,x8605,x8606,x8607),f502(x8603,x8604,x8602,x8605,x8606,x8607))
% 59.73/59.68 [861]~E(x8611,x8612)+E(f502(x8613,x8614,x8615,x8611,x8616,x8617),f502(x8613,x8614,x8615,x8612,x8616,x8617))
% 59.73/59.68 [862]~E(x8621,x8622)+E(f502(x8623,x8624,x8625,x8626,x8621,x8627),f502(x8623,x8624,x8625,x8626,x8622,x8627))
% 59.73/59.68 [863]~E(x8631,x8632)+E(f502(x8633,x8634,x8635,x8636,x8637,x8631),f502(x8633,x8634,x8635,x8636,x8637,x8632))
% 59.73/59.68 [864]~E(x8641,x8642)+E(f823(x8641,x8643,x8644),f823(x8642,x8643,x8644))
% 59.73/59.68 [865]~E(x8651,x8652)+E(f823(x8653,x8651,x8654),f823(x8653,x8652,x8654))
% 59.73/59.68 [866]~E(x8661,x8662)+E(f823(x8663,x8664,x8661),f823(x8663,x8664,x8662))
% 59.73/59.68 [867]~E(x8671,x8672)+E(f870(x8671,x8673,x8674),f870(x8672,x8673,x8674))
% 59.73/59.68 [868]~E(x8681,x8682)+E(f870(x8683,x8681,x8684),f870(x8683,x8682,x8684))
% 59.73/59.68 [869]~E(x8691,x8692)+E(f870(x8693,x8694,x8691),f870(x8693,x8694,x8692))
% 59.73/59.68 [870]~E(x8701,x8702)+E(f229(x8701,x8703),f229(x8702,x8703))
% 59.73/59.68 [871]~E(x8711,x8712)+E(f229(x8713,x8711),f229(x8713,x8712))
% 59.73/59.68 [872]~E(x8721,x8722)+E(f360(x8721),f360(x8722))
% 59.73/59.68 [873]~E(x8731,x8732)+E(f120(x8731,x8733,x8734),f120(x8732,x8733,x8734))
% 59.73/59.68 [874]~E(x8741,x8742)+E(f120(x8743,x8741,x8744),f120(x8743,x8742,x8744))
% 59.73/59.68 [875]~E(x8751,x8752)+E(f120(x8753,x8754,x8751),f120(x8753,x8754,x8752))
% 59.73/59.68 [876]~E(x8761,x8762)+E(f122(x8761,x8763),f122(x8762,x8763))
% 59.73/59.68 [877]~E(x8771,x8772)+E(f122(x8773,x8771),f122(x8773,x8772))
% 59.73/59.68 [878]~E(x8781,x8782)+E(f755(x8781,x8783),f755(x8782,x8783))
% 59.73/59.68 [879]~E(x8791,x8792)+E(f755(x8793,x8791),f755(x8793,x8792))
% 59.73/59.68 [880]~E(x8801,x8802)+E(f636(x8801,x8803,x8804),f636(x8802,x8803,x8804))
% 59.73/59.68 [881]~E(x8811,x8812)+E(f636(x8813,x8811,x8814),f636(x8813,x8812,x8814))
% 59.73/59.68 [882]~E(x8821,x8822)+E(f636(x8823,x8824,x8821),f636(x8823,x8824,x8822))
% 59.73/59.68 [883]~E(x8831,x8832)+E(f57(x8831,x8833,x8834),f57(x8832,x8833,x8834))
% 59.73/59.68 [884]~E(x8841,x8842)+E(f57(x8843,x8841,x8844),f57(x8843,x8842,x8844))
% 59.73/59.68 [885]~E(x8851,x8852)+E(f57(x8853,x8854,x8851),f57(x8853,x8854,x8852))
% 59.73/59.68 [886]~E(x8861,x8862)+E(f623(x8861,x8863,x8864,x8865,x8866),f623(x8862,x8863,x8864,x8865,x8866))
% 59.73/59.68 [887]~E(x8871,x8872)+E(f623(x8873,x8871,x8874,x8875,x8876),f623(x8873,x8872,x8874,x8875,x8876))
% 59.73/59.68 [888]~E(x8881,x8882)+E(f623(x8883,x8884,x8881,x8885,x8886),f623(x8883,x8884,x8882,x8885,x8886))
% 59.73/59.68 [889]~E(x8891,x8892)+E(f623(x8893,x8894,x8895,x8891,x8896),f623(x8893,x8894,x8895,x8892,x8896))
% 59.73/59.68 [890]~E(x8901,x8902)+E(f623(x8903,x8904,x8905,x8906,x8901),f623(x8903,x8904,x8905,x8906,x8902))
% 59.73/59.68 [891]~E(x8911,x8912)+E(f374(x8911,x8913,x8914),f374(x8912,x8913,x8914))
% 59.73/59.68 [892]~E(x8921,x8922)+E(f374(x8923,x8921,x8924),f374(x8923,x8922,x8924))
% 59.73/59.68 [893]~E(x8931,x8932)+E(f374(x8933,x8934,x8931),f374(x8933,x8934,x8932))
% 59.73/59.68 [894]~E(x8941,x8942)+E(f606(x8941,x8943),f606(x8942,x8943))
% 59.73/59.68 [895]~E(x8951,x8952)+E(f606(x8953,x8951),f606(x8953,x8952))
% 59.73/59.68 [896]~E(x8961,x8962)+E(f192(x8961,x8963),f192(x8962,x8963))
% 59.73/59.68 [897]~E(x8971,x8972)+E(f192(x8973,x8971),f192(x8973,x8972))
% 59.73/59.68 [898]~E(x8981,x8982)+E(f498(x8981,x8983,x8984,x8985,x8986),f498(x8982,x8983,x8984,x8985,x8986))
% 59.73/59.68 [899]~E(x8991,x8992)+E(f498(x8993,x8991,x8994,x8995,x8996),f498(x8993,x8992,x8994,x8995,x8996))
% 59.73/59.68 [900]~E(x9001,x9002)+E(f498(x9003,x9004,x9001,x9005,x9006),f498(x9003,x9004,x9002,x9005,x9006))
% 59.73/59.68 [901]~E(x9011,x9012)+E(f498(x9013,x9014,x9015,x9011,x9016),f498(x9013,x9014,x9015,x9012,x9016))
% 59.73/59.68 [902]~E(x9021,x9022)+E(f498(x9023,x9024,x9025,x9026,x9021),f498(x9023,x9024,x9025,x9026,x9022))
% 59.73/59.68 [903]~E(x9031,x9032)+E(f114(x9031,x9033),f114(x9032,x9033))
% 59.73/59.68 [904]~E(x9041,x9042)+E(f114(x9043,x9041),f114(x9043,x9042))
% 59.73/59.68 [905]~E(x9051,x9052)+E(f386(x9051,x9053,x9054),f386(x9052,x9053,x9054))
% 59.73/59.68 [906]~E(x9061,x9062)+E(f386(x9063,x9061,x9064),f386(x9063,x9062,x9064))
% 59.73/59.68 [907]~E(x9071,x9072)+E(f386(x9073,x9074,x9071),f386(x9073,x9074,x9072))
% 59.73/59.68 [908]~E(x9081,x9082)+E(f52(x9081),f52(x9082))
% 59.73/59.68 [909]~E(x9091,x9092)+E(f426(x9091,x9093),f426(x9092,x9093))
% 59.73/59.68 [910]~E(x9101,x9102)+E(f426(x9103,x9101),f426(x9103,x9102))
% 59.73/59.68 [911]~E(x9111,x9112)+E(f186(x9111),f186(x9112))
% 59.73/59.68 [912]~E(x9121,x9122)+E(f123(x9121),f123(x9122))
% 59.73/59.68 [913]~E(x9131,x9132)+E(f274(x9131,x9133),f274(x9132,x9133))
% 59.73/59.68 [914]~E(x9141,x9142)+E(f274(x9143,x9141),f274(x9143,x9142))
% 59.73/59.68 [915]~E(x9151,x9152)+E(f775(x9151,x9153,x9154,x9155,x9156,x9157,x9158),f775(x9152,x9153,x9154,x9155,x9156,x9157,x9158))
% 59.73/59.68 [916]~E(x9161,x9162)+E(f775(x9163,x9161,x9164,x9165,x9166,x9167,x9168),f775(x9163,x9162,x9164,x9165,x9166,x9167,x9168))
% 59.73/59.68 [917]~E(x9171,x9172)+E(f775(x9173,x9174,x9171,x9175,x9176,x9177,x9178),f775(x9173,x9174,x9172,x9175,x9176,x9177,x9178))
% 59.73/59.68 [918]~E(x9181,x9182)+E(f775(x9183,x9184,x9185,x9181,x9186,x9187,x9188),f775(x9183,x9184,x9185,x9182,x9186,x9187,x9188))
% 59.73/59.68 [919]~E(x9191,x9192)+E(f775(x9193,x9194,x9195,x9196,x9191,x9197,x9198),f775(x9193,x9194,x9195,x9196,x9192,x9197,x9198))
% 59.73/59.68 [920]~E(x9201,x9202)+E(f775(x9203,x9204,x9205,x9206,x9207,x9201,x9208),f775(x9203,x9204,x9205,x9206,x9207,x9202,x9208))
% 59.73/59.68 [921]~E(x9211,x9212)+E(f775(x9213,x9214,x9215,x9216,x9217,x9218,x9211),f775(x9213,x9214,x9215,x9216,x9217,x9218,x9212))
% 59.73/59.68 [922]~E(x9221,x9222)+E(f413(x9221,x9223),f413(x9222,x9223))
% 59.73/59.68 [923]~E(x9231,x9232)+E(f413(x9233,x9231),f413(x9233,x9232))
% 59.73/59.68 [924]~E(x9241,x9242)+E(f125(x9241,x9243),f125(x9242,x9243))
% 59.73/59.68 [925]~E(x9251,x9252)+E(f125(x9253,x9251),f125(x9253,x9252))
% 59.73/59.68 [926]~E(x9261,x9262)+E(f731(x9261,x9263,x9264),f731(x9262,x9263,x9264))
% 59.73/59.68 [927]~E(x9271,x9272)+E(f731(x9273,x9271,x9274),f731(x9273,x9272,x9274))
% 59.73/59.68 [928]~E(x9281,x9282)+E(f731(x9283,x9284,x9281),f731(x9283,x9284,x9282))
% 59.73/59.68 [929]~E(x9291,x9292)+E(f482(x9291,x9293,x9294,x9295),f482(x9292,x9293,x9294,x9295))
% 59.73/59.68 [930]~E(x9301,x9302)+E(f482(x9303,x9301,x9304,x9305),f482(x9303,x9302,x9304,x9305))
% 59.73/59.68 [931]~E(x9311,x9312)+E(f482(x9313,x9314,x9311,x9315),f482(x9313,x9314,x9312,x9315))
% 59.73/59.68 [932]~E(x9321,x9322)+E(f482(x9323,x9324,x9325,x9321),f482(x9323,x9324,x9325,x9322))
% 59.73/59.68 [933]~E(x9331,x9332)+E(f353(x9331,x9333),f353(x9332,x9333))
% 59.73/59.68 [934]~E(x9341,x9342)+E(f353(x9343,x9341),f353(x9343,x9342))
% 59.73/59.68 [935]~E(x9351,x9352)+E(f585(x9351,x9353,x9354),f585(x9352,x9353,x9354))
% 59.73/59.68 [936]~E(x9361,x9362)+E(f585(x9363,x9361,x9364),f585(x9363,x9362,x9364))
% 59.73/59.68 [937]~E(x9371,x9372)+E(f585(x9373,x9374,x9371),f585(x9373,x9374,x9372))
% 59.73/59.68 [938]~E(x9381,x9382)+E(f532(x9381,x9383,x9384),f532(x9382,x9383,x9384))
% 59.73/59.68 [939]~E(x9391,x9392)+E(f532(x9393,x9391,x9394),f532(x9393,x9392,x9394))
% 59.73/59.68 [940]~E(x9401,x9402)+E(f532(x9403,x9404,x9401),f532(x9403,x9404,x9402))
% 59.73/59.68 [941]~E(x9411,x9412)+E(f383(x9411,x9413,x9414),f383(x9412,x9413,x9414))
% 59.73/59.68 [942]~E(x9421,x9422)+E(f383(x9423,x9421,x9424),f383(x9423,x9422,x9424))
% 59.73/59.68 [943]~E(x9431,x9432)+E(f383(x9433,x9434,x9431),f383(x9433,x9434,x9432))
% 59.73/59.68 [944]~E(x9441,x9442)+E(f760(x9441,x9443,x9444,x9445),f760(x9442,x9443,x9444,x9445))
% 59.73/59.68 [945]~E(x9451,x9452)+E(f760(x9453,x9451,x9454,x9455),f760(x9453,x9452,x9454,x9455))
% 59.73/59.68 [946]~E(x9461,x9462)+E(f760(x9463,x9464,x9461,x9465),f760(x9463,x9464,x9462,x9465))
% 59.73/59.68 [947]~E(x9471,x9472)+E(f760(x9473,x9474,x9475,x9471),f760(x9473,x9474,x9475,x9472))
% 59.73/59.68 [948]~E(x9481,x9482)+E(f375(x9481,x9483,x9484),f375(x9482,x9483,x9484))
% 59.73/59.68 [949]~E(x9491,x9492)+E(f375(x9493,x9491,x9494),f375(x9493,x9492,x9494))
% 59.73/59.68 [950]~E(x9501,x9502)+E(f375(x9503,x9504,x9501),f375(x9503,x9504,x9502))
% 59.73/59.68 [951]~E(x9511,x9512)+E(f520(x9511,x9513,x9514,x9515,x9516),f520(x9512,x9513,x9514,x9515,x9516))
% 59.73/59.68 [952]~E(x9521,x9522)+E(f520(x9523,x9521,x9524,x9525,x9526),f520(x9523,x9522,x9524,x9525,x9526))
% 59.73/59.68 [953]~E(x9531,x9532)+E(f520(x9533,x9534,x9531,x9535,x9536),f520(x9533,x9534,x9532,x9535,x9536))
% 59.73/59.68 [954]~E(x9541,x9542)+E(f520(x9543,x9544,x9545,x9541,x9546),f520(x9543,x9544,x9545,x9542,x9546))
% 59.73/59.68 [955]~E(x9551,x9552)+E(f520(x9553,x9554,x9555,x9556,x9551),f520(x9553,x9554,x9555,x9556,x9552))
% 59.73/59.68 [956]~E(x9561,x9562)+E(f594(x9561,x9563,x9564),f594(x9562,x9563,x9564))
% 59.73/59.68 [957]~E(x9571,x9572)+E(f594(x9573,x9571,x9574),f594(x9573,x9572,x9574))
% 59.73/59.68 [958]~E(x9581,x9582)+E(f594(x9583,x9584,x9581),f594(x9583,x9584,x9582))
% 59.73/59.68 [959]~E(x9591,x9592)+E(f351(x9591,x9593,x9594),f351(x9592,x9593,x9594))
% 59.73/59.68 [960]~E(x9601,x9602)+E(f351(x9603,x9601,x9604),f351(x9603,x9602,x9604))
% 59.73/59.68 [961]~E(x9611,x9612)+E(f351(x9613,x9614,x9611),f351(x9613,x9614,x9612))
% 59.73/59.68 [962]~E(x9621,x9622)+E(f849(x9621),f849(x9622))
% 59.73/59.68 [963]~E(x9631,x9632)+E(f160(x9631,x9633,x9634),f160(x9632,x9633,x9634))
% 59.73/59.68 [964]~E(x9641,x9642)+E(f160(x9643,x9641,x9644),f160(x9643,x9642,x9644))
% 59.73/59.68 [965]~E(x9651,x9652)+E(f160(x9653,x9654,x9651),f160(x9653,x9654,x9652))
% 59.73/59.68 [966]~E(x9661,x9662)+E(f138(x9661,x9663),f138(x9662,x9663))
% 59.73/59.68 [967]~E(x9671,x9672)+E(f138(x9673,x9671),f138(x9673,x9672))
% 59.73/59.68 [968]~E(x9681,x9682)+E(f515(x9681,x9683,x9684,x9685),f515(x9682,x9683,x9684,x9685))
% 59.73/59.68 [969]~E(x9691,x9692)+E(f515(x9693,x9691,x9694,x9695),f515(x9693,x9692,x9694,x9695))
% 59.73/59.68 [970]~E(x9701,x9702)+E(f515(x9703,x9704,x9701,x9705),f515(x9703,x9704,x9702,x9705))
% 59.73/59.68 [971]~E(x9711,x9712)+E(f515(x9713,x9714,x9715,x9711),f515(x9713,x9714,x9715,x9712))
% 59.73/59.68 [972]~E(x9721,x9722)+E(f763(x9721,x9723,x9724),f763(x9722,x9723,x9724))
% 59.73/59.68 [973]~E(x9731,x9732)+E(f763(x9733,x9731,x9734),f763(x9733,x9732,x9734))
% 59.73/59.68 [974]~E(x9741,x9742)+E(f763(x9743,x9744,x9741),f763(x9743,x9744,x9742))
% 59.73/59.68 [975]~E(x9751,x9752)+E(f430(x9751,x9753,x9754),f430(x9752,x9753,x9754))
% 59.73/59.68 [976]~E(x9761,x9762)+E(f430(x9763,x9761,x9764),f430(x9763,x9762,x9764))
% 59.73/59.68 [977]~E(x9771,x9772)+E(f430(x9773,x9774,x9771),f430(x9773,x9774,x9772))
% 59.73/59.68 [978]~E(x9781,x9782)+E(f528(x9781,x9783,x9784,x9785,x9786),f528(x9782,x9783,x9784,x9785,x9786))
% 59.73/59.68 [979]~E(x9791,x9792)+E(f528(x9793,x9791,x9794,x9795,x9796),f528(x9793,x9792,x9794,x9795,x9796))
% 59.73/59.68 [980]~E(x9801,x9802)+E(f528(x9803,x9804,x9801,x9805,x9806),f528(x9803,x9804,x9802,x9805,x9806))
% 59.73/59.68 [981]~E(x9811,x9812)+E(f528(x9813,x9814,x9815,x9811,x9816),f528(x9813,x9814,x9815,x9812,x9816))
% 59.73/59.68 [982]~E(x9821,x9822)+E(f528(x9823,x9824,x9825,x9826,x9821),f528(x9823,x9824,x9825,x9826,x9822))
% 59.73/59.68 [983]~E(x9831,x9832)+E(f706(x9831,x9833,x9834,x9835),f706(x9832,x9833,x9834,x9835))
% 59.73/59.68 [984]~E(x9841,x9842)+E(f706(x9843,x9841,x9844,x9845),f706(x9843,x9842,x9844,x9845))
% 59.73/59.68 [985]~E(x9851,x9852)+E(f706(x9853,x9854,x9851,x9855),f706(x9853,x9854,x9852,x9855))
% 59.73/59.68 [986]~E(x9861,x9862)+E(f706(x9863,x9864,x9865,x9861),f706(x9863,x9864,x9865,x9862))
% 59.73/59.68 [987]~E(x9871,x9872)+E(f686(x9871,x9873,x9874),f686(x9872,x9873,x9874))
% 59.73/59.68 [988]~E(x9881,x9882)+E(f686(x9883,x9881,x9884),f686(x9883,x9882,x9884))
% 59.73/59.68 [989]~E(x9891,x9892)+E(f686(x9893,x9894,x9891),f686(x9893,x9894,x9892))
% 59.73/59.68 [990]~E(x9901,x9902)+E(f499(x9901,x9903,x9904,x9905,x9906),f499(x9902,x9903,x9904,x9905,x9906))
% 59.73/59.68 [991]~E(x9911,x9912)+E(f499(x9913,x9911,x9914,x9915,x9916),f499(x9913,x9912,x9914,x9915,x9916))
% 59.73/59.68 [992]~E(x9921,x9922)+E(f499(x9923,x9924,x9921,x9925,x9926),f499(x9923,x9924,x9922,x9925,x9926))
% 59.73/59.68 [993]~E(x9931,x9932)+E(f499(x9933,x9934,x9935,x9931,x9936),f499(x9933,x9934,x9935,x9932,x9936))
% 59.73/59.68 [994]~E(x9941,x9942)+E(f499(x9943,x9944,x9945,x9946,x9941),f499(x9943,x9944,x9945,x9946,x9942))
% 59.73/59.68 [995]~E(x9951,x9952)+E(f674(x9951,x9953),f674(x9952,x9953))
% 59.73/59.68 [996]~E(x9961,x9962)+E(f674(x9963,x9961),f674(x9963,x9962))
% 59.73/59.68 [997]~E(x9971,x9972)+E(f689(x9971,x9973,x9974),f689(x9972,x9973,x9974))
% 59.73/59.68 [998]~E(x9981,x9982)+E(f689(x9983,x9981,x9984),f689(x9983,x9982,x9984))
% 59.73/59.68 [999]~E(x9991,x9992)+E(f689(x9993,x9994,x9991),f689(x9993,x9994,x9992))
% 59.73/59.68 [1000]~E(x10001,x10002)+E(f493(x10001,x10003,x10004,x10005,x10006),f493(x10002,x10003,x10004,x10005,x10006))
% 59.73/59.68 [1001]~E(x10011,x10012)+E(f493(x10013,x10011,x10014,x10015,x10016),f493(x10013,x10012,x10014,x10015,x10016))
% 59.73/59.68 [1002]~E(x10021,x10022)+E(f493(x10023,x10024,x10021,x10025,x10026),f493(x10023,x10024,x10022,x10025,x10026))
% 59.73/59.68 [1003]~E(x10031,x10032)+E(f493(x10033,x10034,x10035,x10031,x10036),f493(x10033,x10034,x10035,x10032,x10036))
% 59.73/59.68 [1004]~E(x10041,x10042)+E(f493(x10043,x10044,x10045,x10046,x10041),f493(x10043,x10044,x10045,x10046,x10042))
% 59.73/59.68 [1005]~E(x10051,x10052)+E(f690(x10051,x10053),f690(x10052,x10053))
% 59.73/59.68 [1006]~E(x10061,x10062)+E(f690(x10063,x10061),f690(x10063,x10062))
% 59.73/59.68 [1007]~E(x10071,x10072)+E(f817(x10071,x10073,x10074,x10075),f817(x10072,x10073,x10074,x10075))
% 59.73/59.68 [1008]~E(x10081,x10082)+E(f817(x10083,x10081,x10084,x10085),f817(x10083,x10082,x10084,x10085))
% 59.73/59.68 [1009]~E(x10091,x10092)+E(f817(x10093,x10094,x10091,x10095),f817(x10093,x10094,x10092,x10095))
% 59.73/59.68 [1010]~E(x10101,x10102)+E(f817(x10103,x10104,x10105,x10101),f817(x10103,x10104,x10105,x10102))
% 59.73/59.68 [1011]~E(x10111,x10112)+E(f756(x10111,x10113),f756(x10112,x10113))
% 59.73/59.68 [1012]~E(x10121,x10122)+E(f756(x10123,x10121),f756(x10123,x10122))
% 59.73/59.68 [1013]~E(x10131,x10132)+E(f425(x10131,x10133),f425(x10132,x10133))
% 59.73/59.68 [1014]~E(x10141,x10142)+E(f425(x10143,x10141),f425(x10143,x10142))
% 59.73/59.68 [1015]~E(x10151,x10152)+E(f494(x10151,x10153,x10154,x10155,x10156,x10157),f494(x10152,x10153,x10154,x10155,x10156,x10157))
% 59.73/59.68 [1016]~E(x10161,x10162)+E(f494(x10163,x10161,x10164,x10165,x10166,x10167),f494(x10163,x10162,x10164,x10165,x10166,x10167))
% 59.73/59.68 [1017]~E(x10171,x10172)+E(f494(x10173,x10174,x10171,x10175,x10176,x10177),f494(x10173,x10174,x10172,x10175,x10176,x10177))
% 59.73/59.68 [1018]~E(x10181,x10182)+E(f494(x10183,x10184,x10185,x10181,x10186,x10187),f494(x10183,x10184,x10185,x10182,x10186,x10187))
% 59.73/59.68 [1019]~E(x10191,x10192)+E(f494(x10193,x10194,x10195,x10196,x10191,x10197),f494(x10193,x10194,x10195,x10196,x10192,x10197))
% 59.73/59.68 [1020]~E(x10201,x10202)+E(f494(x10203,x10204,x10205,x10206,x10207,x10201),f494(x10203,x10204,x10205,x10206,x10207,x10202))
% 59.73/59.68 [1021]~E(x10211,x10212)+E(f280(x10211,x10213,x10214),f280(x10212,x10213,x10214))
% 59.73/59.68 [1022]~E(x10221,x10222)+E(f280(x10223,x10221,x10224),f280(x10223,x10222,x10224))
% 59.73/59.68 [1023]~E(x10231,x10232)+E(f280(x10233,x10234,x10231),f280(x10233,x10234,x10232))
% 59.73/59.68 [1024]~E(x10241,x10242)+E(f168(x10241,x10243,x10244),f168(x10242,x10243,x10244))
% 59.73/59.68 [1025]~E(x10251,x10252)+E(f168(x10253,x10251,x10254),f168(x10253,x10252,x10254))
% 59.73/59.68 [1026]~E(x10261,x10262)+E(f168(x10263,x10264,x10261),f168(x10263,x10264,x10262))
% 59.73/59.68 [1027]~E(x10271,x10272)+E(f744(x10271,x10273,x10274),f744(x10272,x10273,x10274))
% 59.73/59.68 [1028]~E(x10281,x10282)+E(f744(x10283,x10281,x10284),f744(x10283,x10282,x10284))
% 59.73/59.68 [1029]~E(x10291,x10292)+E(f744(x10293,x10294,x10291),f744(x10293,x10294,x10292))
% 59.73/59.68 [1030]~E(x10301,x10302)+E(f802(x10301,x10303,x10304,x10305),f802(x10302,x10303,x10304,x10305))
% 59.73/59.68 [1031]~E(x10311,x10312)+E(f802(x10313,x10311,x10314,x10315),f802(x10313,x10312,x10314,x10315))
% 59.73/59.68 [1032]~E(x10321,x10322)+E(f802(x10323,x10324,x10321,x10325),f802(x10323,x10324,x10322,x10325))
% 59.73/59.68 [1033]~E(x10331,x10332)+E(f802(x10333,x10334,x10335,x10331),f802(x10333,x10334,x10335,x10332))
% 59.73/59.68 [1034]~E(x10341,x10342)+E(f440(x10341,x10343),f440(x10342,x10343))
% 59.73/59.68 [1035]~E(x10351,x10352)+E(f440(x10353,x10351),f440(x10353,x10352))
% 59.73/59.68 [1036]~E(x10361,x10362)+E(f827(x10361,x10363,x10364),f827(x10362,x10363,x10364))
% 59.73/59.68 [1037]~E(x10371,x10372)+E(f827(x10373,x10371,x10374),f827(x10373,x10372,x10374))
% 59.73/59.68 [1038]~E(x10381,x10382)+E(f827(x10383,x10384,x10381),f827(x10383,x10384,x10382))
% 59.73/59.68 [1039]~E(x10391,x10392)+E(f301(x10391,x10393,x10394,x10395),f301(x10392,x10393,x10394,x10395))
% 59.73/59.68 [1040]~E(x10401,x10402)+E(f301(x10403,x10401,x10404,x10405),f301(x10403,x10402,x10404,x10405))
% 59.73/59.68 [1041]~E(x10411,x10412)+E(f301(x10413,x10414,x10411,x10415),f301(x10413,x10414,x10412,x10415))
% 59.73/59.68 [1042]~E(x10421,x10422)+E(f301(x10423,x10424,x10425,x10421),f301(x10423,x10424,x10425,x10422))
% 59.73/59.68 [1043]~E(x10431,x10432)+E(f484(x10431,x10433,x10434,x10435,x10436),f484(x10432,x10433,x10434,x10435,x10436))
% 59.73/59.68 [1044]~E(x10441,x10442)+E(f484(x10443,x10441,x10444,x10445,x10446),f484(x10443,x10442,x10444,x10445,x10446))
% 59.73/59.68 [1045]~E(x10451,x10452)+E(f484(x10453,x10454,x10451,x10455,x10456),f484(x10453,x10454,x10452,x10455,x10456))
% 59.73/59.68 [1046]~E(x10461,x10462)+E(f484(x10463,x10464,x10465,x10461,x10466),f484(x10463,x10464,x10465,x10462,x10466))
% 59.73/59.68 [1047]~E(x10471,x10472)+E(f484(x10473,x10474,x10475,x10476,x10471),f484(x10473,x10474,x10475,x10476,x10472))
% 59.73/59.68 [1048]~E(x10481,x10482)+E(f372(x10481,x10483,x10484),f372(x10482,x10483,x10484))
% 59.73/59.68 [1049]~E(x10491,x10492)+E(f372(x10493,x10491,x10494),f372(x10493,x10492,x10494))
% 59.73/59.68 [1050]~E(x10501,x10502)+E(f372(x10503,x10504,x10501),f372(x10503,x10504,x10502))
% 59.73/59.68 [1051]~E(x10511,x10512)+E(f133(x10511,x10513,x10514),f133(x10512,x10513,x10514))
% 59.73/59.68 [1052]~E(x10521,x10522)+E(f133(x10523,x10521,x10524),f133(x10523,x10522,x10524))
% 59.73/59.68 [1053]~E(x10531,x10532)+E(f133(x10533,x10534,x10531),f133(x10533,x10534,x10532))
% 59.73/59.68 [1054]~E(x10541,x10542)+E(f714(x10541,x10543,x10544,x10545),f714(x10542,x10543,x10544,x10545))
% 59.73/59.68 [1055]~E(x10551,x10552)+E(f714(x10553,x10551,x10554,x10555),f714(x10553,x10552,x10554,x10555))
% 59.73/59.68 [1056]~E(x10561,x10562)+E(f714(x10563,x10564,x10561,x10565),f714(x10563,x10564,x10562,x10565))
% 59.73/59.68 [1057]~E(x10571,x10572)+E(f714(x10573,x10574,x10575,x10571),f714(x10573,x10574,x10575,x10572))
% 59.73/59.68 [1058]~E(x10581,x10582)+E(f365(x10581,x10583,x10584),f365(x10582,x10583,x10584))
% 59.73/59.68 [1059]~E(x10591,x10592)+E(f365(x10593,x10591,x10594),f365(x10593,x10592,x10594))
% 59.73/59.68 [1060]~E(x10601,x10602)+E(f365(x10603,x10604,x10601),f365(x10603,x10604,x10602))
% 59.73/59.68 [1061]~E(x10611,x10612)+E(f871(x10611,x10613),f871(x10612,x10613))
% 59.73/59.68 [1062]~E(x10621,x10622)+E(f871(x10623,x10621),f871(x10623,x10622))
% 59.73/59.68 [1063]~E(x10631,x10632)+E(f198(x10631,x10633,x10634,x10635),f198(x10632,x10633,x10634,x10635))
% 59.73/59.68 [1064]~E(x10641,x10642)+E(f198(x10643,x10641,x10644,x10645),f198(x10643,x10642,x10644,x10645))
% 59.73/59.68 [1065]~E(x10651,x10652)+E(f198(x10653,x10654,x10651,x10655),f198(x10653,x10654,x10652,x10655))
% 59.73/59.68 [1066]~E(x10661,x10662)+E(f198(x10663,x10664,x10665,x10661),f198(x10663,x10664,x10665,x10662))
% 59.73/59.68 [1067]~E(x10671,x10672)+E(f546(x10671,x10673,x10674),f546(x10672,x10673,x10674))
% 59.73/59.68 [1068]~E(x10681,x10682)+E(f546(x10683,x10681,x10684),f546(x10683,x10682,x10684))
% 59.73/59.68 [1069]~E(x10691,x10692)+E(f546(x10693,x10694,x10691),f546(x10693,x10694,x10692))
% 59.73/59.68 [1070]~E(x10701,x10702)+E(f795(x10701,x10703,x10704),f795(x10702,x10703,x10704))
% 59.73/59.68 [1071]~E(x10711,x10712)+E(f795(x10713,x10711,x10714),f795(x10713,x10712,x10714))
% 59.73/59.68 [1072]~E(x10721,x10722)+E(f795(x10723,x10724,x10721),f795(x10723,x10724,x10722))
% 59.73/59.68 [1073]~E(x10731,x10732)+E(f69(x10731,x10733),f69(x10732,x10733))
% 59.73/59.68 [1074]~E(x10741,x10742)+E(f69(x10743,x10741),f69(x10743,x10742))
% 59.73/59.68 [1075]~E(x10751,x10752)+E(f483(x10751,x10753,x10754,x10755,x10756),f483(x10752,x10753,x10754,x10755,x10756))
% 59.73/59.68 [1076]~E(x10761,x10762)+E(f483(x10763,x10761,x10764,x10765,x10766),f483(x10763,x10762,x10764,x10765,x10766))
% 59.73/59.68 [1077]~E(x10771,x10772)+E(f483(x10773,x10774,x10771,x10775,x10776),f483(x10773,x10774,x10772,x10775,x10776))
% 59.73/59.68 [1078]~E(x10781,x10782)+E(f483(x10783,x10784,x10785,x10781,x10786),f483(x10783,x10784,x10785,x10782,x10786))
% 59.73/59.68 [1079]~E(x10791,x10792)+E(f483(x10793,x10794,x10795,x10796,x10791),f483(x10793,x10794,x10795,x10796,x10792))
% 59.73/59.68 [1080]~E(x10801,x10802)+E(f451(x10801,x10803),f451(x10802,x10803))
% 59.73/59.68 [1081]~E(x10811,x10812)+E(f451(x10813,x10811),f451(x10813,x10812))
% 59.73/59.68 [1082]~E(x10821,x10822)+E(f633(x10821,x10823,x10824,x10825,x10826),f633(x10822,x10823,x10824,x10825,x10826))
% 59.73/59.68 [1083]~E(x10831,x10832)+E(f633(x10833,x10831,x10834,x10835,x10836),f633(x10833,x10832,x10834,x10835,x10836))
% 59.73/59.68 [1084]~E(x10841,x10842)+E(f633(x10843,x10844,x10841,x10845,x10846),f633(x10843,x10844,x10842,x10845,x10846))
% 59.73/59.68 [1085]~E(x10851,x10852)+E(f633(x10853,x10854,x10855,x10851,x10856),f633(x10853,x10854,x10855,x10852,x10856))
% 59.73/59.68 [1086]~E(x10861,x10862)+E(f633(x10863,x10864,x10865,x10866,x10861),f633(x10863,x10864,x10865,x10866,x10862))
% 59.73/59.68 [1087]~E(x10871,x10872)+E(f637(x10871,x10873,x10874),f637(x10872,x10873,x10874))
% 59.73/59.68 [1088]~E(x10881,x10882)+E(f637(x10883,x10881,x10884),f637(x10883,x10882,x10884))
% 59.73/59.68 [1089]~E(x10891,x10892)+E(f637(x10893,x10894,x10891),f637(x10893,x10894,x10892))
% 59.73/59.68 [1090]~E(x10901,x10902)+E(f255(x10901,x10903,x10904),f255(x10902,x10903,x10904))
% 59.73/59.68 [1091]~E(x10911,x10912)+E(f255(x10913,x10911,x10914),f255(x10913,x10912,x10914))
% 59.73/59.68 [1092]~E(x10921,x10922)+E(f255(x10923,x10924,x10921),f255(x10923,x10924,x10922))
% 59.73/59.68 [1093]~E(x10931,x10932)+E(f785(x10931,x10933,x10934),f785(x10932,x10933,x10934))
% 59.73/59.68 [1094]~E(x10941,x10942)+E(f785(x10943,x10941,x10944),f785(x10943,x10942,x10944))
% 59.73/59.68 [1095]~E(x10951,x10952)+E(f785(x10953,x10954,x10951),f785(x10953,x10954,x10952))
% 59.73/59.68 [1096]~E(x10961,x10962)+E(f591(x10961,x10963,x10964,x10965,x10966,x10967,x10968,x10969),f591(x10962,x10963,x10964,x10965,x10966,x10967,x10968,x10969))
% 59.73/59.68 [1097]~E(x10971,x10972)+E(f591(x10973,x10971,x10974,x10975,x10976,x10977,x10978,x10979),f591(x10973,x10972,x10974,x10975,x10976,x10977,x10978,x10979))
% 59.73/59.68 [1098]~E(x10981,x10982)+E(f591(x10983,x10984,x10981,x10985,x10986,x10987,x10988,x10989),f591(x10983,x10984,x10982,x10985,x10986,x10987,x10988,x10989))
% 59.73/59.68 [1099]~E(x10991,x10992)+E(f591(x10993,x10994,x10995,x10991,x10996,x10997,x10998,x10999),f591(x10993,x10994,x10995,x10992,x10996,x10997,x10998,x10999))
% 59.73/59.68 [1100]~E(x11001,x11002)+E(f591(x11003,x11004,x11005,x11006,x11001,x11007,x11008,x11009),f591(x11003,x11004,x11005,x11006,x11002,x11007,x11008,x11009))
% 59.73/59.68 [1101]~E(x11011,x11012)+E(f591(x11013,x11014,x11015,x11016,x11017,x11011,x11018,x11019),f591(x11013,x11014,x11015,x11016,x11017,x11012,x11018,x11019))
% 59.73/59.68 [1102]~E(x11021,x11022)+E(f591(x11023,x11024,x11025,x11026,x11027,x11028,x11021,x11029),f591(x11023,x11024,x11025,x11026,x11027,x11028,x11022,x11029))
% 59.73/59.68 [1103]~E(x11031,x11032)+E(f591(x11033,x11034,x11035,x11036,x11037,x11038,x11039,x11031),f591(x11033,x11034,x11035,x11036,x11037,x11038,x11039,x11032))
% 59.73/59.68 [1104]~E(x11041,x11042)+E(f441(x11041,x11043,x11044),f441(x11042,x11043,x11044))
% 59.73/59.68 [1105]~E(x11051,x11052)+E(f441(x11053,x11051,x11054),f441(x11053,x11052,x11054))
% 59.73/59.68 [1106]~E(x11061,x11062)+E(f441(x11063,x11064,x11061),f441(x11063,x11064,x11062))
% 59.73/59.68 [1107]~E(x11071,x11072)+E(f458(x11071,x11073,x11074,x11075),f458(x11072,x11073,x11074,x11075))
% 59.73/59.68 [1108]~E(x11081,x11082)+E(f458(x11083,x11081,x11084,x11085),f458(x11083,x11082,x11084,x11085))
% 59.73/59.68 [1109]~E(x11091,x11092)+E(f458(x11093,x11094,x11091,x11095),f458(x11093,x11094,x11092,x11095))
% 59.73/59.68 [1110]~E(x11101,x11102)+E(f458(x11103,x11104,x11105,x11101),f458(x11103,x11104,x11105,x11102))
% 59.73/59.68 [1111]~E(x11111,x11112)+E(f352(x11111,x11113,x11114,x11115,x11116),f352(x11112,x11113,x11114,x11115,x11116))
% 59.73/59.68 [1112]~E(x11121,x11122)+E(f352(x11123,x11121,x11124,x11125,x11126),f352(x11123,x11122,x11124,x11125,x11126))
% 59.73/59.68 [1113]~E(x11131,x11132)+E(f352(x11133,x11134,x11131,x11135,x11136),f352(x11133,x11134,x11132,x11135,x11136))
% 59.73/59.68 [1114]~E(x11141,x11142)+E(f352(x11143,x11144,x11145,x11141,x11146),f352(x11143,x11144,x11145,x11142,x11146))
% 59.73/59.68 [1115]~E(x11151,x11152)+E(f352(x11153,x11154,x11155,x11156,x11151),f352(x11153,x11154,x11155,x11156,x11152))
% 59.73/59.68 [1116]~E(x11161,x11162)+E(f709(x11161,x11163,x11164,x11165,x11166),f709(x11162,x11163,x11164,x11165,x11166))
% 59.73/59.68 [1117]~E(x11171,x11172)+E(f709(x11173,x11171,x11174,x11175,x11176),f709(x11173,x11172,x11174,x11175,x11176))
% 59.73/59.68 [1118]~E(x11181,x11182)+E(f709(x11183,x11184,x11181,x11185,x11186),f709(x11183,x11184,x11182,x11185,x11186))
% 59.73/59.68 [1119]~E(x11191,x11192)+E(f709(x11193,x11194,x11195,x11191,x11196),f709(x11193,x11194,x11195,x11192,x11196))
% 59.73/59.68 [1120]~E(x11201,x11202)+E(f709(x11203,x11204,x11205,x11206,x11201),f709(x11203,x11204,x11205,x11206,x11202))
% 59.73/59.68 [1121]~E(x11211,x11212)+E(f663(x11211,x11213,x11214,x11215,x11216,x11217),f663(x11212,x11213,x11214,x11215,x11216,x11217))
% 59.73/59.68 [1122]~E(x11221,x11222)+E(f663(x11223,x11221,x11224,x11225,x11226,x11227),f663(x11223,x11222,x11224,x11225,x11226,x11227))
% 59.73/59.68 [1123]~E(x11231,x11232)+E(f663(x11233,x11234,x11231,x11235,x11236,x11237),f663(x11233,x11234,x11232,x11235,x11236,x11237))
% 59.73/59.68 [1124]~E(x11241,x11242)+E(f663(x11243,x11244,x11245,x11241,x11246,x11247),f663(x11243,x11244,x11245,x11242,x11246,x11247))
% 59.73/59.68 [1125]~E(x11251,x11252)+E(f663(x11253,x11254,x11255,x11256,x11251,x11257),f663(x11253,x11254,x11255,x11256,x11252,x11257))
% 59.73/59.68 [1126]~E(x11261,x11262)+E(f663(x11263,x11264,x11265,x11266,x11267,x11261),f663(x11263,x11264,x11265,x11266,x11267,x11262))
% 59.73/59.68 [1127]~E(x11271,x11272)+E(f747(x11271,x11273,x11274,x11275,x11276),f747(x11272,x11273,x11274,x11275,x11276))
% 59.73/59.68 [1128]~E(x11281,x11282)+E(f747(x11283,x11281,x11284,x11285,x11286),f747(x11283,x11282,x11284,x11285,x11286))
% 59.73/59.68 [1129]~E(x11291,x11292)+E(f747(x11293,x11294,x11291,x11295,x11296),f747(x11293,x11294,x11292,x11295,x11296))
% 59.73/59.68 [1130]~E(x11301,x11302)+E(f747(x11303,x11304,x11305,x11301,x11306),f747(x11303,x11304,x11305,x11302,x11306))
% 59.73/59.68 [1131]~E(x11311,x11312)+E(f747(x11313,x11314,x11315,x11316,x11311),f747(x11313,x11314,x11315,x11316,x11312))
% 59.73/59.68 [1132]~E(x11321,x11322)+E(f373(x11321,x11323,x11324),f373(x11322,x11323,x11324))
% 59.73/59.68 [1133]~E(x11331,x11332)+E(f373(x11333,x11331,x11334),f373(x11333,x11332,x11334))
% 59.73/59.68 [1134]~E(x11341,x11342)+E(f373(x11343,x11344,x11341),f373(x11343,x11344,x11342))
% 59.73/59.68 [1135]~E(x11351,x11352)+E(f675(x11351,x11353,x11354),f675(x11352,x11353,x11354))
% 59.73/59.68 [1136]~E(x11361,x11362)+E(f675(x11363,x11361,x11364),f675(x11363,x11362,x11364))
% 59.73/59.68 [1137]~E(x11371,x11372)+E(f675(x11373,x11374,x11371),f675(x11373,x11374,x11372))
% 59.73/59.68 [1138]~E(x11381,x11382)+E(f684(x11381,x11383,x11384),f684(x11382,x11383,x11384))
% 59.73/59.68 [1139]~E(x11391,x11392)+E(f684(x11393,x11391,x11394),f684(x11393,x11392,x11394))
% 59.73/59.68 [1140]~E(x11401,x11402)+E(f684(x11403,x11404,x11401),f684(x11403,x11404,x11402))
% 59.73/59.68 [1141]~E(x11411,x11412)+E(f427(x11411,x11413),f427(x11412,x11413))
% 59.73/59.68 [1142]~E(x11421,x11422)+E(f427(x11423,x11421),f427(x11423,x11422))
% 59.73/59.68 [1143]~E(x11431,x11432)+E(f431(x11431,x11433,x11434),f431(x11432,x11433,x11434))
% 59.73/59.68 [1144]~E(x11441,x11442)+E(f431(x11443,x11441,x11444),f431(x11443,x11442,x11444))
% 59.73/59.68 [1145]~E(x11451,x11452)+E(f431(x11453,x11454,x11451),f431(x11453,x11454,x11452))
% 59.73/59.68 [1146]~E(x11461,x11462)+E(f841(x11461,x11463,x11464,x11465,x11466,x11467,x11468),f841(x11462,x11463,x11464,x11465,x11466,x11467,x11468))
% 59.73/59.68 [1147]~E(x11471,x11472)+E(f841(x11473,x11471,x11474,x11475,x11476,x11477,x11478),f841(x11473,x11472,x11474,x11475,x11476,x11477,x11478))
% 59.73/59.68 [1148]~E(x11481,x11482)+E(f841(x11483,x11484,x11481,x11485,x11486,x11487,x11488),f841(x11483,x11484,x11482,x11485,x11486,x11487,x11488))
% 59.73/59.68 [1149]~E(x11491,x11492)+E(f841(x11493,x11494,x11495,x11491,x11496,x11497,x11498),f841(x11493,x11494,x11495,x11492,x11496,x11497,x11498))
% 59.73/59.68 [1150]~E(x11501,x11502)+E(f841(x11503,x11504,x11505,x11506,x11501,x11507,x11508),f841(x11503,x11504,x11505,x11506,x11502,x11507,x11508))
% 59.73/59.68 [1151]~E(x11511,x11512)+E(f841(x11513,x11514,x11515,x11516,x11517,x11511,x11518),f841(x11513,x11514,x11515,x11516,x11517,x11512,x11518))
% 59.73/59.68 [1152]~E(x11521,x11522)+E(f841(x11523,x11524,x11525,x11526,x11527,x11528,x11521),f841(x11523,x11524,x11525,x11526,x11527,x11528,x11522))
% 59.73/59.68 [1153]~E(x11531,x11532)+E(f856(x11531,x11533,x11534),f856(x11532,x11533,x11534))
% 59.73/59.68 [1154]~E(x11541,x11542)+E(f856(x11543,x11541,x11544),f856(x11543,x11542,x11544))
% 59.73/59.68 [1155]~E(x11551,x11552)+E(f856(x11553,x11554,x11551),f856(x11553,x11554,x11552))
% 59.73/59.68 [1156]~E(x11561,x11562)+E(f470(x11561,x11563,x11564,x11565),f470(x11562,x11563,x11564,x11565))
% 59.73/59.68 [1157]~E(x11571,x11572)+E(f470(x11573,x11571,x11574,x11575),f470(x11573,x11572,x11574,x11575))
% 59.73/59.68 [1158]~E(x11581,x11582)+E(f470(x11583,x11584,x11581,x11585),f470(x11583,x11584,x11582,x11585))
% 59.73/59.68 [1159]~E(x11591,x11592)+E(f470(x11593,x11594,x11595,x11591),f470(x11593,x11594,x11595,x11592))
% 59.73/59.68 [1160]~E(x11601,x11602)+E(f359(x11601,x11603,x11604),f359(x11602,x11603,x11604))
% 59.73/59.68 [1161]~E(x11611,x11612)+E(f359(x11613,x11611,x11614),f359(x11613,x11612,x11614))
% 59.73/59.68 [1162]~E(x11621,x11622)+E(f359(x11623,x11624,x11621),f359(x11623,x11624,x11622))
% 59.73/59.68 [1163]~E(x11631,x11632)+E(f799(x11631,x11633,x11634,x11635,x11636),f799(x11632,x11633,x11634,x11635,x11636))
% 59.73/59.68 [1164]~E(x11641,x11642)+E(f799(x11643,x11641,x11644,x11645,x11646),f799(x11643,x11642,x11644,x11645,x11646))
% 59.73/59.68 [1165]~E(x11651,x11652)+E(f799(x11653,x11654,x11651,x11655,x11656),f799(x11653,x11654,x11652,x11655,x11656))
% 59.73/59.68 [1166]~E(x11661,x11662)+E(f799(x11663,x11664,x11665,x11661,x11666),f799(x11663,x11664,x11665,x11662,x11666))
% 59.73/59.68 [1167]~E(x11671,x11672)+E(f799(x11673,x11674,x11675,x11676,x11671),f799(x11673,x11674,x11675,x11676,x11672))
% 59.73/59.68 [1168]~E(x11681,x11682)+E(f631(x11681,x11683,x11684),f631(x11682,x11683,x11684))
% 59.73/59.68 [1169]~E(x11691,x11692)+E(f631(x11693,x11691,x11694),f631(x11693,x11692,x11694))
% 59.73/59.68 [1170]~E(x11701,x11702)+E(f631(x11703,x11704,x11701),f631(x11703,x11704,x11702))
% 59.73/59.68 [1171]~E(x11711,x11712)+E(f589(x11711,x11713),f589(x11712,x11713))
% 59.73/59.68 [1172]~E(x11721,x11722)+E(f589(x11723,x11721),f589(x11723,x11722))
% 59.73/59.68 [1173]~E(x11731,x11732)+E(f869(x11731,x11733,x11734),f869(x11732,x11733,x11734))
% 59.73/59.68 [1174]~E(x11741,x11742)+E(f869(x11743,x11741,x11744),f869(x11743,x11742,x11744))
% 59.73/59.68 [1175]~E(x11751,x11752)+E(f869(x11753,x11754,x11751),f869(x11753,x11754,x11752))
% 59.73/59.68 [1176]~E(x11761,x11762)+E(f833(x11761,x11763,x11764,x11765,x11766),f833(x11762,x11763,x11764,x11765,x11766))
% 59.73/59.68 [1177]~E(x11771,x11772)+E(f833(x11773,x11771,x11774,x11775,x11776),f833(x11773,x11772,x11774,x11775,x11776))
% 59.73/59.68 [1178]~E(x11781,x11782)+E(f833(x11783,x11784,x11781,x11785,x11786),f833(x11783,x11784,x11782,x11785,x11786))
% 59.73/59.68 [1179]~E(x11791,x11792)+E(f833(x11793,x11794,x11795,x11791,x11796),f833(x11793,x11794,x11795,x11792,x11796))
% 59.73/59.68 [1180]~E(x11801,x11802)+E(f833(x11803,x11804,x11805,x11806,x11801),f833(x11803,x11804,x11805,x11806,x11802))
% 59.73/59.68 [1181]~E(x11811,x11812)+E(f500(x11811,x11813,x11814,x11815,x11816,x11817),f500(x11812,x11813,x11814,x11815,x11816,x11817))
% 59.73/59.68 [1182]~E(x11821,x11822)+E(f500(x11823,x11821,x11824,x11825,x11826,x11827),f500(x11823,x11822,x11824,x11825,x11826,x11827))
% 59.73/59.68 [1183]~E(x11831,x11832)+E(f500(x11833,x11834,x11831,x11835,x11836,x11837),f500(x11833,x11834,x11832,x11835,x11836,x11837))
% 59.73/59.68 [1184]~E(x11841,x11842)+E(f500(x11843,x11844,x11845,x11841,x11846,x11847),f500(x11843,x11844,x11845,x11842,x11846,x11847))
% 59.73/59.68 [1185]~E(x11851,x11852)+E(f500(x11853,x11854,x11855,x11856,x11851,x11857),f500(x11853,x11854,x11855,x11856,x11852,x11857))
% 59.73/59.68 [1186]~E(x11861,x11862)+E(f500(x11863,x11864,x11865,x11866,x11867,x11861),f500(x11863,x11864,x11865,x11866,x11867,x11862))
% 59.73/59.68 [1187]~E(x11871,x11872)+E(f749(x11871,x11873),f749(x11872,x11873))
% 59.73/59.68 [1188]~E(x11881,x11882)+E(f749(x11883,x11881),f749(x11883,x11882))
% 59.73/59.68 [1189]~E(x11891,x11892)+E(f418(x11891,x11893,x11894),f418(x11892,x11893,x11894))
% 59.73/59.68 [1190]~E(x11901,x11902)+E(f418(x11903,x11901,x11904),f418(x11903,x11902,x11904))
% 59.73/59.68 [1191]~E(x11911,x11912)+E(f418(x11913,x11914,x11911),f418(x11913,x11914,x11912))
% 59.73/59.68 [1192]~E(x11921,x11922)+E(f575(x11921,x11923,x11924),f575(x11922,x11923,x11924))
% 59.73/59.68 [1193]~E(x11931,x11932)+E(f575(x11933,x11931,x11934),f575(x11933,x11932,x11934))
% 59.73/59.68 [1194]~E(x11941,x11942)+E(f575(x11943,x11944,x11941),f575(x11943,x11944,x11942))
% 59.73/59.68 [1195]~E(x11951,x11952)+E(f477(x11951,x11953),f477(x11952,x11953))
% 59.73/59.68 [1196]~E(x11961,x11962)+E(f477(x11963,x11961),f477(x11963,x11962))
% 59.73/59.68 [1197]~E(x11971,x11972)+E(f707(x11971,x11973,x11974,x11975),f707(x11972,x11973,x11974,x11975))
% 59.73/59.68 [1198]~E(x11981,x11982)+E(f707(x11983,x11981,x11984,x11985),f707(x11983,x11982,x11984,x11985))
% 59.73/59.68 [1199]~E(x11991,x11992)+E(f707(x11993,x11994,x11991,x11995),f707(x11993,x11994,x11992,x11995))
% 59.73/59.68 [1200]~E(x12001,x12002)+E(f707(x12003,x12004,x12005,x12001),f707(x12003,x12004,x12005,x12002))
% 59.73/59.68 [1201]~E(x12011,x12012)+E(f22(x12011,x12013),f22(x12012,x12013))
% 59.73/59.68 [1202]~E(x12021,x12022)+E(f22(x12023,x12021),f22(x12023,x12022))
% 59.73/59.68 [1203]~E(x12031,x12032)+E(f419(x12031,x12033,x12034,x12035),f419(x12032,x12033,x12034,x12035))
% 59.73/59.68 [1204]~E(x12041,x12042)+E(f419(x12043,x12041,x12044,x12045),f419(x12043,x12042,x12044,x12045))
% 59.73/59.68 [1205]~E(x12051,x12052)+E(f419(x12053,x12054,x12051,x12055),f419(x12053,x12054,x12052,x12055))
% 59.73/59.68 [1206]~E(x12061,x12062)+E(f419(x12063,x12064,x12065,x12061),f419(x12063,x12064,x12065,x12062))
% 59.73/59.68 [1207]~E(x12071,x12072)+E(f115(x12071,x12073),f115(x12072,x12073))
% 59.73/59.68 [1208]~E(x12081,x12082)+E(f115(x12083,x12081),f115(x12083,x12082))
% 59.73/59.68 [1209]~E(x12091,x12092)+E(f202(x12091,x12093),f202(x12092,x12093))
% 59.73/59.68 [1210]~E(x12101,x12102)+E(f202(x12103,x12101),f202(x12103,x12102))
% 59.73/59.68 [1211]~E(x12111,x12112)+E(f861(x12111,x12113),f861(x12112,x12113))
% 59.73/59.68 [1212]~E(x12121,x12122)+E(f861(x12123,x12121),f861(x12123,x12122))
% 59.73/59.68 [1213]~E(x12131,x12132)+E(f628(x12131,x12133),f628(x12132,x12133))
% 59.73/59.68 [1214]~E(x12141,x12142)+E(f628(x12143,x12141),f628(x12143,x12142))
% 59.73/59.68 [1215]~E(x12151,x12152)+E(f174(x12151),f174(x12152))
% 59.73/59.68 [1216]~E(x12161,x12162)+E(f745(x12161,x12163,x12164,x12165),f745(x12162,x12163,x12164,x12165))
% 59.73/59.68 [1217]~E(x12171,x12172)+E(f745(x12173,x12171,x12174,x12175),f745(x12173,x12172,x12174,x12175))
% 59.73/59.68 [1218]~E(x12181,x12182)+E(f745(x12183,x12184,x12181,x12185),f745(x12183,x12184,x12182,x12185))
% 59.73/59.68 [1219]~E(x12191,x12192)+E(f745(x12193,x12194,x12195,x12191),f745(x12193,x12194,x12195,x12192))
% 59.73/59.68 [1220]~E(x12201,x12202)+E(f362(x12201,x12203),f362(x12202,x12203))
% 59.73/59.68 [1221]~E(x12211,x12212)+E(f362(x12213,x12211),f362(x12213,x12212))
% 59.73/59.68 [1222]~E(x12221,x12222)+E(f409(x12221,x12223,x12224),f409(x12222,x12223,x12224))
% 59.73/59.68 [1223]~E(x12231,x12232)+E(f409(x12233,x12231,x12234),f409(x12233,x12232,x12234))
% 59.73/59.68 [1224]~E(x12241,x12242)+E(f409(x12243,x12244,x12241),f409(x12243,x12244,x12242))
% 59.73/59.68 [1225]~E(x12251,x12252)+E(f178(x12251,x12253,x12254),f178(x12252,x12253,x12254))
% 59.73/59.68 [1226]~E(x12261,x12262)+E(f178(x12263,x12261,x12264),f178(x12263,x12262,x12264))
% 59.73/59.68 [1227]~E(x12271,x12272)+E(f178(x12273,x12274,x12271),f178(x12273,x12274,x12272))
% 59.73/59.68 [1228]~E(x12281,x12282)+E(f322(x12281,x12283,x12284,x12285,x12286),f322(x12282,x12283,x12284,x12285,x12286))
% 59.73/59.68 [1229]~E(x12291,x12292)+E(f322(x12293,x12291,x12294,x12295,x12296),f322(x12293,x12292,x12294,x12295,x12296))
% 59.73/59.68 [1230]~E(x12301,x12302)+E(f322(x12303,x12304,x12301,x12305,x12306),f322(x12303,x12304,x12302,x12305,x12306))
% 59.73/59.68 [1231]~E(x12311,x12312)+E(f322(x12313,x12314,x12315,x12311,x12316),f322(x12313,x12314,x12315,x12312,x12316))
% 59.73/59.68 [1232]~E(x12321,x12322)+E(f322(x12323,x12324,x12325,x12326,x12321),f322(x12323,x12324,x12325,x12326,x12322))
% 59.73/59.68 [1233]~E(x12331,x12332)+E(f834(x12331,x12333,x12334,x12335,x12336),f834(x12332,x12333,x12334,x12335,x12336))
% 59.73/59.68 [1234]~E(x12341,x12342)+E(f834(x12343,x12341,x12344,x12345,x12346),f834(x12343,x12342,x12344,x12345,x12346))
% 59.73/59.68 [1235]~E(x12351,x12352)+E(f834(x12353,x12354,x12351,x12355,x12356),f834(x12353,x12354,x12352,x12355,x12356))
% 59.73/59.68 [1236]~E(x12361,x12362)+E(f834(x12363,x12364,x12365,x12361,x12366),f834(x12363,x12364,x12365,x12362,x12366))
% 59.73/59.68 [1237]~E(x12371,x12372)+E(f834(x12373,x12374,x12375,x12376,x12371),f834(x12373,x12374,x12375,x12376,x12372))
% 59.73/59.68 [1238]~E(x12381,x12382)+E(f414(x12381),f414(x12382))
% 59.73/59.68 [1239]~E(x12391,x12392)+E(f845(x12391,x12393,x12394,x12395,x12396,x12397,x12398),f845(x12392,x12393,x12394,x12395,x12396,x12397,x12398))
% 59.73/59.68 [1240]~E(x12401,x12402)+E(f845(x12403,x12401,x12404,x12405,x12406,x12407,x12408),f845(x12403,x12402,x12404,x12405,x12406,x12407,x12408))
% 59.73/59.68 [1241]~E(x12411,x12412)+E(f845(x12413,x12414,x12411,x12415,x12416,x12417,x12418),f845(x12413,x12414,x12412,x12415,x12416,x12417,x12418))
% 59.73/59.68 [1242]~E(x12421,x12422)+E(f845(x12423,x12424,x12425,x12421,x12426,x12427,x12428),f845(x12423,x12424,x12425,x12422,x12426,x12427,x12428))
% 59.73/59.68 [1243]~E(x12431,x12432)+E(f845(x12433,x12434,x12435,x12436,x12431,x12437,x12438),f845(x12433,x12434,x12435,x12436,x12432,x12437,x12438))
% 59.73/59.68 [1244]~E(x12441,x12442)+E(f845(x12443,x12444,x12445,x12446,x12447,x12441,x12448),f845(x12443,x12444,x12445,x12446,x12447,x12442,x12448))
% 59.73/59.68 [1245]~E(x12451,x12452)+E(f845(x12453,x12454,x12455,x12456,x12457,x12458,x12451),f845(x12453,x12454,x12455,x12456,x12457,x12458,x12452))
% 59.73/59.68 [1246]~E(x12461,x12462)+E(f391(x12461,x12463,x12464,x12465,x12466,x12467),f391(x12462,x12463,x12464,x12465,x12466,x12467))
% 59.73/59.68 [1247]~E(x12471,x12472)+E(f391(x12473,x12471,x12474,x12475,x12476,x12477),f391(x12473,x12472,x12474,x12475,x12476,x12477))
% 59.73/59.68 [1248]~E(x12481,x12482)+E(f391(x12483,x12484,x12481,x12485,x12486,x12487),f391(x12483,x12484,x12482,x12485,x12486,x12487))
% 59.73/59.68 [1249]~E(x12491,x12492)+E(f391(x12493,x12494,x12495,x12491,x12496,x12497),f391(x12493,x12494,x12495,x12492,x12496,x12497))
% 59.73/59.68 [1250]~E(x12501,x12502)+E(f391(x12503,x12504,x12505,x12506,x12501,x12507),f391(x12503,x12504,x12505,x12506,x12502,x12507))
% 59.73/59.68 [1251]~E(x12511,x12512)+E(f391(x12513,x12514,x12515,x12516,x12517,x12511),f391(x12513,x12514,x12515,x12516,x12517,x12512))
% 59.73/59.68 [1252]~E(x12521,x12522)+E(f481(x12521,x12523,x12524,x12525),f481(x12522,x12523,x12524,x12525))
% 59.73/59.68 [1253]~E(x12531,x12532)+E(f481(x12533,x12531,x12534,x12535),f481(x12533,x12532,x12534,x12535))
% 59.73/59.68 [1254]~E(x12541,x12542)+E(f481(x12543,x12544,x12541,x12545),f481(x12543,x12544,x12542,x12545))
% 59.73/59.68 [1255]~E(x12551,x12552)+E(f481(x12553,x12554,x12555,x12551),f481(x12553,x12554,x12555,x12552))
% 59.73/59.68 [1256]~E(x12561,x12562)+E(f725(x12561,x12563,x12564),f725(x12562,x12563,x12564))
% 59.73/59.68 [1257]~E(x12571,x12572)+E(f725(x12573,x12571,x12574),f725(x12573,x12572,x12574))
% 59.73/59.68 [1258]~E(x12581,x12582)+E(f725(x12583,x12584,x12581),f725(x12583,x12584,x12582))
% 59.73/59.68 [1259]~E(x12591,x12592)+E(f842(x12591,x12593),f842(x12592,x12593))
% 59.73/59.68 [1260]~E(x12601,x12602)+E(f842(x12603,x12601),f842(x12603,x12602))
% 59.73/59.68 [1261]~E(x12611,x12612)+E(f476(x12611,x12613),f476(x12612,x12613))
% 59.73/59.68 [1262]~E(x12621,x12622)+E(f476(x12623,x12621),f476(x12623,x12622))
% 59.73/59.68 [1263]~E(x12631,x12632)+E(f381(x12631),f381(x12632))
% 59.73/59.68 [1264]~E(x12641,x12642)+E(f759(x12641,x12643,x12644,x12645,x12646,x12647,x12648,x12649),f759(x12642,x12643,x12644,x12645,x12646,x12647,x12648,x12649))
% 59.73/59.68 [1265]~E(x12651,x12652)+E(f759(x12653,x12651,x12654,x12655,x12656,x12657,x12658,x12659),f759(x12653,x12652,x12654,x12655,x12656,x12657,x12658,x12659))
% 59.73/59.68 [1266]~E(x12661,x12662)+E(f759(x12663,x12664,x12661,x12665,x12666,x12667,x12668,x12669),f759(x12663,x12664,x12662,x12665,x12666,x12667,x12668,x12669))
% 59.73/59.68 [1267]~E(x12671,x12672)+E(f759(x12673,x12674,x12675,x12671,x12676,x12677,x12678,x12679),f759(x12673,x12674,x12675,x12672,x12676,x12677,x12678,x12679))
% 59.73/59.68 [1268]~E(x12681,x12682)+E(f759(x12683,x12684,x12685,x12686,x12681,x12687,x12688,x12689),f759(x12683,x12684,x12685,x12686,x12682,x12687,x12688,x12689))
% 59.73/59.68 [1269]~E(x12691,x12692)+E(f759(x12693,x12694,x12695,x12696,x12697,x12691,x12698,x12699),f759(x12693,x12694,x12695,x12696,x12697,x12692,x12698,x12699))
% 59.73/59.68 [1270]~E(x12701,x12702)+E(f759(x12703,x12704,x12705,x12706,x12707,x12708,x12701,x12709),f759(x12703,x12704,x12705,x12706,x12707,x12708,x12702,x12709))
% 59.73/59.68 [1271]~E(x12711,x12712)+E(f759(x12713,x12714,x12715,x12716,x12717,x12718,x12719,x12711),f759(x12713,x12714,x12715,x12716,x12717,x12718,x12719,x12712))
% 59.73/59.68 [1272]~E(x12721,x12722)+E(f840(x12721,x12723,x12724,x12725,x12726,x12727,x12728),f840(x12722,x12723,x12724,x12725,x12726,x12727,x12728))
% 59.73/59.68 [1273]~E(x12731,x12732)+E(f840(x12733,x12731,x12734,x12735,x12736,x12737,x12738),f840(x12733,x12732,x12734,x12735,x12736,x12737,x12738))
% 59.73/59.68 [1274]~E(x12741,x12742)+E(f840(x12743,x12744,x12741,x12745,x12746,x12747,x12748),f840(x12743,x12744,x12742,x12745,x12746,x12747,x12748))
% 59.73/59.68 [1275]~E(x12751,x12752)+E(f840(x12753,x12754,x12755,x12751,x12756,x12757,x12758),f840(x12753,x12754,x12755,x12752,x12756,x12757,x12758))
% 59.73/59.68 [1276]~E(x12761,x12762)+E(f840(x12763,x12764,x12765,x12766,x12761,x12767,x12768),f840(x12763,x12764,x12765,x12766,x12762,x12767,x12768))
% 59.73/59.68 [1277]~E(x12771,x12772)+E(f840(x12773,x12774,x12775,x12776,x12777,x12771,x12778),f840(x12773,x12774,x12775,x12776,x12777,x12772,x12778))
% 59.73/59.68 [1278]~E(x12781,x12782)+E(f840(x12783,x12784,x12785,x12786,x12787,x12788,x12781),f840(x12783,x12784,x12785,x12786,x12787,x12788,x12782))
% 59.73/59.68 [1279]~E(x12791,x12792)+E(f385(x12791,x12793,x12794),f385(x12792,x12793,x12794))
% 59.73/59.68 [1280]~E(x12801,x12802)+E(f385(x12803,x12801,x12804),f385(x12803,x12802,x12804))
% 59.73/59.68 [1281]~E(x12811,x12812)+E(f385(x12813,x12814,x12811),f385(x12813,x12814,x12812))
% 59.73/59.68 [1282]~E(x12821,x12822)+E(f696(x12821,x12823,x12824,x12825),f696(x12822,x12823,x12824,x12825))
% 59.73/59.68 [1283]~E(x12831,x12832)+E(f696(x12833,x12831,x12834,x12835),f696(x12833,x12832,x12834,x12835))
% 59.73/59.68 [1284]~E(x12841,x12842)+E(f696(x12843,x12844,x12841,x12845),f696(x12843,x12844,x12842,x12845))
% 59.73/59.68 [1285]~E(x12851,x12852)+E(f696(x12853,x12854,x12855,x12851),f696(x12853,x12854,x12855,x12852))
% 59.73/59.68 [1286]~E(x12861,x12862)+E(f860(x12861,x12863),f860(x12862,x12863))
% 59.73/59.68 [1287]~E(x12871,x12872)+E(f860(x12873,x12871),f860(x12873,x12872))
% 59.73/59.68 [1288]~E(x12881,x12882)+E(f63(x12881,x12883,x12884),f63(x12882,x12883,x12884))
% 59.73/59.68 [1289]~E(x12891,x12892)+E(f63(x12893,x12891,x12894),f63(x12893,x12892,x12894))
% 59.73/59.68 [1290]~E(x12901,x12902)+E(f63(x12903,x12904,x12901),f63(x12903,x12904,x12902))
% 59.73/59.68 [1291]~E(x12911,x12912)+E(f256(x12911,x12913,x12914),f256(x12912,x12913,x12914))
% 59.73/59.68 [1292]~E(x12921,x12922)+E(f256(x12923,x12921,x12924),f256(x12923,x12922,x12924))
% 59.73/59.68 [1293]~E(x12931,x12932)+E(f256(x12933,x12934,x12931),f256(x12933,x12934,x12932))
% 59.73/59.68 [1294]~E(x12941,x12942)+E(f728(x12941,x12943),f728(x12942,x12943))
% 59.73/59.68 [1295]~E(x12951,x12952)+E(f728(x12953,x12951),f728(x12953,x12952))
% 59.73/59.68 [1296]~E(x12961,x12962)+E(f462(x12961,x12963,x12964),f462(x12962,x12963,x12964))
% 59.73/59.68 [1297]~E(x12971,x12972)+E(f462(x12973,x12971,x12974),f462(x12973,x12972,x12974))
% 59.73/59.68 [1298]~E(x12981,x12982)+E(f462(x12983,x12984,x12981),f462(x12983,x12984,x12982))
% 59.73/59.68 [1299]~E(x12991,x12992)+E(f557(x12991,x12993),f557(x12992,x12993))
% 59.73/59.68 [1300]~E(x13001,x13002)+E(f557(x13003,x13001),f557(x13003,x13002))
% 59.73/59.68 [1301]~E(x13011,x13012)+E(f551(x13011,x13013,x13014),f551(x13012,x13013,x13014))
% 59.73/59.68 [1302]~E(x13021,x13022)+E(f551(x13023,x13021,x13024),f551(x13023,x13022,x13024))
% 59.73/59.68 [1303]~E(x13031,x13032)+E(f551(x13033,x13034,x13031),f551(x13033,x13034,x13032))
% 59.73/59.68 [1304]~E(x13041,x13042)+E(f382(x13041,x13043,x13044),f382(x13042,x13043,x13044))
% 59.73/59.68 [1305]~E(x13051,x13052)+E(f382(x13053,x13051,x13054),f382(x13053,x13052,x13054))
% 59.73/59.68 [1306]~E(x13061,x13062)+E(f382(x13063,x13064,x13061),f382(x13063,x13064,x13062))
% 59.73/59.68 [1307]~E(x13071,x13072)+E(f276(x13071,x13073),f276(x13072,x13073))
% 59.73/59.68 [1308]~E(x13081,x13082)+E(f276(x13083,x13081),f276(x13083,x13082))
% 59.73/59.68 [1309]~E(x13091,x13092)+E(f512(x13091,x13093,x13094,x13095,x13096),f512(x13092,x13093,x13094,x13095,x13096))
% 59.73/59.68 [1310]~E(x13101,x13102)+E(f512(x13103,x13101,x13104,x13105,x13106),f512(x13103,x13102,x13104,x13105,x13106))
% 59.73/59.68 [1311]~E(x13111,x13112)+E(f512(x13113,x13114,x13111,x13115,x13116),f512(x13113,x13114,x13112,x13115,x13116))
% 59.73/59.68 [1312]~E(x13121,x13122)+E(f512(x13123,x13124,x13125,x13121,x13126),f512(x13123,x13124,x13125,x13122,x13126))
% 59.73/59.68 [1313]~E(x13131,x13132)+E(f512(x13133,x13134,x13135,x13136,x13131),f512(x13133,x13134,x13135,x13136,x13132))
% 59.73/59.68 [1314]~E(x13141,x13142)+E(f545(x13141,x13143,x13144),f545(x13142,x13143,x13144))
% 59.73/59.68 [1315]~E(x13151,x13152)+E(f545(x13153,x13151,x13154),f545(x13153,x13152,x13154))
% 59.73/59.68 [1316]~E(x13161,x13162)+E(f545(x13163,x13164,x13161),f545(x13163,x13164,x13162))
% 59.73/59.68 [1317]~E(x13171,x13172)+E(f47(x13171,x13173),f47(x13172,x13173))
% 59.73/59.68 [1318]~E(x13181,x13182)+E(f47(x13183,x13181),f47(x13183,x13182))
% 59.73/59.68 [1319]~E(x13191,x13192)+E(f492(x13191,x13193,x13194),f492(x13192,x13193,x13194))
% 59.73/59.68 [1320]~E(x13201,x13202)+E(f492(x13203,x13201,x13204),f492(x13203,x13202,x13204))
% 59.73/59.68 [1321]~E(x13211,x13212)+E(f492(x13213,x13214,x13211),f492(x13213,x13214,x13212))
% 59.73/59.68 [1322]~E(x13221,x13222)+E(f767(x13221,x13223,x13224),f767(x13222,x13223,x13224))
% 59.73/59.68 [1323]~E(x13231,x13232)+E(f767(x13233,x13231,x13234),f767(x13233,x13232,x13234))
% 59.73/59.68 [1324]~E(x13241,x13242)+E(f767(x13243,x13244,x13241),f767(x13243,x13244,x13242))
% 59.73/59.68 [1325]~E(x13251,x13252)+E(f218(x13251,x13253),f218(x13252,x13253))
% 59.73/59.68 [1326]~E(x13261,x13262)+E(f218(x13263,x13261),f218(x13263,x13262))
% 59.73/59.68 [1327]~E(x13271,x13272)+E(f395(x13271,x13273,x13274),f395(x13272,x13273,x13274))
% 59.73/59.68 [1328]~E(x13281,x13282)+E(f395(x13283,x13281,x13284),f395(x13283,x13282,x13284))
% 59.73/59.68 [1329]~E(x13291,x13292)+E(f395(x13293,x13294,x13291),f395(x13293,x13294,x13292))
% 59.73/59.68 [1330]~E(x13301,x13302)+E(f573(x13301,x13303,x13304,x13305,x13306,x13307,x13308),f573(x13302,x13303,x13304,x13305,x13306,x13307,x13308))
% 59.73/59.68 [1331]~E(x13311,x13312)+E(f573(x13313,x13311,x13314,x13315,x13316,x13317,x13318),f573(x13313,x13312,x13314,x13315,x13316,x13317,x13318))
% 59.73/59.68 [1332]~E(x13321,x13322)+E(f573(x13323,x13324,x13321,x13325,x13326,x13327,x13328),f573(x13323,x13324,x13322,x13325,x13326,x13327,x13328))
% 59.73/59.68 [1333]~E(x13331,x13332)+E(f573(x13333,x13334,x13335,x13331,x13336,x13337,x13338),f573(x13333,x13334,x13335,x13332,x13336,x13337,x13338))
% 59.73/59.68 [1334]~E(x13341,x13342)+E(f573(x13343,x13344,x13345,x13346,x13341,x13347,x13348),f573(x13343,x13344,x13345,x13346,x13342,x13347,x13348))
% 59.73/59.68 [1335]~E(x13351,x13352)+E(f573(x13353,x13354,x13355,x13356,x13357,x13351,x13358),f573(x13353,x13354,x13355,x13356,x13357,x13352,x13358))
% 59.73/59.68 [1336]~E(x13361,x13362)+E(f573(x13363,x13364,x13365,x13366,x13367,x13368,x13361),f573(x13363,x13364,x13365,x13366,x13367,x13368,x13362))
% 59.73/59.68 [1337]~E(x13371,x13372)+E(f764(x13371,x13373),f764(x13372,x13373))
% 59.73/59.68 [1338]~E(x13381,x13382)+E(f764(x13383,x13381),f764(x13383,x13382))
% 59.73/59.68 [1339]~E(x13391,x13392)+E(f813(x13391,x13393,x13394,x13395),f813(x13392,x13393,x13394,x13395))
% 59.73/59.68 [1340]~E(x13401,x13402)+E(f813(x13403,x13401,x13404,x13405),f813(x13403,x13402,x13404,x13405))
% 59.73/59.68 [1341]~E(x13411,x13412)+E(f813(x13413,x13414,x13411,x13415),f813(x13413,x13414,x13412,x13415))
% 59.73/59.68 [1342]~E(x13421,x13422)+E(f813(x13423,x13424,x13425,x13421),f813(x13423,x13424,x13425,x13422))
% 59.73/59.68 [1343]~E(x13431,x13432)+E(f277(x13431,x13433),f277(x13432,x13433))
% 59.73/59.68 [1344]~E(x13441,x13442)+E(f277(x13443,x13441),f277(x13443,x13442))
% 59.73/59.68 [1345]~E(x13451,x13452)+E(f194(x13451,x13453),f194(x13452,x13453))
% 59.73/59.68 [1346]~E(x13461,x13462)+E(f194(x13463,x13461),f194(x13463,x13462))
% 59.73/59.68 [1347]~E(x13471,x13472)+E(f478(x13471,x13473),f478(x13472,x13473))
% 59.73/59.68 [1348]~E(x13481,x13482)+E(f478(x13483,x13481),f478(x13483,x13482))
% 59.73/59.68 [1349]~E(x13491,x13492)+E(f290(x13491,x13493),f290(x13492,x13493))
% 59.73/59.68 [1350]~E(x13501,x13502)+E(f290(x13503,x13501),f290(x13503,x13502))
% 59.73/59.68 [1351]~E(x13511,x13512)+E(f858(x13511,x13513),f858(x13512,x13513))
% 59.73/59.68 [1352]~E(x13521,x13522)+E(f858(x13523,x13521),f858(x13523,x13522))
% 59.73/59.68 [1353]~E(x13531,x13532)+E(f19(x13531,x13533,x13534,x13535),f19(x13532,x13533,x13534,x13535))
% 59.73/59.68 [1354]~E(x13541,x13542)+E(f19(x13543,x13541,x13544,x13545),f19(x13543,x13542,x13544,x13545))
% 59.73/59.68 [1355]~E(x13551,x13552)+E(f19(x13553,x13554,x13551,x13555),f19(x13553,x13554,x13552,x13555))
% 59.73/59.68 [1356]~E(x13561,x13562)+E(f19(x13563,x13564,x13565,x13561),f19(x13563,x13564,x13565,x13562))
% 59.73/59.68 [1357]~E(x13571,x13572)+E(f742(x13571,x13573,x13574),f742(x13572,x13573,x13574))
% 59.73/59.68 [1358]~E(x13581,x13582)+E(f742(x13583,x13581,x13584),f742(x13583,x13582,x13584))
% 59.73/59.68 [1359]~E(x13591,x13592)+E(f742(x13593,x13594,x13591),f742(x13593,x13594,x13592))
% 59.73/59.68 [1360]~E(x13601,x13602)+E(f676(x13601,x13603,x13604),f676(x13602,x13603,x13604))
% 59.73/59.68 [1361]~E(x13611,x13612)+E(f676(x13613,x13611,x13614),f676(x13613,x13612,x13614))
% 59.73/59.68 [1362]~E(x13621,x13622)+E(f676(x13623,x13624,x13621),f676(x13623,x13624,x13622))
% 59.73/59.68 [1363]~E(x13631,x13632)+E(f357(x13631,x13633,x13634),f357(x13632,x13633,x13634))
% 59.73/59.68 [1364]~E(x13641,x13642)+E(f357(x13643,x13641,x13644),f357(x13643,x13642,x13644))
% 59.73/59.68 [1365]~E(x13651,x13652)+E(f357(x13653,x13654,x13651),f357(x13653,x13654,x13652))
% 59.73/59.68 [1366]~E(x13661,x13662)+E(f503(x13661,x13663,x13664,x13665,x13666,x13667),f503(x13662,x13663,x13664,x13665,x13666,x13667))
% 59.73/59.68 [1367]~E(x13671,x13672)+E(f503(x13673,x13671,x13674,x13675,x13676,x13677),f503(x13673,x13672,x13674,x13675,x13676,x13677))
% 59.73/59.68 [1368]~E(x13681,x13682)+E(f503(x13683,x13684,x13681,x13685,x13686,x13687),f503(x13683,x13684,x13682,x13685,x13686,x13687))
% 59.73/59.68 [1369]~E(x13691,x13692)+E(f503(x13693,x13694,x13695,x13691,x13696,x13697),f503(x13693,x13694,x13695,x13692,x13696,x13697))
% 59.73/59.68 [1370]~E(x13701,x13702)+E(f503(x13703,x13704,x13705,x13706,x13701,x13707),f503(x13703,x13704,x13705,x13706,x13702,x13707))
% 59.73/59.68 [1371]~E(x13711,x13712)+E(f503(x13713,x13714,x13715,x13716,x13717,x13711),f503(x13713,x13714,x13715,x13716,x13717,x13712))
% 59.73/59.68 [1372]~E(x13721,x13722)+E(f672(x13721,x13723),f672(x13722,x13723))
% 59.73/59.68 [1373]~E(x13731,x13732)+E(f672(x13733,x13731),f672(x13733,x13732))
% 59.73/59.68 [1374]~E(x13741,x13742)+E(f598(x13741,x13743),f598(x13742,x13743))
% 59.73/59.68 [1375]~E(x13751,x13752)+E(f598(x13753,x13751),f598(x13753,x13752))
% 59.73/59.68 [1376]~E(x13761,x13762)+E(f424(x13761,x13763),f424(x13762,x13763))
% 59.73/59.68 [1377]~E(x13771,x13772)+E(f424(x13773,x13771),f424(x13773,x13772))
% 59.73/59.68 [1378]~E(x13781,x13782)+E(f286(x13781,x13783,x13784,x13785),f286(x13782,x13783,x13784,x13785))
% 59.73/59.68 [1379]~E(x13791,x13792)+E(f286(x13793,x13791,x13794,x13795),f286(x13793,x13792,x13794,x13795))
% 59.73/59.68 [1380]~E(x13801,x13802)+E(f286(x13803,x13804,x13801,x13805),f286(x13803,x13804,x13802,x13805))
% 59.73/59.68 [1381]~E(x13811,x13812)+E(f286(x13813,x13814,x13815,x13811),f286(x13813,x13814,x13815,x13812))
% 59.73/59.68 [1382]~E(x13821,x13822)+E(f469(x13821,x13823,x13824,x13825),f469(x13822,x13823,x13824,x13825))
% 59.73/59.68 [1383]~E(x13831,x13832)+E(f469(x13833,x13831,x13834,x13835),f469(x13833,x13832,x13834,x13835))
% 59.73/59.68 [1384]~E(x13841,x13842)+E(f469(x13843,x13844,x13841,x13845),f469(x13843,x13844,x13842,x13845))
% 59.73/59.68 [1385]~E(x13851,x13852)+E(f469(x13853,x13854,x13855,x13851),f469(x13853,x13854,x13855,x13852))
% 59.73/59.68 [1386]~E(x13861,x13862)+E(f139(x13861,x13863),f139(x13862,x13863))
% 59.73/59.68 [1387]~E(x13871,x13872)+E(f139(x13873,x13871),f139(x13873,x13872))
% 59.73/59.68 [1388]~E(x13881,x13882)+E(f504(x13881,x13883,x13884,x13885,x13886),f504(x13882,x13883,x13884,x13885,x13886))
% 59.73/59.68 [1389]~E(x13891,x13892)+E(f504(x13893,x13891,x13894,x13895,x13896),f504(x13893,x13892,x13894,x13895,x13896))
% 59.73/59.68 [1390]~E(x13901,x13902)+E(f504(x13903,x13904,x13901,x13905,x13906),f504(x13903,x13904,x13902,x13905,x13906))
% 59.73/59.68 [1391]~E(x13911,x13912)+E(f504(x13913,x13914,x13915,x13911,x13916),f504(x13913,x13914,x13915,x13912,x13916))
% 59.73/59.68 [1392]~E(x13921,x13922)+E(f504(x13923,x13924,x13925,x13926,x13921),f504(x13923,x13924,x13925,x13926,x13922))
% 59.73/59.68 [1393]~E(x13931,x13932)+E(f535(x13931,x13933,x13934,x13935),f535(x13932,x13933,x13934,x13935))
% 59.73/59.68 [1394]~E(x13941,x13942)+E(f535(x13943,x13941,x13944,x13945),f535(x13943,x13942,x13944,x13945))
% 59.73/59.68 [1395]~E(x13951,x13952)+E(f535(x13953,x13954,x13951,x13955),f535(x13953,x13954,x13952,x13955))
% 59.73/59.68 [1396]~E(x13961,x13962)+E(f535(x13963,x13964,x13965,x13961),f535(x13963,x13964,x13965,x13962))
% 59.73/59.68 [1397]~E(x13971,x13972)+E(f461(x13971,x13973,x13974,x13975),f461(x13972,x13973,x13974,x13975))
% 59.73/59.68 [1398]~E(x13981,x13982)+E(f461(x13983,x13981,x13984,x13985),f461(x13983,x13982,x13984,x13985))
% 59.73/59.68 [1399]~E(x13991,x13992)+E(f461(x13993,x13994,x13991,x13995),f461(x13993,x13994,x13992,x13995))
% 59.73/59.68 [1400]~E(x14001,x14002)+E(f461(x14003,x14004,x14005,x14001),f461(x14003,x14004,x14005,x14002))
% 59.73/59.68 [1401]~E(x14011,x14012)+E(f649(x14011,x14013,x14014,x14015,x14016,x14017),f649(x14012,x14013,x14014,x14015,x14016,x14017))
% 59.73/59.68 [1402]~E(x14021,x14022)+E(f649(x14023,x14021,x14024,x14025,x14026,x14027),f649(x14023,x14022,x14024,x14025,x14026,x14027))
% 59.73/59.68 [1403]~E(x14031,x14032)+E(f649(x14033,x14034,x14031,x14035,x14036,x14037),f649(x14033,x14034,x14032,x14035,x14036,x14037))
% 59.73/59.68 [1404]~E(x14041,x14042)+E(f649(x14043,x14044,x14045,x14041,x14046,x14047),f649(x14043,x14044,x14045,x14042,x14046,x14047))
% 59.73/59.68 [1405]~E(x14051,x14052)+E(f649(x14053,x14054,x14055,x14056,x14051,x14057),f649(x14053,x14054,x14055,x14056,x14052,x14057))
% 59.73/59.68 [1406]~E(x14061,x14062)+E(f649(x14063,x14064,x14065,x14066,x14067,x14061),f649(x14063,x14064,x14065,x14066,x14067,x14062))
% 59.73/59.68 [1407]~E(x14071,x14072)+E(f514(x14071,x14073,x14074,x14075,x14076),f514(x14072,x14073,x14074,x14075,x14076))
% 59.73/59.68 [1408]~E(x14081,x14082)+E(f514(x14083,x14081,x14084,x14085,x14086),f514(x14083,x14082,x14084,x14085,x14086))
% 59.73/59.68 [1409]~E(x14091,x14092)+E(f514(x14093,x14094,x14091,x14095,x14096),f514(x14093,x14094,x14092,x14095,x14096))
% 59.73/59.68 [1410]~E(x14101,x14102)+E(f514(x14103,x14104,x14105,x14101,x14106),f514(x14103,x14104,x14105,x14102,x14106))
% 59.73/59.68 [1411]~E(x14111,x14112)+E(f514(x14113,x14114,x14115,x14116,x14111),f514(x14113,x14114,x14115,x14116,x14112))
% 59.73/59.68 [1412]~E(x14121,x14122)+E(f736(x14121,x14123,x14124),f736(x14122,x14123,x14124))
% 59.73/59.68 [1413]~E(x14131,x14132)+E(f736(x14133,x14131,x14134),f736(x14133,x14132,x14134))
% 59.73/59.68 [1414]~E(x14141,x14142)+E(f736(x14143,x14144,x14141),f736(x14143,x14144,x14142))
% 59.73/59.68 [1415]~E(x14151,x14152)+E(f560(x14151,x14153),f560(x14152,x14153))
% 59.73/59.68 [1416]~E(x14161,x14162)+E(f560(x14163,x14161),f560(x14163,x14162))
% 59.73/59.68 [1417]~E(x14171,x14172)+E(f405(x14171,x14173,x14174),f405(x14172,x14173,x14174))
% 59.73/59.68 [1418]~E(x14181,x14182)+E(f405(x14183,x14181,x14184),f405(x14183,x14182,x14184))
% 59.73/59.68 [1419]~E(x14191,x14192)+E(f405(x14193,x14194,x14191),f405(x14193,x14194,x14192))
% 59.73/59.68 [1420]~E(x14201,x14202)+E(f236(x14201,x14203,x14204),f236(x14202,x14203,x14204))
% 59.73/59.68 [1421]~E(x14211,x14212)+E(f236(x14213,x14211,x14214),f236(x14213,x14212,x14214))
% 59.73/59.68 [1422]~E(x14221,x14222)+E(f236(x14223,x14224,x14221),f236(x14223,x14224,x14222))
% 59.73/59.68 [1423]~E(x14231,x14232)+E(f601(x14231,x14233,x14234),f601(x14232,x14233,x14234))
% 59.73/59.68 [1424]~E(x14241,x14242)+E(f601(x14243,x14241,x14244),f601(x14243,x14242,x14244))
% 59.73/59.68 [1425]~E(x14251,x14252)+E(f601(x14253,x14254,x14251),f601(x14253,x14254,x14252))
% 59.73/59.68 [1426]~E(x14261,x14262)+E(f278(x14261,x14263),f278(x14262,x14263))
% 59.73/59.68 [1427]~E(x14271,x14272)+E(f278(x14273,x14271),f278(x14273,x14272))
% 59.73/59.68 [1428]~E(x14281,x14282)+E(f587(x14281,x14283,x14284,x14285,x14286,x14287),f587(x14282,x14283,x14284,x14285,x14286,x14287))
% 59.73/59.68 [1429]~E(x14291,x14292)+E(f587(x14293,x14291,x14294,x14295,x14296,x14297),f587(x14293,x14292,x14294,x14295,x14296,x14297))
% 59.73/59.68 [1430]~E(x14301,x14302)+E(f587(x14303,x14304,x14301,x14305,x14306,x14307),f587(x14303,x14304,x14302,x14305,x14306,x14307))
% 59.73/59.68 [1431]~E(x14311,x14312)+E(f587(x14313,x14314,x14315,x14311,x14316,x14317),f587(x14313,x14314,x14315,x14312,x14316,x14317))
% 59.73/59.68 [1432]~E(x14321,x14322)+E(f587(x14323,x14324,x14325,x14326,x14321,x14327),f587(x14323,x14324,x14325,x14326,x14322,x14327))
% 59.73/59.68 [1433]~E(x14331,x14332)+E(f587(x14333,x14334,x14335,x14336,x14337,x14331),f587(x14333,x14334,x14335,x14336,x14337,x14332))
% 59.73/59.68 [1434]~E(x14341,x14342)+E(f642(x14341,x14343,x14344),f642(x14342,x14343,x14344))
% 59.73/59.68 [1435]~E(x14351,x14352)+E(f642(x14353,x14351,x14354),f642(x14353,x14352,x14354))
% 59.73/59.68 [1436]~E(x14361,x14362)+E(f642(x14363,x14364,x14361),f642(x14363,x14364,x14362))
% 59.73/59.68 [1437]~E(x14371,x14372)+E(f488(x14371,x14373,x14374,x14375,x14376),f488(x14372,x14373,x14374,x14375,x14376))
% 59.73/59.68 [1438]~E(x14381,x14382)+E(f488(x14383,x14381,x14384,x14385,x14386),f488(x14383,x14382,x14384,x14385,x14386))
% 59.73/59.68 [1439]~E(x14391,x14392)+E(f488(x14393,x14394,x14391,x14395,x14396),f488(x14393,x14394,x14392,x14395,x14396))
% 59.73/59.68 [1440]~E(x14401,x14402)+E(f488(x14403,x14404,x14405,x14401,x14406),f488(x14403,x14404,x14405,x14402,x14406))
% 59.73/59.68 [1441]~E(x14411,x14412)+E(f488(x14413,x14414,x14415,x14416,x14411),f488(x14413,x14414,x14415,x14416,x14412))
% 59.73/59.68 [1442]~E(x14421,x14422)+E(f838(x14421,x14423),f838(x14422,x14423))
% 59.73/59.68 [1443]~E(x14431,x14432)+E(f838(x14433,x14431),f838(x14433,x14432))
% 59.73/59.68 [1444]~E(x14441,x14442)+E(f170(x14441,x14443,x14444),f170(x14442,x14443,x14444))
% 59.73/59.68 [1445]~E(x14451,x14452)+E(f170(x14453,x14451,x14454),f170(x14453,x14452,x14454))
% 59.73/59.68 [1446]~E(x14461,x14462)+E(f170(x14463,x14464,x14461),f170(x14463,x14464,x14462))
% 59.73/59.68 [1447]~E(x14471,x14472)+E(f507(x14471,x14473,x14474),f507(x14472,x14473,x14474))
% 59.73/59.68 [1448]~E(x14481,x14482)+E(f507(x14483,x14481,x14484),f507(x14483,x14482,x14484))
% 59.73/59.68 [1449]~E(x14491,x14492)+E(f507(x14493,x14494,x14491),f507(x14493,x14494,x14492))
% 59.73/59.68 [1450]~E(x14501,x14502)+E(f699(x14501,x14503,x14504),f699(x14502,x14503,x14504))
% 59.73/59.68 [1451]~E(x14511,x14512)+E(f699(x14513,x14511,x14514),f699(x14513,x14512,x14514))
% 59.73/59.68 [1452]~E(x14521,x14522)+E(f699(x14523,x14524,x14521),f699(x14523,x14524,x14522))
% 59.73/59.68 [1453]~E(x14531,x14532)+E(f718(x14531,x14533,x14534),f718(x14532,x14533,x14534))
% 59.73/59.68 [1454]~E(x14541,x14542)+E(f718(x14543,x14541,x14544),f718(x14543,x14542,x14544))
% 59.73/59.68 [1455]~E(x14551,x14552)+E(f718(x14553,x14554,x14551),f718(x14553,x14554,x14552))
% 59.73/59.68 [1456]~E(x14561,x14562)+E(f232(x14561,x14563,x14564),f232(x14562,x14563,x14564))
% 59.73/59.68 [1457]~E(x14571,x14572)+E(f232(x14573,x14571,x14574),f232(x14573,x14572,x14574))
% 59.73/59.68 [1458]~E(x14581,x14582)+E(f232(x14583,x14584,x14581),f232(x14583,x14584,x14582))
% 59.73/59.68 [1459]~E(x14591,x14592)+E(f792(x14591,x14593,x14594),f792(x14592,x14593,x14594))
% 59.73/59.68 [1460]~E(x14601,x14602)+E(f792(x14603,x14601,x14604),f792(x14603,x14602,x14604))
% 59.73/59.68 [1461]~E(x14611,x14612)+E(f792(x14613,x14614,x14611),f792(x14613,x14614,x14612))
% 59.73/59.68 [1462]~E(x14621,x14622)+E(f683(x14621,x14623,x14624),f683(x14622,x14623,x14624))
% 59.73/59.68 [1463]~E(x14631,x14632)+E(f683(x14633,x14631,x14634),f683(x14633,x14632,x14634))
% 59.73/59.68 [1464]~E(x14641,x14642)+E(f683(x14643,x14644,x14641),f683(x14643,x14644,x14642))
% 59.73/59.68 [1465]~E(x14651,x14652)+E(f863(x14651,x14653,x14654,x14655),f863(x14652,x14653,x14654,x14655))
% 59.73/59.68 [1466]~E(x14661,x14662)+E(f863(x14663,x14661,x14664,x14665),f863(x14663,x14662,x14664,x14665))
% 59.73/59.68 [1467]~E(x14671,x14672)+E(f863(x14673,x14674,x14671,x14675),f863(x14673,x14674,x14672,x14675))
% 59.73/59.68 [1468]~E(x14681,x14682)+E(f863(x14683,x14684,x14685,x14681),f863(x14683,x14684,x14685,x14682))
% 59.73/59.68 [1469]~E(x14691,x14692)+E(f225(x14691,x14693,x14694),f225(x14692,x14693,x14694))
% 59.73/59.68 [1470]~E(x14701,x14702)+E(f225(x14703,x14701,x14704),f225(x14703,x14702,x14704))
% 59.73/59.68 [1471]~E(x14711,x14712)+E(f225(x14713,x14714,x14711),f225(x14713,x14714,x14712))
% 59.73/59.68 [1472]~E(x14721,x14722)+E(f316(x14721,x14723,x14724),f316(x14722,x14723,x14724))
% 59.73/59.68 [1473]~E(x14731,x14732)+E(f316(x14733,x14731,x14734),f316(x14733,x14732,x14734))
% 59.73/59.68 [1474]~E(x14741,x14742)+E(f316(x14743,x14744,x14741),f316(x14743,x14744,x14742))
% 59.73/59.68 [1475]~E(x14751,x14752)+E(f389(x14751,x14753,x14754,x14755),f389(x14752,x14753,x14754,x14755))
% 59.73/59.68 [1476]~E(x14761,x14762)+E(f389(x14763,x14761,x14764,x14765),f389(x14763,x14762,x14764,x14765))
% 59.73/59.68 [1477]~E(x14771,x14772)+E(f389(x14773,x14774,x14771,x14775),f389(x14773,x14774,x14772,x14775))
% 59.73/59.68 [1478]~E(x14781,x14782)+E(f389(x14783,x14784,x14785,x14781),f389(x14783,x14784,x14785,x14782))
% 59.73/59.68 [1479]~E(x14791,x14792)+E(f693(x14791,x14793,x14794,x14795,x14796),f693(x14792,x14793,x14794,x14795,x14796))
% 59.73/59.68 [1480]~E(x14801,x14802)+E(f693(x14803,x14801,x14804,x14805,x14806),f693(x14803,x14802,x14804,x14805,x14806))
% 59.73/59.68 [1481]~E(x14811,x14812)+E(f693(x14813,x14814,x14811,x14815,x14816),f693(x14813,x14814,x14812,x14815,x14816))
% 59.73/59.68 [1482]~E(x14821,x14822)+E(f693(x14823,x14824,x14825,x14821,x14826),f693(x14823,x14824,x14825,x14822,x14826))
% 59.73/59.68 [1483]~E(x14831,x14832)+E(f693(x14833,x14834,x14835,x14836,x14831),f693(x14833,x14834,x14835,x14836,x14832))
% 59.73/59.68 [1484]~E(x14841,x14842)+E(f804(x14841,x14843,x14844),f804(x14842,x14843,x14844))
% 59.73/59.68 [1485]~E(x14851,x14852)+E(f804(x14853,x14851,x14854),f804(x14853,x14852,x14854))
% 59.73/59.68 [1486]~E(x14861,x14862)+E(f804(x14863,x14864,x14861),f804(x14863,x14864,x14862))
% 59.73/59.68 [1487]~E(x14871,x14872)+E(f246(x14871,x14873),f246(x14872,x14873))
% 59.73/59.68 [1488]~E(x14881,x14882)+E(f246(x14883,x14881),f246(x14883,x14882))
% 59.73/59.68 [1489]~E(x14891,x14892)+E(f852(x14891,x14893,x14894),f852(x14892,x14893,x14894))
% 59.73/59.68 [1490]~E(x14901,x14902)+E(f852(x14903,x14901,x14904),f852(x14903,x14902,x14904))
% 59.73/59.68 [1491]~E(x14911,x14912)+E(f852(x14913,x14914,x14911),f852(x14913,x14914,x14912))
% 59.73/59.68 [1492]~E(x14921,x14922)+E(f588(x14921,x14923,x14924),f588(x14922,x14923,x14924))
% 59.73/59.68 [1493]~E(x14931,x14932)+E(f588(x14933,x14931,x14934),f588(x14933,x14932,x14934))
% 59.73/59.68 [1494]~E(x14941,x14942)+E(f588(x14943,x14944,x14941),f588(x14943,x14944,x14942))
% 59.73/59.68 [1495]~E(x14951,x14952)+E(f549(x14951),f549(x14952))
% 59.73/59.68 [1496]~E(x14961,x14962)+E(f552(x14961,x14963,x14964),f552(x14962,x14963,x14964))
% 59.73/59.68 [1497]~E(x14971,x14972)+E(f552(x14973,x14971,x14974),f552(x14973,x14972,x14974))
% 59.73/59.68 [1498]~E(x14981,x14982)+E(f552(x14983,x14984,x14981),f552(x14983,x14984,x14982))
% 59.73/59.68 [1499]~E(x14991,x14992)+E(f421(x14991,x14993,x14994),f421(x14992,x14993,x14994))
% 59.73/59.68 [1500]~E(x15001,x15002)+E(f421(x15003,x15001,x15004),f421(x15003,x15002,x15004))
% 59.73/59.68 [1501]~E(x15011,x15012)+E(f421(x15013,x15014,x15011),f421(x15013,x15014,x15012))
% 59.73/59.68 [1502]~E(x15021,x15022)+E(f571(x15021,x15023,x15024,x15025,x15026,x15027),f571(x15022,x15023,x15024,x15025,x15026,x15027))
% 59.73/59.68 [1503]~E(x15031,x15032)+E(f571(x15033,x15031,x15034,x15035,x15036,x15037),f571(x15033,x15032,x15034,x15035,x15036,x15037))
% 59.73/59.68 [1504]~E(x15041,x15042)+E(f571(x15043,x15044,x15041,x15045,x15046,x15047),f571(x15043,x15044,x15042,x15045,x15046,x15047))
% 59.73/59.68 [1505]~E(x15051,x15052)+E(f571(x15053,x15054,x15055,x15051,x15056,x15057),f571(x15053,x15054,x15055,x15052,x15056,x15057))
% 59.73/59.68 [1506]~E(x15061,x15062)+E(f571(x15063,x15064,x15065,x15066,x15061,x15067),f571(x15063,x15064,x15065,x15066,x15062,x15067))
% 59.73/59.68 [1507]~E(x15071,x15072)+E(f571(x15073,x15074,x15075,x15076,x15077,x15071),f571(x15073,x15074,x15075,x15076,x15077,x15072))
% 59.73/59.68 [1508]~E(x15081,x15082)+E(f398(x15081,x15083),f398(x15082,x15083))
% 59.73/59.68 [1509]~E(x15091,x15092)+E(f398(x15093,x15091),f398(x15093,x15092))
% 59.73/59.68 [1510]~E(x15101,x15102)+E(f510(x15101,x15103,x15104,x15105,x15106),f510(x15102,x15103,x15104,x15105,x15106))
% 59.73/59.68 [1511]~E(x15111,x15112)+E(f510(x15113,x15111,x15114,x15115,x15116),f510(x15113,x15112,x15114,x15115,x15116))
% 59.73/59.68 [1512]~E(x15121,x15122)+E(f510(x15123,x15124,x15121,x15125,x15126),f510(x15123,x15124,x15122,x15125,x15126))
% 59.73/59.68 [1513]~E(x15131,x15132)+E(f510(x15133,x15134,x15135,x15131,x15136),f510(x15133,x15134,x15135,x15132,x15136))
% 59.73/59.68 [1514]~E(x15141,x15142)+E(f510(x15143,x15144,x15145,x15146,x15141),f510(x15143,x15144,x15145,x15146,x15142))
% 59.73/59.68 [1515]~E(x15151,x15152)+E(f555(x15151,x15153,x15154,x15155),f555(x15152,x15153,x15154,x15155))
% 59.73/59.68 [1516]~E(x15161,x15162)+E(f555(x15163,x15161,x15164,x15165),f555(x15163,x15162,x15164,x15165))
% 59.73/59.68 [1517]~E(x15171,x15172)+E(f555(x15173,x15174,x15171,x15175),f555(x15173,x15174,x15172,x15175))
% 59.73/59.68 [1518]~E(x15181,x15182)+E(f555(x15183,x15184,x15185,x15181),f555(x15183,x15184,x15185,x15182))
% 59.73/59.68 [1519]~E(x15191,x15192)+E(f271(x15191,x15193,x15194,x15195,x15196),f271(x15192,x15193,x15194,x15195,x15196))
% 59.73/59.68 [1520]~E(x15201,x15202)+E(f271(x15203,x15201,x15204,x15205,x15206),f271(x15203,x15202,x15204,x15205,x15206))
% 59.73/59.68 [1521]~E(x15211,x15212)+E(f271(x15213,x15214,x15211,x15215,x15216),f271(x15213,x15214,x15212,x15215,x15216))
% 59.73/59.68 [1522]~E(x15221,x15222)+E(f271(x15223,x15224,x15225,x15221,x15226),f271(x15223,x15224,x15225,x15222,x15226))
% 59.73/59.68 [1523]~E(x15231,x15232)+E(f271(x15233,x15234,x15235,x15236,x15231),f271(x15233,x15234,x15235,x15236,x15232))
% 59.73/59.68 [1524]~E(x15241,x15242)+E(f467(x15241,x15243,x15244,x15245),f467(x15242,x15243,x15244,x15245))
% 59.73/59.68 [1525]~E(x15251,x15252)+E(f467(x15253,x15251,x15254,x15255),f467(x15253,x15252,x15254,x15255))
% 59.73/59.68 [1526]~E(x15261,x15262)+E(f467(x15263,x15264,x15261,x15265),f467(x15263,x15264,x15262,x15265))
% 59.73/59.68 [1527]~E(x15271,x15272)+E(f467(x15273,x15274,x15275,x15271),f467(x15273,x15274,x15275,x15272))
% 59.73/59.68 [1528]~E(x15281,x15282)+E(f136(x15281,x15283),f136(x15282,x15283))
% 59.73/59.68 [1529]~E(x15291,x15292)+E(f136(x15293,x15291),f136(x15293,x15292))
% 59.73/59.68 [1530]~E(x15301,x15302)+E(f217(x15301,x15303),f217(x15302,x15303))
% 59.73/59.68 [1531]~E(x15311,x15312)+E(f217(x15313,x15311),f217(x15313,x15312))
% 59.73/59.68 [1532]~E(x15321,x15322)+E(f355(x15321,x15323,x15324,x15325),f355(x15322,x15323,x15324,x15325))
% 59.73/59.68 [1533]~E(x15331,x15332)+E(f355(x15333,x15331,x15334,x15335),f355(x15333,x15332,x15334,x15335))
% 59.73/59.68 [1534]~E(x15341,x15342)+E(f355(x15343,x15344,x15341,x15345),f355(x15343,x15344,x15342,x15345))
% 59.73/59.68 [1535]~E(x15351,x15352)+E(f355(x15353,x15354,x15355,x15351),f355(x15353,x15354,x15355,x15352))
% 59.73/59.68 [1536]~E(x15361,x15362)+E(f666(x15361,x15363,x15364,x15365),f666(x15362,x15363,x15364,x15365))
% 59.73/59.68 [1537]~E(x15371,x15372)+E(f666(x15373,x15371,x15374,x15375),f666(x15373,x15372,x15374,x15375))
% 59.73/59.68 [1538]~E(x15381,x15382)+E(f666(x15383,x15384,x15381,x15385),f666(x15383,x15384,x15382,x15385))
% 59.73/59.68 [1539]~E(x15391,x15392)+E(f666(x15393,x15394,x15395,x15391),f666(x15393,x15394,x15395,x15392))
% 59.73/59.68 [1540]~E(x15401,x15402)+E(f593(x15401,x15403,x15404,x15405,x15406),f593(x15402,x15403,x15404,x15405,x15406))
% 59.73/59.68 [1541]~E(x15411,x15412)+E(f593(x15413,x15411,x15414,x15415,x15416),f593(x15413,x15412,x15414,x15415,x15416))
% 59.73/59.68 [1542]~E(x15421,x15422)+E(f593(x15423,x15424,x15421,x15425,x15426),f593(x15423,x15424,x15422,x15425,x15426))
% 59.73/59.68 [1543]~E(x15431,x15432)+E(f593(x15433,x15434,x15435,x15431,x15436),f593(x15433,x15434,x15435,x15432,x15436))
% 59.73/59.68 [1544]~E(x15441,x15442)+E(f593(x15443,x15444,x15445,x15446,x15441),f593(x15443,x15444,x15445,x15446,x15442))
% 59.73/59.68 [1545]~E(x15451,x15452)+E(f356(x15451,x15453,x15454),f356(x15452,x15453,x15454))
% 59.73/59.68 [1546]~E(x15461,x15462)+E(f356(x15463,x15461,x15464),f356(x15463,x15462,x15464))
% 59.73/59.68 [1547]~E(x15471,x15472)+E(f356(x15473,x15474,x15471),f356(x15473,x15474,x15472))
% 59.73/59.68 [1548]~E(x15481,x15482)+E(f339(x15481,x15483,x15484,x15485),f339(x15482,x15483,x15484,x15485))
% 59.73/59.68 [1549]~E(x15491,x15492)+E(f339(x15493,x15491,x15494,x15495),f339(x15493,x15492,x15494,x15495))
% 59.73/59.68 [1550]~E(x15501,x15502)+E(f339(x15503,x15504,x15501,x15505),f339(x15503,x15504,x15502,x15505))
% 59.73/59.68 [1551]~E(x15511,x15512)+E(f339(x15513,x15514,x15515,x15511),f339(x15513,x15514,x15515,x15512))
% 59.73/59.68 [1552]~E(x15521,x15522)+E(f112(x15521,x15523,x15524),f112(x15522,x15523,x15524))
% 59.73/59.68 [1553]~E(x15531,x15532)+E(f112(x15533,x15531,x15534),f112(x15533,x15532,x15534))
% 59.73/59.68 [1554]~E(x15541,x15542)+E(f112(x15543,x15544,x15541),f112(x15543,x15544,x15542))
% 59.73/59.68 [1555]~E(x15551,x15552)+E(f480(x15551,x15553,x15554,x15555),f480(x15552,x15553,x15554,x15555))
% 59.73/59.68 [1556]~E(x15561,x15562)+E(f480(x15563,x15561,x15564,x15565),f480(x15563,x15562,x15564,x15565))
% 59.73/59.68 [1557]~E(x15571,x15572)+E(f480(x15573,x15574,x15571,x15575),f480(x15573,x15574,x15572,x15575))
% 59.73/59.68 [1558]~E(x15581,x15582)+E(f480(x15583,x15584,x15585,x15581),f480(x15583,x15584,x15585,x15582))
% 59.73/59.68 [1559]~E(x15591,x15592)+E(f819(x15591,x15593,x15594,x15595,x15596,x15597,x15598),f819(x15592,x15593,x15594,x15595,x15596,x15597,x15598))
% 59.73/59.68 [1560]~E(x15601,x15602)+E(f819(x15603,x15601,x15604,x15605,x15606,x15607,x15608),f819(x15603,x15602,x15604,x15605,x15606,x15607,x15608))
% 59.73/59.68 [1561]~E(x15611,x15612)+E(f819(x15613,x15614,x15611,x15615,x15616,x15617,x15618),f819(x15613,x15614,x15612,x15615,x15616,x15617,x15618))
% 59.73/59.68 [1562]~E(x15621,x15622)+E(f819(x15623,x15624,x15625,x15621,x15626,x15627,x15628),f819(x15623,x15624,x15625,x15622,x15626,x15627,x15628))
% 59.73/59.68 [1563]~E(x15631,x15632)+E(f819(x15633,x15634,x15635,x15636,x15631,x15637,x15638),f819(x15633,x15634,x15635,x15636,x15632,x15637,x15638))
% 59.73/59.68 [1564]~E(x15641,x15642)+E(f819(x15643,x15644,x15645,x15646,x15647,x15641,x15648),f819(x15643,x15644,x15645,x15646,x15647,x15642,x15648))
% 59.73/59.68 [1565]~E(x15651,x15652)+E(f819(x15653,x15654,x15655,x15656,x15657,x15658,x15651),f819(x15653,x15654,x15655,x15656,x15657,x15658,x15652))
% 59.73/59.68 [1566]~E(x15661,x15662)+E(f641(x15661,x15663,x15664),f641(x15662,x15663,x15664))
% 59.73/59.68 [1567]~E(x15671,x15672)+E(f641(x15673,x15671,x15674),f641(x15673,x15672,x15674))
% 59.73/59.68 [1568]~E(x15681,x15682)+E(f641(x15683,x15684,x15681),f641(x15683,x15684,x15682))
% 59.73/59.68 [1569]~E(x15691,x15692)+E(f729(x15691,x15693,x15694),f729(x15692,x15693,x15694))
% 59.73/59.68 [1570]~E(x15701,x15702)+E(f729(x15703,x15701,x15704),f729(x15703,x15702,x15704))
% 59.73/59.68 [1571]~E(x15711,x15712)+E(f729(x15713,x15714,x15711),f729(x15713,x15714,x15712))
% 59.73/59.68 [1572]~E(x15721,x15722)+E(f773(x15721,x15723,x15724,x15725,x15726),f773(x15722,x15723,x15724,x15725,x15726))
% 59.73/59.68 [1573]~E(x15731,x15732)+E(f773(x15733,x15731,x15734,x15735,x15736),f773(x15733,x15732,x15734,x15735,x15736))
% 59.73/59.68 [1574]~E(x15741,x15742)+E(f773(x15743,x15744,x15741,x15745,x15746),f773(x15743,x15744,x15742,x15745,x15746))
% 59.73/59.68 [1575]~E(x15751,x15752)+E(f773(x15753,x15754,x15755,x15751,x15756),f773(x15753,x15754,x15755,x15752,x15756))
% 59.73/59.68 [1576]~E(x15761,x15762)+E(f773(x15763,x15764,x15765,x15766,x15761),f773(x15763,x15764,x15765,x15766,x15762))
% 59.73/59.68 [1577]~E(x15771,x15772)+E(f370(x15771,x15773,x15774,x15775,x15776),f370(x15772,x15773,x15774,x15775,x15776))
% 59.73/59.68 [1578]~E(x15781,x15782)+E(f370(x15783,x15781,x15784,x15785,x15786),f370(x15783,x15782,x15784,x15785,x15786))
% 59.73/59.68 [1579]~E(x15791,x15792)+E(f370(x15793,x15794,x15791,x15795,x15796),f370(x15793,x15794,x15792,x15795,x15796))
% 59.73/59.68 [1580]~E(x15801,x15802)+E(f370(x15803,x15804,x15805,x15801,x15806),f370(x15803,x15804,x15805,x15802,x15806))
% 59.73/59.68 [1581]~E(x15811,x15812)+E(f370(x15813,x15814,x15815,x15816,x15811),f370(x15813,x15814,x15815,x15816,x15812))
% 59.73/59.68 [1582]~E(x15821,x15822)+E(f779(x15821,x15823,x15824),f779(x15822,x15823,x15824))
% 59.73/59.68 [1583]~E(x15831,x15832)+E(f779(x15833,x15831,x15834),f779(x15833,x15832,x15834))
% 59.73/59.68 [1584]~E(x15841,x15842)+E(f779(x15843,x15844,x15841),f779(x15843,x15844,x15842))
% 59.73/59.68 [1585]~E(x15851,x15852)+E(f487(x15851,x15853,x15854,x15855),f487(x15852,x15853,x15854,x15855))
% 59.73/59.68 [1586]~E(x15861,x15862)+E(f487(x15863,x15861,x15864,x15865),f487(x15863,x15862,x15864,x15865))
% 59.73/59.68 [1587]~E(x15871,x15872)+E(f487(x15873,x15874,x15871,x15875),f487(x15873,x15874,x15872,x15875))
% 59.73/59.68 [1588]~E(x15881,x15882)+E(f487(x15883,x15884,x15885,x15881),f487(x15883,x15884,x15885,x15882))
% 59.73/59.68 [1589]~E(x15891,x15892)+E(f36(x15891),f36(x15892))
% 59.73/59.68 [1590]~E(x15901,x15902)+E(f837(x15901,x15903,x15904,x15905,x15906),f837(x15902,x15903,x15904,x15905,x15906))
% 59.73/59.68 [1591]~E(x15911,x15912)+E(f837(x15913,x15911,x15914,x15915,x15916),f837(x15913,x15912,x15914,x15915,x15916))
% 59.73/59.68 [1592]~E(x15921,x15922)+E(f837(x15923,x15924,x15921,x15925,x15926),f837(x15923,x15924,x15922,x15925,x15926))
% 59.73/59.68 [1593]~E(x15931,x15932)+E(f837(x15933,x15934,x15935,x15931,x15936),f837(x15933,x15934,x15935,x15932,x15936))
% 59.73/59.68 [1594]~E(x15941,x15942)+E(f837(x15943,x15944,x15945,x15946,x15941),f837(x15943,x15944,x15945,x15946,x15942))
% 59.73/59.68 [1595]~E(x15951,x15952)+E(f622(x15951,x15953,x15954,x15955),f622(x15952,x15953,x15954,x15955))
% 59.73/59.68 [1596]~E(x15961,x15962)+E(f622(x15963,x15961,x15964,x15965),f622(x15963,x15962,x15964,x15965))
% 59.73/59.68 [1597]~E(x15971,x15972)+E(f622(x15973,x15974,x15971,x15975),f622(x15973,x15974,x15972,x15975))
% 59.73/59.68 [1598]~E(x15981,x15982)+E(f622(x15983,x15984,x15985,x15981),f622(x15983,x15984,x15985,x15982))
% 59.73/59.68 [1599]~E(x15991,x15992)+E(f377(x15991,x15993,x15994),f377(x15992,x15993,x15994))
% 59.73/59.68 [1600]~E(x16001,x16002)+E(f377(x16003,x16001,x16004),f377(x16003,x16002,x16004))
% 59.73/59.68 [1601]~E(x16011,x16012)+E(f377(x16013,x16014,x16011),f377(x16013,x16014,x16012))
% 59.73/59.68 [1602]~E(x16021,x16022)+E(f350(x16021,x16023),f350(x16022,x16023))
% 59.73/59.68 [1603]~E(x16031,x16032)+E(f350(x16033,x16031),f350(x16033,x16032))
% 59.73/59.68 [1604]~E(x16041,x16042)+E(f190(x16041,x16043,x16044,x16045),f190(x16042,x16043,x16044,x16045))
% 59.73/59.68 [1605]~E(x16051,x16052)+E(f190(x16053,x16051,x16054,x16055),f190(x16053,x16052,x16054,x16055))
% 59.73/59.68 [1606]~E(x16061,x16062)+E(f190(x16063,x16064,x16061,x16065),f190(x16063,x16064,x16062,x16065))
% 59.73/59.68 [1607]~E(x16071,x16072)+E(f190(x16073,x16074,x16075,x16071),f190(x16073,x16074,x16075,x16072))
% 59.73/59.68 [1608]~E(x16081,x16082)+E(f543(x16081,x16083,x16084,x16085,x16086,x16087,x16088,x16089),f543(x16082,x16083,x16084,x16085,x16086,x16087,x16088,x16089))
% 59.73/59.68 [1609]~E(x16091,x16092)+E(f543(x16093,x16091,x16094,x16095,x16096,x16097,x16098,x16099),f543(x16093,x16092,x16094,x16095,x16096,x16097,x16098,x16099))
% 59.73/59.68 [1610]~E(x16101,x16102)+E(f543(x16103,x16104,x16101,x16105,x16106,x16107,x16108,x16109),f543(x16103,x16104,x16102,x16105,x16106,x16107,x16108,x16109))
% 59.73/59.68 [1611]~E(x16111,x16112)+E(f543(x16113,x16114,x16115,x16111,x16116,x16117,x16118,x16119),f543(x16113,x16114,x16115,x16112,x16116,x16117,x16118,x16119))
% 59.73/59.68 [1612]~E(x16121,x16122)+E(f543(x16123,x16124,x16125,x16126,x16121,x16127,x16128,x16129),f543(x16123,x16124,x16125,x16126,x16122,x16127,x16128,x16129))
% 59.73/59.68 [1613]~E(x16131,x16132)+E(f543(x16133,x16134,x16135,x16136,x16137,x16131,x16138,x16139),f543(x16133,x16134,x16135,x16136,x16137,x16132,x16138,x16139))
% 59.73/59.68 [1614]~E(x16141,x16142)+E(f543(x16143,x16144,x16145,x16146,x16147,x16148,x16141,x16149),f543(x16143,x16144,x16145,x16146,x16147,x16148,x16142,x16149))
% 59.73/59.68 [1615]~E(x16151,x16152)+E(f543(x16153,x16154,x16155,x16156,x16157,x16158,x16159,x16151),f543(x16153,x16154,x16155,x16156,x16157,x16158,x16159,x16152))
% 59.73/59.68 [1616]~E(x16161,x16162)+E(f877(x16161,x16163,x16164,x16165,x16166,x16167,x16168),f877(x16162,x16163,x16164,x16165,x16166,x16167,x16168))
% 59.73/59.68 [1617]~E(x16171,x16172)+E(f877(x16173,x16171,x16174,x16175,x16176,x16177,x16178),f877(x16173,x16172,x16174,x16175,x16176,x16177,x16178))
% 59.73/59.68 [1618]~E(x16181,x16182)+E(f877(x16183,x16184,x16181,x16185,x16186,x16187,x16188),f877(x16183,x16184,x16182,x16185,x16186,x16187,x16188))
% 59.73/59.68 [1619]~E(x16191,x16192)+E(f877(x16193,x16194,x16195,x16191,x16196,x16197,x16198),f877(x16193,x16194,x16195,x16192,x16196,x16197,x16198))
% 59.73/59.68 [1620]~E(x16201,x16202)+E(f877(x16203,x16204,x16205,x16206,x16201,x16207,x16208),f877(x16203,x16204,x16205,x16206,x16202,x16207,x16208))
% 59.73/59.68 [1621]~E(x16211,x16212)+E(f877(x16213,x16214,x16215,x16216,x16217,x16211,x16218),f877(x16213,x16214,x16215,x16216,x16217,x16212,x16218))
% 59.73/59.68 [1622]~E(x16221,x16222)+E(f877(x16223,x16224,x16225,x16226,x16227,x16228,x16221),f877(x16223,x16224,x16225,x16226,x16227,x16228,x16222))
% 59.73/59.68 [1623]~E(x16231,x16232)+E(f559(x16231,x16233,x16234),f559(x16232,x16233,x16234))
% 59.73/59.68 [1624]~E(x16241,x16242)+E(f559(x16243,x16241,x16244),f559(x16243,x16242,x16244))
% 59.73/59.68 [1625]~E(x16251,x16252)+E(f559(x16253,x16254,x16251),f559(x16253,x16254,x16252))
% 59.73/59.68 [1626]~E(x16261,x16262)+E(f697(x16261,x16263,x16264,x16265),f697(x16262,x16263,x16264,x16265))
% 59.73/59.68 [1627]~E(x16271,x16272)+E(f697(x16273,x16271,x16274,x16275),f697(x16273,x16272,x16274,x16275))
% 59.73/59.68 [1628]~E(x16281,x16282)+E(f697(x16283,x16284,x16281,x16285),f697(x16283,x16284,x16282,x16285))
% 59.73/59.68 [1629]~E(x16291,x16292)+E(f697(x16293,x16294,x16295,x16291),f697(x16293,x16294,x16295,x16292))
% 59.73/59.68 [1630]~E(x16301,x16302)+E(f387(x16301,x16303,x16304),f387(x16302,x16303,x16304))
% 59.73/59.68 [1631]~E(x16311,x16312)+E(f387(x16313,x16311,x16314),f387(x16313,x16312,x16314))
% 59.73/59.68 [1632]~E(x16321,x16322)+E(f387(x16323,x16324,x16321),f387(x16323,x16324,x16322))
% 59.73/59.68 [1633]~E(x16331,x16332)+E(f128(x16331),f128(x16332))
% 59.73/59.68 [1634]~E(x16341,x16342)+E(f572(x16341,x16343,x16344),f572(x16342,x16343,x16344))
% 59.73/59.68 [1635]~E(x16351,x16352)+E(f572(x16353,x16351,x16354),f572(x16353,x16352,x16354))
% 59.73/59.68 [1636]~E(x16361,x16362)+E(f572(x16363,x16364,x16361),f572(x16363,x16364,x16362))
% 59.73/59.68 [1637]~E(x16371,x16372)+E(f648(x16371,x16373,x16374,x16375),f648(x16372,x16373,x16374,x16375))
% 59.73/59.68 [1638]~E(x16381,x16382)+E(f648(x16383,x16381,x16384,x16385),f648(x16383,x16382,x16384,x16385))
% 59.73/59.68 [1639]~E(x16391,x16392)+E(f648(x16393,x16394,x16391,x16395),f648(x16393,x16394,x16392,x16395))
% 59.73/59.68 [1640]~E(x16401,x16402)+E(f648(x16403,x16404,x16405,x16401),f648(x16403,x16404,x16405,x16402))
% 59.73/59.68 [1641]~E(x16411,x16412)+E(f378(x16411,x16413,x16414),f378(x16412,x16413,x16414))
% 59.73/59.68 [1642]~E(x16421,x16422)+E(f378(x16423,x16421,x16424),f378(x16423,x16422,x16424))
% 59.73/59.68 [1643]~E(x16431,x16432)+E(f378(x16433,x16434,x16431),f378(x16433,x16434,x16432))
% 59.73/59.68 [1644]~E(x16441,x16442)+E(f720(x16441,x16443,x16444,x16445),f720(x16442,x16443,x16444,x16445))
% 59.73/59.68 [1645]~E(x16451,x16452)+E(f720(x16453,x16451,x16454,x16455),f720(x16453,x16452,x16454,x16455))
% 59.73/59.68 [1646]~E(x16461,x16462)+E(f720(x16463,x16464,x16461,x16465),f720(x16463,x16464,x16462,x16465))
% 59.73/59.68 [1647]~E(x16471,x16472)+E(f720(x16473,x16474,x16475,x16471),f720(x16473,x16474,x16475,x16472))
% 59.73/59.68 [1648]~E(x16481,x16482)+E(f319(x16481),f319(x16482))
% 59.73/59.68 [1649]~E(x16491,x16492)+E(f485(x16491,x16493,x16494,x16495,x16496),f485(x16492,x16493,x16494,x16495,x16496))
% 59.73/59.68 [1650]~E(x16501,x16502)+E(f485(x16503,x16501,x16504,x16505,x16506),f485(x16503,x16502,x16504,x16505,x16506))
% 59.73/59.68 [1651]~E(x16511,x16512)+E(f485(x16513,x16514,x16511,x16515,x16516),f485(x16513,x16514,x16512,x16515,x16516))
% 59.73/59.68 [1652]~E(x16521,x16522)+E(f485(x16523,x16524,x16525,x16521,x16526),f485(x16523,x16524,x16525,x16522,x16526))
% 59.73/59.68 [1653]~E(x16531,x16532)+E(f485(x16533,x16534,x16535,x16536,x16531),f485(x16533,x16534,x16535,x16536,x16532))
% 59.73/59.68 [1654]~E(x16541,x16542)+E(f450(x16541,x16543),f450(x16542,x16543))
% 59.73/59.68 [1655]~E(x16551,x16552)+E(f450(x16553,x16551),f450(x16553,x16552))
% 59.73/59.68 [1656]~E(x16561,x16562)+E(f444(x16561,x16563,x16564,x16565),f444(x16562,x16563,x16564,x16565))
% 59.73/59.68 [1657]~E(x16571,x16572)+E(f444(x16573,x16571,x16574,x16575),f444(x16573,x16572,x16574,x16575))
% 59.73/59.68 [1658]~E(x16581,x16582)+E(f444(x16583,x16584,x16581,x16585),f444(x16583,x16584,x16582,x16585))
% 59.73/59.68 [1659]~E(x16591,x16592)+E(f444(x16593,x16594,x16595,x16591),f444(x16593,x16594,x16595,x16592))
% 59.73/59.68 [1660]~E(x16601,x16602)+E(f701(x16601,x16603,x16604,x16605,x16606),f701(x16602,x16603,x16604,x16605,x16606))
% 59.73/59.68 [1661]~E(x16611,x16612)+E(f701(x16613,x16611,x16614,x16615,x16616),f701(x16613,x16612,x16614,x16615,x16616))
% 59.73/59.68 [1662]~E(x16621,x16622)+E(f701(x16623,x16624,x16621,x16625,x16626),f701(x16623,x16624,x16622,x16625,x16626))
% 59.73/59.68 [1663]~E(x16631,x16632)+E(f701(x16633,x16634,x16635,x16631,x16636),f701(x16633,x16634,x16635,x16632,x16636))
% 59.73/59.68 [1664]~E(x16641,x16642)+E(f701(x16643,x16644,x16645,x16646,x16641),f701(x16643,x16644,x16645,x16646,x16642))
% 59.73/59.68 [1665]~E(x16651,x16652)+E(f669(x16651,x16653,x16654,x16655,x16656,x16657),f669(x16652,x16653,x16654,x16655,x16656,x16657))
% 59.73/59.68 [1666]~E(x16661,x16662)+E(f669(x16663,x16661,x16664,x16665,x16666,x16667),f669(x16663,x16662,x16664,x16665,x16666,x16667))
% 59.73/59.68 [1667]~E(x16671,x16672)+E(f669(x16673,x16674,x16671,x16675,x16676,x16677),f669(x16673,x16674,x16672,x16675,x16676,x16677))
% 59.73/59.68 [1668]~E(x16681,x16682)+E(f669(x16683,x16684,x16685,x16681,x16686,x16687),f669(x16683,x16684,x16685,x16682,x16686,x16687))
% 59.73/59.68 [1669]~E(x16691,x16692)+E(f669(x16693,x16694,x16695,x16696,x16691,x16697),f669(x16693,x16694,x16695,x16696,x16692,x16697))
% 59.73/59.68 [1670]~E(x16701,x16702)+E(f669(x16703,x16704,x16705,x16706,x16707,x16701),f669(x16703,x16704,x16705,x16706,x16707,x16702))
% 59.73/59.68 [1671]~E(x16711,x16712)+E(f867(x16711,x16713,x16714),f867(x16712,x16713,x16714))
% 59.73/59.68 [1672]~E(x16721,x16722)+E(f867(x16723,x16721,x16724),f867(x16723,x16722,x16724))
% 59.73/59.68 [1673]~E(x16731,x16732)+E(f867(x16733,x16734,x16731),f867(x16733,x16734,x16732))
% 59.73/59.68 [1674]~E(x16741,x16742)+E(f519(x16741,x16743),f519(x16742,x16743))
% 59.73/59.68 [1675]~E(x16751,x16752)+E(f519(x16753,x16751),f519(x16753,x16752))
% 59.73/59.68 [1676]~E(x16761,x16762)+E(f784(x16761,x16763,x16764,x16765,x16766),f784(x16762,x16763,x16764,x16765,x16766))
% 59.73/59.68 [1677]~E(x16771,x16772)+E(f784(x16773,x16771,x16774,x16775,x16776),f784(x16773,x16772,x16774,x16775,x16776))
% 59.73/59.68 [1678]~E(x16781,x16782)+E(f784(x16783,x16784,x16781,x16785,x16786),f784(x16783,x16784,x16782,x16785,x16786))
% 59.73/59.68 [1679]~E(x16791,x16792)+E(f784(x16793,x16794,x16795,x16791,x16796),f784(x16793,x16794,x16795,x16792,x16796))
% 59.73/59.68 [1680]~E(x16801,x16802)+E(f784(x16803,x16804,x16805,x16806,x16801),f784(x16803,x16804,x16805,x16806,x16802))
% 59.73/59.68 [1681]~E(x16811,x16812)+E(f752(x16811,x16813,x16814,x16815),f752(x16812,x16813,x16814,x16815))
% 59.73/59.68 [1682]~E(x16821,x16822)+E(f752(x16823,x16821,x16824,x16825),f752(x16823,x16822,x16824,x16825))
% 59.73/59.68 [1683]~E(x16831,x16832)+E(f752(x16833,x16834,x16831,x16835),f752(x16833,x16834,x16832,x16835))
% 59.73/59.68 [1684]~E(x16841,x16842)+E(f752(x16843,x16844,x16845,x16841),f752(x16843,x16844,x16845,x16842))
% 59.73/59.68 [1685]~E(x16851,x16852)+E(f770(x16851,x16853,x16854,x16855,x16856),f770(x16852,x16853,x16854,x16855,x16856))
% 59.73/59.68 [1686]~E(x16861,x16862)+E(f770(x16863,x16861,x16864,x16865,x16866),f770(x16863,x16862,x16864,x16865,x16866))
% 59.73/59.68 [1687]~E(x16871,x16872)+E(f770(x16873,x16874,x16871,x16875,x16876),f770(x16873,x16874,x16872,x16875,x16876))
% 59.73/59.68 [1688]~E(x16881,x16882)+E(f770(x16883,x16884,x16885,x16881,x16886),f770(x16883,x16884,x16885,x16882,x16886))
% 59.73/59.68 [1689]~E(x16891,x16892)+E(f770(x16893,x16894,x16895,x16896,x16891),f770(x16893,x16894,x16895,x16896,x16892))
% 59.73/59.68 [1690]~E(x16901,x16902)+E(f798(x16901,x16903,x16904,x16905),f798(x16902,x16903,x16904,x16905))
% 59.73/59.68 [1691]~E(x16911,x16912)+E(f798(x16913,x16911,x16914,x16915),f798(x16913,x16912,x16914,x16915))
% 59.73/59.68 [1692]~E(x16921,x16922)+E(f798(x16923,x16924,x16921,x16925),f798(x16923,x16924,x16922,x16925))
% 59.73/59.68 [1693]~E(x16931,x16932)+E(f798(x16933,x16934,x16935,x16931),f798(x16933,x16934,x16935,x16932))
% 59.73/59.68 [1694]~E(x16941,x16942)+E(f284(x16941),f284(x16942))
% 59.73/59.68 [1695]~E(x16951,x16952)+E(f750(x16951,x16953,x16954,x16955,x16956),f750(x16952,x16953,x16954,x16955,x16956))
% 59.73/59.68 [1696]~E(x16961,x16962)+E(f750(x16963,x16961,x16964,x16965,x16966),f750(x16963,x16962,x16964,x16965,x16966))
% 59.73/59.68 [1697]~E(x16971,x16972)+E(f750(x16973,x16974,x16971,x16975,x16976),f750(x16973,x16974,x16972,x16975,x16976))
% 59.73/59.68 [1698]~E(x16981,x16982)+E(f750(x16983,x16984,x16985,x16981,x16986),f750(x16983,x16984,x16985,x16982,x16986))
% 59.73/59.68 [1699]~E(x16991,x16992)+E(f750(x16993,x16994,x16995,x16996,x16991),f750(x16993,x16994,x16995,x16996,x16992))
% 59.73/59.68 [1700]~E(x17001,x17002)+E(f646(x17001,x17003,x17004,x17005),f646(x17002,x17003,x17004,x17005))
% 59.73/59.68 [1701]~E(x17011,x17012)+E(f646(x17013,x17011,x17014,x17015),f646(x17013,x17012,x17014,x17015))
% 59.73/59.68 [1702]~E(x17021,x17022)+E(f646(x17023,x17024,x17021,x17025),f646(x17023,x17024,x17022,x17025))
% 59.73/59.68 [1703]~E(x17031,x17032)+E(f646(x17033,x17034,x17035,x17031),f646(x17033,x17034,x17035,x17032))
% 59.73/59.68 [1704]~E(x17041,x17042)+E(f364(x17041,x17043),f364(x17042,x17043))
% 59.73/59.68 [1705]~E(x17051,x17052)+E(f364(x17053,x17051),f364(x17053,x17052))
% 59.73/59.68 [1706]~E(x17061,x17062)+E(f644(x17061,x17063,x17064),f644(x17062,x17063,x17064))
% 59.73/59.68 [1707]~E(x17071,x17072)+E(f644(x17073,x17071,x17074),f644(x17073,x17072,x17074))
% 59.73/59.68 [1708]~E(x17081,x17082)+E(f644(x17083,x17084,x17081),f644(x17083,x17084,x17082))
% 59.73/59.68 [1709]~E(x17091,x17092)+E(f632(x17091,x17093,x17094),f632(x17092,x17093,x17094))
% 59.73/59.68 [1710]~E(x17101,x17102)+E(f632(x17103,x17101,x17104),f632(x17103,x17102,x17104))
% 59.73/59.68 [1711]~E(x17111,x17112)+E(f632(x17113,x17114,x17111),f632(x17113,x17114,x17112))
% 59.73/59.68 [1712]~E(x17121,x17122)+E(f231(x17121,x17123,x17124,x17125),f231(x17122,x17123,x17124,x17125))
% 59.73/59.68 [1713]~E(x17131,x17132)+E(f231(x17133,x17131,x17134,x17135),f231(x17133,x17132,x17134,x17135))
% 59.73/59.68 [1714]~E(x17141,x17142)+E(f231(x17143,x17144,x17141,x17145),f231(x17143,x17144,x17142,x17145))
% 59.73/59.68 [1715]~E(x17151,x17152)+E(f231(x17153,x17154,x17155,x17151),f231(x17153,x17154,x17155,x17152))
% 59.73/59.68 [1716]~E(x17161,x17162)+E(f402(x17161,x17163),f402(x17162,x17163))
% 59.73/59.68 [1717]~E(x17171,x17172)+E(f402(x17173,x17171),f402(x17173,x17172))
% 59.73/59.68 [1718]~E(x17181,x17182)+E(f412(x17181,x17183),f412(x17182,x17183))
% 59.73/59.68 [1719]~E(x17191,x17192)+E(f412(x17193,x17191),f412(x17193,x17192))
% 59.73/59.68 [1720]~E(x17201,x17202)+E(f828(x17201,x17203,x17204,x17205,x17206),f828(x17202,x17203,x17204,x17205,x17206))
% 59.73/59.68 [1721]~E(x17211,x17212)+E(f828(x17213,x17211,x17214,x17215,x17216),f828(x17213,x17212,x17214,x17215,x17216))
% 59.73/59.68 [1722]~E(x17221,x17222)+E(f828(x17223,x17224,x17221,x17225,x17226),f828(x17223,x17224,x17222,x17225,x17226))
% 59.73/59.68 [1723]~E(x17231,x17232)+E(f828(x17233,x17234,x17235,x17231,x17236),f828(x17233,x17234,x17235,x17232,x17236))
% 59.73/59.68 [1724]~E(x17241,x17242)+E(f828(x17243,x17244,x17245,x17246,x17241),f828(x17243,x17244,x17245,x17246,x17242))
% 59.73/59.68 [1725]~E(x17251,x17252)+E(f435(x17251,x17253,x17254),f435(x17252,x17253,x17254))
% 59.73/59.68 [1726]~E(x17261,x17262)+E(f435(x17263,x17261,x17264),f435(x17263,x17262,x17264))
% 59.73/59.68 [1727]~E(x17271,x17272)+E(f435(x17273,x17274,x17271),f435(x17273,x17274,x17272))
% 59.73/59.68 [1728]~E(x17281,x17282)+E(f204(x17281),f204(x17282))
% 59.73/59.68 [1729]~E(x17291,x17292)+E(f700(x17291,x17293,x17294,x17295,x17296),f700(x17292,x17293,x17294,x17295,x17296))
% 59.73/59.68 [1730]~E(x17301,x17302)+E(f700(x17303,x17301,x17304,x17305,x17306),f700(x17303,x17302,x17304,x17305,x17306))
% 59.73/59.68 [1731]~E(x17311,x17312)+E(f700(x17313,x17314,x17311,x17315,x17316),f700(x17313,x17314,x17312,x17315,x17316))
% 59.73/59.68 [1732]~E(x17321,x17322)+E(f700(x17323,x17324,x17325,x17321,x17326),f700(x17323,x17324,x17325,x17322,x17326))
% 59.73/59.68 [1733]~E(x17331,x17332)+E(f700(x17333,x17334,x17335,x17336,x17331),f700(x17333,x17334,x17335,x17336,x17332))
% 59.73/59.68 [1734]~E(x17341,x17342)+E(f459(x17341,x17343,x17344,x17345),f459(x17342,x17343,x17344,x17345))
% 59.73/59.68 [1735]~E(x17351,x17352)+E(f459(x17353,x17351,x17354,x17355),f459(x17353,x17352,x17354,x17355))
% 59.73/59.68 [1736]~E(x17361,x17362)+E(f459(x17363,x17364,x17361,x17365),f459(x17363,x17364,x17362,x17365))
% 59.73/59.68 [1737]~E(x17371,x17372)+E(f459(x17373,x17374,x17375,x17371),f459(x17373,x17374,x17375,x17372))
% 59.73/59.68 [1738]~E(x17381,x17382)+E(f472(x17381,x17383,x17384,x17385),f472(x17382,x17383,x17384,x17385))
% 59.73/59.68 [1739]~E(x17391,x17392)+E(f472(x17393,x17391,x17394,x17395),f472(x17393,x17392,x17394,x17395))
% 59.73/59.68 [1740]~E(x17401,x17402)+E(f472(x17403,x17404,x17401,x17405),f472(x17403,x17404,x17402,x17405))
% 59.73/59.68 [1741]~E(x17411,x17412)+E(f472(x17413,x17414,x17415,x17411),f472(x17413,x17414,x17415,x17412))
% 59.73/59.68 [1742]~E(x17421,x17422)+E(f562(x17421,x17423,x17424),f562(x17422,x17423,x17424))
% 59.73/59.68 [1743]~E(x17431,x17432)+E(f562(x17433,x17431,x17434),f562(x17433,x17432,x17434))
% 59.73/59.68 [1744]~E(x17441,x17442)+E(f562(x17443,x17444,x17441),f562(x17443,x17444,x17442))
% 59.73/59.68 [1745]~E(x17451,x17452)+E(f513(x17451,x17453,x17454,x17455),f513(x17452,x17453,x17454,x17455))
% 59.73/59.68 [1746]~E(x17461,x17462)+E(f513(x17463,x17461,x17464,x17465),f513(x17463,x17462,x17464,x17465))
% 59.73/59.68 [1747]~E(x17471,x17472)+E(f513(x17473,x17474,x17471,x17475),f513(x17473,x17474,x17472,x17475))
% 59.73/59.68 [1748]~E(x17481,x17482)+E(f513(x17483,x17484,x17485,x17481),f513(x17483,x17484,x17485,x17482))
% 59.73/59.68 [1749]~E(x17491,x17492)+E(f564(x17491,x17493,x17494,x17495),f564(x17492,x17493,x17494,x17495))
% 59.73/59.68 [1750]~E(x17501,x17502)+E(f564(x17503,x17501,x17504,x17505),f564(x17503,x17502,x17504,x17505))
% 59.73/59.68 [1751]~E(x17511,x17512)+E(f564(x17513,x17514,x17511,x17515),f564(x17513,x17514,x17512,x17515))
% 59.73/59.68 [1752]~E(x17521,x17522)+E(f564(x17523,x17524,x17525,x17521),f564(x17523,x17524,x17525,x17522))
% 59.73/59.68 [1753]~E(x17531,x17532)+E(f509(x17531,x17533,x17534),f509(x17532,x17533,x17534))
% 59.73/59.68 [1754]~E(x17541,x17542)+E(f509(x17543,x17541,x17544),f509(x17543,x17542,x17544))
% 59.73/59.68 [1755]~E(x17551,x17552)+E(f509(x17553,x17554,x17551),f509(x17553,x17554,x17552))
% 59.73/59.68 [1756]~E(x17561,x17562)+E(f762(x17561,x17563,x17564,x17565,x17566),f762(x17562,x17563,x17564,x17565,x17566))
% 59.73/59.68 [1757]~E(x17571,x17572)+E(f762(x17573,x17571,x17574,x17575,x17576),f762(x17573,x17572,x17574,x17575,x17576))
% 59.73/59.68 [1758]~E(x17581,x17582)+E(f762(x17583,x17584,x17581,x17585,x17586),f762(x17583,x17584,x17582,x17585,x17586))
% 59.73/59.68 [1759]~E(x17591,x17592)+E(f762(x17593,x17594,x17595,x17591,x17596),f762(x17593,x17594,x17595,x17592,x17596))
% 59.73/59.68 [1760]~E(x17601,x17602)+E(f762(x17603,x17604,x17605,x17606,x17601),f762(x17603,x17604,x17605,x17606,x17602))
% 59.73/59.68 [1761]~E(x17611,x17612)+E(f436(x17611,x17613,x17614,x17615,x17616),f436(x17612,x17613,x17614,x17615,x17616))
% 59.73/59.68 [1762]~E(x17621,x17622)+E(f436(x17623,x17621,x17624,x17625,x17626),f436(x17623,x17622,x17624,x17625,x17626))
% 59.73/59.68 [1763]~E(x17631,x17632)+E(f436(x17633,x17634,x17631,x17635,x17636),f436(x17633,x17634,x17632,x17635,x17636))
% 59.73/59.68 [1764]~E(x17641,x17642)+E(f436(x17643,x17644,x17645,x17641,x17646),f436(x17643,x17644,x17645,x17642,x17646))
% 59.73/59.68 [1765]~E(x17651,x17652)+E(f436(x17653,x17654,x17655,x17656,x17651),f436(x17653,x17654,x17655,x17656,x17652))
% 59.73/59.68 [1766]~E(x17661,x17662)+E(f536(x17661,x17663,x17664,x17665,x17666,x17667),f536(x17662,x17663,x17664,x17665,x17666,x17667))
% 59.73/59.68 [1767]~E(x17671,x17672)+E(f536(x17673,x17671,x17674,x17675,x17676,x17677),f536(x17673,x17672,x17674,x17675,x17676,x17677))
% 59.73/59.68 [1768]~E(x17681,x17682)+E(f536(x17683,x17684,x17681,x17685,x17686,x17687),f536(x17683,x17684,x17682,x17685,x17686,x17687))
% 59.73/59.68 [1769]~E(x17691,x17692)+E(f536(x17693,x17694,x17695,x17691,x17696,x17697),f536(x17693,x17694,x17695,x17692,x17696,x17697))
% 59.73/59.68 [1770]~E(x17701,x17702)+E(f536(x17703,x17704,x17705,x17706,x17701,x17707),f536(x17703,x17704,x17705,x17706,x17702,x17707))
% 59.73/59.68 [1771]~E(x17711,x17712)+E(f536(x17713,x17714,x17715,x17716,x17717,x17711),f536(x17713,x17714,x17715,x17716,x17717,x17712))
% 59.73/59.68 [1772]~E(x17721,x17722)+E(f259(x17721,x17723,x17724),f259(x17722,x17723,x17724))
% 59.73/59.68 [1773]~E(x17731,x17732)+E(f259(x17733,x17731,x17734),f259(x17733,x17732,x17734))
% 59.73/59.68 [1774]~E(x17741,x17742)+E(f259(x17743,x17744,x17741),f259(x17743,x17744,x17742))
% 59.73/59.68 [1775]~E(x17751,x17752)+E(f783(x17751,x17753,x17754),f783(x17752,x17753,x17754))
% 59.73/59.68 [1776]~E(x17761,x17762)+E(f783(x17763,x17761,x17764),f783(x17763,x17762,x17764))
% 59.73/59.68 [1777]~E(x17771,x17772)+E(f783(x17773,x17774,x17771),f783(x17773,x17774,x17772))
% 59.73/59.68 [1778]~E(x17781,x17782)+E(f868(x17781,x17783,x17784),f868(x17782,x17783,x17784))
% 59.73/59.68 [1779]~E(x17791,x17792)+E(f868(x17793,x17791,x17794),f868(x17793,x17792,x17794))
% 59.73/59.68 [1780]~E(x17801,x17802)+E(f868(x17803,x17804,x17801),f868(x17803,x17804,x17802))
% 59.73/59.68 [1781]~E(x17811,x17812)+E(f721(x17811,x17813,x17814,x17815,x17816),f721(x17812,x17813,x17814,x17815,x17816))
% 59.73/59.68 [1782]~E(x17821,x17822)+E(f721(x17823,x17821,x17824,x17825,x17826),f721(x17823,x17822,x17824,x17825,x17826))
% 59.73/59.68 [1783]~E(x17831,x17832)+E(f721(x17833,x17834,x17831,x17835,x17836),f721(x17833,x17834,x17832,x17835,x17836))
% 59.73/59.68 [1784]~E(x17841,x17842)+E(f721(x17843,x17844,x17845,x17841,x17846),f721(x17843,x17844,x17845,x17842,x17846))
% 59.73/59.68 [1785]~E(x17851,x17852)+E(f721(x17853,x17854,x17855,x17856,x17851),f721(x17853,x17854,x17855,x17856,x17852))
% 59.73/59.68 [1786]~E(x17861,x17862)+E(f786(x17861,x17863,x17864),f786(x17862,x17863,x17864))
% 59.73/59.68 [1787]~E(x17871,x17872)+E(f786(x17873,x17871,x17874),f786(x17873,x17872,x17874))
% 59.73/59.68 [1788]~E(x17881,x17882)+E(f786(x17883,x17884,x17881),f786(x17883,x17884,x17882))
% 59.73/59.68 [1789]~E(x17891,x17892)+E(f753(x17891,x17893,x17894,x17895,x17896),f753(x17892,x17893,x17894,x17895,x17896))
% 59.73/59.68 [1790]~E(x17901,x17902)+E(f753(x17903,x17901,x17904,x17905,x17906),f753(x17903,x17902,x17904,x17905,x17906))
% 59.73/59.68 [1791]~E(x17911,x17912)+E(f753(x17913,x17914,x17911,x17915,x17916),f753(x17913,x17914,x17912,x17915,x17916))
% 59.73/59.68 [1792]~E(x17921,x17922)+E(f753(x17923,x17924,x17925,x17921,x17926),f753(x17923,x17924,x17925,x17922,x17926))
% 59.73/59.68 [1793]~E(x17931,x17932)+E(f753(x17933,x17934,x17935,x17936,x17931),f753(x17933,x17934,x17935,x17936,x17932))
% 59.73/59.68 [1794]~E(x17941,x17942)+E(f121(x17941,x17943,x17944,x17945,x17946),f121(x17942,x17943,x17944,x17945,x17946))
% 59.73/59.68 [1795]~E(x17951,x17952)+E(f121(x17953,x17951,x17954,x17955,x17956),f121(x17953,x17952,x17954,x17955,x17956))
% 59.73/59.68 [1796]~E(x17961,x17962)+E(f121(x17963,x17964,x17961,x17965,x17966),f121(x17963,x17964,x17962,x17965,x17966))
% 59.73/59.68 [1797]~E(x17971,x17972)+E(f121(x17973,x17974,x17975,x17971,x17976),f121(x17973,x17974,x17975,x17972,x17976))
% 59.73/59.68 [1798]~E(x17981,x17982)+E(f121(x17983,x17984,x17985,x17986,x17981),f121(x17983,x17984,x17985,x17986,x17982))
% 59.73/59.68 [1799]~E(x17991,x17992)+E(f496(x17991,x17993,x17994,x17995,x17996),f496(x17992,x17993,x17994,x17995,x17996))
% 59.73/59.68 [1800]~E(x18001,x18002)+E(f496(x18003,x18001,x18004,x18005,x18006),f496(x18003,x18002,x18004,x18005,x18006))
% 59.73/59.68 [1801]~E(x18011,x18012)+E(f496(x18013,x18014,x18011,x18015,x18016),f496(x18013,x18014,x18012,x18015,x18016))
% 59.73/59.68 [1802]~E(x18021,x18022)+E(f496(x18023,x18024,x18025,x18021,x18026),f496(x18023,x18024,x18025,x18022,x18026))
% 59.73/59.68 [1803]~E(x18031,x18032)+E(f496(x18033,x18034,x18035,x18036,x18031),f496(x18033,x18034,x18035,x18036,x18032))
% 59.73/59.68 [1804]~E(x18041,x18042)+E(f566(x18041,x18043,x18044),f566(x18042,x18043,x18044))
% 59.73/59.68 [1805]~E(x18051,x18052)+E(f566(x18053,x18051,x18054),f566(x18053,x18052,x18054))
% 59.73/59.68 [1806]~E(x18061,x18062)+E(f566(x18063,x18064,x18061),f566(x18063,x18064,x18062))
% 59.73/59.68 [1807]~E(x18071,x18072)+E(f226(x18071,x18073,x18074,x18075,x18076),f226(x18072,x18073,x18074,x18075,x18076))
% 59.73/59.68 [1808]~E(x18081,x18082)+E(f226(x18083,x18081,x18084,x18085,x18086),f226(x18083,x18082,x18084,x18085,x18086))
% 59.73/59.68 [1809]~E(x18091,x18092)+E(f226(x18093,x18094,x18091,x18095,x18096),f226(x18093,x18094,x18092,x18095,x18096))
% 59.73/59.68 [1810]~E(x18101,x18102)+E(f226(x18103,x18104,x18105,x18101,x18106),f226(x18103,x18104,x18105,x18102,x18106))
% 59.73/59.68 [1811]~E(x18111,x18112)+E(f226(x18113,x18114,x18115,x18116,x18111),f226(x18113,x18114,x18115,x18116,x18112))
% 59.73/59.68 [1812]~E(x18121,x18122)+E(f35(x18121),f35(x18122))
% 59.73/59.68 [1813]~E(x18131,x18132)+E(f205(x18131,x18133),f205(x18132,x18133))
% 59.73/59.68 [1814]~E(x18141,x18142)+E(f205(x18143,x18141),f205(x18143,x18142))
% 59.73/59.68 [1815]~E(x18151,x18152)+E(f349(x18151,x18153),f349(x18152,x18153))
% 59.73/59.68 [1816]~E(x18161,x18162)+E(f349(x18163,x18161),f349(x18163,x18162))
% 59.73/59.68 [1817]~E(x18171,x18172)+E(f548(x18171,x18173),f548(x18172,x18173))
% 59.73/59.68 [1818]~E(x18181,x18182)+E(f548(x18183,x18181),f548(x18183,x18182))
% 59.73/59.68 [1819]~E(x18191,x18192)+E(f865(x18191,x18193,x18194),f865(x18192,x18193,x18194))
% 59.73/59.68 [1820]~E(x18201,x18202)+E(f865(x18203,x18201,x18204),f865(x18203,x18202,x18204))
% 59.73/59.68 [1821]~E(x18211,x18212)+E(f865(x18213,x18214,x18211),f865(x18213,x18214,x18212))
% 59.73/59.68 [1822]~E(x18221,x18222)+E(f223(x18221,x18223,x18224,x18225),f223(x18222,x18223,x18224,x18225))
% 59.73/59.68 [1823]~E(x18231,x18232)+E(f223(x18233,x18231,x18234,x18235),f223(x18233,x18232,x18234,x18235))
% 59.73/59.68 [1824]~E(x18241,x18242)+E(f223(x18243,x18244,x18241,x18245),f223(x18243,x18244,x18242,x18245))
% 59.73/59.68 [1825]~E(x18251,x18252)+E(f223(x18253,x18254,x18255,x18251),f223(x18253,x18254,x18255,x18252))
% 59.73/59.68 [1826]~E(x18261,x18262)+E(f738(x18261,x18263),f738(x18262,x18263))
% 59.73/59.68 [1827]~E(x18271,x18272)+E(f738(x18273,x18271),f738(x18273,x18272))
% 59.73/59.68 [1828]~E(x18281,x18282)+E(f665(x18281,x18283,x18284,x18285,x18286,x18287),f665(x18282,x18283,x18284,x18285,x18286,x18287))
% 59.73/59.68 [1829]~E(x18291,x18292)+E(f665(x18293,x18291,x18294,x18295,x18296,x18297),f665(x18293,x18292,x18294,x18295,x18296,x18297))
% 59.73/59.68 [1830]~E(x18301,x18302)+E(f665(x18303,x18304,x18301,x18305,x18306,x18307),f665(x18303,x18304,x18302,x18305,x18306,x18307))
% 59.73/59.68 [1831]~E(x18311,x18312)+E(f665(x18313,x18314,x18315,x18311,x18316,x18317),f665(x18313,x18314,x18315,x18312,x18316,x18317))
% 59.73/59.68 [1832]~E(x18321,x18322)+E(f665(x18323,x18324,x18325,x18326,x18321,x18327),f665(x18323,x18324,x18325,x18326,x18322,x18327))
% 59.73/59.68 [1833]~E(x18331,x18332)+E(f665(x18333,x18334,x18335,x18336,x18337,x18331),f665(x18333,x18334,x18335,x18336,x18337,x18332))
% 59.73/59.68 [1834]~E(x18341,x18342)+E(f438(x18341,x18343,x18344,x18345,x18346),f438(x18342,x18343,x18344,x18345,x18346))
% 59.73/59.68 [1835]~E(x18351,x18352)+E(f438(x18353,x18351,x18354,x18355,x18356),f438(x18353,x18352,x18354,x18355,x18356))
% 59.73/59.68 [1836]~E(x18361,x18362)+E(f438(x18363,x18364,x18361,x18365,x18366),f438(x18363,x18364,x18362,x18365,x18366))
% 59.73/59.68 [1837]~E(x18371,x18372)+E(f438(x18373,x18374,x18375,x18371,x18376),f438(x18373,x18374,x18375,x18372,x18376))
% 59.73/59.68 [1838]~E(x18381,x18382)+E(f438(x18383,x18384,x18385,x18386,x18381),f438(x18383,x18384,x18385,x18386,x18382))
% 59.73/59.68 [1839]~E(x18391,x18392)+E(f695(x18391,x18393,x18394,x18395),f695(x18392,x18393,x18394,x18395))
% 59.73/59.68 [1840]~E(x18401,x18402)+E(f695(x18403,x18401,x18404,x18405),f695(x18403,x18402,x18404,x18405))
% 59.73/59.68 [1841]~E(x18411,x18412)+E(f695(x18413,x18414,x18411,x18415),f695(x18413,x18414,x18412,x18415))
% 59.73/59.68 [1842]~E(x18421,x18422)+E(f695(x18423,x18424,x18425,x18421),f695(x18423,x18424,x18425,x18422))
% 59.73/59.68 [1843]~E(x18431,x18432)+E(f788(x18431,x18433,x18434),f788(x18432,x18433,x18434))
% 59.73/59.68 [1844]~E(x18441,x18442)+E(f788(x18443,x18441,x18444),f788(x18443,x18442,x18444))
% 59.73/59.68 [1845]~E(x18451,x18452)+E(f788(x18453,x18454,x18451),f788(x18453,x18454,x18452))
% 59.73/59.68 [1846]~E(x18461,x18462)+E(f195(x18461,x18463,x18464,x18465),f195(x18462,x18463,x18464,x18465))
% 59.73/59.68 [1847]~E(x18471,x18472)+E(f195(x18473,x18471,x18474,x18475),f195(x18473,x18472,x18474,x18475))
% 59.73/59.68 [1848]~E(x18481,x18482)+E(f195(x18483,x18484,x18481,x18485),f195(x18483,x18484,x18482,x18485))
% 59.73/59.68 [1849]~E(x18491,x18492)+E(f195(x18493,x18494,x18495,x18491),f195(x18493,x18494,x18495,x18492))
% 59.73/59.68 [1850]~E(x18501,x18502)+E(f518(x18501,x18503,x18504,x18505),f518(x18502,x18503,x18504,x18505))
% 59.73/59.68 [1851]~E(x18511,x18512)+E(f518(x18513,x18511,x18514,x18515),f518(x18513,x18512,x18514,x18515))
% 59.73/59.68 [1852]~E(x18521,x18522)+E(f518(x18523,x18524,x18521,x18525),f518(x18523,x18524,x18522,x18525))
% 59.73/59.68 [1853]~E(x18531,x18532)+E(f518(x18533,x18534,x18535,x18531),f518(x18533,x18534,x18535,x18532))
% 59.73/59.68 [1854]~E(x18541,x18542)+E(f432(x18541,x18543,x18544,x18545,x18546),f432(x18542,x18543,x18544,x18545,x18546))
% 59.73/59.68 [1855]~E(x18551,x18552)+E(f432(x18553,x18551,x18554,x18555,x18556),f432(x18553,x18552,x18554,x18555,x18556))
% 59.73/59.68 [1856]~E(x18561,x18562)+E(f432(x18563,x18564,x18561,x18565,x18566),f432(x18563,x18564,x18562,x18565,x18566))
% 59.73/59.68 [1857]~E(x18571,x18572)+E(f432(x18573,x18574,x18575,x18571,x18576),f432(x18573,x18574,x18575,x18572,x18576))
% 59.73/59.68 [1858]~E(x18581,x18582)+E(f432(x18583,x18584,x18585,x18586,x18581),f432(x18583,x18584,x18585,x18586,x18582))
% 59.73/59.68 [1859]~E(x18591,x18592)+E(f605(x18591,x18593,x18594,x18595,x18596),f605(x18592,x18593,x18594,x18595,x18596))
% 59.73/59.68 [1860]~E(x18601,x18602)+E(f605(x18603,x18601,x18604,x18605,x18606),f605(x18603,x18602,x18604,x18605,x18606))
% 59.73/59.68 [1861]~E(x18611,x18612)+E(f605(x18613,x18614,x18611,x18615,x18616),f605(x18613,x18614,x18612,x18615,x18616))
% 59.73/59.68 [1862]~E(x18621,x18622)+E(f605(x18623,x18624,x18625,x18621,x18626),f605(x18623,x18624,x18625,x18622,x18626))
% 59.73/59.68 [1863]~E(x18631,x18632)+E(f605(x18633,x18634,x18635,x18636,x18631),f605(x18633,x18634,x18635,x18636,x18632))
% 59.73/59.68 [1864]~E(x18641,x18642)+E(f283(x18641,x18643,x18644,x18645),f283(x18642,x18643,x18644,x18645))
% 59.73/59.68 [1865]~E(x18651,x18652)+E(f283(x18653,x18651,x18654,x18655),f283(x18653,x18652,x18654,x18655))
% 59.73/59.68 [1866]~E(x18661,x18662)+E(f283(x18663,x18664,x18661,x18665),f283(x18663,x18664,x18662,x18665))
% 59.73/59.68 [1867]~E(x18671,x18672)+E(f283(x18673,x18674,x18675,x18671),f283(x18673,x18674,x18675,x18672))
% 59.73/59.68 [1868]~E(x18681,x18682)+E(f655(x18681,x18683,x18684),f655(x18682,x18683,x18684))
% 59.73/59.68 [1869]~E(x18691,x18692)+E(f655(x18693,x18691,x18694),f655(x18693,x18692,x18694))
% 59.73/59.68 [1870]~E(x18701,x18702)+E(f655(x18703,x18704,x18701),f655(x18703,x18704,x18702))
% 59.73/59.68 [1871]~E(x18711,x18712)+E(f630(x18711,x18713,x18714),f630(x18712,x18713,x18714))
% 59.73/59.68 [1872]~E(x18721,x18722)+E(f630(x18723,x18721,x18724),f630(x18723,x18722,x18724))
% 59.73/59.68 [1873]~E(x18731,x18732)+E(f630(x18733,x18734,x18731),f630(x18733,x18734,x18732))
% 59.73/59.68 [1874]~E(x18741,x18742)+E(f639(x18741,x18743,x18744,x18745,x18746,x18747,x18748,x18749),f639(x18742,x18743,x18744,x18745,x18746,x18747,x18748,x18749))
% 59.73/59.68 [1875]~E(x18751,x18752)+E(f639(x18753,x18751,x18754,x18755,x18756,x18757,x18758,x18759),f639(x18753,x18752,x18754,x18755,x18756,x18757,x18758,x18759))
% 59.73/59.68 [1876]~E(x18761,x18762)+E(f639(x18763,x18764,x18761,x18765,x18766,x18767,x18768,x18769),f639(x18763,x18764,x18762,x18765,x18766,x18767,x18768,x18769))
% 59.73/59.68 [1877]~E(x18771,x18772)+E(f639(x18773,x18774,x18775,x18771,x18776,x18777,x18778,x18779),f639(x18773,x18774,x18775,x18772,x18776,x18777,x18778,x18779))
% 59.73/59.68 [1878]~E(x18781,x18782)+E(f639(x18783,x18784,x18785,x18786,x18781,x18787,x18788,x18789),f639(x18783,x18784,x18785,x18786,x18782,x18787,x18788,x18789))
% 59.73/59.68 [1879]~E(x18791,x18792)+E(f639(x18793,x18794,x18795,x18796,x18797,x18791,x18798,x18799),f639(x18793,x18794,x18795,x18796,x18797,x18792,x18798,x18799))
% 59.73/59.68 [1880]~E(x18801,x18802)+E(f639(x18803,x18804,x18805,x18806,x18807,x18808,x18801,x18809),f639(x18803,x18804,x18805,x18806,x18807,x18808,x18802,x18809))
% 59.73/59.68 [1881]~E(x18811,x18812)+E(f639(x18813,x18814,x18815,x18816,x18817,x18818,x18819,x18811),f639(x18813,x18814,x18815,x18816,x18817,x18818,x18819,x18812))
% 59.73/59.68 [1882]~E(x18821,x18822)+E(f739(x18821,x18823,x18824,x18825,x18826),f739(x18822,x18823,x18824,x18825,x18826))
% 59.73/59.68 [1883]~E(x18831,x18832)+E(f739(x18833,x18831,x18834,x18835,x18836),f739(x18833,x18832,x18834,x18835,x18836))
% 59.73/59.68 [1884]~E(x18841,x18842)+E(f739(x18843,x18844,x18841,x18845,x18846),f739(x18843,x18844,x18842,x18845,x18846))
% 59.73/59.68 [1885]~E(x18851,x18852)+E(f739(x18853,x18854,x18855,x18851,x18856),f739(x18853,x18854,x18855,x18852,x18856))
% 59.73/59.68 [1886]~E(x18861,x18862)+E(f739(x18863,x18864,x18865,x18866,x18861),f739(x18863,x18864,x18865,x18866,x18862))
% 59.73/59.68 [1887]~E(x18871,x18872)+E(f346(x18871,x18873,x18874),f346(x18872,x18873,x18874))
% 59.73/59.68 [1888]~E(x18881,x18882)+E(f346(x18883,x18881,x18884),f346(x18883,x18882,x18884))
% 59.73/59.68 [1889]~E(x18891,x18892)+E(f346(x18893,x18894,x18891),f346(x18893,x18894,x18892))
% 59.73/59.68 [1890]~E(x18901,x18902)+E(f735(x18901,x18903,x18904),f735(x18902,x18903,x18904))
% 59.73/59.68 [1891]~E(x18911,x18912)+E(f735(x18913,x18911,x18914),f735(x18913,x18912,x18914))
% 59.73/59.68 [1892]~E(x18921,x18922)+E(f735(x18923,x18924,x18921),f735(x18923,x18924,x18922))
% 59.73/59.68 [1893]~E(x18931,x18932)+E(f793(x18931,x18933,x18934),f793(x18932,x18933,x18934))
% 59.73/59.68 [1894]~E(x18941,x18942)+E(f793(x18943,x18941,x18944),f793(x18943,x18942,x18944))
% 59.73/59.68 [1895]~E(x18951,x18952)+E(f793(x18953,x18954,x18951),f793(x18953,x18954,x18952))
% 59.73/59.68 [1896]~E(x18961,x18962)+E(f625(x18961,x18963,x18964,x18965,x18966),f625(x18962,x18963,x18964,x18965,x18966))
% 59.73/59.68 [1897]~E(x18971,x18972)+E(f625(x18973,x18971,x18974,x18975,x18976),f625(x18973,x18972,x18974,x18975,x18976))
% 59.73/59.68 [1898]~E(x18981,x18982)+E(f625(x18983,x18984,x18981,x18985,x18986),f625(x18983,x18984,x18982,x18985,x18986))
% 59.73/59.68 [1899]~E(x18991,x18992)+E(f625(x18993,x18994,x18995,x18991,x18996),f625(x18993,x18994,x18995,x18992,x18996))
% 59.73/59.68 [1900]~E(x19001,x19002)+E(f625(x19003,x19004,x19005,x19006,x19001),f625(x19003,x19004,x19005,x19006,x19002))
% 59.73/59.68 [1901]~E(x19011,x19012)+E(f475(x19011,x19013,x19014,x19015),f475(x19012,x19013,x19014,x19015))
% 59.73/59.68 [1902]~E(x19021,x19022)+E(f475(x19023,x19021,x19024,x19025),f475(x19023,x19022,x19024,x19025))
% 59.73/59.68 [1903]~E(x19031,x19032)+E(f475(x19033,x19034,x19031,x19035),f475(x19033,x19034,x19032,x19035))
% 59.73/59.68 [1904]~E(x19041,x19042)+E(f475(x19043,x19044,x19045,x19041),f475(x19043,x19044,x19045,x19042))
% 59.73/59.68 [1905]~E(x19051,x19052)+E(f647(x19051,x19053,x19054,x19055),f647(x19052,x19053,x19054,x19055))
% 59.73/59.68 [1906]~E(x19061,x19062)+E(f647(x19063,x19061,x19064,x19065),f647(x19063,x19062,x19064,x19065))
% 59.73/59.68 [1907]~E(x19071,x19072)+E(f647(x19073,x19074,x19071,x19075),f647(x19073,x19074,x19072,x19075))
% 59.73/59.68 [1908]~E(x19081,x19082)+E(f647(x19083,x19084,x19085,x19081),f647(x19083,x19084,x19085,x19082))
% 59.73/59.68 [1909]~E(x19091,x19092)+E(f540(x19091,x19093,x19094,x19095,x19096),f540(x19092,x19093,x19094,x19095,x19096))
% 59.73/59.68 [1910]~E(x19101,x19102)+E(f540(x19103,x19101,x19104,x19105,x19106),f540(x19103,x19102,x19104,x19105,x19106))
% 59.73/59.68 [1911]~E(x19111,x19112)+E(f540(x19113,x19114,x19111,x19115,x19116),f540(x19113,x19114,x19112,x19115,x19116))
% 59.73/59.68 [1912]~E(x19121,x19122)+E(f540(x19123,x19124,x19125,x19121,x19126),f540(x19123,x19124,x19125,x19122,x19126))
% 59.73/59.68 [1913]~E(x19131,x19132)+E(f540(x19133,x19134,x19135,x19136,x19131),f540(x19133,x19134,x19135,x19136,x19132))
% 59.73/59.68 [1914]~E(x19141,x19142)+E(f574(x19141,x19143),f574(x19142,x19143))
% 59.73/59.68 [1915]~E(x19151,x19152)+E(f574(x19153,x19151),f574(x19153,x19152))
% 59.73/59.68 [1916]~E(x19161,x19162)+E(f803(x19161,x19163,x19164),f803(x19162,x19163,x19164))
% 59.73/59.68 [1917]~E(x19171,x19172)+E(f803(x19173,x19171,x19174),f803(x19173,x19172,x19174))
% 59.73/59.68 [1918]~E(x19181,x19182)+E(f803(x19183,x19184,x19181),f803(x19183,x19184,x19182))
% 59.73/59.68 [1919]~E(x19191,x19192)+E(f539(x19191,x19193,x19194,x19195,x19196),f539(x19192,x19193,x19194,x19195,x19196))
% 59.73/59.68 [1920]~E(x19201,x19202)+E(f539(x19203,x19201,x19204,x19205,x19206),f539(x19203,x19202,x19204,x19205,x19206))
% 59.73/59.68 [1921]~E(x19211,x19212)+E(f539(x19213,x19214,x19211,x19215,x19216),f539(x19213,x19214,x19212,x19215,x19216))
% 59.73/59.68 [1922]~E(x19221,x19222)+E(f539(x19223,x19224,x19225,x19221,x19226),f539(x19223,x19224,x19225,x19222,x19226))
% 59.73/59.68 [1923]~E(x19231,x19232)+E(f539(x19233,x19234,x19235,x19236,x19231),f539(x19233,x19234,x19235,x19236,x19232))
% 59.73/59.68 [1924]~E(x19241,x19242)+E(f702(x19241,x19243,x19244,x19245),f702(x19242,x19243,x19244,x19245))
% 59.73/59.68 [1925]~E(x19251,x19252)+E(f702(x19253,x19251,x19254,x19255),f702(x19253,x19252,x19254,x19255))
% 59.73/59.68 [1926]~E(x19261,x19262)+E(f702(x19263,x19264,x19261,x19265),f702(x19263,x19264,x19262,x19265))
% 59.73/59.68 [1927]~E(x19271,x19272)+E(f702(x19273,x19274,x19275,x19271),f702(x19273,x19274,x19275,x19272))
% 59.73/59.68 [1928]~E(x19281,x19282)+E(f422(x19281,x19283,x19284),f422(x19282,x19283,x19284))
% 59.73/59.68 [1929]~E(x19291,x19292)+E(f422(x19293,x19291,x19294),f422(x19293,x19292,x19294))
% 59.73/59.68 [1930]~E(x19301,x19302)+E(f422(x19303,x19304,x19301),f422(x19303,x19304,x19302))
% 59.73/59.68 [1931]~E(x19311,x19312)+E(f155(x19311,x19313),f155(x19312,x19313))
% 59.73/59.68 [1932]~E(x19321,x19322)+E(f155(x19323,x19321),f155(x19323,x19322))
% 59.73/59.68 [1933]~E(x19331,x19332)+E(f501(x19331,x19333,x19334,x19335,x19336,x19337),f501(x19332,x19333,x19334,x19335,x19336,x19337))
% 59.73/59.68 [1934]~E(x19341,x19342)+E(f501(x19343,x19341,x19344,x19345,x19346,x19347),f501(x19343,x19342,x19344,x19345,x19346,x19347))
% 59.73/59.68 [1935]~E(x19351,x19352)+E(f501(x19353,x19354,x19351,x19355,x19356,x19357),f501(x19353,x19354,x19352,x19355,x19356,x19357))
% 59.73/59.68 [1936]~E(x19361,x19362)+E(f501(x19363,x19364,x19365,x19361,x19366,x19367),f501(x19363,x19364,x19365,x19362,x19366,x19367))
% 59.73/59.68 [1937]~E(x19371,x19372)+E(f501(x19373,x19374,x19375,x19376,x19371,x19377),f501(x19373,x19374,x19375,x19376,x19372,x19377))
% 59.73/59.68 [1938]~E(x19381,x19382)+E(f501(x19383,x19384,x19385,x19386,x19387,x19381),f501(x19383,x19384,x19385,x19386,x19387,x19382))
% 59.73/59.68 [1939]~E(x19391,x19392)+E(f874(x19391,x19393,x19394,x19395),f874(x19392,x19393,x19394,x19395))
% 59.73/59.68 [1940]~E(x19401,x19402)+E(f874(x19403,x19401,x19404,x19405),f874(x19403,x19402,x19404,x19405))
% 59.73/59.68 [1941]~E(x19411,x19412)+E(f874(x19413,x19414,x19411,x19415),f874(x19413,x19414,x19412,x19415))
% 59.73/59.68 [1942]~E(x19421,x19422)+E(f874(x19423,x19424,x19425,x19421),f874(x19423,x19424,x19425,x19422))
% 59.73/59.68 [1943]~E(x19431,x19432)+E(f613(x19431,x19433,x19434,x19435,x19436),f613(x19432,x19433,x19434,x19435,x19436))
% 59.73/59.68 [1944]~E(x19441,x19442)+E(f613(x19443,x19441,x19444,x19445,x19446),f613(x19443,x19442,x19444,x19445,x19446))
% 59.73/59.68 [1945]~E(x19451,x19452)+E(f613(x19453,x19454,x19451,x19455,x19456),f613(x19453,x19454,x19452,x19455,x19456))
% 59.73/59.68 [1946]~E(x19461,x19462)+E(f613(x19463,x19464,x19465,x19461,x19466),f613(x19463,x19464,x19465,x19462,x19466))
% 59.73/59.68 [1947]~E(x19471,x19472)+E(f613(x19473,x19474,x19475,x19476,x19471),f613(x19473,x19474,x19475,x19476,x19472))
% 59.73/59.68 [1948]~E(x19481,x19482)+E(f730(x19481,x19483,x19484,x19485,x19486),f730(x19482,x19483,x19484,x19485,x19486))
% 59.73/59.68 [1949]~E(x19491,x19492)+E(f730(x19493,x19491,x19494,x19495,x19496),f730(x19493,x19492,x19494,x19495,x19496))
% 59.73/59.68 [1950]~E(x19501,x19502)+E(f730(x19503,x19504,x19501,x19505,x19506),f730(x19503,x19504,x19502,x19505,x19506))
% 59.73/59.68 [1951]~E(x19511,x19512)+E(f730(x19513,x19514,x19515,x19511,x19516),f730(x19513,x19514,x19515,x19512,x19516))
% 59.73/59.68 [1952]~E(x19521,x19522)+E(f730(x19523,x19524,x19525,x19526,x19521),f730(x19523,x19524,x19525,x19526,x19522))
% 59.73/59.68 [1953]~E(x19531,x19532)+E(f371(x19531,x19533,x19534),f371(x19532,x19533,x19534))
% 59.73/59.68 [1954]~E(x19541,x19542)+E(f371(x19543,x19541,x19544),f371(x19543,x19542,x19544))
% 59.73/59.68 [1955]~E(x19551,x19552)+E(f371(x19553,x19554,x19551),f371(x19553,x19554,x19552))
% 59.73/59.68 [1956]~E(x19561,x19562)+E(f808(x19561,x19563,x19564,x19565),f808(x19562,x19563,x19564,x19565))
% 59.73/59.68 [1957]~E(x19571,x19572)+E(f808(x19573,x19571,x19574,x19575),f808(x19573,x19572,x19574,x19575))
% 59.73/59.68 [1958]~E(x19581,x19582)+E(f808(x19583,x19584,x19581,x19585),f808(x19583,x19584,x19582,x19585))
% 59.73/59.68 [1959]~E(x19591,x19592)+E(f808(x19593,x19594,x19595,x19591),f808(x19593,x19594,x19595,x19592))
% 59.73/59.68 [1960]~E(x19601,x19602)+E(f363(x19601,x19603),f363(x19602,x19603))
% 59.73/59.68 [1961]~E(x19611,x19612)+E(f363(x19613,x19611),f363(x19613,x19612))
% 59.73/59.68 [1962]~E(x19621,x19622)+E(f604(x19621,x19623,x19624,x19625,x19626),f604(x19622,x19623,x19624,x19625,x19626))
% 59.73/59.68 [1963]~E(x19631,x19632)+E(f604(x19633,x19631,x19634,x19635,x19636),f604(x19633,x19632,x19634,x19635,x19636))
% 59.73/59.68 [1964]~E(x19641,x19642)+E(f604(x19643,x19644,x19641,x19645,x19646),f604(x19643,x19644,x19642,x19645,x19646))
% 59.73/59.68 [1965]~E(x19651,x19652)+E(f604(x19653,x19654,x19655,x19651,x19656),f604(x19653,x19654,x19655,x19652,x19656))
% 59.73/59.68 [1966]~E(x19661,x19662)+E(f604(x19663,x19664,x19665,x19666,x19661),f604(x19663,x19664,x19665,x19666,x19662))
% 59.73/59.68 [1967]~E(x19671,x19672)+E(f772(x19671,x19673,x19674,x19675,x19676),f772(x19672,x19673,x19674,x19675,x19676))
% 59.73/59.68 [1968]~E(x19681,x19682)+E(f772(x19683,x19681,x19684,x19685,x19686),f772(x19683,x19682,x19684,x19685,x19686))
% 59.73/59.68 [1969]~E(x19691,x19692)+E(f772(x19693,x19694,x19691,x19695,x19696),f772(x19693,x19694,x19692,x19695,x19696))
% 59.73/59.68 [1970]~E(x19701,x19702)+E(f772(x19703,x19704,x19705,x19701,x19706),f772(x19703,x19704,x19705,x19702,x19706))
% 59.73/59.68 [1971]~E(x19711,x19712)+E(f772(x19713,x19714,x19715,x19716,x19711),f772(x19713,x19714,x19715,x19716,x19712))
% 59.73/59.68 [1972]~E(x19721,x19722)+E(f664(x19721,x19723,x19724,x19725,x19726,x19727),f664(x19722,x19723,x19724,x19725,x19726,x19727))
% 59.73/59.68 [1973]~E(x19731,x19732)+E(f664(x19733,x19731,x19734,x19735,x19736,x19737),f664(x19733,x19732,x19734,x19735,x19736,x19737))
% 59.73/59.68 [1974]~E(x19741,x19742)+E(f664(x19743,x19744,x19741,x19745,x19746,x19747),f664(x19743,x19744,x19742,x19745,x19746,x19747))
% 59.73/59.68 [1975]~E(x19751,x19752)+E(f664(x19753,x19754,x19755,x19751,x19756,x19757),f664(x19753,x19754,x19755,x19752,x19756,x19757))
% 59.73/59.68 [1976]~E(x19761,x19762)+E(f664(x19763,x19764,x19765,x19766,x19761,x19767),f664(x19763,x19764,x19765,x19766,x19762,x19767))
% 59.73/59.68 [1977]~E(x19771,x19772)+E(f664(x19773,x19774,x19775,x19776,x19777,x19771),f664(x19773,x19774,x19775,x19776,x19777,x19772))
% 59.73/59.68 [1978]~E(x19781,x19782)+E(f417(x19781),f417(x19782))
% 59.73/59.68 [1979]~E(x19791,x19792)+E(f577(x19791,x19793),f577(x19792,x19793))
% 59.73/59.68 [1980]~E(x19801,x19802)+E(f577(x19803,x19801),f577(x19803,x19802))
% 59.73/59.68 [1981]~E(x19811,x19812)+E(f298(x19811,x19813,x19814,x19815),f298(x19812,x19813,x19814,x19815))
% 59.73/59.68 [1982]~E(x19821,x19822)+E(f298(x19823,x19821,x19824,x19825),f298(x19823,x19822,x19824,x19825))
% 59.73/59.68 [1983]~E(x19831,x19832)+E(f298(x19833,x19834,x19831,x19835),f298(x19833,x19834,x19832,x19835))
% 59.73/59.68 [1984]~E(x19841,x19842)+E(f298(x19843,x19844,x19845,x19841),f298(x19843,x19844,x19845,x19842))
% 59.73/59.68 [1985]~E(x19851,x19852)+E(f737(x19851,x19853,x19854),f737(x19852,x19853,x19854))
% 59.73/59.68 [1986]~E(x19861,x19862)+E(f737(x19863,x19861,x19864),f737(x19863,x19862,x19864))
% 59.73/59.68 [1987]~E(x19871,x19872)+E(f737(x19873,x19874,x19871),f737(x19873,x19874,x19872))
% 59.73/59.68 [1988]~E(x19881,x19882)+E(f452(x19881,x19883),f452(x19882,x19883))
% 59.73/59.68 [1989]~E(x19891,x19892)+E(f452(x19893,x19891),f452(x19893,x19892))
% 59.73/59.68 [1990]~E(x19901,x19902)+E(f344(x19901,x19903),f344(x19902,x19903))
% 59.73/59.68 [1991]~E(x19911,x19912)+E(f344(x19913,x19911),f344(x19913,x19912))
% 59.73/59.68 [1992]~E(x19921,x19922)+E(f608(x19921,x19923,x19924,x19925,x19926),f608(x19922,x19923,x19924,x19925,x19926))
% 59.73/59.68 [1993]~E(x19931,x19932)+E(f608(x19933,x19931,x19934,x19935,x19936),f608(x19933,x19932,x19934,x19935,x19936))
% 59.73/59.68 [1994]~E(x19941,x19942)+E(f608(x19943,x19944,x19941,x19945,x19946),f608(x19943,x19944,x19942,x19945,x19946))
% 59.73/59.68 [1995]~E(x19951,x19952)+E(f608(x19953,x19954,x19955,x19951,x19956),f608(x19953,x19954,x19955,x19952,x19956))
% 59.73/59.68 [1996]~E(x19961,x19962)+E(f608(x19963,x19964,x19965,x19966,x19961),f608(x19963,x19964,x19965,x19966,x19962))
% 59.73/59.68 [1997]~E(x19971,x19972)+E(f766(x19971,x19973,x19974),f766(x19972,x19973,x19974))
% 59.73/59.68 [1998]~E(x19981,x19982)+E(f766(x19983,x19981,x19984),f766(x19983,x19982,x19984))
% 59.73/59.68 [1999]~E(x19991,x19992)+E(f766(x19993,x19994,x19991),f766(x19993,x19994,x19992))
% 59.73/59.68 [2000]~E(x20001,x20002)+E(f533(x20001,x20003,x20004,x20005),f533(x20002,x20003,x20004,x20005))
% 59.73/59.68 [2001]~E(x20011,x20012)+E(f533(x20013,x20011,x20014,x20015),f533(x20013,x20012,x20014,x20015))
% 59.73/59.68 [2002]~E(x20021,x20022)+E(f533(x20023,x20024,x20021,x20025),f533(x20023,x20024,x20022,x20025))
% 59.73/59.68 [2003]~E(x20031,x20032)+E(f533(x20033,x20034,x20035,x20031),f533(x20033,x20034,x20035,x20032))
% 59.73/59.68 [2004]~E(x20041,x20042)+E(f523(x20041,x20043,x20044,x20045),f523(x20042,x20043,x20044,x20045))
% 59.73/59.68 [2005]~E(x20051,x20052)+E(f523(x20053,x20051,x20054,x20055),f523(x20053,x20052,x20054,x20055))
% 59.73/59.68 [2006]~E(x20061,x20062)+E(f523(x20063,x20064,x20061,x20065),f523(x20063,x20064,x20062,x20065))
% 59.73/59.68 [2007]~E(x20071,x20072)+E(f523(x20073,x20074,x20075,x20071),f523(x20073,x20074,x20075,x20072))
% 59.73/59.68 [2008]~E(x20081,x20082)+E(f471(x20081,x20083,x20084,x20085),f471(x20082,x20083,x20084,x20085))
% 59.73/59.68 [2009]~E(x20091,x20092)+E(f471(x20093,x20091,x20094,x20095),f471(x20093,x20092,x20094,x20095))
% 59.73/59.68 [2010]~E(x20101,x20102)+E(f471(x20103,x20104,x20101,x20105),f471(x20103,x20104,x20102,x20105))
% 59.73/59.68 [2011]~E(x20111,x20112)+E(f471(x20113,x20114,x20115,x20111),f471(x20113,x20114,x20115,x20112))
% 59.73/59.68 [2012]~E(x20121,x20122)+E(f602(x20121,x20123,x20124,x20125,x20126),f602(x20122,x20123,x20124,x20125,x20126))
% 59.73/59.68 [2013]~E(x20131,x20132)+E(f602(x20133,x20131,x20134,x20135,x20136),f602(x20133,x20132,x20134,x20135,x20136))
% 59.73/59.68 [2014]~E(x20141,x20142)+E(f602(x20143,x20144,x20141,x20145,x20146),f602(x20143,x20144,x20142,x20145,x20146))
% 59.73/59.68 [2015]~E(x20151,x20152)+E(f602(x20153,x20154,x20155,x20151,x20156),f602(x20153,x20154,x20155,x20152,x20156))
% 59.73/59.68 [2016]~E(x20161,x20162)+E(f602(x20163,x20164,x20165,x20166,x20161),f602(x20163,x20164,x20165,x20166,x20162))
% 59.73/59.68 [2017]~E(x20171,x20172)+E(f465(x20171,x20173,x20174,x20175),f465(x20172,x20173,x20174,x20175))
% 59.73/59.68 [2018]~E(x20181,x20182)+E(f465(x20183,x20181,x20184,x20185),f465(x20183,x20182,x20184,x20185))
% 59.73/59.68 [2019]~E(x20191,x20192)+E(f465(x20193,x20194,x20191,x20195),f465(x20193,x20194,x20192,x20195))
% 59.73/59.68 [2020]~E(x20201,x20202)+E(f465(x20203,x20204,x20205,x20201),f465(x20203,x20204,x20205,x20202))
% 59.73/59.68 [2021]~E(x20211,x20212)+E(f717(x20211,x20213,x20214,x20215,x20216),f717(x20212,x20213,x20214,x20215,x20216))
% 59.73/59.68 [2022]~E(x20221,x20222)+E(f717(x20223,x20221,x20224,x20225,x20226),f717(x20223,x20222,x20224,x20225,x20226))
% 59.73/59.68 [2023]~E(x20231,x20232)+E(f717(x20233,x20234,x20231,x20235,x20236),f717(x20233,x20234,x20232,x20235,x20236))
% 59.73/59.68 [2024]~E(x20241,x20242)+E(f717(x20243,x20244,x20245,x20241,x20246),f717(x20243,x20244,x20245,x20242,x20246))
% 59.73/59.68 [2025]~E(x20251,x20252)+E(f717(x20253,x20254,x20255,x20256,x20251),f717(x20253,x20254,x20255,x20256,x20252))
% 59.73/59.68 [2026]~E(x20261,x20262)+E(f542(x20261,x20263,x20264),f542(x20262,x20263,x20264))
% 59.73/59.68 [2027]~E(x20271,x20272)+E(f542(x20273,x20271,x20274),f542(x20273,x20272,x20274))
% 59.73/59.68 [2028]~E(x20281,x20282)+E(f542(x20283,x20284,x20281),f542(x20283,x20284,x20282))
% 59.73/59.68 [2029]~E(x20291,x20292)+E(f703(x20291,x20293,x20294,x20295,x20296),f703(x20292,x20293,x20294,x20295,x20296))
% 59.73/59.68 [2030]~E(x20301,x20302)+E(f703(x20303,x20301,x20304,x20305,x20306),f703(x20303,x20302,x20304,x20305,x20306))
% 59.73/59.68 [2031]~E(x20311,x20312)+E(f703(x20313,x20314,x20311,x20315,x20316),f703(x20313,x20314,x20312,x20315,x20316))
% 59.73/59.68 [2032]~E(x20321,x20322)+E(f703(x20323,x20324,x20325,x20321,x20326),f703(x20323,x20324,x20325,x20322,x20326))
% 59.73/59.68 [2033]~E(x20331,x20332)+E(f703(x20333,x20334,x20335,x20336,x20331),f703(x20333,x20334,x20335,x20336,x20332))
% 59.73/59.68 [2034]~E(x20341,x20342)+E(f474(x20341,x20343,x20344,x20345),f474(x20342,x20343,x20344,x20345))
% 59.73/59.68 [2035]~E(x20351,x20352)+E(f474(x20353,x20351,x20354,x20355),f474(x20353,x20352,x20354,x20355))
% 59.73/59.68 [2036]~E(x20361,x20362)+E(f474(x20363,x20364,x20361,x20365),f474(x20363,x20364,x20362,x20365))
% 59.73/59.68 [2037]~E(x20371,x20372)+E(f474(x20373,x20374,x20375,x20371),f474(x20373,x20374,x20375,x20372))
% 59.73/59.68 [2038]~E(x20381,x20382)+E(f207(x20381),f207(x20382))
% 59.73/59.68 [2039]~E(x20391,x20392)+E(f285(x20391,x20393,x20394,x20395),f285(x20392,x20393,x20394,x20395))
% 59.73/59.68 [2040]~E(x20401,x20402)+E(f285(x20403,x20401,x20404,x20405),f285(x20403,x20402,x20404,x20405))
% 59.73/59.68 [2041]~E(x20411,x20412)+E(f285(x20413,x20414,x20411,x20415),f285(x20413,x20414,x20412,x20415))
% 59.73/59.68 [2042]~E(x20421,x20422)+E(f285(x20423,x20424,x20425,x20421),f285(x20423,x20424,x20425,x20422))
% 59.73/59.68 [2043]~E(x20431,x20432)+E(f479(x20431,x20433,x20434,x20435),f479(x20432,x20433,x20434,x20435))
% 59.73/59.68 [2044]~E(x20441,x20442)+E(f479(x20443,x20441,x20444,x20445),f479(x20443,x20442,x20444,x20445))
% 59.73/59.68 [2045]~E(x20451,x20452)+E(f479(x20453,x20454,x20451,x20455),f479(x20453,x20454,x20452,x20455))
% 59.73/59.68 [2046]~E(x20461,x20462)+E(f479(x20463,x20464,x20465,x20461),f479(x20463,x20464,x20465,x20462))
% 59.73/59.68 [2047]~E(x20471,x20472)+E(f797(x20471,x20473,x20474),f797(x20472,x20473,x20474))
% 59.73/59.68 [2048]~E(x20481,x20482)+E(f797(x20483,x20481,x20484),f797(x20483,x20482,x20484))
% 59.73/59.68 [2049]~E(x20491,x20492)+E(f797(x20493,x20494,x20491),f797(x20493,x20494,x20492))
% 59.73/59.68 [2050]~E(x20501,x20502)+E(f448(x20501,x20503),f448(x20502,x20503))
% 59.73/59.68 [2051]~E(x20511,x20512)+E(f448(x20513,x20511),f448(x20513,x20512))
% 59.73/59.68 [2052]~E(x20521,x20522)+E(f876(x20521,x20523,x20524,x20525,x20526),f876(x20522,x20523,x20524,x20525,x20526))
% 59.73/59.68 [2053]~E(x20531,x20532)+E(f876(x20533,x20531,x20534,x20535,x20536),f876(x20533,x20532,x20534,x20535,x20536))
% 59.73/59.68 [2054]~E(x20541,x20542)+E(f876(x20543,x20544,x20541,x20545,x20546),f876(x20543,x20544,x20542,x20545,x20546))
% 59.73/59.68 [2055]~E(x20551,x20552)+E(f876(x20553,x20554,x20555,x20551,x20556),f876(x20553,x20554,x20555,x20552,x20556))
% 59.73/59.68 [2056]~E(x20561,x20562)+E(f876(x20563,x20564,x20565,x20566,x20561),f876(x20563,x20564,x20565,x20566,x20562))
% 59.73/59.68 [2057]~E(x20571,x20572)+E(f38(x20571),f38(x20572))
% 59.73/59.68 [2058]~E(x20581,x20582)+E(f380(x20581,x20583,x20584),f380(x20582,x20583,x20584))
% 59.73/59.68 [2059]~E(x20591,x20592)+E(f380(x20593,x20591,x20594),f380(x20593,x20592,x20594))
% 59.73/59.68 [2060]~E(x20601,x20602)+E(f380(x20603,x20604,x20601),f380(x20603,x20604,x20602))
% 59.73/59.68 [2061]~E(x20611,x20612)+E(f671(x20611,x20613,x20614,x20615),f671(x20612,x20613,x20614,x20615))
% 59.73/59.68 [2062]~E(x20621,x20622)+E(f671(x20623,x20621,x20624,x20625),f671(x20623,x20622,x20624,x20625))
% 59.73/59.68 [2063]~E(x20631,x20632)+E(f671(x20633,x20634,x20631,x20635),f671(x20633,x20634,x20632,x20635))
% 59.73/59.68 [2064]~E(x20641,x20642)+E(f671(x20643,x20644,x20645,x20641),f671(x20643,x20644,x20645,x20642))
% 59.73/59.68 [2065]~E(x20651,x20652)+E(f719(x20651,x20653,x20654,x20655),f719(x20652,x20653,x20654,x20655))
% 59.73/59.68 [2066]~E(x20661,x20662)+E(f719(x20663,x20661,x20664,x20665),f719(x20663,x20662,x20664,x20665))
% 59.73/59.68 [2067]~E(x20671,x20672)+E(f719(x20673,x20674,x20671,x20675),f719(x20673,x20674,x20672,x20675))
% 59.73/59.68 [2068]~E(x20681,x20682)+E(f719(x20683,x20684,x20685,x20681),f719(x20683,x20684,x20685,x20682))
% 59.73/59.68 [2069]~E(x20691,x20692)+E(f612(x20691,x20693,x20694,x20695,x20696),f612(x20692,x20693,x20694,x20695,x20696))
% 59.73/59.68 [2070]~E(x20701,x20702)+E(f612(x20703,x20701,x20704,x20705,x20706),f612(x20703,x20702,x20704,x20705,x20706))
% 59.73/59.68 [2071]~E(x20711,x20712)+E(f612(x20713,x20714,x20711,x20715,x20716),f612(x20713,x20714,x20712,x20715,x20716))
% 59.73/59.68 [2072]~E(x20721,x20722)+E(f612(x20723,x20724,x20725,x20721,x20726),f612(x20723,x20724,x20725,x20722,x20726))
% 59.73/59.68 [2073]~E(x20731,x20732)+E(f612(x20733,x20734,x20735,x20736,x20731),f612(x20733,x20734,x20735,x20736,x20732))
% 59.73/59.68 [2074]~E(x20741,x20742)+E(f850(x20741,x20743),f850(x20742,x20743))
% 59.73/59.68 [2075]~E(x20751,x20752)+E(f850(x20753,x20751),f850(x20753,x20752))
% 59.73/59.68 [2076]~E(x20761,x20762)+E(f645(x20761,x20763,x20764),f645(x20762,x20763,x20764))
% 59.73/59.68 [2077]~E(x20771,x20772)+E(f645(x20773,x20771,x20774),f645(x20773,x20772,x20774))
% 59.73/59.68 [2078]~E(x20781,x20782)+E(f645(x20783,x20784,x20781),f645(x20783,x20784,x20782))
% 59.73/59.68 [2079]~E(x20791,x20792)+E(f862(x20791,x20793,x20794,x20795),f862(x20792,x20793,x20794,x20795))
% 59.73/59.68 [2080]~E(x20801,x20802)+E(f862(x20803,x20801,x20804,x20805),f862(x20803,x20802,x20804,x20805))
% 59.73/59.68 [2081]~E(x20811,x20812)+E(f862(x20813,x20814,x20811,x20815),f862(x20813,x20814,x20812,x20815))
% 59.73/59.68 [2082]~E(x20821,x20822)+E(f862(x20823,x20824,x20825,x20821),f862(x20823,x20824,x20825,x20822))
% 59.73/59.68 [2083]~E(x20831,x20832)+E(f661(x20831,x20833,x20834,x20835,x20836),f661(x20832,x20833,x20834,x20835,x20836))
% 59.73/59.68 [2084]~E(x20841,x20842)+E(f661(x20843,x20841,x20844,x20845,x20846),f661(x20843,x20842,x20844,x20845,x20846))
% 59.73/59.68 [2085]~E(x20851,x20852)+E(f661(x20853,x20854,x20851,x20855,x20856),f661(x20853,x20854,x20852,x20855,x20856))
% 59.73/59.68 [2086]~E(x20861,x20862)+E(f661(x20863,x20864,x20865,x20861,x20866),f661(x20863,x20864,x20865,x20862,x20866))
% 59.73/59.68 [2087]~E(x20871,x20872)+E(f661(x20873,x20874,x20875,x20876,x20871),f661(x20873,x20874,x20875,x20876,x20872))
% 59.73/59.68 [2088]~E(x20881,x20882)+E(f534(x20881,x20883,x20884,x20885),f534(x20882,x20883,x20884,x20885))
% 59.73/59.68 [2089]~E(x20891,x20892)+E(f534(x20893,x20891,x20894,x20895),f534(x20893,x20892,x20894,x20895))
% 59.73/59.68 [2090]~E(x20901,x20902)+E(f534(x20903,x20904,x20901,x20905),f534(x20903,x20904,x20902,x20905))
% 59.73/59.68 [2091]~E(x20911,x20912)+E(f534(x20913,x20914,x20915,x20911),f534(x20913,x20914,x20915,x20912))
% 59.73/59.68 [2092]~E(x20921,x20922)+E(f227(x20921,x20923,x20924,x20925,x20926),f227(x20922,x20923,x20924,x20925,x20926))
% 59.73/59.68 [2093]~E(x20931,x20932)+E(f227(x20933,x20931,x20934,x20935,x20936),f227(x20933,x20932,x20934,x20935,x20936))
% 59.73/59.68 [2094]~E(x20941,x20942)+E(f227(x20943,x20944,x20941,x20945,x20946),f227(x20943,x20944,x20942,x20945,x20946))
% 59.73/59.68 [2095]~E(x20951,x20952)+E(f227(x20953,x20954,x20955,x20951,x20956),f227(x20953,x20954,x20955,x20952,x20956))
% 59.73/59.68 [2096]~E(x20961,x20962)+E(f227(x20963,x20964,x20965,x20966,x20961),f227(x20963,x20964,x20965,x20966,x20962))
% 59.73/59.68 [2097]~E(x20971,x20972)+E(f111(x20971,x20973,x20974),f111(x20972,x20973,x20974))
% 59.73/59.68 [2098]~E(x20981,x20982)+E(f111(x20983,x20981,x20984),f111(x20983,x20982,x20984))
% 59.73/59.68 [2099]~E(x20991,x20992)+E(f111(x20993,x20994,x20991),f111(x20993,x20994,x20992))
% 59.73/59.68 [2100]~E(x21001,x21002)+E(f857(x21001,x21003,x21004),f857(x21002,x21003,x21004))
% 59.73/59.68 [2101]~E(x21011,x21012)+E(f857(x21013,x21011,x21014),f857(x21013,x21012,x21014))
% 59.73/59.68 [2102]~E(x21021,x21022)+E(f857(x21023,x21024,x21021),f857(x21023,x21024,x21022))
% 59.73/59.68 [2103]~E(x21031,x21032)+E(f765(x21031,x21033),f765(x21032,x21033))
% 59.73/59.68 [2104]~E(x21041,x21042)+E(f765(x21043,x21041),f765(x21043,x21042))
% 59.73/59.68 [2105]~E(x21051,x21052)+E(f295(x21051,x21053,x21054),f295(x21052,x21053,x21054))
% 59.73/59.68 [2106]~E(x21061,x21062)+E(f295(x21063,x21061,x21064),f295(x21063,x21062,x21064))
% 59.73/59.68 [2107]~E(x21071,x21072)+E(f295(x21073,x21074,x21071),f295(x21073,x21074,x21072))
% 59.73/59.68 [2108]~E(x21081,x21082)+E(f563(x21081,x21083,x21084),f563(x21082,x21083,x21084))
% 59.73/59.68 [2109]~E(x21091,x21092)+E(f563(x21093,x21091,x21094),f563(x21093,x21092,x21094))
% 59.73/59.68 [2110]~E(x21101,x21102)+E(f563(x21103,x21104,x21101),f563(x21103,x21104,x21102))
% 59.73/59.68 [2111]~E(x21111,x21112)+E(f809(x21111,x21113,x21114,x21115),f809(x21112,x21113,x21114,x21115))
% 59.73/59.68 [2112]~E(x21121,x21122)+E(f809(x21123,x21121,x21124,x21125),f809(x21123,x21122,x21124,x21125))
% 59.73/59.68 [2113]~E(x21131,x21132)+E(f809(x21133,x21134,x21131,x21135),f809(x21133,x21134,x21132,x21135))
% 59.73/59.68 [2114]~E(x21141,x21142)+E(f809(x21143,x21144,x21145,x21141),f809(x21143,x21144,x21145,x21142))
% 59.73/59.68 [2115]~E(x21151,x21152)+E(f726(x21151,x21153,x21154),f726(x21152,x21153,x21154))
% 59.73/59.68 [2116]~E(x21161,x21162)+E(f726(x21163,x21161,x21164),f726(x21163,x21162,x21164))
% 59.73/59.68 [2117]~E(x21171,x21172)+E(f726(x21173,x21174,x21171),f726(x21173,x21174,x21172))
% 59.73/59.68 [2118]~E(x21181,x21182)+E(f654(x21181,x21183,x21184),f654(x21182,x21183,x21184))
% 59.73/59.68 [2119]~E(x21191,x21192)+E(f654(x21193,x21191,x21194),f654(x21193,x21192,x21194))
% 59.73/59.68 [2120]~E(x21201,x21202)+E(f654(x21203,x21204,x21201),f654(x21203,x21204,x21202))
% 59.73/59.68 [2121]~E(x21211,x21212)+E(f293(x21211,x21213),f293(x21212,x21213))
% 59.73/59.68 [2122]~E(x21221,x21222)+E(f293(x21223,x21221),f293(x21223,x21222))
% 59.73/59.68 [2123]~E(x21231,x21232)+E(f592(x21231,x21233,x21234,x21235,x21236,x21237,x21238,x21239),f592(x21232,x21233,x21234,x21235,x21236,x21237,x21238,x21239))
% 59.73/59.68 [2124]~E(x21241,x21242)+E(f592(x21243,x21241,x21244,x21245,x21246,x21247,x21248,x21249),f592(x21243,x21242,x21244,x21245,x21246,x21247,x21248,x21249))
% 59.73/59.68 [2125]~E(x21251,x21252)+E(f592(x21253,x21254,x21251,x21255,x21256,x21257,x21258,x21259),f592(x21253,x21254,x21252,x21255,x21256,x21257,x21258,x21259))
% 59.73/59.68 [2126]~E(x21261,x21262)+E(f592(x21263,x21264,x21265,x21261,x21266,x21267,x21268,x21269),f592(x21263,x21264,x21265,x21262,x21266,x21267,x21268,x21269))
% 59.73/59.68 [2127]~E(x21271,x21272)+E(f592(x21273,x21274,x21275,x21276,x21271,x21277,x21278,x21279),f592(x21273,x21274,x21275,x21276,x21272,x21277,x21278,x21279))
% 59.73/59.68 [2128]~E(x21281,x21282)+E(f592(x21283,x21284,x21285,x21286,x21287,x21281,x21288,x21289),f592(x21283,x21284,x21285,x21286,x21287,x21282,x21288,x21289))
% 59.73/59.68 [2129]~E(x21291,x21292)+E(f592(x21293,x21294,x21295,x21296,x21297,x21298,x21291,x21299),f592(x21293,x21294,x21295,x21296,x21297,x21298,x21292,x21299))
% 59.73/59.68 [2130]~E(x21301,x21302)+E(f592(x21303,x21304,x21305,x21306,x21307,x21308,x21309,x21301),f592(x21303,x21304,x21305,x21306,x21307,x21308,x21309,x21302))
% 59.73/59.68 [2131]~E(x21311,x21312)+E(f54(x21311,x21313,x21314,x21315),f54(x21312,x21313,x21314,x21315))
% 59.73/59.68 [2132]~E(x21321,x21322)+E(f54(x21323,x21321,x21324,x21325),f54(x21323,x21322,x21324,x21325))
% 59.73/59.68 [2133]~E(x21331,x21332)+E(f54(x21333,x21334,x21331,x21335),f54(x21333,x21334,x21332,x21335))
% 59.73/59.68 [2134]~E(x21341,x21342)+E(f54(x21343,x21344,x21345,x21341),f54(x21343,x21344,x21345,x21342))
% 59.73/59.68 [2135]~E(x21351,x21352)+E(f486(x21351,x21353,x21354),f486(x21352,x21353,x21354))
% 59.73/59.68 [2136]~E(x21361,x21362)+E(f486(x21363,x21361,x21364),f486(x21363,x21362,x21364))
% 59.73/59.68 [2137]~E(x21371,x21372)+E(f486(x21373,x21374,x21371),f486(x21373,x21374,x21372))
% 59.73/59.68 [2138]~E(x21381,x21382)+E(f340(x21381),f340(x21382))
% 59.73/59.68 [2139]~E(x21391,x21392)+E(f281(x21391,x21393),f281(x21392,x21393))
% 59.73/59.68 [2140]~E(x21401,x21402)+E(f281(x21403,x21401),f281(x21403,x21402))
% 59.73/59.68 [2141]~E(x21411,x21412)+E(f388(x21411,x21413,x21414),f388(x21412,x21413,x21414))
% 59.73/59.68 [2142]~E(x21421,x21422)+E(f388(x21423,x21421,x21424),f388(x21423,x21422,x21424))
% 59.73/59.68 [2143]~E(x21431,x21432)+E(f388(x21433,x21434,x21431),f388(x21433,x21434,x21432))
% 59.73/59.68 [2144]~E(x21441,x21442)+E(f581(x21441,x21443,x21444,x21445),f581(x21442,x21443,x21444,x21445))
% 59.73/59.68 [2145]~E(x21451,x21452)+E(f581(x21453,x21451,x21454,x21455),f581(x21453,x21452,x21454,x21455))
% 59.73/59.68 [2146]~E(x21461,x21462)+E(f581(x21463,x21464,x21461,x21465),f581(x21463,x21464,x21462,x21465))
% 59.73/59.68 [2147]~E(x21471,x21472)+E(f581(x21473,x21474,x21475,x21471),f581(x21473,x21474,x21475,x21472))
% 59.73/59.68 [2148]~E(x21481,x21482)+E(f473(x21481,x21483,x21484,x21485),f473(x21482,x21483,x21484,x21485))
% 59.73/59.68 [2149]~E(x21491,x21492)+E(f473(x21493,x21491,x21494,x21495),f473(x21493,x21492,x21494,x21495))
% 59.73/59.68 [2150]~E(x21501,x21502)+E(f473(x21503,x21504,x21501,x21505),f473(x21503,x21504,x21502,x21505))
% 59.73/59.68 [2151]~E(x21511,x21512)+E(f473(x21513,x21514,x21515,x21511),f473(x21513,x21514,x21515,x21512))
% 59.73/59.68 [2152]~E(x21521,x21522)+E(f447(x21521,x21523,x21524,x21525),f447(x21522,x21523,x21524,x21525))
% 59.73/59.68 [2153]~E(x21531,x21532)+E(f447(x21533,x21531,x21534,x21535),f447(x21533,x21532,x21534,x21535))
% 59.73/59.68 [2154]~E(x21541,x21542)+E(f447(x21543,x21544,x21541,x21545),f447(x21543,x21544,x21542,x21545))
% 59.73/59.68 [2155]~E(x21551,x21552)+E(f447(x21553,x21554,x21555,x21551),f447(x21553,x21554,x21555,x21552))
% 59.73/59.68 [2156]~E(x21561,x21562)+E(f780(x21561,x21563,x21564),f780(x21562,x21563,x21564))
% 59.73/59.68 [2157]~E(x21571,x21572)+E(f780(x21573,x21571,x21574),f780(x21573,x21572,x21574))
% 59.73/59.68 [2158]~E(x21581,x21582)+E(f780(x21583,x21584,x21581),f780(x21583,x21584,x21582))
% 59.73/59.68 [2159]~E(x21591,x21592)+E(f830(x21591,x21593,x21594,x21595,x21596,x21597,x21598),f830(x21592,x21593,x21594,x21595,x21596,x21597,x21598))
% 59.73/59.68 [2160]~E(x21601,x21602)+E(f830(x21603,x21601,x21604,x21605,x21606,x21607,x21608),f830(x21603,x21602,x21604,x21605,x21606,x21607,x21608))
% 59.73/59.68 [2161]~E(x21611,x21612)+E(f830(x21613,x21614,x21611,x21615,x21616,x21617,x21618),f830(x21613,x21614,x21612,x21615,x21616,x21617,x21618))
% 59.73/59.68 [2162]~E(x21621,x21622)+E(f830(x21623,x21624,x21625,x21621,x21626,x21627,x21628),f830(x21623,x21624,x21625,x21622,x21626,x21627,x21628))
% 59.73/59.68 [2163]~E(x21631,x21632)+E(f830(x21633,x21634,x21635,x21636,x21631,x21637,x21638),f830(x21633,x21634,x21635,x21636,x21632,x21637,x21638))
% 59.73/59.68 [2164]~E(x21641,x21642)+E(f830(x21643,x21644,x21645,x21646,x21647,x21641,x21648),f830(x21643,x21644,x21645,x21646,x21647,x21642,x21648))
% 59.73/59.68 [2165]~E(x21651,x21652)+E(f830(x21653,x21654,x21655,x21656,x21657,x21658,x21651),f830(x21653,x21654,x21655,x21656,x21657,x21658,x21652))
% 59.73/59.68 [2166]~E(x21661,x21662)+E(f835(x21661,x21663),f835(x21662,x21663))
% 59.73/59.68 [2167]~E(x21671,x21672)+E(f835(x21673,x21671),f835(x21673,x21672))
% 59.73/59.68 [2168]~E(x21681,x21682)+E(f442(x21681,x21683,x21684),f442(x21682,x21683,x21684))
% 59.73/59.68 [2169]~E(x21691,x21692)+E(f442(x21693,x21691,x21694),f442(x21693,x21692,x21694))
% 59.73/59.68 [2170]~E(x21701,x21702)+E(f442(x21703,x21704,x21701),f442(x21703,x21704,x21702))
% 59.73/59.68 [2171]~E(x21711,x21712)+E(f394(x21711),f394(x21712))
% 59.73/59.68 [2172]~E(x21721,x21722)+E(f415(x21721,x21723),f415(x21722,x21723))
% 59.73/59.68 [2173]~E(x21731,x21732)+E(f415(x21733,x21731),f415(x21733,x21732))
% 59.73/59.68 [2174]~E(x21741,x21742)+E(f626(x21741,x21743,x21744,x21745,x21746,x21747,x21748),f626(x21742,x21743,x21744,x21745,x21746,x21747,x21748))
% 59.73/59.68 [2175]~E(x21751,x21752)+E(f626(x21753,x21751,x21754,x21755,x21756,x21757,x21758),f626(x21753,x21752,x21754,x21755,x21756,x21757,x21758))
% 59.73/59.68 [2176]~E(x21761,x21762)+E(f626(x21763,x21764,x21761,x21765,x21766,x21767,x21768),f626(x21763,x21764,x21762,x21765,x21766,x21767,x21768))
% 59.73/59.68 [2177]~E(x21771,x21772)+E(f626(x21773,x21774,x21775,x21771,x21776,x21777,x21778),f626(x21773,x21774,x21775,x21772,x21776,x21777,x21778))
% 59.73/59.68 [2178]~E(x21781,x21782)+E(f626(x21783,x21784,x21785,x21786,x21781,x21787,x21788),f626(x21783,x21784,x21785,x21786,x21782,x21787,x21788))
% 59.73/59.68 [2179]~E(x21791,x21792)+E(f626(x21793,x21794,x21795,x21796,x21797,x21791,x21798),f626(x21793,x21794,x21795,x21796,x21797,x21792,x21798))
% 59.73/59.68 [2180]~E(x21801,x21802)+E(f626(x21803,x21804,x21805,x21806,x21807,x21808,x21801),f626(x21803,x21804,x21805,x21806,x21807,x21808,x21802))
% 59.73/59.68 [2181]~E(x21811,x21812)+E(f347(x21811,x21813,x21814,x21815),f347(x21812,x21813,x21814,x21815))
% 59.73/59.68 [2182]~E(x21821,x21822)+E(f347(x21823,x21821,x21824,x21825),f347(x21823,x21822,x21824,x21825))
% 59.73/59.68 [2183]~E(x21831,x21832)+E(f347(x21833,x21834,x21831,x21835),f347(x21833,x21834,x21832,x21835))
% 59.73/59.68 [2184]~E(x21841,x21842)+E(f347(x21843,x21844,x21845,x21841),f347(x21843,x21844,x21845,x21842))
% 59.73/59.68 [2185]~E(x21851,x21852)+E(f597(x21851,x21853,x21854),f597(x21852,x21853,x21854))
% 59.73/59.68 [2186]~E(x21861,x21862)+E(f597(x21863,x21861,x21864),f597(x21863,x21862,x21864))
% 59.73/59.68 [2187]~E(x21871,x21872)+E(f597(x21873,x21874,x21871),f597(x21873,x21874,x21872))
% 59.73/59.68 [2188]~E(x21881,x21882)+E(f300(x21881,x21883,x21884),f300(x21882,x21883,x21884))
% 59.73/59.68 [2189]~E(x21891,x21892)+E(f300(x21893,x21891,x21894),f300(x21893,x21892,x21894))
% 59.73/59.68 [2190]~E(x21901,x21902)+E(f300(x21903,x21904,x21901),f300(x21903,x21904,x21902))
% 59.73/59.68 [2191]~E(x21911,x21912)+E(f658(x21911,x21913,x21914,x21915),f658(x21912,x21913,x21914,x21915))
% 59.73/59.68 [2192]~E(x21921,x21922)+E(f658(x21923,x21921,x21924,x21925),f658(x21923,x21922,x21924,x21925))
% 59.73/59.68 [2193]~E(x21931,x21932)+E(f658(x21933,x21934,x21931,x21935),f658(x21933,x21934,x21932,x21935))
% 59.73/59.68 [2194]~E(x21941,x21942)+E(f658(x21943,x21944,x21945,x21941),f658(x21943,x21944,x21945,x21942))
% 59.73/59.68 [2195]~E(x21951,x21952)+E(f197(x21951,x21953,x21954),f197(x21952,x21953,x21954))
% 59.73/59.68 [2196]~E(x21961,x21962)+E(f197(x21963,x21961,x21964),f197(x21963,x21962,x21964))
% 59.73/59.68 [2197]~E(x21971,x21972)+E(f197(x21973,x21974,x21971),f197(x21973,x21974,x21972))
% 59.73/59.68 [2198]~E(x21981,x21982)+E(f393(x21981),f393(x21982))
% 59.73/59.68 [2199]~E(x21991,x21992)+E(f521(x21991,x21993,x21994),f521(x21992,x21993,x21994))
% 59.73/59.68 [2200]~E(x22001,x22002)+E(f521(x22003,x22001,x22004),f521(x22003,x22002,x22004))
% 59.73/59.68 [2201]~E(x22011,x22012)+E(f521(x22013,x22014,x22011),f521(x22013,x22014,x22012))
% 59.73/59.68 [2202]~E(x22021,x22022)+E(f446(x22021,x22023,x22024,x22025),f446(x22022,x22023,x22024,x22025))
% 59.73/59.68 [2203]~E(x22031,x22032)+E(f446(x22033,x22031,x22034,x22035),f446(x22033,x22032,x22034,x22035))
% 59.73/59.68 [2204]~E(x22041,x22042)+E(f446(x22043,x22044,x22041,x22045),f446(x22043,x22044,x22042,x22045))
% 59.73/59.68 [2205]~E(x22051,x22052)+E(f446(x22053,x22054,x22055,x22051),f446(x22053,x22054,x22055,x22052))
% 59.73/59.68 [2206]~E(x22061,x22062)+E(f423(x22061,x22063,x22064),f423(x22062,x22063,x22064))
% 59.73/59.68 [2207]~E(x22071,x22072)+E(f423(x22073,x22071,x22074),f423(x22073,x22072,x22074))
% 59.73/59.68 [2208]~E(x22081,x22082)+E(f423(x22083,x22084,x22081),f423(x22083,x22084,x22082))
% 59.73/59.68 [2209]~E(x22091,x22092)+E(f354(x22091,x22093),f354(x22092,x22093))
% 59.73/59.68 [2210]~E(x22101,x22102)+E(f354(x22103,x22101),f354(x22103,x22102))
% 59.73/59.68 [2211]~E(x22111,x22112)+E(f796(x22111,x22113,x22114,x22115),f796(x22112,x22113,x22114,x22115))
% 59.73/59.68 [2212]~E(x22121,x22122)+E(f796(x22123,x22121,x22124,x22125),f796(x22123,x22122,x22124,x22125))
% 59.73/59.68 [2213]~E(x22131,x22132)+E(f796(x22133,x22134,x22131,x22135),f796(x22133,x22134,x22132,x22135))
% 59.73/59.68 [2214]~E(x22141,x22142)+E(f796(x22143,x22144,x22145,x22141),f796(x22143,x22144,x22145,x22142))
% 59.73/59.68 [2215]~E(x22151,x22152)+E(f206(x22151,x22153,x22154),f206(x22152,x22153,x22154))
% 59.73/59.68 [2216]~E(x22161,x22162)+E(f206(x22163,x22161,x22164),f206(x22163,x22162,x22164))
% 59.73/59.68 [2217]~E(x22171,x22172)+E(f206(x22173,x22174,x22171),f206(x22173,x22174,x22172))
% 59.73/59.68 [2218]~E(x22181,x22182)+E(f810(x22181,x22183),f810(x22182,x22183))
% 59.73/59.68 [2219]~E(x22191,x22192)+E(f810(x22193,x22191),f810(x22193,x22192))
% 59.73/59.68 [2220]~E(x22201,x22202)+E(f616(x22201,x22203),f616(x22202,x22203))
% 59.73/59.68 [2221]~E(x22211,x22212)+E(f616(x22213,x22211),f616(x22213,x22212))
% 59.73/59.68 [2222]~E(x22221,x22222)+E(f449(x22221,x22223),f449(x22222,x22223))
% 59.73/59.68 [2223]~E(x22231,x22232)+E(f449(x22233,x22231),f449(x22233,x22232))
% 59.73/59.68 [2224]~E(x22241,x22242)+E(f583(x22241,x22243,x22244,x22245),f583(x22242,x22243,x22244,x22245))
% 59.73/59.68 [2225]~E(x22251,x22252)+E(f583(x22253,x22251,x22254,x22255),f583(x22253,x22252,x22254,x22255))
% 59.73/59.68 [2226]~E(x22261,x22262)+E(f583(x22263,x22264,x22261,x22265),f583(x22263,x22264,x22262,x22265))
% 59.73/59.68 [2227]~E(x22271,x22272)+E(f583(x22273,x22274,x22275,x22271),f583(x22273,x22274,x22275,x22272))
% 59.73/59.68 [2228]~E(x22281,x22282)+E(f508(x22281,x22283,x22284),f508(x22282,x22283,x22284))
% 59.73/59.68 [2229]~E(x22291,x22292)+E(f508(x22293,x22291,x22294),f508(x22293,x22292,x22294))
% 59.73/59.68 [2230]~E(x22301,x22302)+E(f508(x22303,x22304,x22301),f508(x22303,x22304,x22302))
% 59.73/59.68 [2231]~E(x22311,x22312)+E(f538(x22311,x22313,x22314,x22315,x22316,x22317),f538(x22312,x22313,x22314,x22315,x22316,x22317))
% 59.73/59.68 [2232]~E(x22321,x22322)+E(f538(x22323,x22321,x22324,x22325,x22326,x22327),f538(x22323,x22322,x22324,x22325,x22326,x22327))
% 59.73/59.68 [2233]~E(x22331,x22332)+E(f538(x22333,x22334,x22331,x22335,x22336,x22337),f538(x22333,x22334,x22332,x22335,x22336,x22337))
% 59.73/59.68 [2234]~E(x22341,x22342)+E(f538(x22343,x22344,x22345,x22341,x22346,x22347),f538(x22343,x22344,x22345,x22342,x22346,x22347))
% 59.73/59.68 [2235]~E(x22351,x22352)+E(f538(x22353,x22354,x22355,x22356,x22351,x22357),f538(x22353,x22354,x22355,x22356,x22352,x22357))
% 59.73/59.68 [2236]~E(x22361,x22362)+E(f538(x22363,x22364,x22365,x22366,x22367,x22361),f538(x22363,x22364,x22365,x22366,x22367,x22362))
% 59.73/59.68 [2237]~E(x22371,x22372)+E(f506(x22371,x22373),f506(x22372,x22373))
% 59.73/59.68 [2238]~E(x22381,x22382)+E(f506(x22383,x22381),f506(x22383,x22382))
% 59.73/59.68 [2239]~E(x22391,x22392)+E(f408(x22391,x22393,x22394,x22395),f408(x22392,x22393,x22394,x22395))
% 59.73/59.68 [2240]~E(x22401,x22402)+E(f408(x22403,x22401,x22404,x22405),f408(x22403,x22402,x22404,x22405))
% 59.73/59.68 [2241]~E(x22411,x22412)+E(f408(x22413,x22414,x22411,x22415),f408(x22413,x22414,x22412,x22415))
% 59.73/59.68 [2242]~E(x22421,x22422)+E(f408(x22423,x22424,x22425,x22421),f408(x22423,x22424,x22425,x22422))
% 59.73/59.68 [2243]~E(x22431,x22432)+E(f640(x22431,x22433,x22434,x22435),f640(x22432,x22433,x22434,x22435))
% 59.73/59.68 [2244]~E(x22441,x22442)+E(f640(x22443,x22441,x22444,x22445),f640(x22443,x22442,x22444,x22445))
% 59.73/59.68 [2245]~E(x22451,x22452)+E(f640(x22453,x22454,x22451,x22455),f640(x22453,x22454,x22452,x22455))
% 59.73/59.68 [2246]~E(x22461,x22462)+E(f640(x22463,x22464,x22465,x22461),f640(x22463,x22464,x22465,x22462))
% 59.73/59.68 [2247]~E(x22471,x22472)+E(f208(x22471),f208(x22472))
% 59.73/59.68 [2248]~E(x22481,x22482)+E(f530(x22481,x22483,x22484),f530(x22482,x22483,x22484))
% 59.73/59.68 [2249]~E(x22491,x22492)+E(f530(x22493,x22491,x22494),f530(x22493,x22492,x22494))
% 59.73/59.68 [2250]~E(x22501,x22502)+E(f530(x22503,x22504,x22501),f530(x22503,x22504,x22502))
% 59.73/59.68 [2251]~E(x22511,x22512)+E(f553(x22511,x22513,x22514,x22515),f553(x22512,x22513,x22514,x22515))
% 59.73/59.68 [2252]~E(x22521,x22522)+E(f553(x22523,x22521,x22524,x22525),f553(x22523,x22522,x22524,x22525))
% 59.73/59.68 [2253]~E(x22531,x22532)+E(f553(x22533,x22534,x22531,x22535),f553(x22533,x22534,x22532,x22535))
% 59.73/59.68 [2254]~E(x22541,x22542)+E(f553(x22543,x22544,x22545,x22541),f553(x22543,x22544,x22545,x22542))
% 59.73/59.68 [2255]~E(x22551,x22552)+E(f732(x22551,x22553,x22554,x22555,x22556),f732(x22552,x22553,x22554,x22555,x22556))
% 59.73/59.68 [2256]~E(x22561,x22562)+E(f732(x22563,x22561,x22564,x22565,x22566),f732(x22563,x22562,x22564,x22565,x22566))
% 59.73/59.68 [2257]~E(x22571,x22572)+E(f732(x22573,x22574,x22571,x22575,x22576),f732(x22573,x22574,x22572,x22575,x22576))
% 59.73/59.68 [2258]~E(x22581,x22582)+E(f732(x22583,x22584,x22585,x22581,x22586),f732(x22583,x22584,x22585,x22582,x22586))
% 59.73/59.68 [2259]~E(x22591,x22592)+E(f732(x22593,x22594,x22595,x22596,x22591),f732(x22593,x22594,x22595,x22596,x22592))
% 59.73/59.68 [2260]~E(x22601,x22602)+E(f213(x22601,x22603,x22604,x22605),f213(x22602,x22603,x22604,x22605))
% 59.73/59.68 [2261]~E(x22611,x22612)+E(f213(x22613,x22611,x22614,x22615),f213(x22613,x22612,x22614,x22615))
% 59.73/59.68 [2262]~E(x22621,x22622)+E(f213(x22623,x22624,x22621,x22625),f213(x22623,x22624,x22622,x22625))
% 59.73/59.68 [2263]~E(x22631,x22632)+E(f213(x22633,x22634,x22635,x22631),f213(x22633,x22634,x22635,x22632))
% 59.73/59.68 [2264]~E(x22641,x22642)+E(f361(x22641),f361(x22642))
% 59.73/59.68 [2265]~E(x22651,x22652)+E(f62(x22651,x22653,x22654),f62(x22652,x22653,x22654))
% 59.73/59.68 [2266]~E(x22661,x22662)+E(f62(x22663,x22661,x22664),f62(x22663,x22662,x22664))
% 59.73/59.68 [2267]~E(x22671,x22672)+E(f62(x22673,x22674,x22671),f62(x22673,x22674,x22672))
% 59.73/59.68 [2268]~E(x22681,x22682)+E(f789(x22681,x22683,x22684,x22685),f789(x22682,x22683,x22684,x22685))
% 59.73/59.68 [2269]~E(x22691,x22692)+E(f789(x22693,x22691,x22694,x22695),f789(x22693,x22692,x22694,x22695))
% 59.73/59.68 [2270]~E(x22701,x22702)+E(f789(x22703,x22704,x22701,x22705),f789(x22703,x22704,x22702,x22705))
% 59.73/59.68 [2271]~E(x22711,x22712)+E(f789(x22713,x22714,x22715,x22711),f789(x22713,x22714,x22715,x22712))
% 59.73/59.68 [2272]~E(x22721,x22722)+E(f489(x22721,x22723,x22724),f489(x22722,x22723,x22724))
% 59.73/59.68 [2273]~E(x22731,x22732)+E(f489(x22733,x22731,x22734),f489(x22733,x22732,x22734))
% 59.73/59.68 [2274]~E(x22741,x22742)+E(f489(x22743,x22744,x22741),f489(x22743,x22744,x22742))
% 59.73/59.68 [2275]~E(x22751,x22752)+E(f275(x22751),f275(x22752))
% 59.73/59.68 [2276]~E(x22761,x22762)+E(f651(x22761,x22763,x22764,x22765),f651(x22762,x22763,x22764,x22765))
% 59.73/59.68 [2277]~E(x22771,x22772)+E(f651(x22773,x22771,x22774,x22775),f651(x22773,x22772,x22774,x22775))
% 59.73/59.68 [2278]~E(x22781,x22782)+E(f651(x22783,x22784,x22781,x22785),f651(x22783,x22784,x22782,x22785))
% 59.73/59.68 [2279]~E(x22791,x22792)+E(f651(x22793,x22794,x22795,x22791),f651(x22793,x22794,x22795,x22792))
% 59.73/59.68 [2280]~E(x22801,x22802)+E(f771(x22801,x22803,x22804,x22805,x22806),f771(x22802,x22803,x22804,x22805,x22806))
% 59.73/59.68 [2281]~E(x22811,x22812)+E(f771(x22813,x22811,x22814,x22815,x22816),f771(x22813,x22812,x22814,x22815,x22816))
% 59.73/59.68 [2282]~E(x22821,x22822)+E(f771(x22823,x22824,x22821,x22825,x22826),f771(x22823,x22824,x22822,x22825,x22826))
% 59.73/59.68 [2283]~E(x22831,x22832)+E(f771(x22833,x22834,x22835,x22831,x22836),f771(x22833,x22834,x22835,x22832,x22836))
% 59.73/59.68 [2284]~E(x22841,x22842)+E(f771(x22843,x22844,x22845,x22846,x22841),f771(x22843,x22844,x22845,x22846,x22842))
% 59.73/59.68 [2285]~E(x22851,x22852)+E(f596(x22851,x22853,x22854,x22855),f596(x22852,x22853,x22854,x22855))
% 59.73/59.68 [2286]~E(x22861,x22862)+E(f596(x22863,x22861,x22864,x22865),f596(x22863,x22862,x22864,x22865))
% 59.73/59.68 [2287]~E(x22871,x22872)+E(f596(x22873,x22874,x22871,x22875),f596(x22873,x22874,x22872,x22875))
% 59.73/59.68 [2288]~E(x22881,x22882)+E(f596(x22883,x22884,x22885,x22881),f596(x22883,x22884,x22885,x22882))
% 59.73/59.68 [2289]~E(x22891,x22892)+E(f117(x22891),f117(x22892))
% 59.73/59.68 [2290]~E(x22901,x22902)+E(f853(x22901,x22903,x22904,x22905),f853(x22902,x22903,x22904,x22905))
% 59.73/59.68 [2291]~E(x22911,x22912)+E(f853(x22913,x22911,x22914,x22915),f853(x22913,x22912,x22914,x22915))
% 59.73/59.68 [2292]~E(x22921,x22922)+E(f853(x22923,x22924,x22921,x22925),f853(x22923,x22924,x22922,x22925))
% 59.73/59.68 [2293]~E(x22931,x22932)+E(f853(x22933,x22934,x22935,x22931),f853(x22933,x22934,x22935,x22932))
% 59.73/59.68 [2294]~E(x22941,x22942)+E(f847(x22941,x22943,x22944,x22945,x22946),f847(x22942,x22943,x22944,x22945,x22946))
% 59.73/59.68 [2295]~E(x22951,x22952)+E(f847(x22953,x22951,x22954,x22955,x22956),f847(x22953,x22952,x22954,x22955,x22956))
% 59.73/59.68 [2296]~E(x22961,x22962)+E(f847(x22963,x22964,x22961,x22965,x22966),f847(x22963,x22964,x22962,x22965,x22966))
% 59.73/59.68 [2297]~E(x22971,x22972)+E(f847(x22973,x22974,x22975,x22971,x22976),f847(x22973,x22974,x22975,x22972,x22976))
% 59.73/59.68 [2298]~E(x22981,x22982)+E(f847(x22983,x22984,x22985,x22986,x22981),f847(x22983,x22984,x22985,x22986,x22982))
% 59.73/59.68 [2299]~E(x22991,x22992)+E(f694(x22991,x22993,x22994,x22995),f694(x22992,x22993,x22994,x22995))
% 59.73/59.68 [2300]~E(x23001,x23002)+E(f694(x23003,x23001,x23004,x23005),f694(x23003,x23002,x23004,x23005))
% 59.73/59.68 [2301]~E(x23011,x23012)+E(f694(x23013,x23014,x23011,x23015),f694(x23013,x23014,x23012,x23015))
% 59.73/59.68 [2302]~E(x23021,x23022)+E(f694(x23023,x23024,x23025,x23021),f694(x23023,x23024,x23025,x23022))
% 59.73/59.68 [2303]~E(x23031,x23032)+E(f710(x23031,x23033,x23034),f710(x23032,x23033,x23034))
% 59.73/59.68 [2304]~E(x23041,x23042)+E(f710(x23043,x23041,x23044),f710(x23043,x23042,x23044))
% 59.73/59.68 [2305]~E(x23051,x23052)+E(f710(x23053,x23054,x23051),f710(x23053,x23054,x23052))
% 59.73/59.68 [2306]~E(x23061,x23062)+E(f367(x23061,x23063,x23064),f367(x23062,x23063,x23064))
% 59.73/59.68 [2307]~E(x23071,x23072)+E(f367(x23073,x23071,x23074),f367(x23073,x23072,x23074))
% 59.73/59.68 [2308]~E(x23081,x23082)+E(f367(x23083,x23084,x23081),f367(x23083,x23084,x23082))
% 59.73/59.68 [2309]~E(x23091,x23092)+E(f403(x23091,x23093),f403(x23092,x23093))
% 59.73/59.68 [2310]~E(x23101,x23102)+E(f403(x23103,x23101),f403(x23103,x23102))
% 59.73/59.68 [2311]~E(x23111,x23112)+E(f429(x23111,x23113,x23114),f429(x23112,x23113,x23114))
% 59.73/59.68 [2312]~E(x23121,x23122)+E(f429(x23123,x23121,x23124),f429(x23123,x23122,x23124))
% 59.73/59.68 [2313]~E(x23131,x23132)+E(f429(x23133,x23134,x23131),f429(x23133,x23134,x23132))
% 59.73/59.68 [2314]~E(x23141,x23142)+E(f580(x23141,x23143,x23144),f580(x23142,x23143,x23144))
% 59.73/59.68 [2315]~E(x23151,x23152)+E(f580(x23153,x23151,x23154),f580(x23153,x23152,x23154))
% 59.73/59.68 [2316]~E(x23161,x23162)+E(f580(x23163,x23164,x23161),f580(x23163,x23164,x23162))
% 59.73/59.68 [2317]~E(x23171,x23172)+E(f212(x23171,x23173,x23174,x23175),f212(x23172,x23173,x23174,x23175))
% 59.73/59.68 [2318]~E(x23181,x23182)+E(f212(x23183,x23181,x23184,x23185),f212(x23183,x23182,x23184,x23185))
% 59.73/59.68 [2319]~E(x23191,x23192)+E(f212(x23193,x23194,x23191,x23195),f212(x23193,x23194,x23192,x23195))
% 59.73/59.68 [2320]~E(x23201,x23202)+E(f212(x23203,x23204,x23205,x23201),f212(x23203,x23204,x23205,x23202))
% 59.73/59.68 [2321]~E(x23211,x23212)+E(f209(x23211,x23213,x23214,x23215),f209(x23212,x23213,x23214,x23215))
% 59.73/59.68 [2322]~E(x23221,x23222)+E(f209(x23223,x23221,x23224,x23225),f209(x23223,x23222,x23224,x23225))
% 59.73/59.68 [2323]~E(x23231,x23232)+E(f209(x23233,x23234,x23231,x23235),f209(x23233,x23234,x23232,x23235))
% 59.73/59.68 [2324]~E(x23241,x23242)+E(f209(x23243,x23244,x23245,x23241),f209(x23243,x23244,x23245,x23242))
% 59.73/59.68 [2325]~E(x23251,x23252)+E(f660(x23251,x23253,x23254),f660(x23252,x23253,x23254))
% 59.73/59.68 [2326]~E(x23261,x23262)+E(f660(x23263,x23261,x23264),f660(x23263,x23262,x23264))
% 59.73/59.68 [2327]~E(x23271,x23272)+E(f660(x23273,x23274,x23271),f660(x23273,x23274,x23272))
% 59.73/59.68 [2328]~E(x23281,x23282)+E(f617(x23281,x23283,x23284,x23285),f617(x23282,x23283,x23284,x23285))
% 59.73/59.68 [2329]~E(x23291,x23292)+E(f617(x23293,x23291,x23294,x23295),f617(x23293,x23292,x23294,x23295))
% 59.73/59.68 [2330]~E(x23301,x23302)+E(f617(x23303,x23304,x23301,x23305),f617(x23303,x23304,x23302,x23305))
% 59.73/59.68 [2331]~E(x23311,x23312)+E(f617(x23313,x23314,x23315,x23311),f617(x23313,x23314,x23315,x23312))
% 59.73/59.68 [2332]~E(x23321,x23322)+E(f558(x23321,x23323),f558(x23322,x23323))
% 59.73/59.68 [2333]~E(x23331,x23332)+E(f558(x23333,x23331),f558(x23333,x23332))
% 59.73/59.68 [2334]~E(x23341,x23342)+E(f624(x23341,x23343,x23344,x23345,x23346),f624(x23342,x23343,x23344,x23345,x23346))
% 59.73/59.68 [2335]~E(x23351,x23352)+E(f624(x23353,x23351,x23354,x23355,x23356),f624(x23353,x23352,x23354,x23355,x23356))
% 59.73/59.68 [2336]~E(x23361,x23362)+E(f624(x23363,x23364,x23361,x23365,x23366),f624(x23363,x23364,x23362,x23365,x23366))
% 59.73/59.68 [2337]~E(x23371,x23372)+E(f624(x23373,x23374,x23375,x23371,x23376),f624(x23373,x23374,x23375,x23372,x23376))
% 59.73/59.68 [2338]~E(x23381,x23382)+E(f624(x23383,x23384,x23385,x23386,x23381),f624(x23383,x23384,x23385,x23386,x23382))
% 59.73/59.68 [2339]~E(x23391,x23392)+E(f390(x23391,x23393,x23394,x23395,x23396),f390(x23392,x23393,x23394,x23395,x23396))
% 59.73/59.68 [2340]~E(x23401,x23402)+E(f390(x23403,x23401,x23404,x23405,x23406),f390(x23403,x23402,x23404,x23405,x23406))
% 59.73/59.68 [2341]~E(x23411,x23412)+E(f390(x23413,x23414,x23411,x23415,x23416),f390(x23413,x23414,x23412,x23415,x23416))
% 59.73/59.68 [2342]~E(x23421,x23422)+E(f390(x23423,x23424,x23425,x23421,x23426),f390(x23423,x23424,x23425,x23422,x23426))
% 59.73/59.68 [2343]~E(x23431,x23432)+E(f390(x23433,x23434,x23435,x23436,x23431),f390(x23433,x23434,x23435,x23436,x23432))
% 59.73/59.68 [2344]~E(x23441,x23442)+E(f420(x23441,x23443),f420(x23442,x23443))
% 59.73/59.68 [2345]~E(x23451,x23452)+E(f420(x23453,x23451),f420(x23453,x23452))
% 59.73/59.68 [2346]~E(x23461,x23462)+E(f600(x23461,x23463,x23464,x23465),f600(x23462,x23463,x23464,x23465))
% 59.73/59.68 [2347]~E(x23471,x23472)+E(f600(x23473,x23471,x23474,x23475),f600(x23473,x23472,x23474,x23475))
% 59.73/59.68 [2348]~E(x23481,x23482)+E(f600(x23483,x23484,x23481,x23485),f600(x23483,x23484,x23482,x23485))
% 59.73/59.68 [2349]~E(x23491,x23492)+E(f600(x23493,x23494,x23495,x23491),f600(x23493,x23494,x23495,x23492))
% 59.73/59.68 [2350]~E(x23501,x23502)+E(f711(x23501,x23503,x23504,x23505),f711(x23502,x23503,x23504,x23505))
% 59.73/59.68 [2351]~E(x23511,x23512)+E(f711(x23513,x23511,x23514,x23515),f711(x23513,x23512,x23514,x23515))
% 59.73/59.68 [2352]~E(x23521,x23522)+E(f711(x23523,x23524,x23521,x23525),f711(x23523,x23524,x23522,x23525))
% 59.73/59.68 [2353]~E(x23531,x23532)+E(f711(x23533,x23534,x23535,x23531),f711(x23533,x23534,x23535,x23532))
% 59.73/59.68 [2354]~E(x23541,x23542)+E(f318(x23541,x23543,x23544),f318(x23542,x23543,x23544))
% 59.73/59.68 [2355]~E(x23551,x23552)+E(f318(x23553,x23551,x23554),f318(x23553,x23552,x23554))
% 59.73/59.68 [2356]~E(x23561,x23562)+E(f318(x23563,x23564,x23561),f318(x23563,x23564,x23562))
% 59.73/59.68 [2357]~E(x23571,x23572)+E(f781(x23571,x23573,x23574),f781(x23572,x23573,x23574))
% 59.73/59.68 [2358]~E(x23581,x23582)+E(f781(x23583,x23581,x23584),f781(x23583,x23582,x23584))
% 59.73/59.68 [2359]~E(x23591,x23592)+E(f781(x23593,x23594,x23591),f781(x23593,x23594,x23592))
% 59.73/59.68 [2360]~E(x23601,x23602)+E(f607(x23601,x23603,x23604,x23605),f607(x23602,x23603,x23604,x23605))
% 59.73/59.68 [2361]~E(x23611,x23612)+E(f607(x23613,x23611,x23614,x23615),f607(x23613,x23612,x23614,x23615))
% 59.73/59.68 [2362]~E(x23621,x23622)+E(f607(x23623,x23624,x23621,x23625),f607(x23623,x23624,x23622,x23625))
% 59.73/59.68 [2363]~E(x23631,x23632)+E(f607(x23633,x23634,x23635,x23631),f607(x23633,x23634,x23635,x23632))
% 59.73/59.68 [2364]~E(x23641,x23642)+E(f610(x23641,x23643,x23644,x23645,x23646),f610(x23642,x23643,x23644,x23645,x23646))
% 59.73/59.68 [2365]~E(x23651,x23652)+E(f610(x23653,x23651,x23654,x23655,x23656),f610(x23653,x23652,x23654,x23655,x23656))
% 59.73/59.68 [2366]~E(x23661,x23662)+E(f610(x23663,x23664,x23661,x23665,x23666),f610(x23663,x23664,x23662,x23665,x23666))
% 59.73/59.68 [2367]~E(x23671,x23672)+E(f610(x23673,x23674,x23675,x23671,x23676),f610(x23673,x23674,x23675,x23672,x23676))
% 59.73/59.68 [2368]~E(x23681,x23682)+E(f610(x23683,x23684,x23685,x23686,x23681),f610(x23683,x23684,x23685,x23686,x23682))
% 59.73/59.68 [2369]~E(x23691,x23692)+E(f317(x23691,x23693,x23694),f317(x23692,x23693,x23694))
% 59.73/59.68 [2370]~E(x23701,x23702)+E(f317(x23703,x23701,x23704),f317(x23703,x23702,x23704))
% 59.73/59.68 [2371]~E(x23711,x23712)+E(f317(x23713,x23714,x23711),f317(x23713,x23714,x23712))
% 59.73/59.68 [2372]~E(x23721,x23722)+E(f296(x23721,x23723,x23724),f296(x23722,x23723,x23724))
% 59.73/59.68 [2373]~E(x23731,x23732)+E(f296(x23733,x23731,x23734),f296(x23733,x23732,x23734))
% 59.73/59.68 [2374]~E(x23741,x23742)+E(f296(x23743,x23744,x23741),f296(x23743,x23744,x23742))
% 59.73/59.68 [2375]~E(x23751,x23752)+E(f297(x23751,x23753,x23754),f297(x23752,x23753,x23754))
% 59.73/59.68 [2376]~E(x23761,x23762)+E(f297(x23763,x23761,x23764),f297(x23763,x23762,x23764))
% 59.73/59.68 [2377]~E(x23771,x23772)+E(f297(x23773,x23774,x23771),f297(x23773,x23774,x23772))
% 59.73/59.68 [2378]~E(x23781,x23782)+E(f724(x23781,x23783),f724(x23782,x23783))
% 59.73/59.68 [2379]~E(x23791,x23792)+E(f724(x23793,x23791),f724(x23793,x23792))
% 59.73/59.68 [2380]~E(x23801,x23802)+E(f279(x23801,x23803,x23804,x23805),f279(x23802,x23803,x23804,x23805))
% 59.73/59.68 [2381]~E(x23811,x23812)+E(f279(x23813,x23811,x23814,x23815),f279(x23813,x23812,x23814,x23815))
% 59.73/59.68 [2382]~E(x23821,x23822)+E(f279(x23823,x23824,x23821,x23825),f279(x23823,x23824,x23822,x23825))
% 59.73/59.68 [2383]~E(x23831,x23832)+E(f279(x23833,x23834,x23835,x23831),f279(x23833,x23834,x23835,x23832))
% 59.73/59.68 [2384]~E(x23841,x23842)+E(f761(x23841,x23843,x23844,x23845,x23846),f761(x23842,x23843,x23844,x23845,x23846))
% 59.73/59.68 [2385]~E(x23851,x23852)+E(f761(x23853,x23851,x23854,x23855,x23856),f761(x23853,x23852,x23854,x23855,x23856))
% 59.73/59.68 [2386]~E(x23861,x23862)+E(f761(x23863,x23864,x23861,x23865,x23866),f761(x23863,x23864,x23862,x23865,x23866))
% 59.73/59.68 [2387]~E(x23871,x23872)+E(f761(x23873,x23874,x23875,x23871,x23876),f761(x23873,x23874,x23875,x23872,x23876))
% 59.73/59.68 [2388]~E(x23881,x23882)+E(f761(x23883,x23884,x23885,x23886,x23881),f761(x23883,x23884,x23885,x23886,x23882))
% 59.73/59.68 [2389]~E(x23891,x23892)+E(f369(x23891,x23893,x23894,x23895,x23896),f369(x23892,x23893,x23894,x23895,x23896))
% 59.73/59.68 [2390]~E(x23901,x23902)+E(f369(x23903,x23901,x23904,x23905,x23906),f369(x23903,x23902,x23904,x23905,x23906))
% 59.73/59.68 [2391]~E(x23911,x23912)+E(f369(x23913,x23914,x23911,x23915,x23916),f369(x23913,x23914,x23912,x23915,x23916))
% 59.73/59.68 [2392]~E(x23921,x23922)+E(f369(x23923,x23924,x23925,x23921,x23926),f369(x23923,x23924,x23925,x23922,x23926))
% 59.73/59.68 [2393]~E(x23931,x23932)+E(f369(x23933,x23934,x23935,x23936,x23931),f369(x23933,x23934,x23935,x23936,x23932))
% 59.73/59.68 [2394]~E(x23941,x23942)+E(f679(x23941,x23943,x23944,x23945,x23946),f679(x23942,x23943,x23944,x23945,x23946))
% 59.73/59.68 [2395]~E(x23951,x23952)+E(f679(x23953,x23951,x23954,x23955,x23956),f679(x23953,x23952,x23954,x23955,x23956))
% 59.73/59.68 [2396]~E(x23961,x23962)+E(f679(x23963,x23964,x23961,x23965,x23966),f679(x23963,x23964,x23962,x23965,x23966))
% 59.73/59.68 [2397]~E(x23971,x23972)+E(f679(x23973,x23974,x23975,x23971,x23976),f679(x23973,x23974,x23975,x23972,x23976))
% 59.73/59.68 [2398]~E(x23981,x23982)+E(f679(x23983,x23984,x23985,x23986,x23981),f679(x23983,x23984,x23985,x23986,x23982))
% 59.73/59.68 [2399]~E(x23991,x23992)+E(f410(x23991,x23993,x23994),f410(x23992,x23993,x23994))
% 59.73/59.68 [2400]~E(x24001,x24002)+E(f410(x24003,x24001,x24004),f410(x24003,x24002,x24004))
% 59.73/59.68 [2401]~E(x24011,x24012)+E(f410(x24013,x24014,x24011),f410(x24013,x24014,x24012))
% 59.73/59.68 [2402]~E(x24021,x24022)+E(f790(x24021,x24023,x24024),f790(x24022,x24023,x24024))
% 59.73/59.68 [2403]~E(x24031,x24032)+E(f790(x24033,x24031,x24034),f790(x24033,x24032,x24034))
% 59.73/59.68 [2404]~E(x24041,x24042)+E(f790(x24043,x24044,x24041),f790(x24043,x24044,x24042))
% 59.73/59.68 [2405]~E(x24051,x24052)+E(f843(x24051),f843(x24052))
% 59.73/59.68 [2406]~E(x24061,x24062)+E(f705(x24061,x24063,x24064,x24065),f705(x24062,x24063,x24064,x24065))
% 59.73/59.68 [2407]~E(x24071,x24072)+E(f705(x24073,x24071,x24074,x24075),f705(x24073,x24072,x24074,x24075))
% 59.73/59.68 [2408]~E(x24081,x24082)+E(f705(x24083,x24084,x24081,x24085),f705(x24083,x24084,x24082,x24085))
% 59.73/59.68 [2409]~E(x24091,x24092)+E(f705(x24093,x24094,x24095,x24091),f705(x24093,x24094,x24095,x24092))
% 59.73/59.68 [2410]~E(x24101,x24102)+E(f670(x24101,x24103,x24104,x24105,x24106,x24107,x24108),f670(x24102,x24103,x24104,x24105,x24106,x24107,x24108))
% 59.73/59.68 [2411]~E(x24111,x24112)+E(f670(x24113,x24111,x24114,x24115,x24116,x24117,x24118),f670(x24113,x24112,x24114,x24115,x24116,x24117,x24118))
% 59.73/59.68 [2412]~E(x24121,x24122)+E(f670(x24123,x24124,x24121,x24125,x24126,x24127,x24128),f670(x24123,x24124,x24122,x24125,x24126,x24127,x24128))
% 59.73/59.68 [2413]~E(x24131,x24132)+E(f670(x24133,x24134,x24135,x24131,x24136,x24137,x24138),f670(x24133,x24134,x24135,x24132,x24136,x24137,x24138))
% 59.73/59.68 [2414]~E(x24141,x24142)+E(f670(x24143,x24144,x24145,x24146,x24141,x24147,x24148),f670(x24143,x24144,x24145,x24146,x24142,x24147,x24148))
% 59.73/59.68 [2415]~E(x24151,x24152)+E(f670(x24153,x24154,x24155,x24156,x24157,x24151,x24158),f670(x24153,x24154,x24155,x24156,x24157,x24152,x24158))
% 59.73/59.68 [2416]~E(x24161,x24162)+E(f670(x24163,x24164,x24165,x24166,x24167,x24168,x24161),f670(x24163,x24164,x24165,x24166,x24167,x24168,x24162))
% 59.73/59.68 [2417]~E(x24171,x24172)+E(f550(x24171,x24173,x24174,x24175,x24176),f550(x24172,x24173,x24174,x24175,x24176))
% 59.73/59.68 [2418]~E(x24181,x24182)+E(f550(x24183,x24181,x24184,x24185,x24186),f550(x24183,x24182,x24184,x24185,x24186))
% 59.73/59.68 [2419]~E(x24191,x24192)+E(f550(x24193,x24194,x24191,x24195,x24196),f550(x24193,x24194,x24192,x24195,x24196))
% 59.73/59.68 [2420]~E(x24201,x24202)+E(f550(x24203,x24204,x24205,x24201,x24206),f550(x24203,x24204,x24205,x24202,x24206))
% 59.73/59.68 [2421]~E(x24211,x24212)+E(f550(x24213,x24214,x24215,x24216,x24211),f550(x24213,x24214,x24215,x24216,x24212))
% 59.73/59.68 [2422]~E(x24221,x24222)+E(f805(x24221,x24223,x24224,x24225),f805(x24222,x24223,x24224,x24225))
% 59.73/59.68 [2423]~E(x24231,x24232)+E(f805(x24233,x24231,x24234,x24235),f805(x24233,x24232,x24234,x24235))
% 59.73/59.68 [2424]~E(x24241,x24242)+E(f805(x24243,x24244,x24241,x24245),f805(x24243,x24244,x24242,x24245))
% 59.73/59.68 [2425]~E(x24251,x24252)+E(f805(x24253,x24254,x24255,x24251),f805(x24253,x24254,x24255,x24252))
% 59.73/59.68 [2426]~E(x24261,x24262)+E(f416(x24261),f416(x24262))
% 59.73/59.68 [2427]~E(x24271,x24272)+E(f544(x24271,x24273,x24274),f544(x24272,x24273,x24274))
% 59.73/59.68 [2428]~E(x24281,x24282)+E(f544(x24283,x24281,x24284),f544(x24283,x24282,x24284))
% 59.73/59.68 [2429]~E(x24291,x24292)+E(f544(x24293,x24294,x24291),f544(x24293,x24294,x24292))
% 59.73/59.68 [2430]~E(x24301,x24302)+E(f454(x24301,x24303),f454(x24302,x24303))
% 59.73/59.68 [2431]~E(x24311,x24312)+E(f454(x24313,x24311),f454(x24313,x24312))
% 59.73/59.68 [2432]~E(x24321,x24322)+E(f517(x24321,x24323),f517(x24322,x24323))
% 59.73/59.68 [2433]~E(x24331,x24332)+E(f517(x24333,x24331),f517(x24333,x24332))
% 59.73/59.68 [2434]~E(x24341,x24342)+E(f854(x24341,x24343),f854(x24342,x24343))
% 59.73/59.68 [2435]~E(x24351,x24352)+E(f854(x24353,x24351),f854(x24353,x24352))
% 59.73/59.68 [2436]~E(x24361,x24362)+E(f214(x24361,x24363,x24364,x24365,x24366,x24367,x24368),f214(x24362,x24363,x24364,x24365,x24366,x24367,x24368))
% 59.73/59.68 [2437]~E(x24371,x24372)+E(f214(x24373,x24371,x24374,x24375,x24376,x24377,x24378),f214(x24373,x24372,x24374,x24375,x24376,x24377,x24378))
% 59.73/59.68 [2438]~E(x24381,x24382)+E(f214(x24383,x24384,x24381,x24385,x24386,x24387,x24388),f214(x24383,x24384,x24382,x24385,x24386,x24387,x24388))
% 59.73/59.68 [2439]~E(x24391,x24392)+E(f214(x24393,x24394,x24395,x24391,x24396,x24397,x24398),f214(x24393,x24394,x24395,x24392,x24396,x24397,x24398))
% 59.73/59.68 [2440]~E(x24401,x24402)+E(f214(x24403,x24404,x24405,x24406,x24401,x24407,x24408),f214(x24403,x24404,x24405,x24406,x24402,x24407,x24408))
% 59.73/59.68 [2441]~E(x24411,x24412)+E(f214(x24413,x24414,x24415,x24416,x24417,x24411,x24418),f214(x24413,x24414,x24415,x24416,x24417,x24412,x24418))
% 59.73/59.68 [2442]~E(x24421,x24422)+E(f214(x24423,x24424,x24425,x24426,x24427,x24428,x24421),f214(x24423,x24424,x24425,x24426,x24427,x24428,x24422))
% 59.73/59.68 [2443]~E(x24431,x24432)+E(f576(x24431,x24433,x24434),f576(x24432,x24433,x24434))
% 59.73/59.68 [2444]~E(x24441,x24442)+E(f576(x24443,x24441,x24444),f576(x24443,x24442,x24444))
% 59.73/59.68 [2445]~E(x24451,x24452)+E(f576(x24453,x24454,x24451),f576(x24453,x24454,x24452))
% 59.73/59.68 [2446]~E(x24461,x24462)+E(f522(x24461,x24463,x24464,x24465),f522(x24462,x24463,x24464,x24465))
% 59.73/59.68 [2447]~E(x24471,x24472)+E(f522(x24473,x24471,x24474,x24475),f522(x24473,x24472,x24474,x24475))
% 59.73/59.68 [2448]~E(x24481,x24482)+E(f522(x24483,x24484,x24481,x24485),f522(x24483,x24484,x24482,x24485))
% 59.73/59.68 [2449]~E(x24491,x24492)+E(f522(x24493,x24494,x24495,x24491),f522(x24493,x24494,x24495,x24492))
% 59.73/59.68 [2450]~E(x24501,x24502)+E(f635(x24501,x24503,x24504),f635(x24502,x24503,x24504))
% 59.73/59.68 [2451]~E(x24511,x24512)+E(f635(x24513,x24511,x24514),f635(x24513,x24512,x24514))
% 59.73/59.68 [2452]~E(x24521,x24522)+E(f635(x24523,x24524,x24521),f635(x24523,x24524,x24522))
% 59.73/59.68 [2453]~E(x24531,x24532)+E(f433(x24531,x24533,x24534),f433(x24532,x24533,x24534))
% 59.73/59.68 [2454]~E(x24541,x24542)+E(f433(x24543,x24541,x24544),f433(x24543,x24542,x24544))
% 59.73/59.68 [2455]~E(x24551,x24552)+E(f433(x24553,x24554,x24551),f433(x24553,x24554,x24552))
% 59.73/59.68 [2456]~E(x24561,x24562)+E(f746(x24561,x24563,x24564,x24565),f746(x24562,x24563,x24564,x24565))
% 59.73/59.68 [2457]~E(x24571,x24572)+E(f746(x24573,x24571,x24574,x24575),f746(x24573,x24572,x24574,x24575))
% 59.73/59.68 [2458]~E(x24581,x24582)+E(f746(x24583,x24584,x24581,x24585),f746(x24583,x24584,x24582,x24585))
% 59.73/59.68 [2459]~E(x24591,x24592)+E(f746(x24593,x24594,x24595,x24591),f746(x24593,x24594,x24595,x24592))
% 59.73/59.68 [2460]~E(x24601,x24602)+E(f497(x24601,x24603,x24604),f497(x24602,x24603,x24604))
% 59.73/59.68 [2461]~E(x24611,x24612)+E(f497(x24613,x24611,x24614),f497(x24613,x24612,x24614))
% 59.73/59.68 [2462]~E(x24621,x24622)+E(f497(x24623,x24624,x24621),f497(x24623,x24624,x24622))
% 59.73/59.68 [2463]~E(x24631,x24632)+E(f570(x24631,x24633,x24634,x24635,x24636,x24637),f570(x24632,x24633,x24634,x24635,x24636,x24637))
% 59.73/59.68 [2464]~E(x24641,x24642)+E(f570(x24643,x24641,x24644,x24645,x24646,x24647),f570(x24643,x24642,x24644,x24645,x24646,x24647))
% 59.73/59.68 [2465]~E(x24651,x24652)+E(f570(x24653,x24654,x24651,x24655,x24656,x24657),f570(x24653,x24654,x24652,x24655,x24656,x24657))
% 59.73/59.68 [2466]~E(x24661,x24662)+E(f570(x24663,x24664,x24665,x24661,x24666,x24667),f570(x24663,x24664,x24665,x24662,x24666,x24667))
% 59.73/59.68 [2467]~E(x24671,x24672)+E(f570(x24673,x24674,x24675,x24676,x24671,x24677),f570(x24673,x24674,x24675,x24676,x24672,x24677))
% 59.73/59.68 [2468]~E(x24681,x24682)+E(f570(x24683,x24684,x24685,x24686,x24687,x24681),f570(x24683,x24684,x24685,x24686,x24687,x24682))
% 59.73/59.68 [2469]~E(x24691,x24692)+E(f392(x24691,x24693,x24694,x24695,x24696,x24697),f392(x24692,x24693,x24694,x24695,x24696,x24697))
% 59.73/59.68 [2470]~E(x24701,x24702)+E(f392(x24703,x24701,x24704,x24705,x24706,x24707),f392(x24703,x24702,x24704,x24705,x24706,x24707))
% 59.73/59.68 [2471]~E(x24711,x24712)+E(f392(x24713,x24714,x24711,x24715,x24716,x24717),f392(x24713,x24714,x24712,x24715,x24716,x24717))
% 59.73/59.68 [2472]~E(x24721,x24722)+E(f392(x24723,x24724,x24725,x24721,x24726,x24727),f392(x24723,x24724,x24725,x24722,x24726,x24727))
% 59.73/59.68 [2473]~E(x24731,x24732)+E(f392(x24733,x24734,x24735,x24736,x24731,x24737),f392(x24733,x24734,x24735,x24736,x24732,x24737))
% 59.73/59.68 [2474]~E(x24741,x24742)+E(f392(x24743,x24744,x24745,x24746,x24747,x24741),f392(x24743,x24744,x24745,x24746,x24747,x24742))
% 59.73/59.68 [2475]~E(x24751,x24752)+E(f439(x24751,x24753),f439(x24752,x24753))
% 59.73/59.68 [2476]~E(x24761,x24762)+E(f439(x24763,x24761),f439(x24763,x24762))
% 59.73/59.68 [2477]~E(x24771,x24772)+E(f615(x24771,x24773,x24774,x24775),f615(x24772,x24773,x24774,x24775))
% 59.73/59.68 [2478]~E(x24781,x24782)+E(f615(x24783,x24781,x24784,x24785),f615(x24783,x24782,x24784,x24785))
% 59.73/59.68 [2479]~E(x24791,x24792)+E(f615(x24793,x24794,x24791,x24795),f615(x24793,x24794,x24792,x24795))
% 59.73/59.68 [2480]~E(x24801,x24802)+E(f615(x24803,x24804,x24805,x24801),f615(x24803,x24804,x24805,x24802))
% 59.73/59.68 [2481]~E(x24811,x24812)+E(f529(x24811,x24813),f529(x24812,x24813))
% 59.73/59.68 [2482]~E(x24821,x24822)+E(f529(x24823,x24821),f529(x24823,x24822))
% 59.73/59.68 [2483]~E(x24831,x24832)+E(f650(x24831,x24833,x24834,x24835,x24836,x24837,x24838),f650(x24832,x24833,x24834,x24835,x24836,x24837,x24838))
% 59.73/59.68 [2484]~E(x24841,x24842)+E(f650(x24843,x24841,x24844,x24845,x24846,x24847,x24848),f650(x24843,x24842,x24844,x24845,x24846,x24847,x24848))
% 59.73/59.68 [2485]~E(x24851,x24852)+E(f650(x24853,x24854,x24851,x24855,x24856,x24857,x24858),f650(x24853,x24854,x24852,x24855,x24856,x24857,x24858))
% 59.73/59.68 [2486]~E(x24861,x24862)+E(f650(x24863,x24864,x24865,x24861,x24866,x24867,x24868),f650(x24863,x24864,x24865,x24862,x24866,x24867,x24868))
% 59.73/59.68 [2487]~E(x24871,x24872)+E(f650(x24873,x24874,x24875,x24876,x24871,x24877,x24878),f650(x24873,x24874,x24875,x24876,x24872,x24877,x24878))
% 59.73/59.68 [2488]~E(x24881,x24882)+E(f650(x24883,x24884,x24885,x24886,x24887,x24881,x24888),f650(x24883,x24884,x24885,x24886,x24887,x24882,x24888))
% 59.73/59.68 [2489]~E(x24891,x24892)+E(f650(x24893,x24894,x24895,x24896,x24897,x24898,x24891),f650(x24893,x24894,x24895,x24896,x24897,x24898,x24892))
% 59.73/59.68 [2490]~E(x24901,x24902)+E(f345(x24901,x24903),f345(x24902,x24903))
% 59.73/59.68 [2491]~E(x24911,x24912)+E(f345(x24913,x24911),f345(x24913,x24912))
% 59.73/59.68 [2492]~E(x24921,x24922)+E(f659(x24921,x24923,x24924,x24925),f659(x24922,x24923,x24924,x24925))
% 59.73/59.68 [2493]~E(x24931,x24932)+E(f659(x24933,x24931,x24934,x24935),f659(x24933,x24932,x24934,x24935))
% 59.73/59.68 [2494]~E(x24941,x24942)+E(f659(x24943,x24944,x24941,x24945),f659(x24943,x24944,x24942,x24945))
% 59.73/59.68 [2495]~E(x24951,x24952)+E(f659(x24953,x24954,x24955,x24951),f659(x24953,x24954,x24955,x24952))
% 59.73/59.68 [2496]~E(x24961,x24962)+E(f621(x24961,x24963,x24964,x24965,x24966,x24967,x24968),f621(x24962,x24963,x24964,x24965,x24966,x24967,x24968))
% 59.73/59.68 [2497]~E(x24971,x24972)+E(f621(x24973,x24971,x24974,x24975,x24976,x24977,x24978),f621(x24973,x24972,x24974,x24975,x24976,x24977,x24978))
% 59.73/59.68 [2498]~E(x24981,x24982)+E(f621(x24983,x24984,x24981,x24985,x24986,x24987,x24988),f621(x24983,x24984,x24982,x24985,x24986,x24987,x24988))
% 59.73/59.68 [2499]~E(x24991,x24992)+E(f621(x24993,x24994,x24995,x24991,x24996,x24997,x24998),f621(x24993,x24994,x24995,x24992,x24996,x24997,x24998))
% 59.73/59.68 [2500]~E(x25001,x25002)+E(f621(x25003,x25004,x25005,x25006,x25001,x25007,x25008),f621(x25003,x25004,x25005,x25006,x25002,x25007,x25008))
% 59.73/59.68 [2501]~E(x25011,x25012)+E(f621(x25013,x25014,x25015,x25016,x25017,x25011,x25018),f621(x25013,x25014,x25015,x25016,x25017,x25012,x25018))
% 59.73/59.68 [2502]~E(x25021,x25022)+E(f621(x25023,x25024,x25025,x25026,x25027,x25028,x25021),f621(x25023,x25024,x25025,x25026,x25027,x25028,x25022))
% 59.73/59.68 [2503]~E(x25031,x25032)+E(f741(x25031,x25033,x25034),f741(x25032,x25033,x25034))
% 59.73/59.68 [2504]~E(x25041,x25042)+E(f741(x25043,x25041,x25044),f741(x25043,x25042,x25044))
% 59.73/59.68 [2505]~E(x25051,x25052)+E(f741(x25053,x25054,x25051),f741(x25053,x25054,x25052))
% 59.73/59.68 [2506]~E(x25061,x25062)+E(f343(x25061),f343(x25062))
% 59.73/59.68 [2507]~E(x25071,x25072)+E(f203(x25071),f203(x25072))
% 59.73/59.68 [2508]~E(x25081,x25082)+E(f445(x25081,x25083,x25084,x25085,x25086),f445(x25082,x25083,x25084,x25085,x25086))
% 59.73/59.68 [2509]~E(x25091,x25092)+E(f445(x25093,x25091,x25094,x25095,x25096),f445(x25093,x25092,x25094,x25095,x25096))
% 59.73/59.68 [2510]~E(x25101,x25102)+E(f445(x25103,x25104,x25101,x25105,x25106),f445(x25103,x25104,x25102,x25105,x25106))
% 59.73/59.68 [2511]~E(x25111,x25112)+E(f445(x25113,x25114,x25115,x25111,x25116),f445(x25113,x25114,x25115,x25112,x25116))
% 59.73/59.68 [2512]~E(x25121,x25122)+E(f445(x25123,x25124,x25125,x25126,x25121),f445(x25123,x25124,x25125,x25126,x25122))
% 59.73/59.68 [2513]~E(x25131,x25132)+E(f777(x25131,x25133,x25134,x25135,x25136,x25137,x25138),f777(x25132,x25133,x25134,x25135,x25136,x25137,x25138))
% 59.73/59.68 [2514]~E(x25141,x25142)+E(f777(x25143,x25141,x25144,x25145,x25146,x25147,x25148),f777(x25143,x25142,x25144,x25145,x25146,x25147,x25148))
% 59.73/59.68 [2515]~E(x25151,x25152)+E(f777(x25153,x25154,x25151,x25155,x25156,x25157,x25158),f777(x25153,x25154,x25152,x25155,x25156,x25157,x25158))
% 59.73/59.68 [2516]~E(x25161,x25162)+E(f777(x25163,x25164,x25165,x25161,x25166,x25167,x25168),f777(x25163,x25164,x25165,x25162,x25166,x25167,x25168))
% 59.73/59.68 [2517]~E(x25171,x25172)+E(f777(x25173,x25174,x25175,x25176,x25171,x25177,x25178),f777(x25173,x25174,x25175,x25176,x25172,x25177,x25178))
% 59.73/59.68 [2518]~E(x25181,x25182)+E(f777(x25183,x25184,x25185,x25186,x25187,x25181,x25188),f777(x25183,x25184,x25185,x25186,x25187,x25182,x25188))
% 59.73/59.68 [2519]~E(x25191,x25192)+E(f777(x25193,x25194,x25195,x25196,x25197,x25198,x25191),f777(x25193,x25194,x25195,x25196,x25197,x25198,x25192))
% 59.73/59.68 [2520]~E(x25201,x25202)+E(f495(x25201,x25203,x25204),f495(x25202,x25203,x25204))
% 59.73/59.68 [2521]~E(x25211,x25212)+E(f495(x25213,x25211,x25214),f495(x25213,x25212,x25214))
% 59.73/59.68 [2522]~E(x25221,x25222)+E(f495(x25223,x25224,x25221),f495(x25223,x25224,x25222))
% 59.73/59.68 [2523]~E(x25231,x25232)+E(f407(x25231,x25233,x25234),f407(x25232,x25233,x25234))
% 59.73/59.68 [2524]~E(x25241,x25242)+E(f407(x25243,x25241,x25244),f407(x25243,x25242,x25244))
% 59.73/59.68 [2525]~E(x25251,x25252)+E(f407(x25253,x25254,x25251),f407(x25253,x25254,x25252))
% 59.73/59.68 [2526]~E(x25261,x25262)+E(f768(x25261,x25263,x25264,x25265),f768(x25262,x25263,x25264,x25265))
% 59.73/59.68 [2527]~E(x25271,x25272)+E(f768(x25273,x25271,x25274,x25275),f768(x25273,x25272,x25274,x25275))
% 59.73/59.68 [2528]~E(x25281,x25282)+E(f768(x25283,x25284,x25281,x25285),f768(x25283,x25284,x25282,x25285))
% 59.73/59.68 [2529]~E(x25291,x25292)+E(f768(x25293,x25294,x25295,x25291),f768(x25293,x25294,x25295,x25292))
% 59.73/59.68 [2530]~E(x25301,x25302)+E(f384(x25301,x25303,x25304),f384(x25302,x25303,x25304))
% 59.73/59.68 [2531]~E(x25311,x25312)+E(f384(x25313,x25311,x25314),f384(x25313,x25312,x25314))
% 59.73/59.68 [2532]~E(x25321,x25322)+E(f384(x25323,x25324,x25321),f384(x25323,x25324,x25322))
% 59.73/59.68 [2533]~E(x25331,x25332)+E(f443(x25331,x25333,x25334,x25335),f443(x25332,x25333,x25334,x25335))
% 59.73/59.68 [2534]~E(x25341,x25342)+E(f443(x25343,x25341,x25344,x25345),f443(x25343,x25342,x25344,x25345))
% 59.73/59.68 [2535]~E(x25351,x25352)+E(f443(x25353,x25354,x25351,x25355),f443(x25353,x25354,x25352,x25355))
% 59.73/59.68 [2536]~E(x25361,x25362)+E(f443(x25363,x25364,x25365,x25361),f443(x25363,x25364,x25365,x25362))
% 59.73/59.68 [2537]~E(x25371,x25372)+E(f627(x25371,x25373),f627(x25372,x25373))
% 59.73/59.68 [2538]~E(x25381,x25382)+E(f627(x25383,x25381),f627(x25383,x25382))
% 59.73/59.68 [2539]~E(x25391,x25392)+E(f404(x25391,x25393,x25394),f404(x25392,x25393,x25394))
% 59.73/59.68 [2540]~E(x25401,x25402)+E(f404(x25403,x25401,x25404),f404(x25403,x25402,x25404))
% 59.73/59.68 [2541]~E(x25411,x25412)+E(f404(x25413,x25414,x25411),f404(x25413,x25414,x25412))
% 59.73/59.68 [2542]~E(x25421,x25422)+E(f527(x25421,x25423,x25424,x25425),f527(x25422,x25423,x25424,x25425))
% 59.73/59.68 [2543]~E(x25431,x25432)+E(f527(x25433,x25431,x25434,x25435),f527(x25433,x25432,x25434,x25435))
% 59.73/59.68 [2544]~E(x25441,x25442)+E(f527(x25443,x25444,x25441,x25445),f527(x25443,x25444,x25442,x25445))
% 59.73/59.68 [2545]~E(x25451,x25452)+E(f527(x25453,x25454,x25455,x25451),f527(x25453,x25454,x25455,x25452))
% 59.73/59.68 [2546]~E(x25461,x25462)+E(f875(x25461,x25463,x25464,x25465,x25466),f875(x25462,x25463,x25464,x25465,x25466))
% 59.73/59.68 [2547]~E(x25471,x25472)+E(f875(x25473,x25471,x25474,x25475,x25476),f875(x25473,x25472,x25474,x25475,x25476))
% 59.73/59.68 [2548]~E(x25481,x25482)+E(f875(x25483,x25484,x25481,x25485,x25486),f875(x25483,x25484,x25482,x25485,x25486))
% 59.73/59.68 [2549]~E(x25491,x25492)+E(f875(x25493,x25494,x25495,x25491,x25496),f875(x25493,x25494,x25495,x25492,x25496))
% 59.73/59.68 [2550]~E(x25501,x25502)+E(f875(x25503,x25504,x25505,x25506,x25501),f875(x25503,x25504,x25505,x25506,x25502))
% 59.73/59.68 [2551]~E(x25511,x25512)+E(f791(x25511,x25513,x25514),f791(x25512,x25513,x25514))
% 59.73/59.68 [2552]~E(x25521,x25522)+E(f791(x25523,x25521,x25524),f791(x25523,x25522,x25524))
% 59.73/59.68 [2553]~E(x25531,x25532)+E(f791(x25533,x25534,x25531),f791(x25533,x25534,x25532))
% 59.73/59.68 [2554]~E(x25541,x25542)+E(f428(x25541,x25543),f428(x25542,x25543))
% 59.73/59.68 [2555]~E(x25551,x25552)+E(f428(x25553,x25551),f428(x25553,x25552))
% 59.73/59.68 [2556]~E(x25561,x25562)+E(f715(x25561,x25563,x25564),f715(x25562,x25563,x25564))
% 59.73/59.68 [2557]~E(x25571,x25572)+E(f715(x25573,x25571,x25574),f715(x25573,x25572,x25574))
% 59.73/59.68 [2558]~E(x25581,x25582)+E(f715(x25583,x25584,x25581),f715(x25583,x25584,x25582))
% 59.73/59.68 [2559]~E(x25591,x25592)+E(f836(x25591,x25593,x25594,x25595),f836(x25592,x25593,x25594,x25595))
% 59.73/59.68 [2560]~E(x25601,x25602)+E(f836(x25603,x25601,x25604,x25605),f836(x25603,x25602,x25604,x25605))
% 59.73/59.68 [2561]~E(x25611,x25612)+E(f836(x25613,x25614,x25611,x25615),f836(x25613,x25614,x25612,x25615))
% 59.73/59.68 [2562]~E(x25621,x25622)+E(f836(x25623,x25624,x25625,x25621),f836(x25623,x25624,x25625,x25622))
% 59.73/59.68 [2563]~E(x25631,x25632)+E(f751(x25631,x25633,x25634,x25635),f751(x25632,x25633,x25634,x25635))
% 59.73/59.68 [2564]~E(x25641,x25642)+E(f751(x25643,x25641,x25644,x25645),f751(x25643,x25642,x25644,x25645))
% 59.73/59.68 [2565]~E(x25651,x25652)+E(f751(x25653,x25654,x25651,x25655),f751(x25653,x25654,x25652,x25655))
% 59.73/59.68 [2566]~E(x25661,x25662)+E(f751(x25663,x25664,x25665,x25661),f751(x25663,x25664,x25665,x25662))
% 59.73/59.68 [2567]~E(x25671,x25672)+E(f547(x25671,x25673),f547(x25672,x25673))
% 59.73/59.68 [2568]~E(x25681,x25682)+E(f547(x25683,x25681),f547(x25683,x25682))
% 59.73/59.68 [2569]~E(x25691,x25692)+E(f643(x25691,x25693,x25694),f643(x25692,x25693,x25694))
% 59.73/59.68 [2570]~E(x25701,x25702)+E(f643(x25703,x25701,x25704),f643(x25703,x25702,x25704))
% 59.73/59.68 [2571]~E(x25711,x25712)+E(f643(x25713,x25714,x25711),f643(x25713,x25714,x25712))
% 59.73/59.68 [2572]~E(x25721,x25722)+E(f713(x25721,x25723,x25724),f713(x25722,x25723,x25724))
% 59.73/59.68 [2573]~E(x25731,x25732)+E(f713(x25733,x25731,x25734),f713(x25733,x25732,x25734))
% 59.73/59.68 [2574]~E(x25741,x25742)+E(f713(x25743,x25744,x25741),f713(x25743,x25744,x25742))
% 59.73/59.68 [2575]~E(x25751,x25752)+E(f800(x25751,x25753),f800(x25752,x25753))
% 59.73/59.68 [2576]~E(x25761,x25762)+E(f800(x25763,x25761),f800(x25763,x25762))
% 59.73/59.68 [2577]~E(x25771,x25772)+E(f376(x25771,x25773,x25774),f376(x25772,x25773,x25774))
% 59.73/59.68 [2578]~E(x25781,x25782)+E(f376(x25783,x25781,x25784),f376(x25783,x25782,x25784))
% 59.73/59.68 [2579]~E(x25791,x25792)+E(f376(x25793,x25794,x25791),f376(x25793,x25794,x25792))
% 59.73/59.68 [2580]~E(x25801,x25802)+E(f401(x25801),f401(x25802))
% 59.73/59.68 [2581]~E(x25811,x25812)+E(f273(x25811,x25813,x25814),f273(x25812,x25813,x25814))
% 59.73/59.68 [2582]~E(x25821,x25822)+E(f273(x25823,x25821,x25824),f273(x25823,x25822,x25824))
% 59.73/59.68 [2583]~E(x25831,x25832)+E(f273(x25833,x25834,x25831),f273(x25833,x25834,x25832))
% 59.73/59.68 [2584]~E(x25841,x25842)+E(f818(x25841,x25843,x25844,x25845,x25846,x25847,x25848),f818(x25842,x25843,x25844,x25845,x25846,x25847,x25848))
% 59.73/59.68 [2585]~E(x25851,x25852)+E(f818(x25853,x25851,x25854,x25855,x25856,x25857,x25858),f818(x25853,x25852,x25854,x25855,x25856,x25857,x25858))
% 59.73/59.68 [2586]~E(x25861,x25862)+E(f818(x25863,x25864,x25861,x25865,x25866,x25867,x25868),f818(x25863,x25864,x25862,x25865,x25866,x25867,x25868))
% 59.73/59.68 [2587]~E(x25871,x25872)+E(f818(x25873,x25874,x25875,x25871,x25876,x25877,x25878),f818(x25873,x25874,x25875,x25872,x25876,x25877,x25878))
% 59.73/59.68 [2588]~E(x25881,x25882)+E(f818(x25883,x25884,x25885,x25886,x25881,x25887,x25888),f818(x25883,x25884,x25885,x25886,x25882,x25887,x25888))
% 59.73/59.68 [2589]~E(x25891,x25892)+E(f818(x25893,x25894,x25895,x25896,x25897,x25891,x25898),f818(x25893,x25894,x25895,x25896,x25897,x25892,x25898))
% 59.73/59.68 [2590]~E(x25901,x25902)+E(f818(x25903,x25904,x25905,x25906,x25907,x25908,x25901),f818(x25903,x25904,x25905,x25906,x25907,x25908,x25902))
% 59.73/59.68 [2591]~E(x25911,x25912)+E(f348(x25911,x25913,x25914),f348(x25912,x25913,x25914))
% 59.73/59.68 [2592]~E(x25921,x25922)+E(f348(x25923,x25921,x25924),f348(x25923,x25922,x25924))
% 59.73/59.68 [2593]~E(x25931,x25932)+E(f348(x25933,x25934,x25931),f348(x25933,x25934,x25932))
% 59.73/59.68 [2594]~E(x25941,x25942)+E(f782(x25941,x25943,x25944),f782(x25942,x25943,x25944))
% 59.73/59.68 [2595]~E(x25951,x25952)+E(f782(x25953,x25951,x25954),f782(x25953,x25952,x25954))
% 59.73/59.68 [2596]~E(x25961,x25962)+E(f782(x25963,x25964,x25961),f782(x25963,x25964,x25962))
% 59.73/59.68 [2597]~E(x25971,x25972)+E(f595(x25971,x25973,x25974),f595(x25972,x25973,x25974))
% 59.73/59.68 [2598]~E(x25981,x25982)+E(f595(x25983,x25981,x25984),f595(x25983,x25982,x25984))
% 59.73/59.68 [2599]~E(x25991,x25992)+E(f595(x25993,x25994,x25991),f595(x25993,x25994,x25992))
% 59.73/59.68 [2600]~E(x26001,x26002)+E(f526(x26001,x26003,x26004,x26005),f526(x26002,x26003,x26004,x26005))
% 59.73/59.68 [2601]~E(x26011,x26012)+E(f526(x26013,x26011,x26014,x26015),f526(x26013,x26012,x26014,x26015))
% 59.73/59.68 [2602]~E(x26021,x26022)+E(f526(x26023,x26024,x26021,x26025),f526(x26023,x26024,x26022,x26025))
% 59.73/59.68 [2603]~E(x26031,x26032)+E(f526(x26033,x26034,x26035,x26031),f526(x26033,x26034,x26035,x26032))
% 59.73/59.68 [2604]~E(x26041,x26042)+E(f230(x26041,x26043,x26044),f230(x26042,x26043,x26044))
% 59.73/59.68 [2605]~E(x26051,x26052)+E(f230(x26053,x26051,x26054),f230(x26053,x26052,x26054))
% 59.73/59.68 [2606]~E(x26061,x26062)+E(f230(x26063,x26064,x26061),f230(x26063,x26064,x26062))
% 59.73/59.68 [2607]~E(x26071,x26072)+E(f586(x26071,x26073,x26074),f586(x26072,x26073,x26074))
% 59.73/59.68 [2608]~E(x26081,x26082)+E(f586(x26083,x26081,x26084),f586(x26083,x26082,x26084))
% 59.73/59.68 [2609]~E(x26091,x26092)+E(f586(x26093,x26094,x26091),f586(x26093,x26094,x26092))
% 59.73/59.68 [2610]~E(x26101,x26102)+E(f228(x26101,x26103,x26104,x26105,x26106),f228(x26102,x26103,x26104,x26105,x26106))
% 59.73/59.68 [2611]~E(x26111,x26112)+E(f228(x26113,x26111,x26114,x26115,x26116),f228(x26113,x26112,x26114,x26115,x26116))
% 59.73/59.68 [2612]~E(x26121,x26122)+E(f228(x26123,x26124,x26121,x26125,x26126),f228(x26123,x26124,x26122,x26125,x26126))
% 59.73/59.68 [2613]~E(x26131,x26132)+E(f228(x26133,x26134,x26135,x26131,x26136),f228(x26133,x26134,x26135,x26132,x26136))
% 59.73/59.68 [2614]~E(x26141,x26142)+E(f228(x26143,x26144,x26145,x26146,x26141),f228(x26143,x26144,x26145,x26146,x26142))
% 59.73/59.68 [2615]~E(x26151,x26152)+E(f245(x26151,x26153),f245(x26152,x26153))
% 59.73/59.68 [2616]~E(x26161,x26162)+E(f245(x26163,x26161),f245(x26163,x26162))
% 59.73/59.68 [2617]~E(x26171,x26172)+E(f681(x26171,x26173,x26174,x26175,x26176),f681(x26172,x26173,x26174,x26175,x26176))
% 59.73/59.68 [2618]~E(x26181,x26182)+E(f681(x26183,x26181,x26184,x26185,x26186),f681(x26183,x26182,x26184,x26185,x26186))
% 59.73/59.68 [2619]~E(x26191,x26192)+E(f681(x26193,x26194,x26191,x26195,x26196),f681(x26193,x26194,x26192,x26195,x26196))
% 59.73/59.68 [2620]~E(x26201,x26202)+E(f681(x26203,x26204,x26205,x26201,x26206),f681(x26203,x26204,x26205,x26202,x26206))
% 59.73/59.68 [2621]~E(x26211,x26212)+E(f681(x26213,x26214,x26215,x26216,x26211),f681(x26213,x26214,x26215,x26216,x26212))
% 59.73/59.68 [2622]~E(x26221,x26222)+E(f848(x26221,x26223,x26224,x26225,x26226),f848(x26222,x26223,x26224,x26225,x26226))
% 59.73/59.68 [2623]~E(x26231,x26232)+E(f848(x26233,x26231,x26234,x26235,x26236),f848(x26233,x26232,x26234,x26235,x26236))
% 59.73/59.68 [2624]~E(x26241,x26242)+E(f848(x26243,x26244,x26241,x26245,x26246),f848(x26243,x26244,x26242,x26245,x26246))
% 59.73/59.68 [2625]~E(x26251,x26252)+E(f848(x26253,x26254,x26255,x26251,x26256),f848(x26253,x26254,x26255,x26252,x26256))
% 59.73/59.68 [2626]~E(x26261,x26262)+E(f848(x26263,x26264,x26265,x26266,x26261),f848(x26263,x26264,x26265,x26266,x26262))
% 59.73/59.68 [2627]~E(x26271,x26272)+E(f455(x26271,x26273),f455(x26272,x26273))
% 59.73/59.68 [2628]~E(x26281,x26282)+E(f455(x26283,x26281),f455(x26283,x26282))
% 59.73/59.68 [2629]~E(x26291,x26292)+E(f851(x26291),f851(x26292))
% 59.73/59.68 [2630]~E(x26301,x26302)+E(f244(x26301,x26303),f244(x26302,x26303))
% 59.73/59.68 [2631]~E(x26311,x26312)+E(f244(x26313,x26311),f244(x26313,x26312))
% 59.73/59.68 [2632]~E(x26321,x26322)+E(f678(x26321,x26323,x26324,x26325,x26326),f678(x26322,x26323,x26324,x26325,x26326))
% 59.73/59.68 [2633]~E(x26331,x26332)+E(f678(x26333,x26331,x26334,x26335,x26336),f678(x26333,x26332,x26334,x26335,x26336))
% 59.73/59.68 [2634]~E(x26341,x26342)+E(f678(x26343,x26344,x26341,x26345,x26346),f678(x26343,x26344,x26342,x26345,x26346))
% 59.73/59.68 [2635]~E(x26351,x26352)+E(f678(x26353,x26354,x26355,x26351,x26356),f678(x26353,x26354,x26355,x26352,x26356))
% 59.73/59.68 [2636]~E(x26361,x26362)+E(f678(x26363,x26364,x26365,x26366,x26361),f678(x26363,x26364,x26365,x26366,x26362))
% 59.73/59.68 [2637]~E(x26371,x26372)+E(f844(x26371),f844(x26372))
% 59.73/59.68 [2638]~E(x26381,x26382)+E(f221(x26381,x26383),f221(x26382,x26383))
% 59.73/59.68 [2639]~E(x26391,x26392)+E(f221(x26393,x26391),f221(x26393,x26392))
% 59.73/59.68 [2640]~E(x26401,x26402)+E(f872(x26401,x26403),f872(x26402,x26403))
% 59.73/59.68 [2641]~E(x26411,x26412)+E(f872(x26413,x26411),f872(x26413,x26412))
% 59.73/59.68 [2642]~E(x26421,x26422)+E(f211(x26421,x26423,x26424,x26425,x26426,x26427,x26428),f211(x26422,x26423,x26424,x26425,x26426,x26427,x26428))
% 59.73/59.68 [2643]~E(x26431,x26432)+E(f211(x26433,x26431,x26434,x26435,x26436,x26437,x26438),f211(x26433,x26432,x26434,x26435,x26436,x26437,x26438))
% 59.73/59.68 [2644]~E(x26441,x26442)+E(f211(x26443,x26444,x26441,x26445,x26446,x26447,x26448),f211(x26443,x26444,x26442,x26445,x26446,x26447,x26448))
% 59.73/59.68 [2645]~E(x26451,x26452)+E(f211(x26453,x26454,x26455,x26451,x26456,x26457,x26458),f211(x26453,x26454,x26455,x26452,x26456,x26457,x26458))
% 59.73/59.68 [2646]~E(x26461,x26462)+E(f211(x26463,x26464,x26465,x26466,x26461,x26467,x26468),f211(x26463,x26464,x26465,x26466,x26462,x26467,x26468))
% 59.73/59.68 [2647]~E(x26471,x26472)+E(f211(x26473,x26474,x26475,x26476,x26477,x26471,x26478),f211(x26473,x26474,x26475,x26476,x26477,x26472,x26478))
% 59.73/59.68 [2648]~E(x26481,x26482)+E(f211(x26483,x26484,x26485,x26486,x26487,x26488,x26481),f211(x26483,x26484,x26485,x26486,x26487,x26488,x26482))
% 59.73/59.68 [2649]~E(x26491,x26492)+E(f468(x26491,x26493,x26494,x26495),f468(x26492,x26493,x26494,x26495))
% 59.73/59.68 [2650]~E(x26501,x26502)+E(f468(x26503,x26501,x26504,x26505),f468(x26503,x26502,x26504,x26505))
% 59.73/59.68 [2651]~E(x26511,x26512)+E(f468(x26513,x26514,x26511,x26515),f468(x26513,x26514,x26512,x26515))
% 59.73/59.68 [2652]~E(x26521,x26522)+E(f468(x26523,x26524,x26525,x26521),f468(x26523,x26524,x26525,x26522))
% 59.73/59.68 [2653]~E(x26531,x26532)+E(f859(x26531,x26533),f859(x26532,x26533))
% 59.73/59.68 [2654]~E(x26541,x26542)+E(f859(x26543,x26541),f859(x26543,x26542))
% 59.73/59.68 [2655]~E(x26551,x26552)+E(f210(x26551,x26553,x26554,x26555),f210(x26552,x26553,x26554,x26555))
% 59.73/59.68 [2656]~E(x26561,x26562)+E(f210(x26563,x26561,x26564,x26565),f210(x26563,x26562,x26564,x26565))
% 59.73/59.68 [2657]~E(x26571,x26572)+E(f210(x26573,x26574,x26571,x26575),f210(x26573,x26574,x26572,x26575))
% 59.73/59.68 [2658]~E(x26581,x26582)+E(f210(x26583,x26584,x26585,x26581),f210(x26583,x26584,x26585,x26582))
% 59.73/59.68 [2659]~E(x26591,x26592)+E(f855(x26591),f855(x26592))
% 59.73/59.68 [2660]~E(x26601,x26602)+E(f456(x26601,x26603,x26604),f456(x26602,x26603,x26604))
% 59.73/59.68 [2661]~E(x26611,x26612)+E(f456(x26613,x26611,x26614),f456(x26613,x26612,x26614))
% 59.73/59.68 [2662]~E(x26621,x26622)+E(f456(x26623,x26624,x26621),f456(x26623,x26624,x26622))
% 59.73/59.68 [2663]~E(x26631,x26632)+E(f282(x26631,x26633,x26634,x26635),f282(x26632,x26633,x26634,x26635))
% 59.73/59.68 [2664]~E(x26641,x26642)+E(f282(x26643,x26641,x26644,x26645),f282(x26643,x26642,x26644,x26645))
% 59.73/59.68 [2665]~E(x26651,x26652)+E(f282(x26653,x26654,x26651,x26655),f282(x26653,x26654,x26652,x26655))
% 59.73/59.68 [2666]~E(x26661,x26662)+E(f282(x26663,x26664,x26665,x26661),f282(x26663,x26664,x26665,x26662))
% 59.73/59.68 [2667]~E(x26671,x26672)+E(f272(x26671,x26673,x26674,x26675,x26676),f272(x26672,x26673,x26674,x26675,x26676))
% 59.73/59.68 [2668]~E(x26681,x26682)+E(f272(x26683,x26681,x26684,x26685,x26686),f272(x26683,x26682,x26684,x26685,x26686))
% 59.73/59.68 [2669]~E(x26691,x26692)+E(f272(x26693,x26694,x26691,x26695,x26696),f272(x26693,x26694,x26692,x26695,x26696))
% 59.73/59.68 [2670]~E(x26701,x26702)+E(f272(x26703,x26704,x26705,x26701,x26706),f272(x26703,x26704,x26705,x26702,x26706))
% 59.73/59.68 [2671]~E(x26711,x26712)+E(f272(x26713,x26714,x26715,x26716,x26711),f272(x26713,x26714,x26715,x26716,x26712))
% 59.73/59.68 [2672]~P1(x26721)+P1(x26722)+~E(x26721,x26722)
% 59.73/59.68 [2673]~P2(x26731)+P2(x26732)+~E(x26731,x26732)
% 59.73/59.68 [2674]~P106(x26741)+P106(x26742)+~E(x26741,x26742)
% 59.73/59.68 [2675]~P107(x26751)+P107(x26752)+~E(x26751,x26752)
% 59.73/59.68 [2676]~P102(x26761)+P102(x26762)+~E(x26761,x26762)
% 59.73/59.68 [2677]~P3(x26771)+P3(x26772)+~E(x26771,x26772)
% 59.73/59.68 [2678]~P127(x26781)+P127(x26782)+~E(x26781,x26782)
% 59.73/59.68 [2679]P49(x26792,x26793,x26794)+~E(x26791,x26792)+~P49(x26791,x26793,x26794)
% 59.73/59.68 [2680]P49(x26803,x26802,x26804)+~E(x26801,x26802)+~P49(x26803,x26801,x26804)
% 59.73/59.68 [2681]P49(x26813,x26814,x26812)+~E(x26811,x26812)+~P49(x26813,x26814,x26811)
% 59.73/59.68 [2682]~P61(x26821)+P61(x26822)+~E(x26821,x26822)
% 59.73/59.68 [2683]P15(x26832,x26833)+~E(x26831,x26832)+~P15(x26831,x26833)
% 59.73/59.68 [2684]P15(x26843,x26842)+~E(x26841,x26842)+~P15(x26843,x26841)
% 59.73/59.68 [2685]P146(x26852,x26853,x26854)+~E(x26851,x26852)+~P146(x26851,x26853,x26854)
% 59.73/59.68 [2686]P146(x26863,x26862,x26864)+~E(x26861,x26862)+~P146(x26863,x26861,x26864)
% 59.73/59.68 [2687]P146(x26873,x26874,x26872)+~E(x26871,x26872)+~P146(x26873,x26874,x26871)
% 59.73/59.68 [2688]~P87(x26881)+P87(x26882)+~E(x26881,x26882)
% 59.73/59.68 [2689]~P66(x26891)+P66(x26892)+~E(x26891,x26892)
% 59.73/59.68 [2690]~P86(x26901)+P86(x26902)+~E(x26901,x26902)
% 59.73/59.68 [2691]~P108(x26911)+P108(x26912)+~E(x26911,x26912)
% 59.73/59.68 [2692]~P80(x26921)+P80(x26922)+~E(x26921,x26922)
% 59.73/59.68 [2693]~P123(x26931)+P123(x26932)+~E(x26931,x26932)
% 59.73/59.68 [2694]~P68(x26941)+P68(x26942)+~E(x26941,x26942)
% 59.73/59.68 [2695]~P4(x26951)+P4(x26952)+~E(x26951,x26952)
% 59.73/59.68 [2696]P12(x26962,x26963,x26964)+~E(x26961,x26962)+~P12(x26961,x26963,x26964)
% 59.73/59.68 [2697]P12(x26973,x26972,x26974)+~E(x26971,x26972)+~P12(x26973,x26971,x26974)
% 59.73/59.68 [2698]P12(x26983,x26984,x26982)+~E(x26981,x26982)+~P12(x26983,x26984,x26981)
% 59.73/59.68 [2699]~P109(x26991)+P109(x26992)+~E(x26991,x26992)
% 59.73/59.68 [2700]~P60(x27001)+P60(x27002)+~E(x27001,x27002)
% 59.73/59.68 [2701]~P38(x27011)+P38(x27012)+~E(x27011,x27012)
% 59.73/59.68 [2702]~P73(x27021)+P73(x27022)+~E(x27021,x27022)
% 59.73/59.68 [2703]~P118(x27031)+P118(x27032)+~E(x27031,x27032)
% 59.73/59.68 [2704]~P97(x27041)+P97(x27042)+~E(x27041,x27042)
% 59.73/59.68 [2705]~P89(x27051)+P89(x27052)+~E(x27051,x27052)
% 59.73/59.68 [2706]~P62(x27061)+P62(x27062)+~E(x27061,x27062)
% 59.73/59.68 [2707]~P63(x27071)+P63(x27072)+~E(x27071,x27072)
% 59.73/59.68 [2708]P145(x27082,x27083,x27084)+~E(x27081,x27082)+~P145(x27081,x27083,x27084)
% 59.73/59.68 [2709]P145(x27093,x27092,x27094)+~E(x27091,x27092)+~P145(x27093,x27091,x27094)
% 59.73/59.68 [2710]P145(x27103,x27104,x27102)+~E(x27101,x27102)+~P145(x27103,x27104,x27101)
% 59.73/59.68 [2711]~P95(x27111)+P95(x27112)+~E(x27111,x27112)
% 59.73/59.68 [2712]P21(x27122,x27123,x27124,x27125)+~E(x27121,x27122)+~P21(x27121,x27123,x27124,x27125)
% 59.73/59.68 [2713]P21(x27133,x27132,x27134,x27135)+~E(x27131,x27132)+~P21(x27133,x27131,x27134,x27135)
% 59.73/59.68 [2714]P21(x27143,x27144,x27142,x27145)+~E(x27141,x27142)+~P21(x27143,x27144,x27141,x27145)
% 59.73/59.68 [2715]P21(x27153,x27154,x27155,x27152)+~E(x27151,x27152)+~P21(x27153,x27154,x27155,x27151)
% 59.73/59.68 [2716]P17(x27162,x27163,x27164)+~E(x27161,x27162)+~P17(x27161,x27163,x27164)
% 59.73/59.68 [2717]P17(x27173,x27172,x27174)+~E(x27171,x27172)+~P17(x27173,x27171,x27174)
% 59.73/59.68 [2718]P17(x27183,x27184,x27182)+~E(x27181,x27182)+~P17(x27183,x27184,x27181)
% 59.73/59.68 [2719]P18(x27192,x27193,x27194)+~E(x27191,x27192)+~P18(x27191,x27193,x27194)
% 59.73/59.68 [2720]P18(x27203,x27202,x27204)+~E(x27201,x27202)+~P18(x27203,x27201,x27204)
% 59.73/59.68 [2721]P18(x27213,x27214,x27212)+~E(x27211,x27212)+~P18(x27213,x27214,x27211)
% 59.73/59.68 [2722]P26(x27222,x27223,x27224,x27225)+~E(x27221,x27222)+~P26(x27221,x27223,x27224,x27225)
% 59.73/59.68 [2723]P26(x27233,x27232,x27234,x27235)+~E(x27231,x27232)+~P26(x27233,x27231,x27234,x27235)
% 59.73/59.68 [2724]P26(x27243,x27244,x27242,x27245)+~E(x27241,x27242)+~P26(x27243,x27244,x27241,x27245)
% 59.73/59.68 [2725]P26(x27253,x27254,x27255,x27252)+~E(x27251,x27252)+~P26(x27253,x27254,x27255,x27251)
% 59.73/59.68 [2726]~P5(x27261)+P5(x27262)+~E(x27261,x27262)
% 59.73/59.68 [2727]~P100(x27271)+P100(x27272)+~E(x27271,x27272)
% 59.73/59.68 [2728]P8(x27282,x27283,x27284)+~E(x27281,x27282)+~P8(x27281,x27283,x27284)
% 59.73/59.68 [2729]P8(x27293,x27292,x27294)+~E(x27291,x27292)+~P8(x27293,x27291,x27294)
% 59.73/59.68 [2730]P8(x27303,x27304,x27302)+~E(x27301,x27302)+~P8(x27303,x27304,x27301)
% 59.73/59.68 [2731]~P77(x27311)+P77(x27312)+~E(x27311,x27312)
% 59.73/59.68 [2732]~P119(x27321)+P119(x27322)+~E(x27321,x27322)
% 59.73/59.68 [2733]~P64(x27331)+P64(x27332)+~E(x27331,x27332)
% 59.73/59.68 [2734]~P110(x27341)+P110(x27342)+~E(x27341,x27342)
% 59.73/59.68 [2735]~P101(x27351)+P101(x27352)+~E(x27351,x27352)
% 59.73/59.68 [2736]~P70(x27361)+P70(x27362)+~E(x27361,x27362)
% 59.73/59.68 [2737]~P83(x27371)+P83(x27372)+~E(x27371,x27372)
% 59.73/59.68 [2738]P46(x27382,x27383,x27384)+~E(x27381,x27382)+~P46(x27381,x27383,x27384)
% 59.73/59.68 [2739]P46(x27393,x27392,x27394)+~E(x27391,x27392)+~P46(x27393,x27391,x27394)
% 59.73/59.68 [2740]P46(x27403,x27404,x27402)+~E(x27401,x27402)+~P46(x27403,x27404,x27401)
% 59.73/59.68 [2741]~P65(x27411)+P65(x27412)+~E(x27411,x27412)
% 59.73/59.68 [2742]P36(x27422,x27423)+~E(x27421,x27422)+~P36(x27421,x27423)
% 59.73/59.68 [2743]P36(x27433,x27432)+~E(x27431,x27432)+~P36(x27433,x27431)
% 59.73/59.68 [2744]~P72(x27441)+P72(x27442)+~E(x27441,x27442)
% 59.73/59.68 [2745]~P84(x27451)+P84(x27452)+~E(x27451,x27452)
% 59.73/59.68 [2746]~P85(x27461)+P85(x27462)+~E(x27461,x27462)
% 59.73/59.68 [2747]~P114(x27471)+P114(x27472)+~E(x27471,x27472)
% 59.73/59.68 [2748]~P111(x27481)+P111(x27482)+~E(x27481,x27482)
% 59.73/59.68 [2749]~P88(x27491)+P88(x27492)+~E(x27491,x27492)
% 59.73/59.68 [2750]P37(x27502,x27503,x27504)+~E(x27501,x27502)+~P37(x27501,x27503,x27504)
% 59.73/59.68 [2751]P37(x27513,x27512,x27514)+~E(x27511,x27512)+~P37(x27513,x27511,x27514)
% 59.73/59.68 [2752]P37(x27523,x27524,x27522)+~E(x27521,x27522)+~P37(x27523,x27524,x27521)
% 59.73/59.68 [2753]~P81(x27531)+P81(x27532)+~E(x27531,x27532)
% 59.73/59.68 [2754]~P67(x27541)+P67(x27542)+~E(x27541,x27542)
% 59.73/59.68 [2755]~P137(x27551)+P137(x27552)+~E(x27551,x27552)
% 59.73/59.68 [2756]~P69(x27561)+P69(x27562)+~E(x27561,x27562)
% 59.73/59.68 [2757]P33(x27572,x27573,x27574,x27575,x27576)+~E(x27571,x27572)+~P33(x27571,x27573,x27574,x27575,x27576)
% 59.73/59.68 [2758]P33(x27583,x27582,x27584,x27585,x27586)+~E(x27581,x27582)+~P33(x27583,x27581,x27584,x27585,x27586)
% 59.73/59.68 [2759]P33(x27593,x27594,x27592,x27595,x27596)+~E(x27591,x27592)+~P33(x27593,x27594,x27591,x27595,x27596)
% 59.73/59.68 [2760]P33(x27603,x27604,x27605,x27602,x27606)+~E(x27601,x27602)+~P33(x27603,x27604,x27605,x27601,x27606)
% 59.73/59.68 [2761]P33(x27613,x27614,x27615,x27616,x27612)+~E(x27611,x27612)+~P33(x27613,x27614,x27615,x27616,x27611)
% 59.73/59.68 [2762]P52(x27622,x27623,x27624)+~E(x27621,x27622)+~P52(x27621,x27623,x27624)
% 59.73/59.68 [2763]P52(x27633,x27632,x27634)+~E(x27631,x27632)+~P52(x27633,x27631,x27634)
% 59.73/59.68 [2764]P52(x27643,x27644,x27642)+~E(x27641,x27642)+~P52(x27643,x27644,x27641)
% 59.73/59.68 [2765]~P82(x27651)+P82(x27652)+~E(x27651,x27652)
% 59.73/59.68 [2766]P20(x27662,x27663,x27664)+~E(x27661,x27662)+~P20(x27661,x27663,x27664)
% 59.73/59.68 [2767]P20(x27673,x27672,x27674)+~E(x27671,x27672)+~P20(x27673,x27671,x27674)
% 59.73/59.68 [2768]P20(x27683,x27684,x27682)+~E(x27681,x27682)+~P20(x27683,x27684,x27681)
% 59.73/59.68 [2769]~P96(x27691)+P96(x27692)+~E(x27691,x27692)
% 59.73/59.68 [2770]~P122(x27701)+P122(x27702)+~E(x27701,x27702)
% 59.73/59.68 [2771]P32(x27712,x27713,x27714)+~E(x27711,x27712)+~P32(x27711,x27713,x27714)
% 59.73/59.68 [2772]P32(x27723,x27722,x27724)+~E(x27721,x27722)+~P32(x27723,x27721,x27724)
% 59.73/59.68 [2773]P32(x27733,x27734,x27732)+~E(x27731,x27732)+~P32(x27733,x27734,x27731)
% 59.73/59.68 [2774]P30(x27742,x27743,x27744)+~E(x27741,x27742)+~P30(x27741,x27743,x27744)
% 59.73/59.68 [2775]P30(x27753,x27752,x27754)+~E(x27751,x27752)+~P30(x27753,x27751,x27754)
% 59.73/59.68 [2776]P30(x27763,x27764,x27762)+~E(x27761,x27762)+~P30(x27763,x27764,x27761)
% 59.73/59.68 [2777]~P136(x27771)+P136(x27772)+~E(x27771,x27772)
% 59.73/59.68 [2778]~P112(x27781)+P112(x27782)+~E(x27781,x27782)
% 59.73/59.68 [2779]~P58(x27791)+P58(x27792)+~E(x27791,x27792)
% 59.73/59.68 [2780]P55(x27802,x27803)+~E(x27801,x27802)+~P55(x27801,x27803)
% 59.73/59.68 [2781]P55(x27813,x27812)+~E(x27811,x27812)+~P55(x27813,x27811)
% 59.73/59.68 [2782]P23(x27822,x27823,x27824,x27825,x27826)+~E(x27821,x27822)+~P23(x27821,x27823,x27824,x27825,x27826)
% 59.73/59.68 [2783]P23(x27833,x27832,x27834,x27835,x27836)+~E(x27831,x27832)+~P23(x27833,x27831,x27834,x27835,x27836)
% 59.73/59.68 [2784]P23(x27843,x27844,x27842,x27845,x27846)+~E(x27841,x27842)+~P23(x27843,x27844,x27841,x27845,x27846)
% 59.73/59.68 [2785]P23(x27853,x27854,x27855,x27852,x27856)+~E(x27851,x27852)+~P23(x27853,x27854,x27855,x27851,x27856)
% 59.73/59.68 [2786]P23(x27863,x27864,x27865,x27866,x27862)+~E(x27861,x27862)+~P23(x27863,x27864,x27865,x27866,x27861)
% 59.73/59.68 [2787]~P71(x27871)+P71(x27872)+~E(x27871,x27872)
% 59.73/59.68 [2788]P53(x27882,x27883,x27884)+~E(x27881,x27882)+~P53(x27881,x27883,x27884)
% 59.73/59.68 [2789]P53(x27893,x27892,x27894)+~E(x27891,x27892)+~P53(x27893,x27891,x27894)
% 59.73/59.68 [2790]P53(x27903,x27904,x27902)+~E(x27901,x27902)+~P53(x27903,x27904,x27901)
% 59.73/59.68 [2791]~P143(x27911)+P143(x27912)+~E(x27911,x27912)
% 59.73/59.68 [2792]~P74(x27921)+P74(x27922)+~E(x27921,x27922)
% 59.73/59.68 [2793]P25(x27932,x27933,x27934,x27935,x27936,x27937)+~E(x27931,x27932)+~P25(x27931,x27933,x27934,x27935,x27936,x27937)
% 59.73/59.68 [2794]P25(x27943,x27942,x27944,x27945,x27946,x27947)+~E(x27941,x27942)+~P25(x27943,x27941,x27944,x27945,x27946,x27947)
% 59.73/59.68 [2795]P25(x27953,x27954,x27952,x27955,x27956,x27957)+~E(x27951,x27952)+~P25(x27953,x27954,x27951,x27955,x27956,x27957)
% 59.73/59.68 [2796]P25(x27963,x27964,x27965,x27962,x27966,x27967)+~E(x27961,x27962)+~P25(x27963,x27964,x27965,x27961,x27966,x27967)
% 59.73/59.68 [2797]P25(x27973,x27974,x27975,x27976,x27972,x27977)+~E(x27971,x27972)+~P25(x27973,x27974,x27975,x27976,x27971,x27977)
% 59.73/59.68 [2798]P25(x27983,x27984,x27985,x27986,x27987,x27982)+~E(x27981,x27982)+~P25(x27983,x27984,x27985,x27986,x27987,x27981)
% 59.73/59.68 [2799]~P6(x27991)+P6(x27992)+~E(x27991,x27992)
% 59.73/59.68 [2800]~P75(x28001)+P75(x28002)+~E(x28001,x28002)
% 59.73/59.68 [2801]P28(x28012,x28013)+~E(x28011,x28012)+~P28(x28011,x28013)
% 59.73/59.68 [2802]P28(x28023,x28022)+~E(x28021,x28022)+~P28(x28023,x28021)
% 59.73/59.68 [2803]~P129(x28031)+P129(x28032)+~E(x28031,x28032)
% 59.73/59.68 [2804]~P138(x28041)+P138(x28042)+~E(x28041,x28042)
% 59.73/59.68 [2805]~P104(x28051)+P104(x28052)+~E(x28051,x28052)
% 59.73/59.68 [2806]~P92(x28061)+P92(x28062)+~E(x28061,x28062)
% 59.73/59.68 [2807]P34(x28072,x28073,x28074)+~E(x28071,x28072)+~P34(x28071,x28073,x28074)
% 59.73/59.68 [2808]P34(x28083,x28082,x28084)+~E(x28081,x28082)+~P34(x28083,x28081,x28084)
% 59.73/59.68 [2809]P34(x28093,x28094,x28092)+~E(x28091,x28092)+~P34(x28093,x28094,x28091)
% 59.73/59.68 [2810]~P79(x28101)+P79(x28102)+~E(x28101,x28102)
% 59.73/59.68 [2811]~P144(x28111)+P144(x28112)+~E(x28111,x28112)
% 59.73/59.68 [2812]~P139(x28121)+P139(x28122)+~E(x28121,x28122)
% 59.73/59.68 [2813]~P116(x28131)+P116(x28132)+~E(x28131,x28132)
% 59.73/59.68 [2814]P45(x28142,x28143,x28144)+~E(x28141,x28142)+~P45(x28141,x28143,x28144)
% 59.73/59.68 [2815]P45(x28153,x28152,x28154)+~E(x28151,x28152)+~P45(x28153,x28151,x28154)
% 59.73/59.68 [2816]P45(x28163,x28164,x28162)+~E(x28161,x28162)+~P45(x28163,x28164,x28161)
% 59.73/59.68 [2817]~P132(x28171)+P132(x28172)+~E(x28171,x28172)
% 59.73/59.68 [2818]~P90(x28181)+P90(x28182)+~E(x28181,x28182)
% 59.73/59.68 [2819]~P115(x28191)+P115(x28192)+~E(x28191,x28192)
% 59.73/59.68 [2820]~P125(x28201)+P125(x28202)+~E(x28201,x28202)
% 59.73/59.68 [2821]P40(x28212,x28213,x28214,x28215,x28216,x28217)+~E(x28211,x28212)+~P40(x28211,x28213,x28214,x28215,x28216,x28217)
% 59.73/59.68 [2822]P40(x28223,x28222,x28224,x28225,x28226,x28227)+~E(x28221,x28222)+~P40(x28223,x28221,x28224,x28225,x28226,x28227)
% 59.73/59.68 [2823]P40(x28233,x28234,x28232,x28235,x28236,x28237)+~E(x28231,x28232)+~P40(x28233,x28234,x28231,x28235,x28236,x28237)
% 59.73/59.68 [2824]P40(x28243,x28244,x28245,x28242,x28246,x28247)+~E(x28241,x28242)+~P40(x28243,x28244,x28245,x28241,x28246,x28247)
% 59.73/59.68 [2825]P40(x28253,x28254,x28255,x28256,x28252,x28257)+~E(x28251,x28252)+~P40(x28253,x28254,x28255,x28256,x28251,x28257)
% 59.73/59.68 [2826]P40(x28263,x28264,x28265,x28266,x28267,x28262)+~E(x28261,x28262)+~P40(x28263,x28264,x28265,x28266,x28267,x28261)
% 59.73/59.68 [2827]~P140(x28271)+P140(x28272)+~E(x28271,x28272)
% 59.73/59.68 [2828]P16(x28282,x28283,x28284)+~E(x28281,x28282)+~P16(x28281,x28283,x28284)
% 59.73/59.68 [2829]P16(x28293,x28292,x28294)+~E(x28291,x28292)+~P16(x28293,x28291,x28294)
% 59.73/59.68 [2830]P16(x28303,x28304,x28302)+~E(x28301,x28302)+~P16(x28303,x28304,x28301)
% 59.73/59.68 [2831]~P142(x28311)+P142(x28312)+~E(x28311,x28312)
% 59.73/59.68 [2832]~P99(x28321)+P99(x28322)+~E(x28321,x28322)
% 59.73/59.68 [2833]~P78(x28331)+P78(x28332)+~E(x28331,x28332)
% 59.73/59.68 [2834]~P128(x28341)+P128(x28342)+~E(x28341,x28342)
% 59.73/59.68 [2835]~P131(x28351)+P131(x28352)+~E(x28351,x28352)
% 59.73/59.68 [2836]~P93(x28361)+P93(x28362)+~E(x28361,x28362)
% 59.73/59.68 [2837]~P135(x28371)+P135(x28372)+~E(x28371,x28372)
% 59.73/59.68 [2838]P7(x28382,x28383)+~E(x28381,x28382)+~P7(x28381,x28383)
% 59.73/59.68 [2839]P7(x28393,x28392)+~E(x28391,x28392)+~P7(x28393,x28391)
% 59.73/59.68 [2840]P56(x28402,x28403,x28404,x28405)+~E(x28401,x28402)+~P56(x28401,x28403,x28404,x28405)
% 59.73/59.68 [2841]P56(x28413,x28412,x28414,x28415)+~E(x28411,x28412)+~P56(x28413,x28411,x28414,x28415)
% 59.73/59.68 [2842]P56(x28423,x28424,x28422,x28425)+~E(x28421,x28422)+~P56(x28423,x28424,x28421,x28425)
% 59.73/59.68 [2843]P56(x28433,x28434,x28435,x28432)+~E(x28431,x28432)+~P56(x28433,x28434,x28435,x28431)
% 59.73/59.68 [2844]P29(x28442,x28443,x28444)+~E(x28441,x28442)+~P29(x28441,x28443,x28444)
% 59.73/59.68 [2845]P29(x28453,x28452,x28454)+~E(x28451,x28452)+~P29(x28453,x28451,x28454)
% 59.73/59.68 [2846]P29(x28463,x28464,x28462)+~E(x28461,x28462)+~P29(x28463,x28464,x28461)
% 59.73/59.68 [2847]P47(x28472,x28473)+~E(x28471,x28472)+~P47(x28471,x28473)
% 59.73/59.68 [2848]P47(x28483,x28482)+~E(x28481,x28482)+~P47(x28483,x28481)
% 59.73/59.68 [2849]P41(x28492,x28493)+~E(x28491,x28492)+~P41(x28491,x28493)
% 59.73/59.68 [2850]P41(x28503,x28502)+~E(x28501,x28502)+~P41(x28503,x28501)
% 59.73/59.68 [2851]~P141(x28511)+P141(x28512)+~E(x28511,x28512)
% 59.73/59.68 [2852]P48(x28522,x28523)+~E(x28521,x28522)+~P48(x28521,x28523)
% 59.73/59.68 [2853]P48(x28533,x28532)+~E(x28531,x28532)+~P48(x28533,x28531)
% 59.73/59.68 [2854]~P91(x28541)+P91(x28542)+~E(x28541,x28542)
% 59.73/59.68 [2855]~P126(x28551)+P126(x28552)+~E(x28551,x28552)
% 59.73/59.68 [2856]P13(x28562,x28563,x28564,x28565)+~E(x28561,x28562)+~P13(x28561,x28563,x28564,x28565)
% 59.73/59.68 [2857]P13(x28573,x28572,x28574,x28575)+~E(x28571,x28572)+~P13(x28573,x28571,x28574,x28575)
% 59.73/59.68 [2858]P13(x28583,x28584,x28582,x28585)+~E(x28581,x28582)+~P13(x28583,x28584,x28581,x28585)
% 59.73/59.68 [2859]P13(x28593,x28594,x28595,x28592)+~E(x28591,x28592)+~P13(x28593,x28594,x28595,x28591)
% 59.73/59.68 [2860]~P59(x28601)+P59(x28602)+~E(x28601,x28602)
% 59.73/59.68 [2861]~P113(x28611)+P113(x28612)+~E(x28611,x28612)
% 59.73/59.68 [2862]P10(x28622,x28623,x28624,x28625,x28626)+~E(x28621,x28622)+~P10(x28621,x28623,x28624,x28625,x28626)
% 59.73/59.68 [2863]P10(x28633,x28632,x28634,x28635,x28636)+~E(x28631,x28632)+~P10(x28633,x28631,x28634,x28635,x28636)
% 59.73/59.68 [2864]P10(x28643,x28644,x28642,x28645,x28646)+~E(x28641,x28642)+~P10(x28643,x28644,x28641,x28645,x28646)
% 59.73/59.68 [2865]P10(x28653,x28654,x28655,x28652,x28656)+~E(x28651,x28652)+~P10(x28653,x28654,x28655,x28651,x28656)
% 59.73/59.68 [2866]P10(x28663,x28664,x28665,x28666,x28662)+~E(x28661,x28662)+~P10(x28663,x28664,x28665,x28666,x28661)
% 59.73/59.68 [2867]P43(x28672,x28673)+~E(x28671,x28672)+~P43(x28671,x28673)
% 59.73/59.68 [2868]P43(x28683,x28682)+~E(x28681,x28682)+~P43(x28683,x28681)
% 59.73/59.68 [2869]P57(x28692,x28693)+~E(x28691,x28692)+~P57(x28691,x28693)
% 59.73/59.68 [2870]P57(x28703,x28702)+~E(x28701,x28702)+~P57(x28703,x28701)
% 59.73/59.68 [2871]~P98(x28711)+P98(x28712)+~E(x28711,x28712)
% 59.73/59.68 [2872]P19(x28722,x28723,x28724)+~E(x28721,x28722)+~P19(x28721,x28723,x28724)
% 59.73/59.68 [2873]P19(x28733,x28732,x28734)+~E(x28731,x28732)+~P19(x28733,x28731,x28734)
% 59.73/59.68 [2874]P19(x28743,x28744,x28742)+~E(x28741,x28742)+~P19(x28743,x28744,x28741)
% 59.73/59.68 [2875]~P117(x28751)+P117(x28752)+~E(x28751,x28752)
% 59.73/59.68 [2876]~P134(x28761)+P134(x28762)+~E(x28761,x28762)
% 59.73/59.68 [2877]~P124(x28771)+P124(x28772)+~E(x28771,x28772)
% 59.73/59.68 [2878]~P42(x28781)+P42(x28782)+~E(x28781,x28782)
% 59.73/59.68 [2879]~P94(x28791)+P94(x28792)+~E(x28791,x28792)
% 59.73/59.68 [2880]P27(x28802,x28803)+~E(x28801,x28802)+~P27(x28801,x28803)
% 59.73/59.68 [2881]P27(x28813,x28812)+~E(x28811,x28812)+~P27(x28813,x28811)
% 59.73/59.68 [2882]P24(x28822,x28823,x28824,x28825,x28826,x28827)+~E(x28821,x28822)+~P24(x28821,x28823,x28824,x28825,x28826,x28827)
% 59.73/59.68 [2883]P24(x28833,x28832,x28834,x28835,x28836,x28837)+~E(x28831,x28832)+~P24(x28833,x28831,x28834,x28835,x28836,x28837)
% 59.73/59.68 [2884]P24(x28843,x28844,x28842,x28845,x28846,x28847)+~E(x28841,x28842)+~P24(x28843,x28844,x28841,x28845,x28846,x28847)
% 59.73/59.68 [2885]P24(x28853,x28854,x28855,x28852,x28856,x28857)+~E(x28851,x28852)+~P24(x28853,x28854,x28855,x28851,x28856,x28857)
% 59.73/59.68 [2886]P24(x28863,x28864,x28865,x28866,x28862,x28867)+~E(x28861,x28862)+~P24(x28863,x28864,x28865,x28866,x28861,x28867)
% 59.73/59.68 [2887]P24(x28873,x28874,x28875,x28876,x28877,x28872)+~E(x28871,x28872)+~P24(x28873,x28874,x28875,x28876,x28877,x28871)
% 59.73/59.68 [2888]P22(x28882,x28883,x28884,x28885)+~E(x28881,x28882)+~P22(x28881,x28883,x28884,x28885)
% 59.73/59.68 [2889]P22(x28893,x28892,x28894,x28895)+~E(x28891,x28892)+~P22(x28893,x28891,x28894,x28895)
% 59.73/59.68 [2890]P22(x28903,x28904,x28902,x28905)+~E(x28901,x28902)+~P22(x28903,x28904,x28901,x28905)
% 59.73/59.68 [2891]P22(x28913,x28914,x28915,x28912)+~E(x28911,x28912)+~P22(x28913,x28914,x28915,x28911)
% 59.73/59.68 [2892]~P133(x28921)+P133(x28922)+~E(x28921,x28922)
% 59.73/59.68 [2893]P54(x28932,x28933,x28934,x28935,x28936)+~E(x28931,x28932)+~P54(x28931,x28933,x28934,x28935,x28936)
% 59.73/59.68 [2894]P54(x28943,x28942,x28944,x28945,x28946)+~E(x28941,x28942)+~P54(x28943,x28941,x28944,x28945,x28946)
% 59.73/59.68 [2895]P54(x28953,x28954,x28952,x28955,x28956)+~E(x28951,x28952)+~P54(x28953,x28954,x28951,x28955,x28956)
% 59.73/59.68 [2896]P54(x28963,x28964,x28965,x28962,x28966)+~E(x28961,x28962)+~P54(x28963,x28964,x28965,x28961,x28966)
% 59.73/59.68 [2897]P54(x28973,x28974,x28975,x28976,x28972)+~E(x28971,x28972)+~P54(x28973,x28974,x28975,x28976,x28971)
% 59.73/59.68 [2898]P31(x28982,x28983,x28984,x28985)+~E(x28981,x28982)+~P31(x28981,x28983,x28984,x28985)
% 59.73/59.68 [2899]P31(x28993,x28992,x28994,x28995)+~E(x28991,x28992)+~P31(x28993,x28991,x28994,x28995)
% 59.73/59.68 [2900]P31(x29003,x29004,x29002,x29005)+~E(x29001,x29002)+~P31(x29003,x29004,x29001,x29005)
% 59.73/59.68 [2901]P31(x29013,x29014,x29015,x29012)+~E(x29011,x29012)+~P31(x29013,x29014,x29015,x29011)
% 59.73/59.68 [2902]P14(x29022,x29023,x29024,x29025,x29026,x29027)+~E(x29021,x29022)+~P14(x29021,x29023,x29024,x29025,x29026,x29027)
% 59.73/59.68 [2903]P14(x29033,x29032,x29034,x29035,x29036,x29037)+~E(x29031,x29032)+~P14(x29033,x29031,x29034,x29035,x29036,x29037)
% 59.73/59.68 [2904]P14(x29043,x29044,x29042,x29045,x29046,x29047)+~E(x29041,x29042)+~P14(x29043,x29044,x29041,x29045,x29046,x29047)
% 59.73/59.68 [2905]P14(x29053,x29054,x29055,x29052,x29056,x29057)+~E(x29051,x29052)+~P14(x29053,x29054,x29055,x29051,x29056,x29057)
% 59.73/59.68 [2906]P14(x29063,x29064,x29065,x29066,x29062,x29067)+~E(x29061,x29062)+~P14(x29063,x29064,x29065,x29066,x29061,x29067)
% 59.73/59.68 [2907]P14(x29073,x29074,x29075,x29076,x29077,x29072)+~E(x29071,x29072)+~P14(x29073,x29074,x29075,x29076,x29077,x29071)
% 59.73/59.68 [2908]P51(x29082,x29083,x29084,x29085,x29086,x29087)+~E(x29081,x29082)+~P51(x29081,x29083,x29084,x29085,x29086,x29087)
% 59.73/59.68 [2909]P51(x29093,x29092,x29094,x29095,x29096,x29097)+~E(x29091,x29092)+~P51(x29093,x29091,x29094,x29095,x29096,x29097)
% 59.73/59.68 [2910]P51(x29103,x29104,x29102,x29105,x29106,x29107)+~E(x29101,x29102)+~P51(x29103,x29104,x29101,x29105,x29106,x29107)
% 59.73/59.68 [2911]P51(x29113,x29114,x29115,x29112,x29116,x29117)+~E(x29111,x29112)+~P51(x29113,x29114,x29115,x29111,x29116,x29117)
% 59.73/59.68 [2912]P51(x29123,x29124,x29125,x29126,x29122,x29127)+~E(x29121,x29122)+~P51(x29123,x29124,x29125,x29126,x29121,x29127)
% 59.73/59.68 [2913]P51(x29133,x29134,x29135,x29136,x29137,x29132)+~E(x29131,x29132)+~P51(x29133,x29134,x29135,x29136,x29137,x29131)
% 59.73/59.68 [2914]~P105(x29141)+P105(x29142)+~E(x29141,x29142)
% 59.73/59.68 [2915]~P103(x29151)+P103(x29152)+~E(x29151,x29152)
% 59.73/59.68 [2916]~P120(x29161)+P120(x29162)+~E(x29161,x29162)
% 59.73/59.68 [2917]~P76(x29171)+P76(x29172)+~E(x29171,x29172)
% 59.73/59.68 [2918]P11(x29182,x29183,x29184)+~E(x29181,x29182)+~P11(x29181,x29183,x29184)
% 59.73/59.68 [2919]P11(x29193,x29192,x29194)+~E(x29191,x29192)+~P11(x29193,x29191,x29194)
% 59.73/59.68 [2920]P11(x29203,x29204,x29202)+~E(x29201,x29202)+~P11(x29203,x29204,x29201)
% 59.73/59.68 [2921]P50(x29212,x29213,x29214,x29215)+~E(x29211,x29212)+~P50(x29211,x29213,x29214,x29215)
% 59.73/59.68 [2922]P50(x29223,x29222,x29224,x29225)+~E(x29221,x29222)+~P50(x29223,x29221,x29224,x29225)
% 59.73/59.68 [2923]P50(x29233,x29234,x29232,x29235)+~E(x29231,x29232)+~P50(x29233,x29234,x29231,x29235)
% 59.73/59.68 [2924]P50(x29243,x29244,x29245,x29242)+~E(x29241,x29242)+~P50(x29243,x29244,x29245,x29241)
% 59.73/59.68 [2925]P44(x29252,x29253,x29254)+~E(x29251,x29252)+~P44(x29251,x29253,x29254)
% 59.73/59.68 [2926]P44(x29263,x29262,x29264)+~E(x29261,x29262)+~P44(x29263,x29261,x29264)
% 59.73/59.68 [2927]P44(x29273,x29274,x29272)+~E(x29271,x29272)+~P44(x29273,x29274,x29271)
% 59.73/59.68 [2928]~P35(x29281)+P35(x29282)+~E(x29281,x29282)
% 59.73/59.68 [2929]~P121(x29291)+P121(x29292)+~E(x29291,x29292)
% 59.73/59.68 [2930]P39(x29302,x29303,x29304,x29305)+~E(x29301,x29302)+~P39(x29301,x29303,x29304,x29305)
% 59.73/59.68 [2931]P39(x29313,x29312,x29314,x29315)+~E(x29311,x29312)+~P39(x29313,x29311,x29314,x29315)
% 59.73/59.68 [2932]P39(x29323,x29324,x29322,x29325)+~E(x29321,x29322)+~P39(x29323,x29324,x29321,x29325)
% 59.73/59.68 [2933]P39(x29333,x29334,x29335,x29332)+~E(x29331,x29332)+~P39(x29333,x29334,x29335,x29331)
% 59.73/59.68 [2934]P9(x29342,x29343,x29344)+~E(x29341,x29342)+~P9(x29341,x29343,x29344)
% 59.73/59.68 [2935]P9(x29353,x29352,x29354)+~E(x29351,x29352)+~P9(x29353,x29351,x29354)
% 59.73/59.68 [2936]P9(x29363,x29364,x29362)+~E(x29361,x29362)+~P9(x29363,x29364,x29361)
% 59.73/59.68 [2937]~P130(x29371)+P130(x29372)+~E(x29371,x29372)
% 59.73/59.68
% 59.73/59.68 %-------------------------------------------
% 59.73/59.71 cnf(10251,plain,
% 59.73/59.71 (~E(f335(f335(f144(x102511),x102512),x102513),x102513)),
% 59.73/59.71 inference(rename_variables,[],[4552])).
% 59.73/59.71 cnf(10258,plain,
% 59.73/59.71 (~E(f335(f335(f144(x102581),x102582),x102583),x102583)),
% 59.73/59.71 inference(rename_variables,[],[4552])).
% 59.73/59.71 cnf(10267,plain,
% 59.73/59.71 (~E(f335(a106,x102671),x102671)),
% 59.73/59.71 inference(rename_variables,[],[4537])).
% 59.73/59.71 cnf(10274,plain,
% 59.73/59.71 (~E(f335(a106,x102741),x102741)),
% 59.73/59.71 inference(rename_variables,[],[4537])).
% 59.73/59.71 cnf(10277,plain,
% 59.73/59.71 (~E(f335(a106,x102771),x102771)),
% 59.73/59.71 inference(rename_variables,[],[4537])).
% 59.73/59.71 cnf(10284,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),f39(a881,x102841,x102842)),x102841))),
% 59.73/59.71 inference(rename_variables,[],[3810])).
% 59.73/59.71 cnf(10287,plain,
% 59.73/59.71 (~P1(f335(f335(f243(a881),f335(f335(f75(a881),x102871),x102872)),x102872))),
% 59.73/59.71 inference(rename_variables,[],[4601])).
% 59.73/59.71 cnf(10290,plain,
% 59.73/59.71 (~P1(f335(f335(f243(a881),f335(f335(f75(a881),x102901),x102902)),x102902))),
% 59.73/59.71 inference(rename_variables,[],[4601])).
% 59.73/59.71 cnf(10293,plain,
% 59.73/59.71 (~P1(f335(f335(f243(a881),x102931),x102931))),
% 59.73/59.71 inference(rename_variables,[],[4574])).
% 59.73/59.71 cnf(10296,plain,
% 59.73/59.71 (~E(f335(a106,x102961),x102961)),
% 59.73/59.71 inference(rename_variables,[],[4537])).
% 59.73/59.71 cnf(10314,plain,
% 59.73/59.71 (P1(f335(f335(f337(x103141),x103142),f252(f888(x103141,a879))))),
% 59.73/59.71 inference(rename_variables,[],[3503])).
% 59.73/59.71 cnf(10317,plain,
% 59.73/59.71 (~E(f335(a106,x103171),x103171)),
% 59.73/59.71 inference(rename_variables,[],[4537])).
% 59.73/59.71 cnf(10320,plain,
% 59.73/59.71 (~E(f335(a106,x103201),f2(a881))),
% 59.73/59.71 inference(rename_variables,[],[4539])).
% 59.73/59.71 cnf(10325,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x103251),x103251))),
% 59.73/59.71 inference(rename_variables,[],[3347])).
% 59.73/59.71 cnf(10342,plain,
% 59.73/59.71 (P1(f335(f335(f337(x103421),x103422),f252(f888(x103421,a879))))),
% 59.73/59.71 inference(rename_variables,[],[3503])).
% 59.73/59.71 cnf(10347,plain,
% 59.73/59.71 (P1(f335(f335(f243(a881),x103471),f335(a106,x103471)))),
% 59.73/59.71 inference(rename_variables,[],[3416])).
% 59.73/59.71 cnf(10371,plain,
% 59.73/59.71 (P1(f335(f335(f243(a881),x103711),f335(a106,x103711)))),
% 59.73/59.71 inference(rename_variables,[],[3416])).
% 59.73/59.71 cnf(10380,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x103801),x103801))),
% 59.73/59.71 inference(rename_variables,[],[3347])).
% 59.73/59.71 cnf(10395,plain,
% 59.73/59.71 (~P1(f335(f335(f243(a881),x103951),x103951))),
% 59.73/59.71 inference(rename_variables,[],[4574])).
% 59.73/59.71 cnf(10410,plain,
% 59.73/59.71 (P1(f335(f335(f243(a881),x104101),f335(a106,x104101)))),
% 59.73/59.71 inference(rename_variables,[],[3416])).
% 59.73/59.71 cnf(10437,plain,
% 59.73/59.71 (~P1(f335(f335(f243(a881),f335(f335(f75(a881),x104371),x104372)),x104372))),
% 59.73/59.71 inference(rename_variables,[],[4601])).
% 59.73/59.71 cnf(10442,plain,
% 59.73/59.71 (~P1(f335(f335(f242(a881),f335(a106,x104421)),x104421))),
% 59.73/59.71 inference(rename_variables,[],[4584])).
% 59.73/59.71 cnf(10445,plain,
% 59.73/59.71 (E(f335(f249(x104451),x104452),x104452)),
% 59.73/59.71 inference(rename_variables,[],[3173])).
% 59.73/59.71 cnf(10456,plain,
% 59.73/59.71 (E(f167(x104561,x104562,f107(x104561)),x104562)),
% 59.73/59.71 inference(rename_variables,[],[3280])).
% 59.73/59.71 cnf(10459,plain,
% 59.73/59.71 (E(f110(x104591,f113(x104591),x104592),x104592)),
% 59.73/59.71 inference(rename_variables,[],[3281])).
% 59.73/59.71 cnf(10466,plain,
% 59.73/59.71 (~P1(f335(f335(f337(x104661),x104662),f188(f888(x104661,a879))))),
% 59.73/59.71 inference(rename_variables,[],[4586])).
% 59.73/59.71 cnf(10469,plain,
% 59.73/59.71 (E(f167(x104691,x104692,f107(x104691)),x104692)),
% 59.73/59.71 inference(rename_variables,[],[3280])).
% 59.73/59.71 cnf(10485,plain,
% 59.73/59.71 (P1(f335(f335(f243(a881),x104851),f335(a106,x104851)))),
% 59.73/59.71 inference(rename_variables,[],[3416])).
% 59.73/59.71 cnf(10508,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x105081),x105081))),
% 59.73/59.71 inference(rename_variables,[],[3347])).
% 59.73/59.71 cnf(10511,plain,
% 59.73/59.71 (P1(f335(f335(f243(a881),x105111),f335(a106,x105111)))),
% 59.73/59.71 inference(rename_variables,[],[3416])).
% 59.73/59.71 cnf(10518,plain,
% 59.73/59.71 (P1(f335(f335(f243(a881),x105181),f335(a106,x105181)))),
% 59.73/59.71 inference(rename_variables,[],[3416])).
% 59.73/59.71 cnf(10521,plain,
% 59.73/59.71 (P1(f335(f335(f243(a881),x105211),f335(a106,x105211)))),
% 59.73/59.71 inference(rename_variables,[],[3416])).
% 59.73/59.71 cnf(10526,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x105261),x105261))),
% 59.73/59.71 inference(rename_variables,[],[3347])).
% 59.73/59.71 cnf(10539,plain,
% 59.73/59.71 (~P1(f335(f335(f243(a881),x105391),x105391))),
% 59.73/59.71 inference(rename_variables,[],[4574])).
% 59.73/59.71 cnf(10546,plain,
% 59.73/59.71 (~E(f335(a106,x105461),f2(a881))),
% 59.73/59.71 inference(rename_variables,[],[4539])).
% 59.73/59.71 cnf(10551,plain,
% 59.73/59.71 (~P1(f335(f335(f243(a881),x105511),x105511))),
% 59.73/59.71 inference(rename_variables,[],[4574])).
% 59.73/59.71 cnf(10562,plain,
% 59.73/59.71 (~E(f335(a106,x105621),x105621)),
% 59.73/59.71 inference(rename_variables,[],[4537])).
% 59.73/59.71 cnf(10565,plain,
% 59.73/59.71 (~E(f335(f335(f144(x105651),x105652),x105653),x105653)),
% 59.73/59.71 inference(rename_variables,[],[4552])).
% 59.73/59.71 cnf(10572,plain,
% 59.73/59.71 (~E(f335(f335(f144(x105721),x105722),x105723),x105723)),
% 59.73/59.71 inference(rename_variables,[],[4552])).
% 59.73/59.71 cnf(10593,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x105931),x105931))),
% 59.73/59.71 inference(rename_variables,[],[3347])).
% 59.73/59.71 cnf(10598,plain,
% 59.73/59.71 (~P1(f335(f335(f243(a881),x105981),x105981))),
% 59.73/59.71 inference(rename_variables,[],[4574])).
% 59.73/59.71 cnf(10608,plain,
% 59.73/59.71 (E(f167(x106081,x106082,f107(x106081)),x106082)),
% 59.73/59.71 inference(rename_variables,[],[3280])).
% 59.73/59.71 cnf(10611,plain,
% 59.73/59.71 (E(f167(x106111,x106112,f107(x106111)),x106112)),
% 59.73/59.71 inference(rename_variables,[],[3280])).
% 59.73/59.71 cnf(10614,plain,
% 59.73/59.71 (~E(f335(a106,x106141),x106141)),
% 59.73/59.71 inference(rename_variables,[],[4537])).
% 59.73/59.71 cnf(10617,plain,
% 59.73/59.71 (~P1(f335(f335(f166(x106171),f107(x106171)),x106172))),
% 59.73/59.71 inference(rename_variables,[],[4582])).
% 59.73/59.71 cnf(10622,plain,
% 59.73/59.71 (~P1(f335(f335(f166(x106221),f107(x106221)),x106222))),
% 59.73/59.71 inference(rename_variables,[],[4582])).
% 59.73/59.71 cnf(10631,plain,
% 59.73/59.71 (~P1(f335(f335(f243(f888(x106311,a879)),x106312),f188(f888(x106311,a879))))),
% 59.73/59.71 inference(rename_variables,[],[4597])).
% 59.73/59.71 cnf(10636,plain,
% 59.73/59.71 (~P1(f335(f335(f242(a881),f335(a106,x106361)),x106361))),
% 59.73/59.71 inference(rename_variables,[],[4584])).
% 59.73/59.71 cnf(10639,plain,
% 59.73/59.71 (~P1(f335(f335(f242(a881),f335(a106,x106391)),x106391))),
% 59.73/59.71 inference(rename_variables,[],[4584])).
% 59.73/59.71 cnf(10644,plain,
% 59.73/59.71 (~E(f335(f313(x106441,f888(x106441,a879),x106442),x106443),f335(f311(x106441),x106443))),
% 59.73/59.71 inference(rename_variables,[],[4585])).
% 59.73/59.71 cnf(10653,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),f2(a881)),x106531))),
% 59.73/59.71 inference(rename_variables,[],[3369])).
% 59.73/59.71 cnf(10656,plain,
% 59.73/59.71 (P1(f335(f335(f242(a1),x106561),x106561))),
% 59.73/59.71 inference(rename_variables,[],[3348])).
% 59.73/59.71 cnf(10661,plain,
% 59.73/59.71 (P1(f335(f335(f243(a881),x106611),f335(a106,f335(f335(f75(a881),x106612),x106611))))),
% 59.73/59.71 inference(rename_variables,[],[3803])).
% 59.73/59.71 cnf(10664,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x106641),f335(f335(f76(a881),x106641),x106641)))),
% 59.73/59.71 inference(rename_variables,[],[3614])).
% 59.73/59.71 cnf(10667,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x106671),f335(f335(f76(a881),x106671),x106671)))),
% 59.73/59.71 inference(rename_variables,[],[3614])).
% 59.73/59.71 cnf(10670,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x106701),f335(f335(f75(a881),x106702),x106701)))),
% 59.73/59.71 inference(rename_variables,[],[3615])).
% 59.73/59.71 cnf(10673,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x106731),f335(f335(f75(a881),x106732),x106731)))),
% 59.73/59.71 inference(rename_variables,[],[3615])).
% 59.73/59.71 cnf(10678,plain,
% 59.73/59.71 (P1(f335(f335(f242(f888(x106781,a879)),f335(f313(x106782,x106781,x106783),f335(f314(x106782,x106781,x106783),x106784))),x106784))),
% 59.73/59.71 inference(rename_variables,[],[4248])).
% 59.73/59.71 cnf(10683,plain,
% 59.73/59.71 (~P1(f335(f335(f243(a881),x106831),x106831))),
% 59.73/59.71 inference(rename_variables,[],[4574])).
% 59.73/59.71 cnf(10686,plain,
% 59.73/59.71 (~P1(f335(f335(f243(a881),x106861),x106861))),
% 59.73/59.71 inference(rename_variables,[],[4574])).
% 59.73/59.71 cnf(10689,plain,
% 59.73/59.71 (P1(f335(f335(f242(a1),x106891),x106891))),
% 59.73/59.71 inference(rename_variables,[],[3348])).
% 59.73/59.71 cnf(10708,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x107081),f335(f335(f76(a881),x107081),x107081)))),
% 59.73/59.71 inference(rename_variables,[],[3614])).
% 59.73/59.71 cnf(10711,plain,
% 59.73/59.71 (P1(f335(f252(f888(x107111,a879)),x107112))),
% 59.73/59.71 inference(rename_variables,[],[3409])).
% 59.73/59.71 cnf(10714,plain,
% 59.73/59.71 (P1(f335(f252(f888(x107141,a879)),x107142))),
% 59.73/59.71 inference(rename_variables,[],[3409])).
% 59.73/59.71 cnf(10717,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),f2(a881)),x107171))),
% 59.73/59.71 inference(rename_variables,[],[3369])).
% 59.73/59.71 cnf(10720,plain,
% 59.73/59.71 (P1(f335(f335(f242(f888(x107201,a879)),f188(f888(x107201,a879))),x107202))),
% 59.73/59.71 inference(rename_variables,[],[3801])).
% 59.73/59.71 cnf(10723,plain,
% 59.73/59.71 (~P1(f335(f335(f243(a881),f335(f335(f75(a881),x107231),x107232)),x107232))),
% 59.73/59.71 inference(rename_variables,[],[4601])).
% 59.73/59.71 cnf(10726,plain,
% 59.73/59.71 (~P1(f335(f335(f243(a881),f335(f335(f75(a881),x107261),x107262)),x107261))),
% 59.73/59.71 inference(rename_variables,[],[4602])).
% 59.73/59.71 cnf(10729,plain,
% 59.73/59.71 (~P1(f335(f335(f243(a881),f335(f335(f75(a881),x107291),x107292)),x107292))),
% 59.73/59.71 inference(rename_variables,[],[4601])).
% 59.73/59.71 cnf(10732,plain,
% 59.73/59.71 (~P1(f335(f335(f243(a881),f335(f335(f75(a881),x107321),x107322)),x107321))),
% 59.73/59.71 inference(rename_variables,[],[4602])).
% 59.73/59.71 cnf(10735,plain,
% 59.73/59.71 (~P1(f335(f335(f242(a881),f335(a106,x107351)),x107351))),
% 59.73/59.71 inference(rename_variables,[],[4584])).
% 59.73/59.71 cnf(10740,plain,
% 59.73/59.71 (~P1(f335(f335(f242(a881),f335(a106,x107401)),x107401))),
% 59.73/59.71 inference(rename_variables,[],[4584])).
% 59.73/59.71 cnf(10747,plain,
% 59.73/59.71 (P1(f335(f335(f243(a881),x107471),f335(a106,x107471)))),
% 59.73/59.71 inference(rename_variables,[],[3416])).
% 59.73/59.71 cnf(10750,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x107501),f335(f335(f76(a881),x107501),x107501)))),
% 59.73/59.71 inference(rename_variables,[],[3614])).
% 59.73/59.71 cnf(10756,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x107561),f335(f335(f75(a881),x107561),x107562)))),
% 59.73/59.71 inference(rename_variables,[],[3616])).
% 59.73/59.71 cnf(10759,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x107591),x107591))),
% 59.73/59.71 inference(rename_variables,[],[3347])).
% 59.73/59.71 cnf(10784,plain,
% 59.73/59.71 (~P1(f335(f335(f166(x107841),f107(x107841)),x107842))),
% 59.73/59.71 inference(rename_variables,[],[4582])).
% 59.73/59.71 cnf(10787,plain,
% 59.73/59.71 (~P1(f335(f57(x107871,x107872,f188(f888(x107871,a879))),x107873))),
% 59.73/59.71 inference(rename_variables,[],[4599])).
% 59.73/59.71 cnf(10790,plain,
% 59.73/59.71 (~P1(f335(f335(f166(x107901),f107(x107901)),x107902))),
% 59.73/59.71 inference(rename_variables,[],[4582])).
% 59.73/59.71 cnf(10813,plain,
% 59.73/59.71 (~E(f335(a106,x108131),f2(a881))),
% 59.73/59.71 inference(rename_variables,[],[4539])).
% 59.73/59.71 cnf(10893,plain,
% 59.73/59.71 (~E(f335(a106,x108931),x108931)),
% 59.73/59.71 inference(rename_variables,[],[4537])).
% 59.73/59.71 cnf(10896,plain,
% 59.73/59.71 (~E(f335(a106,x108961),x108961)),
% 59.73/59.71 inference(rename_variables,[],[4537])).
% 59.73/59.71 cnf(10899,plain,
% 59.73/59.71 (~E(f335(f335(f144(x108991),x108992),x108993),x108993)),
% 59.73/59.71 inference(rename_variables,[],[4552])).
% 59.73/59.71 cnf(10904,plain,
% 59.73/59.71 (~P1(f335(f335(f243(a881),x109041),x109041))),
% 59.73/59.71 inference(rename_variables,[],[4574])).
% 59.73/59.71 cnf(10907,plain,
% 59.73/59.71 (~P1(f335(f335(f242(a881),f335(a106,x109071)),x109071))),
% 59.73/59.71 inference(rename_variables,[],[4584])).
% 59.73/59.71 cnf(10910,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x109101),x109101))),
% 59.73/59.71 inference(rename_variables,[],[3347])).
% 59.73/59.71 cnf(10913,plain,
% 59.73/59.71 (P1(f335(f335(f242(a1),x109131),x109131))),
% 59.73/59.71 inference(rename_variables,[],[3348])).
% 59.73/59.71 cnf(10926,plain,
% 59.73/59.71 (P1(f335(f335(f337(x109261),x109262),f252(f888(x109261,a879))))),
% 59.73/59.71 inference(rename_variables,[],[3503])).
% 59.73/59.71 cnf(10929,plain,
% 59.73/59.71 (P1(f335(f335(f337(x109291),x109292),f335(f335(f312(x109291),x109292),x109293)))),
% 59.73/59.71 inference(rename_variables,[],[3666])).
% 59.73/59.71 cnf(10932,plain,
% 59.73/59.71 (P1(f335(f335(f337(x109321),x109322),f252(f888(x109321,a879))))),
% 59.73/59.71 inference(rename_variables,[],[3503])).
% 59.73/59.71 cnf(10935,plain,
% 59.73/59.71 (~P1(f335(f335(f337(x109351),x109352),f188(f888(x109351,a879))))),
% 59.73/59.71 inference(rename_variables,[],[4586])).
% 59.73/59.71 cnf(10940,plain,
% 59.73/59.71 (~E(f335(a106,x109401),x109401)),
% 59.73/59.71 inference(rename_variables,[],[4537])).
% 59.73/59.71 cnf(11007,plain,
% 59.73/59.71 (P1(f335(f335(f243(a881),x110071),f335(a106,x110071)))),
% 59.73/59.71 inference(rename_variables,[],[3416])).
% 59.73/59.71 cnf(11010,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x110101),x110101))),
% 59.73/59.71 inference(rename_variables,[],[3347])).
% 59.73/59.71 cnf(11015,plain,
% 59.73/59.71 (~P1(f335(f335(f243(a881),x110151),x110151))),
% 59.73/59.71 inference(rename_variables,[],[4574])).
% 59.73/59.71 cnf(11018,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x110181),x110181))),
% 59.73/59.71 inference(rename_variables,[],[3347])).
% 59.73/59.71 cnf(11021,plain,
% 59.73/59.71 (~P1(f335(f57(x110211,x110212,f188(f888(x110211,a879))),x110213))),
% 59.73/59.71 inference(rename_variables,[],[4599])).
% 59.73/59.71 cnf(11028,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x110281),x110281))),
% 59.73/59.71 inference(rename_variables,[],[3347])).
% 59.73/59.71 cnf(11049,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x110491),x110491))),
% 59.73/59.71 inference(rename_variables,[],[3347])).
% 59.73/59.71 cnf(11060,plain,
% 59.73/59.71 (~P1(f335(f335(f243(a881),x110601),f2(a881)))),
% 59.73/59.71 inference(rename_variables,[],[4577])).
% 59.73/59.71 cnf(11063,plain,
% 59.73/59.71 (~P1(f335(f335(f166(x110631),f107(x110631)),x110632))),
% 59.73/59.71 inference(rename_variables,[],[4582])).
% 59.73/59.71 cnf(11078,plain,
% 59.73/59.71 (E(f335(f335(f127(x110781),f107(x110781)),x110782),x110782)),
% 59.73/59.71 inference(rename_variables,[],[3299])).
% 59.73/59.71 cnf(11084,plain,
% 59.73/59.71 (P1(f335(f335(f337(x110841),x110842),f252(f888(x110841,a879))))),
% 59.73/59.71 inference(rename_variables,[],[3503])).
% 59.73/59.71 cnf(11093,plain,
% 59.73/59.71 (E(f167(x110931,x110932,f107(x110931)),x110932)),
% 59.73/59.71 inference(rename_variables,[],[3280])).
% 59.73/59.71 cnf(11096,plain,
% 59.73/59.71 (E(f167(x110961,x110962,f107(x110961)),x110962)),
% 59.73/59.71 inference(rename_variables,[],[3280])).
% 59.73/59.71 cnf(11099,plain,
% 59.73/59.71 (~E(f335(a106,x110991),x110991)),
% 59.73/59.71 inference(rename_variables,[],[4537])).
% 59.73/59.71 cnf(11102,plain,
% 59.73/59.71 (~E(f335(a106,x111021),x111021)),
% 59.73/59.71 inference(rename_variables,[],[4537])).
% 59.73/59.71 cnf(11116,plain,
% 59.73/59.71 (~P1(f335(f335(f337(x111161),x111162),f188(f888(x111161,a879))))),
% 59.73/59.71 inference(rename_variables,[],[4586])).
% 59.73/59.71 cnf(11123,plain,
% 59.73/59.71 (P1(f335(f335(f242(f888(x111231,a879)),f188(f888(x111231,a879))),x111232))),
% 59.73/59.71 inference(rename_variables,[],[3801])).
% 59.73/59.71 cnf(11128,plain,
% 59.73/59.71 (P1(f335(f335(f243(a881),x111281),f335(a106,x111281)))),
% 59.73/59.71 inference(rename_variables,[],[3416])).
% 59.73/59.71 cnf(11133,plain,
% 59.73/59.71 (P1(f335(f335(f242(f888(x111331,a879)),x111332),f335(f335(f312(x111331),x111333),x111332)))),
% 59.73/59.71 inference(rename_variables,[],[3799])).
% 59.73/59.71 cnf(11138,plain,
% 59.73/59.71 (P1(f335(f335(f242(f888(x111381,a879)),x111382),f335(f335(f312(x111381),x111383),x111382)))),
% 59.73/59.71 inference(rename_variables,[],[3799])).
% 59.73/59.71 cnf(11141,plain,
% 59.73/59.71 (P1(f335(f335(f242(a1),x111411),x111411))),
% 59.73/59.71 inference(rename_variables,[],[3348])).
% 59.73/59.71 cnf(11144,plain,
% 59.73/59.71 (P1(f335(f335(f337(x111441),x111442),f252(f888(x111441,a879))))),
% 59.73/59.71 inference(rename_variables,[],[3503])).
% 59.73/59.71 cnf(11153,plain,
% 59.73/59.71 (P1(f335(f335(f337(x111531),x111532),f252(f888(x111531,a879))))),
% 59.73/59.71 inference(rename_variables,[],[3503])).
% 59.73/59.71 cnf(11160,plain,
% 59.73/59.71 (~P1(f335(f335(f243(a881),x111601),x111601))),
% 59.73/59.71 inference(rename_variables,[],[4574])).
% 59.73/59.71 cnf(11175,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x111751),x111751))),
% 59.73/59.71 inference(rename_variables,[],[3347])).
% 59.73/59.71 cnf(11178,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x111781),f335(f335(f76(a881),x111781),x111781)))),
% 59.73/59.71 inference(rename_variables,[],[3614])).
% 59.73/59.71 cnf(11181,plain,
% 59.73/59.71 (P1(f335(f335(f242(a881),x111811),x111811))),
% 59.73/59.71 inference(rename_variables,[],[3347])).
% 59.73/59.71 cnf(11188,plain,
% 59.73/59.71 (P1(f335(f252(f888(x111881,a879)),x111882))),
% 59.73/59.71 inference(rename_variables,[],[3409])).
% 59.73/59.71 cnf(11195,plain,
% 59.73/59.71 (P1(f335(f252(f888(x111951,a879)),x111952))),
% 59.73/59.71 inference(rename_variables,[],[3409])).
% 59.73/59.71 cnf(11212,plain,
% 59.73/59.71 (~P1(f335(f335(f166(x112121),f107(x112121)),x112122))),
% 59.73/59.71 inference(rename_variables,[],[4582])).
% 59.73/59.71 cnf(11219,plain,
% 59.73/59.71 (~E(f335(a106,x112191),x112191)),
% 59.73/59.71 inference(rename_variables,[],[4537])).
% 59.73/59.71 cnf(11224,plain,
% 59.73/59.71 (E(f335(f29(a881),f335(f250(a881),x112241)),x112241)),
% 59.73/59.71 inference(rename_variables,[],[3235])).
% 59.73/59.71 cnf(11234,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x112341,a879)),f188(f888(x112341,a879))),x112342))),
% 59.73/59.72 inference(rename_variables,[],[3801])).
% 59.73/59.72 cnf(11240,plain,
% 59.73/59.72 (~E(f335(f313(x112401,f888(x112401,a879),x112402),x112403),f335(f311(x112401),x112403))),
% 59.73/59.72 inference(rename_variables,[],[4585])).
% 59.73/59.72 cnf(11253,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x112531,a879)),x112532),x112532))),
% 59.73/59.72 inference(rename_variables,[],[3648])).
% 59.73/59.72 cnf(11256,plain,
% 59.73/59.72 (P1(f335(f335(f243(a881),x112561),f335(a106,x112561)))),
% 59.73/59.72 inference(rename_variables,[],[3416])).
% 59.73/59.72 cnf(11259,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x112591),x112592),f188(f888(x112591,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11266,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x112661,a879)),f335(f313(x112662,x112661,x112663),f335(f314(x112662,x112661,x112663),x112664))),x112664))),
% 59.73/59.72 inference(rename_variables,[],[4248])).
% 59.73/59.72 cnf(11285,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x112851),x112852),f188(f888(x112851,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11288,plain,
% 59.73/59.72 (~P1(f335(f335(f243(a881),x112881),f2(a881)))),
% 59.73/59.72 inference(rename_variables,[],[4577])).
% 59.73/59.72 cnf(11291,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x112911),x112912),f188(f888(x112911,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11296,plain,
% 59.73/59.72 (~P1(f335(f335(f166(x112961),f107(x112961)),x112962))),
% 59.73/59.72 inference(rename_variables,[],[4582])).
% 59.73/59.72 cnf(11303,plain,
% 59.73/59.72 (~E(f335(a106,x113031),x113031)),
% 59.73/59.72 inference(rename_variables,[],[4537])).
% 59.73/59.72 cnf(11315,plain,
% 59.73/59.72 (P1(f335(f335(f337(x113151),x113152),f252(f888(x113151,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3503])).
% 59.73/59.72 cnf(11322,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x113221),x113222),f188(f888(x113221,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11325,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x113251,a879)),x113252),f252(f888(x113251,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3734])).
% 59.73/59.72 cnf(11328,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x113281,a879)),x113282),f252(f888(x113281,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3734])).
% 59.73/59.72 cnf(11337,plain,
% 59.73/59.72 (P1(f335(f335(f242(a881),x113371),x113371))),
% 59.73/59.72 inference(rename_variables,[],[3347])).
% 59.73/59.72 cnf(11348,plain,
% 59.73/59.72 (P1(f335(f335(f337(x113481),x113482),f252(f888(x113481,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3503])).
% 59.73/59.72 cnf(11351,plain,
% 59.73/59.72 (P1(f335(f335(f337(x113511),x113512),f252(f888(x113511,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3503])).
% 59.73/59.72 cnf(11364,plain,
% 59.73/59.72 (~P1(f335(f335(f337(f887(x113641,x113641)),f335(f335(f264(x113641,x113641),x113642),x113643)),f146(x113641,f107(f888(x113641,a881)))))),
% 59.73/59.72 inference(rename_variables,[],[4606])).
% 59.73/59.72 cnf(11375,plain,
% 59.73/59.72 (~P1(f335(f335(f243(a881),x113751),f2(a881)))),
% 59.73/59.72 inference(rename_variables,[],[4577])).
% 59.73/59.72 cnf(11380,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x113801,a879)),x113802),x113802))),
% 59.73/59.72 inference(rename_variables,[],[3648])).
% 59.73/59.72 cnf(11383,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x113831),x113832),f188(f888(x113831,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11388,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x113881,a879)),x113882),f252(f888(x113881,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3734])).
% 59.73/59.72 cnf(11391,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x113911,a879)),x113912),f252(f888(x113911,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3734])).
% 59.73/59.72 cnf(11394,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x113941),x113942),f188(f888(x113941,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11399,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x113991,a879)),x113992),f252(f888(x113991,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3734])).
% 59.73/59.72 cnf(11402,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x114021,a879)),x114022),x114022))),
% 59.73/59.72 inference(rename_variables,[],[3648])).
% 59.73/59.72 cnf(11407,plain,
% 59.73/59.72 (~E(f335(a106,x114071),f2(a881))),
% 59.73/59.72 inference(rename_variables,[],[4539])).
% 59.73/59.72 cnf(11410,plain,
% 59.73/59.72 (~E(f335(f235(x114101),x114102),f200(x114101))),
% 59.73/59.72 inference(rename_variables,[],[4545])).
% 59.73/59.72 cnf(11413,plain,
% 59.73/59.72 (E(f335(f313(x114131,x114131,f5(x114131)),x114132),x114132)),
% 59.73/59.72 inference(rename_variables,[],[3405])).
% 59.73/59.72 cnf(11416,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x114161),x114162),f188(f888(x114161,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11419,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x114191),x114192),f188(f888(x114191,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11424,plain,
% 59.73/59.72 (P1(f335(f335(f242(a881),x114241),x114241))),
% 59.73/59.72 inference(rename_variables,[],[3347])).
% 59.73/59.72 cnf(11434,plain,
% 59.73/59.72 (~P1(f335(f335(f166(x114341),f107(x114341)),x114342))),
% 59.73/59.72 inference(rename_variables,[],[4582])).
% 59.73/59.72 cnf(11441,plain,
% 59.73/59.72 (P1(f335(f335(f337(x114411),x114412),f252(f888(x114411,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3503])).
% 59.73/59.72 cnf(11446,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x114461),x114462),f188(f888(x114461,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11449,plain,
% 59.73/59.72 (~P1(f335(f335(f337(f887(x114491,x114491)),f335(f335(f264(x114491,x114491),x114492),x114493)),f146(x114491,f107(f888(x114491,a881)))))),
% 59.73/59.72 inference(rename_variables,[],[4606])).
% 59.73/59.72 cnf(11454,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x114541),x114542),f188(f888(x114541,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11461,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x114611,a879)),x114612),f252(f888(x114611,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3734])).
% 59.73/59.72 cnf(11464,plain,
% 59.73/59.72 (P1(f335(f335(f337(x114641),x114642),f252(f888(x114641,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3503])).
% 59.73/59.72 cnf(11467,plain,
% 59.73/59.72 (P1(f335(f335(f337(x114671),x114672),f335(f335(f312(x114671),x114672),x114673)))),
% 59.73/59.72 inference(rename_variables,[],[3666])).
% 59.73/59.72 cnf(11470,plain,
% 59.73/59.72 (P1(f335(f335(f337(x114701),x114702),f252(f888(x114701,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3503])).
% 59.73/59.72 cnf(11473,plain,
% 59.73/59.72 (P1(f335(f335(f337(x114731),x114732),f335(f335(f312(x114731),x114732),x114733)))),
% 59.73/59.72 inference(rename_variables,[],[3666])).
% 59.73/59.72 cnf(11476,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x114761,a879)),x114762),f252(f888(x114761,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3734])).
% 59.73/59.72 cnf(11485,plain,
% 59.73/59.72 (~P1(f335(f335(f166(x114851),f107(x114851)),x114852))),
% 59.73/59.72 inference(rename_variables,[],[4582])).
% 59.73/59.72 cnf(11500,plain,
% 59.73/59.72 (~P1(f335(f335(f243(a881),x115001),x115001))),
% 59.73/59.72 inference(rename_variables,[],[4574])).
% 59.73/59.72 cnf(11506,plain,
% 59.73/59.72 (E(f167(x115061,x115062,f107(x115061)),x115062)),
% 59.73/59.72 inference(rename_variables,[],[3280])).
% 59.73/59.72 cnf(11509,plain,
% 59.73/59.72 (~E(f335(a106,x115091),x115091)),
% 59.73/59.72 inference(rename_variables,[],[4537])).
% 59.73/59.72 cnf(11522,plain,
% 59.73/59.72 (P1(f335(f335(f337(x115221),x115222),f252(f888(x115221,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3503])).
% 59.73/59.72 cnf(11527,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x115271),x115272),f188(f888(x115271,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11539,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x115391),x115392),f188(f888(x115391,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11546,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x115461,a879)),x115462),x115462))),
% 59.73/59.72 inference(rename_variables,[],[3648])).
% 59.73/59.72 cnf(11551,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x115511),x115512),f188(f888(x115511,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11554,plain,
% 59.73/59.72 (~P1(f335(f335(f337(f887(x115541,x115541)),f335(f335(f264(x115541,x115541),x115542),x115543)),f146(x115541,f107(f888(x115541,a881)))))),
% 59.73/59.72 inference(rename_variables,[],[4606])).
% 59.73/59.72 cnf(11562,plain,
% 59.73/59.72 (P1(f335(f335(f337(x115621),x115622),f252(f888(x115621,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3503])).
% 59.73/59.72 cnf(11565,plain,
% 59.73/59.72 (~P1(f335(f335(f243(a881),x115651),x115651))),
% 59.73/59.72 inference(rename_variables,[],[4574])).
% 59.73/59.72 cnf(11568,plain,
% 59.73/59.72 (P1(f335(f335(f337(x115681),x115682),f252(f888(x115681,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3503])).
% 59.73/59.72 cnf(11571,plain,
% 59.73/59.72 (P1(f335(f335(f337(x115711),x115712),f252(f888(x115711,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3503])).
% 59.73/59.72 cnf(11574,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x115741),x115742),f188(f888(x115741,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11577,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x115771,a879)),x115772),x115772))),
% 59.73/59.72 inference(rename_variables,[],[3648])).
% 59.73/59.72 cnf(11580,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x115801),x115802),f188(f888(x115801,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11583,plain,
% 59.73/59.72 (P1(f335(f335(f242(a881),x115831),x115831))),
% 59.73/59.72 inference(rename_variables,[],[3347])).
% 59.73/59.72 cnf(11586,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x115861),x115862),f188(f888(x115861,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11589,plain,
% 59.73/59.72 (~P1(f335(f335(f337(f887(x115891,x115891)),f335(f335(f264(x115891,x115891),x115892),x115893)),f146(x115891,f107(f888(x115891,a881)))))),
% 59.73/59.72 inference(rename_variables,[],[4606])).
% 59.73/59.72 cnf(11592,plain,
% 59.73/59.72 (P1(f335(f252(f888(x115921,a879)),x115922))),
% 59.73/59.72 inference(rename_variables,[],[3409])).
% 59.73/59.72 cnf(11595,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x115951),x115952),f188(f888(x115951,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11598,plain,
% 59.73/59.72 (~P1(f335(f335(f337(f887(x115981,x115981)),f335(f335(f264(x115981,x115981),x115982),x115983)),f146(x115981,f107(f888(x115981,a881)))))),
% 59.73/59.72 inference(rename_variables,[],[4606])).
% 59.73/59.72 cnf(11601,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x116011),x116012),f188(f888(x116011,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11604,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x116041,a879)),x116042),x116042))),
% 59.73/59.72 inference(rename_variables,[],[3648])).
% 59.73/59.72 cnf(11607,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x116071,a879)),x116072),x116072))),
% 59.73/59.72 inference(rename_variables,[],[3648])).
% 59.73/59.72 cnf(11610,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x116101),x116102),f188(f888(x116101,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11615,plain,
% 59.73/59.72 (P1(f335(f335(f337(x116151),x116152),f252(f888(x116151,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3503])).
% 59.73/59.72 cnf(11618,plain,
% 59.73/59.72 (P1(f335(f335(f337(x116181),x116182),f335(f335(f312(x116181),x116182),x116183)))),
% 59.73/59.72 inference(rename_variables,[],[3666])).
% 59.73/59.72 cnf(11627,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x116271),x116272),f188(f888(x116271,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11630,plain,
% 59.73/59.72 (~P1(f335(f335(f337(f887(x116301,x116301)),f335(f335(f264(x116301,x116301),x116302),x116303)),f146(x116301,f107(f888(x116301,a881)))))),
% 59.73/59.72 inference(rename_variables,[],[4606])).
% 59.73/59.72 cnf(11637,plain,
% 59.73/59.72 (P1(f335(f335(f337(x116371),x116372),f252(f888(x116371,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3503])).
% 59.73/59.72 cnf(11640,plain,
% 59.73/59.72 (P1(f335(f335(f337(x116401),x116402),f252(f888(x116401,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3503])).
% 59.73/59.72 cnf(11643,plain,
% 59.73/59.72 (P1(f335(f335(f337(x116431),x116432),f252(f888(x116431,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3503])).
% 59.73/59.72 cnf(11646,plain,
% 59.73/59.72 (~P1(f335(f335(f243(a881),x116461),x116461))),
% 59.73/59.72 inference(rename_variables,[],[4574])).
% 59.73/59.72 cnf(11651,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x116511),x116512),f188(f888(x116511,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11654,plain,
% 59.73/59.72 (P1(f335(f335(f337(x116541),x116542),f252(f888(x116541,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3503])).
% 59.73/59.72 cnf(11657,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x116571),x116572),f188(f888(x116571,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11662,plain,
% 59.73/59.72 (P1(f335(f335(f337(x116621),x116622),f335(f335(f312(x116621),x116622),x116623)))),
% 59.73/59.72 inference(rename_variables,[],[3666])).
% 59.73/59.72 cnf(11665,plain,
% 59.73/59.72 (P1(f335(f335(f242(a881),x116651),x116651))),
% 59.73/59.72 inference(rename_variables,[],[3347])).
% 59.73/59.72 cnf(11668,plain,
% 59.73/59.72 (~E(f335(f313(x116681,f888(x116681,a879),x116682),x116683),f335(f311(x116681),x116683))),
% 59.73/59.72 inference(rename_variables,[],[4585])).
% 59.73/59.72 cnf(11679,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x116791),x116792),f188(f888(x116791,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11682,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x116821),x116822),f188(f888(x116821,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11685,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x116851),x116852),f188(f888(x116851,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11688,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x116881),x116882),f188(f888(x116881,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11691,plain,
% 59.73/59.72 (P1(f335(f335(f337(f887(f882(x116911),f882(x116911))),f335(f335(f264(f882(x116911),f882(x116911)),x116912),x116912)),f151(x116911,f310(x116911,x116913))))),
% 59.73/59.72 inference(rename_variables,[],[4136])).
% 59.73/59.72 cnf(11694,plain,
% 59.73/59.72 (P1(f335(f335(f337(f887(f882(x116941),f882(x116941))),f335(f335(f264(f882(x116941),f882(x116941)),x116942),x116942)),f151(x116941,f310(x116941,x116943))))),
% 59.73/59.72 inference(rename_variables,[],[4136])).
% 59.73/59.72 cnf(11697,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x116971,a879)),x116972),x116972))),
% 59.73/59.72 inference(rename_variables,[],[3648])).
% 59.73/59.72 cnf(11702,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x117021),x117022),f188(f888(x117021,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11705,plain,
% 59.73/59.72 (~P1(f335(f335(f337(f887(x117051,x117051)),f335(f335(f264(x117051,x117051),x117052),x117053)),f146(x117051,f107(f888(x117051,a881)))))),
% 59.73/59.72 inference(rename_variables,[],[4606])).
% 59.73/59.72 cnf(11712,plain,
% 59.73/59.72 (~P1(f335(f335(f337(f887(x117121,x117121)),f335(f335(f264(x117121,x117121),x117122),x117123)),f146(x117121,f107(f888(x117121,a881)))))),
% 59.73/59.72 inference(rename_variables,[],[4606])).
% 59.73/59.72 cnf(11719,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x117191,a879)),x117192),x117192))),
% 59.73/59.72 inference(rename_variables,[],[3648])).
% 59.73/59.72 cnf(11722,plain,
% 59.73/59.72 (~P1(f335(f335(f337(x117221),x117222),f188(f888(x117221,a879))))),
% 59.73/59.72 inference(rename_variables,[],[4586])).
% 59.73/59.72 cnf(11728,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x117281,a879)),x117282),f252(f888(x117281,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3734])).
% 59.73/59.72 cnf(11731,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x117311,a879)),x117312),f252(f888(x117311,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3734])).
% 59.73/59.72 cnf(11734,plain,
% 59.73/59.72 (P1(f335(f335(f337(x117341),f335(x117342,x117343)),f335(f313(x117344,x117341,x117342),f252(f888(x117344,a879)))))),
% 59.73/59.72 inference(rename_variables,[],[3959])).
% 59.73/59.72 cnf(11826,plain,
% 59.73/59.72 (E(f167(x118261,x118262,f107(x118261)),x118262)),
% 59.73/59.72 inference(rename_variables,[],[3280])).
% 59.73/59.72 cnf(11830,plain,
% 59.73/59.72 (E(f167(x118301,x118302,f107(x118301)),x118302)),
% 59.73/59.72 inference(rename_variables,[],[3280])).
% 59.73/59.72 cnf(11837,plain,
% 59.73/59.72 (E(f167(x118371,x118372,f107(x118371)),x118372)),
% 59.73/59.72 inference(rename_variables,[],[3280])).
% 59.73/59.72 cnf(11839,plain,
% 59.73/59.72 (E(f167(x118391,x118392,f107(x118391)),x118392)),
% 59.73/59.72 inference(rename_variables,[],[3280])).
% 59.73/59.72 cnf(11878,plain,
% 59.73/59.72 (E(f167(x118781,x118782,f107(x118781)),x118782)),
% 59.73/59.72 inference(rename_variables,[],[3280])).
% 59.73/59.72 cnf(11880,plain,
% 59.73/59.72 (~E(f335(a106,x118801),x118801)),
% 59.73/59.72 inference(rename_variables,[],[4537])).
% 59.73/59.72 cnf(11884,plain,
% 59.73/59.72 (P1(f335(f335(f337(x118841),x118842),f252(f888(x118841,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3503])).
% 59.73/59.72 cnf(11893,plain,
% 59.73/59.72 (~E(f335(a106,x118931),x118931)),
% 59.73/59.72 inference(rename_variables,[],[4537])).
% 59.73/59.72 cnf(11896,plain,
% 59.73/59.72 (~E(f335(a106,x118961),x118961)),
% 59.73/59.72 inference(rename_variables,[],[4537])).
% 59.73/59.72 cnf(11908,plain,
% 59.73/59.72 (P1(f335(f335(f337(x119081),f335(x119082,x119083)),f335(f313(x119084,x119081,x119082),f252(f888(x119084,a879)))))),
% 59.73/59.72 inference(rename_variables,[],[3959])).
% 59.73/59.72 cnf(11935,plain,
% 59.73/59.72 (P1(f335(f335(f242(a881),x119351),x119351))),
% 59.73/59.72 inference(rename_variables,[],[3347])).
% 59.73/59.72 cnf(11938,plain,
% 59.73/59.72 (~P1(f335(f335(f242(a881),f335(a106,x119381)),x119381))),
% 59.73/59.72 inference(rename_variables,[],[4584])).
% 59.73/59.72 cnf(11945,plain,
% 59.73/59.72 (~E(f335(a106,x119451),x119451)),
% 59.73/59.72 inference(rename_variables,[],[4537])).
% 59.73/59.72 cnf(11953,plain,
% 59.73/59.72 (E(f167(x119531,x119532,f107(x119531)),x119532)),
% 59.73/59.72 inference(rename_variables,[],[3280])).
% 59.73/59.72 cnf(11956,plain,
% 59.73/59.72 (E(f167(x119561,x119562,f107(x119561)),x119562)),
% 59.73/59.72 inference(rename_variables,[],[3280])).
% 59.73/59.72 cnf(11959,plain,
% 59.73/59.72 (~E(f335(f335(f144(x119591),x119592),x119593),x119593)),
% 59.73/59.72 inference(rename_variables,[],[4552])).
% 59.73/59.72 cnf(11962,plain,
% 59.73/59.72 (~E(f335(f335(f144(x119621),x119622),x119623),x119623)),
% 59.73/59.72 inference(rename_variables,[],[4552])).
% 59.73/59.72 cnf(11969,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x119691,a879)),x119692),f252(f888(x119691,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3734])).
% 59.73/59.72 cnf(11982,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x119821,a879)),x119822),f252(f888(x119821,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3734])).
% 59.73/59.72 cnf(11989,plain,
% 59.73/59.72 (~P1(f335(f335(f243(a881),x119891),x119891))),
% 59.73/59.72 inference(rename_variables,[],[4574])).
% 59.73/59.72 cnf(12018,plain,
% 59.73/59.72 (~P1(f335(f335(f243(a881),x120181),x120181))),
% 59.73/59.72 inference(rename_variables,[],[4574])).
% 59.73/59.72 cnf(12021,plain,
% 59.73/59.72 (~P1(f335(f335(f242(a1),f2(a1)),f335(f74(a1),f335(f94(a1),f335(a106,x120211)))))),
% 59.73/59.72 inference(rename_variables,[],[4603])).
% 59.73/59.72 cnf(12022,plain,
% 59.73/59.72 (P1(f335(f335(f242(a881),f2(a881)),x120221))),
% 59.73/59.72 inference(rename_variables,[],[3369])).
% 59.73/59.72 cnf(12033,plain,
% 59.73/59.72 (~P1(f335(f335(f166(x120331),f107(x120331)),x120332))),
% 59.73/59.72 inference(rename_variables,[],[4582])).
% 59.73/59.72 cnf(12036,plain,
% 59.73/59.72 (P1(f335(f335(f242(a881),x120361),x120361))),
% 59.73/59.72 inference(rename_variables,[],[3347])).
% 59.73/59.72 cnf(12039,plain,
% 59.73/59.72 (~P1(f335(f335(f243(a881),x120391),x120391))),
% 59.73/59.72 inference(rename_variables,[],[4574])).
% 59.73/59.72 cnf(12042,plain,
% 59.73/59.72 (~P1(f335(f335(f243(a881),x120421),x120421))),
% 59.73/59.72 inference(rename_variables,[],[4574])).
% 59.73/59.72 cnf(12049,plain,
% 59.73/59.72 (~E(f335(a106,x120491),x120491)),
% 59.73/59.72 inference(rename_variables,[],[4537])).
% 59.73/59.72 cnf(12052,plain,
% 59.73/59.72 (E(f167(x120521,x120522,f107(x120521)),x120522)),
% 59.73/59.72 inference(rename_variables,[],[3280])).
% 59.73/59.72 cnf(12059,plain,
% 59.73/59.72 (P1(f335(f335(f242(a881),x120591),x120591))),
% 59.73/59.72 inference(rename_variables,[],[3347])).
% 59.73/59.72 cnf(12060,plain,
% 59.73/59.72 (E(f167(x120601,x120602,f107(x120601)),x120602)),
% 59.73/59.72 inference(rename_variables,[],[3280])).
% 59.73/59.72 cnf(12077,plain,
% 59.73/59.72 (P1(f335(f335(f242(a1),x120771),x120771))),
% 59.73/59.72 inference(rename_variables,[],[3348])).
% 59.73/59.72 cnf(12080,plain,
% 59.73/59.72 (~P1(f335(f335(f243(a881),x120801),x120801))),
% 59.73/59.72 inference(rename_variables,[],[4574])).
% 59.73/59.72 cnf(12083,plain,
% 59.73/59.72 (P1(f335(f335(f337(x120831),x120832),f252(f888(x120831,a879))))),
% 59.73/59.72 inference(rename_variables,[],[3503])).
% 59.73/59.72 cnf(12087,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x120871,a879)),f335(f313(x120872,x120871,x120873),f335(f314(x120872,x120871,x120873),x120874))),x120874))),
% 59.73/59.72 inference(rename_variables,[],[4248])).
% 59.73/59.72 cnf(12091,plain,
% 59.73/59.72 (P1(f335(f335(f242(f888(x120911,a879)),x120912),f335(f335(f312(x120911),x120913),x120912)))),
% 59.73/59.72 inference(rename_variables,[],[3799])).
% 59.73/59.72 cnf(12094,plain,
% 59.73/59.72 (~P1(f335(f335(f243(a881),x120941),x120941))),
% 59.73/59.72 inference(rename_variables,[],[4574])).
% 59.73/59.72 cnf(12097,plain,
% 59.73/59.72 (~P1(f335(f335(f243(a881),x120971),x120971))),
% 59.73/59.72 inference(rename_variables,[],[4574])).
% 59.73/59.72 cnf(12102,plain,
% 59.73/59.72 (P1(f335(f335(f242(a881),x121021),x121021))),
% 59.73/59.72 inference(rename_variables,[],[3347])).
% 59.73/59.72 cnf(12109,plain,
% 59.73/59.72 (~P1(f335(f335(f243(a881),x121091),x121091))),
% 59.73/59.72 inference(rename_variables,[],[4574])).
% 59.73/59.72 cnf(12126,plain,
% 59.73/59.72 (P1(f335(f335(f243(a881),x121261),f335(a106,x121261)))),
% 59.73/59.72 inference(rename_variables,[],[3416])).
% 59.73/59.72 cnf(12135,plain,
% 59.73/59.72 (P1(f335(f335(f242(a881),x121351),x121351))),
% 59.73/59.72 inference(rename_variables,[],[3347])).
% 59.73/59.72 cnf(12138,plain,
% 59.73/59.72 (P1(f335(f335(f242(a1),x121381),x121381))),
% 59.73/59.72 inference(rename_variables,[],[3348])).
% 59.73/59.72 cnf(12199,plain,
% 59.73/59.72 (~E(f335(a106,x121991),x121991)),
% 59.73/59.72 inference(rename_variables,[],[4537])).
% 59.73/59.72 cnf(12202,plain,
% 59.73/59.72 (~E(f335(f335(f144(x122021),x122022),x122023),x122023)),
% 59.73/59.72 inference(rename_variables,[],[4552])).
% 59.73/59.72 cnf(12205,plain,
% 59.73/59.72 (P1(f335(f335(f243(a881),f335(f335(f23(a881),x122051),x122052)),f335(a106,x122051)))),
% 59.73/59.72 inference(rename_variables,[],[3805])).
% 59.73/59.72 cnf(12208,plain,
% 59.73/59.72 (~P1(f335(f335(f242(a881),f335(a106,x122081)),x122081))),
% 59.73/59.72 inference(rename_variables,[],[4584])).
% 59.73/59.72 cnf(12209,plain,
% 59.73/59.72 (~E(f335(a106,x122091),x122091)),
% 59.73/59.72 inference(rename_variables,[],[4537])).
% 59.73/59.72 cnf(12214,plain,
% 59.73/59.72 (P1(f335(f335(f243(a881),x122141),f335(a106,x122141)))),
% 59.73/59.72 inference(rename_variables,[],[3416])).
% 59.73/59.72 cnf(12240,plain,
% 59.73/59.72 (P1(f335(f335(f242(a1),x122401),x122401))),
% 59.73/59.72 inference(rename_variables,[],[3348])).
% 59.73/59.72 cnf(12267,plain,
% 59.73/59.72 (~P1(f335(f335(f243(a881),f335(f335(f75(a881),x122671),x122672)),x122672))),
% 59.73/59.72 inference(rename_variables,[],[4601])).
% 59.73/59.72 cnf(12268,plain,
% 59.73/59.72 (P1(f335(f335(f243(a881),x122681),f335(a106,x122681)))),
% 59.73/59.72 inference(rename_variables,[],[3416])).
% 59.73/59.72 cnf(12283,plain,
% 59.73/59.72 (~P1(f335(f335(f243(a1),f335(f94(a1),x122831)),f335(f74(a1),f335(f94(a1),x122832))))),
% 59.73/59.72 inference(rename_variables,[],[4598])).
% 59.73/59.72 cnf(12296,plain,
% 59.73/59.72 (P1(f335(f335(f242(a881),f39(a881,x122961,x122962)),x122961))),
% 59.73/59.72 inference(rename_variables,[],[3810])).
% 59.73/59.72 cnf(12297,plain,
% 59.73/59.72 (P1(f335(f335(f243(a881),f2(a881)),f335(a106,x122971)))),
% 59.73/59.72 inference(rename_variables,[],[3428])).
% 59.73/59.72 cnf(12325,plain,
% 59.73/59.72 (P1(f335(f335(f243(a881),f2(a881)),f335(a106,x123251)))),
% 59.73/59.72 inference(rename_variables,[],[3428])).
% 59.73/59.72 cnf(12328,plain,
% 59.73/59.72 (P1(f335(f335(f243(a881),f2(a881)),f335(a106,x123281)))),
% 59.73/59.72 inference(rename_variables,[],[3428])).
% 59.73/59.72 cnf(12331,plain,
% 59.73/59.72 (P1(f335(f335(f243(a881),f2(a881)),f335(a106,x123311)))),
% 59.73/59.72 inference(rename_variables,[],[3428])).
% 59.73/59.72 cnf(12337,plain,
% 59.73/59.72 (P1(f335(f335(f337(x123371),f335(x123372,x123373)),f335(f313(x123374,x123371,x123372),f252(f888(x123374,a879)))))),
% 59.73/59.72 inference(rename_variables,[],[3959])).
% 59.73/59.72 cnf(12338,plain,
% 59.73/59.72 (~P1(f335(f335(f243(a881),f335(f335(f75(a881),x123381),x123382)),x123382))),
% 59.73/59.72 inference(rename_variables,[],[4601])).
% 59.73/59.72 cnf(12427,plain,
% 59.73/59.72 (~P1(f335(f335(f243(a881),x124271),f2(a881)))),
% 59.73/59.72 inference(rename_variables,[],[4577])).
% 59.73/59.72 cnf(12445,plain,
% 59.73/59.72 ($false),
% 59.73/59.72 inference(scs_inference,[],[4583,3153,4533,3558,2943,2944,2945,2948,2949,2950,2952,2953,2954,2955,2957,2959,2964,2967,2971,2975,2976,2979,2980,2985,2989,2992,2993,2994,2995,2997,2999,3000,3003,3005,3006,3008,3009,3011,3014,3017,3019,3020,3023,3025,3028,3031,3034,3037,3039,3041,3044,3047,3049,3050,3052,3054,3056,3058,3061,3063,3064,3066,3069,3072,3075,3078,3081,3084,3086,3087,3089,3092,3094,3095,3097,3099,3101,3103,3104,3105,3108,3110,3111,3112,3113,3115,3119,3123,3131,3151,3230,3231,4535,2938,2939,3140,3133,3137,4536,4029,4036,4548,4549,3649,3665,3627,3158,3163,3215,4565,4568,4569,3322,3325,3326,4566,4567,4570,3323,3324,3327,3177,3350,4576,4581,4580,3220,3317,3376,3375,3377,3683,3870,3442,3654,4163,4378,4224,4466,3590,3315,3316,3279,4559,4560,3209,4537,10267,10274,10277,10296,10317,10562,10614,10893,10896,10940,11099,11102,11219,11303,11509,11880,11893,11896,11945,12049,12199,12209,3208,3598,4312,4313,3319,3650,3367,4539,10320,10546,10813,11407,3280,10456,10469,10608,10611,11093,11096,11506,11826,11830,11837,11839,11878,11953,11956,12052,12060,3281,10459,3173,10445,3812,4545,11410,3402,3405,11413,4552,10251,10258,10565,10572,10899,11959,11962,12202,3453,3445,3255,3331,3559,3560,3347,10325,10380,10508,10526,10593,10759,10910,11010,11018,11028,11049,11175,11181,11337,11424,11583,11665,11935,12036,12059,12102,12135,3348,10656,10689,10913,11141,12077,12138,12240,4574,10293,10395,10539,10551,10598,10683,10686,10904,11015,11160,11500,11565,11646,11989,12018,12039,12042,12080,12094,12097,12109,3409,10711,10714,11188,11195,11592,3237,3200,3914,3272,3273,3299,11078,3246,3234,3235,11224,3416,10347,10371,10410,10485,10511,10518,10521,10747,11007,11128,11256,12126,12214,12268,4577,11060,11288,11375,12427,4582,10617,10622,10784,10790,11063,11212,11296,11434,11485,12033,3423,3369,10653,10717,12022,3810,10284,12296,4584,10442,10636,10639,10735,10740,10907,11938,12208,4599,10787,11021,3648,11253,11380,11402,11546,11577,11604,11607,11697,11719,4585,10644,11240,11668,3677,3256,3428,12297,12325,12328,12331,3676,3503,10314,10342,10926,10932,11084,11144,11153,11315,11348,11351,11441,11464,11470,11522,11562,11568,11571,11615,11637,11640,11643,11654,11884,12083,4586,10466,10935,11116,11259,11285,11291,11322,11383,11394,11416,11419,11446,11454,11527,11539,11551,11574,11580,11586,11595,11601,11610,11627,11651,11657,11679,11682,11685,11688,11702,11722,3719,4604,3419,3549,4591,3542,3734,11325,11328,11388,11391,11399,11461,11476,11728,11731,11969,11982,4597,10631,3448,3882,3666,10929,11467,11473,11618,11662,3801,10720,11123,11234,4588,3614,10664,10667,10708,10750,11178,3615,10670,10673,3616,10756,4601,10287,10290,10437,10723,10729,12267,12338,4602,10726,10732,3752,3805,12205,3799,11133,11138,12091,3803,10661,3804,3452,3995,3959,11734,11908,12337,4248,10678,11266,12087,3652,3916,3942,4062,4594,4092,4603,12021,4598,12283,3962,4606,11364,11449,11554,11589,11598,11630,11705,11712,4596,4086,3645,3874,4324,4608,4609,4610,4136,11691,11694,4414,4274,4186,4347,4355,2,9669,6310,5287,5088,5040,5000,4999,4828,4726,4725,8635,8634,8097,8096,5246,5234,5157,5090,4951,4950,4787,4786,4623,5120,5037,9,8,9951,9670,8648,7728,7130,6745,6468,6447,6304,6303,6296,6278,6156,6071,5938,5916,5855,5845,5844,5794,5777,5776,5772,5770,5720,5714,5713,5707,5693,5673,5662,5657,5640,5639,5630,5540,5449,5441,5432,5431,5385,5371,5363,5355,5347,5278,5253,5214,5208,5207,5206,5205,5204,5203,5171,5160,5147,5146,5085,5069,5063,4822,4750,4699,4697,4696,4691,9889,8746,8560,8559,8552,7531,7285,6985,6784,6598,6597,6595,6594,6560,6489,6469,6438,6404,6403,6305,6285,6272,6197,6160,6155,6154,6146,6128,6125,6124,6046,6045,5971,5925,5904,5862,5857,5829,5824,5799,5795,5730,5711,5642,5641,5626,5614,5601,5587,5565,5518,5474,5445,5444,5443,5418,5375,5364,5271,5244,5231,5227,5138,5096,5095,4973,4935,4812,4936,10008,9598,9138,9101,8907,8868,8820,8769,8728,8724,8419,7892,7705,7447,7390,7374,7373,7372,7371,7370,7336,6938,6832,6821,6719,6655,6654,6393,6392,6391,6390,6388,6387,6348,6343,6335,6334,6333,6332,6259,6258,6257,6256,6255,6254,6253,6252,6213,6134,6133,6132,6131,6130,6111,6110,6109,6108,6107,6105,6068,5960,5959,5958,5952,5944,5943,5942,5883,5830,5783,5782,5781,5780,5779,5778,5733,5686,5602,5596,5595,5594,5593,5592,5591,5568,5567,5564,5514,5506,5440,5409,5408,5396,5391,5390,5389,5388,5358,5338,5316,5282,5281,5257,5256,5255,5216,5162,5023,5022,4911,4910,4792,4791,4790,4751,4744,4743,4649,4648,4645,9672,9671,9539,9538,8835,8589,8588,8587,8586,8486,8485,8484,7855,7768,7457,7347,7014,6835,6834,6679,6384,6092,6089,6088,5850,5810,5809,5767,5766,5725,5612,5546,5491,5480,5362,9609,9608,9607,9606,8678,8569,8568,8567,8566,8497,7921,7758,7757,7675,7527,7398,7207,7069,6939,6918,6852,6851,6807,6806,6805,6804,6803,6802,6801,6783,6757,6756,6755,6754,6724,6556,6542,6541,6540,6288,6158,5989,5722,5721,5490,5430,5429,5380,5377,5376,5346,5345,5089,8947,8946,8918,8917,8912,8787,8786,8570,8561,8476,8437,8284,8222,8079,8050,7808,7681,7662,7661,7530,7396,7395,7275,7218,7217,7047,7046,6905,6904,6796,6795,6502,6491,6437,6337,6281,6280,6268,6217,6206,6203,6198,6020,5992,5929,5833,5788,5787,5647,5582,5330,5233,8952,8612,8543,8542,8502,8501,8432,8240,8168,8161,8024,7997,7990,7989,7867,7810,7778,7777,7576,7575,7525,7362,6916,6890,6848,6777,6776,6503,5775,5674,5467,5341,5340,9341,9319,9257,8962,8938,8830,8506,8452,8412,8381,8311,8310,8063,8005,8004,8003,8002,7819,7476,7098,6973,6972,6917,6799,6798,6744,6743,6509,6508,9869,9472,9139,9109,9108,8857,8856,8810,8711,8677,8659,8590,8408,8407,8081,7953,7805,7594,7102,6980,6270,6025,5965,5785,5784,9498,9497,9259,9258,8834,8833,8832,8771,8768,8633,8632,8631,8630,8615,8433,8415,8414,8410,7743,7460,7459,7345,7215,7214,7185,7016,6383,6032,9764,9029,8948,8945,8926,8770,8656,8599,8528,8264,6521,6095,9719,9718,9426,9313,9186,9069,9068,9067,8943,8643,8579,10098,9316,9299,9269,9801,9665,9663,9662,9624,9471,9470,9729,9576,9542,9083,9082,9036,9035,8924,8842,10048,9982,9981,9873,9787,9709,9504,9503,9344,9332,9805,9720,9534,9340,9283,9972,9969,9968,9431,9369,10007,10002,9935,9834,9777,9754,9515,9971,9774,9626,9555,9554,9928,9776,9631,9553,10171,10170,10115,10114,10225,10240,10131,10097,2937,2931,2930,2917,2916,2915,2913,2912,2910,2901,2900,2898,2896,2893,2892,2879,2877,2876,2869,2867,2861,2860,2858,2856,2855,2854,2851,2848,2847,2839,2837,2836,2835,2834,2833,2831,2830,2828,2827,2826,2825,2824,2821,2820,2819,2818,2817,2812,2811,2810,2806,2805,2804,2803,2800,2799,2792,2791,2789,2788,2787,2779,2778,2777,2776,2775,2774,2770,2769,2765,2763,2762,2761,2760,2758,2757,2755,2753,2749,2748,2747,2746,2744,2743,2742,2741,2740,2739,2738,2737,2736,2734,2733,2732,2731,2727,2725,2724,2723,2722,2718,2716,2711,2710,2709,2708,2707,2705,2704,2703,2702,2701,2700,2693,2692,2691,2690,2688,2687,2686,2685,2684,2683,2682,2678,2676,2675,2674,2673,2672,3,5093,5238,4655,4637,4636,5114,5113,5087,5086,5074,5649,5648,5323,5322,5321,5320,5319,5318,5317,5053,5052,5051,5050,5049,6077,5697,5696,5437,5314,5285,5062,4719,4718,8681,8680,8651,7918,7767,7759,7333,7332,7331,7209,6945,6507,5880,5298,5296,5436,5351,5145,6555,6554,4971,7004,6626,6351,6341,6340,6339,6329,6218,6153,6070,5962,5947,5868,5867,5579,5439,5438,5428,5427,5426,5324,5280,5279,4952,4827,4716,4657,6200,5797,8745,8136,8011,7786,7785,7751,7558,7186,7168,6828,6697,6696,6695,6694,6690,6689,6650,6634,6620,6619,6550,6549,6490,6429,6405,6360,6344,6336,6306,6302,6150,6053,6049,5951,5950,5843,5837,5670,5344,5156,5155,5154,5153,5152,5151,5044,5043,4781,4780,4779,4778,5659,5566,9533,7239,6911,6910,6909,6908,6907,6499,6498,6497,6496,6495,6326,6325,6086,5230,5229,5166,5165,4987,4730,4689,4686,9496,7838,7258,7257,7256,7115,7094,6894,6678,6677,6676,6674,6137,6073,6059,5988,5987,5986,5985,5984,5983,5982,5981,5980,5979,5930,5901,5900,5899,5898,5871,5870,5832,5831,5800,5739,5738,5737,5736,5607,5606,5581,5557,5556,5550,5536,5535,5534,5533,5532,5531,5530,5529,5528,5527,5526,5525,5489,5487,5486,5485,5484,5483,5482,5481,5395,5394,5393,5392,5367,5366,5223,5164,5066,5065,8204,7463]),
% 59.73/59.72 ['proof']).
% 59.73/59.72 % SZS output end Proof
% 59.73/59.72 % Total time :55.820000s
%------------------------------------------------------------------------------